WORLD BANK INSTITUTE
Promoting knowledge and learning for a better world
- - 26062
-' ~~~~~February 2003
___ V~
--, /
TI~~\jOLL
-ANT ON1OTA HE,,<
\ ERGIO PERM
----a. ~ ~ ~ ~ ~ ~
\~~~~~~~~~~ E I RDE Sf'
X, M' '
WBI DEVELOPMENT STUDIES
A Primer on Efficiency
Measurement for Utilities
and Transport Regulators
Tim Coelli
Antonio Estache
Sergio Perelman
Lourdes Trujillo
This primer is supplemented by a database and computer software
that allows the reader to practice the example described in chapter 4.
Visit http://www.worldbank.org/wbl/regulation/pubs/efficiencybook.html.
The World Bank
Washington, D.C.
Copyright ©D 2003
The International Bank for Reconstruction
and Development / THE WORLD BANK
1818 H Street, NW
Washington, D.C. 20433, U.S.A
All nghts reserved
Manufactured in the United States of America
First printing January 2003
1 2 3 4 5 05 04 03
The World Bank Institute was established by the World 13an!; in 1955 to train oificials coineern.cd
with development planning, policymaking. nsestnient analysis, and project implemcntation In
member developing countries At present the substance of WBI's ssork cnmphaslzes macroeconomic
and sectoral policy analysis. Through a variety of courses, scmin.rs., sorkshops. and other learninp
activities, most of which are given overseas in coopcration witl localinstitutions. NWBI sceks tosharpin
analytical skills used in policy analysis and to broaden undcrstandtiri (if the CxpCriciCee Of 1ndis Id&L!
countries with economic and social developmnmt. Although WRi's publitatioIs aue designed to
support its training activities, many are of interest to a much broader audience
This report has been prepared by the staff of thc World Bantk The judgments cxpresscd di niLt
necessarily rcflect the views of the Board of Executivc Dircc.or, or ortthe goxernments they represent
The material in this publication is copyrighted The World Bi,nl CnLouraocs disseinnation ot ts
work and will normally grant permission promptly.
Permission to photocopy items for intemal or personal use I or th minternal or personal usc ot spectCtL
clients, or for educational classroom use is granted by the Wotd Ban!,, provided that the appropriatc
fee is paid directly to the Copyright Clearance ('enter, Inc ,2'2 Roscs otid Dn%e, Danters., MA 01 923,
U S A., telephone 978-75t)-8400, fax 978-750 "70) t'leasc contact thei Cop) rihlit Clearance CentLr
beforc photocopying items
For permission to reprint individual articles or LhdpterS. please fax 3our request with comprL'2
information to the Republication Department, Copyright Clcarancc ('enitr, tax 978-750-4470
All other queries on rights and licenses shouli' h. addres.Ld to the World Bank at the address Ubos
or faxed to 202-522-2422
The backlist of publications by the World Ban! is shosso in mthe amiual h,iden of PithlIi otio.Js whizh
is available from the Office of the Pubhsher
ISBN 0-8213-5379-9
L brary of Congress -ta'oging-in-l ! crM'h-E 6 -LS b 2
Contents
Foreword v
About the Authors vii
Acknowledgments ix
Abbreviations and Acronyms xi
1. Introduction 1
2. Why Should Regulators Be Interested in Efficiency? 5
Regulation Methods 7
Why Use Sophisticated Performance Measurement Methods? 9
Some Performance Measurement Terminology 10
Summing Up 21
3. Some TFP Measurement and Decomposition Methods 25
Price-Based Index Numbers 27
Production Frontiers, Single Output Case 30
Cost Frontiers, Single Output Case 36
Multiple Output Case 40
Malmquist DEA TFP Indexes 47
Cross-Sectional TFP Comparisons 50
What if Policy or Other Similar Variables Are Relevant? 51
Summing Up 52
4. An Empirical Example 55
Estimation of an SFA Production Frontier 57
TFP Calculation and Decomposition 63
Comparison of Methods 66
A Price Cap Regulation Example 70
III
IV Conte77ts
5. Performance Measurement Issues in RegulaiLen I'
Setting a Single X-Factor for All Firms
Setting Firm-Specific X-Factors 7,
Additional Cornments 8-
6. Dealing with Data Concerns in Pf acilce 0
Inputs
Outputs 89
Quality
Environment
Prices 9>
Panel Data and International Comparisonis c-
Additional Issues '
7. Choice of Methodology 99
8. Concluding Comments -03
Appendix: Capital Measurement 1C0
References 123
Index 13,1
Foreword
The infrastructure privatization wave of the 1990s changed, but did not
eliminate, the government's role in the sector. The scope for introducing
competition continues to be limited in many parts of infrastructure busi-
nesses, resulting in private monopolies operating at least some segments of
most utilities and transport services. Among the main responsibilhties of
infrastructure regulators are the design and implementation of regulatory
processes that will ensure the fair distribution of the gains from the trans-
fer of services to private monopolies. This mandate means that regulators
must be able to assess the extent to which the regulated operators are man-
aging to improve efficiency after taking over from public operators. For
many of the new regulators implementing this mandate has been tougher
than expected. Even more difficult is their role in expanding services to the
unserved.
This book, the fourth in a recent series of World Bank Institute books on
infrastructure regulation, is intended to help regulators learn about the tools
needed to measure efficiency It is based on lecture notes from courses the
World Bank Institute offers in English, French, and Spanish throughout the
developing world and has benefited from feedback received during those
courses It provides an overview of the various dimensions of efficiency
that regulators should be concerned with. It also summarizes the main quan-
tification techniques available to facilitate decisions in the most common
regulatory processes. The issues covered should be of particular interest to
those policymakers and regulators interested in measuring relative effi-
ciency and in implementing any incentive-based regulatory mechamsm that
v
vI Foreword
requires the measurement of efficiency, such as price caps, revenue caps, c --
yardstick competition. The book focuses or metloclology selection, daie
collection, and related issues.
This is not an easy topic, but 'the book does provide ieaders wvith all te i-
conceptual tools they need to make real-li'e decisions. TIt is also supportec'
by a web site from which readers can download sofrware they can use to
implement the techniques described. The web sie also includes a databas c
that will allow readers to try to reproduce the empirical example provide
in chapter 4.
I hope that this Pri7ner on7 Efficiency/ Measz!remml will be as useful .o in
frastructure regulators and policymaikers as the p-;evious books have bec -
and that itwill help enhance the qualiLy and transperency of dialogue among
the actors involved in infrastructure provision and reform.
Frannie A. Leau.ic;
Vice Presiden.
VWorld Bank lnsUitu.e
About the Authors
Tim Coelli is a professor of economics at the University of Queensland,
Australia. He specializes in theoretical and applied econometrics, produc-
tion economics, and performance measurement. He has worked as a con-
sultant for the Independent Pricing and Regulatory Tribunal of New South
Wales, the Water Services Association of Australia, and the Queensland
Water Reform Unit. Email t.coellh@economics.uq.edu.au.
Antonio Estache is an economic advisor at the World Bank and a research
fellow at the European Center for Advanced Research in Economics and
Statistics, Universit6 Libre de Bruxelles. He specializes in industrial orga-
nization and regulatory economics. He has advised many governments in
Africa, Asia, and Latm America on infrastructure sector reform and regula-
tion. Email: aestache@worldbank.org
Sergio Perelman is a professor of economics at the University of Liege,
where he is also director of the Center of Research in Public and Population
Economics. He specializes in applied econometrics and performance mea-
surement and has been working on policy-oriented research projects across
Europe Email: sergio.perelman@ulg.ac.be.
Lourdes Trujillo is the director of the Department of Applied Economic
Analysis of the University of Las Palmas of Grand Canary. She is a profes-
sor of microeconomics and specializes in the empirical analysis of network
industries. She has advised many governments in Latin America on trans-
port sector reform and regulation. Email: lourdes@empresariales.ulpgc.es.
Vil
Acknowledgments
In writing this book we have benefited from discussions with Ian Alexander,
Antonio Alvarez, Phil Burns, Javier Campos, Jose Carbajo, Luis Correia,
Claude Crampes, Alex Galetovic, Andres Gomez-Lobo, Phil Gray, Shawna
Grosskopf, Alan Horncastle, Marc Ivaldi, Racine Kane, Eugene Kouassi,
Gustavo Nombela, Paul Noumba, Martin Rodriguez-Pardina, Martin Rossi,
Christian Ruzzier, and many regulators in Latin America and Africa who
have participated in World Bank-sponsored trainng. Furthermore, we
would like to express our thanks to Knox Lovell, who provided extensive
comments on an earlier draft of this book. Finally, any mistakes and all
interpretations of facts are ours and do not engage in any way the institu-
tions we are affiliated with.
lx
Abbreviations and Acronyms
AE Allocative efficiency
AEC Allocative efficiency change
CAPM Capital asset pricing model
CE Cost efficiency
CEC Cost efficiency change
CPI Consumer price index
CRB Coelli, Rao, and Battese (1998)
CRS Constant returns to scale
DEA Data envelopment analysis
DEAP Data envelopment analysis program
kl Kiloliter
km Kilometer
kWh Kilowatt hour
LLF Log-likelihood function
OLS Ordinary least squares
PIN Price-based index number
xi
xni Abbreviations and Acronymns
SE Scale efficiency
SEC Scale efficiency change
SFA Stochastic frontier analysis
TC Technical change
TE Technical efficiency
TEC Technical efficiency change
TFP Total factor productivity
TFPC Total factor producilvity change
VRS Variable returns to scale
WACC Weighted average cost of capital
1
Introduction
Until relatively recently infrastructure services-electricity, gas, water, sew-
erage, telecommunications, airports, ports, and rail transport-were pro-
vided by vertically and horizontally integrated public firms that also tended
to be self-regulated (the United States, where many infrastructure firms
have been privately owned and regulated for some time, is an exception).
The infrastructure privatization waves of the 1990s that spread across de-
veloping countries and some countries of the Organisation for Economic
Co-operation and Development, most notably Australia, New Zealand, and
the United Kingdom and a few other European countries, have changed
the institutional structure of this sector as well as the policy agenda. The
desire to create a competitive environment is now prevailing in infrastruc-
ture industries, and where competition is limited the search for efficiency
gains is at the core of the regulation debate.
Countries have generally assigned the responsibility for regulation to
new, relatively autonomous agencies, which are now learning to cope with
their mandates. Evidence from the last decade suggests that in both indus-
trial and developing countries, these mandates are provirng to be tougher
than expected for many of the new regulators. Information asymmetries
between monitoring agencies and monitored firms are the norm rather than
the exception, in particular, on the cost side of the business. This reduces
monitoring agencies' ability to carry out their role of watchdog of opera-
tors. It also reduces their ability to ensure that the efficiency gains from
potential or effective competition are shared fairly between operators and
users. This mability to organize a fair sharing of the efficiency gains, which
does not hurt firms' incentives to perform well, is a major source of criti-
cism of the performance of the new regulators and a source of conflict
2 A Prniter on Efficiency Measuremnentfor Utilities and Traisport Regulators
between operators and users.' It also explains the increased interest among
monitoring agencies, producers, and users alike in the quantitative mea-
surement of these gains.2
This book is written as a manual to support a series of courses put LO-
gether by the World Bank Institute, but also to help regulators go through
the relevant academic literature, which has become quite technical and of-
ten assumes a level of knowledge that mos, policymakers and regulators
do not have. For interested regulators the book also provides practical ad-
vice on how to conduct an empirical analysis of efficiency in the infrastruc-
ture industries. The necessary software and examples are available on the
World Bank Institute web site (http://www.worldban-k.org/wbi/regulation/
pubs/efficiencybook.html). The methods discussed here are equally ap-
plicable to situations where the firms are publicly owned, privately owned,
or some combination of the two. Th-e issues covered should be of particu-
lar interest to those regulatory authorities that are required to obtain mea-
sures of relative efficiency and of historical productivity growth and to
assist with the setting of price caps or of any incentive-based regulatory
mechanism requiring the measurement of efficiency, such as yardstick
competition. The focus is on methodology selection, data collection, and
related issues.
The book is designed to be self-contained for regulators that need to
focus on measuring the efficiency of the firms they are monitoring. While
some sections of the book may appear to be somewhat technical and over-
whelming to some readers, it is designed to allow interested users to actu-
ally undertake studies relevant to their sector. All the relevant steps are
discussed, explained, and eventually illustrated. Earlier drafts of the boo',
have been tested by various analysts new to the topic and have benefitec
from their suggestions to ensure that it is as complete as possible in regard
to the practice of efficiency measurement for regulated industries.
1 The price cap revisions in the electricity and gas sectors in Argentina are
good illustrations of the type of conflici tha; can arise (see, for example, Estache
and Rodriguez-Pardina 2000).
2. The Australian, Dutch, and U.K regulators have been among the most rigor
ous participants m this debate and their various web sites are useful sources of
information See, for example, http://www.accc.gov.au, http://www.ipart.
nsw.gov.au, http //www.reggen.vic.gov.au, http //www.dte nl, http //
www.open gov.uk/ofwat, and http.//www.open.gov.uk/ofgen. For a more tradi-
tional approach to benchmarking in the water sector see http://www
worldbank.org/html/fpd/water/topics/uom-bench.himl.
Introduction 3
The book avoids detailed discussions of economic theory and econo-
metric methodology, as these are available elsewhere. Readers may refer to
Laffont and Tirole (1993) for a comprehensive treatment of the economic
theory of the regulated firm, Bogetoft (1994,1995,1997) and Agrell, Bogetoft,
and Tind (2002) for an extension of the incentive regulation theory in a
benchmark and yardstick competition scheme, and to Armstrong, Cowan,
and Vickers (1994) or Newbery (2000) for an mterpretation of the impor-
tance of these principles in practice. A particularly relevant reading is
Bernstein and Sappington (1999), which provides a systematic overview of
the criteria for picking an efficiency measure in the context of price regula-
tion. Finally, while this book provides many insights into the various effi-
ciency measurement methodologies, it does not claim to be a rigorous
introduction to these methodologies. For the interested reader Coelli, Rao,
and Battese (1998) (hereafter referred to as CRB) provide a much more rig-
orous overview of methods and conceptual issues
2
Why Should Regulators
Be Interested in Efficiency?
Efficiency is at the core of many of the standard responsibilities assigned to
regulators. The most common instance in which a government agency
should be interested in measuring efficiency is when implementing some
type of incentive-based regulation in a specific infrastructure sector. These
types of regulatory regimes, such as price cap regulation, aim at promoting
efficiency among operators. Regulators may also be interested in imple-
menting comparative efficiency evaluations to promote yardstick competi-
tion. Indeed, in most cases regulators have multiple objectives, many of
which have something to do with various aspects of efficiency.
To demonstrate that the concern for efficiency is quite real and pervasive
among regulators, consider the case of the Argentinean land transport regu-
lator, for mstance, which is representative of many of the regulatory agencies
created to monitor recent deregulation or privatization in developing econo-
nues. The decree that creates this regulatory agency and specifies its obliga-
tions suggests quite clearly that the promotion of efficiency in various forms
is one of its main responsibilities.1 This includes the obligation to ensure that
1. Govemment of Argentina Decree number 660 of June 24, 1996, m particular
annex 1, where the regulator's responsibilities are defined as protecting the rights
of users, promoting competition in the markets for transport services, ensuring
better safety, operation, reliability, and equity, ensuring generalized use of the road
transport and rail transport systems for passengers and freight, and ensurmg ap-
propriate progress in all modes (see Campos-Mendez, Estache, and Trujillo 2001)
5
6 A Pruner on Efficiency Measutrementfor L*tilties and Transport Regulators
• The interests of current users are taken into account in the operator's
production decisions. In practice this means that the regulator should
check that the operators minimize the cost of delivering their ser-
vices while meeting all their contractual obligations. In more techni-
cal terms it means that the regulator must monitor the operator's
cost efficiency.
o The sector is competitive, interrmodal competition works, and all useis
are treated fairly. In a less positive way the regulator must check that
users are not charged too much, that required subsidy levels are what
the operators claim, and that hidden cross-subsidies are not relied
on for anticompetitive or predatory behavior. In practice this means
that the regulator must check that the price charged for every non-
competitive activity reflects its costs, assuming that every activity
can be ring-fenced.2 In more technical terms it means that the regula-
tor must monitor output mix allocative efficiency.
o The sector grows appropriately, that is, that operators make the right
investment, technology, and management choices to ensure that fu-
ture demand will be met in a smooth way and that service rationing
does not occur, all of which is also known as dynamic efficiency.
Implicitly, the decree states that for any period of observation, the
regulator's performance assessments must offer a balanced view of thc
various sources of efficiency, which is a reasonable request on any regula-
tory agency, but assumes that the regulator is able to measure them. These
obligations are representative of the challenges new regulators have to face
in a difficult political context in most reforming countries. They need to
monitor progress in the performance of the new opera,ors of recently priva-
tized public services to check if the improvements expected from a switch
from public operators are real This means that the performance improve-
ments achieved through the reforms must, at least to some extent, be quan-
tified if the gains are to be shared with users (or the losses shared with
taxpayers) in a fair and transparent way.
The remainder of this chapter provides the various elements that justify
why practitioners need this book.
2. By ring-fencmg we refer to the organization of a firm's accounts so that the
costs associated with various activities or outputs are clearly specified.
Why Sliould Regulators Be Interested In Efficrency? 7
Regulation Methods
Most network industries, for example, utilities and transport, have natural
monopoly characteristics. Economic theory indicates that if left unchecked,
monopolies have the ability to exert their market power and set prices above
costs so as to yield above normal profits. For much of the 20th century, the
answer to this potential problem generally involved one of two options: (a)
government ownership, or (b) private ownership combined with some form
of cost-plus rate of return regulation, where the regulated firm is allowed
to set prices so as to cover noncapital costs plus a fair rate of return on
capital. The United States has favored the latter approach, while the United
Kingdom and many other countries have favored the former approach (see
Green and Rodriguez-Pardina 1999 for a longer discussion).
However, these two options are not without problems. In particular,
both options suffer from a lack of efficiency incentives, which can result in
costs that are above those that would exist in a competitive industry. This
has led to the recent development of new forms of regulation that seek to
be mcentive compatible. U.K. telecommunications regulators championed
these incentive regulation methods in the 1980s and many regulators in
numerous mdustries around the world have since adopted them in vari-
ous forms.
Incentive regulation can take various forms, but the most common form
involves the application of some form of price cap regulation. Price cap
regulation specifies the maximum rate at which regulated prices may
change, after adjusting for inflation, over a specific time period, usually
four or five years. In practice, these prices are usually set to increase at a
rate equal to the rate of increase in the consumer price index (CPI) minus a
so-called productivity offset, designated as X, and thus it is often called
CPI-X regulation. The formula implies that consumers will face a nominal
price decrease if inflation is lower than the X assessed for the period. The
value of X is generally based on the regulator's assessment of the potential
for productivity growth in the regulated firm. This is a crucial variable. If it
is set too low, the firm is earming excessive profits because the tariff ends up
being significantly higher than actual costs. If it is set too high, the firm
may find itself in financial trouble because the tariff may no longer cover
its real costs.
Estimating X is a complex matter. It is supposed to reflect the extent to
which the regulated industry can improve its productivity faster than the
rest of the economy in which it is operating, accounting for differences m
8 A Primer on Efficienicty Measurement for Utiltties and Transport Regulators
the evolution of the input prices in the regulated industry compared with
the input prices in the rest of the economy. Reasonable estimates or aggre-
gate productivity gains are available in most coun.ries, and this is not a ma
jor matter of concern here; however, in most countries regulators lack
information at the sectoral level. Furthermore, in some cases the regulato-
may choose to set different X-factors for different firms in an industry if it has
reason to believe that some firms are more inefficient relative to other firrns.'
In practice, in preparation for tariff revision regulators will generally
commission studies of previous total factor productivity (TFP) growth in
the industry, and perhaps a study of the present levels of firm-level effi-
ciency to help them set the X-factor for each firm in the industry. The X-
factors are usually set so that firms are able to earn a fair rate of return on
capital if they can achieve an efficient level of costs, as defined by the regu -
lator. If the firm can contain cost increases below the allowed CPI-X price
increase, they can pocket the difference, and hence earn above normal prof-
its, that is, a higher rate of return on capital. This is the main incentive
aspect of the method.
Practitioners of CPI-X regulation also stress that the performance mea-
sures used to set the X-factor for a firm must not bo derived solely from the
firm's past performance, because t'his will negate the incentives involved.
That is, if a regulator assigns an X-factor of 3 percent per year to firm A
because it achieved a TFP increase of 3 percent per year in recent years,
firm A will have no incentive to atermpt to increase its performance in t1he
future, because it knows that it will lead to a larger X-factor in the nex.
regulatory period. Thus the regulator must also use data from external
benchmarks, such as other firms in the industry or international compari-
sons, to set the X-factors.
Thus to summarize, the selection of the X-factor is usually based on two
pieces of information.
o What has the rate of productivity growth been in this industry in
recent years?
o To what extent is this firm operating below best practice in th b
industry?
Without this information, it is difficult for the regulator to set the valuc
of X correctly. If the X-factor is set too high, the firm might lose money, anc
perhaps even fold, leaving the government to pick up the pieces. If X is set
3 The design of a price cap is much more complex than our summary here.
Interested readers should refer to Bernstein and Sappington (1999).
Why Shzould Regulatois Be Initerested in Efficiency? 9
too low, the firm might earn excessive profits, which could be politically
damaging.
Why Use Sophisticated Performance Measurement Methods?
The foregoing discussion revealed that correct measurement of potential
productivity growth is crucial. Does this mean we need an entire book on
the topic? We believe that such a book is indeed needed, because of the
complexity of the topic and the importance of many details of its measure-
ment for the effectiveness of the regulator in ensuring fair distribution of
efficiency gains, whether arising from improvements in technology or sim-
ply from improvements in the management of a monopoly.
By way of illustration, consider the case of electricity distribution. What
are the potential dangers in defining productivity using a traditional ratio
measure, such as the volume of electricity supplied in kilowatt hours (kWh)
per dollar of costs? In this case we could measure average annual produc-
tivity growth using the change in kWh/US$ over the past five years in the
industry, and we could measure the relative efficiency of the firm by com-
paring its kWh/US$ with those of other firms in the industry.
Assume that we find that the industry's kWh/US$ has improved by 2
percent per year over the past five years and that the kWh/US$ of the firm
is 20 percent below that of the best firm in the industry. Given this informa-
tion, the regulator could set the X-factor at 6 percent per year for this firm,
that is, the 2 percent expected of all firms in the industry, plus 20/5 = 4
percent in productivity catch-up to ensure that the firm has caught up with
the best firm by the end of the five-year regulatory period.
This process seems quite easy, but it contains many traps for the un-
wary. For example, consider the following five issues:
* Do the firms differ in terms of average customer sizes and/or cus-
tomer density? If so, the chosen productivity measure will not ac-
count for possible differences m output composition across firms.
* Are some firms larger than others and therefore able to achieve scale
economies?
* Do input prices differ across years or across firms? It so, how has
this been accounted for?
* Have the last five years been "typical"? For example, has the regula-
tory system changed recently? If so, could part of the past produc-
tivity growth be due to catch-up, which may not be achievable over
the next five years?
10 A Primer on Efficiency Measurementfor Utilities and Tranisport Regullators
o To what extent are all firms able to achieve the industry average
level of productivity growth? If some distributors are located in ar-
eas with low population growth, are they likely to be less able to
reap the productivity-enhancing benefits embedded in new capital
investments?
These five issues are by no means an exhaustive list of possible prob-
lems, but they do illustrate some of the dangers tha, may result from the
use of suboptimal productivity measures. The good news is that we can
address many of these problems if we can get access to good quality data
and if we use more sophisticated productivity measurement methods.
This is where this book comes in. Our aim is to outline the valuable
information that you can obtam if you have access to good quality data.
Thus in the early chapters we assume that we do have access to good qual
ity data, and then illustrate the wealth of information that you can derive
from the application of sophisticated productivity measurement methods.
We then acknowledge the realities regulators in many developing and in-
dustrial countries face, and discuss how to proceed when data are limited
in quality and quantity. We debate what you can do in this situation and
use the good data case as a bench-mark against which we can assess the
problems that regulators may face when using second-best productivity
information in setting price caps.
Some Performance Measuremeen,i Te=nlMoIogy
In this section we introduce some of the terminology used in performanc e
measurement, and also briefly describe the main performance measure-
ment methods. Box 2.1 summarizes all the information presented. For those
who wish to learn more, the CRB book provides a comprehensive intro-
duction to the terminology and the methodologies.
Productivity is the ratio of outpuL over input. In the simple case when
we have only one input and one output, this is an easy calculation. How-
ever, when we have more than one input and /or more than one output we
need to use weights to construct an output index and an input index so as
to allow the construction of a TFP index, which is equal to the ratio of ihe
output index over the input index. We will discuss TFP index methods
shortly, but first let us look at a one-input, one-output example.
Consider a simple example of five small water-carting firms in India,
where the only input is labor and the only output is volume of water in
kiloliters (kl) delivered per day by bucket. The sample data are listed in
Whty Should Regulators Be Interested in Efficiency? 11
Box 2.1. Performance Measurement Terminology
The prod uctionfrontier (or production fimction) is a function, y = f(x), that
describes the maximum output, y, a firm can produce usmg any particular
set of inputs, x. Production functions are usually estimated using sample
data on a number of firms.
Techinical efficiency (TE) is a firm's ability to achieve maximum output given
its set of inputs. TE scores vary between 0 and 1 A value of 1 indicates full
efficiency and operations are on the production frontier. A value of less than
1 reflects operations below the frontier The wedge between 1 and the value
observed measures technical inefficiency. This is an output-oriented TE mea-
sure An input-oriented TE measure reflects the degree to which a firm that
must produce a particular output level, y, could proportionally reduce its
use of inputs and still remain within the feasible production set (that is, on or
below the production frontier)
Techinical chlange (TC) (or technological progress) is an increase in the
maximum output that can be produced given an input vector, x, and is re-
flected in a shift in the production frontier over time. This is often slow for
utilities and transport with the exception of the telecommunications sector,
where progress has been, and continues to be, dramatic.
Scale efficiency (SE) is a measure of the degree to which a firm is optimiz-
ing the size of its operatons. A firm can be too small or too large, resulting in
a productivity penalty associated with not operating at the technically opti-
mal scale of operation.
Input nix allocative efficiency (AE) is a firm's ability to select the correct mux
of input quantities so as to ensure that the mput price ratios equal the ratios of
the corresponding marginal products, that is, the additional output obtained
from an additional unut of input. The AE score varies between 0 and 1, with a
value of I mdicatng full allocative efficiency. Most microeconomics textbook
assume that all firms are technically efficient In that special case full allocative
efficiency equates to full cost efficiency or cost minimmization.
Output mix allocative efficiency is a firm's ability to select the combmation
of outputs quantities in a way that ensures that the ratio of output prices
equals the ratio of marginal costs, that is, the additional cost corresponding
to the production of an additional unit of product A firm that is technically
efficient, scale efficient, and achieves input mix and output mix allocative
efficiency, is maximizmg profits for given input and output prices
Totalfactor productivity is the ratio of output over input, y/x. When there
is more than one input and/or output, this calculation requires weights to be
specified These weights are usually based on price information The TFP of
two firms facing the same operating environment at one point in time can
differ because of TE, AE, or SE differences TFP can vary over time because of
changes in TE, AE, and SE, but also because of TC
(Box continiues oii thiefollozoiig page)
12 A Prinier o01 Efficienicy Measurementefor Utilities and Troansport Regilators
Box 2.1. (continued)
Cost efficiency (CE) is a firm's ability ro produce a parLicular output, y, at
minimum cost, given the input prices it faces. Note that CE = AE x TE, and
hence that CE varies between 0 and 1, with a valuo of 1 indicating full cost
efficiency
Costfrontier (or cost function) is a function, c - g(y, w), which relates the
minimum cost, c, that is required to produce a particular output vector, y,
given an input price vector, w. We can also estimate a vanable cost frontier,
c,= g(y, x, wj), where cv is variable costs, x, is the quantities of those inputs
assumed fixed in the short run, and w, is the prices of variable inputs. The
distance a firm is above the cost frontier reflects the CE of that firm, which
may be due to AE and/or TE
Dtstancefuniction is a function, d = h(x, y), that measures the efficiency
wedge for a firm in a multi-input, multi-output production context. It is thus
a generalization of the concept of tihe production frontier. A distance func-
tion can also take an input orientation or an output orientation.
table 2.1 and plotted in figure 2.1. The productivity ratio is calculated for
each firm and reported in the final column of table 2.1. It shows that firm 3
is the most productive, delivering 1.67 kl of water per person, while firms
C and D are the least productive, delivering 1 kl of water per person.
One way to visualize these productivity ratios on a diagram is to draw
a line between the origin and each ol the data points. These lines are de-
picted in figure 2.2. This line will have a slope equal to the ratio of output
Table 2.1. Datafor Water-Carting Example
(input = labor, output = kl)
Inpitt Ouitpuit Produictivity
Firm (x) (y) (y/x)
A 5 7 1.40
B 3 5 1.67
C 1 1 100
D 2 2 1.00
E 5 6 1.20
Source. Authors (for this and all other tables and figures throughout the bool)
Wily Shlouild Regulators Be Interested in Efficiency? 13
Figure 2.1. Graphic Illustration of Datafor Water-Carting Example
Output
8
7 *A
6 E
5 *B
4
3
2 *D
I - *~~~~~~~~~~ I
1 *C1
0 1 2 3 4 5 6
Input
over input, that is, the slope of the line reflects the productivity of the firm.
A steeper lme indicates higher productivity. Observe that firm B has the
steepest line and firms C and D have the line with the smallest slope.
A production frontier is a function that represents the maximum output
that can be produced using a given amount of input. That is, it represents
best-practice performance in the industry. Production frontiers are usually
estimated using sample data on the inputs and outputs used by a number
of firms. Frontiers can be constructed using data on firms that have many
inputs and/or many outputs The two methods that are most often used to
construct frontiers are data envelopment analysis (DEA) and stochastic fron-
tier analysis (SFA). We will define these methods shortly, but first let us
look at a simple one-input, one-output example.
Consider the sample data depicted in figure 2.1. We can construct a
DEA frontier over this simple data by using a pencil and ruler. This pro-
duction frontier is depicted in figure 2.3. Note that when we have more
inputs and/or more outputs we need to use a computer to construct the
14 A Primer on Efficiency Measuirenientfor Utilities a,id Transport Regullators
Figure 2.2. Productivity Ratiosfor Water-Carting Example
Output
8
7~~~~~~~~~~~
6 F
5B
4
3
2
0 1 2 3 4 5 6
Input
frontier. In figure 2.3 firms A, B, and C are used to construct the frontier,
and the other two firms, D and E, lie below the frontier.4
The distance between the data point and the frontier determines the -1X
of the firm. For example, firm E in figure 2.3 could potentially increase its
output up to the frontier (at point A). Hence we define the TE of firm E as
being equal to the ratio of what it is producing (6 kl) over what it could
potentially produce (7 kl), given i Ls curren, level of inputs (5 laborers). Thus
for firm E, TE = 6/7 = 0.86, that is, it is producing 86 percent of its potenLial
output.5 The TE of the frontier firms in figure 2.3 (firms A, B, and C) is
4. Standard production functions are usually fitted using regression methods.
These regression methods fit a line through the cenier of the data, and hence nea-
sure average practice. Frontier methods, by contrast, fit a surface over the data,
and hence measure best practice
5 This measure of TE is called output-oriented, because it asks by how much
the firm could increase its output given its level of Inputs. Alternatively, one can
Wlhy Should Regulators Be Interested in Efficiency? 15
Figure 2.3. A Production Frontier
Output
8
A
7
6 E
5
4
3
2
0 1 2 3 4 5 6
Input
equal to 1. This is because they define the frontier The TE of firm D is equal
to 2/3 = 0.67, that is, firm D is producing 67 percent of its potential output.
Note that firms A, B, and C are all fully efficient in terms of TE, while
when we looked at the productivity ratios earlier we saw that firms A and
C had lower productivity than firm B. Indeed, firm C had the lowest pro-
ductivity in the sample. How can this be? The reason is that TE is only one
part of productivity. Another component of productivity is SE. SE reflects
the fact that there is usually an optimal firm size, and not all fiLrms operate
at the optimal size. For example, large firms may be more productive than
defmne input-oriented TE, which asks how much the firm could reduce its inputs
given its level of output The two measures generally produce quite similar TE
scores. The input-oriented measure is most often used in network industries, like
water and electricity, because the firm is usually required to supply a particular
level of service to the community. Hence a request for an mcrease in output is not
very sensible.
16 A Prinmer on Efficiency Measutrementfor Utilities iid Trnatsport Regtulators
small firms because they can have labor teams that specialize in particu-
lar tasks.
To measure scale efficiency we must construct an additional frontier on
figure 2.3, namely, a constant returns to scale (CRS) frontier. This is a fron-
tier that allows firms of any size to be benchmarked against each other, WIr
example, small firms can be benchmarked against big firms and vice versa.
The frontier that we have already drawn in figu-re 2.3 is known as a vari -
able returns to scale (VRS) frontier. This VRS frontier was constructed so
that small firms are benchmarked against small firms and big firms againsi
big firms.
A VRS frontier and a CRS frontier are drawn in figure 2.4. In this simple
example, the CRS frontier is simply equal to the line from the origin through
the point defined by firm B. Firm B is chosen because it has the largest
productivity. The distance between each data point and the CRS frontier is
called TECRS' This measure of efficiency will contain both TE and SE. For
example, consider firm D in figure 2.4. It has TECRS = 2/3.33 = 0.6. The gap
Figure 2.4. CRS and VRS Productioni Frontiers
Output
8
/Z A
7 CRS frontier
6 KE
5~~~~~~~~~
VRS frontier
4
I C
0 1 2 3 4 5 6
Input
Why Should Regulators Be Interested in Efficieniczy? 17
between the CRS and VRS frontier provides a measure of the SE of firm D.
It is able to increase output from 3 kl (on the VRS frontier) up to 3.33 kl on
the CRS frontier, thus its SE = 3/3.33 = 0.9. This implies that firm D could
improve its efficiency by approximately 10 percent if it were to increase its
scale of operation to the optimal scale of operation (as defined by firm B).
Thus for firm D we have found that TE = 0.67, SE = 0.9, and TECRS = 0.6.
Note that TECRs = TE x SE. That is, 0.6 = 0.67 x 0.9 This is always true. Table
2.2 reports the efficiency scores of all five firms .
Furthermore, if we take the productivity ratios reported m table 2.1 and
divide each productivity ratio by the largest productivity ratio in the sample
(the firm B ratio of 1.67) we obtain the TEcRs scores. For example, if we take
the productivity ratio of firm D (1.00) and divide it by 1.67, we obtain 0.6,
which is the TEc,~~' [(r,n, + r,e ),(y,- YInIO
I I
0.5 E [(S., + s,,, ).(x,- x,,)l, )3.4
where the T superscript refers to Tdrnqvist, x,,, and Yint are, respectively, the
log of the j-th input and output of the n-ih firm in the t-th time period, ancd
sjnl (rl) is the cost (revenue) share of the j-th input (output) for the n-th firm
in the t-th time period.3 In sum, with information on the physical quantity
of inputs and outputs and with information provided by balance sheets on
cost and revenue shares of each input and output, a regulator can malke a
fair quantitative assessment of the T7P evolution of any operator.
The main problems with these indexes is that they assume that the regu
lator has a lot of information on the actual physical quantities of outpuis
and inputs. Regulators generally have a good dcal of physical data on ou.-
puts, that is, volume of freight, number of passengers, number of kilowa.
hours of electricity, liters of water, or number of successful telephone calls.
2. This Fisher mdex has a number of useful p;operiies. In particular, it implies
an underlying quadratic production technology, which is mnuch more sensible, tha
is, more flexible, from an economic theory point of view than the linear productiorn
technologies that are implicit in the Laspeyres and Paasche indexes.
3. For further discussion of these various price-based index number options
see chapters 4 and 5 in CRB. Also see Diewert (2000), who argues convmcingly thc.
direct and indirect Fisher and Tbrnqvisi indexes provide ideal measures of TF I
when one looks at the test or axiomatic approach to index number evaluation
Furthermore, when comparing two firms at one point in time one needs to make .
transitivity adjustment to T6mqvist or Fisher mdexes. These are detailed in chap-
ter 4 in CRB
Sonie TFP Measurement and Deconiposition Methods 29
They generally have much less physical data on inputs. Indeed, unless they
are required to provide the information, operators will seldom volunteer
the physical measure of inputs such as energy consumption. This limited
data on quantity pushes the regulator to use as much as possible the in-
formation available in balance sheets, that is, cost and revenue data from
annual reports. This can be frustrating, as little detailed breakdown of this
information is generally available unless the regulator has managed to
impose strict regulatory accounting rules on the operators. In this respect
the Office of Water Services in the United Kingdom is a leader in the field
(see www.open gov.uk/ofwat).
One solution in that type of situation is to rely on an mdirect TFP index.
This indirect index is defined by deflating total revenue and total costs by
suitable price indexes to obtain quantity indexes That is, because price x
quantity = value, then quantity = value/price. One can then define TFP as
the ratio of deflated revenue over deflated cost.4 This is also an approxima-
tion, because often the price indexes that are used for deflating are imper-
fect, as discussed later. They are probably compiled for the industry by a
central statistical agency. Recognizing these constramts is crucial, because
they may introduce biases into the TFP measurements.
To see how these biases could occur in practice, consider the case of a
railways performance study The best input price index available might be
that defined for public transport mdustries in general, while the output
price index may be defined for the rail mdustry alone. These price indexes
would most likely be Laspeyres indexes, that is, based on base period
weights, and would also be calculated using quantity weights for the whole
industry. Hence if the input mix and/or output mix of a particular firm
differs substantially from the average mixes in the industry, for example, if
a firm uses a lower proportion of labor to capital or provides a higher pro-
portion of freight to passenger services, the deflated revenue and/or cost
figures for this firm may not provide a reasonable approximation to the
required quantity indexes. Thus the resulting TFP index for this firm may
be misleading.
How misleading can this be? Imagine a case where the ratio of passen-
ger to freight services is 4 to 1 in the industry in terms of revenue, but firm
4. Once again, the form of the price index formula used (Laspeyres, Paasche,
Thinqvist, or Fisher) will imply a particular functional form for the underlying
production technology. Laspeyres and Paasche will imply restrictive first-order
forms, while Tmrnqvist and Fisher imply more flexible second-order functional
forms
30 A Primer on Efficiency Measurementfor Utilities anzd Transport Regulators
A has a ratio of 1 to 4 (we assume all firms face the same prices). If the pric2
of passenger services increases by 10 percent between two periods while
the other prices and all quantities remain constant, the output price index
for the industry will increase by 8 percent, while the true price index firm A
faces will only increase by 2 percent. However, the revenue of firm A, which
increases by 2 percent, will be deflated by the industry price index, which
increases by 8 percent, which will suggest that the real output of firm A has
fallen, when in reality it has not.5
In sum, the PINs can be useful to many regtilaiors with only limited
databases, but as with any index, unders'tanding the instrument's limita
tions is a requirement for ensuring the credibility of its regulatory uses. A
necessary condition for its effective use is a good understanding of what
each price indicator hides and the extent to which average price applies of
does not apply to any individual operator.
PIN methods have the advantage that they can be used when you only
have access to data on one firm or a few firms, or you only have access to
industry-level data; however, they have the disadvantage that you canno.
use PIN methods to decompose TFP change into components, such as tech-
nical change (frontier shift) and technical efficiency change (catch-up). In
the following sections we assume that we have access to panel data on a
number of firms, that is, we have data on N firms over T time pseriods, for
example, we could have annual data on N = 40 firms over T = 8 years.
Given access to this type of data, we can use frontier methods such as SPFA.
and DEA to measure and decompose TFP growth.
iroduction lFruneiers, Singl C: e : CEse
For the sake of simplicity, we focus first on the standard single output pro-
duction process, and leave the discussion of the multiple output case for
later. This discussion is quite relevant in practice, as many regulators t-en6
to treat the firms they monitor as single output producers and rely on .
5. These types of issues are also important to keep in mind as we discuss pro-
duction and cost frontier approaches to TFP measurement, because our quantity
data often come in the form of deflated value measures. In many cases the prices
we use may be questionable. First, they may be measured with error. Second, the.
may be measured well, but some prices may be distorted by regulatory and othcr
factors, for example, a government-owr:ed utility might set electricity prices below
cost. Third, the market prices may be measured well, but they may not reflec.
society's priorities, for instance, this may be revealed in divergences between the
market price and shadow price of labor in government-owned firms where tie
government and society put a value on high employment levels.
Some TFP Measuremenit and Decomposition Methods 31
constant price valuation of the operator's revenue as an approximation of
this output.
The TFP change (TFPC) measures derived from a production frontier
can be decomposed into three components: technical efficiency change
(TEC), technical change (TC), and scale efficiency change (SEC). This de-
composition is multiplicative, that is,
TFPC = TEC x TC x SEC
Note that allocative efficiency does not appear in this decomposition.
This is because the TFP measures derived from production frontiers do not
include this factor; however, allocative efficiency does come into play when
we consider cost frontiers.
When implementing this simple approach, the first question to address
is the choice of functional form. The Cobb-Douglas is a relatively simple
functional form. For the case when we have one output (Y) and three input
variables (X, = capital, X2 = labor, and X3 = other inputs), the Cobb-Douglas
production function has the form
Y = a0X, X2`X3,` (3.4a)
where ao, 1x2, and 01 are unknown parameters to be estimated. The Cobb-
Douglas is popular largely because the logarithm of equation (3.4a) produces
a function that is linear in parameters, and is therefore easy to estimate using
standard lnear regression methods. The logarithm of equation (3.4a) is
y = (to + A + (X2X2+ O3x3, (3 4b)
where a, = log(a,) and x, = log(X,). Note that otL, (X2 and a3 are the elasticities
of output with respect to capital, labor, and other, respectively. A clear ad-
vantage of this functional form is that it only requires the estimation of four
parameters, which can be done with relatively small data samples. It is
convenient, and this may be why it was so commonly used in the early
literature on efficiency and continues to be contrasted with more flexible
forms in recent literature. However, from the viewpoint of most regulators,
it is likely to be too restrictive. The Cobb-Douglas assumes that all firms
have the same production elasticities, the same scale elasticities, and uni-
tary elasticities of substitution, which is quite restrictive for most studies
trying to compare regulated operators.
One additional advantage of the Cobb-Douglas may be that its analyti-
cal expression is simple enough to allow the derivation of the cost frontier
from the estimation of the production frontier or vice versa. This is quite
32 A Primer on Efficency Measurementfiir Utilities onid Tatusport Regulators
useful when a regulator can only rely on total cost data from balance sheets.
It is, however, quite problematic conceptually, as most of the analytical work
underlying the duality between production and cost frontiers assumes per-
fectly competitive markets, which is rarely the norm among regulated in-
dustries. They are regulated because they are not strictly competitive.'
Because of this, it is often safer to use a production frontier if you have
access to suitable data.
Given the restricted nature of the Cobb-Douglas, regulators will gener-
ally need to seek out a more flexible functional form, irrespective of whether
they decide to estimate a cost or a production frontier. Currently the most
commonly used flexible functional form is the -ranslog functional form.
While it requires the estimation of many more parameters than the Cobb-
Douglas, it does not impose the restrictions imposed by the Cobb-Douglas,
and is therefore generally preferable, unless a hypoothesis test justifies tne
Cobb-Douglas restrictions or data limitations preclude the use of the
translog. A translog stochastic production frontier may be defined as7
K K K K
Yn1 °=0 +E(XlXmt +0 5EEal,X +7 8x,X. \,t + O.5X,1t2 + V-,
-I I 1 (3.5)
n=1,2,...,N; t=l, 2,...,T,
where Yn, is the log of output quantity; x,,, is the log of i-th input quantity; t
is a time trend; vnt is a noise error term tha, picks up whatever the model
could not explain; unl is the inefficiency term, entered with a negative sign
because inefficiency means less output; and th-e Greek letters represent
6. See Schmidt and Lovell (1979) for an example of direct estimation of the cost
frontier applied to electricity supply, and see Bravo-Ureta and Rieger (1991) for an
example involving direct estimation of the produchon frontier applied to agricul-
ture In the latter case, a criticism of possible simultaneous equations bias could be
leveled given that the mputs, which are assumcd to be decision variables, appoar
as regressors in the production frontier. Schmidt and Lovell (1979) also considcr
the case where the production frontier is estimated simultaneously with the first-
order conditions for cost minimization. They use maximum-n likelihood methods Lo
estimate this system of equations, assuming that mputs are endogenous and oui-
puts are exogenous. They consider two forms of this latter model, one where the
average ftrm is assumed to be allocatively efficient and one where systematic cc-
viation from allocative efficiency is permitted, for example, caused by a regulatory
effect such as the Averch-Johnson effeci.
7. In this and all other translog function m this book, symmetry is implicit, thai
is, a,~ = Up etc
Some TFP Measurenient and Decomposition Methods 33
unknown parameters to be estimated.8 The subscripts n and t index firm
and time period, respectively. As is also quite comrmon, in this model we
have used a time trend, t, to approximate technical change. While other
possibilities exist, such as the use of annual dummy variables, the time
trend approach is the most often used.9
A useful trick practitioners use that deserves consideration by most regu-
lators is transforming the data so as to allow direct interpretation of the first-
order translog parameters (the a,s) as the elasticities evaluated at the sample
means.'° This is done by ensuring that the arithmetic sample averages of the
logged variables are 0, which is equivalent to setting the geometric means of
the original (unlogged) data equal to 1. Essentially it consists of dividing
every series by its geometric average. This wiRl not change the results ob-
tained, but is simply a convenient change in units of measurement.
The next stage is the actual calculation of the TFPC for each firm between
any two time periods using estimates of the production frontier. Following
Orea (2002),"i the log of the TFPC between period t = 0 and t = 1, for the
n-th firm can be defined to being equal to
In (TFP,, / TFPnO) = In (TE., /TEnl ) + 0.5 [(dy,0/t) + (ay, /at)]
K (3 6)
+ 0.5L [(SFoekno + SFn( ek36) H Xk1 Xk.0
k=1
8 Those more statistically inclined shoudd note that the most common as-
sumptions are that the error terms, vn, and u,,, could take many different possible
structures The first is symmetrically distributed while the second is one-sided
Generally they are assumed to be independently and identically distributed as
N(0, u(2) and I N(0, u,:) random variables, respectively (see chapters 8 and 9 in
CRB for further discussion)
9 In addition to this general specification, there is the need to ensure that the
sum of the weights in the TFP measure adds up to 1. If the production elasticities
from the estimated production frontier do not add up to 1, the literature usually
picks either one of the followng two choices The first is to impose constant re-
turns to scale on the production technology, but this will generally not be satisfac-
tory in regulated industries, which are often considered to be natural monopolies
with clear economies of scale. The second is to assume variable returns to scale and
ensure that an appropriate scale efficiency change measure is included m the final
TFP calculations, as suggested In Balk (1999), Kumbhakar and Lovell (2000), and
Orea (2002) Most regulators will generally favor this approach.
10 If you do use scaled data to estimate the frontier, then you must be sure to use
scaled data to calculate TFP, and so on, otherwise you will obtain incorrect results.
11. The two main approaches to TFP decomposition are the total differential
approach (see, for example, Bauer 1990; Kumbhakar and Lovell 2000) and the index
34 A Primer on Efficiency Measurement for Utilities a1nd Tranzsport Regulotors
where the three terms on the right-aand-side of equation (3.6) are the TB'C,
TC, and SEC terms, respectively. Tlhe technical efficiency measure, TEDt, is
the technical efficiency prediction of the n-th firm in the t-th time period
obtained from equation (3.5).i2 The technical change measure is the mean
of the technical change measures evaluated at the period 0 and period 1
data points, and can also be derived directly frorn the coefficients estimated
for equation (3.5). The change in scale efficiency requires calculating the
production elasticities from the parameters estimated for equation (3.5),'
that is, you must calculate
e, = ay., /ax,,< - a,; -1- Tc x,8 + o,t (3.7)
. 1
for each input at each data point, and also calculate the scale factors
SFnt = (e.j- 1)/en, at each data point, where e,Z = Z,c is the standard returns
k I
to scale elasticity.'4
The TC measure requires calculating the partial derivative with respect
to time at each data point. For firm n in period t this is
ayn1/at=XI+ )il t+ >7 xknt (3.8)
number approach (see, for example, Caves, Christensen, and Diewert 1982a,b; Crea
2002), whuch exploits the translog identity. Tne two approaches result in almost
identical formulas, the only differences being that the latter approach evaluaies
derivatives at both data points, while the first method chooses just one data point
for derivative evaluation. Diewert (2000) argues in favor of the index number ap-
proach, because the total differential approach is an approxumation to a continu-
ous time measure, which can take many values. Thus in this book we use the index
number approach, however, we do note that in most cases the two approaches will
provide quite similar estimates.
12. Analytically, the TE is equal to the conditional expeciation of exp(-un,), given
the value of (v,j- unt). These measures are routinely reported by the statistical pack-
ages available to assess efficiency, such as the FRON'TIER program by Coelli (1996b).
TIus software can be downloaded from www.uq.edu.au/economncs/staff/coelli.htmn.
13. To be precise, the SEC measures derived from SFA frontlers in this book are
not pure measures of scale efficiency change. First, it is possible that the measures
obtained may also include the effects of scale-biased technical change, if this has
occurred; however, this distinction is not something that regulators should be greatly
concerned about. Second, as stated by Orea (2092 p 12), this term "evaluates the
contribution of non-constant returns to scale on productivity growth when firms
move along the distance function changing their inputs levels over time."
14 With constant returns to scale, c, will equal 1, and hence the scale term Li
equation (3 6) will be equal to 0, as required.
Some TFP Measurement and Decomposition Methods 35
Keep in mind also that the TFP index in equation (3.6) uses shadow
prices, which are derived from the frontier, instead of market prices. If the
regulator has access to input price data, it can also calculate the Tornqvist
TFP change index. For the single output case this is
K
ln(TFP., /TFPn.) =(ynl-y.) -0 5Z (Sk1+ SknO) (Xkni Xk0), (3 9)
k=i
where s,, is the cost share of the k-th input of the n-th firm in the t-th period.
Why should a regulator care about this calculation? Because any differ-
ence between the TFPC calculated from equations (3.6) and (3.9) must be
due to allocative efficiency change (AEC). In fact, we can show that AEC is
as follows: 15
K
AEC = 0.5 E {[(ek.1 /e.1 - skn1) + (eko, /e.0 - skno)] (xknl - xk0)}. (3.10)
k=1
This shows that the relative importance of distortions m the inputs mix
can help explain TFP changes, and their relative importance may be a source
of concern that the regulator may not be able to do much about. Indeed,
allocative efficiency changes may result from distortions in factor markets
not really under the control of the operator. Limited access to capital mar-
kets and national agreements with unions unrelated to the operator's spe-
cialized employment needs are two common examples of sources of
allocative inefficiency for which the operator should not necessarily be
blamed. Understandmg that this is the case is a matter of fairness. Chapter
4 provides a detailed description of the application of these production
frontier and Tornqvist methods to sample data.
15. Thus result will be exact when there is no noise in the model, that is, when
we have a deterministic frontier. The expression in equation (3.10) has a nice intui-
tive interpretation. Essentially it shows that the TFPC index that we constructed in
equation (3.6), is equivalent to a Tornqvist mdex that uses shadow prices mstead of
market prices to calculate the input share weights. These shadow shares are equal
to the production elasticities deflated by the retuins to scale elasticity. This defla-
tion ensures that the shares sum to 1 as required. Thus the AEC measure in equa-
tion (3.10) wllE pick up the effects of any convergence or divergence in the differences
between shadow prices and market prices, which may be due to regulatory and
other change If shadow prices equal market prices m both periods, this term will
clearly be equal to 0. Furthermore, if shadow prices and market prices do not change
between periods, the term will also be 0.
36 A Primer on Efficiency Measurementfor Utilities anid Teaaspod Regulators
This quick introduction to the main concepts that regulators are likely
to come across in the literature would not be complete without some brie.-
comments on a few of the simplest, and yet common, hypothesis tests regu-
lators will want to care about. Generally, testing for Cobb-Douglas versus
translog is not a bad idea, as is testing for neutral versus non-neutral tec7h-
nical change in any model aimed at measuring efficiency in a regulated
industry for which few data are available. If one of 'Lhese sets of restrictions
holds, fewer parameters have to be estimated and the statistical results can
be more reliable with the same database size.
These types of tests are essentially based on likelihood ratio tests, whic'n
compare the likelihood function value of each model, for instance, does the
translog model do a significantly better job olf explaining variation in the
sample data relative to the Cobb-Douglas function? They are quite rou-
tinely carried out in the literature to test these kinds of simple assumptions
and are quite simple to implement. For instance, to test for neutral techni-
cal change in a production frontier with K inputs tlhe steps are as follows:
1. Estimate the standard, unrestricted translog model and note the log-
likelihood function (LLF) value of this unrestricted model (LLFL).
2. Estimate the restricted model, where th-e IK x,t variables, which would
imply a non-neutral technical change, are omitted, and note the re-
stricted LLF value (LLFR).
3. Calculate the likelihood ratio test value, which is two times the dif-
ference between these two LLF values.
4. Reject the null hypothesis of neutral technical change if the test value
exceeds the critical value, obtained from statistical tables. The likeii-
hood ratio test statistic has a chi-square distribution, witlh degrees of
freedom equal to the number of restrictions, in this case (.16
Cost 7Frontiers, SingRe Output CQse
Cost frontiers are commonly used, simply because cost data seem to be
much easier to come by. Ignoring tlhe significant conceptual issues raised
by cost functions in noncompetitive sectors, the main challenge for most
16. The procedure for the Cobb-Douglas versus translog test is similar. In this
case the restricted model (the Cobb-Douglas) will only contain the first-order terms
and the number of restrictions will be larger-!C(K + 1)/2-if a time trend is in-
cluded. Furthermore, looking at efficiency scores and ranks before and after im-
posing restrictions is always wise to see if the imposition of restrictions has a big
effect.
Some TFP Measurement and Decomposition Methods 37
regulators in developing countries without a strong tradition of good ac-
counting standards is to make sure that the data mean something. The
data must be comparable and consistent over time, and the definitions of
the various cost concepts must be what most accountants would expect
them to be. This is not always easy to achieve in developing countries
where manipulating accounting data for tax reasons continues to be quite
widespread.
If and when these data are available, the most common functional form
found in the literature is a translog cost function, which essentially has cost
as a function of input prices and the production level. As for the produc-
tion frontier, technical change is easy to incorporate, and this is often done
when long enough time series are available to track down this change. A
typical translog cost function estimated in the utilities or transport sector
takes the following form:
K K K
= + E a,w,,,+ + 0 5 (Y., + P31 y.t + 0.5 PI,Yn
1=1 1~~~=1 j=i
K K ~~~~~~'1 ~ Jt Vt n,(3 11)
E 1Wt Ynt +Y E w,mt + 41yntt + I,t + 0 5X11t2+v,,+ u,
where Cnt is the log of total cost, Ynt is the log of output quantity, wnt is the
log of i-th input price, t is a time trend that is included as a proxy for tech-
nical change, vnt is a noise error term, u,t is the cost inefficiency term, and
the Greek letters represent unknown parameters to be estimated. Cost inef-
ficiency will contain the combined effects of technical and allocative effi-
ciency. The subscripts n and t index firm and time period, respectively. The
error terms, v, and uin, are assumed to be distributed in the same way as in
the production frontier case, except that the un, term is added, not sub-
tracted, because mefficiency in this context means higher costs, while in
the production frontier case it meant less output.
Note that in the literature homogeneity restrictions are typically imposed
on this function, that is,"7
K K K K
Ea = 1, =O,2, ,K), XY=O, E°8,==. (3 12)
Y,=1 *==12 .=1 K Y, =
17. These restrictions ensure that the function is homogenous of degree one m
input prices. For example, this property ensures that a 10 percent increase in all
input prices will result in a 10 percent mcrease in costs
38 A Primer on Efficiency Measurementfor Utilities and Tranisport Regulators
These restrictions can easily be imposed by estimating a model where
the cost and K-1 input prices are deflated by the K-fit input price. The pa-
rameters associated with the K-th input can then be calculated using the
estimated parameters and the restriciions defined in equation (3.12).18
The rest of the process mirrors that discussed for the production fron-
tier. The TFPC for each firm between any two time periods is calculated
using the estimates of the coefficients of the cost frontier. The general for-
mula to calculate the log of the TFI'C between periods t = 0 and t = 1 for the}
n-th firm is
In (TFP,, /TFP,nO) = ln(CEns /CE.1) -0.5 [(ac", /e)t) + ((cC, /at)] (3.13)
+ 0.5 [(1-0) + (1-0 )] ( YnM Yno) I
where the three terms on the right-hand-side of equation (3.13) are the cost
efficiency change (CEC), TC, and SEC terms, respectively.9
The cost efficiency measure, CEn,, is the cost efficiency prediction of th2
n-th firm in the t-th time period and is calculated from the cost frontier
estimated. This measure takes a value between I and infinity and is rou-
tinely reported by the FRONTIER computer program.20
18. Note that we have not used Shephard's Lemma to derive the first-order cost
share equations, and we have not suggested estimating tnem jointly with the cost
frontier. We have done this for many reasons. First, inclusion of the cost share equa-
tions makes estimation extremely complicated, and we arc not confident that the
possible gains in estimation efficiency warrant the extra effort. Second, the standard
inclusion of the cost share equations implies that there is no systematic deviation
from cost-minumizing behavior in this mdustry. This is unlikely in government-
owned or regulated firms. One can specify a model where extra parameters are
included to allow for systematic departure from allocative cfficiency (see, for ex-
ample, Balk 1998), but these shadow cost models are quite complicated to estimate,
and one must then wonder if there will be any estimation efficiency gains.
19. This decomposition is based upon that presented in Kumbhakar and Lovell
(2000), which was derived using total differential methods. However, we have co- -
verted their differential formula into an exact index number formula. This is done
m the same way that Orea (2002) has done for the distance function case, which we
used in our earlier production frontier discussion The derivation involves the use
of the translog identity.
20. This is equal to the conditional expectation of exp(u,,), given the value of
(Vn,+unl). The FRONTIER computer program (Coelli, 1996b) reports the cost effi-
ciency score as a value between 1 and infimty, with a value of I indicating cost
efficiency. Most studies, however, report the inverse of this value, whlch will vary
between 0 and 1, where a value of 1 indicates cost efficiency. Another computer
Some TFP Measiurement and Decomnposition Methods 39
The TC measure is the mean of the technical change measures evalu-
ated at the period 0 and period 1 data points with the cost frontier. This
requires calculatmg the partial derivatives of cost with respect to time at
each data point as follows:
K
aCn, l/t = Al + X1t +Z8kWknt+ (FIYnt (3 14)
k=1
The final term in equation (3.13), which measures the change in scale
efficiency, requires calculation of the output elasticities
K
em = aCnt Y/Y,t = I3 + tl Ynt + Y W., + 4)tt (3.15)
=1=
at each data point.2"
Recall that in the production frontier case, when price information is
available, the regulator can calculate an AEC component, which is equal to
the difference between the TFPC measure obtained from the production
frontier and a Tdrnqvist TFPC measure. This AEC measure was presented
in equation (3.10). In a similar way, in the cost frontier case with informa-
tion on nput quantities, a Tbrnqvist TFPC index can be calculated and the
difference between this index and the cost-based index is equal to
K
AEC = 0.5y_{[(Kkl - Sknl) + (KknO - Sk)] (Wk1 - WkO)} X (3.16)
k=l
which will not be equal to 0 when the observed cost shares, sml, differ from
the "efficient" cost shares
K
Kk.t =Cn, /aWknt =k + bwknt + Yk Ynt + 8kt* (3.17)
=1=
program that performs DEA Malmquist indexes is OnFront, produced by the EMQ
Group (http://www.emq.se/software.html).
21 Thls is equal to the inverse of the standard returns to scale elasticity As
before, when we have constant returns to scale this will equal 1, and thus the scale
term in equation (3 13) will be equal to 0, as required
40 A Primer on Efficiency Measurement for Utilities and Transport Regulators
Thus in this cost frontier case two terms in the TFP calculations involve
changes in allocative efficiency, namely, the CEC, which also contains the
effects of technical efficiency changes, and 'chis AEC term."2
All this assumes that the estimated cost frontier actually reflects ccst-
minimizing behavior. If this is incorrect because of systematic deviatio-s
from allocative efficiency, for example, as a result of a regulatory bias su ch
as rate of return regulation, then the link (or duality) between the cost fronl-
tier and the production frontier is lost, and tnus our measures of allocati-ve
efficiency, technical efficiency, scale efficiency, and technical change will all
be incorrect. This is one of the main reasons why some efficiency specialists
are reluctant to rely on the cost frontier approach despite its widespread
use among regulators (furthermore, Coelli and Cuesta 2000 and M4undlak
1996 indicate that dual estimators are often more inefficient than primal
estimators). The main arguments for the use of the cost frontier are that it
can accommodate multiple outputs, and also because in most cases the
input prices are more likely to be exogenous than the input quantities.
However, as we discuss next, the input distance function may provide an
even better alternative.
Muliprle output Case
What happens when the regulated firm has outputs that are not homog-
enous enough to be integrated into a single output? Suburban passenger
and long distance railways services, for instance, are no't readily compa-
rable, and neither are the water distribution service and the sewerage treat-
ment business. Yet for many of the operators providing these multiple
outputs, the inputs are shared and jointly determine the production pro-
cess. How then can a regulator assess the efficiency of each business? Two
22. Any attempt to understand the meaning behind these two allocative effi-
ciency components is likely to be frustratmg. Consider some special cases instead.
If the firm is allocatively efficient in both periods, then AEC is equal to 0 and CEC
is due solely to a change m technical efficiency Alternatively, assume there have
been no price or output changes, but that the firm has changed the quantity of
capital to labor, and hence has reduced the to.al cost of producing a paricular
output level In this case the AEC term will be 0, but the total cost will fall, and thus
cost efficiency will improve. Finally, assume that output and input quantities FC
main constant, but the relative price of capital to labor changes so that the total cost
has fallen (this could be an accidental or anticipated allocative improvement) In
this case the observed cost will fall, but what happens to the predicted mimmum
cost for this firm is hard to predict.
Sonme TFP Measurement and Decompositioni Methods 41
possible options are cost frontiers and an input distance function 23 The
first is the most common in the literature, and because it has been so com-
mon we discuss it despite our reluctance to deal with cost frontiers in regu-
lated industries. The second option is a much more recent addition to the
toolbox that provides a promising alternative for regulators.
Multiple Output Cost Frontier
Consider the situation of a regulator monitoring an operator producing M
outputs with K inputs. As usual capital, labor, and "other" are standard
inputs, but each one of these categories can be further disaggregated. A
multiple output translog cost frontier is defined as
K K K M M M
Cnt =ao +Zcwmt+w + 05Y +3ym, + 05 Pq Ymt Y1m
l=l =1 I=l z=l I=l §=l ~~~~~~~~(3 18)
K M K M
+ 'Ylw,nWy,n, +BXnl,,t +E¢4)y,n,t + Att + 0 5X11t2 + Vnt + Unt,
where all notation is as previously defined.
As before, we need to place a restriction on this function to ensure the
homogeneity of degree one in input prices of this function, which says that
the multiplication of all input price by any constant value multiplies the
costs by the same constant. The required homogeneity restrictions are
K K K K
o, = 1, Eoa, = 0 (j = 1, 2.. , K), -y,l = 0 (j = 1, 2. ,M), 8, = 0 (3 19)
1=1 *=.=*1
The TFP change for each firm between any two time periods can be
calculated from the econometric estimates of the coefficients of this cost
model. The log of the TFP change between period t = 0 and t = 1 for the n-
th firm is equal to
In (TFP,, /TFP,,0) = ln (CEn, /CEnl ) -0.5 [(acn0 /at) + (aCnl /at)]
M
+ 0.5Z [(SF,, e,, + SF,, e,,O) (yml - Yrno)] (3.20)
-1=
23 We choose an mput distance function instead of an output distance func-
tion because the input distance function is best suited to the case of endogenous
inputs and exogenous outputs, which is a reasonable assumption in most net-
work industries.
42 A Primer on Efficiency Measuremenitfor Utilities and Transport Regulators
where the three terms on the right-hand-side of equation (3.20) are the CEC,
TC, and SEC terms, respectively.24 'he cost efficiency measure, CEn,, is the
same as specified for the single output case. The technical change measu,e
is the mean of the technical change measures evaluated at the period 0 and
period 1 data points. For firm n in period t this is
K M1
ac,, /at = X1 + kl+t + B + E( X ld *) (3.21)
The final term in equation (3.20), which -neasures the change in scale
efficiency, requires calculation of the output elasticities
M= acn./yY,M= I= +YP,,,y, 1+ -y,w,t+~~