Methodologies& Working papers 85739 Handbook on Residential Property Prices Indices (RPPIs) 2013 edition Methodologies& Working papers Handbook on Residential Property Prices Indices (RPPIs) 2013 edition Europe Direct is a service to help you find answers to your questions about the European Union. Freephone number (*): 00 800 6 7 8 9 10 11 Certain mobile telephone operators do not allow access (*)  to 00 800 numbers or these calls may be billed. More information on the European Union is available on the Internet (http://europa.eu). Cataloguing data can be found at the end of this publication. Luxembourg: Publications Office of the European Union, 2013 ISBN 978-92-79-25984-5 doi:10.2785/34007 Cat. 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Printed in Belgium Printed on elemental chlorine-free bleached paper (ECF) Also available under the title Handbook on Residential Property Prices Indices (RPPIs), ILO ISBN 978-92-2-127359-2 (paperback) ISBN 978-92-2-127360-8 (PDF) OECD ISBN 978-92-6-419718-3 (PDF) The opinions expressed and arguments employed herein do not necessarily reflect the official views of the ILO, IMF, OECD, UNECE, the World Bank or of the governments of their member countries or those of Eurostat or the European Commission. Table of contents  Table of contents Foreword – Rppi 7 Preface 9 1. Introduction 11 2. Uses of Residential Property Price Indices 15 3. Elements for a Conceptual Framework 21 4. Stratification or Mix Adjustment Methods 37 5. Hedonic Regression Methods 49 6. Repeat Sales Methods 65 7. Appraisal-Based Methods 73 8. Decomposing an RPPI into Land and Structures Components 81 9. Data Sources 101 10. Methods Currently Used 113 11. Empirical Examples 139 12. Recommendations 155 Glossary 161 Bibliography 167 Index 177 Handbook on Residential Property Prices Indices (RPPIs) 3  Table of contents List of tables 3.1. Estimated Rent to Value Ratios as Percentages (Capitalization Ratios)......................................................... 35 4.1. Sample Probability of a Sale in Each Cell.................................................................................................................. 43 4.2. Matched Model Fisher Chained and Fixed Base Price Indices, Mean, Median and Representative Model Price Indices................................................................................................................... 45 4.3. Rolling Year Fixed Base Fisher, Fisher Chained Moving Average and Fisher Fixed Base Moving Average Price Indices....................................................................................................................................................... 47 5.1. Log-Linear Time Dummy Price Indices and the Chained Stratified Sample Mean Fisher Price Index............................................................................................................................................................................ 60 5.2. Linear Time Dummy Price Indices, the Log Log Time Dummy Price Index and the Chained Stratified Sample Mean Fisher Price Index..................................................................................... 62 5.3. Chained Laspeyres, Paasche and Fisher Hedonic Imputation Price Indices................................................ 64 6.1. Repeat Sales Price Index, Chained Stratified Sample Mean Fisher Price Index and Hedonic Imputation Fisher Price Index....................................................................................................................................... 71 7.1. SPAR Index, Hedonic Imputation Fisher Price Index and Repeat Sales Index............................................. 79 8.1. The Price of Land (PL1), the Price of Quality Adjusted Structures (PS1), the Overall Cost of Production House Price Index (P1) and the Fisher Hedonic Imputation House Price Index.............. 86 8.2. The Price of Land (PL2), the Price of Structures (PS2), the Overall Price Index Using Splines on Land (P2) and the Fisher Hedonic Imputation Price Index........................................................................... 88 8.3. The Price of Land (PL3), the Price of Quality Adjusted Structures (PS3), the Overall House Price Index with Monotonicity Restrictions on Structures (P3) and the Overall House Price Index Using Splines on Land (P2)......................................................................... 90 8.4. The Price of Land (PL4), the Price of Quality Adjusted Structures (PS4) and the Overall House Price Index using Exogenous Information on the Price of Structures (P4)...... 92 8.5. House Price Indices Using Exogenous Information (P4) and Using Monotonicity Restrictions (P3), the Chained Fisher Hedonic Imputation Index and the Chained Fisher Stratified Sample Index...................................................................................................................................................................... 93 8.6. The Price of Land (PL4), the Price of Quality Adjusted Structures (PS4), the Overall House Price Index using Exogenous Information on the Price of Structures (P4) and their Rolling Window Counterparts (PRWL) and (PRW)....................................................................................................................... 95 8.7. Approximate Stock Price Indices and Based on Hedonic Imputation (PStock1) and Stratification (PStock2) and the Fisher Hedonic Imputation Sales Price Index........................................ 97 8.8. Approximate Price Indices for the Stock of Houses (PStock), the Stock of Land (PLStock), the Stock of Structures (PSStock) and the Corresponding Sales Indices (PL4 and P4)..................................... 99 10.1. Indices of Property Prices Published in Japan......................................................................................................123 10.2. Indices of Residential Property Prices – Published in the UK..........................................................................128 10.3. Tenure Status – All Housing in South Africa (According to Census 2001)..................................................134 10.4. Distribution of Number of Rooms in Informal Dwellings.....................................................................................................................................................135 10.5. Price Determinants.........................................................................................................................................................136 10.6. Percentage of Materials Used in the Construction of Informal and Traditional Dwellings in South Africa..................................................................................................................................................................136 10.7. Evaluation of Barriers.....................................................................................................................................................137 11.1. Means, Medians, Percent Changes, Standard Deviations, and Skewness...................................................141 11.2. Regional Expenditures, Prices and Volumes (Implicit Quantities) Using Median Prices as the Regional Prices....................................................................................................................................................143 11.3. Overall House Price Indices using Median Prices and Alternative Formulae to Aggregate over Regions A, B and C................................................................................................................................................144 4 Handbook on Residential Property Prices Indices (RPPIs) Table of contents  11.4. Regional Expenditures, Prices and Volumes (Implicit Quantities) Using Mean Prices as the Regional Prices....................................................................................................................................................144 11.5. Overall House Price Indices using Mean Prices and Alternative Formulae to Aggregate over Regions A, B and C ..............................................................................................................................................145 11.6. Log-linear Regression Results for a Simple Example..........................................................................................146 11.7. Results from a Pooled Regression for Years 2006 and 2007.............................................................................148 11.8. Results from a Pooled Regression for Years 2006 to 2008................................................................................148 11.9. Results from a Pooled Regression for Years 2007 and 2008.............................................................................149 11.10. Results from a Regression for 2006...........................................................................................................................150 11.11. Results from a Regression for 2007...........................................................................................................................150 11.12. Mean Values of the Characteristics for the Base Period (2006).......................................................................151 11.13. Repeat Sales Data............................................................................................................................................................151 11.14. Dummy Variables for Repeat Sales............................................................................................................................152 11.15. Unweighted Repeat Sales Regression.....................................................................................................................153 11.16. Weighted Repeat Sales Regression...........................................................................................................................153 11.17. Repeat Sales Price Indices (2002 = 100)..................................................................................................................154 11.18. Growth Rates in Percent for the Various House Price Indices (2007)............................................................154 Handbook on Residential Property Prices Indices (RPPIs) 5  Table of contents List of figures 4.1. Matched Model Fisher Chained and Fixed Base Price Indices, Mean, Median and Representative Model Price Indices................................................................................................................... 45 4.2. Rolling Year Fixed Base Fisher, Fisher Chained Moving Average and Fisher Fixed Base Moving Average Price Indices............................................................................................................................ 47 5.1. Log-Linear Time Dummy Price Indices and the Chained Stratified Sample Mean Fisher Price Index.................................................................................................................................................. 59 5.2. Linear Time Dummy Price Indices, the Log Log Time Dummy Price Index and the Chained Stratified Sample Mean Fisher Price Index............................................................................. 61 5.3. Chained Laspeyres, Paasche and Fisher Hedonic Imputation Price Indices................................................ 63 5.4. The Fisher Imputation Price Index, the Chained Stratified Sample Mean Fisher Price Index, the Linear Time Dummy Price Index and the Log Log Time Dummy Price Index............................................................................................................................................................................ 64 6.1. Repeat Sales Price Index, Chained Stratified Sample Fisher Price Index and Hedonic Imputation Fisher Price Index....................................................................................................................................... 70 7.1. SPAR Index, Hedonic Imputation Fisher Price Index and Repeat Sales Index............................................. 79 8.1. The Price of Land (PL1), the Price of Quality Adjusted Structures (PS1), the Overall Cost of Production House Price Index (P1) and the Fisher Hedonic Imputation House Price Index...................................................................................................................................... 86 8.2. The Price of Land (PL2), the Price of Structures (PS2), the Overall Price Index Using Splines on Land (P2) and the Fisher Hedonic Imputation Price Index............................................... 88 8.3. The Price of Land (PL3), the Price of Quality Adjusted Structures (PS3), the Overall House Price Index with Monotonicity Restrictions on Structures (P3) and the Overall House Price Index Using Splines on Land (P2)...................................................................................................................... 89 8.4. The Price of Land (PL4), the Price of Quality Adjusted Structures (PS4) and the Overall House Price Index using Exogenous Information on the Price of Structures (P4)...................................... 91 8.5. House Price Indices Using Exogenous Information (P4) and Using Monotonicity Restrictions (P3), the Chained Fisher Hedonic Imputation Index and the Chained Fisher Stratified Sample Index...................................................................................................................................... 93 8.6. Approximate Stock Price Indices and Based on Hedonic Imputation (PStock1) and Stratification (PStock2) and the Fisher Hedonic Imputation Sales Price Index........................................ 96 8.7. Approximate Price Indices for the Stock of Houses (PStock), the Stock of Land (PLStock), the Stock of Structures (PSStock) and the Corresponding Sales Indices (PL4 and P4)..................................... 98 Diagram: House purchase timeline and house price indices...........................................................................................103 10.1. Four Residential Property Price Indices for Canada ...........................................................................................120 10.2. Property Information Flow...........................................................................................................................................125 10.3. Four Residential Price Indices for Japan (January 1999=100).........................................................................126 10.4. House Purchase Time-line............................................................................................................................................127 10.5. NHB RESIDEX Indices – India Citywise index.........................................................................................................129 10.6. Quarterly National House Price Index for Existing Units – Nominal and Real...........................................131 10.7. Quarterly National Real House Price Index for Existing Units – Annual Percentage Changes..............................................................................................................................................................................131 10.8. Annual National House Price Index for Existing Units (1)...................................................................................132 10.9. Annual Real House Price Index for Existing Units – Principal metropolitan areas ..................................132 10.10. Annual Real House Price Index for Existing units: Houses with Subsidies (VIS) and Houses without (NOVIS).......................................................................................................................................133 11.1: Distribution of House Prices in 2008........................................................................................................................141 6 Handbook on Residential Property Prices Indices (RPPIs) Foreword - RPPI  Foreword – RPPI This Handbook on Residential Property Prices Indices (RPPIs) represents the first comprehensive overview of conceptual and practical issues related to the compilation of price indexes for residential properties. The development of the RPPI Handbook has been co-ordinated by the Statistical Office of the European Union (Eurostat), under the joint responsibility of six organizations - International Labour Organization (ILO), International Monetary Fund (IMF), Organisation for Economic Co-operation and Development (OECD), Statistical Office of the European Union (Eurostat), United Nations Economic Commission for Europe (UNECE) and World Bank - through the mechanism of an Inter-Secretariat Working Group on Price Statistics (IWGPS). The Handbook is published jointly by these organizations. The aim of the RPPI Handbook is to give practical guidance on the compilation of house price indexes and to increase international comparability of residential property price indexes. The Handbook outlines the different user needs, gives details on data needs and methods, and provides recommendations. The primary purpose of the Handbook is to assist producers of residential property price indexes, particularly in countries that are revising or setting up their RPPIs. The Handbook draws on a wide range of experience and expertise in an attempt to describe practical and suitable measurement methods. It should also help countries to produce their RPPIs in a more comparable manner. As it brings together a large body of knowledge on the subject, the Handbook may be used for self-learning, or as a teaching tool for training courses on residential property price indexes. Other RPPI users, such as businesses, policy-makers or researchers may also find the Handbook useful as a source of in- formation, not only about the different methods that are employed in collecting data and compiling such indexes, but also about their limitations. In this respect, it may facilitate the interpretation of the results. The drafting and revision have entailed many meetings over a three-year period, in which RPPI experts from national sta- tistical offices, international and regional organisations, universities and research institutes have participated. Their collec- tive advice and wisdom were indispensable for the compilation of this Handbook. An electronic version of the Handbook is available on the Internet at http://epp.eurostat.ec.europa.eu. The IWGPS views the Handbook as a ‘‘living document’’ that will be amended and updated to address particular points in more detail. Comments on the Handbook are welcomed by the IWGPS, and should be sent to Eurostat (e-mail: ESTAT-hicp-methods@ ec.europa.eu). They will be taken into account in any future revisions. Walter Radermacher Rafael Diez de Medina Chief Statistician of the European Union Chief Statistician Director General Director of the Department of Statistics Eurostat - Statistical Office of the European Union International Labour Organisation Alfredo M. Leone Martine Durand Acting Director Chief Statistician Statistics Department Director of Statistics Directorate International Monetary Fund Organisation for Economic Co-operation and Development Lidia Bratanova Shaida Badiee Director of Statistical Division Director, Development Data Group United Nations Economic Commission for Europe World Bank Handbook on Residential Property Prices Indices (RPPIs) 7 Preface  Preface Introduction The aim of this Handbook is to facilitate the setting-up of residential property price indices in countries where these are still missing and the improvement of existing price indices where this is deemed necessary. It is designed to give practical guidance on the compilation of house price indices, both in developed and less developed countries, and to increase inter- national comparability of residential property price indices. It explains the different user needs, gives details on data and methods that can be used to compile residential property price indices and provides recommendations. The production of the Handbook was funded and supported by Eurostat. Background The need for property price indices that are fit-for-purpose was recognised at a conference organised jointly by the International Monetary Fund (IMF) and the Bank for International Settlements (BIS) in Washington DC, October 2003. As a result, a chapter on residential property price indices was added to the IMF’s “Compilation Guide of Financial Soundness Indicators”. The idea of a more detailed Handbook dates back to a workshop organised by the Organisation for Economic Co-operation and Development (OECD) and the IMF on Real Estate Price Indices in Paris, November 2006. The Handbook would complement the existing international manuals on consumer price indices, producer price indices and import-export price indices that were produced under the auspices of the Inter-Secretariat Working Group on Price Statistics. Eurostat agreed to take this initiative forward by supporting and funding the preparation of the Handbook, given the strong links to its ongoing work on the inclusion of owner-occupied housing in the Harmonized Index of Consumer Prices (HICP) and the role that house price indices have in the set of “Principal European Economic Indicators”. At the Eurostat-IAOS-IFC conference on residential property price indices, held in Basel, 11-12  November 2009, the Handbook plan was discussed. Preliminary versions of the Handbook were presented and discussed at several occasions, in particular at the UNECE-ILO Meeting on Consumer Price Indices in Geneva, 10-12 May 2010, a workshop held in The Hague, 10-11 February 2011, and the twelfth Ottawa Group meeting in Wellington, 4-6 May 2011. A Guide to Readers Although not all of the chapters are self-contained, the Handbook is not designed to be read from cover to cover. For ex- ample, some of the chapters can easily be skipped by compilers who are particularly interested in methodological issues. Further details on the contents of the Handbook are given in Chapter 1. The Handbook cannot be too prescriptive for two reasons. Firstly, it is not always possible to give practical guidance as some of the solutions to conceptual problems are not always clear-cut and there are choices to be made about precisely how a practical solution is implemented. Secondly, what is applicable and what can be achieved will depend on the data and resources available to the individual national statistical institute (or other compiling institute). Acknowledgements The writing of the Handbook was led by Statistics Netherlands; Bert M. Balk co-ordinated the project activities. Jan de Haan and W. Erwin Diewert acted as main editors. The authors of the individual chapters are as follows: Preface Bert Balk, Jan de Haan and David Fenwick 1. Introduction Bert Balk 2. Uses of Residential Property Price Indices David Fenwick 3. Elements for a Conceptual Framework Erwin Diewert 4. Stratification or Mix Adjustment Methods Jan de Haan and Erwin Diewert Handbook on Residential Property Prices Indices (RPPIs) 9  Preface 5. Hedonic Regression Methods Jan de Haan and Erwin Diewert 6. Repeat Sales Methods Jan de Haan 7. Appraisal-Based Methods Jan de Haan 8. Decomposing an RPPI into Land and Structures Components Erwin Diewert 9. Data Sources David Fenwick 10. Methods Currently Used David Fenwick 11. Empirical Examples Marc Prud’homme and Erwin Diewert 12. Recommendations David Fenwick, Erwin Diewert and Jan de Haan Glossary Jan de Haan The quality of the Handbook was increased by the valuable contributions of many individuals and organisations, including input from both compilers and users of residential property price indices in different parts of the world. The number of contributors is, of course, too great to mention them all by name. The BIS (and in particular Paul Van den Bergh) have been excellent hosts for the Basel workshop in 2009. Many thanks go to UNECE (and in particular Carsten Boldsen) who were also heavily involved in the organisation of the Basel workshop, and of the special session on the RPPI Handbook during the joint UNECE/ILO CPI meeting in 2010. Special thanks are due to Irmtraud Beuerlein, Simon Coté, Lee Everts, Gregory Klump, Jose Vicente Romero, Patrick Sabourin, A.P. Saxena, and Chihiro Shimizu for contributing to the country-based case studies and to Emily Carless, Preechaya Chavalittumrony, Ali Hepşen, Marissa Gonzalez Guzman and Hector Zarate, who provided other background information on published indices. Useful comments on preliminary drafts of the Handbook were received from Carlos Brás, Morris Davis, Martin Eiglsperger, Timothy Erickson, Rui Evangelista, Dennis Fixler, John Greenlees, Brian Graf, Vanda Guerreiro, Ronald Johnson, Marcel van Kints, Andrew Leventis, Bogdan Marola, Daniel Santos, Mick Silver, Leo Sveidkauskas, Randall Verbrugge, David Wasshausen, and participants at the workshop in The Hague, in particular Marc Francke and Jan Walschots. Eurostat, the BIS, the IMF and the ECB also provided helpful comments. Thanks are also due to Rens Hendriks and Ning Huang for comments and computational assistance. 10 Handbook on Residential Property Prices Indices (RPPIs) Introduction 1 1 Introduction 1.1 Residential property is both a source of wealth 1.6 Broadly speaking, two separate types of RPPI can and, insofar as property owners live in or on their proper- be distinguished: a constant quality price index for the ty, an important determining factor in their cost of living. stock of residential housing at a particular moment in time The price of a house is something different from the cost of and a constant quality price index for residential property dwelling services it provides, though the two concepts are sales that took place during a particular period of time. The obviously interlinked. construction of these two types of index will be different; most particularly, the weighting associated with the two 1.2 Monitoring the development of house prices is types will differ. considered important, especially in times of economic turbulence. Yet the way house price development is meas- 1.7 Chapter 3  continues by summarizing the four ured varies per country, and even within a country there main approaches to constructing an RPPI. In the final sec- are sometimes two or more competing methods in use. tions a number of miscellaneous topics are addressed, such This situation is of course not favourable for the design of as the frequency of an RPPI, the consistency of monthly consistent policy measures based on solid international with quarterly estimates and the consistency of quarterly comparisons. with annual estimates, revision policies, and seasonal adjustment. 1.3 Against this background it is understandable that it was proposed that a handbook be prepared on housing, 1.8 Chapters 4-7  review in depth the main methods (1) The pri- or broader residential property, price indices.  for compiling RPPIs. The simplest methods are based on mary goals of the handbook are some measure of central tendency of the distribution of transaction prices in a period, in particular the mean or the • to provide guidance for those wishing to set up residen- median. Since house price distributions are generally posi- tial property price indices or modify existing indices in tively skewed (predominantly reflecting the heterogeneous view of international harmonisation; nature of housing, the positive skew in income distribu- • to provide a discussion and comparison of the various tions, and the zero lower bound on transaction prices), the targets and their corresponding conceptual frameworks; median rather than the mean is often used. As no data on • to provide an inventory of existing practices. housing characteristics are required to calculate the medi- an, a price index that tracks changes in the price of the me- The contents of the handbook are briefly outlined below. dian house sold from one period to the next can be easily 1.4 Chapter 2  reviews a number of areas where resi- constructed. Another attraction of median indices is that dential property price indices (RPPIs) play a role. The fol- they are easy to understand. lowing applications are considered: 1.9 One major drawback of simple median based • as a macro-economic indicator of economic activity; indices is that they provide very noisy estimates of price • for use in monetary policy and inflation targeting; change. The set of houses actually traded in a period, or a • as a tool for estimating the value of a component of real sample thereof, is typically small and not necessarily rep- wealth; resentative of the total stock of houses. Changes in the mix of properties sold will therefore affect the sample median • as a financial stability or soundness indicator to measure price more than the median price of the housing stock. A risk exposure; perhaps bigger problem than short-term noise is system- • as a deflator in the National Accounts; atic error, or bias. A median index will be subject to bias • as an input into citizens’ decision making on whether to when the quality of the housing stock changes over time. buy or sell residential property; Bias can also arise if certain types of houses are sold more • as an input into the Consumer Price Index; and frequently than other types of houses and at the same time exhibit different price changes. • for use in making inter-area and international compari- sons. 1.10 A general technique for reducing sample selection bias is (post-) stratification. This technique, which is also 1.5 In Chapter 3 on the uses of an RPPI, the focus will known as mix adjustment, is discussed in Chapter 4. be to fill in gaps in the System of National Accounts and in the compilation of a Consumer Price Index. It is likely that 1.11 Chapter 5  reviews the hedonic regression ap- if appropriate RPPIs can be constructed to fill in these gaps, proach. This approach recognizes that heterogeneous then the resulting family of RPPIs will meet the needs of goods can be described by their attributes or characteris- most users. tics. That is, each good is essentially a bundle of perfor- mance characteristics. In the housing context, this bundle may contain attributes of both the structure and the lo- (1) Actually, this was one of the conclusions of the OECD-IMF Workshop on Real Estate Price Indices (Paris, 6-7 November 2006). cation of the properties. Although there is no market for 12 Handbook on Residential Property Prices Indices (RPPIs) Introduction 1 characteristics, since they cannot be sold separately, the become clear in Chapters 4-7, most methods are unable to demand and supply for the properties implicitly determine decompose an RPPI into a land and a structures compo- the characteristics’ marginal contributions to the prices of nent. Chapter 8 discusses how hedonic regression methods the properties. Regression techniques can be used to esti- can be used to obtain such a decomposition and considers mate those marginal contributions or implicit prices. how to construct an RPPI for the stock of housing when he- donic regression methods are used. Using the actual data, 1.12 This chapter discusses, in a non-technical way, the this chapter also suggests ways to overcome several practi- main models used as well as the methods to form RPPIs cal problems that are often encountered in empirical work from estimation of such models. The overall evaluation of of this nature, such as a high correlation between the size the hedonic regression method is that it is probably the of the structure and the size of the land. best method that could be used in order to construct con- stant quality RPPIs for various types of residential prop- 1.17 In practice, because of the high cost of undertaking erty. However, it is also the most data-intensive method. purpose-designed surveys of house prices, the approaches 1.13 The repeat sales method, reviewed in Chapter 6, adopted by statistical agencies and others to construct utilizes information on the same properties which have RPPIs have been mainly a function of the house price data been sold more than once. Because only “matched mod- sets generated by the legal and other processes associated els” are used, there is no change in the quality mix to con- with buying a house. The indices so constructed can vary trol for. In its basic form, the only information required is according to the point in the house purchasing process at price, sales date and address of the property. So the repeat which the price is measured, for instance whether the final sales method is much less data- intensive than hedonic transaction price or the earlier valuation used for secur- methods. Also, the repeat sales method will automatically ing a loan is taken. Also, the amount of detailed informa- control for micro location (address), something which he- tion available on the characteristics of the properties sold donic methods are unable to do. will affect index compilation methods, often acting as a constraint on the techniques available to quality adjust for 1.14 The matched model methodology, where prices of houses of different sizes and locations. Thus, data availabil- exactly the same item are compared over time, is the natu- ity has historically been a constraint on the approach used ral starting point for the construction of any price index. for index construction. Because of the low incidence of transactions, and because the quality of houses continually changes, the standard 1.18 Chapter 9 qualitatively examines the different data matched model methodology cannot be applied straight- sources that can be used for constructing RPPIs, such as forwardly. The repeat sales method attempts to deal with printed news media, real estate agents, mortgage compa- this issue by looking only at properties that have been sold nies, property registers and tax offices. In the final section, more than once over a sample period. This, however, can attention is paid to the situation in many developing coun- lead to a relatively low number of observations and to sam- tries where data are scarce and the issue of property owner- ple selection bias. To overcome such problems, assessed ship is ambiguous. values of the properties could be used. 1.19 Chapter 10 catalogues the availability of RPPIs in 1.15 In many countries, official government assess- different countries and also presents some case studies. ments are available for all properties, because such data It relies on meta-data gathered by various organisations, are needed for taxation. If the assessments pertain to some including the European Central Bank and the Bank for reference date, an RPPI can be constructed by relating ac- International Settlements, and more recently a fact-finding tual sale prices to assessed values. This constitutes a variant exercise conducted by Eurostat in connection with the in- of the matched model methodology, the distinct feature clusion of owner-occupied housing costs in the European being that compositional change is accounted for. In this Union’s Harmonised Index of Consumer Prices, which was case, there is no need to use econometric techniques. The extended to cover some non-EU countries. various assessment-based methods, and in particular the sale-price appraisal ratio (SPAR) method, are reviewed in 1.20 Chapter 11 provides additional practical guidance Chapter 7. by demonstrating the working of the RPPI construction methods (excluding the SPAR method) that were outlined 1.16 Chapters 4-7  all end with empirical examples in Chapters 4, 5 and 6 on simple examples using small data tested on actual data in order to illustrate the methods sets. discussed and to provide additional background mate- rial. The data set covers 14 quarters of residential property 1.21 Chapter 12 concludes by providing recommenda- sales for a relatively small town in the Netherlands. As will tions. Handbook on Residential Property Prices Indices (RPPIs) 13 Uses of Residential Property Price Indices 2 2 Uses of Residential Property Price Indices Introduction monitoring house inflation, as experienced by purchasers, may best be estimated by collecting information on current 2.1 There are many areas of society where individu- transaction prices and using this information to construct als or organisations use residential property price indices a price index for the sales of housing units. In contrast, to (RPPIs) directly or indirectly either to influence practical estimate an economy’s (real) stock of wealth, information decision making or to inform the formulation and conduct on the sample of transacted dwellings must ideally be sup- of economic policy. Different uses can have a significant plemented by information on the stock of non-transacted impact on the preferred coverage of the index and also on dwellings in order to construct a price index for the housing the appropriate methodology applied for its construction. stock. This may be done by re-weighting to reflect the dif- ferent mix of houses in the housing stock compared with 2.2 From an individual household’s perspective, real transactions but the adequacy of this method depends on estate often represents the single largest investment in their whether the dwellings that are actually transacted can act as portfolio. It also accounts for the largest share of wealth in a proxy for the ones that have not been subject to a change most nations’ balance sheets. Changes in house prices can of ownership. If the price of houses that have not changed have far-reaching implications for individuals. For exam- ownership is not available and information on their num- ple, changes in housing equity and household debt levels bers and characteristics is limited or even non-existent, the can permeate through to the overall economy. In fact, con- user needs to be assured that the profile of the transactions sumer spending is often affected by changes in house prices is representative of the overall housing stock. In practice, as a result of wealth effects and its effect on consumer con- the latter condition may not be fully met as different sec- fidence. House prices influence home improvement and tors of the housing market can be influenced by different renovations expenditures, which in many countries are factors and the limited number of transactions may lead to higher than overall spending on new house construction. unreliable or even non-existent data on prices for some of House prices play a major role in the measurement of the these different strata. affordability of home-ownership, a key housing policy ob- jective in some countries. House price changes also influ- 2.5 The (price determining) attributes of individual ence the decision to build new houses (the supply side) as houses often change over time. These changes include im- well as the decision to become a homeowner (the demand provements to the dwelling in the form of renovations to side). (1) Investors turn to house price indices to not only kitchens and bathrooms, replacement windows with insu- measure wealth but also to help in assessing current and lated glazing, or the installation of energy efficient heating future rates of return. (2) or air-conditioning systems, and also extensions of the structure which reflect the recent trend in many coun- 2.3 From a broader perspective, analysts, policymak- tries towards larger houses. Improvements and extensions ers, and financial institutions follow trends in house prices will be partially offset by depreciation of the structures. to expand their understanding of real estate and credit Irrespective of the purpose of the index, an ideal RPPI market conditions as well as to monitor the impact on eco- should be adjusted for all of those changes. To put it differ- nomic activity, and financial stability and soundness.  (3) ently, the index should represent changes in the prices of For instance, mortgage lenders will use information on properties that are comparable in quality over time. house price inflation to gauge default risk. Central banks often rely on movements in house price indices to monitor 2.6 The need for quality adjustment extends beyond households’ borrowing capacity and debt burden  (4) and controlling for home improvements and depreciation, their effects on aggregate consumption. ( )5 however. The mix of dwellings that are sold in one period is likely to be different from that in the next period when, say, 2.4 In this context it should be emphasised that the the sample of houses sold consists of more larger houses different uses of residential property price indices may compared to the previous period. Such compositional or require different conceptual bases and methodology, al- mix changes may have a cyclical pattern because sales of though in practice, other factors sometimes come into larger houses will typically decline as an economy enters a (6) In general, no single in- play, such as data availability.  recession. Compositional changes of the sample over time, dicator of house price change can satisfy every purpose. just like quality changes of the individual dwellings, should For instance, the price dynamics of the housing market for not be interpreted as price changes – measurement tech- niques are required to adjust the price changes for quality (1) See Duffy (2009). mix changes. A short overview of the various methods that (2) Residential construction investment accounts for about 5% of GDP in the euro area. (3) See Case and Wachter (2005). are available to solve the problems of quality (mix) change (4) See Finocchiaro and von Heideken (2007). will be provided in Chapter 3. A detailed discussion of (5) See Case et al. (2001), Phang (2004) and Belsky and Prakken (2004). (6) See Fenwick (2006) and also Chapter 9. these methods will follow in Chapters 4-7. 16 Handbook on Residential Property Prices Indices (RPPIs) Uses of Residential Property Price Indices 2 A Review of the Different employment and higher incomes for a wide range of workers involved in the housing market, such as real Uses of Residential Property estate agents, construction workers and professionals in the financial and the legal professions. Expectations of Price Indices higher future returns on property investment lead build- ers to start new construction and this is accompanied by 2.7 Residential property price indices have a number higher market demand in property-related sectors from of important uses: owner-occupiers and property investors. (9) In addition, building activity will tend to increase from more home • as a macro-economic indicator of economic growth; renovations. • for use in monetary policy and inflation targeting; • Higher house prices tend to lead to increased sales of • as an input into estimating the value of housing as a com- existing housing units and this in turn can lead to addi- ponent of wealth; tional tax revenues in the form of property transfer taxes • as a financial stability or soundness indicator to measure generated from the higher volume and value of property risk exposure; sales. These increased tax revenues can lead to increased • as a deflator in the national accounts; government spending which in turn provides additional economic stimulus. • as an input into an individual citizen’s decision making on whether to buy (or sell) a residential property; • Rising real estate prices will lead to improvements in the household sector’s balance sheet (the wealth effect) and • as an input into the consumer price index, which in turn this in turn will generally lead to increased household is used for wage bargaining and indexation purposes; (7) spending on consumption and investment.  (10) Accord- • for use in making inter-area and international ing to a report by the U.S. Congressional Budget Of- comparisons. fice (2007), when house prices surged in the 1990s and Each use is considered in turn. 2000s, consumer spending grew faster than incomes. This household wealth effect generally leads to increases in spending by consumers on home renovations and re- As a Macro-Economic Indicator pairs in addition to increased spending on other goods of Economic Growth and services. 2.8 Rising house prices are often associated with pe- 2.10 Of course, the above stimulative effects of increas- riods of economic expansion while falling house prices ing house prices go into reverse when (real) house prices often correspond with a slowing economy. Goodhart and fall. It is therefore important that the public and economic Hofmann (2006) show that for 16 industrialised countries policy makers have at their disposal accurate and timely there exists a strong correlation between house prices and information on movements in real estate prices. economic activity. In fact the six major banking crises in 2.11 Asset prices, including real estate prices, are a key advanced countries since the mid 1970s were all associ- indicator for more fully understanding the dynamics of ated with the bursting of a housing bubble (Reinhart and the economy. (11) According to Plosser (2007), asset prices Rogoff, 2009). (8) In the main, house prices are treated as contain important information about the current and fu- a leading indicator although there is some debate about ture state of the economy and can play an important role in whether house price change is a leading, lagging or coinci- the deliberations of central bankers as they seek to achieve dent economic indicator. their objectives of price stability and sustainable output 2.9 What is clear is that rising house prices are often growth. associated with economic growth through at least three channels: For Use in Monetary Policy • Higher (relative) house prices tend to stimulate increased and Inflation Targeting construction activity, which in turn leads to higher 2.12 In addition to the above general interest in moni- toring property prices, many central banks have inflation (7) The inclusion of a house price index in the calculation of a CPI depends on the objectives of the CPI and, in particular, whether an acquisitions, payments or user cost targets which can directly involve indices of property approach is adopted. Further discussion of these issues is given in the Consumer Price prices. For instance, central banks in some countries uti- Index Manual (ILO et al., 2004) and the Practical Guide to Producing Consumer Price Indices (United Nations, 2009). lize a Monetary Conditions Index (MCI) as a day-to-day (8) Claessens, Kose and Terrones (2008; 25) find that “... recessions associated with house price busts are on average over a quarter longer than those without busts. Moreover, output declines (and corresponding cumulative losses) are typically much larger in recessions with busts, 2.2 (3.7) percent versus 1.5 (2.3) percent in those without busts. (9) See Zhu (2005). These sizeable differences also extend to the other macroeconomic variables, including (10) See Campbell and Cocco (2007). consumption, investment and the unemployment rate.” (11) See Turvey (1989) and Goodhart (2001). Handbook on Residential Property Prices Indices (RPPIs) 17 2 Uses of Residential Property Price Indices operating target for the conduct of monetary policy. In wealth effect that can lead to increases in consumption and an expanded version of this index, as that suggested by increased household borrowing. Jarociński and Smets (2008) and Goodhart and Hofmann 2.15 More generally, individuals will have an indirect (2007), the MCI would include some measure of house stake in real estate asset prices, including residential prop- prices because of the important role this variable plays in erty, through pension funds and other direct investments the inflationary process and for economic performance. in real estate. Other central banks who have an inflation target based on the Consumer Price Index (CPI) will indirectly take into account the movement in house prices when setting in- As a Financial Stability or Soundness terest rates, depending in part on the treatment of Owner Indicator to Measure Risk Exposure Occupied Housing (OOH) in their country’s CPI. This is- sue is discussed further in Chapter 3. 2.16 Financial Soundness Indicators (FSIs) are indica- 2.13 It can be argued that in the future, residential tors of the current health and soundness of the financial property prices are likely to play an increasing role in the system and institutions of a country and of their corporate conduct of monetary policy. Over recent years an inflation and household components. They include both aggregated target has been used by a growing number of countries individual institution data and indicators that are repre- to define and operate their monetary policy frameworks. sentative of the markets in which the financial institutions The IMF (2007) provides a list of 28  countries classified operate, including statistics on real estate prices. FSIs are as inflation “targeters” according to their “exchange rate calculated and disseminated for the purpose of supporting arrangements” (without specifying the target or inflation national and international surveillance of financial systems. measure). Carare and Stone (2003) extend this analysis The IMF developed FSIs with a view to monitoring and further by classifying countries that use an inflation target strengthening the global financial system and to increas- for monetary policy, into fully-fledged inflation “targeters”, ing stability following the financial market crises of the late eclectic “targeters” and inflation targeting lite regimes, us- 1990s, and as a way of combating the subsequent growing ing the clarity and credibility  (12) of the commitment to number of banking crises that have occurred globally. The the inflation target to classify individual countries. The compilation guide for financial soundness indicators pro- authors then identify 42  medium and large country cen- vides some advice on compiling house price indices whilst tral banks who have some form of floating exchange rate acknowledging the relative absence of international expe- mechanism (i.e. not adopting a fixed exchange rate) leav- rience and guidance and the absence of a comprehensive ing their degree of commitment to an inflation target as framework for constructing such indices. More recently, the defining monetary objective. They estimated that by the October 2009  Report to the G-20  Finance Ministers 2001 some 7 industrial and 11 emerging markets operated and Central Bank Governors on the Financial Crisis and fully-fledged inflation targeting, that is “have a medium to Information Gaps (13) mentions that information on dwell- high level of credibility, clearly commit to their inflation ings and their associated price changes are critical ingredi- target and institutionalize this commitment in the form of ents for financial stability policy analysis. a transparent monetary framework that fosters account- 2.17 Sharp falls in real estate prices have a detrimental ability of the central bank to the target”. The number of impact on the health and soundness of the financial sector countries operating fully-fledged inflation targeting has and on the financial situation of individuals and of indi- been increasing over the years. vidual households, by affecting credit ratings, the value of collateral, and the debt to equity ratio. As an Input for Estimating the Value 2.18 It should come as no surprise that the relation- of Housing as a Component of Wealth ship between real estate cycles and economic cycles is well documented and that the role of real estate prices in debt 2.14 House prices are an input into the measurement of finance and financial crises has long been recognised. This aggregate wealth in the economy. Existing dwelling units has led to the use of residential property price indices as are part of the balance sheet accounts in the System of indicators of financial stability, particularly in countries National Accounts (SNA). Thus it is necessary to have a where real estate accounts for a significant proportion of price index for this asset class in order to form estimates national and household wealth, and where the propensity of real household wealth. As was mentioned in the intro- of home ownership is relatively high. duction to this chapter, rising house prices will generate a 2.19 The use of trends in residential property prices, and real estate prices more generally, as an indicator of finan- cial soundness, has been supported by in-depth analytical (12) Clarity is gauged by the public announcement of the inflation target and by the institutional arrangements for accountability. Credibility is measured indirectly using as a proxy the actual inflation outturn and by market ratings of long-term local currency government debt. (13) Available at: http://www.imf.org/external/np/seminars/eng/2010/infogaps/index.htm. 18 Handbook on Residential Property Prices Indices (RPPIs) Uses of Residential Property Price Indices 2 studies. Included amongst the vast amount of material that two of the most recent and widely available references published on this subject is a paper by Nabarro and Key on the compilation and use of national accounts deflators, (2003) who present a model for real estate and lending cy- SNA (1993) and the Eurostat (2001) Handbook on Price cles, supported by case studies. Their paper traces the cycli- and Volume Measures in National Accounts, pre-date the cal evolution from initial indicators provided by the rental CPI Manual (2004) and PPI Manual (2004). market, to property prices and through to balance sheets 2.23 The CPI and PPI Manuals were developed in par- of borrowers and lenders, and draws attention to a number allel and take advantage of the latest research into index of relevant indicators of the real estate market. It describes number theory and practice, which is not fully reflected what the authors call “the dangerous interdependence be- in the official literature on national accounts. (16) The two tween real estate cycles and financial systems”. Whilst the manuals are essentially based on the same underlying eco- authors acknowledge the highly unpredictable nature of nomic principles and statistical theory. They provide a the real estate cycle and its different characteristics and comprehensive and coherent overview of the conceptual properties from one cycle to the next, they discuss the link- and theoretical issues associated with consumer and pro- ages between real estate cycles and debt finance to identify ducer price indices and translate these into available op- areas where improved information could support effective tions for practical measurement. The CPI Manual also act- counteracting strategies and policies. They explain how a ed as a catalyst for the new ILO Resolution on Consumer reliable and cost-effective system of performance measure- Price Indices, which was passed in 2003. ment and monitoring can be developed and implemented and suggest how such a system can provide a mechanism for analytical decision making, designed to impact upon As an Input into an Individual Citizen’s the behaviour of the real estate sector. Decision Making on Whether to Buy 2.20 Information on residential property and other (or Sell) a Residential Property property prices needs to be supplemented by relevant and timely detailed analyses, and by other information such as 2.24 The buying or selling of a dwelling is typically the the proportion of houses being purchased with cash rather largest financial transaction a household will enter into than being financed through a loan. The average ratio of during his or her life. Changes in house prices are there- loan to property price, and how this is distributed, pro- fore likely to influence substantially whether a household vides an indication of the exposure of the borrower and purchases a property and also the budget plans and savings the lender, as does the price to earnings ratio and, to a decisions of the prospective house buyers and sellers. The certain extent, the volume of transactions. (14) Similarly, a purchase of a house is considered by many owner-occupiers more detailed analysis of the types of houses being sold by both as a means of obtaining shelter services and as a region will show whether activity in the housing market capital investment, the latter potentially providing an op- is concentrated in particular segments of the market such portunity for significant capital gains in the longer-term. as high-end properties or in certain geographical locations Current price levels and trends, together with expectations such as the capital city or large urban areas. about future trends in house prices and mortgage interest rates, (17) will influence an individual’s decision on whether to purchase now or postpone the purchase. The opportu- As a Deflator in the National Accounts nity cost associated with the sums of money involved will 2.21 National statistical agencies use house price indi- also come into play as prospective purchasers evaluate the ces in at least two ways. First, the structures component of alternative choices available to them. For instance, pro- a price index for newly-built houses is often used to deflate spective purchasers will often take into account the impact current price values for residential construction in the na- of changes in house prices on market rents. tional accounts; see Bover and Izquierdo (2003). Second, 2.25 More generally, individuals also have an indirect house price indices may be included in the construction of stake in real estate asset prices through pension funds and the CPI, depending on the choice of its conceptual basis. other investments for which house prices will likely have This second use is considered below and in more detail in an effect. For instance, the portfolios of some pension Chapter 3. funds include apartment blocks whose rents provide an 2.22 Price indices and deflators are seemingly differ- ent entities within a wider group of statistics relating to prices. (15) It is pertinent to note against this background most attention in the literature is devoted to price indices…. Once somehow estimated, price indices are in fact used, if at all, primarily to deflate nominal or monetary totals in order to arrive at estimates of underlying “real” magnitudes”. (16) The CPI and PPI Manuals are consistent with the material in Chapter 16 of SNA (1993) (14) Past observation suggests that when price-to-earnings ratios get to an unsustainable and also with the 2008 System of National Accounts but delve deeper into the high level, the adjustment is initially seen in a reduction in the volume of housing problems associated with the construction of price indexes, particularly at lower levels turnover rather than in transaction prices. of aggregation. ( ) However, the underlying theory of deflators and (direct) price indexes is the same; see 15 ( ) Interest rate policy will have an impact both on inflation and on net disposable income 17 Chapter 16 in SNA (1993). Samuelson and Swamy (1974) note the following: “Although after the payment of interest. Handbook on Residential Property Prices Indices (RPPIs) 19 2 Uses of Residential Property Price Indices income and where a capital gain is expected to materialise than making, say, national comparisons over time because from an increase in the property value. inter-area/international comparisons require comparable types of housing across the regions/countries being com- pared (or comparable information on the characteristics As an Input into the Construction of housing units across the regions if a hedonic regression of a Consumer Price Index (CPI) technique is used) in order to construct a constant quality price index. 2.26 House prices will directly affect measured infla- tion when the CPI includes owner-occupier housing costs 2.29 The European Central Bank (ECB) – in co-operation and the method of measurement draws on house prices as with the central banks of the individual countries of the one of the inputs. Measured inflation is indirectly affected euro-zone and the European Union – has an interest in if house prices influence market rents, which constitute comparative measurement of changes in residential prop- another element of a CPI, and where additionally imput- erty prices across different euro-area countries and for the ed rents are used as a proxy for owner-occupied housing euro-area as a whole. The raw data used here come from costs. Renting and buying can be substitutes and the level various national sources and have primarily been collected of house prices will have an impact on the rate of return and documented by the Bank for International Settlements obtained by a landlord on his or her investment and also (BIS). (18) Since 2001, the ECB has compiled an aggregate on the rent charged. index for the euro-area by weighting together changes in prices for houses and flats for the euro-area countries. (19) 2.27 The treatment of Owner Occupied Housing The national methodologies associated with the figures (OOH) is one of the most difficult challenges faced by available for each individual country and for the euro-area compilers of consumer price indices. There are a number aggregate, have improved over recent years but perhaps fall of alternative conceptual treatments and the choice be- short of the standards applied to other economic statistics tween them can have a significant impact on the overall and price indicators for the euro-area. (20) The BIS has also index, affecting both the weight attributed to OOH (and brought together residential property price statistics for the by implication to an RPPI) and the measured rate of infla- non-euro area countries of the European Union and has in tion. In essence there are four possible main approaches many cases been confronted with even more pronounced to including OOH in a CPI: the acquisitions approach, the issues concerning data comparability and quality. payments or money outlays approach, the user cost ap- proach and the rental equivalence approach. The first three 2.30 Such comparisons can be confounded by meth- approaches require the construction of a housing price in- odological and coverage differences and also by differences dex. These various approaches to the treatment of OOH are in the frequency and timeliness of the data. Some of these reviewed in more detail in Chapter 3. differences arise from the different sources of data used to compile national indices. Chapter 9  explores these data sources in more detail and Chapter 10 gives an inventory For Use in Making International of the different methods used by countries to compile their and Inter-area Comparisons indices of residential property prices. It can be observed that a notable proportion of countries, including some de- 2.28 House price indices are also used in conjunction veloped countries, do not have reliable residential property with (comparable) benchmark data on house price levels price indices. across regions or countries to generate inter-area or in- ternational comparisons of living cost differentials. The problems that arise in attempting to price the services of (18) The BIS data set of residential property price statistics is available at: http://www.bis.org/ OOH in a national context also arise in the context of in- statistics/pp.htm. ter-area and international comparisons. In the latter con- (19) See box “Preliminary evidence on developments in euro area residential property prices” in the October-2001 issue of the ECB Monthly Bulletin. text, however, the problems are somewhat more difficult (20) See Eiglsperger (2010), page 233. 20 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 3 Elements for a Conceptual Framework Introduction Such statements indicate that the construction of an RPPI will be much more difficult than the construction of a “nor- 3.1 What makes the construction of a residential mal” price index based on a matched model methodology. property price index (RPPI) so challenging? This question It should be recognized at the outset that, because of the was addressed in Chapter 1 of this Handbook but it will be difficulties resulting from the uniqueness of each dwelling useful to remind readers about the main problems, which unit, it would not be possible to construct a “perfect” RPPI; are as follows: it will only be possible to construct an approximation to the theoretically ideal index for each purpose. • The compilation of price indices typically relies on matching the prices for identical items over time. How- 3.3 The question of what is the purpose of an RPPI ever, in the housing context, each property has a unique has been addressed in Chapter 2, where the many uses of location and usually a unique set of structural charac- an RPPI were considered. This chapter focuses on the uses teristics. Thus, the matched model methodology will be of RPPIs to fill in gaps in the System of National Accounts difficult or impossible to apply. and in the construction of a CPI. It is likely that if appropri- ate RPPIs can be constructed to fill in these gaps, then the • Transactions are sporadic. resulting family of RPPIs will meet the needs of most users. • The desired index number concept may not be clear, or 3.4 Broadly speaking, two separate RPPIs can be dis- put another way, there are several distinct purposes for tinguished: 1) a constant quality price index for the stock of which an RPPI is required and, broadly speaking, differ- residential housing at a particular moment in time; and 2) ent purposes require different indices. a constant quality price index for residential property sales • For some purposes, notably the construction of national that took place during a particular period of time. The con- balance sheets and the estimation of user costs of owner struction of these two types of index will be different; e.g., occupied housing, a decomposition of a property price the weighting associated with the two types will differ. In into land and structures components is required but it is this chapter, the main approaches to constructing an RPPI unclear how best to accomplish such a decomposition. will be briefly discussed. Details on these methods will be This issue will be discussed in more detail in Chapter 8 presented in Chapters 4 to 7. below. 3.5 A variety of miscellaneous topics will be ad- 3.2 The first two difficulties are well recognized in the dressed in the final four sections of this chapter. These top- housing measurement literature as the following quota- ics include the frequency of the RPPI and user needs, the tions indicate: consistency of monthly with quarterly estimates and the consistency of quarterly with annual estimates, revision “The price of housing is harder to measure than that of most policies, and seasonal adjustment. other goods and assets because of three key distinguishing characteristics. First, and most importantly, dwellings are heterogeneous. No two dwellings are identical, if only because they cannot occupy quite the same location. This Residential Property Price means that sampled house prices may be a poor indicator of all house prices because we cannot always reliably Indices and the System predict the sales price of a given dwelling from the price of of National Accounts another.” Robert Wood (2005; 213). 3.6 The System of National Accounts (SNA) 1993 and “The fundamental problem that price statisticians face its recent updating, the System of National Accounts when attempting to construct a real estate price index 2008, (1) provide a comprehensive accounting framework is that exact matching of properties over time is not pos- for an economy. The SNA partitions the value flows in the sible for two reasons: (i) the property depreciates over economy into various meaningful categories and provides time (the depreciation problem) and (ii) the property may a reconciliation of the flow accounts with the correspond- have had major repairs, additions or remodeling done ing stock accounts. It is furthermore recommended to de- to it between the two time periods under consideration compose the values in the cells of these accounts into price (the renovations problem). Because of the above two prob- and volume (or quantity) components. lems, constructing constant quality real estate price in- dices cannot be a straightforward matter; some form of imputation or indirect estimation will be required.” Erwin Diewert (2009b; 92). (1) See Eurostat, IMF, OECD, UN and the World Bank (1993) and (2009). 22 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 3.7 There are three passages in the SNA where residen- 3.11 The real estate industry can be treated as a retailing tial property price indices are required to convert nominal or wholesaling industry; i.e., it is a margin industry that can values into volumes or real values: be thought of as buying a property at the pre-commission • the stock of residential properties that exist at a particular price and selling it at the post-commission price. The value location in the country at a particular point in time; of the service is equal to the commission revenue, VCt , and the quantity of the service is proportional to the volume of • the sales of residential properties that were sold in a particu- the sales, QSt . Thus set the volume of the real estate services, lar location in the country over a particular time period, and QCt , equal to QSt : • the structures part of the sales of new residential proper- (3.2) ties that were sold in a particular location in the country QCt ≡ QSt  over a particular time period. 3.8 A country’s stock of residential properties is a 3.12 Finally, the price index in period t for the subsec- component of its national wealth. Hence, a price index is tor of the real estate industry associated with the property required for residential properties so that balance sheet sales, with value VSt in period t, is set equal to the value of estimates of real wealth by component can be formed.  (2) the corresponding commissions, VCt , divided by the cor- Balance sheet estimates of national wealth typically dis- responding volume, QC t : tinguish between the structures component of residential PCt ≡ VCt / QC t (3.3) property and the land component. If there is a need to provide estimates of the country’s real stock of residential = VCt /[VSt / PSt ]  using (3.1) and (3.2) structures and the real stock of residential land, it will be necessary to decompose residential property values into = [VCt / VSt ]PSt separate land and structures components and to construct = mC t PSt price indices for each of these components. 3.9 It may not be immediately obvious why a price where mC t = VCt / VSt is the period t margin rate for this class index for the sales of residential properties is required for of real estate transactions; i.e., mC t is the ratio of commis- national income accounting purposes. It is used to estimate sions in period t to the corresponding purchaser’s total the real output of the residential real estate services indus- value of the real estate transactions. Thus the period t price try, i.e., the industry that provides services that facilitate index for the output of this segment of the real estate in- residential properties transactions. Some algebra will help dustry is the product of the margin rate mC t times the con- understand why having a price index for the sales of resi- stant quality price index for the properties sold in period dential properties is essential in this area. t, PSt . This demonstration illustrates why constant quality price indices for sales of residential properties are useful 3.10 Suppose that the value of real estate agent commis- for national income accounting purposes. sions is VCt for some class of property transactions in pe- riod t and suppose that the corresponding value of sales for 3.13 The third value cell in the national accounts that the same group of properties (including the commissions) requires a housing price deflator is the value of new housing is VSt . Further, suppose that a constant quality price index produced in various locations in the country over a refer- for this type of sale has been constructed and the period t ence time period. This value flow is part of gross capital for- value of this price index is PSt . (3) An estimate of volume of mation in the country. When a new property is produced sales for this class of real estate transactions in period t, say in the reference period and if there were no improvements QSt , can be calculated with the following relationship: made to the underlying land that the new structure oc- cupies, then the portion of the sale price that can be at- QSt ≡ VSt / PSt (3.1) tributed to the site land should be deducted from the sale price and the residual amount is then part of gross capi- (2) A price index for the stock of residential properties is also of some use to central bankers tal formation and also part of the construction industry’s who are interested in monitoring property prices for the possibility of bubbles in their countries; see Chapter 2. output. Thus, an RPPI for the structure component of the ( ) Instead of using a purchaser’s price index, it is also possible to use a seller’s price 3 sales of new residential properties is required in the national index. When constructing a constant quality price index for housing, should the price determining characteristics of the seller or those of the purchaser be used to do quality accounts. It will be necessary to decompose sales of new adjustment? It could be argued that the quality determining characteristics of the residential properties into separate land and structure com- purchaser should be used in order to quality adjust prices for residential properties, since if the purchaser does not see enough value in the price of a property, it will not ponents and to construct a constant quality price index for be purchased. This suggests that a purchaser’s constant quality price index should the structure component in order to serve the needs of the be constructed as opposed to a seller’s constant quality price index. However, one could also argue that if the selling price of a property (regarded as a function of the national accounts. characteristics of the property) is not high enough, then producers of new housing units will not build a new unit and thus it is the price determining characteristics of 3.14 Recall the above discussion about modeling the the seller that should count, at least in the context of valuing new housing units. Rosen (1974) discusses these issues. In terms of Rosen’s analysis of the determinants of the output of the real estate industry. Because the sale of a new hedonic surface, for the case of new housing units, it is likely that his Case 1 analysis is relevant, where cost conditions are identical across firms and thus the hedonic surface property will have various transactions costs associated is determined by the supply side of the market; see Rosen (1974; 50-51). with it (e.g., real estate commissions), this leads to some Handbook on Residential Property Prices Indices (RPPIs) 23 3 Elements for a Conceptual Framework complexities in the system of national accounts that have but the CPI manual suggests four possible approaches. (7) not yet been definitively resolved. From the viewpoint of These approaches treat the unique character of OOH, the construction industry, these transactions costs are not which involves both the acquisition of a house and the con- part of the revenues that accrue to the construction sec- sumption over time of the flow of services of the house, in tor, so these costs should not be included in the value of a different manner. the output of the construction industry. However, from • The money outlays or payments approach. In this ap- the viewpoint of the sector that purchases the new hous- proach, the out of pocket expenses of home ownership ing unit, these transactions costs are a real cost and they are simply added up. These costs include expenditures must be accounted for. There are a number of ways that on maintenance and repair, mortgage interest costs, in- transactions costs associated with the purchase of a new surance premiums, property taxes and condominium housing unit could be treated (from the viewpoint of the charges (if the housing unit is a condominium). Two purchaser): important types of implicit cost and one important im- • simply attribute all of the costs to the period of purchase plicit benefit of home ownership are not included. The and treat the transactions costs as an expenditure by the two omitted costs are depreciation and the opportunity purchaser (4) (which is an acquisitions approach to these cost of the funds that are tied up in the homeowner’s eq- costs); uity in the house; the implicit omitted benefit is any (net) • include transactions costs as part of the structures compo- capital gains that may accrue to the owner during the nent of the value of the purchase so that these costs would time period under consideration. (8) The money outlays be amortized over time using the same depreciation rate approach is useful if an analyst wishes to focus on the that was being used to depreciate the structure; or disposable income of households. However, it is not par- ticularly useful as a measure of household consumption • separately amortize the transactions costs according to services (because of the omission of the costs and bene- the average length of time a residential property of the fits mentioned above). type under consideration is being held before it is resold. • The (net) acquisitions approach. (9) In this approach, the Conceptually, the last treatment seems preferable  (5) but services of OOH are ignored in the CPI except when a the first and second treatments will lead to a simpler set new housing unit is introduced into the market place. of accounts. These issues need to be studied further by na- The purchase price of the new dwelling unit is charged tional accountants with input from the broader economics to the period of purchase so that a purchase of a new community. house is treated in the same manner as the purchase of a nondurable good or service, i.e. the purchase is treated in the same way as the purchase of other durable goods. A variant of this approach is to decompose the selling Residential Property Price price of the newly built residential property into land and structures components and to use just the structures Indices and the Consumer component as the price which will enter into the CPI. Price Index • The rental equivalence approach. In this approach, a price is imputed for the shelter cost of the owner occupied 3.15 Pricing the services of Owner Occupied Housing housing unit (both for new and existing units), which is (OOH) in a Consumer Price Index (CPI) is extensively equal to the price at which the unit could be rented. (10) dealt with in the Consumer Price Index Manual. (6) There is • The user cost approach. In this approach, the financial no universal consensus on the treatment of OOH in a CPI opportunity cost of owning the house and using its ser- vices during the reference period is calculated. (4) The price index that could be used to convert the nominal value of transaction charges into a real amount (or volume) is a composite purchase price index for the type of property under consideration which includes both the land and structures components. (5) This is the treatment used by the Australian Bureau of Statistics. An unresolved issue is (7) Diewert (2002) (2009a) (2009b) provides more discussion of alternative methods. the choice of price deflator in order to form real amortization charges. That is, should (8) The money outlays concept is explained in some detail in Baldwin, Nakamura and a structures price index be used or should a composite structures and land price be Prud’homme (2010). used? In the case of real estate the commissions are generally proportional to the (9) For a comprehensive practical treatment of the net acquisitions approach, see Eurostat’s overall price of the property (the sum of the land and structures components) so it (2012) Technical Manual on Owner Occupied Housing. would be appropriate to use a composite property price index for the deflation of (10) This approach is consistent with the treatment of OOH in National Accounts. In the this component of transactions costs. Government transactions taxes or stamp duties SNA, OOH is considered a fixed asset, unlike other durables (such as washing machines, may impose different rates on the land and structures components of the sale and so furniture, cars etc). The purchase of a house is considered an investment and included working out an appropriate real price for this component of transactions costs may be in gross fixed capital formation and thus excluded from household final consumption rather complicated. Again, it may be acceptable to avoid all of these complexities and expenditure; the same goes for extensions of the house and major repairs. However, the just use a composite purchase price index to do the deflation. ownership of a house provides a service which is consumed over time by the owner ( ) See ILO, IMF, OECD, Eurostat, UN and World Bank (2004), Chapter 23. 6 and the value of this service is included in household final consumption expenditure. 24 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 Since the CPI Manual (2004) was written, a fifth concept • a price index for the structures component of newly-built for pricing the services of OOH has been suggested: (11) residential properties that were sold during a given pe- • The opportunity cost approach. In this approach, the price riod of time, which is needed for a narrowly defined net for the services of an owned dwelling unit is set equal to acquisitions approach where only the structures compo- the maximum of its rental equivalence and user cost prices. nent would be included in the purchase. 3.16 The conceptual differences between these ap- proaches should be underlined. The rental equivalence ap- proach and the user cost approach price the services of an owner occupied dwelling. The payments approach meas- Main Methods ures the out of pocket expenses of home ownership. The 3.19 To measure pure price change, real estate prices net acquisitions approach takes a completely different per- must be adjusted for quality change. In other words, to spective, implicitly allocating all the services of the newly compile a constant quality RPPI, it will be necessary to purchased dwelling to the period of purchase. somehow control for any variations in the amounts of the 3.17 In the above approaches except the payments and price determining characteristics of the properties. The rental equivalence approaches, there is a need for constant most important characteristics are: quality price indices for either newly-built dwelling units • the area of the structure (in squared feet or in meters or for the existing stock of dwelling units. The user cost and squared); opportunity cost approaches to pricing the services of a resi- dential housing unit are not entirely straightforward. The • the area of the land that the structure sits on (in squared Appendix to this chapter outlines the mechanics of these feet or meters squared); approaches. • the location of the property; 3.18 To summarize, RPPIs are needed in the construc- • the age of the structure; tion of a CPI and to deflate several value flows and stock • the type of structure; the structure can sit entirely in the holdings in the national accounts. For both CPI and na- lot without sharing any walls with an adjacent struc- tional accounts purposes, it will be useful or necessary to ture (detached dwelling unit) or share one wall with a have a decomposition of the price indices into structures neighbouring unit (semi-detached dwelling unit), or and land components. More specifically, it would be useful the dwelling unit can be a single apartment or unit in to be able to construct the following set of RPPIs: (12) a multifamily residence (apartment or condominium • a price index for the total stock of residential housing at building); a particular moment in time, which is needed for esti- • the materials used in the construction of the house (pri- mating real changes of the economy’s stock of residential marily wood, brick, concrete or traditional materials; i.e., housing, a component of a nation’s real wealth; a shack or shanty), and • a price index for the owner occupied stock of residen- • other price determining characteristics such as the num- tial housing (a subindex of the index in the bullet point ber of bedrooms, the number of bathrooms, a garage, a above), which is needed to construct estimates for the swimming pool, air conditioning, distance to amenities, value of OOH services based on user cost or opportunity etc. cost principles; 3.20 Four main methods have been suggested in the lit- • a price index for residential property sales (both newly- erature to control for changes in the amounts of the prop- built and existing dwelling units) that took place during a erty characteristics: stratification or mix adjustment, repeat given period of time, which is needed for estimating the sales methods, hedonic regression methods, and the use of real output of the residential real estate services sector; property assessment information. Below, a brief overview • a price index for the sales of newly-built residential prop- of the four methods is provided. More details can be found erties during a given period of time, which is required if a in Chapters 4-7. broadly defined net acquisitions approach is used where both the structures and land components would be in- 3.21 Stratification of transactions according to some of cluded in the purchase; the price determining characteristics is a straightforward and computational simple way to adjust for changes in the quality mix of the samples in different time periods. By de- (11) See Diewert (2009b), Diewert and Nakamura (2009) and Diewert, Nakamura and fining a number of reasonably homogeneous strata or cells, Nakamura (2009). (12) Fenwick (2005) (2006) argued that it would be useful to develop a coherent conceptual the average selling price within each cell can be used as a framework for a family of real estate price indexes. “It can be seen that user needs (proxy to a) constant quality price for that type of property. will vary and that in some instances, more than one measure of house price or real estate inflation may be required. It can also be seen that coherence between different Regular index number theory can then be applied to aggre- measures and with other economic statistics is important and that achieving this will be especially difficult as statisticians are unlikely to have an ideal set of price indicators gate up the average prices by cell into an overall index. Such available to them.” David Fenwick (2006; 8). stratification methods are also known as mix adjustment Handbook on Residential Property Prices Indices (RPPIs) 25 3 Elements for a Conceptual Framework methods. Wood (2005) describes this method in the fol- another variant of the method known as the hedonic impu- lowing way: tation method. “House price observations are grouped into sets or 3.24 Many countries tax real estate property and are ‘cells’ of observations on houses with similar location and likely to have an official property valuation office that pro- physical attributes. […..] The mean prices in each cell are vides periodic appraisals of all taxable real estate proper- weighted together to give a ‘mix adjusted’ price. A change ties. Assessment-based methods combine selling prices with in the composition of the sample will alter the number of appraisals to compute price relatives (sale price appraisal observations in each cell. But if the cells are defined suffi- ratios) and control for quality mix changes. The Sale Price ciently precisely, so that all elements of the cell have similar Appraisal Ratio (SPAR) method is based on the matched prices and price trends, then such compositional changes model methodology. In contrast to the repeat sales meth- will not systematically affect the mix adjusted house price. od, it relies on all (single and repeat) sales data, and there Robert Wood (2005; 214). is no revision of previously estimated indices. Of course the method can only be applied in countries where reliable 3.22 The repeat sales method addresses the quality mix assessed values of the properties are available. problem by comparing properties that have sold more than once over the sample period. Restricting the comparison to 3.25 If the reference period is a year, all methods will units that have sold repeatedly ensures that the price rela- tend to generate similar estimates of the trend in residential tives compare like with like, provided that the quality of property price changes for an entire country. However, as the houses remained unchanged. The standard repeat sales will be seen in the examples presented in Chapters 4-7 and method is based on a regression model where the repeat Chapter 11, different methods do generate small but sig- sales data pertaining to all periods are pooled. A poten- nificant differences in trends while for shorter periods they tial drawback of this approach is the issue of “revisions”: can lead to rather different estimates of price change. The when new periods are added to the sample and the model various methods could also produce different signals of is re-estimated, the previously estimated price indices will turning points. change. An advantage of repeat sales methods is that, be- 3.26 As hedonic methods assume that information on cause properties are matched at the address level, loca- the characteristics of the properties sold is known, the tion, an important factor affecting real estate prices, is held samples can be stratified and, if a sufficient number of ob- constant. servations is available, separate indices can be estimated 3.23 One other potential drawback of the repeat sales for the strata. In other words, hedonic regression meth- method is that it does not account for quality changes of ods can provide a set of constant quality price indices for the sampled houses; over time a dwelling unit can undergo various types of property. Obviously, if data on some price renovations and be subject to depreciation. Consequently, determining characteristics are available, then repeat sales the quality of the property can vary with time. Hedonic re- and assessment-based methods can also be combined with gression methods can in principle adjust for such quality stratification. changes in addition to changes in the quality mix of the 3.27 Stratification can also be used to approximate a samples. These methods utilize information on the relevant stock based RPPI. In this case the stratum weights will be property characteristics to estimate quality adjusted price based on census data pertaining to the value of the owner indices using regression techniques, though it may prove occupied housing stock. The stratum price indices will still difficult to sufficiently control for location. There are differ- be based on sample data of properties sold. Within each ent ways to estimate hedonic price indices. The time dum- stratum, the properties traded are now treated as a (ran- my variable method has been prominent in the real estate dom) sample from the stock. Since long time intervals be- literature. This method models the price of a property as tween two censuses is the norm, stock value weights can a function of its characteristics and a set of time dummy usually only be updated very infrequently. variables. Because the data for all periods are pooled, the resulting indices are subject to revisions like with the re- 3.28 As was discussed previously, for various purposes peat sales method. Another drawback of the time dummy it is necessary to decompose the overall price of a prop- method is that it places perhaps unwarranted restrictions erty into (additive) components that reflect the price of the on variations in the price of land and structures across structure and the price of the land the structure is located time. These difficulties with the time dummy variant of on. In Chapter 8 it is shown how hedonic regression tech- the hedonic regression approach can be avoided by using niques can be used to accomplish this decomposition. 26 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 The Frequency of the RPPI 3.31 There are also conflicting objectives with some of the other requirements: having many strata and asking for and User Needs monthly indices may lead to a situation where some strata have only few transactions, resulting in rather volatile and 3.29 For inflation monitoring purposes, most central inaccurate sub-indices. Although taking moving aver- banks would prefer an RPPI on a monthly or quarterly ba- ages of the monthly indices can reduce volatility, (15) such sis. For national accounts purposes quarterly indices will a strategy will not provide timely signals of price change. suffice, while for CPI purposes monthly indices are gener- That is, the resulting average index will be centered in the ally required. Given that the number of observations for a middle of the time period for the moving average and will monthly price index will only be approximately one third not be available until some months have passed. (16) In par- of the number for a quarterly index, statistical agencies will ticular, this could give a misleading picture of the upswings have to carefully evaluate the tradeoff between publication and downturns in the housing market. So in general, it will frequency, timeliness and accuracy. The use of monthly not be possible to meet with a single price index all the data may lead to rather noisy figures, whatever method above listed user needs, and statistical agencies will have used to compile an RPPI. To mitigate the noise, a moving to make some compromises in their attempts to meet the average could be computed but this creates new problems, different user needs. as will be explained below. (13) 3.30 It is useful to outline some of the tradeoffs that statistical agencies may face when attempting to construct house price indices that meet the needs of users. Before Consistency of Monthly examining the tradeoffs, it will be necessary to review the user needs for a family of residential property price indi- with Quarterly Estimates ces. The following list of user needs is borrowed from the 3.32 How can monthly estimates of real estate price list compiled by Emily Carless (2011) from the National changes be made consistent with quarterly estimates? The Statistician’s Office of the UK Statistics Authority. The fam- answer to this question is reasonably straightforward if the ily of RPPIs should: (14) same average price or unit value methodology is applied • be based on the price paid for transacted properties; to the quarterly data as is applied to the monthly data. Suppose that a monthly sales RPPI is constructed using the • be stratified by region; stratification (or mix adjustment) method. As will be ex- • be stratified by type of housing (e.g., detached, row, high plained in Chapter 4 more thoroughly, the monthly price rise, type of construction, etc.); for a particular cell is the average transaction price or unit • be computed on a monthly basis; value and the corresponding quantity is the total number • aggregate up to a consistent national index; of properties traded. The quarterly RPPI for that cell would start out by calculating a quarterly unit value, and the cor- • be accurate and timely with minimal revisions. responding quantity is the quarterly total number of stra- The fifth requirement, that the various sub-indices aggre- tum transactions. Some algebra will make clearer the rela- gate up to a consistent national index is not too difficult to tionship between the quarterly cell price and quantity data satisfy. Whether the first requirement, that the price indi- to the corresponding monthly data. (17) ces be based on transaction prices, can be met, depends 3.33 Suppose that there are T quarters of monthly data. on availability of the data. In many countries, actual sell- Denote the value of quarterly transactions in a particu- ing prices are used to compile RPPIs, but not all statistical lar cell in the stratification scheme by V t for t = 1,..., T . agencies may have access to transaction data. Even if trans- Within each quarter t, the value of first month transac- action data are available, there can be a time lag involved tions is denoted by V1 , of second month transactions by t (as will be discussed in Chapter 9), so that in practice the V2 and of third month’s transactions by V3t . The quarter t first requirement could be at odds with the sixth require- t monthly unit value prices are denoted by P1t , P2t and P3t ment, i.e., that the indices should be timely. (15) The volatility may also be mitigated by combining some strata, but then users may (13) Nevertheless, moving averages are, for example, used in Iceland. It may also be necessary lose some of the desired geographical detail or type of housing coverage they were to use slightly out of date information in a monthly CPI context; see Gudnason and expecting. In addition, the new combined strata may not be subject to the same price Jónsdóttir (2006; 4). trend and thus there is the possibility of some resulting unit value bias due to the (14) In addition to the requirements listed, Carless noted that users desire a clear aggregation of the strata. explanation of the methods used to construct the statistics and indicators of the quality (16) This number is equal to half the window length of the moving average. of the measures. Also, some users want seasonally adjusted series in addition to the (17) The same type of analysis can be applied to the relationship between an annual (mix unadjusted series. adjustment) sales RPPI and the corresponding quarterly estimates. Handbook on Residential Property Prices Indices (RPPIs) 27 3 Elements for a Conceptual Framework and the corresponding monthly number of transactions are is dependent on census information on housing, which is denoted by Q1t , Q2t and Q3t . Note that Vmt equals Pmt Qm t often subject to long delays. Moreover, when a new census for m = 1,2,3 and t = 1,..., T . The value of transactions for becomes available, it is generally desirable to use this infor- quarter t, V t , is equal to the sum of the monthly transac- mation to retrospectively adjust the stock type RPPI back tions within the quarter: to the time of the previous housing census. Thus, it will gen- erally be desirable to allow stock RPPIs to be revised. This V t = V1t + V2t + V3t = P1t Q1t + P2t Q2t + P3t Q3t (3.4) should not pose any major problems for national accounts t = 1,..., T purposes, since they are routinely subject to revisions. The quarterly quantity series, Q , is the sum of the month- t 3.36 Revisions do cause problems, however, in the con- ly transactions within the quarter and the quarterly price text of non-revisable statistics such as the CPI. The treat- series, P t , is the quarterly unit value for the cell under ment of owner occupied housing in a CPI requires a stock consideration; i.e.: type RPPI if either the user cost or opportunity cost ap- proach is used. (18) It may then be necessary to use prelimi- Q t = Q1t + Q2t + Q3t (3.5) nary information to compile the RPPI. When additional t = 1,..., T data become available, a revised CPI could be published as an analytical series so that analysts could form some rough P t = V t / Q t (3.6) estimates of the possible bias in using the unadjusted CPI based on a preliminary estimate of the RPPI for owner oc- = [ P1t Q1t + P2t Q2t + P3t Q3t ] /[Q1t + Q2t + Q3t ] cupied housing. = s1t P1t + s 2 t P2t + s3t P3t t = 1,..., T Seasonal Adjustment where the month m share of transactions in quarter t, s , t m 3.37 Although the situation may differ somewhat across is defined as countries, in general there are substantial seasonal fluctua- tions in the quantities of properties traded over the year. sm t = Qm t / Q t (3.7) For the construction of an RPPI, the question is whether m = 1,2,3 ; t = 1,..., T seasonality in quantities leads to seasonality in prices. The empirical evidence is somewhat mixed. Meese and Wallace Thus, the quarterly price level for the cell under considera- (1991) find limited seasonality in prices in their economet- tion, P t , is equal to a transaction share weighted average of ric study. Prasad and Richards (2008) report that median the monthly price levels Pmt for the months m in quarter t. prices in Australian cities are seasonal, but this seasonal- ity vanishes after controlling for compositional change 3.34 For RPPI construction methods other than strati- through stratification. At aggregate levels, and particularly fication (hedonic regression, repeat sales, use of appraisal at the nation-wide level, it seems therefore unlikely that data), the relationship between the quarterly estimates of RPPI series exhibit strong seasonal fluctuations. However, price change and the corresponding monthly estimates will at lower levels of aggregation it would be useful to check be more complex. However, in the end, these methods will whether any seasonality in prices is present and adjust for generate a price index, say Pt for period t, that is associated this if seasonally adjusted series are required. Some users with a certain group of transactions (or stocks). Generally, do want seasonally adjusted series made available to them the corresponding period t value associated with these (in addition to the unadjusted series) if there is evidence of stocks, say Vt, will be available and thus a corresponding seasonality in prices. period t volume, Qt = Vt/Pt, can be defined, so the above algebra can be applied. 3.38 In Chapter 4, a numerical example is worked out which shows how seasonality can be treated using simple index number techniques. Standard seasonal adjustment methods could also be used. Revision Policies 3.35 It would seem that an RPPI for the sales of proper- ties could be constructed without a need for revisions but (18) The acquisitions approach requires a new house price index which probably should as it turns out, it is not always easy to gather timely data exclude the land component of the selling price of a new dwelling unit. This new house price index could be adequately approximated by a suitable new house construction on property sales. The construction of a stock type RPPI price index. 28 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 Appendix: The Role purchasing the durable good at the beginning of the pe- riod, using the services of the durable over many periods of House Price Indices and then netting off from these costs the benefits that could be received by selling the durable good at the end of the pe- in the Construction riod, taking into account the interest foregone from having one’s capital tied up in purchasing the durable. However, of User Costs there are several details that are somewhat controversial such as the treatment of depreciation, interest and capital 3.39 This Appendix shows how user costs and oppor- gains or holding gains. tunity costs can be constructed. The first section discusses 3.43 Another complicating factor with the user cost ap- how user costs are constructed for durable goods in gen- proach is that it makes a distinction between current pe- eral. Next, additional difficulties are brought in which arise riod purchases within the period under consideration and from the fact that properties are unique goods and are a the holding of physical stocks of the durable at the begin- mixture of land and structures components. Finally, the ning and end of the accounting period. Normally in the opportunity cost approach to pricing the services of Owner system of national accounts, all purchases are thought of Occupied Housing (OOH) is discussed. as taking place at a single point in time, say in the middle of the period under study, and consumption is thought of The Construction of User Costs as taking place within the period as well. Thus, in this case for Durable Goods in General where the commodity is entirely consumed within the pur- chasing period, there is no need to consider the valuation 3.40 In this section, the elements of user cost theory for of stocks of consumer durables that households may have a durable consumer good are laid out. The essence of dura- at their disposal. The complexity involved in accounting for bility is that it provides some sort of service to the purchas- stocks and flows are unfamiliar to many price statisticians, er over many time periods. For many purposes (including so it may be useful to describe these problems in some de- the valuation of household consumption expenditures on tail here. owner occupied housing services) it is not appropriate to 3.44 To determine the net cost of using a particular du- apply the entire purchase cost of a durable good to the ini- rable good during say period 0, assume that one unit of the tial period of purchase; the purchase cost should be spread durable good is purchased at the beginning of period 0 at over its useful life. The question then becomes: how should the price P0. The “used” or “second-hand” durable good this intertemporal cost be allocated over time? can be sold at the end of period 0 at the price PS1. It might 3.41 There are two main approaches to pricing the ser- seem that a reasonable net cost for the use of one unit of vices of an owner occupied dwelling unit:  (19) the rental the consumer durable during period 0 would be its initial equivalence approach and the user cost approach. The user purchase price P0 less its end of period 0 “scrap value” or cost approach is important in its own right – when only market opportunity selling price, PS1. However, money re- few dwelling units in a country are rented, it is not realistic ceived at the end of the period is not as valuable as money to value the services of owner occupied housing using the received at the beginning of the period. To convert the end rental equivalence approach – but it also is important as of period value into its beginning of the period equivalent a way to explain how landlords might set their rents for value, it is necessary to discount the term PS1 by the term rental dwelling units. However, pricing shelter services is 1+r0 where r0 is the beginning of period 0 nominal inter- more difficult than pricing the services of, say, a standard est rate that the household (or purchaser) faces. Hence, the model automobile because housing services are more com- period 0 user cost u0 for the consumer durable (21) is defined plex. (20) Therefore, in this section the problems of pricing as the services of an ordinary durable consumer good (that is u0 ≡ P0 - PS1/(1+r0)(3.A1) available in the same form over many periods) will first be presented before dealing with the complexities associated 3.45 There is another way to interpret the user cost for- with housing. mula (3.A1): the consumer purchases the durable at the be- ginning of period 0 at the price P0 and charges himself or 3.42 The user cost approach to the treatment of durable herself the rental price u0. The remainder of the purchase goods is in some ways very simple: it calculates the cost of price, I0, defined as I0 ≡ P0 - u0(3.A2) (19) The acquisitions approach implicitly allocates all of the services of a newly purchased housing unit to the period of purchase but the System of National Accounts does not recognize this approach as a valid approach to pricing the services of OOH. For other durable goods, the SNA does recognize the acquisitions approach as a valid approach (21) This approach to the derivation of a user cost formula was used by Diewert (1974) who for pricing the services of a durable good. in turn based it on an approach due to Hicks (1946; 326). Note that later, this user cost ( ) In particular, housing services provide the joint services of the structure and the land 20 will be interpreted as a beginning of the period user cost since all costs are discounted that the structure sits on and houses are generally unique goods. to the beginning of the period. Handbook on Residential Property Prices Indices (RPPIs) 29 3 Elements for a Conceptual Framework can be regarded as an investment, which is to yield the ap- ex ante user cost as the expected cost for using the servic- propriate opportunity cost of capital r0 the consumer faces. es of the durable during the period. Thus, the ex ante user At the end of period 0, this rate of return could be realized cost is likely to be the relevant charge for the services of provided that I0, r0 and the selling price of the durable at the durable that motivates consumer behavior. the end of the period PS1 satisfy The issue of how exactly one forms expectations for the I0(1+r0) = PS1(3.A3) selling price of a used durable will be examined later when the pricing of housing services is discussed. Given PS1 and r0, (3.A3) determines I0, which in turn, given P0, determines the user cost u0 via (3.A2). (22) 3.49 With all of the above complications, it is under- standable that many price statisticians would like to avoid 3.46 From the above it is clear that the user cost ap- using user costs as a pricing concept. However, the use of proach to pricing the services of a durable good for a pe- user costs may be unavoidable in the context of pricing the riod involves an investment aspect. Note that the user cost services of owned dwellings under certain conditions. The approach is also a financial opportunity cost approach; i.e., user cost formula (3.A1) can be expressed in a more fa- the opportunity cost of the financial capital that is tied up miliar form using the end of period 0  depreciation rate  d0 in the purchase (or continued holding) of the durable good and the period 0  asset inflation rate i0. Define the end of is taken into account. Finally, note that user costs are not period 0 depreciation rate d0 by like the prices of nondurables or services because the user cost concept involves pricing the durable at two points in (1 - d0) ≡ PS1/P1(3.A4) time rather than at a single point in time. Because the user where PS1 is the price of a used asset at the end of period cost concept involves prices at two points in time, money 0 and P1 is the price of a new asset at the end of period 0. (24) received or paid out at the first point in time is more valu- The period 0 inflation rate for the new asset, i0, is defined by able (assuming prices are going up in the economy) than money paid out or received at the second point in time and 1+i0 ≡ P1/P0(3.A5) so interest rates filter into the user cost formula. Eliminating P1 from equations (3.A4) and (3.A5) leads to the 3.47 Also, because the user cost concept involves prices following formula for the end of period 0 used asset price: at two points in time, expected prices can be involved if the PS1 = (1 - d0)(1 + i0)P0(3.A6) user cost is calculated at the beginning of the period under consideration instead of at the end. So the price statistician Substitution of (3.A6) into (3.A1) yields the following ex- has two options for the choice of PS1: pression for the period 0 user cost u0: • Use the expected price of the durable at the end of the peri- u0 = [(1 + r0) - (1 - d0)(1 + i0)]P0/(1 + r0)(3.A7) od from the perspective of the beginning of the period, or Note that r0 - i0 can be interpreted as a period 0  real inter- • Use the actual market price of a similar second hand dura- est rate and that δ0(1+i0) can be interpreted as an inflation ble at the end of the period (if such a market price exists). adjusted depreciation rate. 3.48 The use of an expected price leads to an ex ante 3.50 In (3.A7), the user cost u0  is expressed in terms user cost whereas the use of an actual market price for the of prices that are discounted to the beginning of period 0. used durable at the end of the period leads to an ex post However, it is also possible to express the user cost in terms user cost. Which concept should be used in practice? In the of prices that are “antidiscounted” or “appreciated” to the present context it is reasonable to favour the ex ante con- end of period 0. (25) The end of period 0 user cost p0 is defined cept for two reasons: as • The ex ante user cost concept is likely to be closer to a p0 ≡ (1 + r0)u0 = [(1 + r0) - (1 - d0)(1 + i0)]P0 rental price of the durable good (if it exists), (23) which = [r0 - i0 + d0(1 + i0)]P0 (3.A8) many price statisticians would view as a preferred price where the second equation follows using (3.A7). If the real for the services of the durable during the period, and interest rate r0* is defined as the nominal interest rate r0 less • The ex ante user cost is closer to the purchaser’s expected cost for using the durable good during the period; the purchaser cannot know exactly what the end of period (24) If the durable that was purchased (or held) by the household at the beginning of the period was a used durable, then interpret P1 as the second hand market price of a used price will be and hence must form expectations about durable that is in the same condition as the initially held durable. (25) Thus, the beginning of the period user cost u0 discounts all monetary costs and benefits the end of period price of the durable, which leads to the into their dollar equivalent at the beginning of period 0 whereas p0 accumulates or appreciates all monetary costs and benefits into their dollar equivalent at the end of period 0. This leaves open how flow transactions that take place within the period (22) This derivation for the user cost of a consumer durable was also made by Diewert (1974; should be treated. Following the conventions used in financial accounting suggests 504). that flow transactions taking place within the accounting period be regarded as taking (23) If a company is in the business of leasing the services of an automobile for a certain period, place at the end of the accounting period and hence following this convention, end it has to form expectations about the price of its used autos at the end of the leasing period of period user costs should probably be used by the price statistician. For additional in order to calculate its schedule of rental or leasing prices for its stock of automobiles. material on beginning and end of period user costs, see Diewert (2005; 485). 30 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 the asset inflation rate i0  and if the generally small term declines at a constant linear or geometric rate, then we have d0i0 is neglected, then the end of the period user cost de- straight line or geometric depreciation. (29) fined by (3.A8) reduces to (26) 3.53 How can one tell whether one hoss shay or geo- p = (r + d )P (3.A9) 0 0* 0 0 metric depreciation is applicable for a certain consumer durable? The two patterns of depreciation (and user valua- Abstracting from transactions costs, it can be seen that tion) can be distinguished if cross sectional information on the end of the period user cost defined by (3.A9) is an ap- rentals of the consumer durable by the age of the rented proximate rental cost; the rental cost for the use of a dura- asset is available. If depreciation is thought to follow that ble good should equal the (real) opportunity cost of the of the one hoss shay, then the rental rates for the consumer capital tied up, r0*P0, plus the decline in value of a new asset durable at a given point in time should be approximately over the period, d0P0. Formulae (3.A8) and (3.A9) thus cast constant for all ages of the durable good whereas if there some light on the economic determinants of rental or leas- is geometric depreciation, the rental rates for the good ing prices for consumer durables. should decline at a geometric rate according to the age of the used durable good. Thus, the various patterns of de- 3.51 If the simplified user cost formula defined by preciation can be distinguished if rental markets for used (3.A9) above is used, then forming a price index for the durables exist. In a similar fashion, when cross sectional in- user cost of a durable good is not very much more difficult formation on the prices of used units of the consumer dura- than forming a price index for the purchase price of the ble is available, alternative patterns of depreciation can be durable good, P0. The price statistician needs only to distinguished.  (30) • Make a reasonable assumption as to what an appropriate monthly or quarterly real interest rate r0* should be; (27) The User Cost of Owner Occupied • Make an assumption as to what a reasonable monthly, quarterly or annual depreciation rate d0 should be; (28) Housing • Collect purchase prices P0 for the durable and form the 3.54 An owner occupied dwelling is different from a nor- user cost. mal consumer durable good because of its unique charac- 3.52 There are some additional difficulties associated ter. Consequently, it will be difficult to use information on with the user cost approach to measuring the services of used asset prices in order to determine the pattern of de- a consumer durable. The above discussion deals only with preciation, which is required to measure a user cost for an the formation of a user cost for a newly purchased con- owned dwelling unit. As was mentioned in the introduc- sumer durable. It is necessary to extend the analysis to tion to this chapter, a particular dwelling unit in a particu- price the services of used units of the consumer durable lar country is unique for a number of reasons: as well. In order to price out the services of a used durable • The location of each dwelling unit is unique and location good, it is necessary to make assumptions about the form will affect the price of the unit. of depreciation of the good; does the service flow given to the consumer remain constant throughout the useful life • Over time, the dwelling unit depreciates; unless there of the durable good or does it decline as the good ages? If is one hoss shay depreciation, the utility generated by the service flow remains constant, then we have one hoss a particular dwelling for the occupying household will shay or light bulb depreciation whereas if the service flow tend to decline over time due to the effects of the aging of the structure. • On the other hand, the effects of depreciation can be off- (26) If one takes the ratio of the approximate rental price for the durable good, p0, to its asset set by renovation expenditures, which increase the utility value, P0, the rent to value ratio p0/P0 = r0* + d0 is obtained, which is equal to the sum of the dwelling unit. of the appropriate real interest rate r0* plus the appropriate depreciation rate d0. Since real rates of interest and depreciation rates are approximately constant over time, the rent to value ratio will also be approximately constant over time and hence a historical 3.55 For some purposes, it is important to decompose rent to value ratio times a current asset price index will generally give an adequate the price of a property into land and structures compo- approximation to an imputed rental rate for the consumer durable. In the housing literature, a rent to value ratio is often called a capitalization rate; e.g., see Garner and nents. To model the fact that housing is a composite good, Short (2009; 237) or Crone, Nakamura and Voith (2009; 70). (27) This is not completely straightforward. It is difficult to determine exactly what the appropriate household nominal opportunity cost of capital should be and even if we come to agreement on this point, there will be difficulties in estimating expected (29) For descriptions of how to construct user costs by the age of the asset for each of these inflation rates. In the end, it may boil down to picking a somewhat arbitrary real interest depreciation models, see Diewert and Lawrence (2000) or Diewert (2005; 506-521). rate in the 2% to 5% range (for annual rates), depending on the recent experience of the (30) In the housing context where each house can be regarded as a unique asset, it is country under consideration. necessary to make some additional assumptions in order to identify the form of (28) The geometric model for depreciation requires only a single monthly or quarterly depreciation. The extra assumptions are of the following type: it is assumed that all depreciation rate. Other models of depreciation may require the estimation of a housing units in a certain class of structures have a similar pattern of depreciation. Using sequence of vintage depreciation rates. If the estimated annual geometric depreciation this type of assumption, empirical evidence suggests that one hoss shay depreciation is rate is da, then the corresponding monthly geometric depreciation rate δ can be unlikely in the housing market since renters are generally willing to pay a rent premium obtained by solving the equation (1 - δ)12 = 1 - da. Similarly, if the estimated annual real for a new unit over an older unit of the same type. For empirical evidence of this age interest rate is ra*, then the corresponding monthly real interest rate r* can be obtained premium, see Malpezzi, Ozanne and Thibodeau (1987; 378) and Hoffman and Kurz by solving the equation (1 + r*)12 = 1 + ra*. (2002; 19). Handbook on Residential Property Prices Indices (RPPIs) 31 3 Elements for a Conceptual Framework consider a particular newly constructed dwelling unit that = [PS0QS0 + PL0QL0](1 + r0) - [PS0 (1 + iS0)(1 - d0)QS0 + PL0 is purchased at the beginning of period 0. Suppose that the (1 + iL0)QL0] purchase price is V0. This value can be regarded as the sum = pS0QS0 + pL0QL0 of the cost of producing the structure, PS0QS0, where QS0 is the number of square meters of floor space in the structure where separate period 0  user costs of structures and land, and PS0 is the beginning of period 0 price of construction pS0 and pL0, are defined as follows: per square meter, and the cost of the land, PL0QL0, where pS0 = [(1 + r0) - (1 + iS0)(1 - d0)]PS0 QL0  is the number of square meters of the land that the = [r0 - iS0 + d0(1 + iS0)]PS0  (3.A15) structure sits on and the associated yard and PL0 is the be- ginning of period 0 price of the land per square meter.  (31) pL0 = [(1 + r0) - (1 + iL0)]PL0 = [r0 - iL0]PL0 (3.A16) Thus at the beginning of period 0, the value of the dwelling Note that the above algebra indicates some of the most unit is V0 defined as follows: important determinants of market rents for rental prop- V0 = PS0QS0 + PL0QL0(3.A10) erties. (34) The user cost formulae defined by (3.A15) and (3.A16) can be further simplified if the approximations that 3.56 Suppose that the anticipated price of a unit of a were made in the previous section are made here as well new structure at the beginning of period 1 is PS1a and that (recall equation (3.A9) above); i.e., assume that the terms the anticipated price of a unit of land at the beginning of r0 - iS0 and r0 - iL0 can be approximated by a real interest rate period 1  is PL1a. Define the period 0  anticipated inflation r0* and neglect the small term d0 times iS0 in (3.A15). Then rates for new structures and land, iS0 and iL0 respectively, as the user costs defined by (3.A15) and (3.A16) simplify to follows: pS0 = (r0* + d0)PS0(3.A17) 1 + iS0 ≡ PS1a/PS0(3.A11) pL0 = r0*PL0 (3.A18) 1 + iL0 ≡ PL1a/PL0(3.A12) 3.58 The above exposition has neglected two other Let d0 be the period 0 depreciation rate for the structure. sources of period 0 cost associated with owning a dwelling The anticipated beginning of period 1 value for the struc- unit: ture and the associated land is then equal to • Various maintenance and insurance costs that are associ- V1a = PS1a(1 - d0)QS0 + PL1aQL0(3.A13) ated with the ownership of a dwelling unit and So the anticipated value of the dwelling unit at the end of • Property taxes that may be payable by the owner to local period 1, V1a, equals the anticipated price (per unit of new or state governments. structure of the same quality) at the end of the period, PS1a, times one minus the period 0  depreciation rate, (1 - δ0), Assume that period 0  maintenance and insurance costs, times the quantity of structure purchased at the beginning MS0, are mainly associated with the structure rather than of period 0, QS0,  (32) plus the anticipated price of land at the land under the structure. Suppose that these costs are the end of period 0, PL1a, times the quantity of land that the paid at the end of period 0. These costs can be converted structure associated with the structure, QL0. into a per unit structure charge mS0 as follows: 3.57 Now calculate the cost (including the imputed op- mS0 ≡ MS0/(PS0QS0)(3.A19) portunity cost of capital r0)  (33) of buying the dwelling unit Suppose the property taxes that fall on the structure, TS0, at the beginning of period 0 and (hypothetically) selling it and the property taxes that fall on the land under the struc- at the end of period 0. The following end of period 0  user ture, TL0, are paid at the end of period 0. Then the period cost or imputed rental cost R0 for the dwelling unit is ob- 0 structure and land property tax rates, tS0 and tL0, can be tained using (3.A11)-(3.A13): defined as follows: R0 ≡ V0(1 + r0) - V1a(3.A14) tS0 ≡ TS0/(PS0QS0) and tL0 ≡ TL0/(PL0QL0)  (3.A20) = [PS QS + PL QL ](1 + r ) - [PS (1 - d )QS + PL QL ] 0 0 0 0 0 1a 0 0 1a 0 These additional maintenance and property tax costs need to be added to the imputed rental cost for using the dwell- (31) If the dwelling unit is part of a multiple unit structure, then the land associated with it ing unit R0. Thus (3.A14) now becomes: will be the appropriate share of the total land area. This share could be 1 divided by the number of units on the plot or the floor space of the unit divided by the total floor space R0 ≡ V0(1 + r0) - V1a + MS0 + TS0 + TL0(3.A21) of the entire structure. Either share allocation could be justified. ( ) Thus the period 0 depreciation rate d0 is an end of period anticipated cross sectional 32 = pS0QS0 + pL0QL0 depreciation rate; i.e., d0 is defined by the equation (1-d0) = VS1a/(PS1aQS0), where VS1a is the anticipated market value of the (depreciated) structure at the end of period 0 and PS1aQS0 is the anticipated end of period 0 value of a newly constructed structure with floor space area QS0. (33) More elaborate discussions on how to choose the appropriate opportunity cost of (34) Looking at (3.A16), it can be seen that the land user cost could be negative if the capital when the owner of a dwelling unit has a mortgage on the unit can be found anticipated rate of land price appreciation, iL0, is greater than the beginning of the in Diewert and Nakamura (2009), Diewert, Nakamura and Nakamura (2009) and Garner period opportunity cost of capital, r0. Possible solutions to this complication will be and Verbrugge (2009b; 176). discussed below. 32 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 where the new separate period 0 user costs of structures and • The user costs can be used to value the services of owner land, pS0 and pL0, are defined as follows: occupied housing. pS0 = [r0 - iS0 + d0(1 + iS0) + mS0 + tS0]PS0(3.A22) As will be seen later in this section, it turns out that user costs do approximate market rents (for lower cost housing pL0 = [r0 - iL0 + tL0]PL0(3.A23) in the US at least), provided expectations of future inflation The imputed rent for a dwelling unit using the user cost ap- in house prices are formed in a certain way. proach to the valuation of housing services is thus made up 3.62 As mentioned before, two main methods for valu- of six main costs: ing the services of owner occupied housing have been sug- • The real opportunity cost of the financial capital tied up gested for national accounts purposes: the user cost ap- in the structure, (r0 - iS0)PS0QS0; proach just explained and the rental equivalence approach. • The real opportunity cost of the financial capital tied up The rental equivalence approach is straightforward; for in the land, (r0 - iL0)PL0QL0; owner occupied houses in a certain stratum, we look for similar rented dwelling units and impute the market rent- • The depreciation cost of the structure, d0(1 + iS0)PS0QS0; al to the corresponding owner occupied house. In many • The maintenance and insurance costs associated with the countries, the rental equivalence approach works well, but structure, mS0PS0QS0; it does not work well if rental markets are thin or if there • The property taxes associated with the structure, are price controls on rents. tS0PS0QS0, and 3.63 If user costs are used to value the services of owner • The property taxes associated with the land underneath occupied dwelling units in a country, then the maintenance and surrounding the structure, tL0PL0QL0. and insurance rate term mS0 in the user cost of structures 3.59 The above user cost approach to pricing the servic- formula (3.A22) should be dropped from the formula, es of a dwelling unit in period 0 can be applied to various since maintenance and insurance expenditures for owner housing strata, e.g., to detached dwellings, row houses or occupied houses will generally be captured elsewhere in duplexes or town houses and apartment blocks. For the last the household expenditure accounts. two types of dwelling units, the land component for each 3.64 The simplified approach to the user cost of hous- individual dwelling unit needs to be constructed. For ex- ing explained above in equations (3.A17) and (3.A18) can ample, if there are 20 dwelling units in an apartment block, be even further simplified by assuming that the ratio of the then the land share of each individual dwelling unit could quantity of land to structures is fixed and so the aggregate be set to 1/20th of the total land area that the apartment user cost of housing is equal to [r0* + δ + µ + τ]PH0, where block occupies. (35) Dwelling units can also be grouped ac- PH is a quality adjusted price index that is applicable to the cording to their construction type, which could be primar- country’s entire housing stock (including both structures ily wood, brick, concrete or “traditional”. and the underlying land) for the period under consider- 3.60 If a statistical agency produces national balance ation and δ, µ and τ are respectively a depreciation rate, sheet estimates, then data on the total value of residen- a maintenance and insurance rate and a property tax rate tial land and residential structures should be available. that applies to the composite of structures and land. Under However, data on the quantity of residential land may not this simplified approach to value the services of owner oc- be known. Estimates of the country’s total real stock of cupied housing, as was seen in the last paragraph above, the residential structures can be obtained by deflating the bal- term µ should be dropped from the simplified user cost. ance sheet estimate of the value of residential housing by The resulting simplified approach is applied in Iceland; see the country’s corresponding investment price deflator for Gudnason (2004) and Gudnason and Jónsdóttir (2009) (36) residential housing. and in some European countries; see the detailed exposi- tion of the method by Katz (2009).  (37) A variant of this 3.61 There are at least two uses for the above user cost approach is used by the US Bureau of Economic Analysis: approach to pricing the services of housing: Lebow and Rudd (2003; 168) note that the US national • The user costs can be compared to market rents for accounts imputation for the services of owner occupied dwelling units that are actually rented during the period housing is obtained by applying rent to value ratios for under consideration, and (36) The real interest rate that is used is approximately 4% per year and the combined depreciation rate for land and structures is assumed to equal 1.25% per year. The depreciation rate for structures alone is estimated to be 1.5% per year. Property taxes are accounted for separately in the Icelandic CPI. Housing price information is provided by (35) It is not completely straightforward to allocate the common land shared by the the State Evaluation Board based on property sales data of both new and old housing. dwelling units into individual shares; i.e., instead of an equal division of the land, we The SEB also estimates the value of the housing stock and land in Iceland, using a could use the relative floor spaces of each apartment as the allocator. There are also hedonic regression model based on property sales data. The value of each household’s problems associated with the relative height of the individual apartment units; i.e., an dwelling is collected in the Household Budget Survey. apartment on a higher floor will typically rent for more than an apartment on a lower ( ) Katz (2009) and Garner and Verbrugge (2009b; 176) give further references to the 37 floor. literature on the simplified user cost method. Handbook on Residential Property Prices Indices (RPPIs) 33 3 Elements for a Conceptual Framework tenant occupied housing to the stock of owner occupied CPI inflation as a proxy for expected house price inflation housing with the same characteristics as the rented prop- gives rise to reasonable user costs that are likely to be fairly erty. (38) The rent to value ratio can be seen as an estimate similar to market rents, at least for relatively inexpensive of the applicable real interest rate plus the depreciation rate housing units. plus a maintenance and insurance rate plus the property 3.68 It is evident that the main drivers for the user costs tax rate, r0* + δ + µ + τ. (39) of structures and land are price indices for new dwelling 3.65 How exactly should the real interest rate, r0*, be es- construction, PSt, and for residential land, PLt. Most statis- timated? One possible method is to just make a reasonable tical agencies have a constant quality price index for new guess: (40) residential structures, because this index is required in the national accounts in order to deflate investment expendi- “The remaining question was what value of the real rate tures on residential structures. This index could be used as of return is appropriate? Evidence was presented to the an approximation to PSt. (42) task force that suggested that, at least in Western European countries, the appropriate real rate of return for owner- 3.69 This completes the overview of the user cost ap- occupied dwellings was lower than that for other durables, proach to pricing residential housing services. In the fol- perhaps in the 2.5 to 3.0 percent range. It was the consensus lowing section, another approach to pricing the services of of the task force that given the actual situation in the CCs owner occupied housing will be reviewed: the opportunity [Candidate Countries from Eastern Europe], real rates of cost approach. return on both dwellings and land should be assumed to be 2.5 percent.” Arnold J. Katz (2009; 46). The Opportunity Cost Approach 3.66 A second method is to use mortgage interest rates as estimates for the nominal opportunity cost of financial to the Valuation of Owner Occupied capital tied up in housing and to use econometric forecast- Housing Services ing techniques to estimate predicted house price inflation 3.70 Recall the two main methods for valuing the ser- rates (and then the real interest rate can be set equal to the vices of owner occupied housing (OOH): the rental equiv- nominal interest rate less the predicted house price infla- alence approach and the user cost approach. In the rental tion rate). Several variants of this second approach were equivalence approach, an owner of a dwelling unit who tried by Verbrugge (2008) and Garner and Verbrugge chooses to live in it (or at least not rent it out to someone (2009a) (2009b) using US data. However, as these authors else) values the services of the dwelling by the market rent show, this approach was not successful in that the resulting which is foregone. This is a very direct opportunity cost of user cost estimates were extremely volatile (and frequent- using the dwelling. On the other hand, the user cost ap- ly negative) and not at all close to corresponding market proach to valuing dwelling services is basically a financial rents. opportunity cost of using the services of the dwelling unit 3.67 A third approach to the determination of an ap- during the period under consideration. It has been sug- propriate real interest rate to be used in a user cost for- gested that the true opportunity cost of using the services mula for housing services was carried out by Garner and of an owned dwelling unit is the maximum of the rent fore- Verbrugge (2009b) using US data. They used applicable gone and the user cost: mortgage interest rates as estimates for the nominal op- “We conclude this section with the following (controver- portunity cost of financial capital and used current period sial) observation: perhaps the ‘correct’ opportunity cost estimates of consumer price index inflation as their esti- of housing for an owner occupier is not his or her inter- mate of expected house price appreciation. Much to their nal user cost but the maximum of the internal user cost surprise, they found that the resulting user costs tracked and what the property could rent for on the rental market. market rents rather well. (41) The conclusion is that either After all, the concept of opportunity cost is supposed to making a reasonable guess for the real interest rate or using represent the maximum sacrifice that one makes in order to consume or use some object and so the above point would (38) See also Crone, Nakamura and Voith (2009) and Garner and Short (2009; 237) for a seem to follow.” W. Erwin Diewert (2009b; 113). description of this capitalization method for determining rental prices for housing units from estimates of the corresponding asset values. It can be seen that this method is Diewert and Nakamura (2009) and Diewert, Nakamura actually a method for implementing the rental equivalence approach to valuing the and Nakamura (2009) pursued this opportunity cost ap- services of owner occupied dwelling units. ( ) If an owned dwelling unit has the value V0 and a rented dwelling unit with the same 39 proach to the valuation of owner occupied housing ser- characteristics has the rent to value ratio g = r0* + δ + µ + τ, then the imputed rent for vices in more detail but it can be seen that this approach the owned dwelling unit is set equal to (g - µ)V0 = (r0* + δ + τ)V0, since insurance and maintenance expenditures on the owned dwelling will be recorded elsewhere in the seems to be a valid one. Moreover, it has the advantage System of National Accounts. (40) The Australian Bureau of Statistics assumes a constant real interest rate equal to 4% per year when constructing its estimates of capital services. (41) Using this approach, Garner and Verbrugge (2009b; 179) also found that there were no (42) This index may only be an approximation since it covers the construction of rental negative estimated user costs in their US data set. properties as well as owner occupied dwellings. 34 Handbook on Residential Property Prices Indices (RPPIs) Elements for a Conceptual Framework 3 of eliminating the problem with the user cost approach: COLA areas relative to the Washington D.C. housing namely, that the user cost approach can generate negative area. (43) user costs if ex post or forecasted housing inflation rates Two facts emerge from the Table 3.1: are used in the user cost formula. • Capitalization ratios differ substantially across re- 3.71 In practice, the opportunity cost approach to pric- gions (44), and ing OOH services may lead to similar results as the rental • As one moves from inexpensive properties to more ex- equivalence approach provided that expected inflation in pensive properties the capitalization ratio for the high the user cost formula is set equal to CPI inflation, since end properties is about one half the ratio for low end Garner and Verbrugge (2009b) show that for most low end properties for all regions. rental properties, the rental equivalence and user cost ap- proaches give much the same answer, at least in the US. The second point listed above also emerges from the much However, there is evidence that user costs may be consid- more extensive US data on annual rents for the years 2004- erably higher than the corresponding market rentals for 2006 as a function of the corresponding home values found high end properties. Table 3.1  is taken from Heston and in Figure 1  in Garner and Verbrugge (2009b; 178). For a Nakamura (2009a; 113) (2009b; 277) and shows average $100 000 home, the corresponding average annual rent was annual market rent to market value of rental properties in about $10 000 while for a $900 000 home the correspond- a number of regions; i.e., it shows capitalization ratios as ing average annual rent was about $30 000. Thus the capi- a function of the value of the rental property. Table 3.1 is talization ratio fell from about 10 % to about 3.3 % as the based on a survey of US federal government employees home value increased from $100 000 to $900 000. conducted as part of a Safe Harbor process regarding the Cost of Living Allowance (COLA) program administered (43) This program is directed at comparing the costs of living for federal employees in the by the United States Office of Personnel Management. This non-continental United States to Washington D.C. area. Housing is one of the most important and most difficult of the comparisons required under this program. The program began in 1948 and pays an allowance above the COLA areas include Alaska, Guam, Hawaii, Puerto Rico, and the U.S. Virgin Islands: a very federal salary schedule in three geographic areas (Alaska, diverse range of climates and housing needs. ( ) The relatively high capitalization ratios for Alaska may be due to the inclusion of heating 44 the Caribbean and the Pacific) based on prices in these services in the rent. Table 3.1. Estimated Rent to Value Ratios as Percentages (Capitalization Ratios) Renter Alaska Wash D.C. Carib Hawaii-Pacific Value($) (1) (2) (3) (4) 50 000 13.0 8.9 6.3 6.9 100 000 12.0 8.2 5.8 6.4 200 000 10.2 6.9 4.9 5.4 500 000 6.2 4.3 3.0 3.3 Source: Heston and Nakamura (2009a) 3.72 What factors could explain this dramatic drop in value of the property due to aging of the structure, will in the capitalization ratio as we move from inexpensive be smaller as the land to structure ratio increases. (45) properties to more expensive properties? As was indicated • A substantial fraction of a landlord’s monitoring, ac- previously, the rent to value ratio can be regarded as an es- counting and billing expenses may be in the nature of a timate of the applicable real interest rate plus the deprecia- fixed cost and hence these costs will drop as a fraction of tion rate plus the property tax rate, r0* + δ + µ + τ, and these the rent as the value of the property increases. rates should not be all that different for properties of differ- ing value. There are at least three possible explanations: • High value properties may have a much higher proportion (45) This explanation was suggested by Diewert (2009a; 486) and Garner and Verbrugge of land, hence the depreciation rate δ, regarded as a decline (2009b; 182). Handbook on Residential Property Prices Indices (RPPIs) 35 3 Elements for a Conceptual Framework • Rentals of high value residential properties are not made explain the declines in the capitalization ratios. Similarly, on a commercial basis; i.e., they may be made on a tem- the costs of maintaining and insuring a rental property that porary basis, with the renters serving as “house sitters” are collected in the term µ are likely to be relatively small who pay somewhat subsidized rents as compared to the and thus are unlikely to fully explain the phenomenon. owner’s financial opportunity cost. Thus it may be that the third explanation is an important explanatory factor. If this is indeed the case, then the op- It seems unlikely that the imperfect determination of the portunity cost approach to the valuation of OOH services depreciation rate can explain the big decline in capitaliza- would give a much higher valuation to OOH services than tion ratios as the value of the property increases; estimates the rental equivalence approach. (47) of housing depreciation rates are generally in the 1 to 2 % per year range,  (46) and these rates are too low to fully (47) Thus the discrepancy between the rental equivalence approach to the valuation of OOH services and the opportunity cost approach may not be very important in the time series (46) Garner and Verbrugge (2009b; 176) and Garner and Short (2009; 244) assume annual context because both measures may move in tandem. But in the context of making depreciation rates (as fractions of the value of the property including both structures international comparisons, this argument will not be applicable due to the fact that the and land) of 1% per year. percentage of owner occupied dwelling units differs substantially across countries. 36 Handbook on Residential Property Prices Indices (RPPIs) Stratification or Mix Adjustment Methods 4 4 Stratification or Mix Adjustment Methods Simple Mean or Median hedonic and repeat sales methods (to be discussed in Chapters 5 and 6). Indices 4.1 The simplest measures of house price change are based on some measure of central tendency from the dis- Stratification tribution of house prices sold in a period, in particular the mean or the median. Since house price distributions are 4.4 Post-stratification of a sample is a general tech- generally positively skewed (predominantly reflecting the nique for reducing sample selection bias. In the case of heterogeneous nature of housing, the positive skew in in- residential property price indices, stratification is the sim- come distributions and the zero lower bound on transac- plest tool for controlling for changes in the composition or tion prices), the median is typically used rather than the “quality mix” of the properties sold. The method is there- mean. As no data on housing characteristics are required fore also known as mix adjustment. Stratification is also to calculate the median, a price index that tracks changes needed if users desire price indices for different housing in the price of the median house sold from one period to market segments. the next can be easily constructed. Another attraction of 4.5 Stratification is nothing else than separating the median indices is that they are easy to understand. total sample of houses into a number of sub-samples or 4.2 An important drawback of simple median indices strata. After constructing a measure of the change in the is that they will provide noisy estimates of price change. central tendency for each stratum, such as a mean or me- The set of houses actually traded in a period, or a sample dian price index, the aggregate mix-adjusted RPPI is typi- thereof, is typically small and not necessarily representa- cally calculated as a weighted average of indices for each tive of the total stock of housing. Changes in the mix of stratum. With M different strata, the mix-adjusted index, properties sold will therefore affect the sample median as calculated in practice in various countries, can be writ- price much more than the median price of the housing ten in mathematical form as follows: stock. For example, think of a city with two regions, A and M B, and that region A has more expensive houses than re- P 0t = ∑w P (4.1) 0 m m 0t gion B. Suppose that the median house sold in 2006  and m=1 2008  comes from region A, while the median house in where Pm0 t is the index for stratum m which compares the 2007 comes from region B. It follows that the median in- mean (median) price in the current or comparison period dex could record a large rise from 2006 to 2007 and then t with the mean (median) price in an earlier or base pe- a large fall from 2007 to 2008. Such an index would be a riod 0, and where wm 0 denotes the weight of stratum m. very poor indicator of what is actually happening in the The weights are value shares pertaining to the strata. They housing market. Thus, a median (or mean) index will be refer to the base period, which is usually a year (whereas a very inaccurate guide to price change when there is sub- the comparison periods may be months or quarters). For stantial change in the composition of houses sold between practical reasons, the weights are often kept fixed for sev- periods. If there is a correlation between turning points in eral years, but keeping weights fixed for a long time is gen- house price cycles and compositional change, then a me- erally not good practice. More details on aggregation and dian could be especially misleading in periods when the weighting issues in this context are provided below. premium on accuracy is highest. 4.6 Which type of value weights is used, depends on 4.3 A perhaps bigger problem than short-term noise the target index that the RPPI is supposed to estimate. If is systematic error, or bias. A simple median index will the purpose is to track the price change of the housing be subject to bias when the quality of the housing stock stock then obviously stock-weights – the stock value shares changes over time. The median index will be upward bi- of the strata – should be used. If, on the other hand, the tar- ased if the average quality improves over the years. Bias get is a sales or acquisitions RPPI, then sales (expenditure) can also arise if certain types of houses are sold more fre- weights should be applied. (1) quently than other types of houses and at the same time 4.7 The effectiveness of stratification will depend upon exhibit different price changes. For example, when higher the stratification variables used because a mix-adjusted quality houses sell more frequently and also rise in price measure only controls for compositional change across the faster than lower quality houses, a downward bias may various groups. For example, if house sales are separated result if the number of sales per type of house does not solely according to their location, a mix-adjusted index will properly reflect the number of houses in stock. This is control for changes in the mix of property types across the sometimes referred to as a sample selection problem. The defined locations. But the mix-adjusted measure will not fact that houses traded are usually a small and not nec- essarily representative part of the total housing stock can (1) The house price indices compiled in the EU as part of a Eurostat pilot study are examples bias other property price index methods as well, including of such acquisitions indices (see Makaronidis and Hayes, 2006 or Eurostat, 2010). 38 Handbook on Residential Property Prices Indices (RPPIs) Stratification or Mix Adjustment Methods 4 account for any changes in the mix of property types sold on market segmentation using statistical techniques like that are unrelated to location. Also, a mix-adjusted index cluster analysis and factor analysis; see e.g. Dale-Johnson does not account for changes in the mix of properties sold (1982), Goodman and Thibodeau (2003), and Thibodeau within each subgroup, in this case changes in the mix of (2003). These techniques could in principle be used to de- properties sold within the boundaries of each location. fine housing sub-markets, which could subsequently be used as strata for the construction of a mix-adjusted RPPI. 4.8 Very detailed stratification according to housing The Australian Bureau of Statistics experimented with this characteristics such as size of the structure, plot size, type approach (ABS, 2005). of dwelling, location and amenities will increase homoge- neity and thus reduce the quality-mix problem, although 4.12 Prasad and Richards (2006) (2008) proposed a some quality mix changes will most likely remain. There novel stratification method and tested it on an Australian is, however, a tradeoff to be considered. Increasing the data set. They grouped together suburbs according to the number of strata reduces the average number of observa- long-term average price level of dwellings in those regions, tions per stratum, and a very detailed stratification might rather than just clustering smaller geographic regions into raise the standard error of the overall RPPI. Needless to larger regions. Their method of stratification was specifi- say, a detailed stratification scheme can be constructed cally designed to control for what may be the most impor- only if the strata-defining characteristics are available for tant form of compositional change, namely changes in the all sample data. Another potential practical problem is that proportion of houses sold in higher- and lower-priced re- it might be difficult to obtain accurate data on the (stock) gions in any period. (3) Note that they used median price weights for small subgroups. indices at the stratum level. McDonald and Smith (2009) followed-up on this study and constructed a similar strati- 4.9 When using only physical and locational stratifica- fied median house price measure for New Zealand. tion variables, like those mentioned above, then the strati- fication method does not control for quality changes of the individual properties. By quality changes we mean the ef- fect of renovations and remodeling done to the properties in combination with depreciation of the structures. This Aggregation can also be called “net depreciation”. Depreciation obvious- ly depends on the age of the structure, although deprecia- and Weighting Issues tion rates may differ across different types of dwellings or even across different locations. This is why age of the struc- ture was listed in Chapter 3 as one of the most important First-stage aggregation price determining quality attributes. Consequently, strati- 4.13 Stratification involves a two-stage procedure: price fying according to age class may help reduce the problem indices are compiled at the stratum level, which are then of quality change. aggregated across the various strata. As was mentioned 4.10 Introducing age class as another stratification vari- above, median strata indices have typically been used, in able will further reduce the average number of observa- particular because they will often be more stable than the tions per stratum and may give rise to unreliable estimates corresponding mean indices. Yet, we will focus on means of price changes. Under these circumstances, hedonic re- rather than medians. Conventional index number theory gression techniques – which are discussed in Chapter 4 – deals with aggregation issues, in this case aggregation of will generally work better than stratification. As mentioned house price observations within strata. Unlike the median, earlier, some sort of hedonic regression method will also be means are aggregator functions, which link up with index needed to decompose the overall RPPI into land and struc- number theory. The question then arises: what kind of tures components if this is required for any of the purposes mean should be taken? discussed in Chapter 2. Such a decomposition cannot be 4.14 The CPI Manual (2004) makes recommendations provided by stratification methods. about how to construct price indices at the first stage of 4.11 Mix-adjusted RPPIs have been compiled by nu- aggregation if information on quantities is unavailable and merous statistical offices and other government agencies, then at the second stage of aggregation when both price including the UK Department of the Environment (1982) and value (or quantity) information is available. At the first and the Australian Bureau of Statistics (ABS, 2006). While stage of aggregation, Chapter 20 in the CPI Manual gener- mix adjustment has received relatively little attention in ally recommends using the unweighted geometric mean or the academic literature, (2) there is a growing body of work (3) A general rule is that stratification according to the variable of interest should not be used since that can lead to biased results. The study variable used by Prasad and Richards (2006) (2008) is (long-term) house price change, not house price level, so their (2) However, stratified median house price indices have been used by several researchers, stratification method could perhaps be defended. However, little is known about the mostly for comparison purposes; see e.g. Mark and Goldberg (1984), Crone and Voith statistical properties of this type of stratification index and it would be advisable to (1992), Gatzlaff and Ling (1994), and Wang and Zorn (1997). investigate the issue of potential bias before producing such an index. Handbook on Residential Property Prices Indices (RPPIs) 39 4 Stratification or Mix Adjustment Methods Jevons index to aggregate individual price quotations into Note that equation (4.4) can be rewritten in the form of an index. However, this general advice is not applicable in (4.1) if s = 0 with cell price indices Pm0 t = Pmt / Pm0 and ∑ M the present context. value shares wm = Pm Qm / m=1 Pm0 Qm 0 0 0 0 . The Paasche price index going from period s to t, PP , is defined as follows: t s 4.15 If the aim is to construct a price index for the M sales of residential properties, the appropriate concept of (elementary) price in some time period t for a homoge- Pmt Qmt ∑ PPst ( P s , P t , Q t ) ≡ m =1 (4.5) neous stratum or cell in the stratification scheme is a unit M value. Because each sale of a residential property comes m=1 Pm s Qm t ∑ with its own quantity, which is equal to one, the cor- responding quantity for that cell is the simple sum of The Fisher price index for period t relative to period s, PFst , the properties transacted in period t . We can formally can be defined as the geometric mean of (4.4) and (4.5): describe this as follows. Suppose that in period t there PFst ( P s , P t , Q s , Q t ) ≡ [ PLst ( P s , P t , Q s ) × PPst ( P s , P t , Q t )]1 / 2 are N (t , m) property sales observed in a particular t cell PF ( P , P , Q , Q ) ≡ [ PLst ( P s , P t , Q s ) × PPst ( P s , P t , Q t )]1 / 2 (4.6) st s s t m , with the selling price (value) of property n equal to Vnt for n = 1,...,N(t,m). Then the appropriate price and Recall that all the quantities occurring in these three for- quantity for cell m in period t are: mulas are numbers of transactions; that is, numbers of ob- N ( t ,m ) Pmt ≡ ∑V n t / N (t , m) (4.2) served prices. Thus, for calculating a Laspeyres, Paasche, or Fisher price index one needs the same information. n =1 Qmt ≡ N (t , m) (4.3) 4.18 The Laspeyres, Paasche and Fisher price indices de- This narrowly defined unit value concept is actually recom- fined by equations (4.4), (4.5) and 4.6) are fixed base indices. mended in the CPI Manual (2004; 356). If the stratifica- For example, if there are 3 periods of sales data, including the tion scheme leads to cells that are not sufficiently narrow base period 0, then the Fisher formula (4.6) would generate defined, then of course some unit value bias may arise, the following index number series for those 3 periods: which is equivalent to saying that some quality mix bias may remain. (4) 1; PF01 ( P 0 , P 1 , Q 0 , Q 1 ); PF02 ( P 0 , P 2 , Q 0 , Q 2 ) (4.7) Second-stage aggregation Chaining 4.16 The next issue to be resolved is: what index number 4.19 An alternative to the fixed base method is the use formula should be used to aggregate the elementary pric- of chaining. The chain method uses the data of the last two es and quantities into one overall RPPI? The CPI Manual periods to calculate a period to period chain link index discusses this choice of formula issue at great length. A which is used to update the index level from the previous number of index number formulae are recommended but period. Chaining would, for example, generate the follow- a good overall choice appears to be the Fisher ideal index ing Fisher index number series for the 3 periods: since this index can be justified from several different per- spectives. (5) The Fisher index is the geometric mean of the 1; PF01 ( P 0 , P 1 , Q 0 , Q 1 ); PF01 ( P 0 , P 1 , Q 1 , Q 1 ) PF12 ( P 1 , P 2 , Q 1 , Q 2 ) Laspeyres and Paasche indices. (4.8) 4.17 To illustrate this point, let P t ≡ [ P1t ,..., PM t ] and 4.20 The next issue to be discussed is whether RPPIs Q ≡ [Q1 ,..., QM ] denote the period t vectors of cell prices t t t should be constructed by using fixed base or chain indices. and quantities. The Laspeyres price index, PLst , going from Both the System of National Accounts and the CPI Manual (the base) period s to (the comparison) period t can be de- recommend the use of chain indices provided that the un- fined as follows: derlying price data have reasonably smooth trends. (6) On M the other hand, if there is a great deal of variability in the ∑P Q m t s m data, particularly when prices bounce erratically around P (P , P , Q ) ≡ L st s t s m=1 M (4.4) a trend, the use of fixed base indices is recommended. ∑ Pms Qms Property price changes tend to be fairly smooth,  (7) so it m=1 is likely that chained indices will work well in many cas- es. However, more experimentation with actual data is (4) In practice, crude stratification according to region and type of dwelling is often used. The stratification method according to price bands proposed by Prasad and Richards (6) See SNA (2008) and CPI Manual (2004; 349). (2008), could be useful to militate against unit value bias. See Balk (1998) (2008; 72-74), (7) Although prices do not bounce around erratically in the real estate context, quantities Silver (2009a) (2009b) (2010), and Diewert and von der Lippe (2010) for more general do exhibit considerable variability, particularly if there are a large number of cells in discussions of unit value bias. the stratification setup with a limited number of observations in each cell. There is ( ) See CPI Manual (2004; Chapters 15-18) for alternative justifications for the use of the 5 also a considerable amount of seasonal variation in quantities; i.e., sales of residential Fisher formula. properties fall off dramatically during the winter months of the year. 40 Handbook on Residential Property Prices Indices (RPPIs) Stratification or Mix Adjustment Methods 4 required in order to give definitive advice on this issue. periodic housing census collects information on whether There may also be seasonal variation in house prices as the each dwelling unit is owned or rented. example for the Dutch town of “A”, presented below, sug- 4.24 It should be noted that the construction of a strati- gests. In such cases too, one should be careful with using fied (stock or sales) RPPI becomes more complex when chain indices. some of the cells in the stratification scheme are empty for some periods. At the end of this chapter, where an empiri- Stock RPPIs cal example using data on housing sales for the Dutch town of “A” is presented, a matched-model approach will be out- lined that can be used in case some cells are empty. 4.21 The above discussion was on the construction of a price index for the sales of residential properties when using a stratification method. But how should an RPPI be con- structed for the stock of residential properties? Assuming that, for each cell m, the properties sold are random (or Main Advantages ‘representative’) selections from the stock of dwelling units defined by cell m, the period t unit value prices Pmt defined and Disadvantages by (4.2) can still be used as (estimates of the) cell prices 4.25 We will summarize the main advantages and dis- for a stock RPPI. The quantities Qm t defined by (4.3) are, advantages of the stratified median or mean approach. The however, no longer appropriate; they need to be replaced main advantages are: by (estimates of) the number of dwelling units of the type defined by cell m that are in the reference stock at time t, • Depending on the choice of stratification variables, say Qm t* , for m = 1,..., M . With these population quantity the method adjusts for compositional change of the weights, the rest of the details of the index construction are dwellings. the same as was the case for the sales RPPI. • The method is reproducible, conditional on an agreed list of stratification variables. 4.22 To compile stock weights, it will be necessary to • Price indices can be constructed for different types and have a periodic census of the housing stock with enough locations of housing. details on the properties so that it can be decomposed into • The method is relatively easy to explain to users. the appropriate cells in the stratification scheme for a base 4.26 The main disadvantages of the stratified median or period. If information on new house construction and on mean method are: demolitions is available in a timely manner, then the census • The method cannot deal adequately with depreciation of information can be updated and estimates for the housing the dwelling units unless age of the structure is a strati- stock by cell (the Qmt* ) can be made in a timely manner. The fication variable. stock RPPI can be constructed using a (chained) Fisher in- • The method cannot deal adequately with units that have dex as was the case for the sales RPPI. On the other hand, undergone major repairs or renovations (unless renova- if timely data on new construction and demolitions is tions are a stratification variable). lacking, it will only be possible to construct a fixed base • The method requires information on housing character- Laspeyres index using quantity data from the last available istics so that sales transactions can be allocated to the housing census (in say period 0), Q 0* = [Q10* ,..., QM 0* ] , until correct strata. information from a new housing census is made available • If the classification scheme is very coarse, compositional (in say period T). The Laspeyres stock RPPI thus is changes will affect the indices, i.e., there may be some M unit value bias in the indices. ∑P Q m t 0* m • If the classification scheme is very fine, the cell indi- P (P , P , Q ) ≡ L 0t 0 t 0* m=1 M (4.9) ces may be subject to a considerable amount of sam- ∑P Q m 0 0* m pling variability due to small sample sizes or some cells m=1 may be empty for some periods causing index number t = 0,..., T difficulties. 4.23 In Chapter 3 it was mentioned that for some pur- 4.27 An overall evaluation of the stratification method poses it is useful to have a stock RPPI for Owner Occupied is that it can be satisfactory if: Housing, i.e. excluding rented homes. The construction of • an appropriate level of detail is chosen; such an index proceeds in the same way as for the con- • age of the structure is one of the stratification variables, struction of an RPPI for the entire housing stock except and that the cells in the stratification scheme are now restricted • a decomposition of the index into structure and land to owner occupied dwellings. This will be possible if the components is not required. Handbook on Residential Property Prices Indices (RPPIs) 41 4 Stratification or Mix Adjustment Methods Stratification can be interpreted as a special case of regres- • S nt is the living space area of the structure for the sale of sion. (8) Chapter 5  discusses this more general technique, property n in quarter t in meters squared; known as hedonic regression when applied to price index construction and quality adjustment. • Ant is the approximate age (in decades) of the structure on property n in quarter t. 4.30 It can be seen that not all of the price determin- An Example Using Dutch ing characteristics listed above were used in the present study. In particular, the last five sets of characteristics of Data for the Town of “A” the property were neglected. There is an implicit assump- 4.28 This chapter will be concluded by a worked exam- tion that quarter to quarter changes in the amount of ple for the construction of a stratified index using data on renovations that have been undertaken for the structures, sales of detached houses for a small town (the population the location of the house, the type of structure, the type of is around 60 000) in the Netherlands, town “A”, for 14 quar- construction and any other price determining character- ters, starting in the first quarter of 2005 and ending in the istics of the properties sold in the quarter did not change second quarter of 2008. The same data set will be exploited enough to be a significant determinant of the average in Chapters 5, 6, 7 and 8 to illustrate the other methods for price for the properties sold once changes in land size, constructing house price indices and the numerical differ- structure size and the age of the structures were taken ences that can arise in practice. (9) into account. (10) 4.29 A dwelling unit has a number of important price 4.31 The determination of the values for the age vari- determining characteristics: able Ant needs some explanation. The original data were coded as follows: if the structure was built in 1960-1970, • The land area of the property; then the observation was assigned the decade indica- • The floor space area of the structure; i.e., the size of the tor variable BP = 5; 1971-1980, BP=6; 1981-1990, BP=7; structure that sits on the land underneath and surround- 1991-2000, BP=8; 2001-2008, BP=9. The age variable in ing the structure; this study was set equal to 9 - BP. For a recently built structure n in quarter t, Ant = 0. Thus, the age variable • The age of the structure; this determines (on average) gives the (approximate) age of the structure in decades. how much physical deterioration or depreciation the structure has experienced; 4.32 Houses which were older than 50  years at the time of sale were deleted from the data set. Two observa- • The amount of renovations that have been undertaken tions which had unusually low selling prices (36  000  and for the structure; 40 000 Euros) were deleted as were 28 observations which • The location of the structure; i.e., its distance from amen- had land areas greater than 1200 m2. No other outliers were ities such as shopping centers, schools, restaurants and deleted from the sample. After this cleaning of the data, work place locations; we were left with 2289  observations over the 14  quarters in the sample, or an average of 163.5  sales of detached • The type of structure; i.e., single detached dwelling unit, dwelling units per quarter. The overall sample mean sell- row house, low rise apartment or high rise apartment or ing price was 190  130  Euros, whereas the median price condominium; was 167 500 Euros. The average plot size was 257.6 m2 and • The type of construction used to build the structure; the average size of the structure (living space area) was 127.2  m2. The average age of the properties sold was ap- • Other special price determining characteristics that proximately 18.5 years. are different from “average” dwelling units in the same general location such as swimming pools, air condition- 4.33 The stratification approach to constructing a ing, elaborate landscaping, the height of the structure or house price index is conceptually very simple: for each of views of oceans or rivers. the important price explaining characteristic, divide up the sales into relatively homogeneous groups. Thus in the The variables used in this study can be described as follows: present case, sales were classified into 45 groups or cells, • Vnt is the selling price of property n in quarter t in Euros; consisting of 3 groupings for the land area L, 3 groupings • Ltn is the area of the plot for the sale of property n in quarter t in meters squared; (10) To support this assumption, it should be noted that the hedonic regression models discussed in later chapters consistently explained 80-90% of the variation in the price data using just the three main explanatory variables: L, S and A. The R2 between the (8) See Diewert (2003a) who showed that stratification techniques or the use of dummy actual and predicted selling prices ranged from .83 to .89. The fact that it was not variables can be viewed as a nonparametric regression technique. In the statistics necessary to introduce more price determining characteristics for this particular data literature, these partitioning or stratification techniques are known as analysis of set can perhaps be explained by the nature of the location of the town of “A” on a flat, variance models; see Scheffé (1959). featureless plain and the relatively small size of the town; i.e., location was not a big price ( ) This material is drawn from Diewert (2010). 9 determining factor since all locations have more or less the same access to amenities. 42 Handbook on Residential Property Prices Indices (RPPIs) Stratification or Mix Adjustment Methods 4 for the structure area S and 5  groups for the age A (in the 14 quarters were .24, .51 and .25 respectively. Similarly, decades) of the structure (3´3´5 = 45  separate cells). if S < 110 m2, the observation fell into the small structure Once quarterly sales were classified into the 45 groupings size cell; if 110 m2 ≤ S < 140 m2, then the observation fell of sales, the sales within each cell in each quarter were into the medium structure size cell and if 140 m2 ≤ S, then summed and then divided by the number of units sold the observation fell into the large structure size cell. The in that cell in order to obtain unit value prices, the cell resulting sample probabilities for falling into these three S prices Pmt . These unit values were then combined with the cells over the 14 quarters were .21, .52 and .27 respectively. number of units sold in each cell, the Qm t , to form the 4.35 As mentioned earlier, the data that were used did usual p’s and q’s that can be inserted into a bilateral index not have an exact age for the structure; only the decade number formula, like the Laspeyres, Paasche and Fisher when the structure was built was recorded. So there was ideal formulae defined by (4.4)-(4.6) above,  (11) yielding no possibility of choosing exact cutoff points for the age a stratified index of house prices of each of these types. of the structure. A = 0 corresponds to houses that were However, since there are only 163 or so observations for built during the years 2001-2008; A = 1 for houses built each quarter and 45 cells to fill, each cell had only an av- in 1991-2000; A = 2 for houses built in 1981-1990, A = 3 erage of 3 or so observations in each quarter, and some for houses built in 1971-1980; and A = 4 for houses built cells were empty for some quarters. This problem will be in 1961-1970. The resulting sample probabilities for fall- addressed subsequently. ing into these five cells over the 14 quarters were .15, .32, 4.34 How should the size limits for the L and S group- .21, .20  and .13  respectively. See Table 4.1  for the sample ings be chosen? One approach would be to divide the joint probabilities of a house sale belonging to each of the range of L and S by three and create three equal size cells. 45 cells. However, this approach leads to a large number of obser- vations in the middle cells. In the present study, size limits 4.36 There are several points of interest to note about were therefore chosen such that roughly 50  % of the ob- Table 4.1: servations would fall into the middle sized categories and • There were no observations for houses built during the roughly 25 % would fall into the small and large categories. 1960s ( A = 4 ) which had a small lot (L = small) and a For the land size variable L, the cutoff points chosen were large structure (S = large), so this cell is entirely empty; 160 m2 and 300 m2, while for the structure size variable S, • There are many cells which are almost empty; in particu- the cutoff points chosen were 110 m2 and 140 m2. Thus if lar the probability of a sale of a large plot with a small L < 160  m2, then the observation fell into the small land house is very low as is the probability of a sale of a small size cell; if 160 m2 ≤ L < 300 m2, then the observation fell plot with a large house; (12) into the medium land size cell and if 300 m2 ≤ L, then the observation fell into the large land size cell. The resulting • The “most representative model” sold over the sample sample probabilities for falling into these three L cells over period corresponds to a medium sized lot, a medium sized structure and a house that was built in the 1990s ( A = 1 ). The sample probability of a house sale falling (11) The international manuals on price measurement recommend this unit value approach to the construction of price indices at the first stage of aggregation; see CPI Manual into this highest probability cell is 0.09262. (2004), PPI Manual (2004), and XMPI Manual (2009). However, the unit value aggregation should take place over homogeneous items and this assumption may not be fulfilled in the present context, since there is a fair amount of variability in L, S and A within (12) Thus lot size and structure size are positively correlated with a correlation coefficient each cell. But since there are only a small number of observations in each cell for the of .6459. Both L and S are fairly highly correlated with the selling price variable P: data set under consideration, it would be difficult to introduce more cells to improve the correlation between P and L is .8234 and between P and S is .8100. These high homogeneity since this would lead to an increased number of empty cells and a lack of correlations lead to multicollinearity problems in the hedonic regression models to be matching for the cells. considered later. Table 4.1. Sample Probability of a Sale in Each Cell L S A=0 A=1 A=2 A=3 A=4 small small 0.00437 0.02665 0.01660 0.02053 0.02097 medium small 0.00349 0.02840 0.01966 0.01092 0.03888 large small 0.00087 0.00175 0.00044 0.00218 0.00612 small medium 0.01223 0.05242 0.04281 0.02053 0.00699 medium medium 0.03277 0.09262 0.08869 0.07907 0.02141 large medium 0.00786 0.02315 0.01005 0.01442 0.01398 small large 0.00306 0.00218 0.00175 0.00568 0.00000 medium large 0.03145 0.03495 0.00786 0.02097 0.00306 large large 0.04893 0.05461 0.02315 0.02490 0.01660 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 43 4 Stratification or Mix Adjustment Methods 4.37 The average selling price of the representative  house, falling into the medium L, medium S and A = 1 ∑P Q m t t m PMP st ≡ m∈S ( s ,t ) (4.11) category, is graphed in Figure 4.1  along with the overall sample mean and median price in each quarter. These av- ∑P Q m∈S ( s ,t ) m s t m erage prices have been converted into indices which start at PMF st ≡ [ PML st PMP ] (4.12) st 1 / 2 1 for quarter 1, which is the first quarter of 2005. It should be noted that these three house price indices are rather In Figure 4.1, the Fixed Base Fisher index is the matched variable. model Fisher price index defined by (4.12), where the base 4.38 Some additional indices are plotted in Figure 4.1, period s is kept fixed at quarter 1; i.e., the indices PMF 1,1 , including a fixed base matched model Fisher index and a PMF 1, 2 P 1,14 ,…, MF are calculated and labeled as the Fixed Base chained matched model Fisher price index. It is necessary to Fisher Index, PFFB. The index that is labeled the matched explain what a “matched model” index in this context means. model Chained Fisher Index, PFCH, is the price index PMF , PMF PMF PMF , …, PMF PMF 1,1 1, 2 PMF , PMF 1, 2 1,1 1, 2 2,3 13,14 1,14 If at least one house was sold in each quarter for each of the 1,1 1,1 … PMF PMF . 45  cells, the ordinary Laspeyres, Paasche and Fisher price Notice that the Fixed Base and Chained (matched model) indices comparing the prices of quarter t to those of quar- Fisher indices are quite close to each other and are much ter s would be defined by equations (4.4)-(4.6) respectively, smoother than the corresponding Mean, Median and where M = 45. This algebra is applicable to the situation Representative Model indices. (14) The data for these 5 se- where there are transactions in all cells for the two quarters ries plotted in Figure 4.1 are listed in Table 4.2. being compared. But for the present data set, on average only 4.39 The matched model Fisher indices must be regard- about 30 out of the 45 categories can be matched across any ed as being more accurate than the other indices which use two quarter, and the formulae (4.4)-(4.6) need to be modi- only a limited amount of the available price and quantity fied in order to deal with this lack of matching problem. Thus, information. As the trend of the Fisher indices is fairly when considering how to form an index number compari- smooth, the chained Fisher index should be preferred over son between quarters s and t, define the set of cells m that the fixed base Fisher index, following the advice given in have at least one transaction in each of quarters s and t as the Hill (1988) (1993) and in the CPI Manual (2004). Recall set S ( s, t ) . Then the matched model counterparts, PML st , PMP st also that there is no need to use Laspeyres or Paasche in- and PMF , to the regular Laspeyres, Paasche and Fisher indi- st dices in this situation since data on sales of houses con- ces between quarters s and t given by (4.4), (4.5) and (4.6) are tains both value and quantity information. Under these defined as follows: (13) conditions, Fisher indices are preferred over the Laspeyres ∑P Q m t s m and Paasche indices (which do not use all of the available PML st ≡ m∈S ( s ,t ) (4.10) price and quantity information for the two periods being ∑P Q m s s m compared). m∈S ( s ,t ) (13) A justification for this approach to dealing with a lack of matching in the context of bilateral index number theory can be found in the discussion by Diewert (1980; 498- 501) on the related problem of dealing with new and disappearing goods. Other approaches are also possible. For approaches based on maximum matching over all (14) The means (and standard deviations) of the 5 series mentioned thus far are as follows: pairs of periods; see Ivancic, Diewert and Fox (2011) and de Haan and van der Grient PFCH = 1.0737 (0.0375), PFFB = 1.0737 (0.0370), PMean = 1.0785 (0.0454), PMedian = 1.0785 (2011) for approaches based on imputation methods; see Alterman, Diewert and (0.0510), and PRepresent = 1.0586 (0.0366). Thus the representative model price index has Feenstra (1999). A useful imputation approach could be to estimate imputed prices for a smaller variance than the two matched model Fisher indices but it has a substantial the empty cells using hedonic regressions. The discussion is left until various hedonic bias relative to the two matched model Fisher indices: the representative model price regression methods have been discussed. index is well below the Fisher indices for most of the sample period. 44 Handbook on Residential Property Prices Indices (RPPIs) Stratification or Mix Adjustment Methods 4 Figure 4.1. Matched Model Fisher Chained and Fixed Base Price Indices, Mean, Median and Representative Model Price Indices 1.20 1.18 1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PFCH PFFB PMEAN PMEDIAN PREP Source: Authors’ calculations based on data from the Dutch Land Registry Table 4.2. Matched Model Fisher Chained and Fixed Base Price Indices, Mean, Median and Representative Model Price Indices Quarter PFCH PFFB PMean PMedian PRepresent 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.02396 1.02396 1.02003 1.05806 1.04556 3 1.07840 1.06815 1.04693 1.02258 1.03119 4 1.04081 1.04899 1.05067 1.03242 1.04083 5 1.04083 1.04444 1.04878 1.04839 1.04564 6 1.05754 1.06676 1.13679 1.17581 1.09792 7 1.07340 1.07310 1.06490 1.06935 1.01259 8 1.06706 1.07684 1.07056 1.10000 1.10481 9 1.08950 1.06828 1.07685 1.05806 1.03887 10 1.11476 1.11891 1.16612 1.16048 1.07922 11 1.12471 1.12196 1.08952 1.06290 1.07217 12 1.10483 1.11321 1.09792 1.10323 1.03870 13 1.10450 1.11074 1.10824 1.12903 1.12684 14 1.11189 1.10577 1.12160 1.10323 1.08587 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 45 4 Stratification or Mix Adjustment Methods 4.40 Since there is a considerable amount of heteroge- basic idea is to compare the current rolling year of price neity in each cell of the stratification scheme, there is the and quantity data to the corresponding data of a base year strong possibility of some unit value bias in the matched where the data pertaining to each season is compared. (15) model Fisher indices. However, if a finer stratification were In the present context, we have in principle, (16) price and used, the amount of matching would drop dramatically. quantity data for 45  classes of housing commodities in Already, with the present stratification, only about 2/3  of each quarter. If the sale of a house in each season is treated the cells could be matched across any two quarters. There is as a separate good, then there are 180 annual commodities. a trade-off between having too few cells with the possibil- 4.43 For the first index number value, the four quarters ity of unit value bias and having a more detailed stratifica- of price and quantity data on sales of detached dwellings tion scheme but with a much smaller degree of matching in the town of “A” (180 series) are compared with the same of the data within cells across the two time periods being data using the Fisher ideal formula. Naturally, the resulting compared. index is equal to 1. For the next index number value, the 4.41 Looking at Table 4.2 and Figure 4.1, it can be seen data for the first quarter of 2005 are dropped and the data that the chained Fisher index shows a drop in house prices pertaining to the first quarter of 2006 are appended to the during the fourth quarters of 2005, 2006 and 2007. There is data for quarters 2-4 of 2005. The resulting Fisher index is a possibility that house prices drop for seasonal reasons in the second entry in the Rolling Year (RY) Matched Model the fourth quarter of a year. In order to deal with this pos- series that is illustrated in Figure 4.2. However, as was the sibility, in the next section a rolling year matched model case with the chained and fixed base Fisher indices that ap- Fisher index will be constructed. peared in Figure 4.1, not all cells could be matched using the rolling year methodology; i.e., some cells were empty in the first quarter of 2006 which corresponded to cells in the first quarter of 2005 which were not empty and vice versa. The Treatment So when constructing the rolling year index PRY plotted in Figure 4.2, the comparison between the rolling year and of Seasonality the data pertaining to 2005 was restricted to the set of cells which were non empty in both years; i.e., the Fisher roll- for the Dutch Example ing year indices plotted in Figure 4.2 are matched model indices. Unmatched models are omitted from the index 4.42 Assuming that each commodity in each season of number comparison. (17) the year is a separate “annual” commodity is the simplest and theoretically most satisfactory method for dealing 4.44 The results are shown in Figure 4.2. Note that there with seasonal goods when the goal is to construct annual is a definite downturn at the end of the sample period but price and quantity indices. This idea can be traced back to that the downturns which showed up in Figure 4.1  for Mudgett in the consumer price context and to Stone in the quarters 4 and 8 can be interpreted as seasonal downturns; producer price context: i.e., the rolling year indices in Figure 4.2 did not turn down until the end of the sample period. Note further that the “The basic index is a yearly index and as a price or quan- index value for observation 5 compares the data for calen- tity index is of the same sort as those about which books dar year 2006 to the corresponding data for calendar year and pamphlets have been written in quantity over the 2005 and the index value for observation 9 compares the years.” Bruce D. Mudgett (1955; 97). data for calendar year 2007 to the corresponding data for “The existence of a regular seasonal pattern in prices calendar year 2005; i.e., these index values correspond to which more or less repeats itself year after year suggests Mudgett-Stone annual indices. very strongly that the varieties of a commodity available at different seasons cannot be transformed into one an- other without cost and that, accordingly, in all cases where (15) For additional theory and examples of this rolling year approach, see the chapters on seasonal variations in price are significant, the varieties seasonality in the CPI Manual (2004) and the PPI Manual (2004), Diewert (1998), and Balk (2008; 151-169). To justify the rolling year indices from the viewpoint of the economic available at different times of the year should be treated, in approach to index number theory, some restrictions on preferences are required; details can be found in Diewert (1999; 56-61). It should be noted that weather and the lack principle, as separate commodities.” Richard Stone (1956; of fixity of Easter can cause “seasons” to vary and a breakdown in the approach; see 74-75). Diewert, Finkel and Artsev (2009). However, with quarterly data, these limitations of the rolling year index are less important. ( ) In practice, as we have seen in the previous section, many of the cells are empty in each Diewert (1983) generalized the Mudgett-Stone annual 16 period. framework to allow for rolling year comparisons for 12 con- (17) There are 11 rolling year comparisons that can be made with the data for 14 quarters that are available. The numbers of unmatched or empty cells for rolling years 2, 3, ..., 11 are as secutive months of data with a base year of 12 months of follows: 50, 52, 55, 59, 60, 61, 65, 65, 66, 67. The relatively low number of unmatched or data or for comparisons of 4 consecutive quarters of data empty cells for rolling years 2, 3 and 4 is due to the fact that for rolling year 2, ¾ of the data are matched, for rolling year 3, ½ of the data are matched and for rolling year 4, ¼ of the with a base year of 4 consecutive quarters of data; i.e., the data are matched. 46 Handbook on Residential Property Prices Indices (RPPIs) Stratification or Mix Adjustment Methods 4 4.45 It is a fairly labour intensive job to construct the PFFB listed in Table 4.2, is to simply take a 4 quarter mov- rolling year matched model Fisher indices because the ing average of these series. The resulting rolling year se- cells that are matched over any two periods vary with the ries, PFCHMA and PFFBMA, can be compared with the roll- periods. A short-cut method (which is less accurate) for ing year Mudgett-Stone-Diewert series PRY; see Figure seasonally adjusting a series, such as the matched model 4.2. The data that corresponds to Figure 4.2 are listed in chained Fisher index PFCH and the fixed base Fisher index Table 4.3. Figure 4.2. Rolling Year Fixed Base Fisher, Fisher Chained Moving Average and Fisher Fixed Base Moving Average Price Indices 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 PFFBRY PFCHMA PFFBMA Source: Authors’ calculations based on data from the Dutch Land Registry Table 4.3. Rolling Year Fixed Base Fisher, Fisher Chained Moving Average and Fisher Fixed Base Moving Average Price Indices Rolling Year PFFBRY PFCHMA PFFBMA 1 1.00000 1.00000 1.00000 2 1.01078 1.01021 1.01111 3 1.02111 1.01841 1.02156 4 1.02185 1.01725 1.02272 5 1.03453 1.02355 1.02936 6 1.04008 1.03572 1.03532 7 1.05287 1.04969 1.04805 8 1.06245 1.06159 1.05948 9 1.07135 1.07066 1.06815 10 1.08092 1.07441 1.07877 11 1.07774 1.07371 1.07556 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 47 4 Stratification or Mix Adjustment Methods 4.46 It can be seen that a moving average of the data in any one quarter is always lined up with the data chained and fixed base Fisher quarter to quarter indi- in the corresponding quarter of the base year. A similar ces, PFCH and PFFB, listed in Table 4.2, approximates the argument applies to the moving average index PFCHMA; the theoretically preferred rolling year fixed base Fisher in- comparisons that go into the links in this index are from dex PFFBRY fairly well. There are differences of up to 1  % quarter to quarter and they are unlikely to be as accurate between the preferred rolling year index and the moving as comparisons across the years for the same quarter. (18) average index, however. Recall that the fixed base Fisher index compared the data of quarters 1 to 14 with the cor- (18) The stronger is the seasonality, the stronger will be this argument in favour of the responding data of quarter 1. Thus the observations for, accuracy of the rolling year index. The strength of this argument can be seen if all house say, quarters 2 and 1, 3 and 1, and 4 and 1 are not as like- price sales for each cell turn out to be strongly seasonal; i.e., the sales for any given cell occur in only one quarter in each year. Quarter to quarter comparisons are obviously ly to be as comparable as the rolling year indices where impossible in this situation but rolling year indices will be perfectly well defined. 48 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 5 Hedonic Regression Methods Hedonic Modeling 5.3 For products such as high-tech goods, the log- linear model (5.3) is usually preferred, among other things and Estimation because it most likely reduces the problem of heteroske- dasticity (non-constant variance of the errors) as prices 5.1 The hedonic regression method recognizes that tend to be log-normally distributed (Diewert, 2003b). In heterogeneous goods can be described by their attributes the housing context, on the other hand, the linear mod- or characteristics. That is, a good is essentially a bundle el has much to recommend. In Chapter 3, the size of the of (performance) characteristics.  (1) In the housing con- structure and the size of the land it is built on were men- text, this bundle may contain attributes of both the struc- tioned as two important price determining variables. Since ture and the location of the properties. There is no market the value of a property is generally equal to the sum of the for characteristics, since they cannot be sold separately, price of the structure and the price of land, it can be argued so the prices of the characteristics are not independently that land and structures should be included in the model observed. The demand and supply for the properties im- in a linear fashion, provided that the data are available. plicitly determine the characteristics’ marginal contribu- Chapter 8 will discuss this issue in more detail, including tions to the prices of the properties. Regression techniques a decomposition of the hedonic price index into land and can be used to estimate those marginal contributions or structures components. Unfortunately, not all data sources shadow prices. One purpose of the hedonic method might will contain information on lot and structure size. Lot size be to obtain estimates of the willingness to pay for, or mar- in particular may be lacking. When lot (or structure) size ginal cost of producing, the different characteristics. Here is not included as an explanatory variable, many empirical we focus on the second main purpose, the construction of studies have found log-linear models to perform reason- quality-adjusted price indices. ably well. 5.4 The characteristics parameters β kt in (5.2) and Hedonic Modeling (5.3) are allowed to change over time. This is in line with the idea that housing market conditions determine the mar- 5.2 The starting point is the assumption that the price ginal contributions of the characteristics: when demand pn t of property n in period t is a function of a fixed num- and supply conditions change, there is no a priori reason to ber, say K, characteristics measured by “quantities” z nk t . expect that those contributions are constant (Pakes, 2003). With T+1  time periods, going from the base period 0  to Yet, it seems most likely that market conditions change period T, we have gradually. Therefore, the simplifying assumption can con- fidently be made, perhaps only for the short term, that the pn = f ( zn 1 ,..., z nK , ε n ) (5.1) t t t t characteristics parameters (but not the intercept term) are t = 0,..., T constant over time. In the log-linear case this would give where ε nt is a random error term (white noise). In order rise to the following constrained version of (5.3): K to be able to estimate the marginal contributions of the characteristics using standard regression techniques, equa- ln p n t = β 0t + ∑β z k t nk + ε nt (5.4) k =1 tion (5.1) has to be specified as a parametric model. The As will be seen below, the time dependent intercept terms two best-known hedonic specifications are the fully linear (the β 0t ) can be converted into a constant quality price model index. K pn t = β 0t + ∑ β kt z nk t + ε nt (5.2) 5.5 Suppose we have data on selling prices and char- k =1 acteristics for the samples S (0), S (1),..., S (T ) of properties and the logarithmic-linear model sold in periods t = 0,..., T with sizes N (0), N (1),..., N (T ). K Under the classic error assumptions, in particular a zero ln p n t = β 0t + ∑β z t k t nk + ε nt (5.3) mean and constant variance, the parameters of the hedon- k =1 ic models (5.2) and (5.3) can be estimated by Ordinary where β 0t and β kt are the intercept term and the character- istics parameters to be estimated. In both specifications the Least Squares (OLS) regression on the sample data of each characteristics may be transformations, like logarithms, of time period separately. The constrained version (5.4) can continuous variables. In practice, many explanatory vari- be estimated on the pooled data pertaining to all time pe- ables will be categorical rather than continuous and repre- riods, provided that dummy variables are included which sented by a set of dummy variables which take the value of indicate the time periods (leaving out one dummy to pre- 1 if a property belongs to the category in question and the vent perfect collinearity). The estimating equation for the value of 0 otherwise. constrained log-linear model (5.4), which is generally re- ferred to as the time dummy variable hedonic model, thus (1) The hedonic regression approach dates back at least to Court (1939) and Griliches becomes T K (1961). Lancaster (1966) and Rosen (1974) laid down the conceptual foundations of the approach. Colwell and Dilmore (1999) argue that the first published hedonic study was ln p n t = β 0 + ∑ δ τ Dn τ + ∑ β k z nk t + ε nt (5.5) a 1922 University of Minnesota master’s thesis on agricultural land values. τ =1 k =1 50 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 where the time dummy variable Dn t has the value 1 if the 5.8 Multicollinearity is a well-known problem in he- observation comes from period t and 0 otherwise; a time donic regressions. A high correlation between some of dummy for the base period 0 is left out. Although unusual, the included variables increases the standard errors of the it is also possible to specify a time dummy model with the regression coefficients; the coefficients become unstable. untransformed price as the dependent variable. This speci- Again, it is difficult to say a priori how this will affect he- fication will be considered in the empirical example given donic indices. For some purposes, multicollinearity may at the end of this chapter. not be too problematic. For example, if we are not so much interested in the values of the parameters but merely in the predicted prices to be used in the estimation of the over- Some Practical Issues all quality-adjusted house price index, then the problem of 5.6 An important issue is the choice of the set of ex- multicollinearity should not be exaggerated. In this case it planatory variables included in the hedonic equation. If is better to include a relevant variable, even if this would some relevant variables – characteristics that can be ex- cause multicollinearity, than leaving it out as the latter gives pected to affect the price of a property (listed in Chapter rise to omitted variables bias. But when the parameter val- 3) – are excluded, then the estimated parameters of the ues are of interest as such, for example when we are trying included characteristics will suffer from omitted variables to decompose the property prices into land and structures bias. The bias carries over to the predicted prices computed components, then multicollinearity does pose problems. In from the regression coefficients and to the hedonic indi- Chapter 8 it will be shown that this is indeed a problem. ces. Each property can be viewed as a unique good, for a 5.9 As with other methods, some data cleaning might large part due to its location. But detailed information on be necessary. Obvious entry errors should be deleted. Yet location and neighbourhood can be hard to obtain (Case, a cautious approach is called for. Deleting outliers from a Pollakowski, and Wachter, 1991). Other characteristics may regression with the aim of producing more stable coeffi- be unavailable also and some could be difficult to measure cients (hence, more stable price indices) is often arbitrary directly. So it is fair to say that in practice some omitted and could lead to biased estimates. The use of hedonics variables bias will always be present when estimating a he- requires data on all characteristics included in the model. donic model for housing. (2) The sign and magnitude of the Unfortunately, partial non-response is present in many data bias, and its impact on the price index, are difficult to pre- sets. That is, the information on one or more characteris- dict. The magnitude depends among other things on the tics may be missing for a part of the sample. Procedures correlation between the omitted and included variables. have been developed to impute the missing data, but again 5.7 The importance of location has led researchers to it is important to avoid arbitrary choices that can have an make use of longitude and latitude data of individual prop- impact on the results. erties in hedonic regressions. This is usually achieved by 5.10 In the next two sections, the two main hedonic constructing a matrix of distances between all properties in approaches, the time dummy approach and the imputa- the data set and then using appropriate (though rather spe- tions approach, to constructing quality-adjusted house cialized) econometric methods to allow for spatial depend- price indices will be discussed. Without denying potential ence in the estimated equation. Explicitly accounting for econometric problems, our focus will be on the use of least spatial dependence can ameliorate the omitted locational squares regression to estimate the models. variables problem. Spatial dependence can be captured ei- ther in the regressors or the error term. The first approach, i.e., including location as an explanatory variable using ge- ospatial data, is the most straightforward one. This can be done parametrically or nonparametrically, for example by Time Dummy Variable making use of splines, as demonstrated by Hill, Melser and Reid (2010). For an elaborate discussion and a review of Method the literature on spatial dependence, the use of geospatial 5.11 The time dummy variable approach to construct- data and also on nonparametric estimation, we refer the ing a hedonic house price index has been used frequently reader to Hill (2011). (3) in academic studies but not so much by statistical agen- cies. (4) One advantage of this approach is its simplicity; the price index follows immediately from the estimated (2) A related point is that the characteristics of each house in the sample should be available in real time. House characteristics can change over time (which is actually (4) This method was originally developed by Court (1939; 109-111) as his hedonic the reason why they are given a superscript for time t in the hedonic models above). suggestion number two. The terminology adopted by us is not uniformly employed in Keeping the characteristics fixed implies that the hedonic price index would not be the real estate literature. For example, Crone and Voith (1992) refer to the time dummy adjusted for such quality changes. method as the “constrained hedonic” method, Gatzlaff and Ling (1994) call it the “explicit ( ) Colwell (1998) proposed a nonparametric spatial interpolation method which seems 3 time-variable” method, while Knight, Dombrow and Sirmans (1995) name it the “varying well adapted to model land prices as a function of the property’s geographical two- parameter” method. Other terms also appear in the literature so that statements about dimensional coordinates. the relative merits of different hedonic methods require careful interpretation. Handbook on Residential Property Prices Indices (RPPIs) 51 5 Hedonic Regression Methods pooled time dummy regression equation (5.5). Running does not change. Suppose further that S (0) and S (t ) one overall regression on the pooled data of the sam- are random or “representative” selections from the hous- ples S (0), S (1),..., S (T ) relating to periods t = 0,..., T ing stock. In that case the time dummy method implicitly (with sizes N(0), N(1),..., N(T )) yields coefficients βˆ0 , dˆt aims at a ratio of geometric mean prices for the total stock, ˆ (t = 1,..., T ) and β k (k = 1,..., K ) . The time dummy pa- which is equal to the geometric mean of the individual rameter shifts the hedonic surface upwards or downwards price ratios. (6) Although it is true that the target of meas- and measures the effect of “time” on the logarithm of price. urement may be different for different purposes, it is dif- Exponentiating the time dummy coefficients thus controls ficult to see what purposes a geometric stock RPPI would for changes in the quantities of the characteristics and pro- meet. Arithmetic target RPPIs, such as an index that tracks vides a measure of quality-adjusted house price change be- the value of the fixed housing stock over time, seem to be tween the base period 0 and each comparison period t. In more appropriate (see also Chapters 4 and 8). other words, the time dummy index going from period 0 to 5.15 The samples of houses traded, S (0) and S (t ) , period t is given by (5) may not be representative for the total housing stock (or PTD 0t = exp(δˆ t ) (5.6) for the total population of houses sold). A solution could be to weight the samples in order to make them representa- 5.12 Pooling cross-section data preserves degrees of ˆ will therefore tive. Running an OLS regression on the (pooled) weighted freedom. The regression coefficients β k data set is equivalent to running a Weighted Least Squares generally have lower standard errors than the coefficients ˆ t that would be obtained by estimating model (5.19) (WLS) regression on the original data set. Under the as- β k sumption of a constant variance of the errors, econometric separately on the data of the samples S (0), S (1),..., S (T ) . textbooks do not suggest the use of WLS since this will in- Although the increased efficiency can be seen as an advan- troduce heteroskedasticity. Note that a WLS time dummy tage, it comes at an expense: the assumption of fixed char- method will still generate a geometric index, in this case a acteristics parameters is a disadvantage of the time dummy weighted one. hedonic method. 5.16 A better option than using WLS regressions could 5.13 When using OLS, the time dummy hedonic index be to stratify the samples, run separate OLS regressions on can be written as (see e.g. Diewert, Heravi and Silver, 2009; the data of the different strata, and then explicitly weight de Haan, 2010a) the stratum-specific hedonic indices using stock (or sales) ∏( p ) t 1 / N (t ) n K ˆ 0  weights to construct an overall RPPI with an arithmetic PTD 0t = n∈S ( t ) ∑ exp  β ( z k − z kt )(5.7) structure at the upper level of aggregation. This stratified ∏( p ) 0 1 / N (0) k n  k =1  hedonic approach has several other advantages as well, as n∈S ( 0 ) will be explained later. where z ks = ∑n∈S ( s ) z nk s / N ( s ) is the sample mean of char- 5.17 A problem with the time dummy method is the acteristic k in period s ( s = 0, t ) . Equation (5.7) tells us revision that goes with it. If the time series is extended to that the time dummy index is essentially the product of T + 1 and new sample data is added, the characteristics co- two factors. The first factor is the ratio of the geometric efficients will change. Consequently, the newly computed mean prices in the periods t and 0. The second factor, price index numbers for the periods t = 1,..., T will differ exp[∑k =1 β ˆ ( z 0 − z t )] , adjusts this ratio of raw sample K k k k from those previously computed. (7) When additional data means for differences in the average characteristics z k0 and become available, the efficiency due to the pooling of data z kt ; it serves as a quality-adjustment factor which accounts increases and better estimates can be made. This can ac- for both changes in the quality mix and quality changes tually be seen as a strength rather than a weakness of the of the individual properties (provided that all relevant method. On the other hand, statistical agencies and their quality-determining attributes are included in the hedonic users will most likely be reluctant to accept continuous re- model). Notice that the time dummy price index simplifies visions of previously published figures. to the ratio of geometric mean prices if z kt = z k0 , i.e. if the average characteristics in period t and period 0 happen to 5.18 The multiperiod time dummy method therefore be equal. appears to be of limited use for the production of official house price indices although there are ways to deal with 5.14 Suppose for simplicity that the housing stock is the problem of revisions. One way would be to estimate constant, in the sense that there are no houses entering or time dummy indices for adjacent periods t-1  and t and exiting, and that the quality of the individual properties then multiply them to obtain a time series which is free of revisions. This high-frequency chaining has the additional advantage of relaxing the assumption of fixed parameters. (5) The expected value of the exponential of the time dummy coefficient is not exactly equal to the exponential of the time dummy parameter. The associated bias is often referred to as small sample bias: it diminishes when the sample size grows. Unless the sample size is extraordinary small, the bias will be small compared to the standard error (6) In index number theory such an index is referred to as a Jevons index. and can usually be neglected in practice. (7) In the words of Hill (2004), the time dummy approach violates time fixity. 52 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 It is, however, not entirely without problems. Drift in the 5.21 Suppose that we were aiming at a sales-based RPPI. index can occur when the data exhibit systematic fluctua- There are two natural choices for z k* in (5.8): the sample av- tions such as seasonal fluctuations. (8) erage characteristics of the base period, z k0 , and the sample averages of the comparison period t (t = 1,..., T ) , z kt . The usual solution in index number theory is to treat the result- ing price indices – which are equally valid – in a symmetric Characteristics Prices manner by taking the geometric mean. Setting z k * = z k0 in (5.8) generates a Laspeyres-type characteristics prices (CP) and Imputation Methods index: K 5.19 In the second main approach to compiling a he- ∑ ˆkt z k0 ˆt + β β 0 donic price index, separate regressions are run for all time PCPL 0t = k =1 K (5.9) periods and the index is constructed by making use of ˆ0 + β 0 ∑ βˆk0 z k0 the predicted prices based on the regression coefficients. k =1 Because the implicit characteristics prices are allowed Setting z k * = z kt in (5.8) yields a Paasche-type index: to vary over time, this method is more flexible than the K time dummy variable method. Two variants can be distin- guished: the characteristics prices approach and the impu- ∑ ˆkt z kt ˆt + β β 0 PCPP 0t = k =1 K (5.10) tations approach. It will be shown that, under certain cir- cumstances, both approaches are equivalent. We will first ˆ0 + β 0 ∑ βˆk0 z kt k =1 discuss the characteristics prices approach. (9) By taking the geometric mean of (5.9) and (5.10) the Fisher-type characteristics prices index is obtained: Characteristics Prices Approach = [PCPL ] (5.11) 1/ 2 PCPF 0t 0t PCPP 0t 5.20 To illustrate this approach, suppose as before that 5.22 The characteristics prices method can also ap- sample data are available on prices and relevant character- plied in combination with the log-linear model given by istics of houses sold in the base period 0 and each compari- (5.3). Running separate regressions of this model on the son period t. We will first assume that the linear hedonic sample data for periods 0  and t yields predicted prices model (5.2) holds true and is estimated on the data of pe- riod 0 and period t separately. This yields regression coeffi- (after exponentiating) p ˆn0 = exp( β 0 ∑k =1 ˆk0 z nk ˆ 0 ) exp[ K β 0 ] and ˆ s and βˆ s (k = 1,..., K ) for s = 0, t . The predicted ˆ ˆ ∑ K cients β 0 k pˆ = exp( β ) exp[ t n t 0 β z ]. Similar to what was done t t k nk k =1 prices for each individual property are p ˆn 0 =β ˆ0 + K β 0 ∑ ˆ 0z0 k nk in (5.8) for the linear model, prices can be predicted for a ˆ ∑ ˆ K k =1 and p ˆ n = β0 + t t β k z nk. It is also possible to compute pre- t t standardized house. Using the sample averages of the char- k =1 dicted period 0  and period t prices for a “standardized” acteristics in the base period to define the standardized property with fixed (quantities of) characteristics z k* . The house, the geometric counterpart to the Laspeyres-type resulting estimated price relative is characteristics prices index (5.9) is found: ˆ t ) exp   K ∑ βˆ z K exp( β ˆt + ∑ ˆ t z* t 0 β β 0  k k ˆ 0 ) exp  ( β ˆ 0 )z 0  K ˆ p t k k  k =1  = exp( β ∑ 0 PCPGL 0t = ˆt − β ˆt − β = k =1 (5.8) 0 0  k k k  ˆ 0 ) exp  ˆ0z0 K ˆ0 p K  k =1  ˆ0 + β 0 ∑ βˆk0 z k* exp( β 0  ∑  k =1 β k k   k =1 K  Expression (5.8) is a quality-adjusted price index ˆ exp( β t ) exp because 0  ∑ βˆ z t k  0 k ˆ 0 ) exp  ( β ˆ 0 ) z 0  (5.12) K = values of z k K  = exp( β ˆt − β ˆt − β ∑ * k =1 PCPGL the characteristics are kept fixed. But different 0t 0 0  k k k   ˆ0z0  k =1  will give rise to different index numbers. So what the preferred choice? exp(would βˆ 0 ) exp 0 be   k =1 ∑ β k k   The geometric counterpart to the Paasche-type hedonic in- dex (5.10) is obtained by using the sample averages of the characteristics in the comparison period: (8) An alternative approach would be the use of a moving window. For example, suppose ˆ t ) exp   we initially estimated a time dummy index on the data of twelve months. Next, we K delete the data of the first month and add the data of the thirteenth month and exp( β 0  ∑ βˆ z  t k t k ˆ 0 ) exp  ( β ˆ 0 )z t  K  k =1  ∑ estimate a time dummy index on this data set, and so on. By multiplying (chaining) the PCPGP 0t = ˆt − β = exp( β ˆt − β last month-to-month changes a non-revised time series is obtained. For an application, 0 0  k k k ˆ 0 ) exp  ˆ0zt  K  k =1  ∑ see Shimizu, Nishimura and Watanabe (2010). In the example for the town of “A”, given at the end of this chapter, drift does not seem to be a major problem; the moving window exp( β 0  β k k method gives much the same results as the multiperiod time dummy regression.  k =1  K ˆ z  (9) Again, the terminology differs between authors. For example, Crone and ˆ and Knight, Dombrow and Sirmans (1995) refer to this approach exp( β Voith as the t (1992) ) exp  0 “hedonic ∑ βt k  t k ˆ 0 ) exp  ( β ˆ 0 ) z t  (5.13) K  k =1  = exp( β method” (as opposed to the “constrained hedonic” or “varying we have called the time dummy variable approach), while 0 t parameter” method, what PCPGP = and Ling (1994) refer Gatzlaff K  ˆt − β 0 0   ˆt − β k k∑ k  to it as the “strictly cross-sectional” method. ˆ0 exp( β 0 ) exp   k =1 ∑ ˆ0zt β k k  k =1 Handbook on Residential Property Prices Indices (RPPIs) 53 5 Hedonic Regression Methods Taking the geometric mean of (5.12) and (5.13) yields Arithmetic Imputation Indices = [PHGL ]1 / 2 = exp(βˆ0t − βˆ00 ) exp ˆ t ˆ 0 0t  K PCPGF 0t 0t PHGP 0t  k =1 ∑  (β k − β k ) zk   5.26 The Laspeyres imputation index imputes period = [PHGL ]1 / 2 = exp(βˆ0t − βˆ00 ) exp ˆ 0 ) z 0 t  (5.14) K t prices for the properties belonging to the base period P0t CPGF 0t PHGP 0t   k =1 (∑ˆt − β β k k k   sample S (0) , evaluated at base period characteristics to control for quality changes. Using the linear model (5.1), where z k0 t = ( z k0 + z kt ) / 2 in (5.14) denotes the mean of the average characteristics in the base and comparison period. ˆn the imputed prices are p t ˆt + K β (0) = β 0 ∑k =1 ˆkt z nk 0 , and the he- donic imputation Laspeyres index becomes 5.23 If the target index is a stock-based rather than a  ˆt K ˆt 0  K sales-based RPPI, the two natural choices for the character- ∑ 1 pˆ t n ( 0 ) ∑  n∈S ( 0 )  β 0 + ∑ β k z nk  β  ˆt + β 0 ∑ ˆtz0 k k istics z k in equation (5.8) would be the average stock char- * PHIL = 0 t n∈S ( 0 ) = k =1 = k =1 acteristics of the base period and those of the comparison ∑1 p n n∈S ( 0 ) 0 ∑ pn n∈S ( 0 ) 0 ∑ pn / N (0) n∈S ( 0 ) 0 period. The first choice would produce a Laspeyres-type stock RPPI, the second choice a Paasche-type stock ˆRPPI. K ˆt 0  β K ∑ Both indices measure the quality-adjusted 1pˆnt (0) ∑  β value change 0 + ∑ β k z nk  t of = ˆt + β 0 ∑ ˆtz0 k k P 0t = n∈S ( 0 ) = n∈S ( 0 ) k =1 k =1 (5.15) the housing stock, but the results will ∑ usually ∑ differ. Not ∑ HIL 1p 0 n pn 0 pn 0 / N (0) only does the average quality of the n∈Shousing (0) stock change n∈S ( 0 ) n∈S ( 0 ) over time, the Laspeyres-type index ignores new properties Notice that the quantity associated with each price is 1; ba- that entered the housing market whereas the Paasche-type sically, every house is unique and cannot be matched ex- index does not take into account disappearing properties. cept through the use of a model. 5.24 Of course the assumption of known stock averages 5.27 The hedonic imputation Laspeyres index (5.15) for all property characteristics included in the hedonic is an example of a single imputation index in which the model is unrealistic. In most situations we have to rely on observed prices are left unchanged. It can be argued that estimates, i.e. on the sample averages z k0 and z kt which are it would be better to use a double imputation approach, based on the same characteristics data that is used to esti- where the observed prices are replaced by the predicted mate the hedonic equations. This leads to formulae (5.9) values. This is because biases in the period 0 and period t and (5.10), or the geometric mean (5.11), which describe estimates resulting from omitted variables are likely to off- sales-based RPPIs. Once again we are reminded that sales set each other, at least to some degree; see e.g. Hill, 2011. RPPIs can be seen as estimators of stock RPPIs, provided that the samples are representative of the total stock. The Using p ˆn 0 =β ˆ0 + K β 0 ∑k =1 ˆk0 z nk 0 , the hedonic double imputa- tion (DI) Laspeyres price index is latter is rather doubtful, however, and the usual approach is to stratify the samples and weight the estimated stratum  ˆt K ˆt 0  K indices using stock weights. ∑ 1p ˆn t (0) ∑  n∈S ( 0 )  β 0 + ∑ β k z nk   β ˆt + β 0 ∑ ˆtz0 k k PHDIL = = PCPL n∈S ( 0 ) k =1 0t = = k =1 0t ∑ n ∑ βˆ00 + ∑ βˆk0 z nk 1 pˆ 0  K 0   β0 + ∑ ˆ 0 K βˆ z 0 0 Hedonic Imputation Approach n∈S ( 0 ) n∈S ( 0 )  k =1  k =1 k k 5.25 The question arises how the 1  prices K  K method described above relates n∈the to ˆn p t (0) S ( 0 ) standard ∑ characteristics (matched- S (0)  β  0 ˆt + ∑ ∑ βˆ zt k 0 k n ˆt  β 0 + β k zk  = ∑ˆt 0 PHDIL = PCPL n∈ k =1 0t = = k =1 0t (5.16) model) methodology to construct price index number point of view we cann∈look 1 pn S (0) ˆ 0 ∑ indices. at the issue From ˆ0 K βin + an 0 the ∑ ∑ ˆ 0z0  β β k nk  ˆ0 + β 0 K ∑ˆ0z0 k k n∈S ( 0 )  k =1  k =1 following way. The period t prices of properties sold in pe- A comparison with equation (5.12) shows that, using the riod 0 cannot be observed and are “missing” because those linear model, the double imputation index equals the properties, or at least the greater part, will not be resold Laspeyres-type characteristics prices index. This result in period t. Similarly, the period 0  prices of the proper- does not depend on the estimation method. If we would ties sold in period t are unobservable. To apply standard use OLS regression to estimate the linear model, then the index number formulae these “missing prices” must be single imputation index would be equal to the double im- imputed. (10) Hedonic imputation indices do this by using putation index and also coincide with the characteristics predicted prices, evaluated at fixed characteristics, based on the hedonic regressions for all time periods. prices index as in this case n∈S ( 0 ) pn 0 ∑ ˆn = n∈S ( 0 ) p 0 ∑ , due to the fact that the hedonic model includes an intercept term so that the OLS regression residuals sum to zero. (10) As noted earlier, the hedonic theory dates back at least to Court (1939; 108). Imputation was his hedonic suggestion number one. His suggestion was followed up by 5.28 The hedonic single imputation Paasche index im- Griliches (1971a; 59-60) (1971b; 6) and Triplett and McDonald (1977; 144). More recent contributions to the hedonic imputations literature include Diewert (2003b), de Haan putes base period prices for the properties belonging to the (2004) (2009) (2010a), Triplett (2004) and Diewert, Heravi and Silver (2009). In a housing context the hedonic imputation method is discussed in detail by Hill and Melser (2008) period t sample S (t ) , evaluated at period t characteristics. and Hill (2011). Using again the linear model (5.1), these imputed prices 54 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 ˆn are given by p 0 (t ) = β 0 ∑k =1 ˆk0 z nk ˆ0 + K β t . To save space we will the double imputation unweighted geometric index, in which the base period prices are replaced by predicted val- only show the double imputation variant. Here, the ob- served (period t) prices are replaced by their model-based ˆn ues p 0 = exp( β 0 ∑k =1 ˆk0 z nk ˆ 0 ) exp[ K β 0 ], is predictions pˆnt =β ˆt + K β ∑ ˆ t z t . Thus, the hedonic dou- ∏( p 0 k =1 k nk ble imputation Paasche price index is ˆ (0) t n 1 / N (0) ˆ 0 ) exp  ( β ˆ 0 ) z 0  = P 0t K  K  K PHDIGL 0t = n∈S ( 0 ) ˆt − β = exp( β  ∑ ˆt − β k  ∑1 p ∑ ∑ˆz ˆ + β  β0 + ∑ βk zk ˆt ˆt t ∏( p k k CPGL ˆ ) 0 0 ˆ β t n t 0 t k t nk 0 1 / N (0) n  k =1    = n∈S ( 0 ) PHDIP ∏ P n∈S ( t ) n∈S ( t ) k =1 = = (= 0t k =1 0 t pˆn t ( 0) 1 / N ( 0 ) ∑1 p ˆ (t ) K CPP ˆ 0 K t  ∑ β +∑βˆ z ˆ ∑ ˆ ˆ 0 ) exp  ( β ˆ 0 ) z 0  = P 0 t (5.19) K βP + βnk∈S z(k0 ) 0 t ∑ 0 n 0 0 = exp( β ˆt − β ˆt − β HDIGL = 0 t nk  0 k 0  k  ∏ n∈S ( t )  n∈S ( t ) k =1  k =1 (pˆn ) 0 1 / N (0) 0 0  k =1 k k  CPGL  ˆt K ˆt t  K n∈S ( 0 )   β 0 + ∑ β k z nk   = ∑ ˆt + β β 0 ˆtzt k k Similarly, the geometric counterpart to the imputation Paasche price index (5.16) is obtained by imputing period = PCPP k =1 k =1 0t (5.17)  ˆ0 K  K 0 prices for the properties belonging to the periodK t sample  β 0 + ∑ β k z nk  β 0 + ∑ ˆ ˆ ˆ βk zk ˆ 0 ) exp[ ∑ ˆ 0zt ] , 0 t 0 0 t S (t ) , which are given by p ˆn0 (t ) = exp( β β  k =1  k =1 0 k =1 k nk and replacing the observed period t prices by the predic- which coincides with the Paasche-type characteristics pric- es index. If OLS regression is used, then (5.17) is equal to tions p ˆn t ˆ t ) exp[ K β = exp( β 0 ∑k =1 ˆkt z nk t ]. So we have the single imputation Paasche index because in this par- ticular case the numerator equals ∑n∈S ( t ) p n (p∏ˆn ) t 1 / N (t ) ˆ 0 ) exp  ( β ˆ 0 ) z t  = P 0t t K . It will then PHDIGP = 0t n∈S ( t ) = exp( β ˆt − β  ∑ ˆt − β k ∏ k k CPGP ˆ n (t ) 0 0 be unnecessary to estimate the hedonic equations for the (p 0 1 / N (t )  k =1  comparison periods t = 1,..., T ; estimating the base period( p ∏ n∈S ( t ) ˆn ) t 1 / N (t ) hedonic equation to obtain the base period imputed values ˆ 0 ) exp  ( β K ˆ 0 ) z t  = P 0 t (5.20) P 0t = n∈ S ( t ) = exp( βˆt − β  ˆt − β ∑ k will suffice. ∏ HDIGP k k CPGP ˆ n (t ) 0 0 (p 0 1 / N (t )  k =1  n∈S ( t ) 5.29 The hedonic double imputation Fisher index is found by taking the geometric mean of (5.16) and (5.17): 5.31 When OLS is used to estimate the log-linear re- gression equations, the denominator of (5.19) and the nu- = [PHDIL ]1/ 2 PHDIF 0t 0t PHDIP 0t (5.18) merator of (5.20) will equal the geometric sample means The above imputation indices can be given two interpreta- of the prices in period 0 and period t, respectively, and the tions. They can be viewed either as estimators of the qual- double imputation indices coincide with single imputation ity-adjusted value change of the entire housing stock, i.e., indices. Taking the geometric mean of (5.19) and (5.20) as stock-based RPPIs, or as estimators of quality-adjusted yields = [PHDIGL ] ˆ 0 ) exp  ( β ˆ 0 ) z 0t  = P 0t K sales-based RPPIs. Under the first interpretation, to pro- ˆt − β ∑ˆt − β 1/ 2 PHDIGF 0t 0t PHDIGP 0t = exp( β 0 0  k k k  CPGF duce approximately unbiased results, each sample should  k =1  be a random or representative selection from the housing = [PHDIGL ]1 / 2 = exp(βˆ0t − βˆ00 ) exp ˆ t ˆ 0 0t  K stock. Sample selection bias problems could be PHDIGF 0t less severe 0t PHDIGP 0t  k =1 ∑  ( β k − β k ) z k  = PCPGF (5.21)  0t under the second interpretation, although this depends on the sampling design. (11) where z k0 t = ( z k0 + z kt ) / 2 denotes the mean of the average characteristics in periods 0 and t, as before. Geometric Imputation Indices 5.32 The symmetric imputation index equation (5.21) can be rewritten in a way that is surprisingly similar to 5.30 The imputation approach can also be applied to equation (5.7) for the time dummy index when OLS is used geometric price index number formulae. Let us start with to estimate the hedonic equations (see Diewert, Heravi and what might be called the geometric counterpart to the im- Silver, 2009, and de Haan, 2010a): putation Laspeyres price index (5.15). For reasons of “con- sistency” the imputations will now be computed using the ∏( p ) t 1 / N (t ) n  K ˆ 0t 0  log-linear hedonic model (5.3) instead of the linear model. PHDIGF 0t = n∈S ( t ) exp  β ∑ k ( zk − z kt ) (5.22) The imputed period t prices for the properties belonging ∏( p ) 0 1 / N (0) n  k =1  to the base period sample S (0) , evaluated at base period n∈S ( 0 ) ˆn characteristics, are p t (0) = exp( β 0 ∑k =1 ˆkt z nk ˆ t ) exp[ K β 0 ]. Hence, where β ˆ0 + β ˆ 0t = ( β k k ˆ t ) / 2 denotes the average value of the k k-th coefficient in periods 0 and t. Equation (5.22) adjusts the ratio of observed geometric mean prices for any differ- (11) If all property transactions are observed, there is no sampling involved from a sales point of view, and sample selection bias is not an issue. In many countries the Land ences in the average sample characteristics. Triplett (2006) Registry records all transactions, at least for resold houses. However, such data sets usually have limited information on characteristics; see e.g. Lim and Pavlou (2007) or refers to this as “hedonic quality adjustment”. A compari- Academetrics (2009). son with equation (5.7) shows that if the sample averages of Handbook on Residential Property Prices Indices (RPPIs) 55 5 Hedonic Regression Methods agency to publish different RPPIs for different market seg- all characteristics stay the same ( z k0 = z kt ) , then the sym- ments. Users will benefit from this because it is well known metric hedonic imputation index and the time dummy that different types of houses, different regions, etc. can index coincide and equal the ratio of observed geometric exhibit quite different price trends. Second, stratification mean prices, but this will obviously, rarely happen. Both can be helpful for reducing sample selection bias, including types of hedonic indices also coincide if, for each charac- bias due to non-response, in particular for a stock-based ˆ 0 t from the two separate teristic, the average coefficient β k RPPI. regressions would be equal to the coefficient β ˆ from the k time dummy regression. This is rare as well, but it suggests 5.37 When using hedonic regression techniques to ad- that both approaches generate similar results if the charac- just for quality (mix) changes, stratification is highly rec- teristics parameters are approximately constant over time. ommended. It is very unlikely that a single hedonic model holds true for all market segments, hence separate regres- 5.33 If the characteristics parameters can be assumed sions should be run for different types of properties, dif- constant over time, the average coefficients β ˆ 0 t in equa- k ferent locations, etc. There are in fact two issues involved. tion (5.22) can be replaced by the base period coefficients Perhaps the biggest issue is that different sets of property βˆ 0 . In that case there would be no need to run a regres- k characteristics will be needed for different market seg- sion in each time period, and we would in fact be using the ments. For example, the characteristics that are relevant for non-symmetric imputation price index given by equation detached dwelling units differ from those that are relevant (5.13). (12) The base period regression could be run on a for high rise apartments, if only because the floor of the bigger data set to increase the stability of the coefficients. It apartment seems an important price determining variable. is advisable to regularly check if the coefficients have sig- The second, though probably less important, issue is that nificantly changed and to update them when necessary. the parameter values for the same characteristics can dif- 5.34 As mentioned earlier, geometric price indices are fer across housing market segments. Statistical tests for dif- less suitable as estimators of quality-adjusted RPPIs. This is ferences in parameter values between sub-samples can be not to say that they should never be used. In conjunction found in any econometrics textbook. with stratification, the use of (5.21) could produce satisfac- 5.38 The stratified hedonic approach can be illustrated tory results since this would combine quality adjustment most easily with reference to the imputation method, es- (using a log-linear hedonic regression model) and a sym- pecially in combination with the Laspeyres index formula. metric index number formula within the different strata Recall the third expression on the right-hand side of the with mix adjustment across strata. The stratified hedonic hedonic single imputation Laspeyres price index (5.15), approach will be discussed in the next section. where the period t prices for the houses in the base period sample S (0) are “missing” and imputed (using the estimat- ed hedonic regression model for period t) by p ˆn t (0) . Suppose, as in Chapter 4, that the total sample is (post) stratified into Stratified Hedonic Indices M sub-samples S m (0) . Equation (5.15) can then be rewrit- ten as 5.35 Chapter 4  dealt with stratification or mix adjust- M M   ment. Stratification is a simple and powerful tool to ad- ∑ ˆn p t (0) ∑∑ pˆn t (0) ∑∑ pn0  ∑ pˆn t (0) ∑ pn0  just for changes in the quality mix of the properties sold. PHIL 0t = n∈S ( 0 ) = m=1 n∈S ( 0 ) m = m=1 n∈S ( 0 ) m n∈S ( 0 ) m n∈S ( 0 ) m = However, some quality mix changes within the strata are ∑ pn 0 M ∑∑ pn 0 M ∑∑ pn 0 likely to remain, as essentially every property is a unique n∈S ( 0 ) m=1 n∈S ( 0 ) m m=1 n∈S ( 0 ) m good, and some unit value bias could therefore occur. M A M   more detailed stratification scheme may be ∑ ˆn p t ∑∑ 0) (unfeasible, pˆn t (0) ∑∑ pn∑ 0  pˆn t (0) ∑ pn0  M n∈S ( 0 ) = especially when the number of observations is relatively ∑ m=1 n∈S ( 0 ) m=1 n∈S ( 0 ) n∈S ( 0 ) PHIL sm PHIL n∈S ( 0 ) 0t = = = 0 0t ,m (5.23) m m m m small. Provided that the necessary data on characteristics ∑ pn 0 ∑∑ M p 0 n ∑∑ M p 0 n m=1 are available, it could be worthwhile to work n∈S ( 0 ) with a less m=1 n∈S ( 0 ) m m=1 n∈S ( 0 ) m fine stratification scheme and use hedonic regression at the stratum level to adjust for quality mix changes. This two- where PHIL 0t ∑ ,m = n∈S ( 0 ) m ˆn p t ∑ (0) / n∈S ( 0 ) p n m 0 denotes the stage approach combines hedonics at the lower (stratum) hedonic (single) imputation Laspeyres price index level and explicit weighting at the upper level to form an between the base period and period t for cell m; overall RPPI. sm∑0 = n∈S ( 0 ) p n m ∑0 / n∈S ( 0 ) p n 0 is the corresponding sales 5.36 Two advantages of stratification have been men- value share, which serves as the weight for PHIL 0t ,m . Note that tioned earlier. First, stratification enables the statistical the last expression of (5.23) has a similar structure as the mix-adjusted index given by equation (4.1), but in the pre- ( ) In Europe this type of hedonic quality adjustment is called “hedonic re-pricing”, 12 sent case the cell indices are hedonic imputation indices especially in case the sample size is fixed (Destatis, 2009). rather than unit value indices. 56 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 5.39 Equation (5.23) shows that if the imputed prices • While the method is essentially reproducible, different ˆn p t (0) for all houses in the sample S (0) are based on one choices can be made regarding the set of characteristics overall hedonic regression, then the aggregate hedonic included in the model, the functional form, possible imputation Laspeyres index can be written in the form of transformations of the dependent variable  (14), the sto- a stratified index. But this is just another way of writing chastic specification, etc., which could lead to varying things, not what is meant by a stratified hedonic approach. estimates of overall price change. Thus, a lot of metadata Also, as argued above, the use of a common model is very may be required. unrealistic. So instead of running one big hedonic regres- • The general idea of the hedonic method is easily under- sion, separate regressions should be performed on the data stood but some of the technicalities may not be easy to of the sub-samples in each time period to obtain imputed explain to users. (period t) prices and imputation cell indices. That would lead to a stratified Laspeyres-type hedonic imputation 5.43 The overall evaluation of the hedonic regression index. method is that it is probably the best method that could be used in order to construct constant quality RPPIs for vari- 5.40 It would be preferable to estimate a stratified ous types of property.  (15) We are in favor of the (double) Fisher hedonic index rather than a Laspeyres one. This is imputation variant because this is the most flexible hedon- perfectly feasible for a sales RPPI but may not be feasible ic approach and because this approach is analogous to the for a stock RPPI, as was already mentioned in Chapter 3, standard matched-model methodology to construct price since up-to-date census data on the number of properties indices. is often lacking. 5.44 In the next three sections, the various hedonic re- gression methods will be illustrated using the data for the town of “A” that was described at the end of Chapter 4. The Main Advantages following two sections show the results of time dummy he- donic regressions, using the log of the selling price as the and Disadvantages dependent variable and using the untransformed selling price, respectively. The last section illustrates the hedonic 5.41 This section summarizes the advantages and dis- imputation method. All of the resulting price indices are advantages of hedonic regression methods to construct an for the sales of detached houses; some results using the data RPPI. The main advantages are: for the town of “A” for indices of the stock of houses will be • If the list of available property characteristics is suffi- postponed until Chapter 8. ciently detailed, hedonic methods can in principle adjust for both sample mix changes and quality changes of the individual properties. • Price indices can be constructed for different types of Time Dummy Models Using dwellings and locations through a proper stratification of the sample. Stratification has a number of other ad- the Logarithm of Price vantages as well. as the Dependent Variable • The hedonic method is probably the most efficient meth- od for making use of the available data. • The imputation variant of the hedonic regression meth- The Log Linear Time Dummy Model od is analogous to the matched model methodology that 5.45 Recall the description of the data for the Dutch is widely used in order to construct price indices. town of “A” on sales of detached houses. In quarter t, there 5.42 The main disadvantages of hedonic regression are: were N(t) sales of detached houses in “A” where p n t is the selling price of house n sold during quarter t. There is in- • It may be difficult to control sufficiently for location if formation on three characteristics of house n sold in pe- property prices and price trends differ across detailed re- riod t: Ltn is the area of the plot in square meters (m2); S nt is gions. However, a stratified approach to hedonic regres- the floor space area of the structure in m2 and Ant is the age sions will help overcome this problem to some extent. in decades of house n in period t. Using these variables, the • The method is data intensive since it requires data on all relevant property characteristics, so it is relatively expen- sive to implement. (13) (14) For example, the dependent variable could be the sales price of the property or its logarithm or the sales price divided by the area of the structure and so on. (15) This evaluation agrees with that of Hoffmann and Lorenz (2006; 15): “As far as quality (13) However, as will be seen from the Dutch example given below, just having information adjustment is concerned, the future will certainly belong to hedonic methods.” on location, type of property, its age, its floor space area and the plot area may explain Gouriéroux and Laferrère (2009) have shown that it is possible to construct an official most of the variation in the selling price. nationwide credible hedonic regression model for real estate properties. Handbook on Residential Property Prices Indices (RPPIs) 57 5 Hedonic Regression Methods standard log linear time dummy hedonic regression model is The Log Linear Time Dummy Model defined by the following system of regression equations: (16) with Quality Adjustment of Structures ln p n t = α + βLtn + γS nt + δAnt + τ t + ε nt (5.24) 5.49 If age A interacts with the quantity of structures S t = 1,...,14; n = 1,...,N(t); t 1 ≡ 0 in a multiplicative manner, an appropriate explanatory var- where t is a parameter which shifts the hedonic surface in t iable for the selling price of a house would be g (1 − d ) A S quarter t upwards or downwards as compared to the sur- (i.e., geometric depreciation where δ is the decade geomet- face in quarter 1. (17) ric depreciation rate) or g (1 − dA) S (straight line deprecia- 5.46 It is easy to construct a price index using the log line- tion where δ is the decade straight line depreciation rate) ar time dummy hedonic model (5.24). Exponentiating both instead of the additive specification gS + dA . In what fol- sides of equation (5.24), and neglecting the error term, yields lows, the straight line variant of this class of models will pnt = exp(α )[exp( Ltn )]β [exp(S nt )]γ [exp( Ant )]δ exp(τ t ). If we be estimated (19). Thus, the log linear time dummy hedonic could observe a property with the same characteristics in regression model with quality adjusted structures becomes the base period 1 and in some comparison period t (> 1) , ln p n t = α + βLtn + γ (1 − δAnt ) S nt + τ t + ε nt (5.25) then the corresponding price relative (again neglecting error terms) would simply be equal to exp(t t ) . For two t = 1,...,14; n = 1,...,N(t); t 1 ≡ 0 consecutive periods t and t+1, the price relative (again ne- 5.50 Regression model (5.25) was run using the 14 quar- glecting error terms) would equal exp(t t +1 ) / exp(t t ) , and ters of sales data for the town of “A”. Note that a single com- this can serve as the chain link in a price index. Figure 5.1 mon straight line depreciation rate δ is estimated. The es- shows the resulting index, labeled as PH 1 (hedonic index timated decade (net) depreciation rate (20) was δ ˆ = 11 .94% no. 1), and Table 5.1 lists the index numbers. The R 2 for (or around 1.2  % per year), which is very reasonable. As this model was .8420, which is quite satisfactory for a he- was the case with model (5.24), if a house with the same donic regression model with only three explanatory vari- characteristics in two consecutive periods t and t+1 could ables. (18) For later comparison purposes, note that the log be observed, the corresponding price relative (neglecting likelihood was 1407.6. error terms) exp(t t +1 ) / exp(t t ) can serve as the chain link 5.47 A problem with this model is that the underlying in a price index; see Figure 5.1 and Table 5.1 for the result- price formation model seems implausible: S and L inter- ing index, labeled PH 2 . The R 2 for this model was .8345, act multiplicatively in order to determine the overall house a bit lower than the previous model and the log likelihood price whereas it seems most likely that lot size L and house was 1354.9, which is quite a drop from the previous log size S interact in an approximately additive fashion to de- likelihood of 1407.6. (21) termine the overall house price. 5.51 It appears that the imposition of more theory – 5.48 Another problem with the regression model (5.24) with respect to the treatment of the age of the house – has is that age is entered in an additive fashion. The problem led to a drop in the empirical fit of the model. However, is that we would expect age to interact directly with the it is likely that this model and the previous one are mis- structures variable S as a (net) depreciation variable and specified (22): they both multiply together land area times not interact directly with the land variable L, because land structure area to determine the price of the house while does not depreciate. In the following model, this direct in- it is likely that an additive interaction between L and S is teraction of age with structures will be made. more appropriate than a multiplicative one. (16) The estimating equation for the pooled data set will include time dummy variables to indicate the quarters. For all the models estimated for the town of “A”, it is assumed that the error terms ent are independently distributed normal variables with mean 0 (19) This regression is essentially linear in the unknown parameters and hence it is very easy and constant variance. Maximum likelihood estimation is used in order to estimate the to estimate. unknown parameters in each regression model. The nonlinear option in Shazam was (20) It is a net depreciation rate because we have no information on renovation expenditures, used for the actual estimation. i.e., δ is equal to gross wear and tear depreciation of the house less average expenditures ( ) The 15 parameters a, t 1,...,t 14 correspond to variables that are exactly collinear in the 17 on renovations and repairs. regression (5.24) and thus the restriction t1 = 0 is imposed in order to identify the (21) The levels type R 2 for this model was R *2 = .7647, which again is quite a drop from remaining parameters. the corresponding levels R 2 for the previous log price model. (18) Later on in this chapter and in Chapter 8, some hedonic regressions will be run that use (22) If the variation in the independent variables is relatively small, the difference in indexes prices p n as the dependent variables rather than the logs of the prices. To facilitate t generated by the various hedonic regression models considered in this section and the comparisons of goodness of fit across models, we will transform the predicted values following two sections is likely to be small since virtually all of the models considered for the log price models into predicted price levels by exponentiating the predicted can offer roughly a linear approximation to the “truth”. But when the variation in the prices and then calculating the correlation coefficient between these predicted price independent variables is large, as it is in the present housing context, the choice of levels and the actual prices. Squaring this correlation coefficient gives us a levels type functional form can have a substantial effect. Thus a priori reasoning should be applied measure of goodness of fit for the log price models which is denoted by R *2 . For this to both the choice of independent variables in the regression as well as to the choice of particular model, R *2 = .8061. functional form. For additional discussion on functional form issues, see Diewert (2003a). 58 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 5.52 Note that, given the depreciation rate δ, quality ad- 5.54 Using the data for the Dutch town of “A”, the es- justed structures (adjusted for the aging of the structure) timated decade (net) depreciation rate was d ˆ = 0.1050 for each house n in each quarter t can be defined as follows: (standard error 0.00374). If both sides of (5.27) were exponentiated and the error terms were neglected, the S nt* ≡ (1 − dAnt ) S nt (5.26) house price p n t would equal exp(α )[ Ltn ]β [ S nt* ]γ exp(τ t ), t = 1,...,14; n = 1,...,N(t) where S n denotes quality adjusted structures as defined t* by (5.26). So if we could observe a house with the same characteristics in two consecutive periods t and t+1, the The Log Log Time Dummy Model corresponding price relative (neglecting error terms) would be equal to exp(t t +1 ) / exp(t t ) and this again can with Quality Adjustment serve as the chain link in a price index; see Figure 5.1 and of Structures for Age Table 5.1 for the resulting index, labeled PH 3 . The R 2 for this model was .8599 (the levels measure of fit was 5.53 In the remainder of this section, quality adjusted R *2 = .8880), which is an increase over models (5.25) and (for age) structures, (1 − dA) S , will be used as an explana- (5.26); the log likelihood was 1545.4, a big increase over tory variable, rather than the unadjusted structures area, the log likelihoods for the other two models (1407.6 and S. The log log model is similar to the previous log linear 1354.9). model, except that now, instead of using L and (1 − dA) S as explanatory variables in the regression model, the loga- 5.55 The house price series generated by the three rithms of the land and quality adjusted structures areas are log-linear time dummy regressions described in this sec- used as independent variables. Thus the log log time dummy tion, PH 1 , PH 2 and PH 3 , are plotted in Figure 5.1 along hedonic regression model with quality adjusted structures is with the chained stratified sample mean Fisher index, the following: (23) PFCH . These four house price series are listed in Table ln p n t = α + β ln Ltn + γ ln[(1 − δAnt ) S nt ] + τ t + ε nt (5.27) 5.1. All four indices capture the same trend but there can be differences of over 2 percent between them in some t = 1,...,14; n = 1,...,N(t); t 1 ≡ 0 quarters. Notice that all of the indices move in the same direction from quarter to quarter with decreases in quar- (23) This hedonic regression model turns out to be a variant of McMillen’s (2003) consumer ters 4, 8, 12 and 13 except that PH 3 – the index that cor- oriented approach to hedonic housing models. His theoretical framework draws on the earlier work of Muth (1971) and is outlined in Diewert, de Haan and Hendriks (2010). See responds to the log log time dummy model – increases also McDonald (1981). in quarter 12. Figure 5.1. Log-Linear Time Dummy Price Indices and the Chained Stratified Sample Mean Fisher Price Index 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PH1 PH2 PH3 PFCH Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 59 5 Hedonic Regression Methods Table 5.1. Log-Linear Time Dummy Price Indices and the Chained Stratified Sample Mean Fisher Price Index Quarter PH1 PH2 PH3 PFCH 1 1.00000 1.00000 1.00000 1.00000 2 1.04609 1.04059 1.03314 1.02396 3 1.06168 1.05888 1.05482 1.07840 4 1.04007 1.03287 1.03876 1.04081 5 1.05484 1.05032 1.03848 1.04083 6 1.08290 1.07532 1.06369 1.05754 7 1.09142 1.08502 1.07957 1.07340 8 1.06237 1.05655 1.05181 1.06706 9 1.10572 1.09799 1.09736 1.08950 10 1.10590 1.10071 1.09786 1.11476 11 1.10722 1.10244 1.09167 1.12471 12 1.10177 1.09747 1.09859 1.10483 13 1.09605 1.08568 1.09482 1.10450 14 1.10166 1.09694 1.10057 1.11189 Source: Authors’ calculations based on data from the Dutch Land Registry 5.56 Although model (5.27) performs the best of the importance in determining the price of the property, then simple hedonic regression models considered thus far, it has the following linear time dummy hedonic regression model the unsatisfactory feature that the quantities of land and of might be an appropriate one: quality adjusted structures determine the price of a property pn t = a + βLtn + gS nt + dAnt + t t + ε nt (5.28) in a multiplicative manner. It is more likely that house prices are determined by a weighted sum of their land and quality t = 1,...,14; n = 1,...,N(t); t 1 ≡ 0 adjusted structures amounts. In the following section, an ad- 5.58 The above linear regression model was run using ditive time dummy model will therefore be estimated. The the data for the town of “A”. The R 2 for this model was expectation is that this model will fit the data better. .8687, much higher than those obtained in the previous regressions (25); the log likelihood was -10790.4 (which cannot easily be compared to the previous log likelihoods Time Dummy Hedonic since the dependent variable has changed from the loga- rithm of price to just price (26). Regression Models using 5.59 Using the linear model defined by equations (5.28) to form an overall house price index is a bit more difficult Price as the Dependent than using the previous log-linear or log log time dummy Variable regression models. In the previous section, holding char- acteristics constant and neglecting error terms, the relative price for the same house over any two periods turns out to The Linear Time Dummy Hedonic be constant, leading to an unambiguous overall index. In the present situation, holding characteristics constant and Regression Model neglecting error terms, the difference in price for the same 5.57 There are reasons to believe that the selling price house turns out to be constant, but the relative prices for of a property is linearly related to the plot area of the prop- different houses will not in general be constant. Therefore, erty plus the area of the structure due to the competitive an overall index will be constructed which uses the prices nature of the house building industry. (24) If the age of the generated by the estimated parameters for model (5.28) structure is treated as another characteristic that has an (25) However, recall that the levels adjusted measure of fit for the log log model described by (5.27) was .8880, which is higher than .8687. (24) See Clapp (1980), Francke and Vos (2004), Gyourko and Saiz (2004), Bostic, Longhofer (26) Marc Francke has pointed out that it is possible to compare log likelihoods across two and Redfearn (2007), Davis and Heathcote (2007), Francke (2008), Diewert (2009b), Koev models where the dependent variable has been transformed by a known function and Santos Silva (2008), Statistics Portugal (2009), Diewert, de Haan and Hendriks (2010), in the second model; see Davidson and McKinnon (1993; 491) where a Jacobian Diewert (2010) and Chapter 8 below. adjustment makes it possible to compare log likelihoods across the two models. 60 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 and evaluated at the sample average amounts of L, S and the to (1 − dA) S instead of having A and S as completely inde- sample average age of a house A. (27) The resulting quarterly pendent variables that enter into the regression in a linear prices for this “average” house were converted into an index, fashion. PH 4 , which is listed in Table 5.2 and charted in Figure 5.2. 5.62 The results for this model were a clear improve- 5.60 The hedonic regression model defined by (5.28) is ment over the results of model (5.28). The log likelihood perhaps the simplest possible one but it is a bit too simple increased by 92  to -10697.8  and the R 2 increased to since it neglects the fact that the interaction of age with the .8789  from the previous .8687. The estimated decade de- selling price of the property takes place via a multiplica- preciation rate was dˆ = 0.1119 (0.00418), which is reason- tive interaction with the structures variable and not via a able as usual. This linear regression model has the same general additive factor. In what follows, model (5.28) is re- property as the model (5.28): house price differences are estimated using quality adjusted structures as an explana- constant over time for all constant characteristic models tory variable rather than just entering age A as a separate but house price ratios are not constant. So again an overall stand alone characteristic. index will be constructed which uses the prices generated by the estimated parameters in (5.29) and evaluated at the sample average amounts of L, S and the average age of a The Linear Time Dummy Model house A. The resulting quarterly house prices for this “av- with Quality Adjusted Structures erage” model were converted into an index, PH 5 , which is listed in Table 5.2 and charted in Figure 5.2. For compari- 5.61 The linear time dummy hedonic regression model son purposes, PH 3 (the time dummy Log Log model index) with quality adjusted structures is described by and PFCH (the chained stratified sample mean Fisher in- pn t = a + βLtn + g (1 − dAnt ) S nt + t t + ε nt (5.29) dex) will be charted along with PH 4 and PH 5 . The preferred indices thus far are PFCH and PH 5 . t = 1,...,14; n = 1,...,N(t); t 1 ≡ 0 5.63 It can be seen that again, all four indices capture This is the most plausible hedonic regression model so far. the same trend but there can be differences of over 2 per- It works with quality adjusted (for age) structures S* equal cent between the various indices for some quarters. Note that all of the indices move in the same direction from (27) The sample average amounts of L and S were 257.6 m2 and 127.2 m2 respectively quarter to quarter with decreases in quarters 4, 8, 12 and and the average age of the detached dwellings sold over the sample period was 1.85 decades. 13, except that PH 3 increases in quarter 12. Figure 5.2. Linear Time Dummy Price Indices, the Log Log Time Dummy Price Index and the Chained Stratified Sample Mean Fisher Price Index 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PH4 PH5 PH3 PFCH Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 61 5 Hedonic Regression Methods Table 5.2. Linear Time Dummy Price Indices, the Log Log Time Dummy Price Index and the Chained Stratified Sample Mean Fisher Price Index Quarter PH4 PH5 PH3 PFCH 1 1.00000 1.00000 1.00000 1.00000 2 1.04864 1.04313 1.03314 1.02396 3 1.06929 1.06667 1.05482 1.07840 4 1.04664 1.03855 1.03876 1.04081 5 1.05077 1.04706 1.03848 1.04083 6 1.08360 1.07661 1.06369 1.05754 7 1.09593 1.09068 1.07957 1.07340 8 1.06379 1.05864 1.05181 1.06706 9 1.10496 1.09861 1.09736 1.08950 10 1.10450 1.10107 1.09786 1.11476 11 1.10788 1.10588 1.09167 1.12471 12 1.10403 1.10044 1.09859 1.10483 13 1.09805 1.08864 1.09482 1.10450 14 1.11150 1.10572 1.10057 1.11189 Source: Authors’ calculations based on data from the Dutch Land Registry 5.64 A problem with the hedonic time dummy regres- Thus the hedonic imputation model involves the estima- sion models considered thus far is that the prices of land tion of 56 parameters, the time dummy model only 17, so it and quality adjusted structures are not allowed to change is likely that the hedonic imputation model will fit the data in an unrestricted manner from period to period. The class much better. of hedonic regression models to be considered in the fol- 5.66 In the housing context, precisely matched models lowing section does not suffer from this problem. across periods do not exist; there are always depreciation and renovation activities that make a house in the exact same location not quite comparable over time. This lack of matching, say between quarters t and t+1, can be overcome Hedonic Imputation in the following way: take the parameters estimated using the quarter t+1 hedonic regression and price out all of the Regression Models housing models (i.e., sales) that appeared in quarter t. This generates predicted quarter t+1 prices for the quarter t mod- 5.65 The theory of hedonic imputation indices explained els, pˆn t +1 (t ) , as follows: earlier is applied to the present situation as follows. For ˆn p t +1 (t ) ≡ aˆ t +1 + βˆ t +1 Lt + gˆ t +1 (1 − dˆ t +1 At ) S t (5.31) n n n each period, run a linear regression of the following form: t = 1,...,13; n = 1,...,N(t) pn t = a t + β t Ltn + g t (1 − d t Ant ) S nt + ε nt (5.30) ˆ , β ˆ , gˆ and d ˆ are the parameter estimates for where a t t t t t = 1,...,14; n = 1,...,N(t) model (5.30) for t = 1,...,14. Now we have a set of pseudo matched quarter t+1 prices for the models that appeared in Using the data for the town of “A”, there are only four pa- quarter t and the following Laspeyres type hedonic imputa- rameters to be estimated for each quarter: a t , β t , g t and tion (or pseudo matched model) index, going from quarter t d t for t = 1,...,14. Note that (5.30) is similar in form to the to t+1, can be formed: (28) model defined by equations (5.29), but with some signifi- N (t ) cant differences: ∑1 p ˆ t +1 n (t ) P t ,t +1 HIL ≡ n =1 (5.32) • Only one depreciation parameter is estimated in the mod- N (t ) el defined by (5.29) whereas in the present model, there ∑ 1 pn t n =1 are 14 depreciation parameters; one for each quarter. t = 1,...,13 • Similarly, in model (5.29), there was only one a , β and g parameter whereas in (5.30), there are 14 a t , 14 β t (28) Due to the fact that the regressions defined by (5.30) have a constant term and are essentially linear in the explanatory variables, the sample residuals in each of the regressions and 14 g t parameters to be estimated. On the other will sum to zero. Hence the sum of the predicted prices will equal the sum of the actual hand, model (5.29) had an additional 13 time shifting prices for each period. Thus the sum of the actual prices in the denominator of (5.32) will equal the sum of the corresponding predicted prices and similarly, the sum of the actual parameters (the t t ) that required estimation. prices in the numerator of (5.34) will equal the corresponding sum of the predicted prices. 62 Handbook on Residential Property Prices Indices (RPPIs) Hedonic Regression Methods 5 As mentioned earlier, the quantity that is associated with 5.68 Once the above Laspeyres and Paasche imputa- each price is 1 as each housing unit is basically unique and tion price indices have been calculated, the corresponding can only be matched through the use of a model. Fisher type hedonic imputation index going from period t to t+1 can be formed by taking the geometric average of the 5.67 The same method can be applied going backwards two indices defined by (5.32) and (5.34): from the housing sales that took place in quarter t+1; take the parameters for the quarter t hedonic regression and ≡ [PHIL ] (5.35) 1/ 2 PHIF t ,t +1 t ,t +1 PHIP t ,t +1 price out all of the housing models that appeared in quar- ter t+1 and generate predicted prices, pˆnt (t + 1) , for these t = 1,...,13 t+1 models: 5.69 The resulting chained Laspeyres, Paasche and ˆn p t ˆ t Lt +1 + gˆ t (1 − dˆ t At +1 ) S t +1 (5.33) ˆt + β (t + 1) ≡ a Fisher imputation price indices, PHIL , PHIP and PHIF , based n n n t = 1,...,13; n = 1,...,N(t+1) on the data for the town of “A”, are plotted below in Figure 5.3 and are listed in Table 5.3. The three imputation indi- Now we have a set of “matched” quarter t prices for the ces are amazingly close. The Fisher imputation index is our models that appeared in period t+1 and we can form the preferred hedonic price index thus far; it is better than the following Paasche type hedonic imputation (or pseudo time dummy indices because imputation allows the price matched model) index, going from quarter t to t+1: of land and of quality adjusted structures to change in- N ( t +1) dependently over time, whereas the time dummy indices ∑1 p t +1 n shift the hedonic surface in a parallel fashion. The empiri- P t ,t +1 HIP ≡ n =1 N ( t +1) (5.34) cal results indicate that, at least for the present data set for ∑1 p ˆ (t + 1) t n the town of “A”, the Laspeyres imputation index provides n =1 a close approximation to the preferred Fisher imputation t = 1,...,13 index. Figure 5.3. Chained Laspeyres, Paasche and Fisher Hedonic Imputation Price Indices 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PHIL PHIP PHIF Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 63 5 Hedonic Regression Methods Table 5.3. Chained Laspeyres, Paasche and Fisher Hedonic Imputation Price Indices Quarter PHIL PHIP PHIF 1 1.00000 1.00000 1.00000 2 1.04234 1.04479 1.04356 3 1.06639 1.06853 1.06746 4 1.03912 1.03755 1.03834 5 1.04942 1.04647 1.04794 6 1.07267 1.07840 1.07553 7 1.08923 1.10001 1.09460 8 1.05689 1.06628 1.06158 9 1.09635 1.10716 1.10174 10 1.09945 1.10879 1.10411 11 1.11062 1.11801 1.11430 12 1.10665 1.11112 1.10888 13 1.09830 1.09819 1.09824 14 1.11981 1.11280 1.11630 Source: Authors’ calculations based on data from the Dutch Land Registry Figure 5.4. The Fisher Imputation Price Index, the Chained Stratified Sample Mean Fisher Price Index, the Linear Time Dummy Price Index and the Log Log Time Dummy Price Index 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PHIF PH5 PH3 PFCH Source: Authors’ calculations based on data from the Dutch Land Registry 5.70 To conclude: our two “best” indices are the Fisher with the log-log time dummy index PH 3 and the linear imputation index PHIF and the stratified chained Fisher in- time dummy index with quality adjusted structures PH 5 . dex PFCH . Overall, the imputation index PHIF should prob- All of the price indices except PH 3 show downward move- ably be preferred to PFCH since the stratified sample indices ments in quarters, 4, 8, 12 and 13 and upward movements will have a certain amount of unit value bias which will in the other quarters; PH 3 moves up in quarter 12 instead most likely be greater than any functional form bias in PHIF . of falling like the other indices. These two “best” indices are plotted in Figure 5.4  along 64 Handbook on Residential Property Prices Indices (RPPIs) Repeat Sales Methods 6 6 Repeat Sales Methods The Basic Repeat Sales 6.4 The following stochastic model explaining the log- arithm of the value (price) p n t for property n in period t Model can be found in the literature: ln p n t = P t + H nt + ε nt (6.1) 6.1 The repeat sales method was initially proposed by Bailey, Muth and Nourse (1963). They saw their procedure where P t is a common term for all properties (the log of as a generalization of the chained matched model methodol- “price level” in some region or city), H nt is a Gaussian ran- ogy applied by the pioneers in the construction of real estate dom walk that represents the drift in individual housing price indices like Wyngarden (1927) and Wenzlick (1952). value over time, and ε nt is a random error term or white The best-known repeat sales indices are the Standard and noise. Model (6.1) is often taken as the starting point for Poor’s/Case-Shiller Home Price Indices in the US, which deriving the estimating repeat sales equation. are computed for 20 cities (Standard and Poor’s, 2009). The 6.5 Another point of departure could be the con- Federal Housing Finance Agency (FHFA) also computes strained log-linear hedonic model (5.4), where the pa- a repeat sales index for the US,  (1) using a slightly differ- rameters β k of the price-determining characteristics are ent approach. Residex and the UK Land Registry compute constrained to be fixed over time. As “identical” properties repeat sales indices for Australian cities and for the UK, are compared, there is a second restriction involved: the respectively. (2) (amounts of the) characteristics of an individual property 6.2 As the name indicates, the method utilizes infor- are also assumed fixed over time. Denoting the k’th char- mation on properties which have been sold more than acteristic for property n by z nk , the constrained log-linear once. Because it is a matched-properties type of method, model now becomes K controlling for period-to-period differences in the sam- ln p n t = β 0t + ∑ β k z nk + ε nt (6.2) ple of properties is not required. However, because of the k =1 low incidence of resale units at times, it would not be very 6.6 A model for the logarithm of the change in value of useful to compute a repeat sales RPPI using the standard property n between two periods, say s and t (0 ≤ s < t ≤ T ) , matched model methodology and conventional index is found by subtracting (6.2) for those periods. It follows number formulae. Therefore, a stochastic model is pos- that tulated which “explains” the price changes of houses that ln p nt − ln p ns = ln( p n t / p ns ) = ( β 0t − β 0s ) + (ε nt − ε ns ) = ln P st + (ε nt − ε ns ) have been sold repeatedly. This t (dummy variable) regres- ln p n − ln p ns = ln( p n t / p s ) = ( β 0t − β 0s ) + (ε nt − ε ns ) = ln P st + (ε nt − ε ns ) (6.3) sion model is then estimated on the pooled data n(i.e., on the pooled price changes) across the sample period. Model (6.3) is essentially saying that, neglecting the error 6.3 The only information required to estimate a stand- term ε nt − ε ns , the logarithm of the price change is the same ard repeat sales regression equation is price, sales date and for all properties, denoted by P st . address of the properties; therefore this method is much 6.7 Now suppose we have a sample of houses that less data intensive than hedonic methods. Also, the repeat have been sold more than once over the sample period sales method controls by default for location at the finest t = 0,..., T for which we have data on transaction prices, level of detail (the address), something which hedonic re- hence on their price changes. The (holding) period be- gression methods are often unable to do with great preci- tween subsequent sales will differ among those properties. sion. (3) One problem with the repeat sales method howev- However, given that in model (6.3) all individual property er is that a dwelling unit that is sold at two different points prices are expected to change at the same rate (excluding in time is not necessarily identical due to such factors as random disturbances), the repeat sales data can be pooled depreciation and renovations. Consequently, the longer and the model estimated with the standard repeat sales the span of time between sales, the more questionable the equation constant-quality assumption underlying the repeat sales T approach becomes. ln( p n t / p ns ) = ∑g t Dnt + m nt (6.4) t =0 where Dnt is a dummy variable with the value 1 in the peri- od that the resale occurs, -1 in the period that the previous (1) The FHFA was established in 2008 as a combination of the former US Office of Federal sale occurs, and 0 otherwise; m it is again an error term. (4) Housing Enterprise Oversight (OFHEO), who published the repeat sales index until then, and the Federal Housing Finance Board (FHFB). Under the so-called classical assumptions, in particular (2) The Dutch Land Registry computed a repeat sales index for the Netherlands until 2007 when they changed over to a SPAR index, which is published jointly with Statistics Netherlands. For the SPAR method, see Chapter 7. ( ) However, the use of geospatial data to allow for spatial dependence in the hedonic 3 (4) Multiple resales are treated as independent observations. As noted by Shiller (1991), equation could remedy the omitted locational variables problem; see Chapter 5 and this should not be overly problematic because there is no overlap between the holding Hill (2011) for more details. periods of multiple resales. 66 Handbook on Residential Property Prices Indices (RPPIs) Repeat Sales Methods 6 that the errors have a zero mean and constant variance, distressed sales arising from, for example, divorce or job equation (6.4) can be estimated by OLS regression. Some loss, or speculative transactions. Jansen et al. (2008), us- multicollinearity may be present in the data, but solutions ing data from the Dutch Land Registry, found that houses to remedy this issue are limited if this is the case. resold within 12  months showed relatively strong price increases. 6.8 The repeat sales index going from period 0 to pe- riod t is obtained by exponentiating the corresponding re- 6.12 Reproducibility is one of the strengths of the repeat gression coefficients gˆ t : sales method. But if the procedure for excluding “atypical” ˆ t )(6.5) observations differs from time to time, then reproducibility PRS 0t = exp(γ might be compromised. The simplicity and attractiveness of the standard repeat sales model resides on the fact that it only requires dummy variables; no characteristics data other than the location Heteroskedasticity (address) are needed. (5) This, coupled with the straightfor- 6.13 Case and Shiller (1987, 1989) argued that changes ward way to compute the repeat sales price index, might in house prices include components whose variance in- explain part of the popularity of the method in the real es- creases with the interval of sales, so that the assumption of tate and housing literature. a constant variance of the errors is violated. They proposed 6.9 Wang and Zorn (1997) derived an analytical ex- a Weighted Least Squares (WLS) approach to correct for pression for the repeat sales index. It appears to have a this type of heteroskedasticity. The weights are derived by rather complex geometric structure. Thus, despite the fact regressing the squared residuals from the standard (OLS) that the idea of matching is easily understood, the method repeat sales regression on an intercept and the time interval may be difficult to explain in detail. Moreover, as men- between sales. A modified version of their weighted repeat tioned earlier, a geometric property price index may be un- sales approach is used by the US Federal Housing Finance desirable as a target, especially for a stock RPPI. A solution Agency to construct quarterly price indices for single- could be the use of an arithmetic version of the repeat sales family homes. It can be argued that the error variance will method, which was suggested by Shiller (1991). Standard be non-linear in time intervals (Calhoun, 1996), hence the and Poor’s (Case-Shiller) Home Price Indices are based squared OLS residuals are regressed on an intercept term, on the arithmetic repeat sales method (see Standard and the time interval and the square of the time interval. Poor’s, 2009). 6.14 Some studies found ambiguous results for heter- oskedasticity adjustment. Leishman, Watkins and Fraser (2002), using Scottish data, and Jansen et al. (2008), using Dutch data, applied the standard (OLS) repeat sales meth- Issues and Improvements od and various weighted methods. Both studies concluded that the standard method was not inferior. to the Basic Model 6.10 In this section we will discuss a number of issues Sample Selection Bias related to the repeat sales method and give a brief overview of extensions and improvements to the basic model that 6.15 An important problem with repeat sales indices is have been proposed in the literature. the possibility of sample selection bias. The problem is that some types of houses may trade more frequently on the market than other types so that they will be over-represent- Data Cleaning ed in the repeat sales sample (with respect to the stock of houses or the sales during some period). When these types 6.11 In practical applications, properties that were re- of houses exhibit different price changes, then the repeat sold very rapidly as well as those that were not resold for sales index tends to be biased. For example, if low quality long periods, have sometimes been excluded from the re- houses sell more frequently than high quality houses but peat sales regressions as such transactions might be “atypi- high quality houses rise in price at a slower rate, a repeat cal” and therefore bias the resulting price index. Clapp and sales index will tend to have an upward bias. Giacotto (1998) and Steele and Goy (1997) suggested elim- inating very short holds from the dataset as these could be 6.16 There are various reasons why the holding dura- tion of properties can be unevenly distributed. Life-cycle theories on property holding periods suggest that less ex- (5) In some countries, such as the UK and the Netherlands, the Land Registry collects pensive houses are traded more frequently; when people all transaction price data but only a very limited number of characteristics, like type of dwelling and of course address. It is therefore not surprising to see that in those move up the property ladder they will tend to move home countries repeat sales indices have been computed from Land Registry data. Note that the FHFE’s repeat sales index in the US is based on data obtained from Fannie Mae and less often. Lower transaction costs for less expensive prop- Freddie Mac for mortgages. erties, for instance due to lower stamp duties, may also Handbook on Residential Property Prices Indices (RPPIs) 67 6 Repeat Sales Methods result in a higher turnover rate of less expensive homes. In approximations for past or current values of houses that addition, the Buy-to-Let market in some countries is more have not been resold during the sample period. Some of active in lower ranges of the price segments. the data on which the repeat sales index would then be based would be pseudo rather than genuine repeat data. 6.17 Quite a few studies addressed the issue of hold- Most empirical studies on this issue are based on apprais- ing duration and sample selection bias in repeat sales price als of dwellings that are about to be re-financed. It has been indices; see for example Case, Pollakowski and Wachter suggested that appraisals tend to over-estimate the actual (1991) (1997), Cho (1996), Clapp, Giacotto and Tirtiroglu selling price of the property. But the magnitude of the bias (1991), Gatzlaff and Haurin (1997), Hwang and Quigley could depend on the purpose for which assessment infor- (2004), and Steele and Goy (1997). Not all of these stud- mation is collected. De Vries et al. (2009) investigated the ies found strong evidence of sample selection bias. Clapp, reliability of the Dutch appraisal data, which are collected Giacotto and Tirtiroglu (1991) did not find any system- on the government’s behalf for income and local tax pur- atic differences between the repeat sales sample and the poses, and concluded that the quality was quite satisfac- full sample of transactions over the long run. They argued tory and even improving over time. For more on the use that arbitrage typically forces prices for the repeat sample of assessment information in a repeat sales index and the to grow at the same rate as the prices for the full sample. removal of appraisal bias, see for example Geltner (1996), Wallace and Meese (1997) concluded that their repeat sales Edelstein and Quan (2006), and Leventis (2006). sample was sufficiently representative of all sales during the sample period in question. However, the “sample” of all 6.21 Similar to the multi-period time dummy method, housing sales themselves may not be representative of the the repeat sales method suffers from revision of previously total housing stock. computed indices: when additional repeat sales informa- tion becomes available, re-estimation will result in changes 6.18 Potential sample selection problems are inherent to the estimated coefficients and thus in the price indices to the repeat sales method. To some extent they can be cor- inferred. There have been few empirical studies on this is- rected for by stratifying the repeat sales sample. A problem sue to date, e.g. Clapp and Giaccotto (1999), Butler, Chang in this context is that the sub-samples may become very and Crews Cutts (2005), and Clapham et al. (2006). The small and produce volatile indices. Thus there may be an last authors found evidence to suggest that repeat-sales in- argument for smoothing the index numbers. Moreover, it dices are relatively less stable than time dummy hedonic can be argued that selling prices do not always exactly rep- indices. Note that revisions may be related to sample selec- resent the market values of the properties, which can be tion bias; when the sample period is extended and the coef- viewed as a latent variable. There may be transaction noise ficients re-estimated, sample selection bias might decrease involved that causes volatility of the measured price indi- as the number of observed repeat sales increases. ces. Francke (2010) proposed a smoothing procedure that takes into account the fact that selling prices of repeatedly sold properties depend on the time interval between sub- Quality Change sequent sales. 6.22 Repeat sales indices are estimated on the prem- ise that the quality of the individual properties (as meas- Inefficiency and Revision ured by their characteristics) is unchanging over time. It is sometimes argued that in the aggregate, the value of reno- 6.19 The repeat sales method is often criticized for be- vations is approximately equal to the value of depreciation. ing inefficient since, by its nature, it is wasteful of data. For individual dwelling units, however, this cannot be true This is true compared with the multi-period time dummy because over time, many units are demolished. One way to hedonic method: since only housing units that have sold avoid this issue is to limit the sample of repeated sales ob- more than once are used with the repeat sales method, the servations to those units for which their quality is thought resulting data set is usually much smaller than the sam- to be relatively constant from one sale period to the next. ple of transactions over a given period. On the other hand, Case and Shiller (1989), for example, “extracted [.…] data the longer the sample period, the more data will be used on houses sold twice for which there was no apparent qual- by the repeat sales method (as more and more houses will ity change”. The problem is that the price changes inferred have been resold). Thus, when the sample period grows may not be indicative of the price changes for the full sam- and more data are added, the efficiency of the repeat sales ple of repeated sales and may exacerbate the sample selec- method will increase faster than that of the hedonic ap- tion bias problem. (6) proach. Besides, the repeat sales method is efficient in the sense that it does not use any other housing characteristics than the unit’s address. 6.20 It is possible to augment a repeat sales dataset by (6) Meese and Wallace (1997) report that repeat sales units with changed characteristics tend to be larger and in worse condition than the average of units with single using assessment data (also referred to as appraisals) as transactions. 68 Handbook on Residential Property Prices Indices (RPPIs) Repeat Sales Methods 6 6.23 If information on maintenance and renovation ex- to an (say double) imputation hedonic price relative. He penditures was available at the micro level, this could be notes that: “If repeat-sales price relatives are not deemed used in the context of estimating a repeat sales (or hedonic) more reliable than double imputation price relatives, there regression model for housing. In practice this kind of in- is no reason to prefer hybrid methods to hedonic methods”. formation is often lacking. Abraham and Schauman (1991) In the end, the complexity of hybrid models most likely suggested adjusting the repeat sales index from aggregate makes them unsuitable for implementation by statistical data on renovation expenditures and make an adjustment agencies. for depreciation of the structures; see also Palmquist (1980) (1982). This approach to measuring net depreciation seems too crude and arbitrary to be suitable for the compilation of official statistics, however. Main Advantages 6.24 Shimizu, Nishimura and Watanabe (2010) recently developed a repeat sales method that takes net deprecia- and Disadvantages tion into account. Their method relies on an unknown taste 6.28 Below, the main advantages and disadvantages of parameter for which a guesstimate has to be made. While the repeat sales method are listed. The main advantages are: making an adjustment seems to be better than completely ignoring the (net) depreciation problem, making guesses • The repeat sales method in its basic form needs no might not be an attractive option for statistical agencies. characteristics other than address of the properties that are transacted more than once over the sample period. 6.25 Shiller (1993a) developed a repeat sales method Source data may be available from administrative re- that accounts for possible changes in housing characteris- cords such as those from the Land Registry. tics between first and second sales. The method involves in- cluding characteristics in a traditional repeat sales model. • Standard repeat sales regressions are easy to run and the Clapp and Giaccotto (1998) advocated the use of assessed price indices easy to construct. values at time of first and second sales as a parsimonious • The repeat sales method is a matched-model type of control for quality changes of the properties. Goetzmann method without any imputations. By construction, loca- and Spiegel (1997) suggested including a constant term tion is automatically controlled for. in the repeat-sales regression to capture average quality • The results are essentially reproducible provided that the change across all characteristics over the average holding treatment of outliers and possible corrections for heter- period. oskedasticity (as well as the choice between a geometric 6.26 Case and Quigley (1991) were the first to advo- or arithmetic method) are clearly described. cate hybrid models. Hybrid models exploit all sales data by 6.29 The main disadvantages of the repeat sales method combining repeat sales and hedonic regressions and ad- are: dress not only the quality change problem but also sample • The method is inefficient in the sense that it does not use selection bias and inefficiency problems. Case and Quigley all of the available transaction prices; it uses only infor- (1991) and Quigley (1995) used samples of single-sale and mation on units that have sold more than once during repeat-sale properties to jointly estimate price indices us- the sample period. ing generalized least squares regression. Hill, Knight and Sirmans (1997) undertook a similar though more general • The basic version of the method ignores (net) deprecia- exercise. Their model stacks two equations, a time dummy tion of the dwelling unit. (8) hedonic model (including age of the dwelling) and a repeat • There may be a sample selection bias problem in repeat sales model, which are jointly estimated using maximum sales data. likelihood. They used a characteristics prices method to • The method cannot provide separate price indices for derive the price indices; see Chapter 5, equation (5.9). (7) land and for structures. 6.27 The rationale for hybrid methods is to try and • The method cannot be used if indices are required for combine the best features of the repeat sales and hedon- very fine classifications of the type of property sold. In ic approaches. By combining both approaches, no data particular, if monthly property price indices are required, are discarded while repeat sales are still allowed to play a the method may fail due to a lack of market sales for prominent role in the index construction methodology. smaller categories of property. However, we agree with Hill (2011) who has difficulty ac- • In principle, estimates for past price change obtained by cepting that a repeat-sales price relative should be preferred the repeat sales method should be updated as new trans- action information becomes available. Thus the repeat (7) Other papers on the use of hybrid models include Clapp and Giaccotto (1992), Knight, Dombrow and Sirmans (1995), Englund, Quigley and Redfearn (1998), and Hwang and (8) As mentioned previously, there are ways to deal with this problem but they all appear Quigley (2004). to be too crude or too complex to be used for the compilation of official statistics. Handbook on Residential Property Prices Indices (RPPIs) 69 6 Repeat Sales Methods sales property price index could be subject to perpetual Chapters 4 and 5 to show the effect of having a very small revision. (9) repeat sales data set. 6.30 Haurin and Hendershott (1991) summarize the disadvantages of the repeat sales method as follows: “The method is subject to many criticisms: (1) it does An Example Using not separate house price change from depreciation, (2) renovation between sales is ignored, (3) the sample is Data for the Town of “A” not representative of the stock of housing, (4) attribute 6.31 Recall that, after deleting houses which were older prices may change over time, and (5) a large number of than 50 years at the time of sale and also deleting observa- sales are required before a reasonable repeat-sales sample tions which had land areas greater than 1200 m 2 , we were is obtained.” Donald R. Haurin and Patric H. Hendershott left with 2289 sales in the 14 quarter sample period, start- (1991; 260) ing in the first quarter of 2005 and ending in the second quarter of 2008. That is, we had an average of 163.5 single The fifth criticism in this quotation – the large number of sales of detached dwelling units per quarter for the Dutch sales required to obtain a reasonable data set with repeat town of “A”. A few houses were sold twice during the same sales– was not mentioned thus far. In the next section a quarter, and we deleted those short holds for the estimation basic OLS repeat sales index will be constructed using the of the repeat sales index (as they could be distressed sales). data for the town of “A” that was used earlier in We ended up with only 85 repeat sales over the 14 quarter period. The OLS repeat sales index computed using this small data set, labeled as PRS , is plotted in Figure 6.1 along with the chained stratified sample mean Fisher index, (9) In practice, this is not necessarily a big problem. A similar problem occurs when monthly scanner data are used in a CPI; a moving window of observations can be used PFCH , described in Chapter 4 and the hedonic imputation to construct a monthly CPI component where only the incremental inflation rate for the Fisher index, PHIF , described in Chapter 5. These three last month is used to update the index; see Ivancic, Diewert and Fox (2011) and de Haan and van der Grient (2011). price series are listed in Table 6.1. Figure 6.1. Repeat Sales Price Index, Chained Stratified Sample Fisher Price Index and Hedonic Imputation Fisher Price Index 1.18 1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 0.96 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PRS PHIF PFCH Source: Authors’ calculations based on data from the Dutch Land Registry 70 Handbook on Residential Property Prices Indices (RPPIs) Repeat Sales Methods 6 Table 6.1. Repeat Sales Price Index, Chained Stratified Sample Mean Fisher Price Index and Hedonic Imputation Fisher Price Index Quarter PRS PFCH PHIF 1 1.00000 1.00000 1.00000 2 1.00650 1.02396 1.04356 3 1.02802 1.07840 1.06746 4 1.02473 1.04081 1.03834 5 1.03995 1.04083 1.04794 6 1.04206 1.05754 1.07553 7 1.08663 1.07340 1.09460 8 1.07095 1.06706 1.06158 9 1.14474 1.08950 1.10174 10 1.15846 1.11476 1.10411 11 1.12709 1.12471 1.11430 12 1.13689 1.10483 1.10888 13 1.14903 1.10450 1.09824 14 1.12463 1.11189 1.11630 Source: Authors’ calculations based on data from the Dutch Land Registry 6.32 Compared to the other two price indices, the re- a price increase. Of course we cannot draw any definitive peat sales index turns out to be highly erratic during the conclusions from this simple example, but it does con- second half of the sample period. In quarter 14, the repeat firm that repeat sales methods require a large number sales index shows a price decrease whereas the hedonic of observations to estimate price indices with acceptable imputation and stratified sample means indices measure precision. Handbook on Residential Property Prices Indices (RPPIs) 71 Appraisal-Based Methods 7 7 Appraisal-Based Methods Introduction 7.5 The SPAR method has been used in New Zealand since the early 1960s and is currently also used in several European countries, notably in Denmark, the Netherlands 7.1 As was mentioned in previous chapters, the and Sweden. Given that a few countries around the world matched model methodology to construct price indices, are actually using the SPAR method, it is not surprising where prices of identical items are compared over time, that there is only a small though expanding literature avail- cannot be applied in the housing context. One of the able. It would appear that Bourassa, Hoesli and Sun (2006) reasons is the low incidence of re-sales and the resulting were the first to publish a paper on this method. According change in the composition of the properties sold. The re- to them, “the advantages and the relatively limited draw- peat sales method, which was discussed in Chapter 6, at- backs of the SPAR method make it an ideal candidate for tempts to deal with the quality mix problem by looking at use by government agencies in developing house price in- properties that were sold more than once over the sample dices”. Rossini and Kershaw (2006) found that the SPAR period. However, using only repeat-sales data could be very method outperformed several other methods in terms of inefficient since all single sales observations are “thrown reduced volatility of weekly index numbers. De Vries et al. out” and could also lead to sample selection bias. (2009) reported a higher precision of monthly SPAR in- 7.2 In several countries information on assessed values dices for the Netherlands compared with monthly repeat or appraisals of properties is available, which might be useful sales indices. Shi, Young and Hargreaves (2009) compared as proxies for selling prices or, more generally, market val- SPAR and repeat sales indices for New Zealand and found ues. In countries where they have been collected for tax pur- a rather low correlation on a monthly basis. poses, appraisals will typically be available for all properties 7.6 When the properties are reassessed and new ap- at a particular reference period. In a number of studies as- praisal data become available, the SPAR index can, and sessed values were used in addition to sale prices in a repeat probably should be, rebased. A long-term index series is ob- sales framework to reduce the problem of inefficiency and tained by “splicing” the existing and new series. Properties the potential problem of sample selection bias. For example, in the Netherlands are currently being re-valued each year, Gatzlaff and Ling (1994) used sale prices as the first meas- which makes it possible to construct an annually chained ure and appraisals as the second measure in a repeat “sales” RPPI, where the valuation period (which is January) serves regression. Clapp and Giaccotto (1998) did the reverse and as the link month. Shi, Young and Hargreaves (2009) ar- used appraisals as the first and selling prices as the second gued that bias could arise from frequent reassessments. De measure. Both studies found that these methods produced Vries et al. (2009) did not find any chain-link bias but ob- price indices similar to a standard repeat sales index. served that the standard error of the chained SPAR index 7.3 The above assessed-values repeat sales methods increases each time new appraisals are introduced because are based on pseudo price relatives in which the appraised an additional source of sampling error is added. values may be derived from different periods. But when as- sessed values for all properties are available that do relate to a single valuation period or reference date, then it will be possible to use the standard matched model method- ology. For each property sold in some comparison period The SPAR Method in Detail for which we have a sale price, a base period “price” – the 7.7 Suppose that we have samples of properties sold assessed value – is now available also. Price relatives with a at our disposal for the starting or base period 0  and for common base period – the valuation period – can then be comparison periods t (t = 1,..., T ) . As in earlier chapters, constructed, and these sale price appraisal ratios can be ag- the samples will be denoted by S (0) and S (t ) . In each gregated using a standard index number formula, though period we know the sale prices of all sampled properties; some re-scaling may be required. the price of property n in period t is represented by p n t . As mentioned before, houses that were sold in period t were 7.4 The use of a conventional matched model index generally not sold in period 0, so there is a lack of match- number formula simplifies the computation of the index ing. However, suppose that assessed values or appraisals because there is no need to use econometric techniques to are available for all properties in the housing stock, and estimate the index or to adjust for compositional change, that they relate to a single valuation period. The valuation as is the case with hedonic and repeat sales methods; see period will serve as the base period, and the appraisal for Chapters 5 and 6. Another feature of the sale price apprais- property n will be denoted by a n 0 . Thus, for each property al ratio method (SPAR) method discussed in the present belonging to the period t sample S (t ) we know both the chapter is that it is free from revisions because there is no period t selling price p n t and the base period assessed value modeling and pooling of data involved. Thus, in contrast to a n . In other words, for all n ∈ S (t ) we can establish a price 0 the repeat sales method and the multiperiod time dummy relative – a sale price appraisal ratio – p n t / an 0 , which can be hedonic method, previously computed price indices are used in a matched model framework to compute an RPPI. not re-estimated when new sales data become available. 74 Handbook on Residential Property Prices Indices (RPPIs) Appraisal-Based Methods 7 7.8 Although it would be possible to construct geo- where N (0) and N (t ) denote the number of properties metric appraisal-based indices, we will focus here on arith- sold in periods 0 and t (the respective sample sizes). metic indices as these seem to be more appropriate in the 7.11 The second expression on the right-hand side of housing context. The arithmetic appraisal-based index can (7.2) writes the SPAR index as the product of the ratio be defined as of sample means and a bracketed factor. Since the SPAR ∑1 p t n  pn t  method is a matched model method (with respect to periods 0  and t), the bracketed factor adjusts the ratio P = 0t n∈S ( t ) = ∑ w (t ) a 0  (7.1) 0  ∑1a AP n 0 n n∈S ( t )  n  of sample means for compositional changes occurring n∈S ( t ) between each period t and the base period 0. So, while Expression (7.1) describes a Paasche-type index because we short-term volatility is likely to be present due to period are using the comparison period sample S (t ) in both the to period mix changes, the SPAR method is expected numerator and the denominator. The quantities are equal to exhibit much less volatility than the ratio of sample to 1 as every property is basically a unique good. The con- means. struction of a Laspeyres-type price index would be prob- 7.12 The arithmetic SPAR index can be interpreted as lematic or even impossible: period t price information for a proxy for a sales based Paasche RPPI. (1) But many coun- dwelling units belonging to the base period sample S (0) tries, including EU member states, are typically aiming at a is only available for those few units, if any, that were resold Laspeyres index rather than a Paasche index. Stratification in period t. This means that the construction of a Fisher- could be used as a means to approximate this target index type index will not be feasible either. As shown by the sec- while using the SPAR method. The SPAR (Paasche) indi- ond expression, (7.1) can be written as a value-weighted ces at the stratum level will then be aggregated using base average of the sale price appraisal ratios p n t / an 0 , where the period expenditure share weights to obtain the overall ∑ weights wn (t ) = a n / n∈S ( t ) a n reflect the base period as- 0 0 0 “Laspeyres-type” index. The RPPI in the Netherlands is an sessed value shares with respect to the sample S (t ) . example of such a stratified SPAR approach, where region 7.9 The appraisal-based Paasche-type index, PAP 0t , given and type of house are used as stratification variables. The by (7.1) is obviously a matched model index. Accordingly, index is compiled monthly and published jointly with the there is no compositional change to account for when Dutch Land Registry Office. Stratification might also help comparing period t directly with period 0. However, as to account for any systematic differences between apprais- there is generally no overlap, the samples S (t ) in periods als and market values across regions or different types of t = 1,..., T will be completely different and compositional houses (de Vries et al., 2009; de Haan, van der Wal and de change will be present from one period to the next. Those Vries, 2009). period to period sample mix changes cannot be adjusted 7.13 The SPAR index can alternatively be interpreted for, which suggests that short-term volatility will most like- as a sample estimator of a stock RPPI. If in each period ly occur. This feature is not unique to the appraisal-based the properties sold are viewed as random samples from the index; we would expect to observe more or less the same base period housing stock, then the SPAR index is an es- for the Paasche-type hedonic imputation indices discussed timator of the Laspeyres stock RPPI. Properties sold that in Chapter 5. The similarity with the imputation Paasche were added to the stock after the base period should in this index will be addressed in the next section. case be excluded. (2) As mentioned in earlier chapters, the 7.10 The appraisal-based price index (7.1) does not sample of houses sold may not be representative of the total make use of the observed selling prices in the base period. stock so that sample selection bias could arise. Stratification As a result, the index will differ from 1 in the base period, will again be a helpful tool to mitigate this problem. which is problematic. However, this problem can easily be resolved by normalizing the indices by dividing them by the base period value. We then obtain the following arith- metic SPAR index: (1) Administrative data sets, particularly those from the land registry, typically contain all sales (excluding newly-built properties) in each period. From a sales point of view there ∑p  ∑p ∑p ∑ −1 t n 0 n  t n / N (t )  an 0 / N (0 is)  sampling involved. In this interpretation, the SPAR index has no sampling error, but no    n∈S ( 0 )  it does have error due to the use of appraisals, which are estimates of the “true” market PSPAR n∈S ( t ) n∈S ( 0 ) n∈S ( t ) 0t =  = values. ∑a  ∑  a n∈S ( t ) 0 n n∈S ( 0 ) 0 n   ∑p n∈S ( 0 ) 0 n / N ( 0 )   ∑ a0  n∈S ( t ) n /N (tIt (2) )  seem that properties which are new to the stock cannot even be used because may thenecessary appraisals are lacking. However, this depends on the appraisal system.  rental houses have been sold and are thus added to the stock of owner If former occupied housing, then they will have a base period appraisal value if rental houses are ∑p  ∑p ∑p ∑ −1 t n 0 n  t n / N (t )  an 0 / N ( 0)  also assessed. Moreover, if property taxes are uniformly based on period 0 valuations    n∈S ( 0 )  for a number of years, then the authorities would need those values for newly built PSPAR n∈S ( t ) n∈S ( 0 ) n∈S ( t ) 0t =  = (7.2) houses as well. The difficulty is of course that the authorities would have to “invent” an ∑a  ∑  a n∈S ( t ) 0 n n∈S ( 0 ) 0 n   ∑p n∈S ( 0 ) 0 n / N (0)   a / N (t )  0  n∈S ( t ) n ∑   assessed value for a new house in period 0, even if it did not exist in that period. Such assessments might be problematic and hence should probably be excluded from the computation of the index. Handbook on Residential Property Prices Indices (RPPIs) 75 7 Appraisal-Based Methods Methodological 7.18 Bourassa, Hoesli and Sun (2006) noted that the appraisals in New Zealand are derived from hedonic re- and Practical Issues gressions, but unfortunately they did not present the exact method. In Chapter 5 it was explained that there are differ- ent hedonic approaches and that the predicted prices – in Quality Change this case the appraisals – depend on the type of data used and the number of observations, the specified functional 7.14 Since the appraisals relate to the base period, in form, the variables included and other choices made. Thus, general the properties will have been valued at their base even though hedonic regression is the least arbitrary of the period characteristics. But for the SPAR index (7.1) to be a three assessment methods mentioned above, there can still constant quality price index, the appraisals should be eval- be a lot of uncertainty and error involved, which has an uated at characteristics of the comparison period. Thus, if unknown impact on the sale price appraisal ratios and the housing characteristics change over time, the SPAR meth- resulting SPAR index. od will not adjust for those changes, similar to the repeat 7.19 The use of comparable properties seems to be sales method. This is an important drawback. widespread. Chinloy, Cho and Megbolugbe (1997) com- 7.15 Yet in practice there could be some implicit adjust- pared a sample of U.S. private sector appraisals to selling ment for quality changes. In the case of the New Zealand prices. They suspected that the reliance on a relatively small SPAR index, Bourassa, Hoesli and Sun (2006) note: “the number of comparable houses leads to more volatility than base appraisal is adjusted for subsequent improvements can be observed in market-wide selling prices. More im- to the property that require a building permit”. If this is portantly perhaps, they found that appraisals exceeded sale done in real time, adjustments for major quality improve- prices in approximately 60 percent of the cases, leading to ments will indeed be made. However, apart from the fact an average upward bias of two percent. that not all property improvements require a building per- 7.20 In countries where official assessments are designed mit, it is unlikely that these adjustments adequately deal for property taxation purposes, like in the Netherlands, the with the net effect of improvements and depreciation of the assessed values may not to be too far off the mark since the structures. government has an incentive to make the assessments as 7.16 In the Netherlands there may also be some implicit large as possible in order to maximize tax revenue while quality adjustment in the SPAR index. The assessments are taxpayers have the opposite incentive to have the assess- typically carried out some time after the appraisal reference ments as small as possible. In the Netherlands the munici- month and may take into account major improvements to palities are responsible for making the assessments. The the properties. Furthermore, as mentioned above, the as- methods used differ across the municipalities. Some of sessments are nowadays performed every year. Annual them, for example the capital city of Amsterdam, use the chaining by itself could alleviate the problem of qual- comparable house method whereas others apparently use ity change if the updated appraisals properly account for some kind of hedonic regression method. De Vries et al. changes in the characteristics. Of course this will depend (2009) argued that Dutch authorities may in fact have an on the exact way the properties are valued, which may not incentive to make the assessments not too high to avoid be known to the index compilers. court procedures because households who feel the ap- praised value is too high can lodge an appeal. Quality of the Assessment Information Other Issues 7.17 Abstracting now from quality adjustment issues, the SPAR method is obviously dependent on the quality of 7.21 The advantage of the SPAR method as compared the assessment information. There are three broad ways in to hedonic regression methods is that information on only which assessments of (non-traded) properties can be car- a few property characteristics is needed: assessed values ried out: by using hedonic regression, by comparing them (relating to a common reference period), possibly some to similar traded properties, and by expert judgment. The stratification variables, and addresses to merge the data methods used differ among countries and sometimes even files if the selling prices and appraisals come from differ- within a particular country. In various countries, private ent sources. In the Netherlands, for example, transaction companies are engaged in mass appraisal. Although the prices and a limited number of stratification variables are details of the methods used are often not publicly avail- recorded by the Land Registry whereas the appraisals are able, some of those companies appear to combine he- from a second administrative data source. It is well known donic regression with local market information or expert that merging data files by address can be difficult, although judgment. in the Netherlands this does not seem to be a major issue. 76 Handbook on Residential Property Prices Indices (RPPIs) Appraisal-Based Methods 7 7.22 Data cleaning is another important practical is- βˆ ≅ 1 if the appraisal system works well. (4) Equation (7.5) 1 sue. The SPAR method is dependent on the quality of the will be used below to predict the “missing prices” in the de- appraisals. Some of the sale price appraisal ratios might nominator of the imputation Paasche index (7.3). be found implausible, perhaps because the appraisals are deemed “wrong”, and deleted from the data set. (3) Deleting 7.26 For convenience we first rewrite (7.3) as erroneous observations, such as obvious entry errors, is good practice. A cautious approach is called for, however, ∑ pn t / N (t ) ∑ pn0 / N (0) ∑ pn t / N (t ) ∑ ˆn p 0 / N (0) PIP = n∈S ( t ) n∈S ( 0 ) n∈S ( t ) n∈S ( 0 ) 0t = as deleting price relatives can lead to biased results. At least a rule for deleting outliers should be explicitly formulated n∈S ( 0 ) ∑ pn 0 / N (0) n∈S ( t ) ∑ pˆn 0 (t ) / N (t ) ∑ n∈S ( 0 ) pn 0 / N (0) ∑ n∈S ( t ) ˆn p 0 (t ) / N (t ) to inform users. pn t / N (t ) ∑ pn∑ 0 / N (0) ∑ pnt / N (t ) ∑ ˆn p 0 / N (0) PIP = n∈S ( t ) n∈S ( 0 ) n∈S ( t ) n∈ S ( 0 ) 0t = (7.6) pn 0 / N (0) ∑ pˆn 0 ∑ (t ) / N (t ) ∑ pn 0 / N (0) ∑ pˆn 0 (t ) / N (t ) n∈S ( 0 ) n∈S ( t ) n∈S ( 0 ) n∈S ( t ) A Regression-Based In the second step of (7.6) we have used Imputation Interpretation ∑ n∈S ( 0 ) pn 0 ∑ ˆn / N (0) = n∈S ( 0 ) p 0 / N (0) , which holds true be- cause the OLS regression residuals sum to zero. The first 7.23 In this section we will show that the SPAR method problem we face is that the housing characteristics should is essentially an imputations approach in which the “miss- be kept fixed when predicting the base period prices p ˆn 0 (t ) ing” base period prices are estimated from a linear regres- for n ∈ S (t ) . This is obviously not possible using equation sion of selling prices on appraisals. Recall first that the base (7.5). Thus, the first assumption is that of no quality change, period prices of the properties belonging to the period t and we accordingly replace p ˆn 0 ˆn (t ) in (7.6) by p 0 (0) = pˆn0 . sample S (t ) cannot be observed directly since those prop- Using (7.5) for both n ∈ S (0) and n ∈ S (t ) , equation (7.6) erties were generally not traded in period 0. We can try becomes to estimate the “missing” prices to obtain the imputation Paasche price index ∑p / N (t )  β t n  ˆ +β 0 ˆ 1 ∑an0 / N (0)   PIP = 0t n∈S ( t ) n∈S ( 0 )  ˆ  (7.7) ∑1 p t n ∑p ˆ n / N (0)  β 0 + β 1 0 ∑ a n / N (t )  0 P =0t n∈S ( t ) (7.3) n∈S ( 0 )  n∈S ( t )  ∑1 p ˆ (t ) IP 0 n ˆ Notice that if β 0 = 0 , that is, if the regression line passes n∈S ( t ) through the origin, (7.7) simplifies to the SPAR index (7.2), 7.24 The imputed value p ˆn 0 (t ) in (7.3) should predict ˆ . So, if the aim is to irrespective of the slope coefficient β the period 0 price for property n, evaluated at its period t 1 estimate an imputation Paasche index, the second assump- characteristics. Keeping the (quantities of the) characteris- tion underlying the SPAR method seems to be that the in- tics fixed is necessary to adjust for quality change. The use ˆ is negligible. tercept term β of hedonic imputation was discussed in Chapter 5. Hedonic 0 regression models explain the selling price of a property 7.27 The third assumption is that equation (7.5) holds in terms of a set of price-determining characteristics that for n ∈ S (t ) : the linear relationship between base period relate to the structure and the location. This section ad- selling prices and appraisals postulated and estimated for dresses a different type of regression-based imputation. the properties actually sold during the valuation or base period 0 (for n ∈ S (0) ) is assumed to hold also for proper- 7.25 Consider the following two-variable regression ties that were not sold. But this is a very restrictive assump- model for the base period: tion. While the linear relation can be tested for n ∈ S (0) , (5) pn 0 = β 0 + β1an 0 + ε n0 (7.4) it would be difficult if not impossible to test it for n ∈ S (t ) as the selling prices are “missing”. The presence of ap- Equation (7.4) is a simple descriptive model where sell- praisal bias, in the sense that the appraisals over- or un- ing prices are regressed on appraisals. We assume that this derestimate the unknown market values (the prices at model is estimated by Ordinary Least Squares (OLS) on which the properties would have been sold), can bias the the data of the base period sample S (0) . The predicted SPAR index. Bias in the SPAR index will particularly arise prices for n ∈ S (0) are ˆn p 0 =β ˆ +βˆ a 0 (7.5) 0 1 n ˆ where β 0 is the estimated intercept term and β ˆ the es- 1 (4) If the selling prices would be used as official valuations, then of course the values 0 and ˆ timated slope coefficient. We expect to find β 0 ≅ 0 and 1 would exactly hold and we would find a perfect fit of (7.4) to the period 0 data. (5) Van der Wal, ter Steege and Kroese (2006) and de Vries et al. (2009) compared Dutch government appraisals to selling prices. In the latter study the linear relationship (7.4) was explicitly tested (for the properties traded in the valuation month) for various (3) The example for the town of “A” at the end of this chapter shows that the removal of a valuation months. It turned out that the constant term was indeed very small and that relatively low number of outliers can have a substantial effect on the SPAR index. the slope coefficient did not significantly differ from 1. Handbook on Residential Property Prices Indices (RPPIs) 77 7 Appraisal-Based Methods if the “true” value of β1 for n ∈ S (t ) would be very differ- ent from β1 for n ∈ S (0) . An Example on Data 7.28 In this section we focused on the SPAR index for the Town of “A” as a sales RPPI. A related approach, where the appraisals serve as auxiliary information in a “generalized regression” 7.31 Using the data set for the town of “A”, which was (GREG) framework in order to estimate a stock based described in Chapter 4, a SPAR index was computed. Recall RPPI, was described by de Haan (2010b). The GREG meth- that this data set contained sales of detached houses for od uses population information on the appraisals instead 14 quarters, starting in the first quarter of 2005 and ending of sample information. He showed that the SPAR index is a in the second quarter of 2008. After some data cleaning – straightforward estimator of the GREG stock based index in particular deleting houses that were older than 50 years which, when applied to Dutch data, turned out to be almost at the time of sale were – a total of 2289 sales remained. as efficient. 7.32 To compute SPAR index numbers we also need assessed values for the properties sold. Our appraisal data relate to the first quarter (i.e., January) of 2005. Matching Main Advantages the sales data set and the appraisal data set was quite suc- cessful; 99.3 % of the selling prices could be matched with and Disadvantages the corresponding appraisals; i.e. for only 15 observations we could not find an appraisal, so these were deleted. The 7.29 The merits of the SPAR method are listed below. resulting SPAR index, PSPAR , is plotted in Figure 7.1  and The main advantages are: listed in Table 7.1, along with the hedonic imputation Fisher index, PHIF , described in Chapter 5, and the repeat • The SPAR method is essentially based on the standard sales index, PRS , estimated in Chapter 6. The trend of PSPAR matched model methodology and links up with tradi- is very similar to that of PHIF , but PSPAR is slightly more tional index number theory. volatile. • The method is computationally simple. 7.33 A potential drawback of the SPAR method is that • Information on housing characteristics is not required is entirely dependent on the accuracy of the appraisal data. in order to implement this method; the only informa- An inspection of the distribution of the sale price apprais- tion required is data on sale prices and appraisals. In al ratios indicated a number of big outliers. Specifically, some countries the data is available from administrative there were several observations with very high sale price sources such as the land registry, and usually covers all appraisal ratios (up to 10.5), in most instances as a result transactions (for resold properties). of unusually low appraised values. It is most likely that a • This method uses much more data than the repeat sales significant proportion of these outliers were recording method and hence there are fewer problems due to errors. Hence, we decided to delete the biggest outliers. sparse data. In particular, sample selection bias is likely to Following Statistics Netherlands data cleaning methods at be smaller. Also, the SPAR method does not suffer from the time, based on the distribution of the natural logarithm revision of previously calculated figures when new data of the sale price appraisal ratios, 26 observations were re- becomes available. moved for which the log of price ratio differed more than • Conditional on the data cleaning rules, the SPAR meth- 5 standard deviations from the mean. (8) We ended up with od is reproducible. 2248 observations. 7.30 The main disadvantages of the SPAR method are: 7.34 The improved SPAR index, labeled PSPAR* , comput- • The method cannot deal adequately with quality changes ed on the cleaned data set is also shown in Figure 7.1 and (major repairs or renovations and depreciation) of the Table 7.1. As can be seen, cleaning of the data had a sub- dwelling units. (6) stantial impact on the result: PSPAR* is much less volatile than the index PSPAR that was computed on the initial data • The SPAR method is dependent on the quality of the set. The trend was also affected: PSPAR* is generally lower base period assessment information. The exact way the than PSPAR due to the fact that most of the deleted ob- valuations are carried out may not always be clear and servations had unusually high sale price appraisal ratios. has an unknown impact on the results. • The method cannot decompose the overall property provided that the assessments decomposed the total assessed value of the property price index into land and structures components. (7) into land and structures components. Unfortunately, official assessments generally are made only once a year or once every few years. This low frequency information could however be used to check the land and structures price indices generated by hedonic (6) In countries where the assessments provide separate information on the value of the regression methods. structures and the value of the land, the SPAR index could in principle be adjusted by using (8) As a first step in the data cleaning procedure, Statistics Netherlands removed all exogenous information on the net depreciation of houses of the type being considered. properties with selling prices or appraisals below 10 000 or above 5 000 000 Euros. In ( ) If fresh property assessment information appeared every month or quarter, this 7 our data set, however, there were no such properties. Note that Statistics Netherlands information could be used to form separate price indices for both land and structures, recently changed the outlier detection and removal procedures. 78 Handbook on Residential Property Prices Indices (RPPIs) Appraisal-Based Methods 7 Figure 7.1 confirms that – using a relatively small data set period, in quarter 14, the difference amounts to 0.026 in- which covers a short time period – the SPAR method gen- dex points. At first sight this seems to suggest that PSPAR* erates more credible results than the standard repeat sales has a downward bias. However, a difference of the same method, especially after cleaning the data. magnitude (0.027 points) is already found in quarter 2. So if we had normalized both series to equal 1 in quarter 2, 7.35 A comparison of PSPAR* with the hedonic imputa- the two methods would have produced approximately the tion Fisher index PHIF reveals that in several periods, for same index value in quarter 14. This is an illustration of example in the last four quarters, the price changes accord- a general starting problem encountered when comparing ing to the two methods are in opposite directions. Also, volatile time series: the choice of starting or base period PSPAR* is generally lower than PHIF ; at the end of the sample affects the average difference during the sample period. Figure 7.1. SPAR Index, Hedonic Imputation Fisher Price Index and Repeat Sales Index 1.18 1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PSPAR PHIF PRS PSPAR Source: Authors’ calculations based on data from the Dutch Land Registry Table 7.1. SPAR Index, Hedonic Imputation Fisher Price Index and Repeat Sales Index Quarter PSPAR PHIF PRS PSPAR 1 1.00000 1.00000 1.00000 1.00000 2 1.01769 1.04356 1.00650 1.01693 3 1.05196 1.06746 1.02802 1.04204 4 1.02958 1.03834 1.02473 1.02883 5 1.02040 1.04794 1.03995 1.04273 6 1.09938 1.07553 1.04206 1.06655 7 1.09635 1.09460 1.08663 1.07076 8 1.08169 1.06158 1.07095 1.06604 9 1.10173 1.10174 1.14474 1.07378 10 1.11333 1.10411 1.15846 1.08609 11 1.08477 1.11430 1.12709 1.08396 12 1.10742 1.10888 1.13689 1.08869 13 1.13206 1.09824 1.14903 1.09642 14 1.08132 1.11630 1.12463 1.09003 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 79 Decomposing an RPPI into Land and Structures Components 8 8 Decomposing an RPPI into Land and Structures Components Introduction or resold houses we should account for the fact that older structures will be worth less than newer structures due to 8.1 In Chapter 3  it was mentioned that for national depreciation of the structures. Information on the age of accounts and CPI purposes, it will be useful or necessary the structure will therefore be needed. The next section to have a decomposition of the residential property price shows how depreciation can be incorporated into the mod- index (RPPI) into two components: a quality adjusted el, similar to what was done in the examples for the town price index for structures and a price index for the land of “A” presented in Chapter 5. It will also be shown how ad- on which the house is built. The present chapter outlines ditional land and structures characteristics can be included how hedonic regression can be utilized to derive such a de- as explanatory variables. composition. Hedonic regression methods were discussed in Chapter 5. 8.2 Some economic reasoning will be helpful to derive an appropriate hedonic regression model. Think of a prop- Accounting erty developer who is planning to build a structure on a particular property. He or she will likely determine the sell- for Depreciation ing price of the property after the structure is completed and Additional Characteristics by first calculating the total expected cost. This cost will be equal to the floor space area of the structure, say S square meters, times the building cost per square meter, g say, Depreciation plus the cost of the land, which will be equal to the cost per square meter, β say, times the area of the land site, L. 8.5 Suppose that in addition to information on the We follow a cost of production approach to modeling the selling price of property n at time period t, p n t , the land property price. That is, the functional form for the hedonic area of the property, Ln , and the structure area, S nt , infor- t price function is assumed to be determined by the supply mation on the age of the structure at time t, say Ant , is avail- side of the market, i.e., by independent contractors. (1) able. If straight line depreciation is assumed, the following model is a straightforward extension of (8.1) to include 8.3 Now consider a sample of properties of the same “existing” houses: general type, which have structure areas S nt and land areas Ltn in period t for n = 1,..., N (t ) ; the prices p n t are equal to costs pn t = β t Ltn + g t (1 − dAnt ) S nt + ε nt (8.2) of the above types plus error terms ε n which are assumed to t t = 1,..., T ; n = 1,..., N (t ) have means 0. This gives rise to the following hedonic regres- sion model for period t where β t and γ t are the parameters where the parameter d reflects the (straight line) depre- to be estimated: (2) ciation rate as the structure ages one additional period. If structure age is measured in years, d will probably be pn t = β t Ltn + g t S nt + ε nt (8.1) between 0.5  % and 2  %. This will be an underestimate of t = 1,..., T ; n = 1,..., N (t ) “true” depreciation because it will not account for major renovations or additions to the structure. The estimated The quantity of land L and the quantity of structures t n straight line depreciation rate in (8.2) should therefore be S nt associated with the sale of property n in period t are interpreted as a net depreciation rate; i.e., a gross deprecia- the only two property characteristics included in this very tion rate less the rate of renovations and additions to the simple model; the corresponding prices in period t are the structure. Model (8.2) will not work for very old structures price of a square meter of land β t and the price of a square since, if they are still in use, they will likely have been ex- meter of structure floor space g t . Separate linear regres- tensively renovated. (3) sions of the form (8.1) can be performed for each time pe- riod t in the sample. 8.6 Notice that (8.2) is a nonlinear regression model whereas (8.1) is a linear regression model. (4) Because the 8.4 The “builder’s model” (8.1) essentially relates to depreciation parameter d is regarded as fixed over time, newly-built dwellings. To make it applicable to existing (8.2) would have to be estimated as one nonlinear regres- sion over all time periods in the sample, whereas model (1) McMillen (2003) discusses a Cobb Douglas demand side model. On identification issues (8.1) can be run as a period by period linear regression. in hedonic regression models, see Rosen (1974). The period t price of land in model (8.2) will be the es- (2) Following Muth (1971), Thorsnes (1997; 101) has a related cost of production model. He assumed that the value of the property under consideration in period t, ρt, timate for the parameter β t and the price of a unit of a is equal to the price of housing output in period t, ρt, times the quantity of housing newly built structure for period t will be the estimate for output H(L,K) where the production function H is a CES function. Thus Thorsnes assumed that pt = ρt  H(L,K) = ρt [αLσ + βKσ]1/σ where ρt, σ, α and β are parameters, L is the lot size of the property and K is the amount of structures capital (in constant quality units). Our problem with this model is that there is only one independent time (3) See for example Meese and Wallace (1991; 320) who found that the age variable in their parameter ρt whereas our model has two, βt and γt for each t, which allow the price of hedonic regression model had the wrong sign. land and structures to vary freely between periods. (4) The model defined by (8.2) can be converted into a linear regression model. 82 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 γ t . The period t quantity of land for property n is Ltn and X nt 1 , X nt 2 ,..., X nK t that are price determining characteristics the period t quantity of structures for property n, expressed for the land on which the structure was built and a similar in equivalent units of a new structure, is (1 − dAnt ) S nt , where list of M characteristics Ynt1 , Ynt2 ,..., YnM t that are price deter- S nt is the floor space area of property n in period t. mining characteristics for the type of structure. The follow- ing equations generalize (8.2) to the present setup: (7) 8.7 Expensive properties probably have relatively large absolute errors compared to inexpensive properties, so it  K   M  pnt = β t 1 + ∑ X nk t η k  Ltn + γ t (1 − δAnt ) 1 + ∑ Ynm t λm  S nt + ε nt might be better to assume multiplicative rather than addi-  k =1   m=1  tive errors. However, we prefer an additive model specifica- t = 1,..., T ; n = 1,..., N (t )  (8.3) tion as the purpose is to decompose the aggregate value of housing into the sum of structures and land components; where the parameters to be estimated are now the K qual- the use of additive errors facilitates this decomposition. ity of land parameters, η1 ,...,η K , the M quality of structures When there is evidence of heteroskedasticity, weighted parameters, λ1 ,..., λM , the period t quality adjusted price for regressions can be considered. Several researchers sug- land β t and the period t quality adjusted price for struc- gested hedonic regression models that lead to additive de- tures g t . The quality adjusted amount of land, Ltn* , and the compositions of a property price into land and structures corresponding quality adjusted amount of structures, S nt* , components. (5) for property n in period t are defined as follows: 8.8 There is a potential problem with the above build-  K  er’s model, namely multicollinearity. Large structures are Ltn* ≡ 1 +  k =1 ∑X nk t η k  Ltn(8.4)  generally built on large plots of land, so that S nt and Ltn  M  could be highly collinear (i.e., the land-structure ratios S nt* ≡ 1 + ∑ Ynm t λm  S nt Ltn / S nt could be centered around a constant). This could  m=1  give rise to unstable estimates of the quality adjusted prices t = 1,..., T ; n = 1,..., N (t ) β t and g t for land and structures. As will be seen in the example using data for the Dutch town of “A”, the prob- 8.11 To illustrate how X and Y variables can be formed, lems of multicollinearity and instability do indeed occur. consider the list of explanatory variables in the hedonic In general, multicollinearity is not a major problem if the housing regression model reported by Li, Prud’homme goal is to produce an overall house price index, but it is and Yu (2006; 23). The following variables in their list of problematic if the goal is to produce separate price indices explanatory variables can be viewed as variables that affect for land and structures components. Some possible meth- structures quality; i.e., they are Y type variables: number ods for overcoming the multicollinearity problem will be of bedrooms, number of bathrooms, number of garages, suggested in later on. number of fireplaces, age of the unit, age squared of the unit, exterior finish is brick or not, dummy variable for new 8.9 The hedonic regression model (8.2) has the impli- units, unit has hardwood floors or not, heating fuel is natu- cation that the parameters would have to be re-estimated ral gas or not, unit has a patio or not, unit has a central built whenever the data for a new period became available. To in vacuum cleaning system or not, unit has an indoor or overcome this problem, a “rolling window” approach could outdoor swimming pool or not, unit has a hot tub unit or be applied. A suitable window length T would be chosen, (6) not, unit has a sauna or not, and unit has air conditioning the model defined by (8.2) or (8.3) would be estimated us- or not. The following variables can be assumed to affect the ing the data for the last T periods, and the existing series for quality of the land; i.e., they are X type location variables: price of land and for price of structures would be updated unit is at the intersection of two streets or not (corner lot or using the chain link factors β T / β T −1 and g T / g T −1 . This ap- not), unit is at a cul-de-sac or not, shopping center is near- proach will be illustrated below. by or not, and various suburb location dummy variables. 8.12 Equations (8.3) and (8.4) show how the quality Adding More Characteristics adjusted amounts of land and structures would be calcu- lated if the goal is to construct price indices for the sales of 8.10 The above basic nonlinear hedonic regression properties of the type that are included in the hedonic re- framework can be generalized to encompass the tradi- gression model. If the goal is to construct price indices for tional array of characteristics used in real estate hedonic the stock of properties of the type included in the regres- regressions. Suppose that we can associate with each sion, then the construction of appropriate weights becomes property n transacted in period t a list of K characteristics more complex. These weighting problems will be discussed in the next section. (5) See Clapp (1980), Francke and Vos (2004), Gyourko and Saiz (2004), Bostic, Longhofer and Redfearn (2007), Diewert (2007), Francke (2008), Koev and Santos Silva (2008), Statistics Portugal (2009), Diewert, de Haan and Hendriks (2010) (2011) and Diewert (2010). ( ) The model becomes a modified adjacent period hedonic regression model for T = 2. 6 (7) This generalization was suggested by Diewert (2007). Handbook on Residential Property Prices Indices (RPPIs) 83 8 Decomposing an RPPI into Land and Structures Components Aggregation and Weighting 8.15 As was the case with stratification methods, it is now necessary to consider how to construct an RPPI for Issues: Indices for Sales the stock of residential properties when hedonic regression methods are used. The period t hedonic cell prices PLr t and versus Stocks of Housing PSr defined by the region r counterparts to (8.5) and (8.6) t can still be used as cell prices to construct stock price indi- 8.13 As was explained in Chapter 5, the construction of ces for land and structures, but the counterpart quantities an RPPI for the sales of property using standard hedonic QLrt and QSrt defined by (8.7) and (8.8) are no longer ap- regression techniques is fairly straightforward. Typically, a propriate; these quantities need to be replaced by estimates separate hedonic regression of the type defined by (8.3) will that apply to the total stock of dwelling units in the region be run for each locality or region in a country. (8) Recall that (or some other reference population) for regression r at once a particular regression has been run, period t quality time t, say QLr t* and QSrt* , for r = 1,..., R . Thus, the counter- adjusted prices for land, PLt , and for structures, PSt , for the part summations in (8.7) and (8.8) are now taken over the region under consideration can be defined in terms of the entire stock of dwellings in region r in period t instead of estimated parameters for the model as follows: just the dwelling units that were sold in period t. Period  t PLt ≡ β t (8.5) information on the quantity of land Ltnr for every unit n in the region that is in scope for the hedonic regression t = 1,..., T model m is now required, along with the accompanying PSt ≡ g t (8.6) characteristics information X nrk t for every land character- istic k, as well as data on the quantity of the structures S nr t , t = 1,..., T along with the accompanying characteristics information The corresponding quality adjusted quantities of land and Ynrm t for every structures characteristic m. With these new structures for the region, say QL t and QSt can also be de- population quantity weights, the rest of the details of the fined in terms of the estimated parameters using defini- index construction are the same as was the case for the tions (8.4) above as follows: sales RPPI. N (t ) N (t )  K  8.16 In order to construct appropriate period t popula- QL t ≡ ∑L = ∑ n =1  1+ ∑ X t* n n =1 k =1 t nk η k  Ltn (8.7)  tion stock weights, it will be necessary for the country to have census information on the housing stock with enough t = 1,..., T details on each dwelling unit in the stock so that the re- quired information on the quantity of land and structures N (t ) N (t )  M  QSt ≡ ∑S t* n = ∑  1+ ∑Y t nm λm  S nt (8.8)  and the accompanying characteristics can be calculated. If n =1 n =1 m=1 information on new house construction (plus the required t = 1,..., T characteristics data) and on demolitions is available in a 8.14 If hedonic regressions, for say R regions, of the timely manner, the census information can be updated type defined by (8.3) have been run for the T periods of and period t estimates for the constant quality amounts data, then the algebra associated with (8.5)-(8.8) can be of land and structures, the QLr t* and QSr t* , can be approxi- repeated for each region r. Denote the resulting prices mated in a timely manner. Hence, stock RPPIs for land and quantities for region r that are the counterparts to and structures can be constructed using Fisher indices, (8.5)-(8.8) by PLr t , PSr t , QLr t and QSr t for r = 1,..., R and as was the case for the sales RPPI. If timely data on new t = 1,..., T . Now Fisher (sales) RPPIs for land can be con- construction and demolitions is unavailable, it may only structed using the regional price and quantity data for be possible to construct fixed base Laspeyres type price land, PLt ≡ [ PLt1 ,..., PLR ] and QL ≡ [QL indices using the quantity weights from the last available 1 ,..., QLR ], for each time t t t t period t (t = 1,..., T ) . Similarly, Fisher (sales) RPPIs for housing census. structures can be constructed using the price and quan- 8.17 If census information is not available at all (or if tity data for structures in each period t, PSt ≡ [ PSt1 ,..., PSR t ] data on the characteristics of the dwelling units is miss- and QS ≡ [QS 1 ,..., QSR ], for t = 1,..., T . ( ) t t t 9 ing), it still may be possible to approximate RPPIs for land and structures using hedonic regression techniques. If (8) Separate hedonic regressions may also be run for different types of property as well as characteristics data on the residential properties that are for different locations. However, cost considerations may mean that a comprehensive system of regressions covering all properties in the country cannot be implemented so sold in each period is stored over a large period of time, that there will only be a sample of representative hedonic regressions. The aggregation an approximate distribution of dwelling units by type can issues in the sampling case are too complex to be considered here; the exact details for constructing a national index would depend on the nature of the sampling design. be constructed. This information may then be used to ap- ( ) As was the case for stratification methods, fixed base or chained indices could be proximate a stock based RPPI in the manner explained 9 constructed. Rolling window hedonic regressions could also be run. The rolling window approach will be explained later. above. 84 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 Main Advantages We have data on sales of detached dwellings for 14 quar- ters, starting in the first quarter of 2005. Recall the notation and Disadvantages used above and in Chapters 4 and 5: there were N (t ) sales of detached houses in quarter t, where p n t is the selling 8.18 This section summarizes the main advantages price of house n. There is information available on three and disadvantages of using hedonic regression methods to characteristics: area of the plot in square meters, Ltn ; floor construct an RPPI for land and structure components. The space area of the structure in square meters, S nt ; and age in main advantages are: decades of house n in period t, Ant . • If the list of available property characteristics is suffi- ciently detailed, the method adjusts for both sample mix The Simple Case changes and quality changes of the individual houses. 8.21 The simple hedonic regression model defined by • Price indices can be constructed for different types of (8.2) will be estimated on this data set and is repeated here dwellings and locations through a proper stratification for convenience: of the sample. Stratification has a number of additional advantages. pn t = β t Ltn + g t (1 − dAnt ) S nt + ε nt (8.9) • The method is probably the most efficient method for t = 1,...,14; n = 1,..., N (t ) making use of the available data. The parameters to be estimated are β t (i.e., the price of • The method is virtually the only method that can be land in quarter t), g t (the price of constant quality struc- used to decompose the overall price index into land and tures in quarter t) and δ (the common depreciation rate for structures components. all quarters). Model (8.9) has 14 unknown β t parameters, 8.19 The main disadvantages of the hedonic regression 14 unknown g t parameters and one unknown δ or 29 un- approach are: known parameters in all. (10) • The method is data intensive since it requires data on all 8.22 The R2  for this model was equal to .8847, which relevant property characteristics (in particular, the age, is the highest yet for regressions using the data set for the type and the location of the properties in the sample the town of “A”. The log likelihood was -10642.0, which as well as information on the structure and lot size) so it is considerably higher than the log likelihoods for the is relatively expensive to implement. two time dummy regressions that used prices as the de- pendent variable; recall the regression results associated • The method may not lead to reasonable results due to with the construction of indices PH 4 and PH 5 defined in multicollinearity problems. Chapter  5  where the log likelihoods were -10790.4  and • While the method is essentially reproducible, different -10697.8. The estimated decade straight line net deprecia- choices can be made regarding the set of characteristics tion rate was 0.1068 (0.00284). entered into the regression, the functional form for the 8.23 The estimated land price series β ˆ 14 (rescaled ˆ 1 ,..., β model, the stochastic specification, possible transforma- tions of the dependent variable, etc., which could lead to to equal 1 in quarter 1), labeled PL1 , and quality adjusted varying estimates of overall price change. price series for structures γˆ 1 ,..., γˆ 14 (rescaled also), la- beled PS 1 , are plotted in Figure 8.1 and listed in Table 8.1. • The general idea of the hedonic method is easily under- Using these price series and the corresponding quantity stood but some of the technicalities may not be easy to data for Neach quarter t, i.e., the amount of land transacted, explain to users. ∑ (t ) Lt ≡ n=1 Ltn , Nand the quantity of constant quality struc- ∑ ˆAt ) S t , an overall property price in- (t ) tures, S t* ≡ n=1 (1 − d n n dex has been constructed using the Fisher formula. This overall index, labeled P1 , is also plotted in Figure 8.1 and Application on Data listed in Table 8.1. For comparison purposes, the Fisher hedonic imputation index from Chapter 5, PHIF , is also for the Town of “A”: presented. Preliminary Approaches (10) Model (8.9) is similar in structure to the hedonic imputation model described earlier except that the present model is more parsimonious; there is only one depreciation 8.20 The general techniques explained in this chapter rate, as opposed to 14 depreciation rates in the imputation model defined by will now be illustrated using the data set for the Dutch equations (5.25), and there is no constant term. The important factor in both models is that the prices of land and quality adjusted structures are allowed to vary independently town of “A”, which was described at the end of Chapter 4. across time periods. Handbook on Residential Property Prices Indices (RPPIs) 85 8 Decomposing an RPPI into Land and Structures Components Figure 8.1. The Price of Land (PL1), the Price of Quality Adjusted Structures (PS1), the Overall Cost of Production House Price Index (P1) and the Fisher Hedonic Imputation House Price Index 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PL1 PS1 P1 PHIF Source: Authors’ calculations based on data from the Dutch Land Registry Table 8.1. The Price of Land (PL1), the Price of Quality Adjusted Structures (PS1), the Overall Cost of Production House Price Index (P1) and the Fisher Hedonic Imputation House Price Index Quarter PL1 PS1 P1 PHIF 1 1.00000 1.00000 1.00000 1.00000 2 1.29547 0.91603 1.04571 1.04356 3 1.42030 0.89444 1.07482 1.06746 4 1.12290 0.99342 1.03483 1.03834 5 1.25820 0.94461 1.05147 1.04794 6 1.09346 1.08879 1.08670 1.07553 7 1.26514 1.01597 1.09941 1.09460 8 1.13276 1.03966 1.06787 1.06158 9 1.31816 0.98347 1.09713 1.10174 10 1.08366 1.13591 1.11006 1.10411 11 1.32624 1.00699 1.11782 1.11430 12 1.30994 1.00502 1.11077 1.10888 13 0.94311 1.17530 1.09373 1.09824 14 1.50445 0.9032 1.11147 1.11630 Source: Authors’ calculations based on data from the Dutch Land Registry 8.24 It can be seen that the new overall hedonic price between the land and quality adjusted structures variables, index based on a cost of production approach to the he- which leads to highly unstable estimates for the prices of donic functional form, P1 , is very close to the Fisher he- land and structures. donic imputation index PHIF . However, the price series for land, PL1 , and the price series for quality adjusted struc- tures, PS 1 , are not credible at all: there are large random The Use of Linear Splines fluctuations in both series. Notice that when the price of 8.25 There is a tendency for the price of land per land spikes upwards, there is a corresponding dip in the meter squared to decrease for large lots. In order to ac- price of structures. This is a clear sign of multicollinearity count for this, a linear spline model for the price of land 86 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 will be used. (11) For lots that are less than 160  m2, it is assumed that the cost of land per meter squared is β St VLS t ≡ ∑ βˆ L (8.13) n∈S S ( t ) t S t n in quarter  t. For properties that have lot sizes between t = 1,...,14 160  m2  and 300  m2, it is assumed that the cost of land changes to a price of β M t per additional square meter in quarter t. Finally, for plots above 300  m2, the marginal VLM t ≡ ∑{βˆ [160] + βˆ n∈S M ( t ) t S t M [ Ltn − 160]}(8.14) price of an additional unit of land is set equal to β Lt per t = 1,...,14 square meter in quarter t. Let the sets of sales of small, medium and large plots be denoted by S S (t ) , S M (t ) and S L (t ) , respectively, for t = 1,...,14. For sales n of properties VLL t ≡ ∑{βˆ [160] + βˆ n∈S L ( t ) t S t M ˆ t [ Lt − 300]}(8.15) [140] + β L n that fall into the small land size group during quarter t, t = 1,...,14 the hedonic regression model is given by (8.10); for the medium group by (8.11) and for the large land size group by (8.12): LtLS ≡ ∑ L (8.16) t n n∈S S ( t ) t = 1,...,14 p = β L + g (1 − dA ) S + ε (8.10) t n t S t n t t n t n t n t = 1,...,14; n ∈ S S (t ) LtLM ≡ ∑ L (8.17) n∈S M ( t ) t n t = 1,...,14 pn t = β St [160] + β M t [ Ltn − 160] + g t (1 − dAnt ) S nt + ε nt (8.11) t = 1,...,14; n ∈ S S (t ) LtLL ≡ ∑L t n (8.18) n∈S L ( t ) t = 1,...,14 p = β [160] + β [140] + β [ L − 300] + g (1 − dA ) S + ε , t n t S t M t L t n t t n t n t n The corresponding average quarterly prices, P , PLM t and t LS PLL , for the three types of lot are defined as the above val- t t = 1,...,14; n ∈ S S (t ) (8.12) ues divided by the above quantities: 8.26 Estimating the model defined by (8.10)-(8.12) PLS t ≡ VLS t / LtLS ; PLM t ≡ VLM t / LtLM ; PLL t ≡ VLL t / LtLL (8.19) on the data for the town of “A”, the estimated decade de- preciation rate was d ˆ = 0.1041 (0.00419). The R2 for this t = 1,...,14 model was .8875, which is an increase over the previous 8.28 The average land prices for small, medium and no-splines model where the R2  was .8847. The log likeli- large lots defined by equation (8.19) and the correspond- hood was -10614.2 (an increase of 28  from the previous ing quantities of land defined by (8.16)-(8.18) can be used model’s log likelihood.) The first period parameter values ˆ 1 = 281.4 to construct a chained Fisher land price index, which is for the three marginal prices for land were β ˆ = 380.4 (48.5) and β S ˆ = 188.9 (27.5). In other denoted by PL 2 . This index is plotted in Figure 8.2  and (55.9), β 1 1 M L listed in Table 8.2. As before, the estimated quarter t price words, in quarter 1, the marginal cost per m2 of small lots is per meter squared of quality adjusted structures is gˆ t estimated to be 281.4 Euros per m2, for medium sized lots, and the quantity of constant quality structures is given by the estimated marginal cost is 380.4 Euros/m2, and for large ∑ ˆAt ) S t . The structures price and quantity N (t ) lots, the estimated marginal cost is 188.9  Euros/m2. The S t* ≡ n=1 (1 − d n n first period parameter value for quality adjusted structures series gˆ and S were combined with the three land price t t* is gˆ 1 = 978.1 Euros/m2 with a standard error of 82.3. The and quantity series to form a chained overall Fisher house lowest t statistic for all of the 57 parameters was 3.3, so all price index P2 , which is also graphed in Figure 8.2  and of the estimated coefficients in this model are significantly listed in Table 8.2. The constant quality structures price in- different from zero. dex PS 2 (which is a normalization of the series γ ˆ 1 ,..., γˆ 14 ) is presented as well. 8.27 Once the parameters for the model have been esti- mated, then in each quarter t, the predicted value of land for 8.29 The overall house price index resulting from the small, medium and large lot sales, VLS t , VLM t and VLL t , respec- spline model, P2 , is fairly close to the Fisher hedonic im- tively, can be calculated along with the associated quantities putation index PHIF . However, the spline model does not of land, LtLS , LtLM and LtLL , as follows: generate sensible series for the price of land, PL 2 , and the price of structures, PS 2 : both series are extremely volatile but in opposite directions. As was the case with the pre- (11) This approach follows that of Diewert, de Haan and Hendriks (2010) (2011). The use of vious cost of production model, the present model suffers linear splines to model nonlinearities in the price of land as a function of lot size is due to Francke (2008). from a multicollinearity problem. Handbook on Residential Property Prices Indices (RPPIs) 87 8 Decomposing an RPPI into Land and Structures Components 8.30 Comparing Figures 8.1 and 8.2, it can be seen that this pattern reverses. This instability is again an indication in Figure 8.1  the price index for land is above the over- of multicollinearity. In the following section an attempt to all price index for the most part and the price index for cure this problem will be made by imposing monotonicity structures is below the overall index while in Figure 8.2, restrictions on the prices of the constant quality structures. Figure 8.2. The Price of Land (PL2), the Price of Structures (PS2), the Overall Price Index Using Splines on Land (P2) and the Fisher Hedonic Imputation Price Index 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PL2 PS2 P2 PHIF Source: Authors’ calculations based on data from the Dutch Land Registry Table 8.2. The Price of Land (PL2), the Price of Structures (PS2), the Overall Price Index Using Splines on Land (P2) and the Fisher Hedonic Imputation Price Index Quarter PL2 PS2 P2 PHIF 1 1.00000 1.00000 1.00000 1.00000 2 1.10534 0.99589 1.04137 1.04356 3 1.02008 1.09803 1.06465 1.06746 4 1.05082 1.02542 1.03608 1.03834 5 0.99379 1.08078 1.04294 1.04794 6 0.74826 1.31122 1.06982 1.07553 7 0.93484 1.20719 1.08912 1.09460 8 0.77202 1.26718 1.05345 1.06158 9 1.19966 1.01724 1.09425 1.10174 10 0.77139 1.34813 1.09472 1.10411 11 0.92119 1.24884 1.10596 1.11430 12 0.97695 1.19188 1.09731 1.10888 13 0.84055 1.27531 1.08811 1.09824 14 1.29261 0.97875 1.10613 1.11630 Source: Authors’ calculations based on data from the Dutch Land Registry 88 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 An Approach Based a decrease of 16.3  over the previous unrestricted model. Eight of the 13  new parameters φ t are zero in this mo- on Monotonicity Restrictions notonicity restricted hedonic regression. The first period parameter values for the three marginal land prices are β ˆ 1 = 380.3 (41.0) and β ˆ 1 = 278.6 (37.2), β ˆ 1 = 188.0 ; 8.31 It is likely that Dutch construction costs did not S M L fall significantly during the sample period.  (12) If this is these values are almost identical to the corresponding es- indeed the case, monotonicity restrictions on the quarterly timates in the previous unrestricted model. The first pe- prices of quality adjusted structures, γ 1 , γ 2 , γ 3 ,..., γ 14 , can riod parameter estimate for quality adjusted structures is be imposed on the hedonic regression model (8.10)-(8.12) gˆ 1 = 980.5 (49.9) Euros/m2., which is little changed from by replacing the constant quality quarter t structures price the previous unrestricted estimate of 978.1 Euros/m2. parameters by the following sequence of parameters 8.33 Once the parameters for the model have been esti- for the 14 quarters: g 1 , g 1 + (φ 2 ) 2 , g 1 + (φ 2 ) 2 + (φ 3 ) 2 ,..., mated, convert the estimated φ t parameters into estimated γ 1 + (φ 2 ) 2 + (φ 3 ) 2 + ... + (φ 14 ) 2, where φ , φ ,..., φ are sca- 2 3 14 parameters using the following recursive equations: lar parameters. ( ) For each quarter t starting at quarter 2, 13 the price of a square meter of constant quality structures gˆ t +1 ≡ gˆ t + (φˆ t ) 2 (8.19) g t is thus equal to the previous period’s price γ t −1 plus t = 2,...,14 the square of a parameter φ t −1 , (φ t −1 ) 2 . Now replace this reparameterization of the structures price parameters g t Now use equations (8.13)-(8.19) in the previous section in in (8.10)-(8.12) in order to obtain a linear spline model order to construct a chained Fisher index of land prices, for the price of land with monotonicity restrictions on the which is denoted by PL 3 . This index is plotted in Figure price of constant quality structures. 8.3 and listed in Table 8.3. As in the previous two models, 8.32 Implementing this new model using the data for the estimated period t price for a squared meter of quality the Dutch town of “A”, the estimated decade depreciation adjusted structures is gˆ t and the corresponding quantity rate was dˆ = 0.1031 (0.00386). The R2 for this model was ∑ ˆAt ) S t . N (t ) of constant quality structures is S t* ≡ n=1 (1 − d n n .8859, a drop from the previous unrestricted spline model The price and quantity series gˆ and S were combined t t* where the R2 was .8875. The log likelihood was -10630.5, with the three land price and quantity series to construct a chained overall Fisher house price index P3 which is also graphed in Figure 8.3 and listed in Table 8.3. The constant (12) Some direct evidence on this assertion will be presented in the following section. (13) This method for imposing monotonicity restrictions was used by Diewert, de Haan and quality structures price index PS 3 (a normalization of the Hendriks (2010) with the difference that they imposed monotonicity on both structures series γˆ 1 ,..., γˆ 14) may be found in Figure 8.3 and Table 8.3 as and land prices, whereas here, monotonicity restrictions are imposed on structures prices only. well. Figure 8.3. The Price of Land (PL3), the Price of Quality Adjusted Structures (PS3), the Overall House Price Index with Monotonicity Restrictions on Structures (P3) and the Overall House Price Index Using Splines on Land (P2) 1.3 1.2 1.1 1.0 0.9 0.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PL3 PS3 P2 P3 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 89 8 Decomposing an RPPI into Land and Structures Components Table 8.3. The Price of Land (PL3), the Price of Quality Adjusted Structures (PS3), the Overall House Price Index with Monotonicity Restrictions on Structures (P3) and the Overall House Price Index Using Splines on Land (P2) Quarter PL3 PS3 P3 P2 1 1.00000 1.00000 1.00000 1.00000 2 1.10047 1.00000 1.04148 1.04137 3 1.07431 1.05849 1.06457 1.06465 4 1.00752 1.05849 1.03627 1.03608 5 0.99388 1.08078 1.04316 1.04294 6 0.89560 1.20300 1.07168 1.06982 7 0.93814 1.20300 1.08961 1.08912 8 0.85490 1.20300 1.05408 1.05345 9 0.95097 1.20300 1.09503 1.09425 10 0.94424 1.21031 1.09625 1.09472 11 0.96514 1.21031 1.10552 1.10596 12 0.94596 1.21031 1.09734 1.09731 13 0.92252 1.21031 1.08752 1.08811 14 0.96262 1.21031 1.10427 1.10613 Source: Authors’ calculations based on data from the Dutch Land Registry 8.34 The new overall house price index P3 that imposed of growth over the study period across all cities in the monotonicity on the quality adjusted price of structures in Netherlands, the information on construction costs can be Figure 8.3 can hardly be distinguished from the previous used to eliminate the multicollinearity problem encoun- overall house price index P2 , which was based on a similar tered in the previous sections. hedonic regression model except that the movements in 8.37 Recall equations (8.10)-(8.12) above. These are the the price of structures were not restricted. The fluctuations estimating equations for the unrestricted hedonic regres- in the price of land and quality adjusted structures are no sion model based on costs of production. In the present longer violent. section, the constant quality price parameters for the struc- 8.35 While the above results seem “reasonable”, the ear- tures, the g t for t = 2,...,14 in (8.10)-(8.12), are replaced ly rapid rise in the price of structures and the slow growth by the following numbers, which involve only the single in structures prices from quarter 6 to 14 are not very likely. unknown parameter g 1 : (15) In the following section, one more method for extracting separate structures and land components out of real estate γ t = γ 1 µ t(8.20) sales data will therefore be tried. t = 2,...,14 where m is the statistical agency’s construction cost price t index for the location and the type of house under con- sideration, normalized to equal 1  in quarter 1. The new An Approach Based hedonic regression model is again defined by equations (8.10)-(8.12) except that the 14  unknown g t parameters on Exogenous Information are now defined by (8.20), so that only g 1 needs to be es- on the Price of Structures timated. The number of parameters to be estimated in this new restricted model is 44 whereas the old number was 57. 8.36 Many countries have new construction price indi- 8.38 Using the data for the town of “A”, the estimated ces available on a quarterly basis. This is the case for the decade depreciation rate was dˆ = 0.1028 (0.00433). The Netherlands. (14) If one is willing to make the assump- R2 for this model was .8849, a small drop from the previ- tion that construction costs for houses have the same rate ous restricted spline model, where the R2 was .8859, and a larger drop from the unrestricted spline model R2 in sec- tion 8.5, which was .8875. The log likelihood was -10640.1, (14) From the Statistics Netherlands (2010) online source, Statline, the following series was downloaded for the New Dwellings Output Price Index for the 14 quarters in our sample of house sales: 98.8, 98.1, 100.3, 102.7, 99.5, 100.5, 100.0, 100.3, 102.2, 103.2, 105.6, 107.9, (15) The technique suggested here for decomposing property prices into land and 110.0, 110.0. This series was normalized to 1 in the first quarter by dividing each entry by structures components can be viewed as a variant of a technique used by Davis and 98.8. The resulting series is denoted by μ1 (=1), μ2,...,μ14. Heathcote (2007) and Davis and Palumbo (2008). 90 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 a decrease of 10  over the monotonicity restricted model. combined with the three land price and quantity series to The first period parameter estimates for the 3  marginal form a chained overall Fisher house price index P4 , which prices for land are now β ˆ 1 = 215.4 (30.0), βˆ 1 = 362.6 is graphed in Figure 8.4 and listed in Table 8.4. The con- S M ˆ (46.7) and β L = 176.4 (28.4). They differ slightly from the 1 stant quality structures price index PS 4 (a normalization of previous figures. The first period parameter estimate for the the series γˆ 1 ,..., γˆ 14) is also presented. quality adjusted structures is gˆ 1 = 1085.9 (22.9) Euros/m2, 8.40 A comparison of Figures 8.3 and 8.4 shows that the which is significantly higher than the unrestricted estimate imposition of the national growth rates for new dwelling of 980.5  Euros/m2. So the imposition of a (nationwide) construction costs has changed the nature of the land and growth rate on the change in the price of quality adjusted structures price indices: in Figure 8.3, the price series for structures has had some effect on the estimates for the lev- land lies below the overall house price series for most of the els of land and structures prices. sample period while in Figure 8.4, the pattern is reversed: 8.39 As usual, equations (8.13)-(8.19) were used in or- the price series for land lies above the overall house price der to construct a chained Fisher index of land prices, which series for most of the sample period (and vice versa for the is denoted by PL 4 . This index is plotted in Figure 8.4 and price of structures). But which model is best? Although the listed in Table 8.4. As for the previous three models, the previous model can be preferred on statistical grounds be- estimated price in quarter t for a square meter of quality cause the log likelihood is somewhat higher, we would nev- adjusted structures is gˆ t (which now equals gˆ 1 m t ) and ertheless prefer the present model that uses of exogenous ∑ ˆAt ) S t . N (t ) the corresponding quantity is S ≡ n=1 (1 − d t* n n information on structures prices because it yields a more These structures price and quantity series were again plausible pattern of price changes for land and structures. Figure 8.4. The Price of Land (PL4), the Price of Quality Adjusted Structures (PS4) and the Overall House Price Index using Exogenous Information on the Price of Structures (P4) 1.25 1.20 1.15 1.10 1.05 1.00 0.95 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PL4 PS4 P4 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 91 8 Decomposing an RPPI into Land and Structures Components Table 8.4. The Price of Land (PL4), the Price of Quality Adjusted Structures (PS4) and the Overall House Price Index using Exogenous Information on the Price of Structures (P4) Quarter PL4 PS4 P4 1 1.00000 1.00000 1.00000 2 1.13864 0.99291 1.04373 3 1.16526 1.01518 1.06752 4 1.04214 1.03947 1.03889 5 1.11893 1.00709 1.04628 6 1.18183 1.01721 1.07541 7 1.23501 1.01215 1.09121 8 1.13257 1.01518 1.05601 9 1.21204 1.03441 1.09701 10 1.19545 1.04453 1.09727 11 1.17747 1.06883 1.10564 12 1.11588 1.09211 1.09815 13 1.05070 1.11336 1.08863 14 1.09648 1.11336 1.10486 Source: Authors’ calculations based on data from the Dutch Land Registry indices paint much the same picture. Note that P3 and P4 Choosing the “Best” Overall are virtually identical. Index 8.42 All things considered, the hedonic imputation in- dex PHIF is our preferred index since it has fewer restric- tions than the other indices and seems closest to a matched 8.41 This section is concluded by listing and chart- model index in spirit, followed by the two cost of produc- ing our four “best” overall indices: the chained stratified tion hedonic indices P4 and P3 , followed by the stratified sample Fisher index PFCH constructed in Chapter 4, the sample index PFCH . The latter likely suffers from some unit chained hedonic imputation Fisher index PHIF studied in value bias. Hedonic indices can be biased too (if impor- Chapter 5, the index P3 that resulted from the cost based tant explanatory variables are omitted or if an “incorrect” hedonic regression model with monotonicity restrictions functional form is chosen), but in general we would prefer constructed earlier, and the index P4 that resulted from hedonic regression methods over stratification methods. If the cost based hedonic regression model using exoge- separate land and structures indices are required, we are nous information on the price of structures studied in the in favour of the cost based hedonic regression model that present section. As can be seen from Figure 8.5, all four uses exogenous information on the price of structures. 92 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 Figure 8.5. House Price Indices Using Exogenous Information (P4) and Using Monotonicity Restrictions (P3), the Chained Fisher Hedonic Imputation Index and the Chained Fisher Stratified Sample Index 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 P4 P3 PHIF PFCH Source: Authors’ calculations based on data from the Dutch Land Registry Table 8.5. House Price Indices Using Exogenous Information (P4) and Using Monotonicity Restrictions (P3), the Chained Fisher Hedonic Imputation Index and the Chained Fisher Stratified Sample Index Quarter P4 P3 PHIF PFCH 1 1.00000 1.00000 1.00000 1.00000 2 1.04373 1.04148 1.04356 1.02396 3 1.06752 1.06457 1.06746 1.07840 4 1.03889 1.03627 1.03834 1.04081 5 1.04628 1.04316 1.04794 1.04083 6 1.07541 1.07168 1.07553 1.05754 7 1.09121 1.08961 1.09460 1.07340 8 1.05601 1.05408 1.06158 1.06706 9 1.09701 1.09503 1.10174 1.08950 10 1.09727 1.09625 1.10411 1.11476 11 1.10564 1.10552 1.11400 1.12471 12 1.09815 1.09734 1.10888 1.10483 13 1.08863 1.08752 1.09824 1.10450 14 1.10486 1.10427 1.11630 1.11189 Source: Authors’ calculations based on data from the Dutch Land Registry Handbook on Residential Property Prices Indices (RPPIs) 93 8 Decomposing an RPPI into Land and Structures Components Rolling Window Hedonic (8.10)-(8.12) and (8.20) was initially estimated for the first 9 quarters. The resulting price indices for land and for con- Regressions stant quality structures and the overall index are denoted by PRWL 4 , PRWS 4 and PRW 4 and are listed in the first 9 rows 8.43 A problem with the hedonic regression model dis- of Table 8.6. (17) Next, a regression covering quarters 2-10 cussed in the previous section (and all other hedonic mod- was run and the resulting land, structures and overall price els discussed in this Handbook except hedonic imputation indices were used to update the initial indices; i.e., the price models) was mentioned in Chapter 5: when more data are of land in quarter 10 of Table 8.6 is equal to the price of added, the indices generated by the model change. This fea- land in quarter 9 times the price relative for land (quarter ture of these regression based methods makes these mod- 10 land index divided by the quarter 9 land index) obtained els unsatisfactory for statistical agency use, where users from the regression covering quarters 2-10, etc. Similar up- expect the official numbers to remain unchanged as time dating was done for the next 4 quarters using regressions passes. Users may tolerate a few revisions to recent data but covering quarters 3-11, 4-12, 5-13 and 6-14. typically, they would not like all the numbers to be revised 8.46 The rolling window indices can be compared to back into the indefinite past as new data become available. the corresponding indices based on the data pertaining A simple solution to this problem is available, however. the to all 14  quarters constructed in the previous section so-called rolling window approach. This approach will be by looking at Table 8.6. Recall that the estimated depre- outlined in more detail and applied to the cost based he- ciation rate and the estimated quarter 1 price of quality donic regression model that uses exogenous information adjusted structures for the last model were dˆ = 0.1028 on the price of structures. and gˆ 1 = 1085.9 , respectively. If by chance the 6  rolling 8.44 First, one chooses a “suitable” number of time pe- window hedonic regressions generated the exact same riods (equal to or greater than two) where it is thought estimates for d and g , then the indices resulting from that the hedonic model yields “reasonable” results; this will the rolling window regressions would coincide with the be the window length (say M periods) for the sequence of indices PL 4 , PS 4 and P4 . The estimates for d generated regression models which will be estimated. Secondly, an by the 6 rolling window regressions are 0.10124, 0.10805, initial regression model is estimated and the appropriate 0.11601, 0.11103, 0.10857 and 0.10592. The estimates for indices are calculated using data pertaining to the first M g 1 generated by the 6  rolling window regressions are periods in the data set. Next, a second regression model 1089.6, 1103.9, 1088.1, 1101.0, 1123.5 and 1100.9. While is estimated where the data consist of the initial data less these estimates are not identical to the corresponding es- the data for period 1 but adding the data for period M+1. timates of 0.1028 and 1085.9 for P4 , they are fairly close. Appropriate price indices are calculated for this new re- So we can expect the rolling window indices to be close to gression model but only the rate of increase of the index their counterparts for the last model in the previous sec- going from period M to M+1 is used to update the previous tion. The R2  values for the 6  rolling window regressions sequence of M index values. This procedure is continued were .8803, .8813, .8825, .8852, .8811 and .8892. with each successive regression dropping the data of the 8.47 The rolling window series for the price of quality previous earliest period and adding the data for the next adjusted structures, PRWS , is not listed in Table 8.6 since period, with one new update factor being added with each it is identical to the series PS 4 . (18) The rolling window regression. If the window length is a year, then this proce- price series for land, PRWL , is extremely close to its coun- dure is called a rolling year hedonic regression model; for a terpart PL 4 , and the overall rolling window price series general window length, it is called a rolling window hedonic for detached dwellings in the town of “A”, PRW , is also regression model. (16) close to its counterpart P4 . The corresponding series in 8.45 Using the data for the town of “A”, the rolling win- Table 8.6 are so close to each other that we decided not dow procedure was applied with a window length of 9 quar- to provide a chart. ters. The hedonic regression model defined by equations (16) This procedure was recently used by Shimizu, Nishimura and Watanabe (2010) and (17) We imposed the restrictions (33) on the rolling window regressions and so the rolling Shimizu, Takatsuji, Ono and Nishimura (2010) in their hedonic regression models for window constant quality price index for structures, PRWS, is equal to the constant quality Tokyo house prices. An analogous procedure has also been recently applied by Ivancic, price index for structures listed in Table 8.4, PS4. Diewert and Fox (2011) and de Haan and van der Grient (2011) in their adaptation of the (18) By construction, PS4 and PRWS are both equal to the official Statistics Netherlands GEKS method for making international comparisons to the scanner data context. construction price index for new dwellings, μt/μ1 for t = 1,...,14. 94 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 Table 8.6. The Price of Land (PL4), the Price of Quality Adjusted Structures (PS4), the Overall House Price Index using Exogenous Information on the Price of Structures (P4) and their Rolling Window Counterparts (PRWL) and (PRW) Quarter PRWL PL4 PRW P4 PS4 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.14073 1.13864 1.04381 1.04373 0.99291 3 1.16756 1.16526 1.06766 1.06752 1.01518 4 1.04280 1.04214 1.03909 1.03889 1.03947 5 1.12055 1.11893 1.04635 1.04628 1.00709 6 1.18392 1.18183 1.07542 1.07541 1.01721 7 1.23783 1.23501 1.09123 1.09121 1.01215 8 1.13408 1.13257 1.05602 1.05601 1.01518 9 1.21417 1.21204 1.09698 1.09701 1.03441 10 1.19772 1.19545 1.09738 1.09727 1.04453 11 1.18523 1.17747 1.10718 1.10564 1.06882 12 1.11889 1.11588 1.09779 1.09815 1.09201 13 1.05191 1.05070 1.08893 1.08863 1.11335 14 1.09605 1.09648 1.10436 1.10486 1.11335 Source: Authors’ calculations based on data from the Dutch Land Registry 8.48 Using the data for the town of “A”, rolling window information is not available to us, but we can treat the total hedonic regressions gave much the same results as a he- number of detached houses sold over the sample period as donic regression that covers the whole sample period. This an approximation to the stock of this type. (19) In our data supports our view that the rolling window approach can be set there were N (1) + N (2) + ... + N (14) = 2289 of such used by statistical agencies to compile an RPPI based on transactions. (20) hedonic regressions, including a decomposition into land 8.51 The estimated parameters for land size, structure and structures components. size and depreciation in quarter t are denoted by β ˆ t , gˆ t ˆ ˆ and d ; a denotes the constant term. Our approximation t t to the total value of the housing stock for quarter t, V t , is defined as The Construction of Price 14 N (s) Vt ≡ ∑∑ [α ˆ t ˆ t Ls + γ +β ˆ t (1 − δˆ t A s ) S s ] (8.21) Indices for the Stock s =1 n =1 n n n t = 1,...,14 of Dwelling Units That is, V t is (approximated by) the imputed value of all 8.49 This section shows how hedonic regression mod- houses traded during the 14 quarters in our sample, where els can be used to form an approximate RPPI for the stock the regression coefficients from the quarter t hedonic im- of dwelling units. We will first look at the hedonic imputa- putation model given by (5.25) serve as weights for the tion model discussed in Chapter 5 and compare the result- characteristics of each house. Dividing the V t series by the ing index with an approximate stock based index using the value for quarter 1, V 1 , is our first estimated stock price stratification approach. index, PStock 1 , for the town of “A”.  (21) This is a form of a Lowe index; see the CPI Manual (2004) for the properties The Hedonic Imputation Model (19) This approximation would probably be an adequate one if the sample period 8.50 Recall that the hedonic imputation model was de- were a decade or so. Obviously, our sample period of 14 quarters is too short to be accurate and there are also sample selectivity problems, i.e., newer houses will be over fined by equations (5.25), where Ltn , S nt and Ant denot- represented. However, the method we are suggesting here can be illustrated using this rough approximation. ed, respectively, the land area, structure area, and age (in (20) We did not delete the observations for houses that were transacted multiple times over decades) of property n sold in period t. To form a price the 14 quarters since a particular house transacted during two or more of the quarters is not actually the same house due to depreciation and renovations. index for the stock of detached houses in the town of “A”, (21) Since Vt is a value, it does not appear to be a price series at first glance. But in each it would in principle be necessary to know L, S and A for quarter, the quantity vector which underlies this value is a vector of ones of dimension 2289, which is constant over the 14 quarters. Hence Vt can also be interpreted as a price all detached houses in “A” during some base period. This series, which is normalized to equal one in quarter 1. Handbook on Residential Property Prices Indices (RPPIs) 95 8 Decomposing an RPPI into Land and Structures Components of Lowe indices. In Table 8.7 and Figure 8.6 this price index hedonic imputation indices during several quarters. These for the stock of houses is compared with the corresponding differences are due to the existence of some unit value bias sales based Fisher hedonic imputation price index, PHIF . in the stratification indices. Thus, although stratification indices can be constructed for the stock of dwelling units 8.52 An additional approximate stock price index based of a certain type and location (with the help of hedonic on stratification, PStock 2 is also graphed in Figure 8.6  and imputation for empty cells), it appears that the resulting listed in Table 8.7. This index uses the unit value prices stock indices will not be as accurate as indices that are en- for the nonempty cells in the stratification scheme in each tirely based on the use of hedonic regressions. (22) quarter, as explained in Chapter 4, and uses the imputed prices based on the hedonic imputation regressions from Chapter 5 for the empty cells in each quarter. The quantity (22) If the imputed prices are used for every one of the 45 cell prices for each period vector used for PStock 2 is the (sample) total quantity vec- (instead of just for the zero transaction cells as was the case for the construction of PSctock2) and the same total sample quantity vector is used as the approximate stock tor by cell, which makes PStock 2 an alternative Lowe price quantity vector, then the resulting Lowe index turns out to be exactly equal to PStock1. index. It can be seen that while PStock 2 has the same general Thus these two different ways for constructing a stock index turn out to be equivalent. The fact that PStock1 is not equal to PStock2 is clear evidence that there is unit value bias in trend as PStock 1 and PHIF , it differs substantially from these the cells of the stratification scheme: the cells are simply not defined narrowly enough. Figure 8.6. Approximate Stock Price Indices and Based on Hedonic Imputation (PStock1) and Stratification (PStock2) and the Fisher Hedonic Imputation Sales Price Index 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PStock1 PStock2 PHIF Source: Authors’ calculations based on data from the Dutch Land Registry 96 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 Table 8.7. Approximate Stock Price Indices and Based on Hedonic Imputation (PStock1) and Stratification (PStock2) and the Fisher Hedonic Imputation Sales Price Index Quarter PStock1 PStock2 PHIF 1 1.00000 1.00000 1.00000 2 1.04791 1.02712 1.04356 3 1.07255 1.07986 1.06746 4 1.04131 1.03257 1.03834 5 1.05040 1.05290 1.04794 6 1.07549 1.05934 1.07553 7 1.09594 1.07712 1.09460 8 1.06316 1.07172 1.06158 9 1.10137 1.08359 1.10174 10 1.10708 1.11482 1.10411 11 1.11289 1.12616 1.11430 12 1.10462 1.11291 1.10888 13 1.09278 1.10764 1.09824 14 1.11370 1.10686 1.11630 Source: Authors’ calculations based on data from the Dutch Land Registry The Use of Exogenous Information 14 N (s) on the Price of Structures VSt ≡ ∑∑ γˆ µ (1 − δˆA )S 1 t s n s n (8.25) s =1 n =1 t = 1,...,14 8.53 The same kind of construction of an approximate stock price index can be applied to the other hedonic re- where all structures traded during the 14  quarters are gression models discussed in this chapter. Here we will included. show how this works for the cost based model that used ex- 8.54 The quantities that correspond to the above period ogenous information on the price of structures. This model t valuations of the three land stocks and the stock of struc- was defined by equations (8.10)-(8.12) and (8.20). Recall tures are defined as follows: (23) that the sets of period t sales of small, medium and large lot 14 houses were denoted by S S (t ) , S M (t ) and S L (t ) , respec- tively; the total number of sales in period t was denoted by QLS t ≡ ∑ ∑ L (8.26) s =1 n∈S S ( s ) s n N (t ) for t = 1,...,14 . The estimated model parameters are t = 1,...,14 ˆ1 , β dˆ t , gˆ t and β S ˆ 1 and β M ˆ 1 for t = 1,...,14 . The estimated L period t values of all small, medium and large lot houses 14 traded over the 14 quarters, VLS t , VLM t and VLL t , respectively, QLM t ≡ ∑ ∑L s =1 n∈S M ( s ) s n (8.27) are defined by (8.22)-(8.24): t = 1,...,14 14 V ≡ t LS ∑∑ ˆ t Ls (8.22) β S n 14 ∑ ∑ L (8.28) s =1 n∈S S ( s ) QLL t ≡ s t = 1,...,14 s =1 n∈S L ( s ) n 14 t = 1,...,14 VLM t ≡∑ ∑{βˆSt [160] + βˆM t [ Lsn − 160]} (8.23) 14 N (s) QSt ≡ ∑∑ (1 − δˆA s ) S s (8.29) s =1 n∈S M ( s ) t = 1,...,14 n n s =1 n =1 14 t = 1,...,14 VLL t ≡ ∑∑ ˆ t [160] + β {β s =1 n∈S L ( s ) S ˆ t [ Ls − 300]} (8.24) ˆ t [140] + β M L n t = 1,...,14 The estimated period t value of quality adjusted structures, (23) The quantities defined by (8.26)-(8.29), which are constant over the 14 quarters, are equal to 77455, 258550, 253590 and 238476 for small lots, medium size lots, large lots VSt , is defined by and structures, respectively. Handbook on Residential Property Prices Indices (RPPIs) 97 8 Decomposing an RPPI into Land and Structures Components 8.55 Approximate stock prices, PLS t , PLM t , PLL t and PSt , overall stock index, PStock , is obtained by aggregating the that correspond to the values and quantities defined by three types of land with the constant quality structures (or, (8.22)-(8.29), can be computed in the usual way: equivalently, by aggregating PLStock and PSStock ). Since the quantities are constant over all 14 quarters, the Laspeyres, PLS t ≡ VLS t / QLS t (8.30) Paasche and Fisher price indices are all equal.  (24) The PLM t ≡ VLM t / QLM t stock price indices PLStock , PSStock and PStock are charted in Figure 8.7 and listed in Table 8.8. For comparison purpos- PLL t ≡ VLL t / QLL t es, the corresponding price indices based on sales of prop- PSt ≡ VSt / QSt erties for the model presented previously, PL 4 , PS 4 and P4 , are also listed in Table 8.8. As can be seen from Table 8.8, t = 1,...,14 the approximate stock price index for structures PSStock co- incides with the sales based price index for constant qual- Using the above prices and quantities, an approximate ity structures PS 4 , so PS 4 is not charted in Figure 8.7. stock index of land prices, PLStock , is formed by aggregat- ing the three types of land and an approximate constant quality stock price index for structures, PSStock , is simply (24) Fixed base and chained Laspeyres, Paasche and Fisher indices are also equal under formed by normalizing the series PSt . The approximate these circumstances. Figure 8.7. Approximate Price Indices for the Stock of Houses (PStock), the Stock of Land (PLStock), the Stock of Structures (PSStock) and the Corresponding Sales Indices (PL4 and P4) 1.25 1.20 1.15 1.10 1.05 1.00 0.95 1 2 3 4 5 6 7 8 9 10 11 12 13 14 PStock P4 PLStock PL4 PSStock Source: Authors’ calculations based on data from the Dutch Land Registry 98 Handbook on Residential Property Prices Indices (RPPIs) Decomposing an RPPI into Land and Structures Components 8 Table 8.8. Approximate Price Indices for the Stock of Houses (PStock), the Stock of Land (PLStock), the Stock of Structures (PSStock) and the Corresponding Sales Indices (PL4 and P4) Quarter PStock P4 PLStock PL4 PSStock PS4 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.04331 1.04373 1.13279 1.13864 0.99291 0.99291 3 1.06798 1.06752 1.16171 1.16526 1.01518 1.01518 4 1.04042 1.03889 1.04209 1.04214 1.03947 1.03947 5 1.04767 1.04628 1.11973 1.11893 1.00709 1.00709 6 1.07540 1.07541 1.17873 1.18183 1.01721 1.01721 7 1.09192 1.09121 1.23357 1.23501 1.01215 1.01215 8 1.05763 1.05601 1.13299 1.13257 1.01518 1.01518 9 1.09829 1.09701 1.21171 1.21204 1.03441 1.03441 10 1.10065 1.09727 1.20029 1.19545 1.04453 1.04453 11 1.10592 1.10564 1.17178 1.17747 1.06883 1.06883 12 1.10038 1.09815 1.11507 1.11588 1.09211 1.09211 13 1.08934 1.08863 1.04668 1.05070 1.11336 1.11336 14 1.10777 1.10486 1.09784 1.09648 1.11336 1.11336 Source: Authors’ calculations based on data from the Dutch Land Registry 8.56 The overall approximate price index for the total 8.57 Our conclusion is that the hedonic regression stock of detached houses in the town of “A” ( PStock ) can models for the sales of houses can readily be adapted to hardly be distinguished from the corresponding overall compute Lowe type price indices for the stock of houses. sales price index ( P4 ) in Figure 8.7. Similarly, the approxi- There do not appear to be major differences between the mate price index for the stock of land in “A” ( PLStock ) can two index types when using our data set, but this result barely be distinguished in Figure 8.7 from the correspond- may not hold for other data sets. ing sales price index for land ( PL 4 ) . Nevertheless, there are small differences between the stock and sales indices, as Table 8.8 shows. Handbook on Residential Property Prices Indices (RPPIs) 99 Data Sources 9 9 Data Sources Introduction • Mortgage applications. Typical data source: mortgage lenders. 9.1 In practice, because of the high cost of undertak- • Mortgage approved. Typical data source: mortgage ing purpose-designed surveys of house prices, the meth- lenders. ods adopted by statistical agencies and others to construct • Signing of binding contract. Typical data source: lawyers, residential property price indices have mainly made use of notaries. administrative data, the latter usually being a function of the house price data sets generated by a country’s legal and • Transaction completed. Typical data sources: land regis- administrative processes associated with buying a house. tries, tax authorities. The indices so constructed can vary according to the 9.4 Each source of price data has its advantages and point in the house purchasing process at which the price disadvantages. For example, a disadvantage of advertised is measured. For example, the final transaction price or the prices and prices on mortgage applications and approvals is earlier valuation used for securing a loan could be used that not all of the advertised prices will end in transactions, as the “price” of the property. Furthermore, different ad- and the price may differ from the final negotiated transac- ministrative data sets will generally collect information on tion price. These prices are likely to be available sometime different sets of characteristics associated with the sales of before the final transaction price. Indices that measure the the properties. These differing information sets will gen- price earlier in the purchase process are able to detect price erally affect index compilation methods, often acting as a changes first, but they will measure final prices with error constraint on the techniques available to quality adjust for because prices can be renegotiated extensively before the houses of different sizes, locations, etc. Thus data sets have deal is finalized. historically acted as a constraint on index construction. 9.2 This chapter examines the different sources of 9.5 It should be noted that the availability of different data used for constructing residential property prices in- sources of price information at different points in the buy- dices. Although it focuses mainly on price data, the chapter ing and selling process can be an advantage. For instance, also considers how the choice of weighting scheme can be changes in the relationship between asking price and sell- constrained by the information generated from the house- ing price may provide an early indication of a change in the purchasing process. Different weighting schemes, notably housing market. The diagram below illustrates the situation whether an index is stock or sales weighted, produce price in the UK; see also the case study for the UK in Chapter 10. indices which measure different concepts. In these circum- 9.6 Most data sources are susceptible to all the dis- stances it is important that there is a clear understanding advantages of using administrative systems for statistics. of what the target measure is so that the indices compiled The use of administrative data in economic statistics has can be evaluated against the target measure to determine been associated with four challenges: definitions, coverage, fitness-for-purpose. quality, and timeliness – with expected trade-offs against compilation costs. Definitions and coverage are sometimes placed under the one heading of “coverage”: to embrace the types of units covered and the degree of coverage. For ex- Prices ample, cash sales could be recorded but properties bought with a mortgage may not be covered or some cash sales may not be recorded if, for example, they are under the The Process of Buying threshold for tax liability. and Selling a House 9.7 The underlying problem arises from the fact that the data are primarily recorded as a step in the admin- 9.3 The process of buying and selling a property nor- istrative process and not as an input into a statistical mally takes place over a period of several months or more. system. The data are not under the control of the stat- The particular stage in this process at which the price is istician. The inherent weaknesses in administrative data entered into an index will depend on the source of the data need to be taken into account when using the data and and this has consequences for what is being measured and in interpreting the results, in particular when they are for the comparability of different indices. Price data for a used as a substitute for statistical data rather than as a residential property price index may be taken at the follow- supplement to or in conjunction with purpose-designed ing stages: statistics. Some of the weaknesses may be overcomed by • As soon as the property is on the market (advertised or an appropriate methodology, such as combining comple- asking price). Typical data sources: newspapers, real es- mentary data sources, and possibly by using some form of tate agents. modeling. 102 Handbook on Residential Property Prices Indices (RPPIs) Data Sources 9 Diagram: House purchase timeline and house price indices House purchasing process House price indices 1. Begin search Rightmove 10 weeks 2. Verbal offer 4 weeks 3. Mortgage approved Halifax, Nationwide, Hometrack 4 weeks 4. Exchange of contracts 1 week 5. Transaction completed ODPM index 4-6 weeks 6. Transaction registered Land Registry Source: Bank of England and former Office of the Deputy Prime Minister (ODPM) 9.8 A number of basic characteristics come into play authority is likely to focus on validating the informa- in considering the suitability of different data sources. tion which is pertinent to the sale and to the execution of its duties and which reflect the laws and regulations • Definition. This is closely associated with conceptual is- which it is required to comply with. There may be other sues and what the target measure of an index is. information which is collected which is of interest to the • Coverage. Issues relating to coverage will be determined statistical agency, but which is only of limited relevance by the operational boundaries of the agency or business to the administrative authority. For instance, this may be providing the housing data. For example, the agency the case for some house characteristics which the statisti- could cover country-wide property sales or just cover a cal agency may wish to use for quality adjustment. At the particular region or the transactions covered could relate end of the day, the reliability of administrative data will only to cash purchases or to properties purchased using depend on the incentive for data suppliers to give cor- a mortgage loan. For a government agency, the opera- rect information and complete information. There can tional boundaries will be dictated by the regulations and be mutual advantage to both parties from the statistical legal processes involved with the purchase of residential agency helping the administrative authority to improve property. Inevitably, for public and private data providers the quality of its data. This can be done by giving feed- coverage will also be heavily dependent on the resources back on the consistency of data entries and from advis- at the disposal of the agency or business and its efficiency ing on more general weaknesses. Some statistical agen- in providing data. All these factors are outside the con- cies provide the administrative agency with an incentive trol of the index compiler and can impact on data quality to improve their data collection by compiling custom- and on any divergence between intended coverage of the designed statistics for the data supplier in return for ac- residential property price index and actual coverage. cess to the raw data. • Quality. When considering the issue of data qual- • Timeliness. The timeliness of administrative data will ity, it should be borne in mind that the administrative depend on who is responsible for reporting to the Handbook on Residential Property Prices Indices (RPPIs) 103 9 Data Sources administrative authority and on the incentive for timely to actual transaction price also imply that the calcula- reporting. For instance, there may be a big incentive for tion of “average house price estimates” can sometimes be a buyer to obtain approval from the mortgage company, misleading. for a house loan and for the mortgage company, to quick- ly get an accurate and up-to-date valuation so that the 9.11 Information collected on a seller’s asking price can- sale can go through, with all parties safeguarded, before not always be easily verified and, as well as depending on a another potential purchaser takes an interest in the prop- balanced and representative sample, relies on the honesty erty. On the other hand, there may be less of an incentive and knowledge of those being surveyed and when drawn to register the sale quickly with the official land registry from advertisements, the accuracy of the information, es- once completed. pecially when it is from a website. For example, it has been One of the keys to the successful use of administrative data argued that real estate agents are more likely to be optimis- is to have an intimate and detailed knowledge of the data tic about prices and have a vested interest in prices going collection processes and associated operational systems. up rather than down and that this may influence survey results. On the other hand, an estate agent might suggest 9.9 Each source of price data is considered separately to a seller an unrealistically low asking price in order to get below. Where more than one data source is available to the property off their books quickly to get the commission. the index compiler, the opportunity arises for consistency It has also been argued that websites will tend to be biased checks and for data from different sources to be combined. towards properties that have a competitive asking price to For instance, it may be possible to use the property valu- entice potential sellers. All this is, of course, speculation but ations carried out for the approval of loans to predict the it does bring home some of the potential difficulties associ- final transaction price recorded much later on by the land ated with these sources. registry. This depends of course on the stability of any cor- relation found between the two. 9.12 Surveys of real estate agents have some inherent advantages over surveys of advertisements. Agency sur- veys can be based on a more scientifically selected sample Seller’s Asking Price: Estate Agents, and can provide information on a representative selection Newspapers, Etcetera of those properties on the market, including those which typically are not covered in advertisements. Data from real 9.10 Information on the seller’s asking price can be estate agents might include extensive information on the collected through surveys of real estate agents or from characteristics of the property and this information is ex- an examination of advertisements in newspapers, maga- tremely important for quality adjustment (using either he- zines or online. One of the main advantages of indices donic regression methods or stratification methods as was constructed from such information is their timeliness. By seen in previous chapters). Also the survey questionnaire taking asking prices, indices constructed using this infor- could collect information on issues such as: what is the av- mation can provide a timelier estimate of house prices erage selling time or what has been the recent difference than those indices that are based on subsequent trans- between asking prices and selling prices (e.g. “higher” or actions. They also have an advantage over house price “lower”) or on the number of potential buyers registering indices based on information from mortgage lenders, as and the number of properties listed with the agent. This in- the latter are limited to transactions involving mortgag- formation can help put the price information used in com- es. However, indices based on initial asking prices have a piling the index into context and can be useful for interpre- major drawback. Houses can be withdrawn from market tation of the final results. But such surveys typically do not and the agreed selling price may not equal the seller’s ask- record the asking price of a specific property. Rather, the ing price. These indices ignore reductions in prices that questionnaire would normally ask the real estate agent to sellers subsequently make, for example when the housing give the “average asking price” for a selection of representa- market is on a downturn, or offer prices above the asking tive properties. (1) For example, this might be for each of price when the housing market is buoyant. Such indices four standard property types (flat, terraced, semi-detached can therefore present an over-optimistic outlook when and detached) in a number of different locations. It is this the housing market becomes depressed and an over-pes- information which is used to create an average property simistic outlook when the housing market is recovering. price for each property type in each location, which is used The fact that they cannot be relied upon to present an in turn to compile the corresponding price index. In con- accurate picture of the housing market in the short term trast, the inherent advantage of a survey of advertisements devalues their usefulness to most users, most particularly is that the latter will collect the actual asking price for each those interested in the early detection of turning points of the advertised properties. in the housing market or an advanced indicator of the future direction of house prices. It should be noted that (1) Some surveys also ask for “achievable” price and use this to construct a house price the differences between initial asking price compared index. 104 Handbook on Residential Property Prices Indices (RPPIs) Data Sources 9 9.13 In summary, although a house price index based price and the buyer has made the initial application for on surveys of asking prices may be more timely, the diffi- a loan. In practice there is a negotiation process between culties in determining exactly how the survey information these two stages in which it is possible for the agreed pur- was compiled and the uncertain relationship between ask- chase price of the dwelling to change. This can be the case ing price and selling price mean that care should taken if when the independent valuation differs from the price the such an index is to be used as a barometer of house prices. purchaser and buyer had agreed upon or where the pur- chaser has paid for a detailed survey of the property which reveals that substantial repairs are necessary. For instance, The Initial Offer Price Accepted it is fairly common for a buyer to try to leverage a price by Seller: Mortgage Companies reduction if the valuation by the mortgage company turns out to be significantly lower than the previously agreed 9.14 Many countries turn to mortgage lenders as the price, or if a survey of the condition of the property reveals main data source for their house price index. The informa- the need for new roofing. Clearly, the difference between tion is stored in the lender’s computer system and serves the initial offer price and the follow-up valuation and any the operational business needs of the mortgage lenders. This database may include the initial offer price made by process of re-negotiation which takes place subsequently the potential purchaser, the valuation price used for author- can result in the measured rate of house price inflation to ising a loan and sometimes also the final transaction price. differ from the true rate as measured by the actual transac- Information from mortgage companies can suffer from all tion price. the disadvantages of using data drawn from administrative 9.17 The house price change measured by indices based systems, as described above, but these databases can be a on valuations by mortgage companies  (2) can differ from rich source of timely information. the price change shown by the offer price and both may 9.15 However, data from mortgage lenders suffer from differ from the price change based on final transaction a major drawback: they exclude non-financed home pur- prices even when taken from the same sample of mortgage chases. Research has indicated that cash buyers account for lenders. Thus, it is important to understand exactly what an about a third of the UK market and cash buyers tend to index is measuring. purchase either very cheap or very expensive properties. This would not be problematic if it was not for the fact that The Final Transaction Price: dwellings purchased for cash can experience different price developments compared to those financed by a mortgage. Mortgage Companies This is likely to be particularly the case at turning points 9.18 The time lag between the mortgage application, in the market where different ends of the housing market mortgage approval and purchase completion stages and may react differently to the economic circumstances and the differences in the corresponding values of the house the premium for a cash-buyer increase. For instance in a prices illustrate the trade-off between timeliness and accu- down-turn, people at the top end of the market who were racy. The final transaction price is not always recorded by considering selling their homes to release equity may hold mortgage lenders and is often extracted instead from legal back from putting their homes on the market at a reduced records such as entries made in land registers, which addi- price, so the supply of houses for sale falls and is mainly tionally also include sales that did not require a mortgage. from owners who, for one reason or another, are very keen But there can be a long time lag between the completion to sell. However, at the same time the number of active po- of the transaction and the recording of the sale in the land tential mortgage-based buyers could drop significantly as register. One of the main advantages of data from mortgage people are reluctant to take out larger mortgages. But some lenders is its timeliness. Initial offer prices and valuations people will need to sell. In this situation a cash-buyer for provide an earlier indication of current prices, as these a house at the upper end of the market will be in a rela- data are available earlier, and final transaction prices may tively stronger position to negotiate a bargain price than in be available sooner from the mortgage lender than from a more stable market. the land registry. It is for this reason that the exploitation of information from mortgage lenders on final transaction The Valuation Price for a Loan: price may be a preferred option. The final transaction price Mortgage Companies held by mortgage lenders can be easily verified against land registry records to alleviate any concerns regarding accu- 9.16 Mortgage companies will obtain an independent racy and credibility. valuation of a property before approving a loan. The valu- ation that the mortgage company provides the customer (2) It has to be taken into account that prices from mortgage valuations, like prices based with at the time of the mortgage approval can be some on any valuation, depend on the objectivity of the evaluation process. Thus, it has been mentioned that the mortgage valuations can sometimes be influenced by the credit weeks after the buyer and seller have negotiated a final policy of the bank, indicating potential difficulties associated with these sources. Handbook on Residential Property Prices Indices (RPPIs) 105 9 Data Sources The Final Transaction Price: That said, this source of official valuation information has been exploited by statistical agencies; see the material Administrative Data from Property on the SPAR method of index construction described in Registers and Tax Offices Chapter 7. 9.19 Ideally a house price index would be based on actual transaction prices at the time when the property is Other Expert Opinion Information: sold and the sale completed. The signing of the first bind- Surveys of Estate Agents Organisations, ing contract best fits this requirement because of its timeli- other Professional Bodies ness but in practice there can be some ambiguity about the point at which a contract is binding, e.g. whether this is at and their Members the point where an offer is formally accepted (e.g. when 9.22 In some countries, regular surveys are conducted sealed bids are opened), or when a contract is signed or of real estate agents, chartered surveyors or their corre- when the contract is exchanged. Similarly, there can be a sponding professional bodies, asking about house prices difference between when a contract is signed and when the and housing stock. These “opinion” surveys are typically transfer of ownership takes place and when it is recorded restricted to asking respondents to give a view on whether in the property registers or at the tax office. house prices are moving up, down or flat. These surveys 9.20 In theory, information from property registers or do not give an indication of how much houses are worth tax offices will cover all properties, including cash purchas- or by how much prices are falling or rising but they can es as well as purchases via a mortgage and thus these data- provide an up-to-date and broad-based picture on the di- bases should be the most comprehensive of all the sources rection of price change in the housing market to supple- available to the index compiler. But, in practice, compre- ment and help to add credibility to the latest figures from a hensiveness cannot be guaranteed, particularly if there is a residential property price index. For instance, a significant disincentive for the owner to register a property. For exam- change in the difference in the proportions of real estate ple, when the primary purpose of registration is for taxa- agents who think prices are going up and those who think tion purposes, properties may not get registered at all, or prices are going down might provide an early indication may be registered with some relevant detail such as square of a change in the housing market not yet detected by the metres of floor space missing or incorrectly recorded, in currently available statistics on mortgage lender valuations. order to avoid tax or reduce the tax charges. (3) Contextual information of this kind adds value and is reg- ularly used by commentators when interpreting official house price indices. Valuation Price for Taxation and Payment for Local Services: Tax Offices 9.21 In many countries, the central or a local govern- Evaluation of Data Sources ment may impose a monthly or annual tax or service charge on residential properties, for funding the provi- for Fitness-for-Purpose sion of public services such as road maintenance, police and fire services or refuse collection. In many cases, the 9.23 The overall usefulness of the above sources of in- tax bill faced by an individual is proportional to the as- formation on residential property prices will very much sessed value of property and the latter is usually based depend on their fitness-for-purpose for the particular ap- on a valuation undertaken by professional chartered plications to which they are being used. To gauge fitness- surveyors either under contract or directly employed by for-purpose requires an evaluation of the intrinsic advan- the taxation authority. The valuations should take into tages and disadvantages of the index against an agreed set account characteristics of the property, such as location of criteria, i.e. an evaluation against user needs. and size of plot. However, they rely on accurate informa- 9.24 Chapter 2  reviewed the many different uses of tion about the properties and also on the chartered sur- house price indices: as a macro-economic indicator of veyors’ assessments, which are difficult to verify. Also the inflation; for monetary policy targeting; as a measurement updating of the valuations tends to be infrequent due to of change in wealth; as a financial stability indicator the field costs involved. Because of these drawbacks, the to measure risk exposure; as a deflator for the national information collected can sometimes be of limited use accounts; as an input into an individual citizen’s decision in the construction of residential property price indices. making on whether to invest in residential property; as an input into other price indices, in particular the Consumer (3) There is a related problem: the transaction price may not be a market price because the transaction, while genuine, is between relatives or friends. For example, parents may Price Index (CPI), and for use in wage bargaining or decide to pass on the family home to their children at a below market price. indexation. 106 Handbook on Residential Property Prices Indices (RPPIs) Data Sources 9 9.25 An effective evaluation of the different sources of solely from data supplied by mortgage lenders represents a data on house prices is dependent on a systematic analysis serious deficiency. Conceptually, land registry data would of user requirements. User needs have a significant impact represent a better source as it should cover all transactions. on decisions relating to the conceptual basis of an index The challenge is to find a source of price data which readily and the associated statistical requirement. This may take fits, or can be manipulated to meet, the requirements of us- the form of a series of questions reflecting the different rea- ers interested in the inclusion of owner-occupier housing sons why users may want information on house prices. For costs in a CPI on a net acquisition cost basis, that is, exclud- instance, whether an index of house prices is to be used as ing the price of land. (5) one of a suite of general macroeconomic indicators, as an 9.29 In contrast, users interested in an analysis of the input into the measurement of consumer price inflation, current value of the real estate portfolio against which out- as an element in the calculation of household wealth or as standing mortgages are secured, will require an index of a direct input into an analysis of lenders’ exposure. Such changes in the price of the properties for which mortgag- an analysis can then be transformed into a statistical user es were issued, weighted by the amounts loaned for each requirement and an associated conceptual framework by type of property at the time at which they were issued. For expressing the needs in statistical terms and identifying the both of these measures, the value of the land underlying common linkages and corresponding relationships at a mi- the buildings is as important as the value of the buildings cro and macro level. The different data sources can then be themselves and it is the total value of the land and buildings evaluated against the statistical need. which is of interest. For these users, data from mortgage 9.26 The following list of desirable properties for a providers on property prices and the size of new mortgages residential property price index constitute a possible set of and outstanding debt will fit the purpose. criteria for an evaluation of alternative data sources for fit- 9.30 Now consider the needs of employers and trade ness-for-purpose for different uses. (4) The list builds upon unions when negotiating wage settlements. Their primary the discussion at the beginning of this chapter. The rela- focus will be the effects of price changes on the standard tive importance of each of the criteria will depend on use of living of workers. For this purpose users will be looking and in essence constitutes a statistical requirement. There to a CPI that includes the cost of keeping a roof over their will also be the usual trade-offs between fully meeting user heads – for owner-occupiers the cost of mortgage interest needs and the costs of data collection. payments and the repairs costs. The measurement of this will require the calculation of the mortgage outlay at time Definitions and Measurement Concept of purchase and the subsequent repayment history will need a sales weighted house price index. In an ideal world 9.27 This also covers coherence with other statistical re-financing would be excluded. The repairs element may outputs. It represents the user requirement at the most ba- be measured by the calculation of depreciation. For this, sic level. Consider the needs of governments and analysts a stock-weighted smoothed house price index is most ap- looking at inflationary pressures and those with a direct propriate. In addition, there is the issue of land where it is investment in real estate. The primary focus of these us- often argued that in most circumstances land is an invest- ers may be the cyclical nature of prices and the ability of ment which appreciates and that its inclusion in a deprecia- real estate prices to lead to destabilising booms and slumps tion calculation is inappropriate. (6) Thus an index exclud- in the economy as a whole. For this purpose, users will be ing the price of land may be required. looking to a variety of indicators, including indices of the volume and price of real estate transactions, as well as mac- 9.31 For the calculation of mortgage outlay, the user ro-economic indicators for modelling the economic cycle can again rely on information supplied by mortgage lend- and predicting peaks and troughs. Analysts looking at the ers, but not for the estimation of depreciation, where the inflationary pressures of real estate price rises in compari- value of land may again need to be separately identified. son to other price rises may be interested in including in a 9.32 As a final example, consider the needs of national CPI the inflationary costs of owner-occupier housing costs accountants, who are seeking appropriate deflators for na- by means of a house price index based on the net acquisi- tional accounts. Their needs again will be different. Real es- tion cost basis but excluding land. tate appears in the National Accounts in several ways (for 9.28 For users wanting a general macro-economic indi- details, see Chapter 3): cator, an index based on all purchases – both cash and those with a mortgage – is appropriate. Taking transaction prices (5) In most countries for most transactions, land and building are purchased together as a “single package”, so the two components are typically not separated in the information generated by records relating to the transfer of ownership. As such separating the pric- (4) See also Chapter 3 where a listing of user needs is presented based on discussions es would require a supplementary exercise. In Chapter 8 it was outlined how hedonic between users of house price indices and the Office for National Statistics. In that regression can be used to decompose the overall price index into land and structures section, it was pointed out that there is a trade-off between the desires of users to have components. a family of more detailed indices (stratified by location and type of housing) and the ( ) There are other more general issues, which are not addressed here, to do with the 6 quality of the indices: more detail inevitably leads to less accurate indices. measurement of depreciation and its inclusion in a consumer price index. Handbook on Residential Property Prices Indices (RPPIs) 107 9 Data Sources • The imputed rental value received by owner occupiers particularly important when used, say, for macro-economic for buildings is part of household final consumption. policy and monetary targeting but less important for a na- • The capital formation in buildings, as opposed to land, tional accounts deflator. Data from mortgage lenders may is part of gross fixed capital formation, depreciation, and better suit the needs of those engaged in macro-economic the measurement of the stock of fixed capital. policy and monetary targeting, even though cash purchas- es are excluded, whilst land registry data may better suit the • Land values, which are an important part element of the needs of, for example, those calculating deflators. national stock of wealth. In each case the derivation of volumes from values requires price indices for respectively: the imputed rent of owner Detail for Quality Adjustment occupied dwelling units weighted by the stock of different and Mix-Adjustment types of owner occupied housing; new house purchases 9.37 This relates to two (related) issues: the degree to weighted by the transactions in new houses but excluding which residential property price indices are able to adjust the land component; and of the whole housing stock in- for changes in the mix of properties sold and to eliminate cluding land weighted by the housing stock the effect of quality changes of the individual dwellings. For 9.33 It can be seen that user needs will vary and that in this purpose, “real time” information is needed on price de- some instances more than one measure of house price or termining attributes such as size of plot, size of house, type real estate inflation may be required. It can also be seen that of property (flat, house, semi-detached or detached), loca- coherence between different measure and with other eco- tion, the condition of the property, whether it has central nomic statistics is important and that achieving this will be heating, a fully-fitted kitchen and bathroom, etc. Quality especially difficult as statisticians are unlikely to have an (or mix) adjustment is essential in order to construct an ideal set of price indicators available to them. accurate price index for housing components. (7) It is un- likely that any of the sources of prices data listed above will be ideal for all purposes. The amount of detailed and Coverage relevant characteristics data will depend on the individual 9.34 Coverage includes not just whether all properties data set. (8) are covered irrespective of whether the property is owned outright or being funded by a mortgage but also wheth- Frequency er country-wide property sales or valuations are covered or just those in a particular region and whether all price 9.38 Frequency essentially relates to how frequently ranges are covered. It can be noted that even where the pri- an index can be computed, e.g. once a month or once a mary need is for a national index, regional indices can be quarter. There is a tradeoff between frequency and accu- in demand for analytical purposes. House price informa- racy. For a particular geographic area and type of hous- tion from any individual mortgage lender is unlikely to be ing, current information on the price of houses in a given representative of the country as a whole, not only because strata will come from sales of old and new houses in that of the exclusion of cash purchases but also because lenders strata during the chosen time period. If the frequency is often focus their business on particular regions. chosen to be a month as opposed to a quarter, the month- ly sample size will only be approximately one third of the quarterly sample size. Thus a monthly house price index Quality based on sales of properties in the given strata will be subject to increased sample volatility (and hence will not 9.35 Quality relates to the accuracy and completeness be as accurate) as compared to the corresponding quar- of the information, i.e. there are no serious errors and the terly index. Volatility of a monthly index may be reduced information is what it purports to be. Compared with other by making the strata “bigger”, (9) e.g., different neighbour- administrative data, house price information from a land hoods could be combined within the same general loca- registry is likely to score relatively highly in terms of accu- tion but this leads to another tradeoff between fineness racy due to the legal requirements to record property trans- actions and exchanges of ownership. However, the reliability (7) The various methods available for constructing quality adjusted house price indices of data from any administrative source is difficult to validate. were discussed in Chapters 4-8. (8) In cases where the real estate agent data base includes the final selling price of the listed properties along with the main characteristics of the properties, this information base is probably the “best” for most purposes. However, the sample of listed properties Timeliness needs to be compared with the properties listed in land registry offices to ensure that the coverage of listed properties is adequate for the purpose at hand. When constructing price indices for the stock of housing, it will be necessary to have census 9.36 Indices that measure prices earlier in the purchas- information on housing stocks along with post census information on demolitions and ing process are able sooner to detect price changes and the construction of new dwelling units. ( ) It is not certain that combining strata will reduce index volatility if house prices in the 9 turning points in house price inflation. This is likely to be different micro strata have different trends. 108 Handbook on Residential Property Prices Indices (RPPIs) Data Sources 9 of the strata (which many users may want) and accuracy 9.42 Valuation prices kept by tax offices for taxation of the index (which all users want). and payment for local services and the final transaction price recorded by mortgage companies are least likely to be 9.39 It may be possible to provide smoothed monthly subject to revision, whilst the final transaction price based house price indices that are say a three month moving aver- on administrative data held on property registers and tax age of the raw monthly indices (10) or the statistical agency offices could be subject to revision over a long period de- could provide both monthly and quarterly indices and let pending on the time-lags involved in the legal processes of users choose their preferred index. (11) It is not possible to recording changes in ownership. provide definitive advice on how frequent a house price in- dex covering a certain stratum should be published. The is- sue of frequency must be decided by the national statistical Comparability agency, taking into account user needs and data availability. 9.43 Comparability refers to the degree of inter-coun- try comparability between house price indices. This is Revisions important because comparing house prices from non- harmonised national data can be problematic as differenc- 9.40 Revisions can refer to either revisions resulting es in concept, index construction, market coverage, quality from subsequent returns (so that the series itself is revised) adjustment procedures, etc. can make cross country com- or from other sources of more relevant data subsequently parisons difficult. Differences in frequency, timeliness and coming on stream (so an early indicative measure is even- revisions policy can also cause comparability problems. tually replaced by a precise measure of what needs to be measured). (12) For instance, an example of the former 9.44 Problems can arise at both the national and inter- might be revisions arising from late registration of prop- national levels: erty sales. An example of the latter might be where an ini- • Users in individual countries can be confronted either tial offer price recorded on the mortgage application form with a lack of relevant statistics or with different statistics is used as an early indication of movements in transaction for different time periods and with varying time-lags and prices but is subsequently discarded when land registry these statistics can be based on different data sources or data on actual transaction prices (which takes into account compilation methods. any price renegotiation before the sale is finalised) eventu- • For users seeking international comparisons the situ- ally comes on stream at a much later point. ation is complicated by significant differences among 9.41 The extent to which figures are revised due to the countries with regards to the availability of data and the receipt of subsequent returns is partly determined by the challenge this represents for compiling like-for-like com- reference point of the prices data and partly by the point in parisons and interpreting relative trends among coun- time when the particular data set is received by the statis- tries. The complication of aggregate price indices cover- tical agency: the earlier is the data reference period in the ing groups of countries – a requirement for co-ordinated purchasing cycle and the earlier the particular data set is re- economic policy and monitoring across an economic ceived, the more the index will be subject to revision. Thus, area such as the Eurozone (13) – is a further challenge. although information from the registration of property sales From Chapter 10 it can be seen that the methods employed is appropriately referenced and provides a definitive source for the compilation of residential property price indicators of information on property prices, the time delay that can vary considerably between countries, and even between al- sometimes take place in some countries for the legal regis- ternative sources within individual countries. tration of property transfers can mean that the register is not final until, say, twelve months the sale of the property. (10) The Australian Bureau of Statistics makes frequent use of this technique for a wide range of its statistics. If the window length is 12 months, then the resulting smoothed index Weights can be regarded as a seasonally adjusted index, centered in the middle of the 12 month period under consideration. For a variant of this smoothing technique, see Chapter 4. 9.45 The data sources drawn on for the weights in (11) There is a possibility that some users may be confused by having more than one index covering essentially the same housing strata. However, the Bureau of Labor Statistics a residential property price index are a function both of now has two monthly published Consumer Price Indices: their headline Lowe type CPI which is not revised and a second index which is an approximation to a superlative the data needs of the target index and of the availability Törnqvist index (which is revised). Users in the U.S. seem to have accepted multiple of the required information. Also the data needs depend indices in this context. ( ) A related issue is that some of the methods for constructing an RPPI, such as the 12 not only on the conceptual basis of the index but also on multiperiod time dummy hedonic method (see Chapter 5) and the repeat sales detailed aspects of index construction, such as the method method (Chapter 6) suffer from revision in the sense that previously computed figure will change when new data is added to the sample. In some cases, revised indices are of quality adjustment and any subindices that are required published while in other cases, the rolling window technique with updating due to Shimizu, Nishimura and Watanabe (2010) and Shimizu, Takatsuji, Ono and Nishimura (2010) is used. The rolling window with updating technique does not revise the (13) Consisting of the seventeen member states of the European Union that have adopted historical index up to the current period. the Euro as of 2012. Handbook on Residential Property Prices Indices (RPPIs) 109 9 Data Sources for analytical and other purposes. For instance, the con- houses could be considered incomplete. The use of formal struction of a mix adjusted property price index based on mortgage finance is often very limited but informal finance transactions requires that enough information is known may be used. House construction can vary from shanties about the sales in each period for them to be classified into built on compacted soil with salvaged materials to sub- groups sufficiently homogenous so that the unit values can stantial multi-room dwellings built on concrete founda- be treated as prices. In the housing market, the problems tions with concrete blocks. Amenity levels can vary from are compounded by the low volumes of sales for certain virtually none to the elaborate. Housing mobility, particu- house types in particular geographical areas which could larly with owner-constructed dwellings, is usually very low lead to many cells being empty. (14) and consequently the markets for rental or sale of owner- constructed houses are limited and there is very little 9.46 Putting these detailed issues of construction to one movement between the two. In principle the compilation side, the conceptual basis of the index is the main factor of a house price index is the same for owner-constructed determining the data needs relating to weights. One price housing as for third party constructed housing, but the index cannot meet the diverse needs of users. For estimat- measurement problems are, at the least, different and are ing gross capital formation, for instance, only new houses generally more difficult. (15) should be included while estimating the effect of price changes on capital stocks requires the index to cover all 9.49 The above complications mean that formal records transactions. will rarely be kept of the cost of building the new dwelling or of upgrading an old house, for example, by incorporat- 9.47 The weights can be derived from a number of ing running water, an internal WC or additional rooms. sources, in particular, from national accounts data, peri- Formal transfers of ownership sometimes do not take place, odic national censuses which collect information on the formal valuations are often not available and methods of fi- housing stock, information from banks on the loans tak- nancing can be informal through the family or may simply en out for house purchase, construction statistics, official not be recorded or records not kept centrally. Thus in these registers recording ownership, etc. There can be a lack of circumstances it will not be possible to calculate mortgage coherence between these different data sources resulting interest payments (including or excluding notional interest from the long and quite often involved processes associ- payments to relatives), or to estimate net acquisition costs. ated with buying and selling a house and the fact that a valuation or offer price associated with an application for a 9.50 The lack of such basic information often means mortgage will not necessarily lead to a sale and change of that the rental equivalence or an imputed rent approach is ownership. Other issues arise also, such as the distinction the only practical option for constructing a housing price between what is being built for selling and what is being index. The price indicator for imputed rents can be derived built for renting out. This sort of information is rarely read- either from a readily available price series for rents, re- ily available from one statistical source. It is for this reason weighted to reflect the current composition of the stock of that the construction of weights may draw on a multitude owner-occupier housing, which can then be applied to the of different sources. rental equivalents in the base period, or from asking an ex- pert to provide on a monthly basis the equivalent rents for a sample of houses which is representative of the owner- occupier housing stock. Developing Countries, 9.51 In each case, stratification by type of dwelling Traditional Dwellings (house or flat), location (region or area, urban or ru- ral), plus other characteristics which will influence rent and the Informal Housing is important so that the rents data can be combined to reflect the composition of owner-occupied property. Market Other stratification variables may include such things as the total size of the plot, floor area and number of rooms, 9.48 For many developing countries, a significant pro- whether there is mains water, an internal WC and mains portion of the housing stock consists of newly constructed electricity, the material used in construction and whether buildings on family owned land or of old buildings which the building is of traditional design. The price statistician have been significantly upgraded since they were first con- should seek the advice of an expert active in the field of structed. There can also be a significant element of owner- renting domestic property, such as a housing corporation, constructed housing. Construction may take many years and at any point in time a substantial proportion of the (15) In particular, the important price determining characteristics of the structure can be quite different for a developing country than for a developed country. In a developed country, there is perhaps less variation in the type of construction and the materials (14) The stratification or mix adjustment method was discussed in Chapter 4. In the example used whereas the quality of shanties could differ more markedly. Also land title may be for the Dutch town of “A”, many cells were indeed empty. A “matched-model” approach missing in many instances in developing countries which again can create problems for was suggested to cope with this problem. mix adjustment and hedonic regression techniques for adjusting housing quality. 110 Handbook on Residential Property Prices Indices (RPPIs) Data Sources 9 to ascertain the most important rent-determining char- 9.53 Relevant characteristics for the computation of a acteristics and should bear in mind the need to keep price index, that are encountered in traditional and other these to a manageable number. Weights information can dwellings in the informal market include: be derived from the latest Housing Census or Census of • Electricity supply. This will often be electricity supplied Population and Housing. In practice this information by a generating or distribution company. However, elec- may not be up-to-date due to the change in the owner-oc- tricity may also be generated by the household itself, e.g. cupied housing stock which can occur in the time period from a diesel generator or wind power, or may be taken between censuses. Where this is the case special surveys illegally from the distributor. may need to be conducted or, particularly in urban areas • Running water. This may be piped into the dwelling itself including townships, use made of planning applications to update the latest census. or the dwelling takes water from a communal standpipe or well. 9.52 But the measurement problems can be signifi- • A private or communal toilet, which may be either a wa- cant. In summary, traditional or informal dwellings are ter-flushing WC-type or a chemical toilet. generally built by family members or other unpaid la- In addition there is, as with any home the issue of living bour. The walls can be made of less durable materials space, recorded in terms of number of rooms, m2, or both. such as dried clay, bamboo or latticework and the roofs For this there need to be relevant definitions. In particular, can be made from reeds, straw or palm fronds or corru- definitions of usable floor space (the floor area of the liv- gated iron. The dwellings may or may not have electric- ing room, kitchen, hall, bathroom and all adjoining rooms ity or piped water in the dwelling, let alone other facili- minus the wall thickness and door and window recesses ties. Traditional dwellings are generally located in rural and excluding e.g. stairs) and of the number of rooms (e.g. areas. Some associated complications when attempting to whether to include or exclude hall-ways) are required. to include the owner-occupier housing costs in a con- sumer prices index are: 9.54 Finally, even if information on the characteristics of these dwellings is available there may not be an “equiva- • Many such dwellings are located in or very near to lent” rental unit to value the services of an owner-occupied large cities, such as shanty-towns. These dwellings may unit. Thus the indirect measurement of prices may not be be rented or owner-occupied and it may be difficult to possible. In this situation, statisticians can put a system in obtain details of ownership. Conducting surveys can be place to measure input prices (construction costs) and then problematic. use this information to construct a user cost measure of the • There are many such dwellings in rural areas that may be housing services as a proxy for the prices of the housing built with family labour on family or unregistered land services consumed. (16) For own-account consumption, the or land in “common” ownership. System of National Accounts 1993 (SNA 1993) recognises that it may only be practicable to measure input prices. In these circumstances, the concept of “ownership” be- The issues discussed above are considered in the case study comes a grey area. Thus the definition of owner-occupied on the compilation of residential property price indices in housing and what a family actually own is subject to debate South Africa, which can be found in Chapter 10. and even when there is an agreed upon definition, even ba- sic records of the number of such owner-occupied housing (16) See Blades (2009) for additional material on constructing these user costs for traditional may not exist let alone details of the dwellings. housing in developing countries. Handbook on Residential Property Prices Indices (RPPIs) 111 Methods Currently Used 10 10 Methods Currently Used Introduction also begs the question of whether international best prac- tice in the methods for constructing such indices can be 10.1 In practice, the methods used for constructing res- identified, or whether the techniques adopted inevitably idential property price indices can be constrained in large are governed and dependent on local conditions. part by the nature of the data available. The data required 10.6 Other sections of this handbook provide recom- to construct the target index, once defined, are not always mendations on best practice. This chapter describes the available on a regular and timely basis, if at all. Moreover, range of available indices by different countries and also even where suitable data are available to construct a price presents some case studies. It relies on meta-data gath- index to meet the needs of one set of users, more often than ered by various organisations, including the Bank for not, the data does not fit the requirements of another set International Settlements and the European Central Bank of users. For many countries setting up the required infra- and more recently a fact-finding exercise conducted by structure and procedures for the collection of the data nec- Eurostat in connection with the inclusion of owner occu- essary for producing a property price index can sometimes pied housing costs in the European Union’s Harmonised be prohibitively costly. Also, changes in methodologies and Index of Consumer Prices, which was extended to cover in the underlying data sources can frustrate the construc- some non-EU countries. Meta-data on residential property tion of historical series, which are often required for econo- price indices published by different countries are available metric modelling and analyses over more than one cycle from the website of the Bank for International Settlements of housing market developments to inform policy options (BIS); see www.bis.org/statistics. (1) for the management of the economy. Last but not least, the timeliness and frequency of the data, when available, may not be suitable for producing the kind of house price index that the users want or need. Index Availability 10.2 For users, this data shortcoming for the construc- tion of house price indices and related indicators has 10.7 At a European level, Eurostat has started releasing sometimes been a source of frustration. For example, the since December 2010  quarterly reports on experimental then Governor of the Bank of Canada in a speech to the house price indices in the EU and euro area. (2) These re- Conference of European Statisticians (Dodge, 2003) stat- ports contain, for those EU statistical offices that have giv- ed: “Given that the investment in housing represents a big en their permission for publication, experimental data on chunk of household spending, and that for most people house price indices. The annexes to these quarterly reports their homes represent their most valuable asset, it is sur- contain all currently available links to National Statistical prising that in many countries there are no comprehensive, Institutes web pages dealing with house price indices, quality-adjusted data on housing prices or rents”. where details concerning the compilation are given. 10.3 In addition, the data sources and the methods are 10.8 It can be seen from the available meta-data on the not always well documented, and surveys of meta-data on BIS website (3) that the methods used to compile residen- residential property prices confirm that there is a lack of tial property price indices vary considerably, both among harmonisation in the practices. This represents a further countries and even within individual countries. The latter challenge for users. In particular, it compromises the pos- raises a key question for users with regard to which series sibility of making meaningful international comparisons should be used to meet their particular needs. With re- of trends in house prices and makes any comparative gards to the former, a key issue is raised for users about the economic analysis extremely difficult. This can bring into validity of available international comparisons. question the credibility of the results. 10.9 The differences between the available house price 10.4 Data availability apart, the methods used by coun- indices cover almost every aspect of price index construc- tries to compile residential property price indices have also tion. These have been referred to in earlier chapters: the to confront some inherent problems, most particularly, that conceptual basis of index (i.e., what is the appropriate properties have unique characteristics, resulting in hetero- target index to suite each user need); data sources (prop- geneity in different dimensions, many of which are difficult erty registrations, tax records, mortgage applications and to measure objectively, and that transactions of individual properties are infrequent. Both of these issues make the compilation of price indices especially challenging. In ad- (1) The property price statistics on the BIS website include data from thirty-seven countries and are available at different frequencies. The data differ significantly from country to dition, the fact that asking prices are negotiable means that country, for instance in terms of sources of information on prices, type of property, area covered, property vintage, priced unit, detailed compilation methods and seasonal the transaction price may differ from the initial or final adjustment. This reflects two facts. First, that the processes associated with buying and asking price, the offer price and an expert valuation. selling a property, and hence the data available, vary between countries and, second, that there are currently no specific international standards for property price statistics. 10.5 The identification of the techniques most widely ( ) See http://epp.eurostat.ec.europa.eu/portal/page/portal/hicp/methodology/owner_ 2 occupied_housing_hpi/experimental_house_price_indices used in compiling indices of residential property prices (3) See http://bis.org/statistics/pp.htm. 114 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 completions, real estate agents, print media such as news- the department which has policy, operational or legal re- papers and other forms of advertisements); market cover- sponsibility for the housing sector. The latter is the case age (geographical coverage, type of property, mortgage/ with the Federal Housing Finance Agency in the USA, for cash transactions); quality adjustment (hedonics, mix- example, and in the UK. The government department with adjustment) and weighting (stock or sales weighted). The policy or operational or legal responsibilities for the sector problems caused by these different factors can be exacer- is often in a better position to gain access to administra- bated by the fact that housing markets can be highly het- tive information for statistical purposes and should also be erogeneous. Thus not only do properties vary in price ac- well-informed about the sector and may even have access cording to their physical attributes such as floor area and to additional useful background information. whether they are detached houses on their own plot of land or an apartment in a high-rise complex. The prices can also diverge widely depending on, for example, the region of Data Sources the country, the area of the town or whether the location 10.12 In Canada, the USA and several European coun- is classified as rural or urban. Location affects desirability tries (5), data on residential property prices are collected by which leads to different demand conditions, thus explain- the national statistical institutes or ministries. The source ing why an otherwise identical house may have a different of official residential property price indices in Denmark, price depending on its location. For instance, a property in Finland, Lithuania, the Netherlands, Norway, Hong Kong, a region with a high GDP per capita and low unemploy- Slovenia, Sweden and the UK is data gathered for regis- ment and in a locality known for the quality of its schools tration or taxation purposes. In Germany, the Federal and pleasant surroundings will command a higher price Statistical Office collects prices from the local expert com- than an otherwise identical property but in an area plagued mittees for property valuation. The statistical institutes in by high unemployment, low household incomes, poor Spain and France calculate price indices from informa- quality schools, and a high crime rate. (4) tion provided by notaries. In Belgium, Germany, Greece, 10.10 An overview of the current situation is presented France, Italy, Portugal and Slovakia, real estate agencies below. It should be noted that the position is changing as and associations, research institutes or property consultan- more countries develop their residential property price cies are the sources of price data. Data from newspapers indices and review the indices currently published. The or websites are collected for the compilation of residential reader should refer to the information from the websites property price indices in, e.g., Malta, Hungary (“Origo”) of the BIS, Eurostat and the ECB for more facts about the and Austria (“Austria Immobilienbörse”). The limited residential property price indices for a particular country. number of cases of integration of different data sources to add value and produce a better index is interesting given the number of countries that report multiple sources of in- Responsibility for Compilation formation on property prices. In Germany, Ireland and the UK, residential property price data are, inter alia, provided 10.11 In the EU, statistical offices have been cooperat- by mortgage lenders. The price index compiled by the UK’s ing in developing and compiling residential property price Department for Communities and Local Government is indices that are based on broadly harmonised statistical based on a mortgage survey conducted by the Council of approaches, thereby pioneering the work towards interna- Mortgage Lenders; the long time-lag associated with the tionally comparable house price indices. Also, several na- registration of property ownership transfers undermines tional central banks compile house price indicators, includ- the use of the latter as a timely indicator. In Germany, the ing Belgium, Germany, Greece, Italy, Cyprus, Luxembourg, Association of German Pfandbrief banks uses the data Hungary, Malta, Austria, Poland and Slovakia. In Austria, of its member banks for compiling a residential property the national central bank works jointly with the Vienna price index. University of Technology, while the price index compiled by the Central Bank of Luxembourg is based on the data 10.13 Comparability between indices can be very lim- from the country’s national statistical institute. In Ireland, ited as a result of the different data sources listed above – France, Spain, the UK and the USA, residential property mortgage versus cash purchases; urban versus rural prices; price indices are compiled by government departments the prices of old properties versus new properties; valua- other than the statistical office. In some instances, such as tions versus advertised prices versus initial offer prices ver- in the UK, this reflects in part the fact that the statistical sus final transaction prices. The net result is that published system is decentralised with government statisticians lo- indices can in practice measure very different aspects of cated in government departments and working alongside the price development in the housing markets. The de- their policy and service-delivery colleagues. In some cases, ployment of different data sources and compilation prac- responsibility for the compilation of the index resides with tices, and the use to which the index is put (i.e., the index (4) See for example Chiodo, Hernandez-Murillo and Oryang (2010). (5) Regarding the data sources in EU countries, see also Eiglsperger (2010). Handbook on Residential Property Prices Indices (RPPIs) 115 10 Methods Currently Used purpose) all explain the wide variation both in timeliness quarterly house price indices for each of the eight capital and in revisions policy. cities. Their approach stratifies houses according to two characteristics: the long-term level of prices for the sub- urb in which the house is located, and the neighbourhood Index Methodology characteristics of the suburb, as represented by the ABS Socio-Economic Indexes for Areas (SEIFA) (6). In practice, 10.14 The inherent difficulties with price measurement the number of characteristics included in the classifica- and the varying data sources used, lead to an array of dif- tion is often limited by the number of observations that ferent methodological approaches being adopted in the can regularly be found for each cell, i.e. by the ability to construction of house price indices. populate the “price-determining characteristics database” from the available data sources as well as by the availability Quality (Mix) Adjustment of information on price-determining characteristics. 10.18 The most sophisticated form of quality adjust- 10.15 Quality adjustment, to control for compositional ment used by countries is the hedonic regression approach changes (mix-adjustment) and for changes in the quality (discussed in Chapter 5) which uses a regression model to of the individual properties, is an essential part of index isolate the value of each of the chosen characteristics and methodology. It ensures that price comparisons are on a control for changes in the characteristics of the proper- “like with like” basis and avoids the possibility of bias in the ties sold. But this method is usually more data intensive. series when, for instance, the quality of the housing stock It is sometimes used in conjunction with stratification (by is improving as a result of, amongst other reasons, renova- type of structure and location). The use of hedonics in the tions to the dwelling, which can take various forms, such compilation of residential property price indices is, in large as the modernisation of kitchens and bathrooms, the intro- part, a fairly recent innovation. Countries which publish duction of improved insulation and central heating or air indices that have been compiled using hedonic regres- conditioning systems. Quality adjustment techniques also sion include Austria, Germany, Ireland, Finland, France, play an important role in the compilation of house price Norway and the UK. The hedonic model used in the com- indices because houses that come onto market will change pilation of the Norwegian house price index includes only from period to period. a few explanatory variables and does not adjust for housing 10.16 Quality adjustment is applied in a number of dif- standards and for the age of the building; (7) the index ad- ferent ways. For instance, a residential property price in- justs only for size and location of the dwelling. The index is dex for Estonia is derived from unit values, i.e., the aver- likely to be biased (unless the age of the structure and type age transaction price per square metre of floor space (in of dwelling sold is stable over time). This shortcoming is this particular case, the sum of the value of all real estate acknowledged by Statistics Norway. transactions divided by the sum of the square metres of 10.19 An additional method used in, for example, the floor space of all real estate sales, with outliers excluded). USA and Canada, is the repeat sales method (described in But unit value indices based on price per square meter of Chapter 6); i.e., the Case-Shiller home price index in the structure floor space, whilst adjusting for the size of the USA and the Teranet -National Bank House Price Index™ dwellings in each period, does not adjust for differences in in Canada. This approach matches pairs of sales of the the quality of construction or the age of the structure and same dwellings over time. It requires a huge database of perhaps more importantly, does not adjust for changes in transactions and is not used by any of the European index the mix of plot sizes in the sample of properties sold in compilers. any particular period. Other changes to the features of the house can potentially occur which, together with general 10.20 It is interesting to note that one of the residential trends in the housing market, are reflected in composi- property price indices for Germany is based on data that tional changes to the sample such as location, physical and is limited to “good quality” dwellings, which might imply environmental amenities, the general quality of housing, that the issue of quality adjustment is by-passed. In prac- etc. tice, there could be a built-in measurement problem, since it is unlikely that the market definition of “good quality” 10.17 The main alternative of mix-adjustment (dis- is independent of the general increase in housing stand- cussed in Chapter 4) utilises a classification of dwellings ards over time. For this reason there is potential for bias by what are generally recognised as important price deter- in the resulting index in the longer term. This is in addi- mining characteristics to calculate individual price indices tion to any concerns about sampling and, in particular, the for each cell in the classification matrix. The overall index is then calculated as the weighted average of these sub-in- dices. Mix-adjustment is in essence a form of stratification. This method is adopted by, e.g., the Australian Bureau of (6) See http://www.abs.gov.au/ausstats/abs@.nsf/mf/6464.0. (7) As was seen in previous chapters using the data for the town of “A”, the age of the Statistics to control for compositional change to compile structure is an important price determining characteristic. 116 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 capability of “good quality” housing to be able to represent for indexation of benefits but does not fully suit the needs the price trend of all houses. of users who want to calculate “wealth”, where stock rather than expenditure weights are most appropriate. The latter 10.21 It can be seen from the above paragraphs that two may be addressed either by a re-weighting of the official crucial questions for all quality adjustment procedures are: index or by reference to one of the many indices published (1) whether the chosen characteristics used for quality ad- by lenders. However, the latter suffer from limited cover- justment are the main determinants of price differences, age. Thus re-weighting of the official index may provide a and (2) whether the application of different techniques to cost effective solution to filling this particular data gap. the same data set will produce the same results (i.e., the issue of statistical robustness). In reality, while some of the 10.25 A more detailed gap analysis may point to solu- price-determining characteristics – such as the size of the tions involving synthetic estimates, based on the integra- living area – are easy to measure, other important factors tion of data from different sources. For example, it can be such as location (8) and the quality of construction, can be noted in the context of the UK that the DCLG house price inherently difficult to capture and measure. Also, it should index referred to above has the advantages of being timely be noted that the application of different quality adjust- and not subject to revision but has the drawback that it ex- ment techniques to the same data set will not necessarily cludes cash purchases. produce the same results. (9) 10.26 A systematic approach to the construction of indices of residential property prices in the UK might The Value of Meta-Data conclude that it is possible to supplement the official in- dex with information on cash purchases from the Land 10.22 A number of organisations have websites provid- Registry. Although the latter is less up to date due to the ing meta-data on the residential property price indices time-lag in registering transactions in the official registry, published by different countries. Most particularly, the time series modelling may be able to address this misalign- Bank for International Settlements provides such informa- ment. The Land Registry constructs a repeat sales index by tion (see the earlier reference). This is in addition to any tracking the average growth in house prices using multiple information provided by individual countries on, for in- transactions associated with the same home in an attempt stance, the websites of the national statistical institute or to hold quality constant. central bank. In the next section a series of case studies are presented 10.23 As well as providing the user with guidance on the relating to the residential property price indices published strengths and weaknesses of a particular price index and its in a selection of countries. appropriate use, a systematic and more detailed analysis of the meta-data on the currently available statistics and data sources can help to identify: • major gaps in data provision; Case Studies • options for filling these gaps cost effectively from readily available sources; • data coherence issues; Case Study: Canada • the scope for further data integration and the need for 10.27 In Canada there are four house price indices that new data sources. are currently available. These are Statistics Canada’s New House Price Index, the Teranet-National Bank Composite 10.24 Such an analysis of the basic meta-data also pro- House Price Index ™, the Canadian Real Estate Association’s vides evidence of the compromises made in relying on measure of average house prices, and the Royal LePage readily available data and where one all-purpose house Survey of Canadian House Prices. Each one will be ex- price index is used for a multitude of purposes. For ex- plained in turn. ample, the main official house price index published in the UK by the Department for Communities and Local Government (DCLG) uses sales weights and is appropriate The New House Price Index for inclusion in, for example, a Consumer Price Index used 10.28 The New Housing Price Index (NHPI) is a monthly price index that measures changes over time in the builders’ selling prices of new residential houses. Prices (8) The physical location of a property can be measured rather precisely but the problem with “location” is one of grouping of properties. Stratification and hedonic regression that are collected are from a survey of builders from vari- methods need to group together sales of properties in the same location but how ous areas of the country. It is a constant quality price index exactly should the boundaries of a location be determined (9) This point is illustrated by the differing indices that resulted from the application of inasmuch that the features and characteristics of the units different methods of quality adjustment described in Chapters 4-8 above using the same data set for the town of “A”. However, all of the methods did result in roughly in the sample are identical between successive months; in similar trends in prices. other words, the NHPI is a matched-model index. Separate Handbook on Residential Property Prices Indices (RPPIs) 117 10 Methods Currently Used estimates provided by the builder about the current value 10.31 From its conceptual basis, the Canadian NHPI (evaluated at market price) of the lots are also an impor- measures changes in the price of new houses only, so it is tant part of the survey. Consequently, given this informa- not representative of resale houses in Canada (or for most tion, Statistics Canada also publishes an independent price new houses built in the core of the cities surveyed). The index series for land excluding the structure. The residual houses surveyed for the index are generally found in new value (total selling price less land value), provides an in- tracts in suburbs of the survey cities where the price of land dicator of the trend in the cost of the structure and is also is significantly lower than in the city core areas. The move- published as an independent series. At the present time, ments over time in land prices in suburbs are generally dif- the three variants of the NHPI are published for 21 metro- ferent than the movements in the well established areas of politan areas in Canada. Canadian cities. While the construction price index part of the NHPI is likely to be accurate (the cost related to build- 10.29 Housing market analysts, academics, and the ing the house structure is approximately the same regard- public use the NHPI as a timely indicator of past and cur- less of the area), the land component probably understates rent housing market conditions. The NHPI is also used residential land price inflation for the existing housing as an input in the compilation of other economic statis- stock by a significant amount in recent years. (10) tics. For instance, it is used for estimating certain shelter components of the Consumer Price Index. Moreover, the Canadian System of National Accounts uses the NHPI in Teranet–National Bank Composite House Price estimating the constant price value of new residential con- Index ™ (11) struction. Due to the level of geographic detail provided 10.32 The Teranet-National Bank House Price Index™ and the sensitivity to changes in supply and demand, the (TNBHPI) is an independent estimate of the rate of change NHPI series are of particular interest to the real estate in- of home prices in six metropolitan areas, namely Ottawa, dustry for providing a proxy estimate of changes in the Toronto, Calgary, Vancouver, Montreal and Halifax. The value of resale houses sold. The information provided by price indices for the six metropolitan areas are then ag- the NHPI is also of interest to building contractors, market gregated into a composite national index. The indices are analysts interested in housing policy, suppliers and manu- estimated on a monthly basis using transaction prices for facturers of building products, insurance companies, fed- condominiums, row/town houses, and single-family de- eral government agencies such as Canada Mortgage and tached homes within the six metropolitan areas. Housing Corporation (CMHC), and provincial and mu- nicipal organizations that are responsible for housing and 10.33 The TNBHPI uses the repeat sales methodology. social policy. Estimating the indices is therefore based on the premise that houses that are traded more than once in the sample 10.30 The prices collected are asking prices by the build- periods are of a constant quality. The TNBHPI attempts to ers and exclude the Goods and Services Tax and other tax adjust for quality changes of the individual housing units related rebates. Missing prices as a result for example of by minimizing or eliminating the influence of any changes the absence of a sale by a builder in a particular month, in the physical characteristics (e.g., renovations, addi- are imputed using the best estimate the builder can provide tions, etc.). Insofar as (net) depreciation of the properties as if a house was to be sold. Not all types of housing are that are resold is neglected, the index is likely to exhibit included in the NHPI. Condominiums are excluded from a small downward bias. (12) Properties that are affected by the sample, while single-family detached units as well as row (terrace) and detached houses are included. Given that builders do not report the price of building lots uniformly, (10) See Figure 10.1 for a comparison of the NHPI with other indices for Canada. This figure the land price indices may be less accurate and precise than provides support for the likely downward bias of the land component of the NHPI. (11) ©Teranet and National Bank of Canada, all rights reserved. the overall NHPI. The same caveat applies to the derived (12) This downward bias does not seem to show up in Figure 10.1, since the TNBHPI is more or less in between its two competitor indices that cover the resale market, but residual values that are used for constructing the price in- the latter indices also do not make adjustments for net depreciation. Some housing dices for the structure only. Large builders as well as small- economists argue that the repeat sales method may have an upward bias due to a sample selectivity problem; it may be that dwelling units that are sold more frequently er independent builders are represented in the sample used than the average unit are being more intensively renovated and upgraded and hence for the NHPI. the quality of a repeat sales unit has actually increased between the two sale dates (rather than decreased due to depreciation). 118 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 endogenous factors are excluded from the calculation of data, and the classification of housing is more refined. For the repeat sales index. These factors may include: non- example, the survey includes prices on four types of sin- arms-length sale; change of type of property (for example gles or detached houses (detached bungalow, executive de- after renovations); data error, and high turnover frequency tached two-storey, standard two-storey, senior executive), (biannual or higher). two types of condominium apartment units (standard and luxury), and a townhouse. Royal LePage standardizes each The MLS® Average Resale House Price Indicator type in terms of the square footage, the number of bed- rooms, the number of bathrooms, the type of garage, lot 10.34 The Canadian Real Estate Association (CREA) characteristics, the status of the basement, and other crite- tracks, on a monthly basis, the number and prices of prop- ria. In addition, the properties in the survey are considered erties sold via the Multiple Listing Service® (MLS®) systems to lie within average commuting distance to the city centre of real estate boards in Canada. The statistics are availa- and are typical of other housing in the neighbourhood. As ble by paid subscription to those who want to use them. long as the broker filling in the survey sticks to these guide- Although the coverage of the indicator is limited to only lines, this is one way of ensuring some degree of constant houses that are sold through the MLS®, the system is quite quality. A comparative disadvantage of the Royal LePage active with about 70 % of all marketed residential proper- price data is its long publication lag. ties using it. The data are available for over 25 urban mar- kets defined by CREA, as well for the provinces and two 10.37 This survey is a basis for one of the house price territories; a national aggregate is also published. indicators used by the Bank of Canada for monitoring de- velopments in housing markets in Canada (13). Despite the 10.35 The indicators are simple arithmetic averages of wealth of price information on many other types of houses all sales prices in the market of interest, regardless of hous- in the Royal LePage survey, the indicator developed at the ing type. In addition, no consideration is given to the is- Bank relates only to a subset of singles that were regard- sue of compositional shifts in the sample over time or for ed as representative of the market when it was created in disparities in quality in the sample of units. So a change 1988. (14) For Canada and 11 local markets, the Bank’s price in the price indicator could reflect many factors other indicator is calculated as a weighted sum of the price of than the true price development. These factors range from detached bungalow (weight of 0.75) and the price of execu- quality differences that exist in the sample from period to tive detached two-storey (weight of 0.25). The price of each period to the influence of outliers with extremely high or type of housing is in turn a weighted sum of sub-regions, low prices due to special circumstances. In their monthly with weights set to be the sub-regional share of units sold reports, CREA staff have recently published a weighted as of a fixed date in the late 1980s. The “units” data were version of the national index (available back to 2006 only), obtained from MLS®. with weights corresponding to the share of owned dwell- ing units by major markets derived from the 2006 Census. A Comparative Analysis However, the price for each major market is still calculated as a simple average, and no attempt is made to track the 10.38 A comparative analysis of the four types of prop- potentially different trends among various housing types. erty price indices available in Canada is given in Figure The one major advantage of the MLS® price indices over 10.1. The period of analysis covers February 1999 to March other indicators is their timeliness, since data are typically 2010. All four series show an upward trend in residential released two weeks after the reference month. property prices over this period. However, the growth rates differ among the four series. The NHPI recorded the small- Bank of Canada - Royal LePage Survey est increase at 55 % over the entire period. By contrast, of Canadian House Prices the MLS® showed an increase of 122 %, more than double that of the NHPI. The Teranet-National Bank House Price 10.36 Prices in the Royal LePage survey reflect the opin- Index™ and the Bank of Canada- Royal Lepage indicator ions of Royal LePage with regards to the “fair market val- increased by 100 % and 92 % respectively. ue” for seven types of properties in a large number of geo- graphical areas. The information obtained is based on local data and market knowledge provided by Royal LePage bro- (13) http://www.bankofcanada.ca/en/rates/indinf.html kers. The geographical coverage is broad, just like the MLS (14) The Bank of Canada indicator is limited to detached bungalows and executive detached two storey houses. Handbook on Residential Property Prices Indices (RPPIs) 119 10 Methods Currently Used Figure 10.1. Four Residential Property Price Indices for Canada (February 1999 = 100) 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 Feb-1999 Oct-1999 Feb-2000 Oct-2000 Feb-2001 Oct-2001 Feb-2002 Oct-2002 Feb-2003 Oct-2003 Feb-2004 Oct-2004 Feb-2005 Oct-2005 Feb-2006 Oct-2006 Feb-2007 Oct-2007 Feb-2008 Oct-2008 Feb-2009 Oct-2009 Feb-2010 Jun-1999 Jun-2000 Jun-2001 Jun-2002 Jun-2003 Jun-2004 Jun-2005 Jun-2006 Jun-2007 Jun-2008 Jun-2009 MLS® Teranet -National Bank™ NHPI Bank of Canada - Royal Lepage 10.39 The higher growth rate of the MLS® price indicator starts slightly later and is not as acute. All four indices may be explained, at least partly, by the average price meth- start to show an upswing early in 2009 but the MLS® in- odology which is used for its calculation. As is well known, dex starts to turn earlier while the turning point from this approach does not control for period-to-period com- the NHPI index occurs last.  (15) In terms of volatility, positional shifts and this can result in a higher rate of in- the MLS® is the more volatile around its trend due to the crease in the index if there is a shift towards the upper end compositional shifts in the sample of houses sold each of the market in the houses being sold. The NHPI’s slower month. The other three indices, which to some extent ad- rate of increase is probably explained by the fact that the just for quality changes, show less erratic behaviour over index, although it controls for house type over time, does time. not control for location. New houses are constructed far- ther and farther away from the city centre where markets behave differently compared to properties sold in or near Case study: Germany the city core. 10.41 Quarterly residential property price index series 10.40 All four indices show the drop in house prices for Germany are available from 2000. Prior to that date that occurred during the economic downturn which be- the situation in Germany could be characterised as an gan late in 2008. But the MLS® index starts falling slight- ly sooner than the three others and its drop is deeper. (15) For an illustration of the impact on turning points of the different methodologies, see Compared to the other three indices, the fall in the NHPI Shimizu, Nishimura and Watanabe (2010). 120 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 uncoordinated set of different indicators provided by sev- house, freehold flat); type of house (free-standing, ter- eral private institutes. “These indicators mostly lacked a raced, semi-detached); type of construction (convention- clear methodological foundation and had a restricted cov- ally built, prefabricated); year of construction; size of plot erage. Moreover they gave – to some extent – contradictory of land; size of living area; furnishing/luxury elements signals.” (16) (kitchen, sauna/swimming-pool, attic storey); car parking facilities; characteristics of location (state, district, munic- 10.42 The Federal Statistical Office of Germany ipality; general rating of location: simple/medium/good); (Destatis) took action to improve the situation building number of rooms/floors. In addition, a land valuation is on available data sources. Germany had well-established provided. construction price statistics and statistics on purchas- ing values of building land. In addition, at the local level, 10.45 A combination of hedonic techniques and strati- the nationwide institution of Expert Committees for fication (one stratum for single-family/two-family houses Property Valuation, regulated by federal law, provided ac- and one for flats in apartment blocks) is used to adjust cess to comprehensive databases which contained trans- for the effects of quality changes in the type of properties action prices of building land and dwellings and the cor- being sold. The hedonic regression method that has been responding property characteristics. The main barrier to adopted is the “double imputation” approach, which was the exploitation centrally of the available data had been described in Chapter 5, where prices are estimated both for the differences in the collection systems across the feder- the base period and for the comparison period. Outliers are al states and among the individual local committees. The excluded. methods followed by Germany provide an interesting example of data integration i.e. the drawing on multiple Newly-built single family residential data sources. properties (17) Residential Property Price Indices 10.46 The compilation of a price index for this partic- ular type of newly-built properties draws on information 10.43 Different data sources and compilation methods from official country-wide construction price indices. are used to construct price indices for different market Construction price indices are available for various types segments. These are then combined to compute a resi- of structure (e.g., residential/non-residential buildings, dential property price index covering all types of proper- roads, road bridges) as well as for maintenance work. ties and sub-indices relating to existing and new dwell- Prices are collected quarterly for about 190  construc- ings respectively. The weights used in the compilation of tion operations (including materials). In total, about a price index for existing dwellings are the transaction 30 000 prices are reported by about 5 000 enterprises at expenditures in the base-year broken down into houses every collection date. The prices refer to the transaction and flats and by the federal state. For turn-key dwellings, prices relating to contracts concluded in the quarter, ex- the weights are derived from official building activity sta- cluding value added tax (VAT), i.e., profits and changes tistics and for self-builds construction weights are used. in productivity are taken into account. For self-builds, Indices are published within 90  days of the end of the the construction price index for “conventionally built reporting. single-family residential buildings” is used. A matched model approach is followed for the construction of the Newly built turnkey-ready dwellings index. and existing dwellings Prefabricated dwellings 10.44 Data is taken from the information gathered by the local Expert Committees for Property Valuation. 10.47 The price index uses official producer price sta- This data, that is collected at the time a contract is con- tistics for industrial products, in particular the price index cluded, covers all sales (cash and mortgage) and consists for prefabricated single-family houses without a basement of actual transaction price (both cash and mortgage) and with a specific set of characteristics. Again a matched a number of price-determining property characteris- tics – type of dwelling (single-family house, two-family (17) These are sometimes referred to as “self-built properties”. The builders include both future owners who do a major part of the building themselves and future owners who involve a building firm that is responsible for the main part of the building work (where (16) See Hoffmann and Lorenz (2006). the owner finalizes the work). Handbook on Residential Property Prices Indices (RPPIs) 121 10 Methods Currently Used model approach is adopted for the computation of the in- Case study: Japan dex. A specific feature of prefabricated dwellings is that the contracts usually provide for the purchase/sale of complete houses (e.g., single-family house without cellar), the char- Information on Property Prices acteristics of which do not change significantly over the 10.50 In Japan, official property price indices only relate short-term. to land prices. Information provided by the public sector includes the Public Notice of Land Prices (PNLP) con- ducted by the Ministry of Land, Infrastructure, Transport Building land and Tourism (MLIT), the Land Price Survey of each pre- fecture, the Land Value for Inheritance Tax of the National 10.48 The price indices for prefabricated dwellings Tax Agency, and the Land Value for Fixed Asset Tax of each and “self-builds” exclude the cost of the land. A price in- municipal government. All of these sources of information dex for building land is compiled from official figures on represent appraisal values estimated by licensed real estate the transaction prices of building land, recorded at the appraisers. time a contract is concluded. Each data set incorporates the following characteristics: location; characteristics of 10.51 Information on residential property price indi- the municipality; sale date; size of plot; the details of the ces (including structures) is collected by the private sec- outline planning permission e.g. whether for a house tor. The most representative property data set is called or for flats and building size. Unlike Statistics Canada’s REINS, which stands for the Real Estate Information NHPI, coverage is not restricted to development tracts Network System. REINS is a data network that was de- – the German index attempts to cover all newly-built veloped using the multi-listing service (MLS) of the US homes. and Canada as a model; the information is obtained via real estate brokers. The REINS data set contains both 10.49 The aggregate price index for developed build- the asking price when the property is put on the market ing land is a weighted average, using the total sales value, and the final transaction price at the time of the sale of unit value indices for sub-aggregates. These sub-ag- contract. A second, and quite unique, housing price data gregates are formed on the basis of regional differentia- source is accumulated through housing advertisement tion, mainly a differentiation by districts, building area vendors. Both data sources have been used by the pri- types and municipality size classes within federal states. vate sector to compute and publish housing price indi- The federal states are weighted by combining data on ces. However, all of these indices have shortcomings and the total of prices paid for developed building land in do not fully meet the needs of users. MLIT has there- residential building areas and in rural areas, turnover fore begun a work programme which should lead to the achieved through building activity and the number of construction of an improved index. This will be the first building permits for residential buildings with one or two residential property price index to be published by the dwellings. public sector. 122 Handbook on Residential Property Prices Indices (RPPIs) Table 10.1. Indices of Property Prices Published in Japan Seasonally adjusted? Weighing Index Sample Method Stage of process And (frequency) method Land Price Cumulative Appraisal prices in Public Preceding term index × Avg. No No Appraisal value in January 1st every Change Rate Index(MLIT) Notice of Land Prices by MLIT Volatility (Annual) year (published in the end of March) Major City Land Transac- Sales prices Average value of unit price No No Survey after sale registration tion Price Basic Statistic per square metre, median (Quarterly or annually) (sales price) (MLIT) value, standard deviation, quartile, etc. Urban Land Price Index Appraisal prices in Public No- Preceding term index × Avg. No No Appraisal value in the end of March (Japan Real Estate Insti- tice of Land Prices by Japan change rate (Semi-annual) and September every year tute) Real Estate Institute Recruit Residential Price Final asking prices in Overlapping Periods He- Yes Volume Offer made Handbook on Residential Property Prices Indices (RPPIs) Index (Recruit Housing Magazine or Online prices in donic Regression (Monthly) (final asking price) Institute) Magazine or Online Residential Market Index Asking prices or sales prices Unit price per square metre No No Offer made? (Japan Real Estate Institute, (building age adjusted by (Semi-annual) (asking price or sales price) At Home Co., Ltd., Ken hedonic regression) Corporation) Tokyo Area Condominium Sales prices registered at Hedonic regression No No Completion of sales Market Price Index (Japan the Real Estate Information (Monthly) (sales price) Research Institute, Limited Network for East Japan Real Estate Information Network for East Japan) Newly-Built Condominium Asking prices Moving average No No (asking price) Price Change Index (Tokyo (Quarterly) Kantei Co., Ltd.) Source: Shimizu, Nishimura and Watanabe Methods Currently Used 123 10 10 Methods Currently Used An overview of all property price indices in Japan is pro- are registered by the Legal Affairs Bureau which then sends vided in Table 10.1. This includes indices based on land ap- “Change in Register Information” to MLIT. Based on this praisal values as well as indices relating to property sales. It information, MLIT sends a questionnaire to the buyer on is the latter that generates the material for residential prop- vacant lots, land with buildings, buildings with compart- erty price indices. mentalised ownership (such as office, retail, and apartments) asking for the transaction price. Next, information is added Asking Prices and Selling Prices by real estate appraisers or their counterparts. This informa- tion includes building use, lot conditions (land form, etc.), 10.52 In Japan, the seller of a house usually sells it road conditions (width of fronting road, etc.), distance to through a real estate broker. Individuals that contract with the nearest railway station and other information related a broker have to sign one of two forms of a sales agent to convenience, and legal regulations such as city planning. contract: the exclusive agency contract or the sole agency The resulting “Transaction Case Data” collected in this way contract. The other option is to select a general agency con- is then made anonymous so that the actual property can- tract. These contracts are regulated under Article 34-2 of not be identified, and is then published as transaction price the Building Lots and Buildings Transaction Business Law. information on MLIT’s website. (18) Since neither the supply 10.53 In the case of the exclusive agency contract, the of information on transaction prices nor the supply of the seller can receive a report at least once a week from the real information requested from real estate appraisers is manda- estate broker, but the seller loses the right to ask another tory, non-response and timeliness are issues. The informa- broker to find a buyer and to look for a buyer himself. In tion supplied, including the transaction price, cannot be in- the case of the sole agency contract, another broker can- dependently verified. not be asked to find a buyer, but the seller can look for a buyer on his own and the report from the broker will be at Time Line for Buying and Selling a House least bi-weekly. In the case of a general agency contract, the and Price Accuracy seller can look for a buyer on their own and ask multiple brokers to find a buyer. On the other hand, the seller does 10.56 The choice of data source is of importance when not receive reports from brokers. calculating a housing price index. There are various issues involved, such as the moments at which price data is col- 10.54 In the case of the exclusive agency contract, lected, the change in “price” (from the initial asking price to the contracted broker must register the listing in REINS the final transaction price), and how timely the price data within five days of concluding the listing agreement and is released. Figure 10.2, which is borrowed from Shimizu, is required to widely look for buyers. In the case of the Nishimura and Watanabe (2011), shows the real estate sole agency contract, the broker must register the listing price information which is currently available in Japan on in REINS within seven days and do the same. For regis- a time axis. On the right, four stages are distinguished with tration in REINS, brokers are not only required to record prices P1 to P4. The corresponding time periods between the asking price at the moment of registration but also the those moments are: the “term” TM1  between the start of final transaction price. Thus for some transactions made the selling process and the moment a buyer is found; the via brokers, both the asking price and the final transaction term TM2 from when a buyer is found until the sale con- price are registered. tract is finalized; and the term TM3 between the final sale contract and the registration of the selling price in the gov- Public Data Gathering System ernment’s database. of Transaction Prices 10.55 MLIT has compiled and published information on property transaction prices since 2005. Property transactions (18) See www.land.mlit.go.jp/webland. 124 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 Figure 10.2. Property Information Flow Timing of events in real estate transaction process Real estate price information T1.House placed on market P1.Asking price in Magazine or Online (10 weeks) TM1 T2.Offer made P2.Final asking price in Magazine or Online T3.Mortgage approved (5.5 weeks) TM2 T4.Contracts exchanged T5.Completion of sale with Land Registry or REINS P3.Transaction price in REINS T6.Transaction registered with Land Registry (15.5 weeks) TM3 T7.Transaction price survey based on Land Registry P4.Transaction price in Government database Source: UK Office for National Statistics 10.57 The average duration of TM1 is 70 days. That is, on is 4.4 % lower than the final asking price. TM3 is on average average a buyer is found 70 days after the seller enters into 109 days. This means that (for surveyed transaction price the selling process; the maximum duration was 3.72 years. data) there is a time lag of approximately 3 months until The ratio of P2 to P1 is 0.976 on average, meaning that the the selling price is registered in the government’s database. price drops by 2.4 % from the initial asking price to the last The price differentials at different points in the selling pro- asking price. On average, TM2 is 39 days. The ratio of P3 to cess can, of course, vary over time depending on the state P2 is 0.956 on average, i.e. on average the transaction price of the owner-occupier housing market. Handbook on Residential Property Prices Indices (RPPIs) 125 10 Methods Currently Used Figure 10.3. Four Residential Price Indices for Japan (January 1999=100) 130 120 110 100 90 80 70 60 50 Jul-1999 Jul-2000 Jul-2001 Jul-2002 Jul-2003 Jul-2004 Jul-2005 Jul-2006 Jul-2007 Jul-2008 Jul-2009 Jul-2010 Jan-1999 Jan-2000 Jan-2001 Jan-2002 Jan-2003 Jan-2004 Jan-2005 Jan-2006 Jan-2007 Jan-2008 Jan-2009 Jan-2010 RRPI (Monthly) REINS (Monthly) PLPI (Yearly) ULPI (Half Yearly) Source: Shimizu, Takatsuji, Ono and Nishimura (2010) Comparative Analysis of House Price Indices latter continued to decrease. Notice that the REINS index in Tokyo Metropolitan Area is much lower than the RRPI, in spite of the fact that both are hedonic indices. 10.58 Figure 10.3 compares four property price indices. The REINS data are used by the Real Estate Information Network for East Japan and the Japan Research Institute Case Study: United Kingdom who jointly produce the Tokyo Used Condominium Price Index. This monthly index has been published 10.59 The UK probably has more house price indices since 1995  and is constructed using a hedonic regres- published on a regular basis than any other country. The sion method. The Recruit Residential Price Index (RRPI) range of residential property price indices that are pub- is also a hedonic price index (19), based on the final offer lished in the UK mainly stems from the interrogation and price of properties in Recruit’s magazine, and relates to exploitation by different organisations of the different data re-sold single family homes and condominiums. This in- sets which are generated at different points in the process dex is also monthly and has been published since January of buying and selling a house. The latter often takes place 1986 (20), although only widely available in its current over a period of several months or more and the particular form since the beginning of 2000. Two land price indi- stage in this process at which the price is abstracted and ces, thus excluding buildings, are shown in Figure 10.3, entered into an index can impact on the measured rate of the bi-annually ULPI and the yearly PNLP. These are ap- house price inflation. In the UK the exploitation of data on praisal-based indices. (21) The property price indices that property prices occurs at the following stages: include the structures clearly show a different trend than • As soon as the property is on the market. Asking price. the land price indices. Also, the former began to recover (22) Publisher: estate agents, Data source: estate agents.  some years after the financial crisis in 2008 whereas the Financial Times and property websites. (19) The Recruit Residential Price Index uses the time dummy method and, in consequence, is subject to revision (see Chapter 5). (20) See Shimizu, Takatsuji, Ono and Nishimura (2010) for details. (22) Although not related to the issue of timing, a disadvantage of advertised prices and ( ) Shimizu and Nishimura (2006) (2007) compare appraisal values and selling prices and 21 mortgage approvals is that not all of the prices included end in transactions, and in the point to the problems of valuation errors and smoothing in the appraisal-based indices. former case, the price will tend to be higher than the final negotiated transaction price. 126 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 • Mortgage approved. Valuation by mortgage lender. Data Communities and Local Government (DCLG) and is based source: mortgage lenders. Publishers: various mortgage on information provided by mortgage lenders, through the lenders. Council of Mortgage Lenders, on valuation price at the • Mortgage completed. Mortgage completion price. Data point when the sale is completed. It is published about six source: mortgage lenders. Publishers: The Department weeks after the reference date for the house sale – or, on for Communities and Local Government (DCLG) average, about four-five months after a house is first put up • Transaction registered. Transaction price. Data source: for sale. It only covers purchases involving a mortgage. The Land Registry. other is published monthly by Land Registry based on sales The time-line for buying and selling a house in the UK, includ- of properties registered with them. It is published a month ing the different points at which information is collected and after the reference date; i.e., one month after the registra- used to produce a house price index, is given in Figure 10.4. tion of the sale but suffers from a lack of timeliness due to 10.60 The UK currently has two official house price delays from homebuyers or their agents notifying the Land indices. One is published monthly by the Department of Registry of transfers of ownership. Figure 10.4. House Purchase Time-line DCLG, £ Land Registry, SOLD Registers of Scotland, LSL/Acadametrics £ UNDER Nationwide, E Halifax £ OFFER M FOR Rightmove £ SALE I RICS, Hometrack T Source: UK Office for National Statistics 10.61 Two mortgage lenders, Halifax and Nationwide, Hometrack conducts a monthly survey of estate agents publish indices based on their valuations of a property at who are asked to gives their view on the achievable selling the time that they grant a mortgage. These indices are pro- price for each of four standard property types. It is the most duced within a few weeks of the reference data for granting timely of all the published indices, being published about the mortgage and about three to four months after a prop- three to four weeks after the reference period with in effect erty is put up for sale. They are a little more timely than the no other time-lags involved, but it is an opinion survey of official DCLG index but have a much more restrictive cov- the likely selling price of properties on the market. erage with no guarantee that the properties that they have A research based consultancy firm, Acadametrics, also pub- granted mortgages on are representative of either all prop- lishes a house price index based on data provided by the erty transactions or all purchases involving a mortgage. Land Registry. The LSL/Acadametrics index is published a 10.62 Another index is compiled by an organisation few weeks after the end of the reference period based on an named Hometrack, a business service company which pro- “index of indices” forecast method. The index for each time vides a range of market intelligence on the housing mar- period is subsequently revised until all transactions have ket to organisations across the residential sector including been included. An index based on asking prices advertised Developers, Housing Associations, Corporate Investors, on the Rightmove property website is also widely used in Estate Agents, and Local and Central Government. the UK. Handbook on Residential Property Prices Indices (RPPIs) 127 10 Methods Currently Used Table 10.2. Indices of Residential Property Prices – Published in the UK Seasonally Weighing Index Sample Method Stage of process adjusted? method DCLG (1) Sample of Mortgage Mix-adjustment and hedonic Yes Expenditure Mortgage completion Lenders regression (transaction price on mortgage document) Land Registry Sales Registered in Repeat Sales Regression Yes Expenditure Sale registration (monthly) England and Wales with a (transaction price) previous sale since 1995. Halifax Halifax loans approved for Hedonic regression (quality Yes Volume Mortgage approval house purchase adjustment) (valuation price) Nationwide Nationwide loans Hedonic regression (quality Yes Volume Mortgage Approval approved for house adjustment) (valuation price) purchase Hometrack Survey of estate agents Mix-adjustment No? Expenditure Achievable selling (valuations) price Rightmove Asking prices posted on Mix-adjustment No Expenditure (asking price) website LSL/ Sales Registered in Eng- Forecasting model, includes Yes Volume Sale registration Acadametrics land and Wales mix adjustment. (transaction price) (1) Department of Communities and Local Government. A review into house prices indices by the UK National Statistician can be found on web pages: http://www.statisticsauthority.gov. uk/national-statistician/ns-guidance-and-reports/national-statistician-s-reports/index.html. Source: UK Office for National Statistics 10.63 Table 10.2  summarises the scope and definition house. Furthermore, the registration procedure and records plus the main aspects of compilation method for the sev- maintenance are not computerized and the records are en indices available in the UK shown in the time-line in maintained in regional languages which necessitates further Figure 10.4. Given the differences in definition, scope and work with respect to bringing them into common format. coverage it is not surprising that these indices when taken 10.66 For these reasons, the administrative data relating together do not always show a coherent picture. to the registration of changes of ownership are not exploited and an alternative source of data has had to be found. This Case Study: India alternative data source relates to market data based on trans- action prices collected by the National Council of Applied 10.64 Movement in prices of real estate, particularly Economic Research (NCAER), a national level research residential housing, is of vital importance to the macro organisation, from Resident Welfare Associations (RWAs), economy of India as well as to individual households. It real estate agents and brokers. The valuation data of housing is not surprising that there is a user demand for a relevant loans financed by Banks and Housing Finance Companies and reliable index for tracking house price movements. But (HFCs) are collected to supplement the actual transaction a lack of transparency in the residential property market price data collected through survey. These data are then used transactions and limited availability of price information to compile the National Housing Bank’s RESIDEX index. pose important challenges for keeping track of real estate price dynamics. The NHB RESIDEX Index 10.65 Registration of the property price is a legal neces- 10.67 NHB RESIDEX is a pioneering attempt by the sity for any property transaction in India. So in principle, National Housing Bank (NBH), an apex bank for the the official authority of property registration has the details housing sector owned by the Central Bank of India, to of all transactions during a reference period. In theory the measure residential prices in India. As a pilot, five cities data are available on a daily basis with a month lag from first – Bangalore, Bhopal, Delhi, Kolkata and Mumbai – were reporting a change of ownership. However, it is well known studied. The process of data collection posed many chal- that the registered prices of houses are grossly underesti- lenges. There were also several methodological issues re- mated due to very high registration fees and stamp duty. lating to the analysis of data. In the event and after much The subsequent obligations for the payment of property tax work, the NHB launched its first RESIDEX for tracking acts as a further disincentive to individual purchasers (ex- prices of residential properties in India, in July 2007. The cept corporate bodies) for revealing the exact sale price of a index is based on actual transactions using the sale price 128 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 plus supplementary data on valuations. Primary data on • No quality adjustment is currently made in terms of lo- housing prices is collected from real estate agents by com- cation, size etc. missioning the services of a consultancy/research organi- • It is revisable to take account of late data. zation of national repute, who obtain transaction prices. In addition, data on housing prices are also collected from • Information on the movement in prices of residential the housing finance companies and commercial banks. properties by location, zone and city, is also available, e.g., The latter relates to the valuation prices associated with the separate indices are available for each zone in each of the housing loans contracted by these institutions. fifteen towns covered. 10.68 The salient features of NHB’s RESIDEX are: 10.69 For a country the size of India the geographical dimension is important. For example, the city-wise price • It covers all types of residential properties in fifteen indices, shown in Figure 10.5, help home buyers with their cities. (23) purchase decisions by enabling comparisons between lo- • With 2007 as base, NHB RESIDEX index is produced on calities and help builders and developers in making future a quarterly basis. (24) investment decisions. • Alternative series are compiled based on transaction 10.70 Development of the NHB RESIDEX to increase weights and stock weights. its relevance to users continues: • It covers cash purchases and purchases financed via a loan. • The index will be expanded in a phased manner to cover • It covers new and old constructions. all 35 cities in India having a million plus population as • The index is constructed “using weighted averages of price per the 2001 Census. relatives”. (25) • There is a proposal is to expand NHB RESIDEX to 63 cities which are covered under the Jawaharlal Nehru (23) In due course, based on experience and depending upon the availability of data, it may be expanded to cover commercial properties, as well. National Urban Renewal Mission, the flagship national (24) 2001 was taken as the base year for the pilot index based on five cities to be comparable mission of the Government of India, to make it a Na- with the base year(s) of Wholesale Price Index and Consumer Price Index. Year on-year- price movements during the period 2001-2005 were captured, and subsequently tional Index. updated for two more years i.e. up to 2007. The index was then expanded to cover ten more cities viz., Ahmedabad, Faridabad, Chennai, Kochi, Hyderabad, Jaipur, Patna, • In due course, based on experience and depending upon 25 Lucknow, Pune and Surat, at which point the base year shifted from 2001 to 2007. ( ) It should be noted that this is a weighted Carli index and as such is likely to have an the availability of data, it may be expanded to cover com- upward bias; see CPI Manual (2004), page 361. mercial properties. Figure 10.5. NHB RESIDEX Indices – India Citywise index 200 175 150 125 100 75 50 t hi i ne r a ta l ch ai i ra w pu ru pa ad ad tn ba ad l ka nn Pu no De Su Ko lu Pa o i ab b um ab Ja l Bh Ko ga ck ra e rid Ch ed M de Lu n Be Fa m Hy Ah Jan- June 2008 Index July- Dec 2008 Index Jan-Jun 2009 Index July-Dec 2009 Index Jan –Mar 2010 Index Base Year (2007) Index Source: National Housing Bank of India Handbook on Residential Property Prices Indices (RPPIs) 129 10 Methods Currently Used Case Study: Colombia (see below). In addition an index is published based on an- nual averages. Sub-indices are produced for the principal 10.71 A house price index for existing houses, the IPVU, metropolitan areas: Bogota; Medellin; and Cali. is compiled by the Banco de la República (Central Bank 10.74 Houses are classified according to whether they of Colombia). There are some other indices that relate to receive subsidies or not. These relate to the VIS and NOVIS construction costs and the prices of new housing units, indices, respectively. The receipt of a subsidy depends on which are produced by DANE (the national statistics office the value and location of the house. The term Low-Income of Colombia). No series is produced which amalgamates Housing (LIH or VIS in Spanish) refers to residences which the information from the two series to produce an index are developed to guarantee the right to a house for low-in- covering sales of all residential property in Colombia. (26) come households. On each development plan, the national In the past, consideration was given to the exploitation of government will establish the maximum price and type administrative data but this was found not to be possible of residences meant for these households. They will take due to the complexities involved. into account, amongst other aspects, households’ access to credit markets, the amount of credit funding available from The IPVU the financial sector, and available government funds aimed 10.72 The project to construct a price index for existing to target housing programs. (27) houses in Colombia, the IPVU, started in 2003. In the past, 10.75 The methodology applied is similar to the Case- the lack of access to basic information had been the prin- Shiller repeat sales methodology. There is a lack of detailed cipal barrier to the construction of such index. After con- information on the characteristics of housing needed sulting with several lending banks about the importance of to address the constant “mix” requirements of the Case- having a measure of the value of existing houses, the pro- Shiller method through the use of stratification. However, ject was launched with finance from the Central Bank of progress is being made with the expectation that the in- Colombia (Banco de la República). The Statistics Section formation provided by the mortgage lending banks will in of Banco de la República is in charge of the production and the future include a wide array of data on house specific publication of the index. characteristics. The current lack of detailed characteris- 10.73 The IPVU is restricted to the principal metro- tics is dealt with by data editing. If the property shows an politan areas of Colombia, covering the cities of Bogotá, “abnormal” price change, i.e. if it is deemed to be an out- Medellín, Cali and Soacha in Cundinamarca, and Bello, lier, the price information is discarded and does not enter Envigado and Itaguí in Antioquia. The index is calculated the index. This is in order to prevent re-modelled or ne- using information from loan’s appraisals reported by the glected houses from entering the index. The index is revis- mortgage lending banks Davivienda, BBVA, Av. Villas, able, reflecting one of the characteristics of the repeat sales Bancolombia, Colmena BCSC and Colpatria. In conse- methodology. quence, the index covers only properties purchased using a loan – cash purchases are excluded. The banks provide A comparative Analysis the Banco de la República with the commercial values and 10.76 The detailed sub-indices which are available pro- addresses of all approved mortgages. The prices which are vide the opportunity for a more-detailed analysis of the entered into the index are taken from independent valu- market in existing homes. An indication of the range of ations required by the mortgage lender. The valuation is outputs available to the user is given by Figures 10.6-10.10. close to the market price when the disbursement is made. The “indice nominal” uses the prices reported by the Banks, The index is published on the Bank’s webpage, on a quar- i.e., it is not deflated; the “indice real” is the IPVU deflated terly basis with a lag of a quarter and is revisable on a quar- by the CPI average for the year. In the case of quarterly terly basis, reflecting the repeat sales methodology used indices the IPVU is deflated by the CPI quarterly average. (26) The integration of the two indices would raise the issues of a lack of consistency and incoherence. For example, the IPVU index is based on independent valuations when a (27) For more information on this topic, see http://www.cijuf.org.co/codian03/junio/c31847. mortgage is applied for and the DANE index is based on asking price. htm. 130 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 Figure 10.6. Quarterly National House Price Index for Existing Units – Nominal and Real (Base 1990 = 100) 120 1200 110 1000 100 800 Indice Nominal Indice Real 90 600 80 400 70 200 60 0 1988-Q1 1989-Q1 1990-Q1 1991-Q1 1992-Q1 1993-Q1 1994-Q1 1995-Q1 1996-Q1 1997-Q1 1998-Q1 1999-Q1 2000-Q1 2001-Q1 2002-Q1 2003-Q1 2004-Q1 2005-Q1 2006-Q1 2007-Q1 2008-Q1 2009-Q1 2010-Q1 2011-Q1 2012-Q1 Real Nominal Source: Departamento de Programación e Inflación Banco de la República, Colombia Figure 10.7. Quarterly National Real House Price Index for Existing Units – Annual Percentage Changes 30 20 10 0 – 10 – 20 1989-Q1 1990-Q1 1991-Q1 1992-Q1 1993-Q1 1994-Q1 1995-Q1 1996-Q1 1997-Q1 1998-Q1 1999-Q1 2000-Q1 2001-Q1 2002-Q1 2003-Q1 2004-Q1 2005-Q1 2006-Q1 2007-Q1 2008-Q1 2009-Q1 2010-Q1 2011-Q1 2012-Q1 Real Source: Departamento de Programación e Inflación Banco de la República, Colombia Handbook on Residential Property Prices Indices (RPPIs) 131 10 Methods Currently Used Figure 10.8. Annual National House Price Index for Existing Units (1) (Base 1990 = 100) 120 1200 110 1000 100 800 Indice Nominal Indice Real 90 600 80 400 70 200 60 0 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Real Nominal (1) The annual publication of the IPVU takes the average index level over a period of twelve months and compares it with the average for the previous twelve months. Source: Departamento de Programación e Inflación Banco de la República, Colombia Figure 10.9. Annual Real House Price Index for Existing Units – Principal metropolitan areas (Base 1990 = 100) 125 115 105 95 85 75 65 55 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Cali Medellin Bogotá Source: Departamento de Programación e Inflación Banco de la República, Colombia 132 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 Figure 10.10. Annual Real House Price Index for Existing units: Houses with Subsidies (VIS) and Houses without (NOVIS) (Base 1990 = 100) 120 110 100 90 80 70 60 2011 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 VIS NOVIS Source: Departamento de Programación e Inflación Banco de la República, Colombia Case Study: South Africa townhouses and flats (apartments), whereas informal housing, that is housing which does not have planning 10.77 The following case study from South Africa pro- consent and will not be registered by the authorities, vides an illustration of the obstacles to the compilation of a includes shacks (typically built out of corrugated steel residential property price index when a significant propor- plates) and traditional dwellings includes rondavels tion of the housing stock relates to informal or traditional and huts made of traditional meterials. Backyard hous- dwellings. ing consists of dwellings that are situated in a backyard of a property with a main house, and shared property Introduction to the South African Housing housing occurs when more than one dwelling is con- Market structed on a single stand. The distribution of the South African housing market is as in Table 10.3. According to 10.78 Diverse dwelling types characterise the South the 2001 Population Census, the number of dwellings in African housing stock; it consists of formal, informal, trib- the formal market has increased by 37.1 % from 1996 to al, and other accommodation in backyard or shared prop- 2001; informal housing by 26.4 % and traditional dwell- erty housing. Formal housing includes stand-alone houses ings by 0.6 %. In contrast, backyard or shared property (government subsidised and private houses), attached has decreased by 14.5 %. Handbook on Residential Property Prices Indices (RPPIs) 133 10 Methods Currently Used Table 10.3. Tenure Status – All Housing in South Africa (According to Census 2001) Housing type Total Owner-occupiers (%) Renters (%) Houses 6 238 454 66.1 45.6 Subsidised housing (*) 1 074 028 9.6 – Flats 589 109 2.9 16.3 Townhouses 319 868 3.3 4.1 Informal 1 836 230 10.3 18.4 Traditional 1 654 787 15.0 4.1 Backyard or shared property 532 986 2.4 11.5 Total 11 171 434 100.0 100.0 (*) National Treasury estimate. Source: Statistics South Africa 10.79 In South Africa, builders and/or property devel- is applied to the data and the data may be revised. The FNB opers construct all residential property, with the excep- index is calculated monthly. tion of tribal and informal housing. For the construction of formal housing, a monetary transaction takes place by 10.82 ABSA House Price Index (HPI) measures the financing the dwelling with the money of the buyer and/ nominal year on year house price movements of houses or a mortgage bond. The dwellings and their values are re- purchased through approved mortgage loans from ABSA. corded at the local municipality and deeds office. For tribal The ABSA HPI is based on the total purchase price of hous- and informal housing, very few monetary transactions take es in the 80m²- 400m² size category, priced at R3 1 million place. Where they do take place, the transactions will be or less (including improvements). Prices were smoothed in small cash expenditures but the dwelling will generally not an attempt to exclude the effect of seasonal factors and out- be recorded by a local municipality. However, due to the liers in the data. The index is calculated monthly. demand for basic services, government has begun to re- 10.83 Standard Bank’s index is based on the median cord the number of dwellings in informal settlements and house price of the full spectrum of houses, using a five- rural areas, but the value of the dwelling is not recorded. month moving average. National data from the Deeds The situation represents an exceptional challenge for com- Office are available only with a lag of up to nine months, pilers of residential property price indices. so data from Standard Bank, which has a market share of about 27.7  % and whose data are generally highly corre- Residential Property Price Indices in South lated with those of the Deeds Office, are considered a good Africa proxy for the national market. The index is constructed on 10.80 There are various house indices published in a monthly basis. South Africa, but not by Statistics South Africa. Published house price indices include the First National Bank (FNB) Limitations to the Construction of a Residential House Price Index, the ABSA House Price Index and the Property Price Index Standard Bank Median House Price Index. (28) 10.84 In the construction of the above house price in- 10.81 The FNB house price series is constructed us- dices only formal housing (i.e., houses, townhouses and ing the average value of housing transactions financed by flats) purchased by means of a loan are included – cash FNB. To eliminate outliers from the data sample, transac- sales and “informal” housing are excluded. The difficulty tion values included in the sample must be above 70 % of in constructing an RPPI in South Africa is mainly due FNB Valuations Division’s valuation of the property but to the lack of acceptable estimates on housing stock and below 130 %, while purchase prices recorded as above R10- price information on informal and traditional dwellings. million are excluded. In order to reduce the impact on the These dwellings make up 19.6  % of all structures and index of rapid short-term changes in weightings of differ- therefore constitute a significant sector of the market in ent property segments, due to relative shifts in transaction South Africa. volumes, the weightings of the different market segments according to number of rooms are kept constant at their 10.85 The sector also has its own distinct features. For 5-year average weighting. A statistical smoothing function example, what defines an informal dwelling? • Residential areas where a group of housing units has ( ) ABSA, FNB and Standard Bank have the majority of the banking market share in South 28 been constructed on land to which the occupants have Africa no legal claim, or which they occupy illegally; 134 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 • Unplanned settlements and areas where housing is Table 10.4. Distribution of Number of Rooms not in compliance with current planning and building in Informal Dwellings regulations; • Informal dwellings are typically built out of corrugated Number % of total informal dwellings steel plates for the walls and roof (shack); of rooms 1  40.0 • The households themselves mostly build these dwellings. 2  27.2 What is a traditional dwelling? 3  15.1 • This is a general term, which includes huts, rondavels (29), 4  10.5 etc. Such dwellings can be found as single units or in 5 + 7.2 clusters. Source: Statistics South Africa • The dwelling can be made of clay, mud, reeds or other locally available materials. Weighting of Non-Formal Housing Primary Concerns in the Construction 10.88 Weighting of non-formal (informal and tradi- tional) housing will be complex in nature as the owners of a Residential Property Price Index construct most of the dwellings themselves and monetary 10.86 As stated elsewhere in this handbook, two main transactions are limited. In addition, materials for the con- problems in the construction of a residential property price struction of an informal dwelling are mostly second-hand index are the sporadic nature of transactions and a lack and for traditional dwellings, natural materials are used; of matching due to the fact that houses have unique price cost estimates for these types of materials are difficult to determining characteristics. In the case of formal hous- obtain and, indeed, they may have been gathered rather ing, these two factors apply, but for informal housing, the than purchased. second factor is much less important. Informal dwellings 10.89 Although most of the characteristics of the dwell- have, exceptionally, standard attributes since most of them ings are known from the population census, the value of are made of corrugated steel and have one to four rooms. an informal or traditional dwelling is difficult to estimate Similarly their location will tend to be in the same types of because there are no organised markets and the values are areas. In these circumstances the matching principle may not registered at a deeds or land registration office. Also, not be difficult to apply. In addition, the fact that the owner the movement of informal dwellings from one settlement of the shack does not own the land that the dwelling stands to another may pose a problem in the estimation of the on, implies that a decomposition of the index into land and housing stock. The rate of new constructions and demoli- structures is not relevant. The census 2001 indicated that tions would be unknown, since it is uncertain whether all the distributions of rooms are as in Table 10.4. dwellings that were broken down were erected once more 10.87 For traditional dwellings, the decomposition into in the new area. land and structures is not relevant either. In this case, the land is allocated to the person or household by the chief Pricing of Non-Formal Housing of the tribal area, and no cost or only a small fee is levied. However, to estimate the price of the dwelling may prove 10.90 Non-formal house prices do not depend on nor- problematic if, unlike formal dwellings, mainly natural ma- mal market price determinants. The plot area, location, age terials are used in the construction. and renovations typically do not affect the price. The only aspects that influence the cost of the dwelling are the mate- rials used and this is of course influenced by the size of the (29) A circular often thatched building with a conical roof. structure; see Table 10.5. Handbook on Residential Property Prices Indices (RPPIs) 135 10 Methods Currently Used Table 10.5. Price Determinants Price determinants Traditional dwellings Informal dwellings Formal dwellings Area of structure No No Yes Area of land No No Yes Location No No Yes Age No No Yes Renovations No No Yes Type of structure No No Yes Materials Yes Yes Yes Other price determining characteristics No No Yes Source: Statistics South Africa Table 10.6. Percentage of Materials Used in the Construction of Informal and Traditional Dwellings in South Africa Year 2002 2003 2004 2005 2006 2007 2008 2009 Materials used for roof Corrugated iron/zinc 72.1 72.1 71.6 78.2 79.5 78.6 78.6 83.6 Organic materials 23.2 24.2 23.8 16.8 16.2 17.1 15.8 13.3 Asbestos 1.9 1.6 1.4 1.7 1.8 1.2 2.1 0.5 Other 2.6 2.1 3.1 3.2 2.1 3.1 3.1 2.2 Total 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Materials used for walls Bricks 2.6 3.3 2.3 1.8 1.4 1.6 2.3 1.9 Cement block/concrete 2.9 2.2 2.8 1.9 2.5 2.3 2.4 1.4 Corrugated iron/zinc 35.1 36.1 33.9 40.0 43.6 43.9 41.4 42.2 Wood 9.8 9.4 8.9 9.6 10.5 10.8 10.1 8.6 Mud and cement mix 7.0 5.2 6.3 5.0 5.8 6.5 6.7 10.4 Wattle and daub 1.4 1.1 1.7 1.0 0.5 0.9 1.3 1.2 Mud 38.2 39.8 41.8 37.2 33.7 31.8 32.8 31.8 Other 2.6 2.9 2.3 2.6 1.8 2.2 2.9 2.5 Total 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Source: Statistics South Africa 10.91 Price collection for traditional and informal Summary dwellings would be very difficult, since the owner con- 10.92 It would be a very complex task to calculate a structs the dwelling him/herself in most cases and mon- comprehensive residential property price index for South etary transaction for the complete dwelling rarely takes Africa, due to the diverse nature of housing in the coun- place (the purchases of materials are normally in cash). try. Different methods will be required for the collection of The only way to obtain prices of newly constructed infor- prices for different housing types. In addition, weight esti- mal and traditional dwelling is to conduct a survey of new- mation for each type of housing will be difficult, as differ- ly constructed dwellings on a frequent basis, since most of ent housing types have different cost determining charac- these are not registered at the deeds office, and if registered, teristics. Furthermore, the limited data availability for each the value of the dwelling is not recorded. An alternative for housing type exacerbates the problem. these types of dwelling, yet to be explored, is to compile a “notional cost of construction” index based on the pricing 10.93 The primary barriers to the construction of an in- of quantity information of the type that is shown in Table clusive residential property price index in South Africa are 10.6. (30) listed in Table 10.7 and include: • The absence of an organised market for informal and (30) See Blades (2009). traditional housing; 136 Handbook on Residential Property Prices Indices (RPPIs) Methods Currently Used 10 • The absence of reliable data estimates on the cost of in- • There is no registration of property at the Deeds Office; formal and traditional housing; • Monetary transactions do not always take place to obtain • The nomadic life-style. If a survey is conducted, move- or build the dwelling; ments of informal settlements from one area to another • Prices do not depend on typical price determining fac- pose a problem in terms of measuring the price develop- tors such as the price of land, and labour and material ment of this type of housing because prices are normally costs. collected in specific areas; Table 10.7. Evaluation of Barriers Possible problems Traditional dwellings Informal dwellings Formal dwellings Organised market No No Yes Reliable price estimates exist about the cost of housing No No Yes Movements of dwelling from one settlement to another No Yes No Registration of property at deeds office No No Yes Monetary transaction at lending institution No No Yes Transfer of cash for building of structure Sometimes Sometimes Yes Dwelling constructed by property developer or builder No No Yes Price depends on typical price determining factors No No Yes Source: Statistics South Africa Handbook on Residential Property Prices Indices (RPPIs) 137 Empirical Examples 11 11 Empirical Examples Introduction as agricultural land, commercial properties, and units found in multi-unit dwellings, which are considered out- 11.1 The purpose of this chapter is to provide addi- side the scope of the intended index. If this is the case, then tional empirical examples dealing with the construction of these observations need to be excluded from the sample house price indices based on the methods that were out- when measuring price trends for specific types of proper- lined in Chapters 5-9. These are broadly defined as follows: ties. Outliers should also be identified and removed from measures of central tendency (mean or median), hedonic the sample if it is believed that they may skew or distort in regression methods, repeat sales methods, and methods any other way the outcome. based on appraisal data. The following three sections of this 11.6 A simple numerical example using 5  and 7  price chapter illustrate how the first three classes of methods can observations respectively for periods 1 and 2 (3) will illus- be implemented on very small data sets. Hopefully, work- trate the approach used for measuring the progression of ing through these simple examples will enable readers to the simple mean of house prices for a given geographical more readily follow the rather terse algebraic descriptions area, usually for a city or other well-defined area. (4) of the various methods that were provided in Chapters 5-9. Period 1 house prices and mean 11.2 The following section also illustrates various methods that can be used to aggregate regional house price (350 K + 352 K + 378 K + 366 K + 402 K ) / 5 = 370 K indices into overall house price indices. This topic was not covered in any detail in other chapters of this Handbook. Period 2 house prices and mean (360 K + 350 K + 382 K + 395 K + 380 K + 400 K + 450 K ) / 7 = 388 K (360 K + 350 K + 382 K + 395 K + 380 K + 400 K + 450 K ) / 7 = 388 K Central Tendency Methods Once the average prices for each period, e.g., a month, a and Stratification Methods quarter or a year, are obtained, it is then straightforward to calculate the period-to-period progression (typically in per 11.3 Central price tendency estimates, such as mean cent) between $370K and $388K. For instance, in this spe- and median prices, for constructing an RPPI are among cific example, average house prices have increased about the least data intensive of all the methods currently avail- 5 % over both periods. able to compilers. The basic mean or median methods only need the selling prices of the properties in a given location 11.7 The presence of outliers is mitigated when the me- to build a price index. Thus location information will be dian price of properties in the sample is used instead of required. In addition, it is usual to stratify by the type of the mean price. For instance, if one or more very expen- dwelling unit and if this is the case, then information on sive houses are sold in a given period, the resulting average the type of dwelling unit will also be required. price will likely not be typical of houses that on the market at that time. As was discussed in Chapter 4, the median ap- 11.4 As a first exercise, an index is constructed using the proach does not however completely control for period-to- mean price. It consists in calculating the simple average of period compositional shifts in the sample of houses sold. the observed prices for a sample of houses in a given period In spite of this shortcoming the median is nevertheless a and for a given geographical area. The indicator, which can very popular residential property price indicator mainly be expressed in monetary terms or in index form, is then because it is simple to compile and is not very data inten- measured simply as the change (in per cent usually) of the sive, thus resulting in a timely indicator. Moreover, its in- average price of the sampled units between two periods. (1) terpretation is straightforward. 11.5 It is important that the sample of houses drawn for 11.8 Based on the same data used for calculating the calculating the price indicator be representative of the tar- mean, the median prices from the example samples for pe- get universe. Therefore some data editing may be required, riods 1 and 2 are found to be respectively $366K and $382K. the extent of which will depend on the instructions that the Consequently, the median house price has increased 4.4 % data provider received from the compiler and his willing- over these two periods. ness and ability to deliver the data according to the com- piler’s stated criteria. (2) For example, the sample of prices 11.9 The above exercise is repeated below but with a initially collected may include certain property types, such more extensive dataset containing 5787  sampled price observations for single-family houses drawn from actual (1) Regardless of the form used, expressed either in terms of values or indices, the per cent (3) Since the number of transactions will likely vary from period to period, the number of change will be the same. price observations in the sample for each period will also vary. (2) Of course the particular circumstances will dictate the extent of the data cleaning. If the (4) Note that most central tendency measures of house prices when published do not principal user is also managing the collection of information, then the survey will be typically include indicators of statistical quality such as the coefficient of variation or tailored to his or her needs and the extent of the cleaning will likely be less extensive. standard deviation. 140 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 transactions over many years for a small municipality.  (5) that were sold that year. A similar graph constructed for Some descriptive statistics are presented in Table 11.1. the remaining years for this example yields similar price Note that in this particular case, the mean price of houses distributions. (7) sold in any year is always higher than the corresponding 11.10 As for the annual per cent changes, they vary ac- median. For instance, in 2002 the mean is $249 702 against cording to the measure of central tendency that is used 236 000 for the median; in 2008 the mean is $365 195 against here. (8) In some years, the difference in the result between $340 600 for the median. Since for any given year the sam- the median and mean can be quite small. For instance, in ple is characterized by the sale of some higher priced units, 2002 the difference is only one tenth of a percentage point this result is to be expected. In fact, the distribution of % vs. 8.1  (8.2  %) with mean recording a slightly higher prices is right-skewed with a skewness coefficient ranging increase. In other years, such as in 2008, the difference is from 1.44 to 1.87 over the various years. (6) Chart 11.1 il- more pronounced such as in 2008 when the annual change lustrates the distribution of prices in 2008 for the houses measured using the median price increased by 6.8 % com- pared to an increase in the mean price of 5.2 %. (5) Note that the required data is obtained for calculating either the median or mean prices; the steps involved are quite simple. Most statistical software packages can do the entire exercise quite rapidly with little intervention from the compiler. (7) With these particular data, the mean was always greater than the corresponding (6) Skewness is a measure of the asymmetry of a distribution. When the degree of skewness median. This result need not always hold, particularly with very small samples. is zero this means that the distribution is symmetric around its mean. A positive skew (8) Typically, the mean price will be higher than the corresponding median price. However, means that a relatively high number of observations from the sample is concentrated when mean and median indices are formed, there is no presumption that the mean on the left of the centre point and vice versa. index will increase more rapidly than the median index. Table 11.1. Means, Medians, Percent Changes, Standard Deviations, and Skewness 2002 2003 2004 2005 2006 2007 2008 Observations 777 804 894 808 834 874 796 Standard deviation 64 130 62 042 73 405 76 432 84 587 96 559 96 152 Skewness 1.63 1.51 1.71 1.87 1.58 1.46 1.44 Mean ($) 249 702 270 174 290 686 299 087 315 099 347 009 365 195 Per cent change 8.2% 7.6% 2.9% 5.4% 10.1% 5.2% Median ($) 236 000 255 000 273 000 280 000 292 000 319 000 340 600 Per cent change 8.1% 7.1% 2.6% 4.3% 9.2% 6.8% Source: Authors’ calculations based on MLS® data for a Canadian city Chart 11.1: Distribution of House Prices in 2008 140 120 100 80 Frequency 60 40 20 0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 e or 50 00 50 00 50 00 50 00 50 00 50 00 50 00 M 19 24 28 33 37 42 46 51 55 60 64 69 73 78 Prices Source: Authors’ calculations based on MLS® data for a Canadian city Handbook on Residential Property Prices Indices (RPPIs) 141 11 Empirical Examples 11.11 As is well known, location plays an important role sample of transactions in any given period, thus resulting in the determination of not only the level of house prices in some sampling bias. The objective is therefore to design but also in their behaviour over time. Therefore, to im- the individual strata in such a way that the homogeneity prove the reliability of the indicator, a stratified or mix-ad- of price determining characteristics is balanced against a justment approach is routinely recommended, provided of sample size that is sufficiently robust to yield a reliable and course that the information for segmenting the market (or representative measure of changes in house prices. sample of transactions) is readily available. Geographical 11.14 As previously mentioned, the construction of sub- stratification has the advantage of reducing the effects of market (or stratum) price indices that are then aggregated period-to-period compositional shifts in the housing units to the level of the market of interest will often use median that characterize the simple mean and median methods. A prices in practice. Constructing a mixed-adjusted price in- popular approach to segmenting the housing market is to dex consists in first defining the stratum. The second step is group houses according to geographical area, thus ensuring to calculate the median price for houses transacted within a certain degree of homogeneity of the units found within the stratum for the period in question. Thirdly, the median the strata; other locational effects on house prices are also prices for all sub-markets must be weighted together into minimized by this method. Stratification can also benefit an aggregate price measure for the market under study, users by providing them with additional house price indi- which likely will be a city or even the country as a whole. cators for various sub-markets, such as by neighbourhood or type of house. Goodman and Thibodeau (2003) add that 11.15 The following provides a simple example of the there is also a practical reason for grouping house by loca- procedure and steps involved with calculating a mixed- tion in that geographic variables are almost always includ- adjustment price index for residential properties. (9) ed in databases on housing transactions. This information • Step 1: Define the stratum. For the purpose of this exer- should, when available, be leveraged since stratification cise, the stratum is a geographical subdivision of a city makes efficient use of these data. such as the west-zone or centre town. There is no strict 11.12 Some countries, such as Australia (Branson 2006), rule for delineating the stratum in question but geogra- have taken advantage of the traditionally strong relation- phy appears to be a popular and obvious choice which ship between price and location that typifies residential can, if data permitting, be combined with other housing real estate by stratifying the sample of properties according features such as by house type or according to number of to geographical area or other submarket structures. This bedrooms in order to narrow the stratum. (10) can be a viable, albeit imperfect, alternative (or compro- • Step 2: Calculate the median price for a stratum such mise solution) for measuring constant quality price change as a neighbourhood for the relevant period (month or in the absence of the resources and the data needed to ap- quarter). It is assumed that the median will be the repre- ply some of the more sophisticated methods for construct- sentative price of all sales in that stratum. However, the ing an RPPI such as hedonic regressions. In fact, Prasad mean price could alternatively be used. Repeat this step and Richards (2008) construct a measure of median house for future periods. prices for six Australian capital cities where the markets are • Step 3: Estimate the “average” price of houses sold for a stratified according to long-term price movements. Using given period by calculating a sales weighted median of a database of over 3 million observations, the authors find the neighbourhood or stratum prices. (11) that their approach to measuring changes in house prices, (i.e., using the median approach but stratified by zone as 11.16 Suppose that data on house sales for two periods defined by long term price trends), will generate results (0 and 1) and three geographical regions or neighbourhoods that are comparable to those using more sophisticated and (A, B and C) have been collected. Suppose prices are meas- data intensive methods such as hedonics or repeat sales. ured in thousands of dollars and that for region A in period 0, there were 4 sales with prices 290, 450, 250 and 310. Thus, 11.13 Stratifying by geography thus likely ensures that the mean price for this period was 325, the median price was the cluster of observations within each group (or stratum) 300 (the arithmetic average of the two middle prices 290 and is more homogeneous than observations from the entire 310) and the total expenditure was 1300. For period 1, re- population. Stratification can be extended to include, in gion A had 5 sales of 300, 500, 250, 400 and 275. Thus, the addition to geography, other price determining factors mean and median price for this period was 345 and 300 re- such as house type and/or number of bedrooms. Grouping spectively and the total period 1 expenditure in region A was of houses by geography and other criteria will result in a 1725. For region B, there was only one sale in each period: sample of even more homogeneous properties, which is a desirable outcome for mitigating fluctuations in the index that are caused by compositional shifts in the sample that (9) This example is loosely based on an example in McDonald and Smith (2009). (10) This example uses the neighbourhood as the sub-stratum but in reality it can be any occur over time. One potential drawback however with geographical area for which the compiler is confident that a sufficiently large enough this approach is that the compiler must be aware that a sample of transactions is available today and in the future to generate a reliable representative price. too finely defined stratum can sometimes generate a thin ( ) This is assuming that the compiler is using sales as the basis for the weighting. 11 142 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 500  in period 0  and 400  in period 1. Thus, the mean and 11.17 Suppose that the median price in each region cor- median price in period 0 for region B was 500, which was responds to houses of comparable quality over the two pe- also equal to expenditure in this period. The mean and me- riods being compared. Since it is desirable to have price dian price in period 1 for region B was 400, which was also times volume equal to expenditure in each period for each equal to expenditure in this period. For region C, there were region, once a constant quality price concept has been cho- 3 sales in each period. For period 0, the sales were equal to sen, the corresponding volume should equal expenditures 200, 300 and 175 and so the median price was 200, the mean divided by price. Using the median price in each region price was 225  and expenditure was 675. For period 1, the as a constant quality price for each time period leads to sales in region C were equal to 250, 350 and 225 and so the the data on expenditures (the v t ), prices (the p t ) and vol- median price was 250, the mean price was 275 and expendi- umes or implied quantities q t = v t / p t that are listed in ture was 825. These are the basic data for the example. Table 11.2 below. Table 11.2. Regional Expenditures, Prices and Volumes (Implicit Quantities) Using Median Prices as the Regional Prices Period vA t vB t vC t pA t pB t pC t qA t qB t qC t 0 1300 500 675 300 500 200 4.333 1.000 3.375 1 1725 400 825 300 400 250 5.750 1.000 3.300 Source: Authors’ calculations based on MLS® data for a Canadian city Note that the regional price indices for period 1 are equal geometric average of the regional price indices, p 1 A / pA 0 , A / p A = 1.0 , p B / p B = 0.80 , and p C / p C = 1.25 for to p 1 0 1 0 1 0 p B / p B and pC / pC , where the weights are the arithmetic 1 0 1 0 regions A, B and C respectively. Thus there are widely dif- averages of the period 0 expenditure shares, s A0 , sB 0 and sC 0 , fering house price inflation rates in the three regions. and the period 1 expenditure shares, s A , s B and sC . 1 1 1 11.18 At this point, we can apply normal index number 11.20 The results for the four indices defined by (11.1)- theory to the problem of aggregating up the regional price (11.4) are listed in Table 11.3 below. It should be noted that movements into an overall house price inflation rate. For the two superlative indices, PF and PT , are fairly close to example, Laspeyres and Paasche overall price indices, PL each other while the Laspeyres index PL lies above these and PP , for period 1 can be constructed. The formulae for superlative indices and the Paasche index PP lies below these indices are as follows: them. This is a typical empirical result. A q A + p B q B + p C q C ] [ p A q A + p B q B + p C q C ] (11.1) PL ≡ [ p 1 0 1 0 1 0 0 0 0 0 0 0 11.21 Organizations that compile residential property price indices tend to use somewhat different formulas PP ≡ [ p q + p q + p q ] [ p q + p q + p q ] (11.2) 1 1 1 1 1 1 0 1 0 1 0 1 A A B B C C A A B B C C when aggregating over regions. A common form of ag- 11.19 The CPI Manual (2004) recommends the con- gregation is to use a weighted average of the regional price struction of superlative indices if price and quantity data indices to form an overall index, using the sales weights are available for the periods under consideration, as they of period 0 (or some average of sales weights that pertain are in the present situation. Two such superlative indices to periods prior to period 0). Denote the share weighted are the Fisher ideal index PF and the Törnqvist-Theil index index that uses the sales weights of period 0 by P0 and the PT , defined as follows for the period 1 overall indices: share weighted index that uses the sales weights of period 1 by P1 . The period 1 values (12) for the indices P0 , P1 and PF ≡ [PL PP ] (11.3) 1/ 2 the arithmetic average of P0 and P1 , denoted by PA , are defined 1 as follows: PT ≡ exp[0.5( s A + s A ) ln( p A / p A ) + 0.5( s B + s B ) ln( p B / p B ) + 0.5( sC 0 1 1 0 0 1 1 0 0 + sC ) ln( pC 1 / pC 0 ) ] P0 ≡ 1pA / pA 0 sA ( 0 1 0 1) + s0 0 ( p1 B / p B ) + s C ( p C / p C ) (11.5) 0 0 1 0 PT ≡ exp[0.5( s A 0 + s1 A ) ln( p 1 A / pA 0 ) + 0.5( s B 0 + s1 B ) ln( p 1 B / pB 0 ) + 0.5( sC + sC ) ln( pC / pCB)] + 0.5( s B 0 + s1 ) ln( p 1 / pB 0 ) + 0.5( sC 0 + sC 1 ) ln( pC 1 / pC 0 )](11.4) P1 ≡ s 1 A ( p A / p A ) + s B ( p B / p B ) + s C ( p C / p C ) (11.6) 1 0 1 1 0 1 1 0 B B where the period t shares of sales in regions A, B and C are PA ≡ 0.5 P0 + 0.5 P1 (11.7) given by s A ≡ v A /(v A + v B + vC ), s B ≡ v B /(v A + v B + vC ) and t t t t t t t t t t sC ≡ vC /(v A + v B + vC ), respectively. Note that the Fisher t t t t t (1922) index PF is equal to the geometric average of the Laspeyres and Paasche indices, PL and PP and that the Törnqvist-Theil index PT is equal to a share weighted (12) The period 0 values for all of the indices defined in this section are set equal to 1. Handbook on Residential Property Prices Indices (RPPIs) 143 11 Empirical Examples The above three indices are also listed in Table 11.3. (13) It P1 is about 1.77  percentage points above PF . This result can be seen that P0 is equal to PL and is about 0.26 per- is not unexpected; the indices P0 and P1 do not generally centage points above the Fisher index PF in period 1, while closely approximate superlative indices and so their use is not recommended. (13) Fisher (1922; 466) showed that P0 defined by (11.5) is equal to the Laspeyres index PL defined by (11.1). Fisher also attributed the index P1 defined by (11.6) to Palgrave. Table 11.3. Overall House Price Indices using Median Prices and Alternative Formulae to Aggregate over Regions A, B and C Period PF PT PL PP P0 P1 PA PGL PGP 0 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 1.02515 1.02425 1.02778 1.02253 1.02778 1.04280 1.03529 1.01590 1.03267 Source: Authors’ calculations based on MLS® data for a Canadian city 11.22 Two additional indices are listed in Table 11.3: the Hence, the use of the geometric Laspeyres or Paasche geometric Laspeyres and Paasche price indices, PGL and PGP . formulae cannot be recommended when constructing The period 1 values for these indices are defined as follows: aggregates of regional price indices; these formulae are unlikely to closely approximate a superlative index, which PGL ≡ exp[ s A 0 ln( p 1 A / pA 0 ) + sB 0 ln( p 1 B / pB 0 ) + sC 0 ln( pC 1 / pC 0 )] can readily be constructed using regional data on house 1 A / pA 0 ) + sB 0 ln( p 1 B / p B 0 ) + sC 0 ln( pC 1 / pC 0 )](11.8) price sales. PGP ≡ exp[ s 1 A ln( p 1 A / pA 0 ) + s1 B ln( p 1 B / pB 0 ) + sC 1 ln( pC 1 / pC 0 )] 11.23 The above methods for aggregating over re- gional price indices assumed that median prices in each A / p ) + s ln( p / p ) + s ln( p / p )] (11.9) 0 A 1 B 1 B 0 B 1 C 1 C 0 C region correspond to houses of comparable quality over Thus, the period 1 values for each of these two indices are the two periods being compared. Now suppose that in- equal to share weighted geometric averages of the regional stead of using median prices in each region to represent price indices, p 1 pC 1 / pC 0 constant quality house prices, it was decided to use mean A / p A , p B / p B and 0 1 0 , where PGL uses the regional share weights pertaining to period 0, s A 0 , prices in each region. Again, since it is desirable to have s B and sC , and PGP uses the regional share weights per- 0 0 price times volume equal to expenditure in each period taining to period 1, s 1 for each region, once it is decided to use mean prices A , s B and s C . From Table 11.3 it can 1 1 be seen that the geometric Laspeyres index PGL is approxi- as the constant quality a price concept, the correspond- mately 1 percentage point below the superlative indices PF ing volume should equal expenditures divided by price. and PT while the geometric Paasche index PGP is approxi- Thus using the mean price in each region as a constant mately 1 percentage point above the superlative indices. (14) quality price for each time period leads to the data on regional expenditures (the v t ), prices (the p t ) and vol- (14) It can be verified that the geometric mean of PGL and PGP is exactly equal to PT. Thus if umes (or implied quantities q t = v t / p t ) that are listed in PGL is below PT, then PGP will necessarily be above PT. Table 11.4 below. Table 11.4. Regional Expenditures, Prices and Volumes (Implicit Quantities) Using Mean Prices as the Regional Prices Period vA t vB t vC t pA t pB t pC t qA t qB t qC t 0 1300 500 675 325 500 225 4 1 3 1 1725 400 825 345 400 275 5 1 3 Source: Authors’ calculations based on MLS® data for a Canadian city 144 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 11.24 Using means instead of medians as the con- differing house price inflation rates in the three regions stant quality price in each region changes the regional when mean prices are used in place of median prices. price indices. The mean-based period 1  regional price 11.25 Using means instead of medians, the various over- indices are equal to p 1 A / p A = 345 / 325 = 1.06154 , 0 all price indices defined by formulae (11.1) to (11.9) can be p B / p B = 400 / 500 = 0.80 , and pC / pC 1 0 1 0 = 275 / 225 = 1.2 calculated. The following counterpart to Table 11.3  is ob- for regions A, B and C respectively. Again, there are widely tained using these formulae applied to the data in Table 11.4. Table 11.5. Overall House Price Indices using Mean Prices and Alternative Formulae to Aggregate over Regions A, B and C Period PF PT PL PP P0 P1 PA PGL PGP 0 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 1.05305 1.05222 1.05253 1.05357 1.05253 1.07101 1.06177 1.04187 1.06267 Source: Authors’ calculations based on MLS® data for a Canadian city It can be seen that the use of mean prices instead of median prices, some pertinent characteristics (both structural and prices for each region has led to very different indices; the environmental) for each observation that is used in the re- superlative indices PF and PT are now about 3 percentage gression are needed with hedonic methods. In principle, points higher in period 1. However, the use of mean prices the more detailed the set of characteristics is and the larger has led to Laspeyres and Paasche indices, PL and PP , that the sample of housing units, the more reliable and accurate are fairly close to their superlative counterparts. Since the will be the resulting price index. (15) base period share weighted index P0 is numerically equal to 11.27 A hedonic model expresses the price of a good as PL , P0 is also fairly close to PF and PT . However, the other a function of its price-determining characteristics (or at- two shared weighted indices, P1 and PA , are well above the tributes). Chapter 5 covered two frequently used functional superlative indices. Finally, the Geometric Laspeyres index, forms, which are the linear model and the logarithmic- PGL , is well below PT and the Geometric Paasche index, PGP , linear (or semi-log) model, although other options (e.g., the is well above PT . In any case, the use of mean prices in the Box-Cox technique) are often also treated in the literature, housing context is not recommended since the mean price they are not covered here. The semi-log form is conveni- of a house in a region is unlikely to hold the quality of the ent because the interpretation of the regression coefficients houses constant over time. is straightforward: once multiplied by 100, the coefficients can be interpreted as the percent change in the price of the house that results from a unit change in the explanatory variable. Hedonic Regression 11.28 To illustrate as plainly as possible how the various Methods hedonic house price indices are constructed, the extensive version of the dataset used for calculating the mean and 11.26 Chapter 5 discusses the use of hedonic techniques median prices above will also be consulted for the follow- for calculating house price indices. There are various ways ing examples. To simplify the presentation, the number of of applying this technique when calculating price indices price-determining characteristics will be limited to four in general and residential property price indices in particu- (continuous) variables. These are: lot size (land), number lar. The handbook presents three variants of the hedonic of bedrooms (rooms), number of bathrooms (bath), and approach. These are: the time dummy variable method, age (age). The initial results for a regression using OLS the characteristics prices (or imputation) method, and with a semi-log functional form for a single year (2008) are the stratified hedonic method. Compared to the other ap- summarised in Table 11.6. proaches, all these hedonic methods are typically more data intensive, often requiring more information compared (15) Although most hedonic regressions on house prices in the literature will often use to the other approaches for constructing constant quality many more explanatory variables, some studies and the examples in Chapter 5 show that reliable hedonic price indices can be obtained with as few as four independent house price indices. This is because, in addition to data on variables. Handbook on Residential Property Prices Indices (RPPIs) 145 11 Empirical Examples Table 11.6. Log-linear Regression Results for a Simple Example Source | SS df MS Number of obs = 796 _____________________________________________ F( 4, 791) = 156.02 Model | 20.0634692 4 5.0158673 Prob > F = 0.0000 Residual | 25.4293063 791 .032148301 R-squared = 0.4410 _____________________________________________ Adj R-squared = 0.4382 Total | 45.4927755 795 .057223617 Root MSE = .1793 lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] rooms | .1156791 .0098159 11.78 0.000 .0964108 .1349473 bath | .0999522 .0095996 10.41 0.000 .0811086 .1187958 age | -.002561 .0004173 -6.14 0.000 -.0033801 -.001742 land | 9.39e-06 1.28e-06 7.31 0.000 6.87e-06 .0000119 _cons | 12.0647 .0383342 314.72 0.000 11.98945 12.13995 Source: Authors’ calculations based on MLS® data for a Canadian city 11.29 From the regression on a sample of 796 price ob- 11.31 What follows are simplified examples of the vari- servations it is found that all four explanatory variables ous methods, as discussed in Chapter 5, for calculating he- have the expected sign and are significantly different from donic price indices. The time dummy variable method is 0 (using a t-test). The adjusted R-squared (or coefficient of presented first. All examples use OLS regressions. determination) is 44 %, i.e., variations in lot size, the num- ber of bedrooms, bathrooms, and age account for 44 % of house price variability. By adding more explanatory vari- The Time Dummy Variable Method ables to the regression, the R-squared would increase. In 11.32 The time dummy variable method is based on fact, by adding three independent variables (the presence the estimation of a logarithmic-linear hedonic regression of a fireplace, the presence of a garage, and the age squared model where the data are pooled across all periods. The to account for the non-linearity associated with this vari- model is given by equation (6.5) and is repeated here for able) improved the adjusted R-squared to 54 %. convenience: 11.30 The regression results can be interpreted as T K ln p n t = β 0 + ∑ δ τ Dn τ + ∑ β k z nk t + ε nt (11.10) follows: τ =1 k =1 • An extra square foot of lot size will increase the price of where Dn is dummy variable which is equal to one if t the house by 0.000939%, ceteris paribus. the observation comes from period t (t = 1,..., T ) and is • Each additional bedroom adds 11.6% to the price of a zero otherwise. The time dummy variable for the base pe- house, ceteris paribus. riod  0 – i.e., the start period from which the subsequent price changes will be compared – is left out to avoid per- • A house with an extra bathroom cost almost 10% more fect collinearity of all dummies with the intercept term β 0 , than a house without the extra bathroom, ceteris paribus. known as the ‘dummy trap’. With the time dummy vari- • By adding one year to the house, its price declines (or the able approach the base period and the subsequent com- housing unit depreciates) by 0.2%, ceteris paribus. parison periods, t = 1,..., T , are the same units of time, i.e., a month, a quarter, or a year, depending on the par- The Latin locution ceteris paribus means “all variables oth- ticular circumstances such as the needs of the users or data er than the ones being studied are assumed to be constant”. availability. Turning to the variable “number of bedrooms” as an ex- ample, it cannot be concluded that houses with more bed- 11.33 The exponential or anti-logarithm of the estimated rooms will always cost more; other factors are at play that regression coefficient d ˆ t measures the percent change in can affect the price of the house such as its location and ‘constant quality’ property prices between the base period age, and overall quality of its construction. What is meant and period t. To understand why exp(d ˆ t ) is a measure of by qualifying the statement by ceteris paribus is that when quality adjusted, pure price change, the following steps houses vary only in terms of the number of bedrooms for have been worked out. The predicted logarithm of price in instance (i.e., they are comparable in all other respects) period 0 for property i, given its base period characteristics, then those with more bedrooms will cost more. z nk 0 (k = 1,..., K ) , is 146 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 K dependent variable. The right-hand side has the same ex- ˆn ln p 0 ˆ + β =β 0 ∑ ˆk z nk k =1 0 (11.11) planatory variables (except for the time dummy variables) In period 1, the predicted logarithm of price must be eval- that one would find in a one period hedonic regression. In uated at the property’s base period characteristics, because this particular case the explanatory variables are: lot size, quality should be held constant, hence number of bedrooms, number of bathrooms, and age; the K respective parameters range from β1 to β 4 . Since this is a ˆn ln p 1* ˆ +δ =β 0 ∑ ˆk z nk ˆ1 + β 0 (11.12) pooled regression, the estimated parameters (or regression coefficients) will be constrained over the years for which k =1 Taking the differences between the estimates for both pe- data are used in the regression. The error term ε nt indicates riods yields if an observed value is above or below the regression line. ˆ 1 (11.13) Also on right-hand side of the equation is the intercept ˆ1 ln p n − * ˆn ln p 0 ˆ1 = ln( p * /p ˆn 0 ) =δ n term, β 0 . Expression (11.13) does not depend on n. That is, the result holds for all houses in the sample. As pointed out in Berndt 11.35 The regression results using the basic data set are (1991), the estimate of d t can be interpreted as the change listed in Table 11.7. The coefficient of interest is the one associated with year 2007, δ ˆ 07 . Its value is 0.0781548. This in the logarithm of price due to the passage of time, hold- ing all other variables constant. Taking the anti-log of d ˆ1 coefficient is then transformed to arrive at an estimate gives the estimated price index for period 1: of the price index (or the per cent change in prices) for houses between years 2006  and 2007. This transforma- PTD 01 = exp(δ ˆ 1 ) (11.14) ˆ 07 : tion consists in taking the anti-logarithm of coefficient δ A similar exercise can be done for all other periods. The PTD07 / 06 = exp(0.0781548) = 1.08129 . Thus, the per cent time dummy price index going from the base period to a change in house prices between years 2006 and 2007, hold- comparison period t (0 < t ≤ T ) therefore is ing constant all the characteristics of the house, is 8.1  %. Note that the mean and the median yielded increases of PTD 0t = exp(δ ˆ t ) (11.15) 10.1 % and 9.2 %, respectively, for this same period. Obviously, the time dummy hedonic index for the base pe- 11.36 If a third period (year 2008) is added, then the riod is equal to 1. hedonic regression equation becomes: 11.34 The following example illustrates the procedure for calculating a time dummy price index. Suppose that ln p n t = β 0 + β1 Lotsizen + β 2 Bedroom n + β 3 Bathroom n + β 4 Agen + δ 1 Dn 1 +δ 2 detailed information about the houses that were transacted over two years ( t = 2006 to tln =p t 2007 +β = β)0 is + β 2 Bedroom n + β 3 Bathroom n + β 4 Agen + δ 1 Dn LotsizenUsing available. 1 + δ 2 Dn2 + ε nt (11.17) n 1  the same information as in the basic data set above, the data for all periods are combined into the following pooled Table 11.8 contains the regression output. The value of the regression equation: time dummy coefficient for year 2008 is 0.1332734. Taking its1anti-logarithm generates a value of e0.1332734 = 1.14, show- ln p n t = β 0 + β1 Lotsizen + β 2 Bedroom n + β 3 Bathroom n + β 4 Agen +ing δ Dan 1 n + ε t increase n in the constant quality house price index zen + β 2 Bedroom n ++ β 3 Bathroom n + β 4 Agen + δ Dn + ε n (11.16) 1 1 t of 14  % between the base year, 2006  and the most recent year, 2008. By contrast, the price progression over the same The left-hand side of equation (11.16) has the logarithm period generated by the mean and median was respectively of the price of house i in year t (2006  or 2007) as the 16 % and 17 %. Handbook on Residential Property Prices Indices (RPPIs) 147 11 Empirical Examples Table 11.7. Results from a Pooled Regression for Years 2006 and 2007 Source | SS df MS Number of obs = 1708 _____________________________________________ F( 5, 1702) = 286.64 Model | 48.4501865 5 9.6900373 Prob > F = 0.0000 Residual | 57.5372376 1702 .033805663 R-squared = 0.4571 _____________________________________________ Adj R-squared = 0.4555 Total | 105.987424 1707 .062089879 Root MSE = .18386 lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] rooms | .0840483 .0069071 12.17 0.000 .0705009 .0975957 bath | .121815 .0071529 17.03 0.000 .1077855 .1358444 age | -.0029137 .0003183 -9.15 0.000 -.0035381 -.0022894 land | .0000137 9.24e-07 14.78 0.000 .0000119 .0000155 d2007 | .0781548 .0089128 8.77 0.000 .0606736 .095636 cons | 11.96531 .0273032 438.24 0.000 11.91176 12.01886 Source: Authors’ calculations based on MLS® data for a Canadian city Table 11.8. Results from a Pooled Regression for Years 2006 to 2008 Source | SS df MS Number of obs = 2504 _____________________________________________ F(6, 2497) = 366.64 Model | 73.4886776 6 12.2481129 Prob > F = 0.0000 Residual | 83.4154327 2497 .033406261 R-squared = 0.4684 _____________________________________________ Adj R-squared = 0.4671 Total | 156.90411 2503 .06268642 Root MSE = .18277 lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] rooms | .0942001 .0056566 16.65 0.000 .083108 .1052923 bath | .1139931 .0057443 19.84 0.000 .102729 .1252572 age | -.0028112 .0002538 -11.08 0.000 -.0033089 -.0023135 land | .0000122 7.51e-07 16.28 0.000 .0000108 .0000137 d2007 | .0781257 .008856 8.82 0.000 .0607598 .0954916 d2008 | .1332734 .0090681 14.70 0.000 .1154916 .1510552 _cons | 11.95724 .0225891 529.34 0.000 11.91295 12.00154 Source: Authors’ calculations based on MLS® data for a Canadian city 11.37 This technique can be extended to more than 11.38 An alternative approach mentioned in Chapter three periods as more periods become available. This con- 5 is to use the adjacent-period time dummy variable tech- sists in pooling more periods of data and adding additional nique. If the hedonic regression is based on two consecutive time dummy variables. However, multi-period pooled re- periods t and t + 1 , the hedonic relationship becomes: gressions are not necessarily ideal for constructing a time K series since adding new periods of data will likely modify ln p n t = β 0 + δ τ +1 Dn τ +1 + ∑ β k z nk t + ε nt (11.18) the results from the previous periods. For instance, in the k =1 above example, when year 2008 is added to the previously In the context of the three periods of data used in the above pooled regression, the coefficient for year 2007  becomes examples, a hedonic regression is first run for periods 0 and 0.0781257, which in this specific case is only slightly dif- 1, and then a second regression is run for periods 1  and ferent compared to the estimate obtained with the regres- 2 using the four characteristics. The regression output for sion of Table 11.7, where the corresponding coefficient was the first adjacent period regression is obviously the same 0.0781548. Moreover, the stability of the coefficients in a as in Table 11.7, and the resulting period-to-period price pooled regression can become an issue as the number of index yields an estimate of 108.1. Table 11.9 shows the re- periods expands. gression output for adjacent years 2007 and 2008. 148 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 Table 11.9. Results from a Pooled Regression for Years 2007 and 2008 Source | SS df MS Number of obs = 1670 _____________________________________________ F(5, 1664) = 271.91 Model | 45.441478 5 9.0882956 Prob > F = 0.0000 Residual | 55.6172267 1664 .033423814 R-squared = 0.4497 _____________________________________________ Adj R-squared = 0.4480 Total | 101.058705 1669 .060550452 Root MSE = .18282 lprice | Coef. Std. Err. t P>|t| [95 % Conf. Interval] rooms | .1041401 .0068861 15.12 0.000 .0906337 .1176465 bath | .1070142 .0068881 15.54 0.000 .093504 .1205244 age | -.0026926 .0003045 -8.84 0.000 -.0032899 -.0020953 land | .0000117 9.42e-07 12.42 0.000 9.85e-06 .0000135 d2008 | .0555370 .0089625 6.20 0.000 .073116 .037958 _cons | 12.07482 .026871 449.36 0.000 12.02212 12.12753 Source: Authors’ calculations based on MLS® data for a Canadian city 11.39 The constant quality price index is calculated as the index, in a similar way as in a typical price index formula, antilogarithm of the coefficient for year 2008 (0.0555370), but where the regression coefficients assume the role of the so that the index becomes exp(0.0555370) = 1.057 . Recall prices and the quantities are the quantities are the number that this is the price change from period 2007, not from of units of characteristics. Thus, the hedonic equation is es- the base period 2006. From these results, a time series timated for each time period separately. The linear hedonic can be constructed by chaining the two period-to-period models for the base period 0 (2006) and for period 1 (2007) indices (starting with the value 1  for the base period): are PTD 07 / 06 = 1.081; PTD ,chain = 1.081 × 1.057 = 1.143 . This result 08 / 06 pn 0 = β 00 + β10 Lotsizen + β 20 Bedroomn + β 30 Bathroomn + β 40 Agen + ε n0 differs only slightly from the full-period pooled regres- sion (see Table pn0 + β10 Lotsize = β 00where 11.8) n + β 2 Bedroom we estimated 0 n + β 3 Bathroom a price change 0 of n + β 40 Agen + ε n0 (11.19) 14.0 % over the entire period. Now, with chaining adjacent pn 1 = β 01 + β11 Lotsizen + β 21 Bedroomn + β 31 Bathroomn + β 41 Agen + ε n 1 period time dummy indices, the estimated price change is 14.3 %. pn 1 = β 01 + β11 Lotsizen + β 21 Bedroomn + β 31 Bathroom n + β 41 Agen + ε n1 (11.20) 11.42 Estimating these equations on the sample data Characteristics Prices or Imputation from 2006  and 2007, respectively, using OLS regression, generates the results shown in Tables 11.10 and 11.11. In Method this example, the implicit price of an extra bedroom in 11.40 The next hedonic regression approach presented 2006  is $24329  while each additional bathroom will add in Chapter 5  is the characteristics prices or hedonic im- $43190  to the price of the house. The results for 2007  in putation method, henceforth simply the characteristics this highly simplified example are understandably different method. Applying this method to the same data as previ- from those for 2006: an additional bedroom now seems to ously used, a quality-adjusted price index is estimated. For increase the price by $35147, while the price of an extra ease of presentation and interpretation, a linear model will bathroom is now estimated to be $43463. (17) be regressed to generate the results. (16) 11.41 The characteristics prices approach uses the im- (17) Note that the coefficients for the number of bedrooms are somewhat volatile between both years. This is to be expected because hedonic regressions are often characterized plicit prices of the characteristics of the model (the regres- by the presence of multicollinearity between these two predictor variables. It should be stressed however that multicollinearity does not in itself affect the accuracy of sion coefficients) as the basis for constructing the price the overall index. This phenomenon is only an issue if an accurate monetary value is needed for the value of an additional bedroom and/or for an additional bathroom, such as would be the case with a property assessment exercise. It should also be added that for the purpose of this simplified exercise, the sample size is relatively small. This can also (16) There is nothing to prevent however the use of a semi-log or log functional form. Both explain why sometimes the results are not quite as robust as is often the case with larger can be used with this hedonic approach. samples. Handbook on Residential Property Prices Indices (RPPIs) 149 11 Empirical Examples Table 11.10. Results from a Regression for 2006 Source| SS df MS Number of obs = 834 _____________________________________________ F(4, 829) = 141.49 Model | 2.4182e+12 4 6.0454e+11 Prob > F = 0.0000 Residual | 3.5420e+12 829 4.2726e+09 R-squared = 0.4057 _____________________________________________ 0.4029 Adj R-squared = Total | 5.9601e+12 833 7.1550e+09 Root MSE = 65365 price | Coef. Std. Err. t P>|t| [95 % Conf. Interval] rooms | 24329.78 3557.79 6.84 0.000 17346.45 31313.12 bath | 43190.01 3734.288 11.57 0.000 35860.24 50519.79 age | -1083.309 164.5957 -6.58 0.000 -1406.382 -760.2357 land | 5.168582 .4474175 11.55 0.000 4.290378 6.046787 _cons | 98333.45 14450.86 6.80 0.000 69968.88 126698 Source: Authors’ calculations based on MLS® data for a Canadian city Table 11.11. Results from a Regression for 2007 Source | SS df MS Number of obs = 874 _____________________________________________ F(4, 869) = 169.68 Model | 3.5694e+12 4 8.9236e+11 Prob > F = 0.0000 Residual | 4.5702e+12 869 5.2592e+09 R-squared = 0.4385 _____________________________________________ 0.4359 Adj R-squared = Total | 8.1397e+12 873 9.3238e+09 Root MSE = 72520 price | Coef. Std. Err. t P>|t| [95 % Conf. Interval] rooms | 35147.31 3777.91 9.30 0.000 27732.41 42562.2 bath | 43463.76 3858.683 11.26 0.000 35890.33 51037.19 age | -1059.767 173.0922 -6.12 0.000 -1399.495 -720.0394 land | 5.829323 .5388036 10.82 0.000 4.771814 6.886831 _cons | 79248.85 14337.87 5.53 0.000 51107.95 107389.7 Source: Authors’ calculations based on MLS® data for a Canadian city 11.43 The next step is to compute a hedonic price index characteristics are valued at their implicit prices in the from the regression results. A price index for 2007  com- base period and in the current period. Table 11.12 lists the pared to period 2006 can, for example, be expressed as average sample values for the characteristics in this exam- K ple. Using these values and the coefficients from Tables βˆ1 + β 1z 0 + β ˆ1z 0 + βˆ1z 0 + β ˆ1z 0 ∑ βˆ z 1 k 0 k 11.10 and 11.11, the Laspeyres-type hedonic index between P = 0 010 1 1 2 2 3 3 4 4 = k =0 (11.21) the base year (2006) and 2007 is computed as ˆ ˆ 0 0 ˆ 0 0 ˆ β 0 + β1 z1 + β 2 z 2 + β 3 z 3 + β 41 z 40 1 0 ˆ K ∑k =0 ˆ0z0 βk k P 07 / 06 = 79248 + (35147 × 3.63) + (43463 × 2.76) + (−1059 × 23.89) + (5 98333 + (24329 × 3.63) + (43190 × 2.76) + (−1083 × 23.89) + (5 where z k0 is the sample mean value of the k-th characteristic in the base period; z 00 = 1 index + . Price79248 (35147 ×will compilers recog- 3.63) + (43463 × 2.76) + (−1059 × 23.89) + (5.829323 × 6719) P 07 / 06 = nize that the index described by (11.21) is a Laspeyres-type = 1.082 98333 + (24329 × 3.63) + (43190 × 2.76) + (−1083 × 23.89) + (5.168582 × 6719) price index: the estimated characteristics prices in period 0 (2006) and period 1 (2007), β ˆ 0 and β ˆ 1 , are weighted by The 8.2 % increase in prices so obtained compares, in this k k the average base period quantities of the characteristics. particular case, quite closely with the 8.1 % obtained using Put differently, the average base period quantities for all the time-dummy approach from Table 11.7. 150 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 Table 11.12. Mean Values of the Characteristics for the Base Period (2006) | Mean Std. Err. [95 % Conf. Interval] rooms | 3.633094 .0244034 3.585194 3.680993 bath | 2.767386 .0269044 2.714578 2.820195 age | 23.88969 .5693338 22.77219 25.00719 land | 6719.492 184.8605 6356.644 7082.339 Source: Authors’ calculations based on MLS® data for a Canadian city 11.44 For subsequent periods, the compiler has a deci- (or like-for-like) sampling as the basis for selecting the sion to make. He or she can use the same base year quanti- units that will be used in the calculation of the index. For ties to calculate the subsequent indices using the Laspeyres the repeat sales approach to be tractable, one must have formula but replacing the implicit prices in the numera- access to a large database of transactions covering a fairly tor with the relevant ones. Alternatively, quantities (mean long period. Otherwise the data needs are relatively mod- characteristics) from the previous period could be used to est: with the basic repeat sales method, only information generate period-to-period price indices. These bilateral in- on the dwellings address (or another location identifier) is dices would then be chained to create a continuous time required in order to identify which units have sold repeat- series of linked indices. Other options are also available, edly, in addition of course to the selling price and the sale and these are discussed in Chapter 5, but the mechanics date. (18) of constructing the index remain essentially the same as 11.47 A simple example can illustrate the application presented here. of the repeat sales methodology.  (19) Assuming the objec- tive is to estimate an annual index of price change between 2008 and 2010, Table 11.13 shows data for a small number of transactions. Property A sold in 2008 for $100 000 and The Repeat Sales Method sold again in 2009  for $120  000; property B is sold in 2008  for $175  000  and sold again in 2010  for $220  000; 11.45 The most significant problem with using (non- property C sold in 2009  for $180  000  and sold again in stratified) median or mean transaction prices to measure 2010 at the same price. trends in houses prices is that the variation in the composi- tion of the sample of properties sold from period to period is not always accurately accounted for. This issue can be (18) One assumption is that the quality of the house has not changed over the period between the two sales. If information about the features of the property is available partially circumvented by constructing an RPPI based on to the compiler, then it is possible to exclude from the calculation those observations the repeat sales method, which was discussed in Chapter 6. that have undergone significant changes over time and that are likely to affect the price and thus distort the index. Furthermore, given that high turnover is often a sign that In fact, one very popular house price index that is closely certain undesirable features for that particular property may be at play so that these scrutinized in the U.S., the Case-Shiller house price index, observations can also be excluded from the calculation. It should also be mentioned that repeat-sales indices are not always strictly constant quality price indices since is based on the repeat sales methodology. houses are often subject to some loss in value over time as a result of depreciation. Consequently, repeat-sales price indices typically underestimate true house price 11.46 The strategy for constructing a repeat sales house inflation, unless some corrective adjustment is made to the estimates. If the purpose of the index is to act as a short- to medium-term indicator of house prices, then the price index is quite straightforward. It consists in compar- issue of depreciation which the repeat-sales approach does not handle adequately can ing the change in the price of identical properties that have perhaps be set aside. (19) The example is partially drawn from the Canadian Teranet-National Bank® repeat sales sold at two points in time. In other words, it uses matched price index documentation: http://www.housepriceindex.ca/Default.aspx. Table 11.13. Repeat Sales Data 2008 2009 2010 Property A $100 000 $120 000 No sale Property B $175 000 No sale $220 000 Property C No sale $180 000 $180 000 Average $137 500 $150 000 $200 000 Handbook on Residential Property Prices Indices (RPPIs) 151 11 Empirical Examples As a first step, the price change over the 2008 to 2010 pe- repeat-sales transaction which has a P value of 1 because riod is estimated using the mean of prices approach. The the price of this property did not change from 2009 and annual average prices from 2008 to 2010  are respectively 2010. $137 000, $150 000 and $200 000. The corresponding year- 11.49 The independent variables in a repeat sales regres- to-year changes in average prices are 9.1 % and 33.3 % for sion are dummy variables, which take the value -1 during the periods 2009/2008 and 2010/2009. the year of the initial sale, then take the value +1  in the 11.48 These results are now compared with those ob- period of the second sale, and finally take the value 0 for tained if the repeat sales technique is used. Let P be the all other periods. The estimated dummy variable coeffi- price relative of the house between the second and first cients from the regression are used to calculate the repeat sale for each completed transaction  (20) from 2008  to sales price index. Table 11.14 summarizes the values of the 2010. The logarithm of P will serve as the dependent vari- dummy variables for properties A to C. For example, since able in a repeat sales regression. Three repeated sales are property A is sold for a second time in 2009, the dummy identified in Table 11.13 for the period 2008 to 2010. The variable D2009 takes the value of 1 but D2010 takes a value first repeat sale, for property A, has a P value of 1.200 of 0  since this property A is not sold after 2009. A simi- (i.e., the price relative between its sale prices in 2009 and lar reasoning applies to the other properties and the other 2008); the second repeat sale, which occurs for property years. Note that to avoid perfect collinearity, the first pe- B, has a P value of 1.257 (the price relative between its riod (2008) is disregarded from the explanatory variables selling prices in 2010 and 2008); property C is the third and the regression. In other words, if the first sale occurs at the base year, then there is no dummy variable for that (20) Geltner and Pollakowski (2006) use the term “round trip”. period. Table 11.14. Dummy Variables for Repeat Sales P D2009 D2010 Property A 1.200 1 0 Property B 1.257 0 1 Property C 1.000 -1 1 11.50 Given these repeat sales data, the regression equa- Geltner and Pollakowski (2006), the source of the estima- tion – which has no intercept term – can be expressed as tion error (or noise) in property price indices is explained by (see also equation (6.3): the fact that the observed transaction prices are randomly distributed around the “true” but unobservable market val- ln Pnt = γ 2009 Dn2009 + γ 2010 Dn2010 + ε nt (11.22) ues. The authors add that this noise is present in any house where ε nt is an error term (“white noise”). The anti-logarithm price index, regardless of how the index is constructed. To of the estimated parameters, i.e. exp(gˆ 2009 ) and exp(gˆ 2010 ) , mitigate the effects of the noise the sample of repeated sales will represent the price indices of the housing unit for each pe- can be expanded, data availability permitting. riod when compared to the base period 2008. Using Ordinary 11.52 As previously pointed out, an OLS regression Least Squares (OLS) to estimate equation (11.22) on the data can be used to obtain the set of price changes. The Bailey, from Table 11.14, the resulting repeat sales price indices are Muth, and Nourse (1963) model is a classic example of the 1.219 and 1.238 for 2009 and 2010, respectively. The year-to- OLS repeat sales methodology using the technique out- year growth rates of 21.9  % and 23.8  % for this example are lined above. However, subsequent research has suggested quite different from those found with the simple average ap- that the basic OLS repeat sales method may be improved proach, which were 9.1 % and 33.3 %. (21) by applying a weighted least squares (WLS) technique. In a 11.51 The simple repeat sales model can be improved. nutshell, the method consists in giving more weight in the One way of accomplishing this is by reducing the statisti- regression to the observations that are deemed more ac- cal noise in the index series generated. As pointed out by curate. In the context of the repeat sales method, giving less weight to properties for which a long time span has elapsed (21) There are very few observations so no meaningful conclusions should be drawn from between sales and vice versa corrects for this inherent prob- this simplified example. It should only be used for illustrative purposes. lem, better known as the heteroskedasticity problem. 152 Handbook on Residential Property Prices Indices (RPPIs) Empirical Examples 11 11.53 Case and Shiller (1987) suggest the following 3. Run an OLS regression of model (11.22) but where each three-stage approach: observation is divided through by the square root of the fitted value from the second-stage regression. 1. Estimate model (11.22) by OLS regression and retain the vector of regression residuals. The third stage is a weighted least squares regres- 2. Run an OLS regression of the squared residuals on a con- sion of model (11.22) that accounts for the presumed stant term and the time interval between sales. heteroskedasticity. Table 11.15. Unweighted Repeat Sales Regression Source | SS df MS Number of obs = 1186 _____________________________________________ F( 6, 1180) = 379.41 Model | 32.5127473 6 5.41879122 Prob > F = 0.0000 Residual | 16.8531146 1180 .014282301 R-squared = 0.6586 _____________________________________________ Adj R-squared = 0.6569 Total | 49.365862 1186 .04162383 Root MSE = .11951 diflnprice | Coef. Std. Err. t P>|t| [95 % Conf. Interval] dy2003 | .0613539 .0086332 7.11 0.000 .0444157 .0782921 dy2004 | .1198942 .0082047 14.61 0.000 .1037969 .1359915 dy2005 | .1431862 .008343 17.16 0.000 .1268173 .159555 dy2006 | .1845885 .0084578 21.82 0.000 .1679945 .2011826 dy2007 | .2658241 .0083474 31.85 0.000 .2494468 .2822015 dy2008 | .3438869 .0087587 39.26 0.000 .3267025 .3610713 Source: Authors’ calculations based on MLS® data for a Canadian city Table 11.16. Weighted Repeat Sales Regression Source | SS df MS Number of obs = 1186 _____________________________________________ F( 6, 1180) = 348.90 Model | 2098.21619 6 349.702699 Prob > F = 0.0000 Residual | 1182.72363 1180 1.00230816 R-squared = 0.6395 _____________________________________________ Adj R-squared = 0.6377 Total | 3280.93982 1186 2.76639108 Root MSE = 1.0012 ndifprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] ndy2003 | .0635307 .0085609 7.42 0.000 .0467345 .0803269 ndy2004 | .1211754 .0081162 14.93 0.000 .1052516 .1370992 ndy2005 | .1437457 .0082962 17.33 0.000 .1274688 .1600226 ndy2006 | .1864151 .0084621 22.03 0.000 .1698127 .2030175 ndy2007 | .2689894 .0084844 31.70 0.000 .2523433 .2856356 ndy2008 | .3491619 .0091085 38.33 0.000 .3312913 .3670325 Source: Authors’ calculations based on MLS® data for a Canadian city 11.54 Moving to the larger and more realistic set of data intercept is used in the regressions for the repeats sales on single-family houses that were previously used for most approach. One often cited drawback of the repeat sales of the previous examples of this chapter, two versions of method is that it is wasteful of data. The current exercise the repeat sales method are illustrated. The results are first confirms this. Of the 5787  observations that were in the computed for the unweighted repeat sales regression ap- database at the start, only 1186 (or about 20 %) are found to proach and are presented in Table 11.15. Table 11.16 pre- be units that sold more than once during the 6 or so years. sents the results for the weighted version of the repeat sales 11.55 Similar to the time dummy hedonic model pre- regression. Note that for this particular set of data, all the sented earlier, the corresponding price indices are obtained coefficients are significantly different from 0  and that no by taking the antilogarithm of the estimated coefficient as Handbook on Residential Property Prices Indices (RPPIs) 153 11 Empirical Examples the dependent variable is the logarithm of the price. For Note that the indices are quite similar, regardless whether example, the regression for the unweighted repeat sales the unweighted or weighted repeat sales versions are used. approach yields a coefficient of 0.2658241  for 2007; tak- This is a feature of this particular dataset and may not nec- ing the antilogarithm yields exp(0.2658241) = 1.3045 (or essarily hold true for house price indices estimated from 130.5 once rounded and multiplied by 100). The indices for other sources. the entire 2002 to 2008 period are shown in Table 11.17. Table 11.17. Repeat Sales Price Indices (2002 = 100) Year Unweighted Per cent change Weighted Per cent change 2002 100.0 100.0 2003 106.3 6.3 106.6 6.6 2004 112.7 6.0 112.9 5.9 2005 115.4 2.4 115.5 2.3 2006 120.3 4.2 120.5 4.4 2007 130.5 8.5 130.9 8.6 2008 141.0 8.1 141.8 8.3 Source: Authors’ calculations based on MLS® data for a Canadian city 11.56 Table 11.18 summaries the index results using the any generalisation, one important observation is note- various methods presented here using the extended dataset worthy. The non-quality adjusted indicators, i.e., the mean for year 2007. The simple mean shows the largest increase and median, generate the highest growth rates, while the of all the estimated indices at 10.1 % with the median be- hedonic methods generate the smallest. The repeat sales ing slightly lower at 9.2 %. The hedonic indices increased approaches, although they control for many potential as- by 5.7 % and 5.9 % for the adjacent year pooled and char- pects of quality, do not control for age. Therefore, it is not acteristics prices approaches, respectively (calculation not so surprising that the price increases obtained with this shown above). By contract, the repeat sales weighted and approach are larger than those obtained with the hedonic unweighted indices increased by 8.5  % and 8.6  %, respec- approaches. tively. Although the sample size is somewhat small to make Table 11.18. Growth Rates in Percent for the Various House Price Indices (2007) Characteristics Repeat sales Repeat sales Mean Median Pooled hedonics hedonics unweighted weighted 10.1 9.2 5.7 5.9 8.5 8.6 Source: Authors’ calculations based on MLS® data for a Canadian city 154 Handbook on Residential Property Prices Indices (RPPIs) Recommendations 12 12 Recommendations 12.1 This handbook provides detailed and comprehen- property should be stock-weighted. A stock-weighted index sive information on the compilation of residential property is also appropriate for a financial stability indicator, in par- price indices (RPPIs). It provides an overview of the con- ticular for an index which is being used to identify prop- ceptual and theoretical issues that arise, explains the differ- erty price bubbles. ent user needs for such indices and gives advice on how to 12.6 A price index which is required for measuring the deal with the practical problems that statistical offices are real output of the residential real estate construction indus- confronted with in the construction of such indices. Earlier try should be sales-weighted. A sales-weighted index is also chapters cover all relevant topics including: a description appropriate for a consumer price index (CPI) that follows of the different practices currently in use; advice on the an acquisitions approach. alternative methodologies available to the compiler; and the advantages and disadvantages of each alternative. The purpose of this chapter is to draw together all this informa- Index Scope tion and make recommendations on best practice for com- piling residential property price indices, including how to 12.7 A price index which is required to measure the improve international comparability. The recommenda- wealth associated with the ownership of residential prop- tions necessarily take into account the different situations erty should cover all residential property, that is, both ex- countries are confronted with in terms of data availability isting properties and properties which have been recently and therefore cannot be too prescriptive. built. (1) This is also the case for an index used as a financial stability indicator. 12.2 Users of RPPIs are also catered for. The handbook provides information not only on the different methods that 12.8 A price index which is required for measuring real are and can be deployed in compiling such indices, but also investment in the residential real estate industry should on the statistical limitations of what is being measured. Users cover sales of new property.  (2) The construction part of will want to bear the latter in mind so that the results of an new housing produced is part of gross investment. The index can be interpreted correctly. Any set of recommenda- cost of the land, apart from the value of any improvements tions has to start with an understanding of the basic concept made to this element, should be excluded for this purpose. underlying the target index, in other words what a residential However, as was explained in Chapter 3, a price index for property price index is trying to measure. This will, of course, the sales of both new and existing houses is required in depend on user needs and the purpose of the index. order to construct real output measures for the activities of real estate agents in selling new and existing houses to pur- 12.3 The recommendations given below follow the chasers. The scope of the index for this application should same order as Chapters 3  to 8. Chapter 3  describes the cover both the structure and land values of the residential main elements of a conceptual framework for RPPIs, and property sales. Chapters 4 to 8 describe the main statistical methods that can be used in constructing such indices. The different 12.9 A price index restricted to new properties is also methods essentially relate to alternative solutions to the appropriate when a residential property price index is an problem of quality change, that is, how to adjust an RPPI input into a CPI for the measurement of owner-occupier for changes in the quality mix of the properties sold and for housing costs on a net-acquisition cost basis, that is, where quality changes (the net effect of renovations, extensions the CPI covers the cost of acquiring properties which and depreciation) of the individual dwellings. are new to the owner-occupier housing market. This ap- proach, one of a number of alternatives as was explained in Chapter 3, treats the purchase of a dwelling exactly like the purchases of any other consumption good. (3) Conceptual Issues Constant Quality Target and Conceptual Basis 12.10 Regardless of the different uses of the index, the purpose of a residential property price index is to compare 12.4 In principle, the target index, in other words the type of index to be compiled, will depend on its purpose. (1) This includes conversions of existing property, for example where a warehouse has The System of National Accounts 2008 should be used as the been converted into flats or an existing property has been sub-divided. (2) Renovations to existing dwelling units are also part of residential construction conceptual framework for RPPIs. investment. (3) The argument in favour of the net acquisition approach is that it is the closest to the “acquisition” approach which has traditionally been adopted for other parts of a CPI and Weighting is most appropriate for a CPI being used as a general indicator of current economic conditions. But the method can draw criticism from those who require a CPI as a compensation index, as neither the weight nor the price indicator properly reflect 12.5 A price index which is required to measure the shelter costs of owner-occupiers. For instance, a rise in interest rates would not be reflected in a net acquisition index. See CPI Manual (2004) and the Practical Guide to the wealth associated with the ownership of residential Producing Consumer Price Indices (United Nations, 2009). 156 Handbook on Residential Property Prices Indices (RPPIs) Recommendations 12 the values of the sales or of the stock of residential property 12.14 The different methods of index construction used between two time periods after allowing for changes in the by a statistical agency reflect the differing solutions used attributes of the properties. For this purpose it is neces- to meet the above challenges. Four methods have been sary to decompose price changes into those associated with studied in depth in this handbook: stratification or “mix- changes in attributes and the residual which relates to the adjustment”, hedonic regression methods, repeat sales, and underlying “pure price” change. appraisal-based methods (i.e., the SPAR method). Below, recommendations are made on each. Each method at- 12.11 A constant quality price index is appropriate for tempts to adjust for the change in the “quality mix” of the both a stock and sales-weighted price index. There are a houses whose prices are observed and combined to con- number of practical methodologies which can be used to struct the index. Some methods, however, are unable to construct such an index. Recommendations on which of adjust for quality changes of the individual houses, i.e. for the available methods should be used in which circum- the net effect of depreciation of the structures and renova- stances are provided below. tions and extensions. Where data from the administrative processes for buying and selling a residential property are Decomposition between the Building used in the construction of the index, the price will usually and Land Components relate either to the offer price or to the selling price – these can differ from one another. 12.12 A decomposition of the RPPI in structures and land components may be required, particularly if a coun- 12.15 The recommendations do not address the chal- try’s balance sheet estimates of national wealth in the lenge of computing an RPPI in countries where a signifi- National Accounts make this distinction. Such decom- cant proportion of the housing stock relates to informal or position may also be necessary when a residential prop- traditional dwellings. An example of computing an RPPI erty price index is an input into a CPI for the measure- under the latter circumstances is given in Chapter 10 and ment of owner-occupier housing using the net-acquisition draws on the experience of South Africa. In such circum- approach. stances it is not possible to be very prescriptive in terms of recommendations since the situation will vary consider- ably among countries and there is no ideal solution that will deliver a residential property price index which is con- Statistical Methods ceptually pure and does not generate practical difficulties. Rather, the compiler will need to draw on the best available for Compiling Constant sources of information and will no doubt have to make conceptual and methodological compromises in comput- Quality Indices ing an index. In these circumstances it is particularly im- portant that statistical agencies provide evaluations of the 12.13 The methods adopted by statistical agencies to resulting price indices and guide users on their uses. construct constant-quality RPPIs vary among countries and are dictated in large part by the availability of data generated by the processes involved in buying and selling Stratification or mix-adjustment a property. The challenges of compiling constant-quality residential price indices can be summarized by the follow- 12.16 Stratification or mix-adjustment is the most ing three factors: straightforward way to control for changes in the composi- tion or quality mix of the properties sold. It also addresses • Residential properties are notoriously heterogeneous. any user need for sub-indices relating to different housing No two properties are identical. market segments. The effectiveness of stratification will de- • Prices are often negotiated. The (asking) price of a prop- pend upon the stratification variables used because a mix- erty is not fixed and can change throughout the transac- adjusted measure only controls for compositional change tion process until the price is finalised. This means that across the various groups – a mix-adjusted index does not a property’s market value can only be known with cer- account for changes in the mix of properties sold within tainty after it has been sold. (4) each subgroup or stratum. • Property sales are infrequent. In many countries, less than ten per cent of the housing stock changes hands 12.17 In theory, the more detailed the stratification, the every year, which means that a particular house is likely more the index controls for changes in the characteristics to be resold approximately once every ten years. of the properties covered by the index. However, increas- ing the number of strata reduces the average number of price observations per stratum and in fact can quickly lead (4) In some cases even the selling prices may not reflect the “true” market values, for to empty strata. Strata or cells which are empty then lead example when they relate to distressed sales arising from divorce etc. in turn to a lack of matching when the average price and Handbook on Residential Property Prices Indices (RPPIs) 157 12 Recommendations quantity data in each cell are compared across two time Hedonic regression periods. A very detailed stratification might also raise the standard error of the overall index. In addition, it may be 12.22 The application of hedonic techniques for qual- difficult to identify the most important price-determining ity adjustment and for computing price indices has made characteristics in the way that a method using hedonic re- a significant contribution to the methodological develop- gression can do (see next section). ment of price indices in recent years and is rapidly becom- ing a preferred method for compiling constant-quality res- 12.18 The main advantages of stratification/mix- idential property price indices.  (6) There is no uniformity adjustment are: in the practical application of hedonic regression, but the • Depending on the choice of stratification variables, the idea underlying hedonics is rather simple. Hedonic regres- method adjusts for compositional change amongst the sion is a statistical technique that measures the relationship dwellings. between the observable characteristics of a good or service • The method is reproducible, conditional on an agreed list and its price or value. In the context of residential prop- of stratification variables. erty price indices, the “best” form of the hedonic function • It is not subject to revision. may be linear rather than log-linear to reflect the fact that • Price indices can be constructed for different types and the value of a property is generally equal to the sum of the locations of housing. price of the structure and the price of the land. • The method is relatively easy to apply and to explain to 12.23 There are basically two alternative methods of ap- users. plication of hedonics to residential property: 12.19 The main disadvantages of stratification/mix- • The time dummy variables method. This method gen- adjustment are: erally uses a single regression, with time dummies and • It cannot deal adequately with depreciation of the houses fixed characteristics coefficients, which covers all pe- unless the age of the structure is a stratification variable. riods and which is re-run each time the price index is The latter can result in problems associated with cells compiled. The (exponentials of the) time dummy coef- with small numbers of price observations. ficients are taken to represent the period-to-period price • The method cannot deal adequately with houses which changes excluding quality (mix) changes. This method have undergone major repairs or renovations (unless in- has the benefit of simplicity. One of the drawbacks is that formation on renovations is available). it raises the issue of “revisability” of the index because the • It requires information on housing characteristics that time dummy coefficients will be updated each time new are included in the strata so that the sales can be allo- periods are added and the regression is run. cated to the correct strata. However, there is a variant of the time dummy method, • If the stratification scheme is very coarse, compositional called the rolling window time dummy method, which can changes will affect the indices. work well in practice and solves the revisability problem. • If the stratification scheme is very fine, the cells can be A hedonic regression is run using the data for the last N subject to considerable sampling variability due to small periods and the last time dummy is used as a chain link sample sizes or some cells may simply be empty for some factor for updating the index for the previous period. For periods causing index number difficulties. references to the literature on this method and an example, • The value of land cannot be separated out using this see chapter 5. method. • The hedonic imputation method. A separate hedonic re- 12.20 Stratification/mix-adjustment is an appropriate gression is performed in each time period and the “miss- method where ing” current period prices for the properties sold in the • an appropriate level of detail is chosen for the cells and base period are imputed using the predicted prices from can be applied in practice; the estimated hedonic equation. A symmetric approach • the age group of the structure is one of the stratification is possible by also imputing the “missing” base period variables; prices for the properties sold in the current period and • a decomposition of the index into structure and land then taking the geometric mean of both hedonic imputa- components is not required. tion indices. 12.21 Stratification/mix-adjustment is recommended 12.24 Both hedonic regression methods can potentially where the volume of sales is large enough and information suffer from omitted variable bias if some important price on housing characteristics detailed enough to support a de- determining characteristic is omitted from the regression tailed classification of properties. (5) (6) If we look at the harmonised house price indices produced by the European National (5) A coarse stratification by, say, major city and house type, where the latter is simply in Statistical Institutes, as of 2011 more than half were using hedonics for quality terms of “newly-built” or “existing”, is not recommended. adjustment. For more details, see Marola et al. (2012). 158 Handbook on Residential Property Prices Indices (RPPIs) Recommendations 12 equation. Multicollinearity can be a practical problem, hedonic quality (mix) adjustment has advantages over the particularly when a decomposition of the index into struc- time dummy approach. Stratified hedonic indices are pre- tures and land components is required. The time dummy ferred over a straightforward application of hedonic regres- variable method has been frequently used by academics, sion to the whole data set. in part due to its simplicity, but the hedonic imputation method is more flexible – it allows characteristics prices to Repeat Sales change independently over time whereas the time dummy method forces characteristics prices to move in a propor- 12.29 The repeat sales method observes the price devel- tional manner – and is essentially similar to the traditional opment of a specific house over a period of time by ref- matched-model methodology to compute price indices. erence to the selling price each time it is sold. The price change of a selection of houses during overlapping time 12.25 Hedonic regression methods can be used in periods can then be observed to estimate, using a dummy conjunction with stratification to deal with any residual variable regression model, the general trend in residential quality-mix change that remains within the strata. This has property prices. Measuring the average price changes in re- the added advantage of dealing with the fact that different peat sales on the same properties ensures a “like for like” model specifications may be needed for different segments comparison (ignoring the fact that depreciation and reno- of the housing market or that the “value” of some charac- vations on the structure between the periods of sale can teristics will vary across different market segments. change the property). 12.26 The main advantages of hedonics are: 12.30 The main advantages of the repeat sales method • If the list of property characteristics is sufficiently de- are: tailed, the method adjusts for both sample mix changes and quality changes (depreciation and renovation) of the • In its basic form, it requires no information on charac- individual houses. teristics of the dwelling units other than the addresses • Price indices can be constructed for different types of of the properties that are traded. Source data are often dwellings and locations through stratification and the available from administrative records. application of hedonics to each individual stratum. • It follows a matched-model methodology, under the as- • Stratified price indices based on hedonic regressions sumption that depreciation and renovations have not to control for quality mix changes within strata allow changed the dwelling unit over the time period between for relative values of the stock of housing to be used subsequent sales. to weight the quality-mix adjusted strata indices (in a • Many locational and other price determining character- stock-weighted RPPI). istics that are difficult to measure are likely to be auto- • The method maximizes the use of the available data. matically included. • It can in principle be used to decompose the overall price • Standard repeat sales regressions are easy to run and the index into land and structures components, subject to resulting price indices are easy to construct. the availability of data. • No imputations are involved. By construction, location is automatically controlled for. 12.27 The main disadvantages of hedonic regression are: • The results are, in principle, reproducible. • The method is often regarded as being data intensive, es- pecially in terms of the housing characteristics to be used 12.31 The main disadvantages of the repeat sales meth- as explanatory variables. (7) od are: • It may be difficult to control sufficiently for location if • The method does not use all of the available selling pric- property prices and price trends differ across detailed es; it uses information only on those properties that have regions. sold more than once during the sample period. • The method can be sensitive to the variables used in the • The standard version of the method ignores (net) depre- regression and the functional form for the model. ciation of the dwelling unit. • The method is not particularly easy to explain to users • Sample selection bias can arise from the restriction to and from their perspective may lack transparency. properties that have been sold more than once during 12.28 Subject to data being available on salient housing the sample period. characteristics, the hedonic regression method is generally • The method cannot generate separate price indices for the best technique for constructing a constant quality resi- structures and for land. dential property price index. The imputations approach to • The reliance on repeat sales means that there may not be enough data points to compute monthly residential property price indices for smaller categories of property. (7) However, as was seen in previous chapters, in some cases satisfactory results can be obtained with hedonic regression methods using only three or four housing • The sample is updated as new transaction informa- characteristics. tion becomes available. This means that the repeat sales Handbook on Residential Property Prices Indices (RPPIs) 159 12 Recommendations property price index could be subject to retrospective re- • It is straightforward to compute. visions over a long time period. (8) • The method benefits from many more observations than • Since a house must be sold at least twice in a repeat sales the repeat sales method and is therefore less susceptible index, newly built dwelling units are excluded from such to problems arising from having a relatively small num- an index. ber of price observations. • It is less susceptible to sample selection bias than the re- 12.32 Although a natural starting point for constructing peat sales method. an index, the repeat sales method is not preferred over the • It does not suffer from revisions to previously computed (stratified) hedonic method for constructing a constant qual- figures. ity residential property price index. However, it can offer a • It is reproducible. solution where there is limited or no information on hous- ing characteristics and there are a relatively large number 12.36 The main disadvantages of the SPAR method are: of repeat transactions to provide enough data points for the required types of residences and where sample selection bias • It cannot deal adequately with quality changes (deprecia- is not considered a problem. It is not recommended when a tion and renovations) of the dwelling units. (10) distinction needs to be made between the price of the struc- • Data on value assessments at the address level must be ture and the price of the land. available for all properties. • The method is dependent on the quality of the assessments. • It cannot be used to decompose the overall property Appraisal-Based Methods price index into land and structures components. (11) 12.33 Appraisal-based methods use “assessed” values, 12.37 The SPAR methodology addresses some of the such as valuations for taxation purposes or valuations weaknesses of the repeat sales methodology and is to be pre- from specially commissioned surveys using estate agents, ferred to the latter methodology if assessment data of suffi- often done by reference to similar properties that have cient quality are available and if selectivity bias is considered been sold, to overcome the two main problems associated to be a serious feature of the application of the repeat sales with the repeat sales methodology – the relatively small methodology. The SPAR methodology does have its draw- number of price observations which are generated and the backs but is recommended when the use of hedonics is not susceptibility to sample selection bias. Where the valua- possible. The results from the SPAR method are improved if tions all refer to a standard reference period, the matched it is used in conjunction with stratification. model methodology which underlies appraisal-based methods also has the advantage that it can be applied in a straightforward way and with no necessity to use econo- Seasonal Adjustment metrics to adjust for compositional changes. However, like 12.38 If the initial house price series indicates that some the repeat sales methodology, appraisal-based methods seasonal fluctuations occur, then normal seasonal adjust- generally cannot deal adequately with quality changes to ment techniques can be used in order to seasonally adjust individual houses. Also, they generally rely on expert judg- the initial series. However, if the hedonic imputation or the ment on how much a property would sell for rather than stratification method is used to construct the initial index, on an actual transaction price. Thus, it can be argued, at the some more specific recommendations are made below. extreme, that appraisal-based methods are influenced by judgments or opinions, albeit authoritative and objective. 12.39 If the stratification method is used to construct the initial index and it exhibits seasonality, then the roll- 12.34 The Sale Price Appraisal Ratio (or SPAR) method ing year method explained in Chapter 5 can be applied to uses appraisals with a common reference period as base seasonally adjust the series without relying on econometric period prices in a standard matched-model framework methods. (though the results are normalized to obtain an index that equals 1 (or 100) in the base period). The experiences of 12.40 If the hedonic imputation method is used to con- the few countries that have computed a SPAR index (9) are struct the initial price index and it exhibits seasonality, generally positive although some researchers have report- then in order to obtain a seasonally adjusted series, it may ed a bias arising from frequent re-assessments and reduced be useful to construct year-over-year monthly or quarterly precision over time arising from new appraisals. series as an initial step. These initial series can then be ag- gregated using the rolling year method into a smoothened 12.35 The main advantages of the SPAR method are: seasonally adjusted series. • Being based on the standard matched model methodol- ogy, it is consistent with traditional index number theory. (10) As with the repeat sales method, the price index generated by the SPAR method can in principle be adjusted by using exogenous information on the net depreciation of properties of the type being considered. (8) In practice, the link factor for the last two periods in the current repeat sales regression ( ) Where official decompositions of the total assessed value of the property into land 11 can be used to update the ongoing index. and structures components are available, these could be used to check the land and (9) In Europe, Denmark, Sweden and the Netherlands are using the SPAR method. structures price indices that are generated by hedonic regression methods. 160 Handbook on Residential Property Prices Indices (RPPIs) Glossary Glossary Acquisitions approach different contexts. Three types of base period may be An approach in which consumption is identified with distinguished: the goods and services acquired by a household in some • the price reference period – the period that provides the period (as distinct from those wholly or partially used up prices to which the prices in other periods are com- for purposes of consumption). See also net acquisitions pared. The prices of the price reference period appear approach. in the denominators of the price relatives, or price ra- Aggregate tios, used to calculate the index; A set of transactions (or their total value) such as the • the weight reference period – the period for which the total purchases made by households on residential prop- expenditures serve as weights for the index. If the erty in a certain period. expenditures are hybrid (i.e., if the quantities of one period are valued at the prices of some other period), Aggregation the weight reference period is the period to which the Combining, or adding, different sets of transactions to ob- quantities refer; tain larger sets of transactions. The larger set is described • the index reference period – the period for which the as having a higher level of aggregation than the (sub-) value of the index is set equal to 100. sets of which it is composed. The term “aggregation” is It should be noted that, in practice, the duration of the also used to mean the process of adding the values of the weight reference period for an RPPI is often a year, lower-level aggregates to obtain higher-level aggregates. whereas the RPPI is typically calculated monthly or In the case of price indices, it means the process by which quarterly, the duration of the price reference period be- price indices for lower-level aggregates are averaged to ing a month or quarter. Thus, the weight and price refer- obtain price indices for higher-level aggregates. ence period may not coincide in practice, at least when Asking price an RPPI is first calculated, although the price and index The price at which a property is offered for sale. The ask- reference periods frequently coincide. ing price can be adjusted during the process of buying Bias and selling a house until the final transaction price is reached. A systematic tendency for the calculated RPPI to diverge from some ideal or preferred index, resulting from the Assessed value or appraisal method of data collection or processing or the index for- Valuation of the market value of a property. Valuations mula used. See also sample selection bias. may be needed to obtain a mortgage loan. In some coun- Chain index tries assessments are performed on the government’s be- half for (property) tax purposes. Assessed property val- An index number series for a long sequence of periods ues are also referred to as appraisals. See also Sale Price that is obtained by linking together index numbers span- Appraisal Ratio method. ning shorter sequences of periods. A chain index, com- puted according to some index number formula (such Axiomatic (test) approach as the Fisher), is the product of period-on-period indi- The approach to index number theory that determines ces which are computed with the same formula. See also the choice of index number formula, on the basis of its Linking. mathematical properties. A list of tests is drawn up, each test requiring an index to possess a certain property or Characteristics satisfy a certain axiom. An index number may then be The physical and economic attributes of a good or ser- chosen on the basis of the number of tests satisfied. Not vice that serve to identify it and enable it to be classified. all tests may be considered to be equally important and For residential property these relate to both the structure the failure to satisfy one or two key tests may be consid- (the building) and the location/land. ered sufficient grounds for rejecting an index. Characteristics prices hedonic approach Base period An hedonic regression method where the change in the The base period is usually understood to mean the pe- estimated values of the parameters for the characteristics riod with which all the other periods are compared. of the (average) property sold, i.e. the shadow prices of The term may, however, have different meanings in the characteristics, determines the residential property Handbook on Residential Property Prices Indices (RPPIs) 161 Glossary price index. Under certain assumptions this approach is Depreciation equivalent to the hedonic imputation approach. The gradual and permanent decrease in the economic Component value of a structure or the housing stock through physi- cal deterioration or obsolescence over time. A set of the goods and services that make up some de- fined aggregate. Also used in the context of decomposing Domain the price property price (index) into land and structures An alternative term for the scope of an index. components. Drift Consistency in aggregation A chain index is said to drift if it does not return to unity An index is said to be consistent in aggregation when the when prices in the current period return to their levels index for some aggregate has the same value whether it in the base period. Chain indices are liable to drift when is calculated directly in a single operation, without dis- prices fluctuate over the periods they cover. tinguishing its components, or whether it is calculated in Durable consumption good two or more steps by first calculating separate indices, or sub-indices, for its components, or sub-components, and A consumption good that can be used repeatedly or con- then aggregating them, the same formula being used at tinuously for purposes of consumption over a long peri- each step. od of time, typically several years. A house is an extreme form of a durable consumption good due to its very long Consumer price index (CPI) expected lifetime. This has led to different approaches to A monthly or quarterly price index compiled and pub- the treatment of owner-occupied housing in economic lished by an official statistical agency that measures statistics. changes in the prices of consumption goods and ser- Economic approach vices acquired or used by households. Its exact defini- tion, including the treatment of owner-occupied hous- The economic approach to index number theory as- ing, may vary from country to country. In Europe, the sumes that the quantities are functions of the prices, the Harmonised Index of Consumer Prices (HICP) current- observed data being generated as solutions to various ly excludes owner-occupied housing. economic optimization problems. While this approach is very relevant for the CPI as an approximation to a cost- Coverage of-living index, it seems less relevant for a residential The set of properties of which the prices are actually in- property price index. See also axiomatic or test approach. cluded in a price index. For practical reasons, coverage Editing may have to be less than the ideal scope of the index. That The process of scrutinizing and checking the prices re- is, the types of property actually priced may not cover all ported by price collectors. Some checks may be carried of the types that are sold or belong to the housing stock. out by computers using statistical programs written for Current period, or comparison period the purpose. See also data cleaning. In principle, the current period refers to the most recent Elementary aggregate period for which the index has been compiled or is being Usually defined as the lowest aggregate for which ex- compiled. The term is widely used, however, to mean the penditure data are available and used for index construc- comparison period; that is, the period that is compared tion purposes. Elementary aggregates also serve as strata with the base period, usually the price reference or index for the sampling of items to be priced. The values of the reference period. It is also used to mean the later of the elementary aggregates are used to weight the price in- two periods being compared. The exact meaning is usu- dices for elementary aggregates to obtain higher-level ally clear in the context. indices. Data cleaning In the context of a sales-based residential property price Procedures, often automated, used to delete entry errors index, the term elementary aggregate is less appropriate. in data sets, observations which are deemed implausible, As every property is basically unique, the quantities are or outliers. equal to 1, so that weights are available at the most de- tailed level. Deflating The division of the current value of some aggregate by a Existing dwellings price index (in this context referred to as a deflator), in The term “existing dwellings” is sometimes used to dis- order to revalue its quantities at the prices of the price tinguish them from dwellings that are newly built (and reference period. added to the housing stock). 162 Handbook on Residential Property Prices Indices (RPPIs) Glossary Fisher price index Hybrid (repeat sales) models The geometric average of the Laspeyres price index and A regression-based method to estimating residential the Paasche price index. The Fisher index is symmetric property price indices which combines repeat-sales and and superlative. Sales based residential property price in- hedonic approaches. dices can always be computed using the Fisher formula Identity test because the quantities are equal to 1 (as each dwelling is essentially a unique good). A test under the axiomatic approach that requires that, if the price of each item remains the same between the Fixed weight indices periods compared, the price index must equal unity. An abbreviated description for a series of weighted arith- Imputed price metic averages of price relatives of price indices where the weights are kept fixed over time. In a residential The price assigned to an item (e.g. a property) for which property price index context, the weights can be sales the price is “missing” in a particular period. This may be (expenditure) weights or stock weights. done using hedonic regression methods. See also hedonic imputation approach. Geometric Laspeyres index The term “imputed price” may also refer to the price as- A weighted geometric average of the price relatives using signed to a good or service item that is not sold on the the expenditure shares of the price reference period as market, such as a good or service produced for own con- weights. sumption, including housing services produced by own- Goods er-occupiers measured by imputed rent. See also rental equivalence. Physical objects for which a demand exists, over which ownership rights can be established and for which own- Index reference period ership can be transferred between units by engaging in The period for which the value of the index is set at 100 transactions on the market. (or, alternatively, 1). Hedonic regression Informal housing market The estimation of a hedonic model, using regression Residential areas where a group of housing units has been techniques, that explains the price of the property as a constructed on land to which the occupants have no le- function of its characteristics (relating to the structures gal claim, or which they occupy illegally, or unplanned as well as the location). See also hedonic imputation ap- settlements and areas where housing is not in compli- proach and time dummy variable hedonic approach. ance with current planning and building regulations. Hedonic imputation approach Jevons price index An approach to estimating a quality-adjusted residential An elementary price index defined as the unweighted property price index where “missing” prices are imputed geometric average of the sample price relatives. using a hedonic regression model. The model parameters are re-estimated in each time period, which makes this Laspeyres price index approach more flexible than the time dummy variable A price index in which the quantities of the goods and hedonic approach. services refer to the earlier of the two periods compared, the price reference period. The Laspeyres index can also Households be expressed as a weighted arithmetic average of the Households may be either individual persons living price relatives with the expenditure shares in the earlier alone or groups of persons living together who make period as weights. The earlier period serves as both the common provision for food or other essentials for liv- weight reference period and the price reference period. ing. Most countries choose to exclude groups of persons Linking living in large institutional households (barracks, retire- ment homes, etc.) from the scope of their CPIs. Splicing together two consecutive series of price obser- vations, or price indices, that overlap in one or more Housing stock periods. If the two sequences overlap by a single period, The total number of residential units available for non- the usual procedure is simply to rescale one or other se- transient occupancy. Depending on the particular defi- quence so that the value in the overlap period is the same nition used, the housing stock may or may not include in both sequences and the spliced sequences form one mobile homes, etc. continuous series. Handbook on Residential Property Prices Indices (RPPIs) 163 Glossary Lowe price index Offer price A price index that measures the change between periods The price a potential buyer says he will be willing to pay 0 and t in the total value of a set of goods and services at for the property. fixed quantities. The quantities do not necessarily have Outlier to consist of the actual quantities in some period. The class of indices covered by this definition is very broad A term that is generally used to describe any extreme and includes, by appropriate specification of the quantity value in a set of survey data. In an RPPI context, it is terms, the Laspeyres and Paasche indices. used for an extremely high or low property price or price relative, which requires further investigation and should Lower-level index be deleted when deemed incorrect. An sub-index as distinct from an aggregate index. Owner-occupied housing Matched models approach Dwellings owned by the households that live in them. The practice of pricing exactly the same product, or The dwellings are fixed assets that their owners use to model, in two or more consecutive periods. It is designed produce housing services for their own consumption, to ensure that the observed price changes are not affect- these services being usually included within the scope of ed by quality change. The change in price between two a CPI. The rents may be imputed by the rents payable perfectly matched products is sometimes described as a on the market for equivalent accommodation or by user pure price change. costs. See also rental equivalence and User cost. Market value Paasche price index The value of a property at a certain point of time, or the A price index in which the quantities of the goods and price that would result if the property would be sold in services considered refers to the later of the two periods a “free market”. compared. The later period serves as the weight reference Mean index period and the earlier period as the price reference peri- od. The Paasche index can also be expressed as a weight- A price index that is calculated as the ratio of the sample ed harmonic average of the price relatives that uses the means (unit values) of the properties sold in two periods. actual expenditure shares in the later period as weights. Median index Payments approach A price index that tracks the change of the median prop- See money outlays approach. erty price over time. The median is the middle of a (sam- ple) distribution: half the scores are above the median Price reference period and half are below the median. The median is less sensi- The period of which the prices appear in the denomina- tive to extreme scores than the mean and is often pre- tors of the price relatives. See also Base period. ferred to the mean as a measure of central tendency in highly skewed distributions. Price relative The ratio of the price of an individual product in one Mix adjustment period to the price of that same product in some other A term used to describe procedures which attempt to re- period. move or reduce the effect of changes in the mix (compo- sition) of the sample of properties sold on the property Products price index. A generic term used to mean a good or a service. Individual sampled products selected for pricing are of- Money outlays or payments approach ten described as items. One of the three main approaches to including owner- occupied housing into a CPI. In the money outlays ap- Pure price change proach, the out of pocket expenses relating to home The change in the price of a property of which the char- ownership are simply added up. acteristics are unchanged or the change in the property price after adjusting for any change in quality (due to Net acquisitions approach renovations, extensions and depreciation). One of the three main approaches to including Owner Occupied Housing into a Consumer Price Index. Quality change Dwellings added to the owner occupied housing stock A change in the (quality determining) characteristics (in general mainly newly-built dwellings) are part of the of a good or service. In the case of a residential prop- coverage of the index; existing dwellings are excluded. erty this includes both depreciation of the structure and See also Acquisitions approach. renovations, such as the modernisation of kitchens and 164 Handbook on Residential Property Prices Indices (RPPIs) Glossary bathrooms, the introduction of improved insulation and Sample selection bias central heating or air conditioning systems. Bias in an index that can result when the sample is not Quality adjustment representative of the population. In the housing context, the sample of properties may either not be representa- An adjustment to the change in the price of a property tive of all sales (which is particularly relevant for a sales of which the characteristics change over time that is de- based index) or not be representative of the housing signed to remove the contribution of the change in the stock (which is relevant for a stock based index). In all characteristics to the observed price change. In practice, sales are observed, there will be no sample selection bias the required adjustment can only be estimated. Different in a sales based property price index. methods of estimation, including hedonic methods, may be used in different circumstances. These methods can Sampling frame also be used to control for compositional or quality mix A list of the units in the universe from which a sample changes over time in the samples of properties sold. of units can be selected. The list may contain informa- Rental equivalence approach tion about the units, which may be used for sampling purposes. Such lists may not cover all the units in the One of the three main approaches to including owner- designated universe and may also include units that do occupied housing into a CPI Index. The imputed price not form part of that universe. for shelter costs should equal the price at which the dwelling could be rented. Scope Repeat sales method The set of products for which the index is intended to measure the price changes. The coverage of an index de- A method to compile a residential property price index notes the actual set of products included, as distinct from which compares properties that were sold twice or more the intended scope of the index. in the data set at hand. It is a regression-based approach that only includes time dummy variables. Seasonal goods Representative property Seasonal goods are goods that either are not available on the market during certain seasons or periods of the year, A property, or category of properties, that accounts for or are available throughout the year but with regular a significant proportion of the total expenditures with- fluctuations in their quantities and prices that are linked in some aggregate, and/or for which the average price to the season or time of the year. change is expected to be close to the average for all prop- erties within the aggregate. Selling (or transaction) price Residential property The final transaction price of a property. Property zoned for single-family homes, townhouses, Specification multifamily apartments, condominiums, and coops. A description or list of the characteristics that can be Reweighting used to identify an individual dwelling unit to be priced. Replacing the weights used in an index by a new set of SPAR method weights. An acronym for Sale Price Appraisal Ratio method, an Rolling window approach approach to constructing a residential property price in- dex which combines current period selling prices with An approach where a “window” of a fixed number of appraisals (assessed values) pertaining to some earlier time periods is chosen to compute the initial (residen- base period. tial property) price index. The time series is subsequently updated by moving the window one period forward in Stratification method time and linking the last period-on-period index change Stratification and “re-weighting” of a sample is a general to the existing time series. technique for obtaining more stable results or mitigat- Sample ing any bias due to sample selection problems, including non-response. A (random or non-random) selection of elements from a finite population. In the housing context, the properties In the context of a residential property price index, the sold in some time period can be viewed as a sample from sample of properties sold is subdivided into a number the housing stock. This sampling view is particularly rel- of relatively homogeneous strata or cells, according to a evant for a stock based residential property price index. (limited) number of price determining characteristics. Handbook on Residential Property Prices Indices (RPPIs) 165 Glossary Average prices (unit values) or median prices can then User cost be used to compute price indices for each stratum. In the The cost incurred over a period of time by the owner of second stage, these stratum indices are aggregated up us- a fixed asset or consumer durable as a consequence of ing sales weights or stock weights. This method has fre- using it to provide a flow of capital or consumption ser- quently been used to adjust for compositional change of vices. User cost consists mainly of the depreciation of the the samples, or changes in the quality mix of properties asset or durable (measured at current prices and not at sold, and is also known as mix adjustment. historic cost) plus the capital, or interest, cost. Stratification can also be used in conjunction with other Uses approach methods to control for quality mix changes, for example An approach to CPIs in which the consumption in with hedonic regression, repeat sales or SPAR methods. some period is identified with the consumption goods Superlative index and services actually used up by a household to satisfy their needs and wants (as distinct from the consump- Superlative indices are generally symmetric and have tion goods and services acquired). In this approach, the good properties from an index number theoretic point consumption of consumer durables in a given period is of view. Examples are the Fisher index and the Törnqvist measured by the values of the flows of services provided index. by the stocks of durables owned by households. These Symmetric index values may be estimated by the user costs. An index that treats both periods symmetrically by at- Value taching equal importance to the price and expenditure Price times quantity. The value of the expenditures on a data in both periods. The price and expenditure data for set of homogeneous products can be factored uniquely both periods enter into the index formula in a symmetric into its price, or unit value, and quantity components. way. Similarly, the change over time in the value of a set of ho- mogeneous products can be decomposed uniquely into System of National Accounts (SNA) the change in the unit value and the change in the total A coherent, consistent and integrated set of macroeco- quantities. There are, however, many ways of factoring nomic accounts, balance sheets and tables based on in- the change over time in the value of a set of heterogene- ternationally agreed concepts, definitions, classifications ous products into its price and quantity components. and accounting rules. Household income and consump- In a housing context, value may also refer to a single tion expenditure accounts form part of the SNA. property. The “price” of a property is actually a value as it Time dummy variable (hedonic) approach is made up of the price of the structures and the price of the land that the structure is built on. One of the main hedonic regression approaches to con- structing a (residential property) price index. In the Weight reference period standard log-linear time dummy variable model, the The period of which the expenditure shares serve as the characteristics coefficients are constrained to be fixed weights or of which the quantities make up the set of over time, and the price index numbers can be directly properties for a Lowe index. There may be no weight ref- computed from the time dummy coefficients (through erence period when the expenditure shares for the two exponentiation). periods are averaged, as in the Törnqvist index, or when Unit value or average value the quantities are averaged, as in the Walsh index. See also base period. The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of Weights the quantities. It is therefore a quantity-weighted average A set of numbers summing to unity that are used to of the different prices at which the product is purchased/ calculate averages. In an RPPI context, the weights are sold. 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(2005), “The Importance of Property Markets for Monetary Policy and Financial Stability”, pp. 9-29 in Real Estate Indicators and Financial Stability, Volume 21, Bank for International Settlements (ed.). 176 Handbook on Residential Property Prices Indices (RPPIs) Index Index accuracy 9.35 data sources (in different countries) 10.12-13 –– trade-off between frequency and accuracy 9.38 decomposition into land and structures components 8.1-57 (net) acquisitions approach (g) 3.15, 9.28 deflating (g) administrative data 9.1 depreciation (g) aggregate (g) –– depreciation rate 3.48, 8.5 aggregation (g) –– net depreciation 4.9, 8.5-8.9 –– first-stage aggregation 4.13-15 –– one hoss shay (or light bulb) depreciation 3.51 –– examples of aggregation 11.17-11.25 –– straight line (or geometric) depreciation 3.51, 5.49-52 –– sales versus stocks of housing 8.13-17 developing countries 9.48-54 –– second-stage aggregation 4.16-18 discounting 3.43 anticipated inflation rates (for structures and land) 3.55, 3.59 domain (g) see scope asking price (g), 9.10-13 drift (g) assessed value or appraisal (g) 7.2, 7.17-20 durable consumption good (g) 3.40 assessment-based methods 3.23, 7.1-6 economic approach (g) axiomatic (test) approach (g) editing (g) see data cleaning base period (g) elementary aggregate (g) balance sheets 3.8 ex ante user cost 3.47 bias (g) existing dwellings (g) –– omitted variables bias 5.6 expert opinion information 9.22 –– sample selection bias 4.3, 6.15-18 family of residential property price indices 3.29 –– unit value bias 4.15 financial opportunity cost approach 3.45 builder’s model 8.3-4 Fisher (ideal) price index (g) 4.16-18, 11.19 buying and selling a property fixed weight indices (g) –– process of buying and selling 9.3-9.6, 10.59 fixed base indices 4.18 –– time line (Japan) 10.56-57 frequency of residential property price indices 3.28-30, buy-to-let market 6.16 9.38-39 capitalization ratio 3.70-71 geometric Laspeyres index (g) case studies goods (g) –– Canada 10.27-40 gross capital formation 3.13-14 –– Colombia 10.72-77 hedonic regression (g) 3.22, 12.22-28 –– Germany 10.41-49 –– examples of hedonic regression methods 11.26-44 –– India 10.65-71 –– use of monotonicity restrictions 8.31-35 –– Japan 10.50-58 –– use of exogenous information on structures 8.36-40, –– South Africa 10.78-93 8.53-56 –– United Kingdom 10.59-64 hedonic imputation approach (g) 5.25-34, 5.65-69, 11.40-44 chain index(g) 4.19-20 –– arithmetic imputation indices 5.26-29 characteristics (g) 3.18, 4-29, 5.1 –– double imputation 5.27-29 –– adding structures characteristics 8.10-12 double imputation Laspeyres index 5.27, 5.66, ––  –– land (or plot) size 4.34 11.43 –– structure size 4.34 –– double imputation Paasche index 5.28, 5.67 characteristics prices hedonic approach (g), 5.20-24 –– double imputation Fisher index 5.29, 5.68 central tendency measures 4.1, 11.3-10 –– geometric imputation indices 5.30-34 component (g) –– hedonic modeling 5.2-5 consistency in aggregation (g) parametric linear or logarithmic-linear) model 5.2, 11.28-31 consistency of monthly with quarterly estimates 3.31-33 –– single imputation 5.27 construction cost price index 8.37 –– hedonic quality adjustment 5.32-33 consumer price index (CPI) (g) –– in different countries 10.18 comparability (across countries) 9.43-44, 10.13 –– quality adjustment for structures 5.49-52 cost of production approach 8.2-4 –– households (g) coverage (g), 9.6, 9.8, 9.34-35 –– housing stock (g) current period, or comparison period (g) –– approximation of housing stock value 8.51-52 data cleaning (g) 5.9, 6.11-12, 7.22, 7.33 hybrid models (g) see repeat sales method Handbook on Residential Property Prices Indices (RPPIs) 177 Index identity test (g) rental equivalence approach (g) 3.15, 3.61 imputed price (g) rental cost (approximation) 3.49 index reference period (g) rent to value (price) ratio see capitalization ratio inefficiency (of repeat sales approach) 6.19-20 repeat sales method (g) 3.21, 6.1-32, 11.45-56, 12.29-32 informal housing market (g), 9.48-54, 10.85-94 –– arithmetic repeat sales method 6.9 Jevons price index (g) –– Gaussian random walk 6.4 Laspeyres price index (g) 4.16-18 –– holding period 6.7 land –– hybrid models 6.26-27 –– building land price index (Germany) 10.48-49 –– use of assessment information 6.20 decomposition into land and structures components ––  use of information on maintenance and renovation ––  8.1-57 expenditures 6.23 –– price of land 5.3 –– repeat sales equation 6.4 linear splines 8.25-30 –– revisions 6.21 linking (g) –– weighted least squares technique 11.52-56 Lowe price index (g), 8.51-52 representative property (g) lower-level index (g) see (first-stage) aggregation residential property (g) life-cycle theories 6.16 residential real estate services industry output 3.9-12 matched models approach (g) revisions 5.17, 9.40-42 market value (g) revision policy 3.34-35 mean index (g) reweighting (g) median index (g) 11.17 rolling window approach (g) 4.42-45, 8.43-48 meta-data 10.8, 10.22-26 sample (g) mix adjustment (g) see stratification sample probability 4.34-35 money outlays or payments approach (g), 9.30-31 sample selection bias (g) see bias monotonicity restrictions 8.31-35 sampling frame (g) mortgage companies 9.14-18 scope (g), 12.7-9 moving average 4.45 seasonal goods (g) Mudgett-Stone framework 4.42-45 seasonal adjustment 3.36-37, 12.38-40 multicollinearity 5.8, 8.3, 8.24 seasonality (treatment in a esidential property price index) net acquisitions approach (g), 9.28 4.42-46 offer price (g), 9.14-15 selling (or transaction) price (g) opportunity cost approach 3.69-71 outlier (g) see data cleaning spatial dependence 5.7 owner-occupied housing (g) specification (g) Paasche price index (g) 4.16-18 SPAR method (g) 7.4-35, 12.33-37 parameter stability 11.37 –– arithmetic SPAR index 7.10-12 payments approach (g) 3.15 –– descriptive regression model 7.25 pooling (cross section) data 5.11-12 –– estimator of stock-beased index 7.13 price data at different stages 9.3-5 –– generalized regression framework 7.28 price reference period (g) –– model assumptions 7.26-27 price relative (g) –– Paasche-type SPAR index 7.8 products (g) –– quality change bias 7.15-16 pure price change (g) –– sale price appraisal ratio (or relative) 7.7 purpose-designed statistics 9.7-8 splines see linear splines –– fitness-for-purpose of data sources 9.23-26 standardized property 5.20 –– quality change (g) starting problem (of index series) 7.35 –– quality adjusted structures 8.10-11 stock-based index 4.21-24, 5.23-24, 8.15-17 –– quality adjusted price index for structures 8.23 –– using hedonic imputation 8.50-52 real estate agents 9.12-13 –– stratification method (g) 3.20, 4.4-4.12, 12.16-21 regression techniques –– in different countries 10.17, 11.11-16 –– ordinary least squares regression 5.5 –– market segmentation 4.11-12, 5.37 –– nonlinar regression 8.6 –– stratified hedonic indices 5.35-40 –– weighted least squares regression 5.15 –– structures ––  weighted least squares repeat sales regression 6.13, –– price of structures 5.3 11.52-56 –– superlative index (g) 11.19 reproducibility 6.12 symmetric index (g) 178 Handbook on Residential Property Prices Indices (RPPIs) Index system of national accounts (SNA) (g) –– durable goods in general 3.39-52 framework for residential property price indices 3.6- ––  –– for owner occupied housing 3.53-68 14, 12.4 –– user cost approach (g) 3.15, 3.40-52 systematic error see bias –– simplified user cost approach 3.65 time dummy variable (hedonic) approach (g) 5.5, 5.11-18 –– user requirements 9.25 –– adjacent-period technique 11.38-39 –– uses of residential property price indices –– time dummy index 5.11 –– component of wealth 2.14-15 –– linear time dummy model 5.57-60 –– deflator in national accounts 2.21-23 linear time dummy model with quality adjusted ––  –– financial soundness indicators 2.16-20 structures 5.61-63 –– internation and inter-area comparisons 2.28-30 –– log-linear time dummy model 5.45-48, 11.32-39 –– macro-economic indicator 2.8-11 –– log-log time dummy model 5.53-55 –– monetary policy and inflation targeting 2.12-13 timeliness 9.8 –– owner occupied housing in CPI 2.27 Törnqvist-Theil index 11.19 uses approach (g) traditional dwellings (in developing countries), 9.48-54 valuation price (final) transaction price –– from mortgage companies 9.16-17 –– from mortgage companies 9.18 –– from tax offices 9.21 –– from property registers and tax offices 9.19-20 value (g) transaction costs 3.14 weights (g) transaction noise 6.18 –– data sources for weights 9.45-47 turning point 4.2 –– weight reference period (g) unit value or average value (g) 3.32, 4.15 –– non-formal (informal and traditional) housing 10.89-90 unit value bias see bias –– sales weights 4.6 user costs –– stock weights 4.6 Handbook on Residential Property Prices Indices (RPPIs) 179 European Commission Handbook on Residential Property Prices Indices (RPPIs) Luxembourg: Publications Office of the European Union 2013 — 179 pp. — 21 x 29.7 cm Theme: Economy and finance Collection: Methodologies & Working papers ISBN 978-92-79-25984-5 ISSN 1977-0375 doi:10.2785/34007 Cat. No KS-RA-12-022-EN-C HOW TO OBTAIN EU PUBLICATIONS Free publications: • via EU Bookshop (http://bookshop.europa.eu); • at the European Union’s representations or delegations. You can obtain their contact details on the Internet (http://ec.europa.eu) or by sending a fax to +352 2929-42758. Priced publications: • via EU Bookshop (http://bookshop.europa.eu). Priced subscriptions (e.g. annual series of the Official Journal of the European Union and reports of cases before the Court of Justice of the European Union): • via one of the sales agents of the Publications Office of the European Union (http://publications.europa.eu/others/agents/index_en.htm). KS-RA-12-022-EN-C Handbook on Residential Property Prices Indices (RPPIs) For most citizens, buying a residential property (dwelling) is the most important transaction during their lifetime. Residential properties represent the most significant component of households’ expenses and, at the same time, their most valuable assets. The Residential Property Prices Indices (RPPIs) are index numbers measuring the rate at which the prices of residential properties are changing over time. RPPIs are key statistics not only for citizens and households across the world, but also for economic and monetary policy makers. Among their professional uses, they serve, for example, to monitor macroeconomic imbalances and risk exposure of the financial sector. This Handbook provides, for the first time, comprehensive guidelines for the compilation of RPPIs and explains in depth the methods and best practices used to calculate an RPPI. It also examines the underlying economic and statistical concepts and defines the principles guiding the methodological and practical choices for the compilation of the indices. The Handbook primarily addresses official statisticians in charge of producing residential property price indices; at the same time, it addresses the overall requirement on RPPIs by providing a harmonised methodological and practical framework to all parties interested in the compilation of such indices. The RPPIs Handbook has been written by leading academics in index number theory and by recognised experts in RPPIs compilation. Its development has been co-ordinated by Eurostat, the statistical office of the European Union, with the collaboration of the International Labour Organization (ILO), International Monetary Fund (IMF), Organisation for Economic Co-operation and Development (OECD), United Nations Economic Commission for Europe (UNECE) and the World Bank.