Policy Research Working Paper 10698 Are Unit Values Reliable Proxies for Prices? Implications of Better Price Data for Household Consumption Measurement in a Low-Income Context Omoniyi Alimi Wilbert Drazi Vundru Talip Kilic Development Economics Development Data Group February 2024 Policy Research Working Paper 10698 Abstract Household Consumption and Expenditure Surveys are key Survey that is the source of official poverty statistics. The to consumption-based monetary poverty measurement. In analysis demonstrates that Hicksian separability fails to the absence of market price surveys that are linked to House- hold across space and time and that unit values are biased hold Consumption and Expenditure Surveys, unit values proxies for prices. Integrating the Household Consumption are used as proxies for market prices in estimating nomi- and Expenditure Survey and market survey data based on nal consumption aggregates, price deflators, poverty lines, location and timing of fieldwork permits an assessment and poverty statistics. This practice relies on the Hicksian of consumption and poverty estimation based on market separability assumption: within-commodity group relative prices versus unit values. Relative to unit values, using prices are constant across space and the price of a single market prices leads to higher food and overall consump- good is an accurate proxy for the commodity group price. tion expenditures—both in nominal and real terms—while To test, for the first time in a low-income context, whether generating higher poverty lines and higher food and overall Hicksian separability holds, this paper uses the price data poverty rates. Compared to their counterparts based on unit collected for an extensive list of food items, including sev- values, spatially-disaggregated poverty estimates based on eral variety/quality-differentiated products for specific items, market prices exhibit a stronger correlation with nightlights in a national market survey that was conducted in Malawi —an objective proxy for living standards. in sync with the Household Consumption and Expenditure This paper is a product of the Development Data Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at oalimi@worldbank.org and tkilic@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Are Unit Values Reliable Proxies for Prices? Implications of Better Price Data for Household Consumption Measurement in a Low-Income Context Omoniyi Alimi†, Wilbert Drazi Vundru‡, and Talip Kilic⁑1 JEL Codes: C81, I32. Keywords: Household Consumption, Poverty, Market Surveys, Price Data, Household Surveys, Malawi, Sub-Saharan Africa. 1 The authors are listed alphabetically. † Young Professional, Education Global Practice, World Bank, oalimi@worldbank.org. ‡ Survey Specialist, Living Standards Measurement Study (LSMS), Development Data Group, World Bank, wvundru@worldbank.org. ⁑ Senior Program Manager, Living Standards Measurement Study (LSMS), Development Data Group, World Bank, tkilic@worldbank.org. The authors would like to thank (i) Yuri Dikhanov and Giovanni Tonutti for their comments on the earlier draft, (ii) Japan Ministry of Agriculture for providing funding in support of the design and implementation of the Malawi National Market Survey, and (iii) the Malawi National Statistical Office management and survey teams for their dedication and hard work towards the successful implementation of the Malawi Fifth Integrated Household Survey (IHS5) 2019/20 and the Malawi National Market Survey. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the Government of Malawi, the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. 1 Introduction Household Consumption and Expenditure Surveys (HCES) allow for the computation of comprehensive food and non-food consumption aggregates that underlie consumption-based monetary poverty and inequality estimates in low- and middle-income countries. These estimates typically rely on a measure of prices to value household consumption; construct poverty lines such as in the Cost of Basic Needs approach (Ravallion, 1992); and to feed into price deflators for temporally and spatially consistent measures of welfare. In practice, there are two main competing proxies for prices. 2 The first is the unit value proxy, calculated as the ratio of the "consumption line item-specific” self-reported expenditures, or self- valuation of consumption, divided by the associated quantity of consumption – commonly specific to food consumption at home and based on the most knowledgeable respondents’ self-reports. The length and specificity of HCES food consumption modules vary significantly across countries, and “line items”, henceforth referred to as “commodity groups”, that are included in these modules could be a mix of (i) variety/quality-differentiated versions of specific food types, (ii) specific food types listed separately within aggregate food groups, however without variety/quality differentiation, and/or (iii) aggregate food groups that are specified single entries but that combine different food types in their description. The alternative to the unit value proxy is the market price proxy, derived from a market survey that captures prices for consumption items at market locations where surveyed households are expected to shop. The market survey can provide an opportunity to collect price data for a more disaggregated list of commodity groups vis-à-vis the associated HCES (i.e., across a finer breakdown of food types as well as their variety/quality-differentiated versions within aggregate food categories). Research has shown that market survey data collection across a more disaggregated list of commodity groups vis- à-vis the associated HCES would be valuable, even when the length and specificity of HCES consumption items are unchanged (Deaton, 1990; Gibson, 2013). However, in low- and middle-income countries, the use of unit values is the prevailing practice while estimating nominal consumption aggregates, price deflators and poverty lines (Mancini and Vecchi, 2022), since they can readily be estimated from household survey data, without needing to incur separate visits to markets which would bring about higher data collection costs and complexity in design and implementation of large- scale surveys. The implementation of a market survey that is spatially and temporally linked with an HCES is in fact a rare event (Gibson, 2013). One assumption that underpins the use of unit values as proxies for prices is the concept of Hicksian separability. This is the assumption that relative prices of goods within a commodity group are constant across space. At the same time, within a commodity group, consumers can purchase several quality/variety-differentiated products, even concerning items such as “maize flour,” “rice”, or “soft drinks,” that often appear in HCES food consumption modules as line items without quality/variety differentiation. If within-group relative prices vary across space, the composition of consumption 2 There are other price proxies that have been explored in the literature including price opinions of the most knowledgeable household member or key informant about food items (see Gibson and Rozelle, 2005), and other existing price collection efforts for ongoing surveys like the CPI (Gibson, 2007). 2 within the group will shift towards locally cheaper goods and subsequently unit values cannot represent the same quality mix in all areas and cannot be treated as consistent proxies for prices across space (Gibson and Kim, 2019). For example, if consumers in urban areas consume higher-quality items, unit value differences between these areas and elsewhere will not only represent the price differences but also the quality differences. The violation of the Hicksian separability assumption would have direct implications for poverty and inequality statistics to the extent that unit values inform the underlying nominal consumption aggregates; the deflators used to make spatial and temporal price adjustments to these aggregates; and the poverty lines. 3 It may be argued that the assumption of Hicksian separability may no longer be required with more detailed data, including scanner data on individual transactions or data from expanded survey modules and consumption item lists to better capture product specificity and quality variation. However, particularly in low-income countries, scanner data remain a long way away from constituting the majority of transactions (Gibson and Kim, 2019) and expanding consumption item lists in surveys to better capture variety and quality-specificity could non-negligibly increase the costs of survey data collection and respondent burden, with potential adverse effects on data quality – particularly in countries where consumption item lists are already considered “relatively detailed” (Beegle et al., 2012). Furthermore, even in the context of survey modules where important consumption items are sufficiently variety and/or quality-differentiated, as arguably in the case of Malawi, unit values are underlined by self-reported consumption expenditures or self-valuation of consumption originating from purchases. As such, they may exhibit measurement errors vis-à-vis local prices for the identical commodities that can theoretically be elicited in a market survey that is implemented in parallel with the household survey in question. The assumption of Hicksian separability remains central to household consumption-based welfare estimates in developing countries, and despite its importance, there is a dearth of evidence on the validity of this assumption, except for the findings of Gibson and Kim (2015) who previously demonstrated that the assumption does not hold for a range of products in the Vietnamese context and McKelvey’s (2011) rejection of the assumption based on data from a district of Central Java, Indonesia for a single food group (rice). 4 To contribute to this scant literature and provide a comprehensive examination of the validity of this assumption and its implications for poverty measurement for the first time in a low-income setting, we use detailed price data for an extensive list of food items, including a substantial number of quality-differentiated products within specific food groups, that were collected through a 12-month national market survey, which was conducted in Malawi by the National Statistical Office (NSO) in sync with the nationally representative household survey that is the source of official poverty and inequality statistics, namely the Fifth Integrated Household Survey (IHS5) 2019/20. The Market Survey relied on dedicated field teams that were trained, deployed, and managed by the NSO together with the IHS5 field teams. The selection of the markets and the timing of market visits were also informed by the timing of the visits to the IHS5 enumeration areas for consumption data collection. Overall, the Market Survey elicited price data for 3 The Hicksian separability assumption would be invoked even in integrated household-market survey data collection, if the marker survey collects price information for aggregate commodity groups that combine different food items in their description, as opposed to specific commodities within these aggregate groups. 4 Minten and Kyle (1999) also provide evidence of failure of the Hicksian separability assumption in Former Zaire in the context of marketing margins, but do not examine the implications for welfare estimation. 3 a larger number of food products and with greater spatial and temporal resolution vis-à-vis the above referenced studies. The analysis shows that Hicksian separability fails to hold across space and time and that unit values constitute biased proxies for food prices in a low-income setting like Malawi. Mirroring the earlier findings of Gibson and Kim (2015) from Viet Nam, we provide evidence in support of at least one mechanism through which Hicksian separability fails, namely the Alchian-Allen effect – in other words, the fact that relative prices of high-quality and low-quality goods shipped from a common location (such as the nearest port, for imports, or a key geographic location for production and aggregation, for specific domestic products) are not constant over space. Mechanisms such as the Alchian-Allen effect and weak spatial markets integration can be expected to be stronger in low-income countries, thus making Malawi an ideal location to examine this assumption. In view of these findings and taking advantage of the highly disaggregated market price data that were collected in tandem with the IHS5, we conduct a comparative assessment of consumption and poverty estimation based on unit values versus market prices. Relative to unit values, market price data showcase a different pattern of spatial price variation; lead to higher food and overall consumption expenditures – both in nominal and real terms – and higher food and overall poverty lines, culminating in higher food and overall poverty rates but without any effect on inequality estimates. In an attempt to provide operational guidance on the most cost-effective approach to market price data collection in tandem with an HCES, we subsequently examine the sensitivity of the market price-based results to (a) reduced spatial coverage in markets and (b) reduced item coverage in the market survey questionnaire. We find that estimates of food and total poverty rates are sensitive to reducing the spatial scope as well as the item coverage of the market price data collection effort. As such, for generating statistically consistent poverty estimates that are informed by market prices, it is essential to have a market survey that has a sizeable spatial and temporal overlap with household survey data collection, inclusive of price information on the same consumption items that are also featured in the household survey questionnaire. The rest of the study proceeds as follows: Section 2 describes the Malawi national market survey – our source of market price data. Section 3 tests for Hicksian separability over space and time and examines the role of Alchian-Allen as the mechanism by which Hicksian separability fails. Section 4 reports the alternative estimates of poverty and inequality using the market price proxy and compares this with the traditional unit value-derived results. Section 5 reports the findings from the sensitivity analyses and Section 6 concludes. 2 The Malawi National Market Survey The Malawi National Market Survey (henceforth referred to as the Market Survey) was implemented by the Malawi National Statistical Office from April 2019 to April 2020, in parallel with the Integrated Household Panel Survey (IHPS) 2019 and the Fifth Integrated Household Survey 2019/2020 – the latest round of the cross-sectional, nationally representative, multi-topic household survey used, among others, for official poverty and inequality statistics. The Market Survey was designed to achieve two 4 key objectives: (i) collect, from a national sample of markets, monthly price data for an extensive list of item-measurement unit combinations that are captured as part of the IHS5/IHPS data collection on food consumption, and, separately, agricultural production, and (ii) capture kilogram-equivalent conversion factors for all non-standard measurement units used in quantification of the aforementioned food consumption and agricultural production items. The latter improved the existing set of region-specific conversion factors and were used in the computation of the IHS5/IHPS consumption aggregates. The determination of the item-unit combinations that were featured in the Market Survey questionnaire was based on the analysis of the data from the past rounds of the IHS and IHPS in 2010, 2013 and 2016. The Market Survey collected data on Android tablets and a Computer-Assisted Personal Interviewing (CAPI) application that was designed using Survey Solutions. Moreover, the selection of the markets and the decisions regarding their temporal distribution were finalized prior to the start of the IHS5/IHPS fieldwork. This process sought to (i) maximize the visits to the specific markets that were associated with the sampled IHS5/IHPS enumeration area (EA) locations and (ii) ensure that the sampled markets were visited in sync with the IHS5/IHPS field teams’ visits to the associated EAs. This meant that some markets may have been visited once while others could have been visited multiple times during the fieldwork. Furthermore, the Market Survey was piggybacked on the monthly consumer price index (CPI) fieldwork operations and was implemented by the survey teams that were co-supervised by the NSO Prices Department (which is also responsible for the CPI) and the NSO IHS5/IHPS Survey Management Team. In specific months, some markets ended up being visited for both the CPI data collection and the Market Survey – albeit using different questionnaires. 5 Overall, a total of 1,071 visits were made to 377 markets over the 12-month survey period, spread across all 32 districts in Malawi. 47 percent of the selected markets were visited once during the survey period; 40 percent were visited between 2 to 5 times; and 13 percent were visited more than 5 times, mainly because they are the main markets in the different regions or districts. Table 1 provides an overview of the markets visited by month and region. Table 1 Distribution of Market Visits by Month and Region Month Northern Central Southern April 2019 9 14 19 May 2019 19 30 47 June 2019 10 33 37 July 2019 8 26 45 August 2019 17 48 52 September 2019 13 36 37 October 2019 14 30 41 November 2019 20 38 46 December 2019 5 19 29 January 2020 23 41 55 February 2020 13 24 40 March 2020 16 36 46 April 2020 7 19 9 Total 174 394 503 5 The CPI Survey collects data on food prices and weights (only in standard units of measurement) and non-food prices for a fixed basket of foods specifically to measure inflation. 5 The Market Survey aimed to collect measurements of unit-specific prices and weights for a total of 163 food consumption and agricultural produce items. On food consumption specifically, the market survey collected information regarding 138 items and their associated measurement units – for a total of 534 item-unit combinations (i.e., approximately 4 measurement units per item). These 138 items represented 96 percent of the items listed in the IHS5 food consumption module and included 49 were elementary goods that were quality or variety-differentiated versions of 18 items that were included in the IHS5 food consumption module. Table A9 in Appendix 2 provides a full list of these elementary goods that were included in the market survey. For instance, IHS5 “Beef” entry was disaggregated, as part of the market survey, into “Beef with bones”, “Beef without bones”, “Ham beef”, “Liver beef”, “Minced beef”, “Rump steak beef”, and “Fillet beef” because these categories are expected to have differences in prices that would otherwise have been lost by only capturing the single item “Beef”. During each market visit, the survey team sought to collect kilogram weight and price information from up to three different vendors for each of the 534 item-unit combinations in the market survey questionnaire. This gives us highly disaggregated price data and ensures high precision in capturing spatial and temporal differences in prices across a wide range of items in Malawi. A total of 435,956 data points were collected across the markets and the item-unit combinations during the 12-month fieldwork. The full description of the market data collection and processing is discussed in Appendix 1. 3 Hicksian Separability: Are Relative Prices of Elementary Goods Constant across Space and Time? The measurement of household living standards and poverty in many developing countries, including Malawi, relies on unit values to proxy for prices faced by households in different localities and time periods. Unit values are ratios of “item-level” expenditures to associated quantities of consumption - commonly specific to food consumption at home and based on most knowledgeable respondents’ self-reports. The length and specificity of HCES food consumption modules exhibit significant cross- country heterogeneity. As such, food consumption items, referred to as “commodity groups”, can include a mix of (i) variety/quality-differentiated versions of specific food types (e.g., broken rice, medium grain rice and long grain rice, being listed as separate items), (ii) specific food types broken down within aggregate food groups, however without variety/quality differentiation (e.g., Cassava, Sweet Potato, Yellow Potato, being listed as separate items under the Roots and Tubers food group), and/or (iii) aggregate food groups that may appear as single line items in a module but that may combine different types of food items (e.g. Vegetables and Fruits). Under the assumption of Hicksian separability, if the price vector for the elementary goods within a group is decomposed into (i) a scalar term that raises or lowers the price level of all goods in the group across locations, and (ii) a reference price vector of the relative price of each good within the group, it is the inter-area scalar variation that dominates intra-group variation in relative prices (Deaton, 1988). Were this not true, when the unit value from one household is compared to the unit value of a household elsewhere (or to the unit values of the same household in a different season), we would not know if the difference in the unit value is because prices are different in the two places (or two seasons), or because the households are consuming a different mix of elementary goods within the group. 6 Taking maize flour as an example, one driving force for changing the composition of elementary goods within the group is that relative prices of the various types of maize flour may not be constant over space and time. If Hicksian separability does not hold, the poverty analysis risks confusing quality of living (buying higher-quality maize flour) with the cost of living (facing a higher price for all maize flour). There may be several reasons why relative prices within a food group may vary over time and space. If transport, storage, and processing costs are specific and not ad-valorem, then relative prices are unlikely to be constant over time and space. This effect is well documented as the Alchian-Allen effect (Borcherding and Silberberg, 1978; Gibson and Kim, 2015) and it will lead to relative price of quality varying over space and time. The integrated implementation of the Market Survey and the IHS5 gives us an opportunity to examine the evidence for Hicksian separability over space and time. Before formally testing for Hicksian separability, we provide descriptive evidence on relative prices across space (at the district-level) for selected IHS5 consumption food items. 6 Figure 1 shows the variation across space in the price ratio of elementary versions of the selected food items. The figure suggest that within-item price ratios are not constant over districts. Using rice as example, while there is 1.3 times premium in the district median price of medium grain rice relative to broken rice across the Northern districts, the premium declines and is even non-existent in some of the districts in the South. Figure 1 Price ratio of selected food items across districts in Malawi 6 These goods are selected based on their importance in Malawian diets as determined by their budget share. 7 3.1 Method To test for Hicksian separability over space, we check if estimated differences in prices between areas or over time for a given commodity group are the same regardless of which elementary good within the consumption item/group is used to represent the local price. The spatial level of all analysis presented is the district-level. This is because of sparse data at levels below the district. We implement the following regression: = + + + + (1) where g and m denote elementary good and market, respectively; p is market-specific elementary good median price computed over time; D is the vector of district-fixed effects; X is the vector of elementary good identifiers; and α and µ denote constant and error term, respectively. This regression is estimated by consumption item or food group (e.g., rice) using the pooled observations of elementary products (e.g., different types of rice) in that food group. The elementary products in the market survey range from two (sugar) to eight (beef) depending on the food group. If we reject the coefficient = 0 for all districts, we can conclude that the pattern of district price differences is sensitive to which of the elementary goods is used – in violation of the Hicksian separability assumption. This would suggest that using a single representative good to estimate inter-district price differences may cause bias since a different pattern of area-fixed effects results from using one elementary good rather than the others. For Hicksian separability across time, we implement the following regression: = + + + + (2) where g, m, and t denote elementary good, market, and month, respectively; p is month-specific median price in each market; T is the vector of month fixed effects; X is the vector of elementary good identifiers; and α and µ denote constant and error term, respectively. This regression is again estimated by food group (e.g., rice) using the pooled observations of elementary products (e.g., different types of rice) in that food group. If we reject = 0 for all months, we can conclude that the pattern of price differences over time is sensitive to which of the elementary goods is used – again in violation of the Hicksian separability assumption. This would suggest that using a single representative good to estimate inter-period price differences may cause bias since a different pattern of time effects results from using one elementary good rather than the others. 3.2 Results Table 2 reports the results from the estimation of Equation 3 (spatial test) by food group – specifically the F-statistic and the p-value associated with the test of = 0 for all districts. We reject this hypothesis for all food groups, which implies the assumption of Hicksian separability across space is not defensible. We do not find that relative prices of goods within a commodity group are constant over space, as can be seen from the sensitivity of the area-fixed effect to the choice of elementary good. 8 Table 2 Spatial Hicksian Separability Test Dimension = Spatial # of Elementary Goods F-stat P-value R-sq N in Food Group Maize Flour 5 49.33 0.0000 0.96 1174 Rice 3 8.59 0.0000 0.66 780 Bread 2 13.64 0.0000 0.55 684 Buns 2 9.45 0.0000 0.54 739 Cassava 2 24.75 0.0000 0.68 544 Irish Potato 2 5.41 0.0000 0.43 717 Pigeon Pea 2 25.51 0.0000 0.81 670 Beans 3 9.35 0.0000 0.60 575 Onion 2 10.31 0.0000 0.53 677 Chinese Cabbage 2 18.77 0.0000 0.53 405 Eggs 2 126.29 0.0000 0.91 678 Beef 8 26.62 0.0000 0.81 1359 Pork 2 8.50 0.0000 0.81 586 Chicken 5 18.40 0.0000 0.67 1399 Banana 2 8.09 0.0000 0.55 753 Fresh Milk 2 11.50 0.0000 0.71 273 Sugar 2 133.72 0.0000 0.93 687 Cooking Oil 4 62.99 0.0000 0.86 1471 Note. This table reports the results of whether pattern of district price differences is sensitive to the choice of elementary goods used. F-stat, P-value, and R-sq are for the hypothesis of no difference in patterns of prices across districts. Table 3 reports the results from the estimation of Equation 4 (temporal test) by food group – specifically the F-statistic and the p-value associated with the test of = 0 for all months. We reject this hypothesis for all food groups except for Irish Potato and Beans, and this result implies that the assumption of Hicksian separability across time is also not defensible for most items. 9 Table 3 Temporal Hicksian Separability Test Dimension = Temporal # of Elementary Goods F-stat P-value R-sq N in Food Group Maize Flour 5 19.64 0.0000 0.86 1857 Rice 3 6.02 0.0000 0.31 1357 Bread 2 3.24 0.0001 0.21 1221 Buns 2 3.41 0.0001 0.09 1296 Cassava 2 3.01 0.0015 0.11 1017 Irish Potato 2 1.38 0.1674 0.21 1360 Pigeon Pea 2 7.89 0.0000 0.43 869 Beans 3 2.29 0.1307 0.12 971 Onion 2 4.32 0.0000 0.15 1282 Chinese Cabbage 2 3.30 0.0694 0.12 992 Eggs 2 67.76 0.0000 0.63 1236 Beef 8 2.93 0.0000 0.40 1670 Pork 2 4.26 0.0000 0.13 748 Chicken 5 1.83 0.0005 0.09 1963 Banana 2 11.13 0.0000 0.31 1621 Fresh Milk 2 3.24 0.0003 0.26 405 Sugar 2 21.85 0.0000 0.32 1247 Cooking Oil 4 39.43 0.0000 0.54 2780 Note. This table reports the results of whether pattern of district price differences is sensitive to the choice of elementary goods used. F-stat, P-value, and R-sq are for the hypothesis of no different in patterns of prices across districts over time. Taking advantage of the spatial and temporal dimensions of our data, we combine both space and time dimensions by testing for Hicksian separability across space (i.e., estimating Equation 3) separately with observations elicited during the harvest season (April 2019 to September 2019 and including April 2020) versus the lean season (October 2019 to March 2020). Table 4 reports the results from the estimation of Equation 1 by food group during the harvest season and lean season, respectively. We also reject the assumption of Hicksian separability across space in both harvest and lean seasons for most food groups. 10 Table 4 Spatial Hicksian Separability Tests in Harvest and Lean seasons Harvest period Lean period # of Elementary Goods in F-stat P-value R-sq N F-stat P-value R-sq N Food Group Maize Flour 5 10.32 0.000 0.94 955 17.15 0.000 0.92 902 Rice 3 3.47 0.000 0.54 648 2.92 0.000 0.46 709 Bread 2 3.48 0.000 0.21 624 12.45 0.000 0.39 597 Buns 2 7.63 0.000 0.42 724 6.63 0.000 0.49 572 Cassava 2 5.73 0.000 0.34 491 7.71 0.000 0.39 526 Irish Potato 2 4.96 0.000 0.33 672 2.7 0.000 0.29 688 Pigeon Pea 2 6.2 0.000 0.58 475 0.07 0.793 0.44 394 Beans 3 1.23 0.254 0.37 495 NA NA NA NA Onion 2 2.68 0.000 0.3 638 2.28 0.002 0.27 644 Chinese Cabbage 2 9.21 0.003 0.4 497 NA NA NA NA Eggs 2 15.15 0.000 0.42 620 28.86 0.000 0.69 616 Beef 8 5.83 0.000 0.69 974 9.13 0.000 0.67 696 Pork 2 2.16 0.005 0.6 433 12.17 0.000 0.61 315 Chicken 5 2.89 0.000 0.33 1052 6.69 0.000 0.41 911 Banana 2 4.31 0.000 0.39 805 11.32 0.000 0.55 816 Fresh Milk 2 2.27 0.082 0.39 217 NA NA NA NA Sugar 2 47.6 0.000 0.78 668 4.68 0.000 0.25 579 Cooking Oil 4 5.00 0.000 0.33 1388 9.36 0.000 0.54 1392 Note. This table reports the results of whether pattern of district price differences is sensitive to the choice of elementary goods used. F-stat, P-value, and R-sq are for the hypothesis of no difference in patterns of prices across districts in Harvest and Lean periods. Beans, Chinese cabbage, and Fresh milk are not included in the results for the lean season due to insufficient number of price observations for the associated elementary goods during that time. We find strong evidence that within-group prices are not constant over time and space for most items. Inter-district and inter-month differences captured in unit values will thus be capturing both differences in quality mix and differences in prices. Our results are similar to the existing evidence on Hicksian separability found in Viet Nam by Gibson and Kim (2015). Their study found that relative prices within food groups were not constant across space in Viet Nam and suggests the Alchian-Allen effect as the mechanism for why Hicksian separability fails. The Alchian-Allen effect implies that if the prices of two substitutable goods, such as high- and low- quality versions of the same item, are both increased by a fixed per-unit amount, consumption will shift toward the higher-grade product (Alchian and Allen, 1967; Gould and Segall, 1969; Borcherding and Silberberg, 1978). This means that when the prices of two elementary goods in the same food group are both increased by a fixed per-unit amount such as a transportation or storage cost, consumption will shift toward the higher-grade product. In other words, with fixed charges for transportation and storage, relative prices will be expected to vary across time and space, in violation of what is to be expected with Hicksian separability. For goods with a quality gradient over which it costs similar fixed amounts to transport such goods over space and store them over time, we can 11 expect to see a clear pattern of decline in the price ratio of quality in areas far away or over time from excess supply points: ℎ ℎ + > (3) + Where ℎ is price of high-quality gradient elementary items of good B high-quality gradient of good ; is price of low-quality gradient elementary items of good ; and is a fixed amount to transport (store) goods over space (time). In what follows, we check for evidence of the Alchian-Allen effect as the mechanism by which the Hicksian separability assumption is violated in Malawi. To do so, we use beef as an example of a product with a quality gradient and for which the cost of transporting the high- and low-grade versions should be similar. Next, we define a set of markets that should be the excess supply points for beef in Malawi. To identify excess supply points, we relied on (i) an NSO- supplied list of main markets and the items considered to be a main product in the market, and (ii) FEWS NET (2018). Subsequently, we estimate the following regression: = + 1 + (4) where i and m denote food group (beef) and market, respectively; is the price ratio of high/low quality observations for a given food group (beef in this case) in market ; is the Euclidian distance in kilometers between the market that a given price ratio value is associated with and the reference market for beef (based on GPS coordinates for the markets); and α and µ denote the constant and error term, respectively. Table 5 presents the results of our test, based on distance measures with respect to three different excess supply points (i.e., reference markets), namely Nsanje Boma Market, Blantyre City Market, and Lilongwe Area 36 Market). Table 5 Test of Alchian-Allen effect: Beef Beef Nsanje Boma Market Blantyre City market Lilongwe Market Distance (Kms) -0.0151*** -0.0155*** -0.0144** (0.005) (0.005) (0.007) Constant 1.239*** 1.216*** 1.202*** (0.025) (0.019) (0.021) Observations 302 302 302 R-squared 0.034 0.032 0.013 Note. Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1. The price ratio of quality (elementary goods) used is the ratio of Beef without Bones to Beef with Bones. Reference markets are the main markets in Blantyre City, Nsanje Boma, and Lilongwe Market-Area 36, as determined by the NSO-supplied list of main markets for specific products and FEWS NET (2018). The results indicate that the price ratio of high-quality beef to low-quality beef falls by around 1.4 to 1.5 percentage points for every 100 kilometers away from the reference markets of Nsanje Boma, Blantyre City and Lilongwe Market-Area 36. This result is consistent with what we would expect based on Equation 3 and indicates that transport cost represents an important part of transaction costs in Malawian markets (Fafchamps and Gabre-Madhin, 2006). 12 Given the evidence that Hicksian separability fails, this implies that unit values will constitute biased proxies for prices in Malawi, as unit values will be capturing both differences in item quality and prices. We now turn to the comparative assessment of household consumption and poverty estimation based on unit values versus market prices. 4 Comparison of Unit Value- versus Market Price-Based Welfare Analyses The prevailing approach to household consumption and poverty estimation based on the Integrated Household Survey in Malawi has relied on unit values as proxies for prices since 1997/98 (Malawi National Statistical Office, 2021). The results from the previous section have shown that relative prices of elementary goods within a group vary, which in turn means unit values will inaccurately represent food group price levels across locations and can bias consumption and poverty estimation. Given the availability of an alternative source of price data at our disposal, we compare unit value-based estimates of household consumption, price deflators and poverty to those that are obtained by an alternative estimation strategy that is based on market prices. We focus on three areas where prices come into welfare estimation, as summarized in Table 6. Table 6 Framework for the Use of Price Proxy in Welfare Estimation Options Description Estimation of Price Valuation of Estimation of Poverty deflators Household line consumption A Current Unit Value Unit value-based Unit value-based Unit value-based Approach price deflators household estimation of poverty consumption lines valuation B An alternative Market Market price-based Market Price-based Market Price-based Price based approach deflators household estimation of poverty consumption lines valuation Note. This framework describes the different stages of using prices in the estimation of welfare. For our analysis, we keep consistent with the methodology for the estimation of poverty and inequality as described by the Malawi National Statistical Office (2021), with the only difference being that we use market prices instead of unit values in our calculations. Further information on the design of the Fifth Integrated Household Survey (HIS5) 2019/2020 can be found in Malawi National Statistical Office (2020). We discuss the comparison of the estimates of price deflators, consumption valuation, and derivation of poverty lines across our unit value and market price approaches below. 4.1 Estimation of Price Deflators The prevailing choice of welfare measure in Malawi is the total household consumption that comes from aggregating value of food consumption and non-food expenditures. To ensure comparability across households across the country surveyed in different periods and different areas, consumption estimates must be adjusted for differences in price over time and across space. The IHS5 survey was from April 2019 to April 2020 and adjustment must be made for changes in purchasing power over 13 this time, as well as adjustment for differences in purchasing power over space. In Malawi, a spatial– temporal Paasche price index is employed to account for differences across space and time. The temporal adjustment is a regional-specific adjustment implemented using a combination of regional monthly food index derived from unit values of food items in IHS5 and official non-food CPI for non-food items. The food index in region and month is a Paasche price index calculated as: , = � , ,, (5) =1 Where ,, = |,2019 i.e., the relative price of item in region and month . , is the average budget share for item in region . This food index is then combined with official non- food CPI using the food and non-food consumption shares from official data. The regions are (i) Urban, (ii) Rural North, (iii) Rural Center, and (iv) Rural South. Similar to the temporal price adjustment, a regional spatial price index is also estimated to account for differences in prices across regions, the regional food index is derived from unit values from IHS5, and these are combined with the official regional non-food CPI to generate the regional spatial price index. The spatial food index in region is a Paasche price index calculated as: = � , , (6) =1 Where , is the relative price of item in region and , is the average budget share for item in region . The Spatial–temporal Paasche price indices are then created by combining the temporal indices with the regional spatial indices to help capture the variation in price over both space and time. Further details on the methodology for generating the spatial and temporal price index are described by the National Statistics Office and World Bank Poverty and Equity Global practice (2018) and the Malawi National Statistical Office (2021). We follow the same approach, but instead of deriving the food index from unit values of food items like typically done in Malawi, we derive these indices using market prices observed from the Market Survey. For items that had multiple elementary products 7 captured in the Market Survey, there will not be a 1:1 concordance between market prices and the IHS5 consumption module used to derive the budget shares , . For these items, we take a geometric mean of the regional relative prices 8 of the elementary items in these food groups and then combine this with the budget share of the food group when forming the market price-based price deflators. The averaging of price relativities rather than prices treats each multiple elementary market survey item equally when forming the group-level 7 For all the consumption items with multiple elementary products in the market survey, 16 items had more disaggregation in the market survey than the consumption module of IHS5. Maize flour (Ufa) and Maize (Not as Ufa) had the same level of disaggregation in the consumption module of the IHS5 as the market survey and thus had a 1:1 concordance when combining the market price with the budget share weights. See Appendix 2 for details on the consumption items and their elementary products (disaggregation) in the Market Survey. 8 This elementary aggregation issue is common in CPI estimation (Graf, 2020) and it is suggested that a Jevons index (geometric mean) should be used in the aggregation of multiple items in the elementary aggregate when there are no weights. 14 relative price. Figures 2 and 3 present a comparison of the spatial–temporal price deflators from the unit value approach (current method) with our alternative market price-based deflators. Figure 2 Comparison of Spatial and Temporal Deflators Based on Unit Values and Market Prices Spatial and temporal price deflators Spatial and temporal price deflators Unit Value proxy Market price 115 115 110 110 105 105 100 100 95 95 2019m4 2019m7 2019m10 2020m1 2020m4 2019m4 2019m7 2019m10 2020m1 2020m4 Year and Month of survey, GC Year and Month of survey, GC Urban Rural North Urban Rural North Rural Centre Rural South Rural Centre Rural South Figure 3 Spatial and Temporal Deflators by Areas: Comparison of Unit Value Proxy and Market Price Comparing the unit value and market price-derived spatial–temporal price deflators, some interesting patterns emerge. In Urban Malawi, the unit value-derived deflator values are higher than their 15 comparators based on market prices. In Rural North, the opposite is true. In Rural South and Rural Center, the results are mixed. In Rural Center, the unit value-derived deflator values are higher than their comparators based on market prices during the last three quarters of the fieldwork. In Rural South, the market price-based deflator values are higher than their comparators based on unit values for the first three quarters of the fieldwork, after which there appears to be more of a convergence. Our results imply a different ranking of regional price differences when comparing unit value or market price-derived price deflators. Indicative of the fact that unit values could be capturing both differences in prices and quality, Urban Malawi shows the highest cost of living when unit values are used, but for market prices it is the Rural North that is the most expensive region. This pattern of price deflators is suggestive of the fact that urban residents are likely to consume higher-quality products, and the inter- area price differences captured by unit values are a mix of both quality and price differences. Finally, as part of the comparison of the unit value and market price-based price indices, we run a regression of the market price-based index on the unit value-based index, after limiting the computation of the indices to the common food items at the same level of disaggregation in the market survey and the household survey (i.e., excluding items with multiple elementary specification in the market survey and items not included in the market survey – primary those that are listed in “other specify categories” as part of the household survey). If unit value and market prices were perfect proxies, we could expect a coefficient of 1 on the unit value index in a regression of the market price index on the unit value price index. Our results in Table 7 show that for each region, the coefficient on the unit value is significantly different from 1 which indicates differences in derived price indices for seemingly identical items across household and market surveys. These results show that differences in price index derived from the market price and unit values are not driven by the disaggregation of some items in the market survey and generally the process of consumers’ estimation of unit value through the valuation of consumption of items leads to different conclusions about price indices than what is obtained from observing market prices. Table 7 Regression of Market Price-Based Spatial-Temporal Deflators on Unit Value-Based Deflators for Items with One-to-One Mapping in Market Survey and Household Survey Dependent Variable: Urban Rural North Rural Center Rural South Market Price-Based Index Unit Value-Based Index 0.5251*** 0.4491*** 0.3673*** 0.6828*** [0.1485] [0.1420] [0.0711] [0.1126] Constant 36.1523*** 53.8786*** 53.1815*** 29.4820*** [11.2004] [10.7284] [6.2153] [9.1587] Observations 13 13 13 13 R-squared 0.5321 0.4762 0.7080 0.7697 F-Test (Unit value Coeff. =1) 10.23 15.04 79.15 7.94 Note: Standard errors in brackets *** p<0.01, ** p<0.05, * p<0.1. The price indices are derived using items that can be mapped one-to one between the Market Survey and IHS5 consumption module. It excludes that have multiple elementary specifications in the market survey, namely Rice, Bread, Buns, scones, Cassava tubers, Irish Potato, Bean, Pigeon pea (Nandolo), Onion, Chinese cabbage, Eggs, Beef, Pork, Chicken, Banana, Fresh milk, Sugar, Cooking oil, Spices. It also excludes unspecified items in IHS5 survey that are not captured in the Market Survey e.g., “other specify categories”. 16 4.2 Valuation of Household Consumption Next, we examine the implication of our choice of price proxy for the valuation of consumption. The current approach in Malawi derives unit values by dividing (a) the self-reported monetary valuations of purchased food items that were consumed at home with (b) the associated quantity of consumption that is calculated in kilogram-equivalent terms. These unit values are then used to impute the monetary value for the total quantity of food items that were consumed at home during the last 7 days. This takes the following cascading medians approach where median unit values are computed at the district level and if missing are imputed with median values from the immediate upper level provided there are sufficient observations to obtain a reliable estimate (in this case more than 10 observations). From purchases of items, the unit value used in the valuation is calculated as the median unit value for that item in that district during the same month provided there were sufficient observations to obtain a reliable unit value. If median unit value is missing at this level, the missing median unit value is replaced by the median unit value at the region-month level provided there are sufficient observations in that region in that period in which case the unit value is set to missing. If missing at the region-month level, the missing median unit value is replaced by the median unit value at the region level. If missing at this level, the missing unit value is imputed by the median unit value of the item at the national level. This imputation process is illustrated below: , = �ℎ |, � , = �ℎ |, � If , is missing or less than 10 observations ℎ = = �ℎ |� If , is missing or less than 10 observations = �ℎ |, � If is missing or less than 10 observations Where ℎ is the unit value of item household ℎ, , is the median unit value of item in district at month . , is the median unit value of item in region at month . is the median unit value of item in region and is the median unit value of item nationally. For the alternative market price measure, we follow a similar cascading medians approach as the unit value valuation. For each item at the household level, the item median market price at the district level in the same month of visit is used to value household consumption in that district. If the median market price at the district-month level is missing, it is imputed with the item median market price at the region in the same month. If missing at the region month level, it is imputed with the item median market price at the region level and if missing at the region level, it is imputed with the median item price at the national level. This imputation process is as follows: , = �ℎ | , � , = �ℎ | , � If , is missing ℎ = = �ℎ |� If , is missing = �ℎ |, � If is missing Where ℎ is the market price of item household ℎ, , is the median market price of item in district at month . , is the median market price of item in region at month . is the median market price of item in region and is the median market price of item nationally. 17 We compare the consumption aggregate obtained using the current approach with the alternative aggregate that is based on prices from the market survey. Like in the formation of price deflators, for the 16 consumption items where there is no 1:1 concordance between the elementary good in the market survey and the food group in IHS5, we use a geometric mean of the elementary prices of the food group. Using geometric means allows us to be consistent with the way elementary prices have combined in the derivation of price indices, and items that are more expensive will have a lesser influence on the geometric mean than on the arithmetic mean. Table 8 presents the comparison of mean nominal household consumption by COICOP classification category. For nominal consumption, by design, there are no differences between unit value and market price analysis for alcohol and tobacco and non-food items since they were not covered in the Market Survey. For items not covered in the market survey, we use unit values to compute nominal consumption for these items in the market price-based analysis. Only the Food and Beverage and the Hotels and Restaurants COICOP categories differ between both approaches (due to vendor food items, which fall under the Hotels and Restaurants COICOP category being covered in the Market Survey). Tests of differences in means for the Food and Beverage and Hotels and Restaurants categories show statistically significant difference between the unit value-derived valuation and the market price- derived valuation. Mean household consumption for Food and Beverage in the market price approach is 32 percent higher than the unit value approach. Mean household consumption for the Hotels and Restaurants COICOP category is around 5 percent higher than in the unit value approach, although this also reflects that vendor foods only form a small proportion of this COICOP category. Table 9 presents the comparison of real mean household consumption by COICOP classification category. To calculate real consumption, household consumption is adjusted by the spatial–temporal price deflators. For real household consumption, there are differences in both food and non-food consumption estimates. This is because the non-food sub-aggregates are now being deflated by different price deflators derived from unit values or market price (of food). We find statistically significant differences in real means in all COICOP categories at conventional significance levels. 9 The difference in the non-food categories is indicative of the impact that the differently derived price deflators have on the estimation of welfare in Malawi. Figure 4 presents the density distribution of nominal and real total household consumption derived using the unit value and market price approaches. The total consumption derived from the market price approach lies to the right and has a longer right tail than that derived from unit value approach. This is consistent with the results in Tables 8 and 9 which shows higher mean household consumption for households from the market price approach. The results from the Kolmogorov-Smirnov (KS) tests of the equality of distributions, though not reported here, also reject the hypothesis (at the 1 percent level) of the equality of distributions based on the unit value versus market price approach. 9 Tests of differences in means are statistically significant for all COICOP categories at the 99 percent level except for Health (90 percent) and Clothing and Footwear (95 percent). 18 Figure 4 Density distribution of Nominal and Real Household Consumption from Unit Value and Market Price Approach Nominal Consumption Derived from Real Consumption Derived from Unit Value and Market Price Approach Unit Value and Market Price Approach 1.000e-06 1.000e-06 Density Density 0 0 0 10000000 20000000 0 10000000 20000000 Total nominal annual consumption per household Total real annual consumption per household UV: Nominal Cons UV: Real Cons MP: Nominal Cons MP: Real Cons kernel = epanechnikov, bandwidth = 7.0e+04 kernel = epanechnikov, bandwidth = 6.6e+04 Finally, to understand the impact of prices on valuation of consumption, in Tables 10 to 13, we group individuals into deciles using the real household aggregate consumption derived from each price proxy and compare the decile ranking of individuals derived from each method. This shows whether the choice of price proxy has implications for the ranking of individuals in the welfare distribution. Our results show consistent ranking between the two approaches with more than 90 percent of observations from unit value rankings within one decile group ranking in the market price approach. 10 Results for quintile classifications are reported in Appendix Tables A10 to A13. 10 19 Table 8 Comparison of Nominal Consumption Estimates: Unit Value vs Market Price Approaches Unit Value Market Price Test of difference COICOP Category Mean Std. Err Share Mean Std. Err Share Std. Err T-Stat P-value Food and Beverage 606,359 4,853 55% 803,421 6,247 62% 2,267.7 86.9 0.000 Alcohol and Tobacco 8,548 540 1% 8,548 540 1% NA NA NA Clothing and Footwear 24,254 497 2% 24,254 497 2% NA NA NA Housing and Utilities 218,583 2,327 20% 218,583 2,327 17% NA NA NA Furnishings 42,455 1,185 4% 42,455 1,185 3% NA NA NA Health 17,211 449 2% 17,211 449 1% NA NA NA Transport 67,564 2,786 6% 67,564 2,786 5% NA NA NA Communication 28,957 743 3% 28,957 743 2% NA NA NA Recreation 6,984 364 1% 6,984 364 1% NA NA NA Education 41,713 1,859 4% 41,713 1,859 3% NA NA NA Hotels and Restaurants 10,123 227 1% 10,657 251 1% 71.3 7.5 0.000 Misc. Goods & Services 28,206 308 3% 28,206 308 2% NA NA NA Total Consumption 1,100,959 11,124 1,298,555 12,151 2,271.7 87.0 0.000 Note. Mean nominal household consumption by COICOP categories based on prices from market price survey and unit values and test of differences. Only Food and Beverage, and Hotels and Restaurants (due to vendor foods) categories differ in both approaches because items in other categories were not priced in the market survey. 20 Table 9: Comparison of Real Consumption Estimates: Unit Value vs Market Price Approaches Unit values Market Price Test of difference COICOP Category Mean Std. Err Share Mean Std. Err Share Std. Err T-Stat P-value Food and Beverage 574,866 4,481 55% 767,693 5,887 62% 2,089.4 92.3 0.000 Alcohol and Tobacco 8,045 495 1% 8,116 506 1% 23.0 3.1 0.002 Clothing and Footwear 23,125 470 2% 23,176 472 2% 25.7 2.0 0.049 Housing and Utilities 206,632 2,104 20% 208,959 2,187 17% 148.5 15.7 0.000 Furnishings 40,068 1,076 4% 40,502 1,120 3% 65.2 6.7 0.000 Health 16,576 434 2% 16,616 437 1% 21.6 1.9 0.063 Transport 63,471 2,549 6% 64,283 2,618 5% 116.6 7.0 0.000 Communication 27,336 698 3% 27,548 706 2% 38.9 5.4 0.000 Recreation 6,448 330 1% 6,593 342 1% 16.9 8.6 0.000 Education 38,857 1,707 4% 39,498 1,755 3% 82.6 7.8 0.000 Hotels and Restaurants 9,617 213 1% 10,206 241 1% 70.1 8.4 0.000 Misc. Goods & Services 26,731 286 3% 26,916 290 2% 21.1 8.8 0.000 Total Consumption 1,041,771 10,144 1,240,107 11,431 2,133.0 93.0 0.000 Note. Mean real household consumption by COICOP category based on prices from market price survey and unit value proxy and test of differences. 21 Table 10 Number of Individuals in Aggregate per Capita Expenditure Decile Group: Unit Value vs Market Price Approach (Unit Value approach classification is used as the base) Unit Value Deciles Market Price 1 2 3 4 5 6 7 8 9 10 Total Deciles 1 1,473,951 306,263 22,906 6,378 4,244 - - - - - 1,813,743 2 285,757 1,030,676 462,556 30,668 3,111 - 1,528 - - - 1,814,297 3 51,076 357,569 884,433 471,898 33,046 10,774 4,157 - - - 1,812,953 4 4,019 83,379 350,536 847,493 495,554 28,862 3,253 - - - 1,813,096 5 - 27,191 71,570 330,501 862,758 483,631 36,910 963 - - 1,813,524 6 - 7,157 15,536 105,085 354,133 888,895 435,727 9,345 - - 1,815,879 7 - - 2,543 15,140 58,673 342,903 1,022,440 364,493 4,996 - 1,811,188 8 - - 3,215 6,433 5,018 51,968 290,071 1,183,186 273,084 - 1,812,976 9 - - - - - 4,322 18,918 250,674 1,401,855 137,383 1,813,153 10 - - - - - - - 4,013 133,480 1,675,804 1,813,296 Total 1,814,803 1,812,235 1,813,296 1,813,597 1,816,537 1,811,355 1,813,004 1,812,674 1,813,415 1,813,187 18,134,103 Table 11 Number of Individuals in Aggregate per Capita Expenditure Decile Group: Unit Value vs Market Price Approach (Market Price approach classification is used as the base) Market Price Deciles Unit Value 1 2 3 4 5 6 7 8 9 10 Total Deciles 1 1,473,951 285,757 51,076 4,019 - - - - - - 1,814,803 2 306,263 1,030,676 357,569 83,379 27,191 7,157 - - - - 1,812,235 3 22,906 462,556 884,433 350,536 71,570 15,536 2,543 3,215 - - 1,813,296 4 6,378 30,668 471,898 847,493 330,501 105,085 15,140 6,433 - - 1,813,597 5 4,244 3,111 33,046 495,554 862,758 354,133 58,673 5,018 - - 1,816,537 6 - - 10,774 28,862 483,631 888,895 342,903 51,968 4,322 - 1,811,355 7 - 1,528 4,157 3,253 36,910 435,727 1,022,440 290,071 18,918 - 1,813,004 8 - - - - 963 9,345 364,493 1,183,186 250,674 4,013 1,812,674 9 - - - - - - 4,996 273,084 1,401,855 133,480 1,813,415 10 - - - - - - - - 137,383 1,675,804 1,813,187 Total 1,813,743 1,814,297 1,812,953 1,813,096 1,813,524 1,815,879 1,811,188 1,812,976 1,813,153 1,813,296 18,134,103 22 Table 12 Proportion of Individuals in Aggregate per Capita Real Expenditure Decile Group: Unit Value vs Market Price (Unit Value approach classification is used as the base) Unit Value Deciles Market Price Deciles 1 2 3 4 5 6 7 8 9 10 Total 1 81.2% 16.9% 1.3% 0.4% 0.2% - - - - - 1,813,743 2 15.7% 56.9% 25.5% 1.7% 0.2% - 0.1% - - - 1,814,297 3 2.8% 19.7% 48.8% 26.0% 1.8% 0.6% 0.2% - - - 1,812,953 4 0.2% 4.6% 19.3% 46.7% 27.3% 1.6% 0.2% - - - 1,813,096 5 - 1.5% 3.9% 18.2% 47.5% 26.7% 2.0% 0.1% - - 1,813,524 6 - 0.4% 0.9% 5.8% 19.5% 49.1% 24.0% 0.5% - - 1,815,879 7 - - 0.1% 0.8% 3.2% 18.9% 56.4% 20.1% 0.3% - 1,811,188 8 - - 0.2% 0.4% 0.3% 2.9% 16.0% 65.3% 15.1% - 1,812,976 9 - - - - - 0.2% 1.0% 13.8% 77.3% 7.6% 1,813,153 10 - - - - - - - 0.2% 7.4% 92.4% 1,813,296 Total 1,814,803 1,812,235 1,813,296 1,813,597 1,816,537 1,811,355 1,813,004 1,812,674 1,813,415 1,813,187 18,134,103 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% % Ranked Within 97.0% 93.5% 93.6% 91.0% 94.3% 94.7% 96.4% 99.2% 99.7% 100.0% One Decile Table 13 Proportion of Individuals in Aggregate per Capita Real Expenditure Decile Group: Unit Value vs Market Price (Market Price approach classification is used as the base) Market Price Deciles Unit Value Deciles 1 2 3 4 5 6 7 8 9 10 Total 1 81.3% 15.8% 2.8% 0.2% - - - - - - 1,814,074 2 16.9% 56.8% 19.7% 4.6% 1.5% 0.4% - - - - 1,814,659 3 1.3% 25.5% 48.8% 19.3% 3.9% 0.9% 0.1% 0.2% - - 1,813,653 4 0.4% 1.7% 26.0% 46.7% 18.2% 5.8% 0.8% 0.4% - - 1,812,290 5 0.2% 0.2% 1.8% 27.3% 47.6% 19.5% 3.2% 0.3% - - 1,814,115 6 - - 0.6% 1.6% 26.7% 49.0% 18.9% 2.9% 0.2% - 1,812,636 7 - 0.1% 0.2% 0.2% 2.0% 24.0% 56.5% 16.0% 1.0% - 1,812,640 8 - - - - 0.1% 0.5% 20.1% 65.3% 13.8% 0.2% 1,817,768 9 - - - - - - 0.3% 15.1% 77.3% 7.4% 1,809,406 10 - - - - - - - - 7.6% 92.4% 1,812,860 Total 1,814,803 1,812,235 1,813,296 1,813,597 1,816,537 1,811,355 1,813,004 1,812,674 1,813,415 1,813,187 18,134,103 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% % Ranked Within 98.2% 98.1% 94.5% 93.4% 92.5% 92.4% 95.5% 96.3% 98.7% 99.8% One Decile 23 4.3 Derivation of Poverty Lines Our choice of price proxy also plays an important role in the estimation of the poverty line. The poverty line in Malawi is a national absolute poverty line derived using a Cost of Basic Needs (CBN) approach (Haughton and Khandker, 2009). Under this CBN approach, a food poverty line is determined by estimating the cost of meeting the food energy requirements from the foods that are eaten by the poor. The total poverty line is then derived by adding the food poverty line to the average value of non-food spending by households whose food consumption is close to the food poverty line. A household with consumption below the food poverty line is considered food poor. The choice of price proxy plays an important role in the estimation of the poverty line in two respects. Firstly, it directly informs the costing of the daily food basket of the poor. Secondly, it informs the spatial and temporal price deflators which are used to adjust household consumption prior to ranking of households to determine the reference group of the poor. The evidence laid out in Section 4.1 has shown different patterns of spatial and temporal price deflators emerge depending on whether our price deflators are derived from unit values or market prices. Thus, we estimate the poverty line using the market price proxy and compare it to the unit value approach. The current unit value-based poverty line in Malawi assumes a daily energy requirement of 2,215 calories and uses a reference population between the 5th and 6th decile rankings of the real aggregate household consumption distribution (National Statistical Office, 2021). We keep both assumptions for our market price analysis but in Appendix Table A14 and Table A15 (Appendix 4) examine the sensitivity of our market price derived results to these choices. Table 14 presents the daily unit value- and market price-based poverty lines from both approaches. We find that market price-based food and total poverty lines are around 49 percent higher than the unit value-based lines. However, aggregate consumption is also higher with the market price approach (Tables 8 and 9) and market prices lead to a different pattern of spatial and temporal price deflators (Figure 2). As such, the ultimate effects of the market price approach on the poverty estimates are not clear ex-ante. Next section uncovers these effects. Table 14 Comparison of Daily Poverty Lines from Market Price- and Unit Value-Based Price Proxies Daily Daily Reference group Non-Food Shares Food Poverty Line Total Poverty Line Deciles Calorie Market Market Unit Market Unit Value Unit Value Req. Price Price Value Price 2215 MK 277.5 MK 413.0 MK 454.4 MK 679.2 0.64 0.64 Deciles 5 and 6 Note. Daily food and total poverty line estimates (in Malawian Kwacha) derived from market price and unit value price proxies. 24 4.4 Poverty and Inequality Estimates In the previous sections, we have shown that the choice of price proxy does matter for price deflators, valuation of consumption, and poverty lines. In this section, we examine the implications for measures of poverty and inequality across space and time in Malawi. We compare the estimates of both food and total poverty from our unit value- and market price-based approaches. Our measure of poverty is the poverty headcount ratio, which can be estimated as part of the family of poverty indices proposed by Foster et al. (1984): 1 − = � � � ∗ ( < ) (9) =1 where is the consumption of individual ; is the total population; is the poverty line derived from either using the market price or unit value approach; ( < ) is an indicator function which is equal to 1 when individual consumption is below the poverty line and 0 when the consumption is above the poverty line. is a non-negative parameter. The poverty headcount index (α = 0) is the percentage of population whose consumption is below the total poverty line. We also report the food poverty line (food poverty) which is the percentage of population whose consumption is below the food poverty line. Our measure of inequality is the well-known Gini index, which measures the extent to which the distribution of consumption expenditure among individuals deviates from a perfectly equal distribution. A Gini index of 0 represents perfect equality, while an index of 1 implies perfect inequality. Additional inequality statistics are presented in Appendix 8. Table 15 presents the poverty rates by region and across all of Malawi. 11 For both food and total poverty, the current unit value approach shows that poverty is highest in the Rural Center, followed by the Rural South, and is lowest in urban areas. These spatial patterns are also confirmed by the market price analysis, but the market price results show a statistically significant higher level of poverty rates (in both food and total poverty) than the unit value approach. Nationally, the unit value approach estimates a poverty head-count rate of 51 percent, which is less than the market price approach of 64 percent. Total poverty rates derived from the market price approach are about 9 to 15 percentage points higher, with the biggest gap in the Rural Center region where the unit value approach estimates around 63 percent poverty head count rate compared to 76 percent for the market price approach. Taking a temporal view (Table 16), poverty is lowest in the first quarter and increases in subsequent quarters, peaking in the 4th quarter. These patterns are confirmed in the market price approach. Like in the spatial estimates, we find a statistically significant higher level of poverty in the market price approach. The choice of price proxy, however, does not seem to matter for inequality as we find similar spatial and temporal patterns in the levels of inequality from both approaches. 11 We provide a sensitivity analysis of food and total poverty estimates to changes in the daily calorie requirements from between 2,215 kcal and 2,815 kcal in Appendix Tables A10 and A11. 25 Table 15 National and Regional Poverty and Inequality Estimates: Comparison of Unit Value and Market Price Approach Food Poverty Total Poverty Inequality Estimates Test for difference Estimates Test for difference Gini-Unit Value Gini-Market Price Unit Market Unit Market Std. Std. T-Stat Std. error P-value T-Stat Std. error P-value Estimate Estimate Value Price Value Price Error error Urban 3.3% 7.7% 7.13 0.006 0.0000 19.2% 28.6% 10.46 0.009 0.0000 0.3901 0.0093 0.3762 0.0090 Rural- 9.8% 16.0% 5.59 0.011 0.0000 35.9% 51.3% 10.37 0.015 0.0000 0.3196 0.0079 0.2972 0.0073 North Rural- 29.5% 44.6% 18.91 0.008 0.0000 62.8% 75.9% 18.65 0.007 0.0000 0.3264 0.0052 0.3281 0.0050 Center Rural- 22.0% 33.6% 17.10 0.007 0.0000 56.7% 70.2% 21.36 0.006 0.0000 0.3254 0.0049 0.3222 0.0046 South National 20.5% 31.6% 26.77 0.004 0.0000 50.7% 63.7% 31.68 0.004 0.0000 0.3789 0.0039 0.3691 0.0037 Note. National and regional food and total poverty headcount rates derived from market price and unit value price proxy and test of differences between them. Table 16 Quarterly Poverty and Inequality Estimates: Comparison of Unit Value and Market Price Approaches Food Poverty Total Poverty Inequality Estimates Test for difference Estimates Test for difference Gini-Unit Value Gini-Market Price Unit Market Std. Unit Market Std. Std. Std. T-Stat P-value T-Stat P-value Estimate Estimate Value Price error Value Price error error error 1st 17.1% 25.9% 10.11 0.009 0.0000 46.3% 58.9% 13.59 0.009 0.0000 0.3691 0.008 0.3542 0.007 Quarter 2nd 19.5% 30.3% 13.93 0.008 0.0000 50.0% 63.1% 17.11 0.008 0.0000 0.3824 0.009 0.3702 0.009 Quarter 3rd 22.0% 31.4% 11.05 0.009 0.0000 50.7% 63.3% 15.17 0.008 0.0000 0.3836 0.007 0.3710 0.007 Quarter 4th 22.1% 36.0% 17.41 0.008 0.0000 53.9% 67.2% 17.50 0.008 0.0000 0.3772 0.006 0.3732 0.006 Quarter Note. Quarterly food and total poverty headcount rates derived from market price and unit value price proxy and test of differences between them. 26 Furthermore, the shares of individuals living in poor households, as estimated though the two approaches, show a high degree of consistency. For food (Table 17), we find that 97 percent of individuals identified as living in food poor households according to the unit value approach are equally identified as living in food poor households under the market price approach, and that 85 percent of individuals identified as living in non-food-poor households according to the unit value approach also identified as living in non-food-poor households under the market price approach. About 15 percent of individuals identified as living in non-food poor households according to the unit value approach are classified as living in food poor households under the market price approach. Table 17 Comparison of Food-Poor Individuals Based on Unit Value and Market Price Approaches Unit Value Market Price Not Food Poor Food Poor Total Not Food Poor 12,297,040 (85%) 108,556 (3%) 12,405,596 Food Poor 2,128,341 (15%) 3,600,166 (97%) 5,728,507 Total 14,425,381 3,708,722 18,134,103 Similar results emerge for total poverty (Table 18). We find that 99 percent of individuals identified as living in poor households according to the unit value approach are also identified as living in poor households under the market price approach. On the other hand, only 73 percent of individuals identified as living in non-poor households according to the unit value approach are also classified as living in non-poor households under the market price approach. About 27 percent of individuals identified as living in non-poor households according to the unit value approach are in fact classified as living in poor households under the market price approach. Table 18 Cross-tabulation of CBN Poverty Numbers from Unit Value and Market Price Approaches Unit value Market Price Non-Poor (CBN) Poor (CBN) Total Non-poor (CBN) 6,517,294 (73%) 62,605 (1%) 6,579,898 Poor (CBN) 2,418,154 (27%) 9,136,050 (99%) 11,554,204 Total 8,935,448 9,198,655 18,134,103 4.4.1 Validation of poverty and consumption estimates with nightlights We attempt to validate our estimated measures of poverty and consumption from both unit value and market price approaches by comparing them with an exogenous measure of economic activity – nightlights. Nightlights are increasingly gaining prominent in the remote sensing and economic literature as a good proxy for economic performance/activity especially some of the data available from the Visible Infrared Imaging Radiometer Suite (VIIRS) (Gibson, 2021). They have been used to estimate economic activity in data-poor settings including estimation of sub-national GDP level and have found to be good proxy for economic activity (Chen and Nordhaus, 2019; Sutton et al.,2007; Gibson, 2021; Gibson and Boe-Gibson, 2021). We examine the correlation between the competing poverty estimates and night lights at the district level, i.e., the sub-regional, lowest geographic area 27 for which the IHS5 consumption and poverty estimates are deemed to be representative. To do so, we estimate the following regression: , = + 1 ℎ, We take a log-log and levels approach where: • , are the district poverty rates derived from method (i.e., either using unit values or market prices as price proxies) • ℎ, are average VIIRS measured radiance for the month which data was collected from households in the district. The results reported in Table 19 are in line with the previous findings in the literature that indicate a strong association between night lights and measures of economic performance such as GDP per capita and poverty rates. As indicated by the R-squared estimates, in comparison to their unit value- based counterparts, the market price informed estimates of consumption and poverty consistently show a higher level of association with our exogenous measure of economic activity. Given that night lights will be picking up much more than just household sector activity, our main interest here is to show that both our market price derived estimates show similar level of association with an exogenous measure of economic activity as the unit value approach at sub-national levels. These results are also consistent at lower spatial scales at the territorial area (TA) and enumeration area (EA) levels which are reported in Appendix 6 (Appendix Tables A17 and A18). Table 19 Regression of Poverty Rates (CBN and Food) at district level on Night Lights: Comparison of Market Price vs Unit Value Estimates Log District Log District Log Log District District District District CBN CBN District District CBN CBN Food Food Poverty Poverty Food Food Poverty Poverty Poverty Poverty Rates (Unit Rates Poverty Poverty Rates Rates Rates Rates Value) (Market Rates Rates (Unit (Market (Unit (Market Price) (Unit (Market Value) Price) Value) Price) Value) Price) Log District Average -0.44*** -0.37*** -0.80*** -0.64*** Night Lights (0.07) (0.05) (0.20) (0.13) District Average -7.82*** -8.98*** -3.79*** -5.58*** Night Lights (1.59) (1.49) (1.05) (1.47) Constant 3.45*** 3.80*** 1.95*** 2.68*** 53.99*** 68.89*** 21.18*** 33.52*** (0.07) (0.06) (0.22) (0.14) (2.82) (2.66) (1.87) (2.61) Obs. 32 32 32 32 32 32 32 32 R-squared 0.58 0.64 0.34 0.44 0.45 0.56 0.30 0.33 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 28 5 Sensitivity Checks Comprehensive market price questionnaires are an exception in household surveys for a majority of low- and middle-income countries as household surveys in these countries prioritize collecting expenditure or income data over price data (Gibson 2013; Gibson and Rozelle 2011). The additional technical and financial requirements of fielding these surveys have often been an important concern preventing the implementation of detailed market price surveys alongside household surveys. This section examines the sensitivity of our market price derived poverty and inequality estimates to a reduction in the spatial coverage of the market survey (visiting less markets across districts) and reduction in item coverage (collecting prices of less items). We examine whether our market price results are different if we assume scenarios of “more modest” data collection both in terms of market coverage and item coverage. For the reduced market coverage, we consider scenarios where we visit the top 50 to 90 percent of markets in each district based on the number of available price observations from each market. Appendix Table A19 presents the distribution of the number of markets in the reduced market coverage scenarios. For the reduced item coverage, we consider scenarios where market prices are only collected for the most important items i.e., items that make up the top 50 to 90 percent of the household budget share. 5.1 Sensitivity of Poverty and Inequality Estimates to Item Coverage We first examine the sensitivity of our poverty and inequality estimates to reducing the item coverage in the market survey, i.e., instead of pricing almost all the items from the household survey in the market price survey, we examine how our estimates change if the market survey focused on pricing only a subset of main items, as determined by their budget share, ranging from 50 percent, 60 percent, 70 percent, 80 percent, and 90 percent of household consumption. In this context, a 50 percent item coverage means market prices are used for items that make up the top 50 percent of budget share at the national level with unit values used as the price proxy for the rest. This is meant to simulate a scenario in which the market price collection focused on the collection of prices of key items that are important in household consumption instead of all items. The derived poverty lines from each item coverage scenario are reported in Appendix Table A16. Table 22 presents the national and regional food and total poverty rates derived from the market price item coverage assumptions. As with the market coverage scenarios, we find very limited impact of reduced item coverage on inequality as measured by the Gini coefficient. However, for poverty rates, while the results show similar magnitudes under different scenarios, tests of statistical significance show significant differences between the poverty rates derived from the complete coverage and the reduced item coverage scenarios at the 95 percent level – except for food poverty rates in Urban areas, and Rural Center at 70-90 percent item coverage. For total poverty, we find also statistically significant difference between the complete survey poverty rates and the reduced item coverage scenarios at the 95 percent level – except for Rural North at 50 and 70 percent item coverage. Taken together, the sensitivity analyses pertaining to market survey indicate that there are no viable shortcuts in our existing market survey database that can provide us with poverty rates that are statistically indistinguishable from the estimates based on the complete dataset. 29 Table 20 Sensitivity of Poverty Rates to Item Coverage of Market Survey Food Poverty CBN Poverty Inequality Test of difference between Test of difference Item food poverty at complete between CBN poverty at Coverage item coverage and other complete item coverage Level coverage levels and other coverage levels Full Item Reduced T-stat Std. P- Full Item Reduced T-stat Std. P- Full Item Std. Reduced Std. Coverage item Err value Coverage item Err value Coverage Err Item Err coverage coverage Gini Coverage Gini National 31.6 32.3 -5.07 0.00 0.000 63.7 61.0 12.52 0.00 0.000 0.369 0.004 0.366 0.004 90 National 31.6 32.8 -7.50 0.00 0.000 63.7 58.7 17.69 0.00 0.000 0.369 0.004 0.367 0.004 80 National 31.6 33.1 -7.54 0.00 0.000 63.7 62.3 7.13 0.00 0.000 0.369 0.004 0.368 0.004 70 National 31.6 33.1 -6.40 0.00 0.000 63.7 59.2 17.00 0.00 0.000 0.369 0.004 0.365 0.004 60 National 31.6 33.0 -5.63 0.00 0.000 63.7 60.9 12.63 0.00 0.000 0.369 0.004 0.366 0.004 50 Rural-Center 44.6 45.0 -1.86 0.00 0.062 75.9 72.7 8.24 0.00 0.000 0.328 0.005 0.326 0.005 90 Rural-Center 44.6 45.0 -1.73 0.00 0.084 75.9 70.4 11.73 0.00 0.000 0.328 0.005 0.326 0.005 80 Rural-Center 44.6 44.5 0.22 0.00 0.827 75.9 73.5 6.73 0.00 0.000 0.328 0.005 0.325 0.005 70 Rural-Center 44.6 43.6 2.54 0.00 0.011 75.9 70.0 12.40 0.00 0.000 0.328 0.005 0.321 0.005 60 Rural-Center 44.6 42.9 4.21 0.00 0.000 75.9 71.3 11.09 0.00 0.000 0.328 0.005 0.321 0.005 50 Rural-North 16.0 16.7 -1.98 0.00 0.048 51.3 48.0 3.62 0.01 0.000 0.297 0.007 0.293 0.007 90 Rural-North 16.0 17.8 -3.48 0.01 0.001 51.3 44.3 5.39 0.01 0.000 0.297 0.007 0.293 0.007 80 Rural-North 16.0 19.4 -5.37 0.01 0.000 51.3 51.9 -0.86 0.01 0.392 0.297 0.007 0.296 0.008 70 Rural-North 16.0 20.0 -5.11 0.01 0.000 51.3 47.6 3.92 0.01 0.000 0.297 0.007 0.295 0.007 60 Rural-North 16.0 19.4 -5.03 0.01 0.000 51.3 50.7 0.98 0.01 0.328 0.297 0.007 0.295 0.007 50 Rural-South 33.6 34.7 -4.47 0.00 0.000 70.2 67.7 7.95 0.00 0.000 0.322 0.005 0.319 0.005 90 Rural-South 33.6 35.8 -6.82 0.00 0.000 70.2 65.7 11.32 0.00 0.000 0.322 0.005 0.319 0.005 80 Rural-South 33.6 36.5 -7.37 0.00 0.000 70.2 69.1 3.46 0.00 0.001 0.322 0.005 0.321 0.005 70 Rural-South 33.6 37.1 -8.31 0.00 0.000 70.2 66.6 9.16 0.00 0.000 0.322 0.005 0.321 0.005 60 Rural-South 33.6 37.7 -8.92 0.00 0.000 70.2 68.4 5.31 0.00 0.000 0.322 0.005 0.323 0.005 50 Urban 7.7 8.0 -1.18 0.00 0.237 28.6 26.9 4.47 0.00 0.000 0.376 0.009 0.375 0.009 90 Urban 7.7 8.2 -1.92 0.00 0.056 28.6 25.1 6.20 0.01 0.000 0.376 0.009 0.376 0.009 80 Urban 7.7 8.2 -1.76 0.00 0.079 28.6 27.4 3.62 0.00 0.000 0.376 0.009 0.377 0.009 70 Urban 7.7 8.4 -1.65 0.00 0.100 28.6 24.6 6.81 0.01 0.000 0.376 0.009 0.375 0.009 60 Urban 7.7 8.2 -1.04 0.00 0.296 28.6 26.1 5.54 0.00 0.000 0.376 0.009 0.376 0.009 50 Note: Sensitivity of item coverage reported above with complete market coverage 30 5.2 Sensitivity of Poverty and Inequality Estimates to Market Coverage Using market prices of items from each of our sensitivity analysis scenarios, we compute poverty rates and compare these rates with the complete market price survey results. Table 20 presents the daily food and total poverty lines from each of the scenarios. Food price lines under the sensitivity scenarios were between 1 and 14 percent higher compared to the complete market price line. Total poverty lines were between 12 percent less and 6 percent higher than the complete market price survey total poverty line. The estimated poverty rates based on the market prices from the reduced market survey locations are compared with the complete market survey estimates in Table 21. Table 21 Sensitivity of Poverty Lines to Spatial Coverage of Market Survey Price Proxy Approach Calorie Reference Group Daily Food Daily Total Non-food Req. Deciles Poverty Line Poverty Line Share Complete Price Survey 2215 Deciles 5 and 6 MK413 MK679 0.64 Reduced Price Survey-90% coverage 2215 Deciles 5 and 6 MK414 MK569 0.38 Reduced Price Survey-80% coverage 2215 Deciles 5 and 6 MK416 MK627 0.51 Reduced Price Survey-70% coverage 2215 Deciles 5 and 6 MK417 MK599 0.44 Reduced Price Survey-60% coverage 2215 Deciles 5 and 6 MK417 MK621 0.49 Reduced Price Survey-50% coverage 2215 Deciles 5 and 6 MK417 MK599 0.44 Note. Daily food and total poverty line estimates (in Malawian Kwacha) derived from unit value price proxy and market price surveys (complete and reduced samples). The results for food poverty rates derived under each reduced survey scenarios are slightly higher in magnitude than the estimates from the complete market coverage. Depending on which region, the figures indicate around 1 to 2 percent more people in food poverty in the reduced coverage scenarios. The food poverty results are closest in magnitude in the Rural Center region where the reduced scenarios food poverty estimates are between 0.1 and 0.6 percent of the complete coverage results and furthest in the Rural South where it is between 1.0 and 1.7 percent of the complete price survey results. However, although close in magnitude, tests of statistical significance between the reduced market coverage scenarios and the complete price survey reveal that these estimates are statistically significantly different from the complete market coverage results. Except for Rural Center, we reject the hypothesis that the food poverty rates are not statistically significantly different from the food poverty rates derived under the complete market price survey approach. For total poverty rates, the results under the reduced survey scenarios are lower in magnitude than the complete market survey derived results. Tests of statistical significance also show that the derived total poverty estimates are statistically significantly different from the complete scenario results in all coverage scenarios and at both national and regional levels. For inequality, we find very limited impact of reduced market coverage on inequality as measured by the Gini coefficient. Taken together, the findings indicate that for generating statistically consistent poverty estimates that are informed by market prices, it is essential to have a market survey that has a sizeable spatial and temporal overlap with household survey data collection, inclusive of price information on the same consumption items that are also featured in the household survey questionnaire. Indeed, given the evidence on the failure of Hicksian separability, the main benefit of a market survey is to provide proxies of local prices that people face for a well-defined set of items across a wide geographic area. 31 Table 22 Sensitivity of Poverty Rates to Spatial Coverage of Market Survey Food Poverty CBN Poverty Inequality Test of Difference Test of Difference Full Reduced T-stat SE P- Full Reduced T- SE P- Full Std.Err Reduced Std.Err Market Market Market value Market Market stat value Market Market coverage Survey Survey Survey Survey Survey Survey Gini Gini National 31.6% 32.2% 4.35 0.001 0.000 63.7% 52.8% -28.7 0.004 0.000 0.369 0.004 0.369 0.004 90% National 31.6% 32.3% 4.91 0.001 0.000 63.7% 59.1% -18.1 0.003 0.000 0.369 0.004 0.368 0.004 80% National 31.6% 32.3% 4.66 0.001 0.000 63.7% 55.7% -24.1 0.003 0.000 0.369 0.004 0.368 0.004 70% National 31.6% 32.2% 3.71 0.002 0.000 63.7% 58.0% -19.9 0.003 0.000 0.369 0.004 0.367 0.004 60% National 31.6% 32.7% 5.77 0.002 0.000 63.7% 56.0% -23.5 0.003 0.000 0.369 0.004 0.367 0.004 50% Rural-Center 44.6% 44.8% 1.13 0.002 0.259 75.9% 65.4% -16.8 0.006 0.000 0.328 0.005 0.327 0.005 90% Rural-Center 44.6% 45.2% 2.53 0.002 0.012 75.9% 71.5% -10.7 0.004 0.000 0.328 0.005 0.327 0.005 80% Rural-Center 44.6% 44.8% 1.18 0.002 0.238 75.9% 67.8% -14.6 0.006 0.000 0.328 0.005 0.327 0.005 70% Rural-Center 44.6% 44.6% 0.26 0.002 0.798 75.9% 70.1% -11.9 0.005 0.000 0.328 0.005 0.326 0.005 60% Rural-Center 44.6% 44.8% 0.90 0.003 0.366 75.9% 68.0% -14.3 0.006 0.000 0.328 0.005 0.326 0.005 50% Rural-North 16.0% 16.8% 2.57 0.003 0.010 51.3% 36.4% -9.6 0.015 0.000 0.297 0.007 0.297 0.007 90% Rural-North 16.0% 16.8% 3.10 0.003 0.002 51.3% 44.4% -6.1 0.011 0.000 0.297 0.007 0.297 0.007 80% Rural-North 16.0% 16.8% 3.00 0.003 0.003 51.3% 40.5% -7.7 0.014 0.000 0.297 0.007 0.297 0.007 70% Rural-North 16.0% 16.8% 2.67 0.003 0.008 51.3% 42.8% -6.6 0.013 0.000 0.297 0.007 0.296 0.007 60% Rural-North 16.0% 17.9% 3.01 0.006 0.003 51.3% 40.7% -7.6 0.014 0.000 0.297 0.007 0.297 0.007 50% Rural-South 33.6% 34.7% 3.58 0.003 0.000 70.2% 58.6% -20.1 0.006 0.000 0.322 0.005 0.322 0.005 90% Rural-South 33.6% 34.6% 3.25 0.003 0.001 70.2% 65.5% -12.4 0.004 0.000 0.322 0.005 0.321 0.005 80% Rural-South 33.6% 34.8% 3.66 0.003 0.000 70.2% 62.2% -16.4 0.005 0.000 0.322 0.005 0.321 0.005 70% Rural-South 33.6% 34.8% 3.41 0.003 0.001 70.2% 64.6% -13.7 0.004 0.000 0.322 0.005 0.321 0.005 60% Rural-South 33.6% 35.4% 5.01 0.003 0.000 70.2% 62.6% -16.2 0.005 0.000 0.322 0.005 0.321 0.005 50% Urban 7.7% 8.0% 1.72 0.002 0.085 28.6% 21.3% -8.8 0.008 0.000 0.376 0.009 0.376 0.009 90% Urban 7.7% 8.0% 2.05 0.002 0.040 28.6% 25.6% -6.3 0.005 0.000 0.376 0.009 0.376 0.009 80% Urban 7.7% 8.1% 2.42 0.002 0.016 28.6% 23.0% -8.0 0.007 0.000 0.376 0.009 0.376 0.009 70% Urban 7.7% 8.0% 1.69 0.002 0.092 28.6% 24.9% -6.8 0.005 0.000 0.376 0.009 0.376 0.009 60% Urban 7.7% 8.5% 2.25 0.003 0.024 28.6% 23.5% -7.4 0.007 0.000 0.376 0.009 0.376 0.009 50% 32 6. Conclusion Household Consumption and Expenditure Surveys (HCESs) are key to consumption-based monetary poverty measurement in low- and middle-income countries. In the absence of market price surveys that are linked to HCESs, unit values (commonly limited to food items) are used as proxies for market prices while estimating nominal consumption aggregates, price deflators, poverty lines and poverty statistics. This practice relies on the Hicksian separability assumption: within-commodity group relative prices are constant across space and the price of a single good is an accurate proxy for the commodity group price. Our analysis tests, for the first time in a low-income context, whether Hicksian separability holds. To do so, we use novel price data that were collected for an extensive list of food items, including several variety/quality-differentiated products for specific items, as part of a national market survey that was conducted in Malawi by the National Statistical Office (NSO) in sync with the Fifth Integrated Household Survey (IHS5) 2019/20 – i.e., the HCES that is the source of official poverty statistics. The key features of the market survey were that (a) the selection of the markets and the timing of market visits were informed by the timing of the visits to the IHS5 enumeration areas for consumption data collection and that (b) the IHS5 and the market survey were managed in an integrated fashion by the NSO, albeit relying on separate but coordinated field teams. We show that Hicksian separability fails to hold across space and time and that unit values constitute biased proxies for prices. The analysis also suggests the Alchian-Allen effect as a mechanism through which Hicksian separability fails. The weak spatial market integration in settings like Malawi (Chitete et al., 2021) can imply that the relative price of quality may not be constant over space and time as required by Hicksian separability. In view of the evidence regarding the untenability of the Hicksian separability assumption, we conduct a comparative assessment of consumption and poverty estimation based on market prices versus unit values – the business as usual. Relative to unit values, market price data showcase a different pattern of spatial price variation and lead to higher food and overall consumption expenditures – both in nominal and real terms, while also generating higher poverty lines and culminating in higher food and overall poverty rates. Our results show that 98 percent of individuals identified as living in poor households according to the unit value approach are also classified as living in poor households under the market price approach, although an additional 18 percent of people classified as living in non-poor households according to the unit value approach are now classified as living in poor households under the market price approach. Compared to their counterparts based on unit values, district-level poverty estimates based on market prices also exhibit a greater degree of correlation with night lights – a geospatial proxy for living standards. Finally, the analysis reveals that the poverty estimates based on market prices are sensitive to any degree of simulated reduction in (a) the spatial coverage of markets and (b) the list of items for which prices are collected. Overall, the results are indicative of the benefits of market price data collection that is spatially and temporally in sync with household consumption data collection and that covers the full scale of consumption items in the household survey, with a focus on capturing quality- and variety- differentiated versions of key food items. The analysis shows that the resulting data can inform not only the computation of deflators to account for within-survey price differences across space and time but also the creation of nominal consumption aggregates and poverty lines. 33 In view of (a) the critical role that unit values play in the computation of consumption-based welfare estimates in low- and middle-income countries and (b) the lack of empirical support, at least in Malawi, for the Hicksian separability assumption, the findings point to the need for more concerted efforts to integrate market surveys into future HCESs. 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(2021). Malawi Poverty Report 2020. National Statistical Office: Zomba Prais, S. J., & Houthakker, H. S. (1971). The analysis of family budgets. Cambridge University Press. Ravallion, M. (1992). Poverty comparisons: A guide to concepts and methods (LSMS Working Paper No. 88). Living Standards Measurement Study, World Bank, Washington DC. Sutton, P. C., Elvidge, C. D., & Ghosh, T. (2007). Estimation of gross domestic product at sub-national scales using nighttime satellite imagery. International Journal of Ecological Economics & Statistics, 8(S07), 5-21. 36 Appendix 1: Details on Market Survey Data Collection and Processing The Market Survey aimed to collect measurement unit-specific prices and weights for a total of 163 food consumption and agricultural produce items. For every item-unit combination, up to three different vendors were approached in each market to record the kilogram weight and price. Table A1 provides the distribution of samples collected by month. Table A1 Distribution of Number of Samples Collected by Month Month Samples April 2019 21,894 May 2019 47,526 June 2019 41,118 July 2019 39,516 August 2019 54,468 September 2019 44,856 October 2019 43,254 November 2019 51,264 December 2019 27,768 January 2020 58,206 February 2020 39,516 March 2020 48,060 April 2020 18,156 Total 535,602 Planned versus Actual Months of Market Visits The timing of the visits to the markets was planned to be in parallel with IHS5; however, due to COVID- 19-related disruptions and administrative/logistical delays in different points of the fieldwork, there is a slight difference between the planned versus actual schedule of market visits. Table A2 compares the planned versus actual months of market visits, overall and by region. 37 Table A2 Distribution of Market Visits: Planned versus Actual Month of Data Collection Planned Data Collection Actual Data Collection Diff. Between Actual North Central South Total North Central South Total & Planned April 2019 15 29 42 86 9 14 19 42 -44 May 2019 15 34 42 91 19 30 47 96 5 June 2019 9 33 42 84 10 33 37 80 -4 July 2019 14 34 42 90 8 26 45 79 -11 August 2019 15 34 41 90 17 48 52 117 27 September 2019 15 34 41 90 13 36 37 86 -4 October 2019 15 33 42 90 14 30 41 85 -5 November 2019 15 32 43 90 20 38 46 104 14 December 2019 15 33 42 90 5 19 29 53 -37 January 2020 15 32 42 89 23 41 55 119 30 February 2020 16 33 42 91 13 24 40 77 -14 March 2020 15 33 42 90 16 36 46 98 8 April 2020 7 19 9 35 35 Total 174 394 503 1,071 174 394 503 1,071 0 Data Cleaning We implement several data cleaning techniques to make the market data suitable for analysis: • We winsorized price and weight data at the top and bottom of the distribution i.e., if prices and weights were higher (lower) than the 95th (5th) percentile of their distribution, they are replaced by the 95th (5th) percentile. Each item-unit combination price was winsorized with cuts at the 5th and 95th percentile distribution of prices for that month while each item-unit combination weight was winsorized with cuts at the 5th and 95th percentile distribution of the region. This affected 13 percent of raw price and weight observations collected. • In some cases, a single market may have been visited several times in a particular month; in cases like this, we combine these visits and define the item-unit prices for this market in this month as the median prices across the multiple visits for that month. • We use the survey-gathered weights for item-unit combinations to convert prices of non- standard unit measures to KG-equivalent terms. Handling Missing Data As expected in a high-frequency survey of hundreds of food item-unit combinations sought after in a national sample of markets, gathering price data at the item-unit level can lead to a high proportion of missing entries, due to (a) items not being sold in specific units of measurement in specific markets, and (b) items not being available in a given month due to seasonality. Table A3 presents the proportion of missing price (and weight) data at the item-unit-month level across all markets and months. 38 Table A3 Frequency and Proportion of Missing Data at the Item-Unit-Month Level Status at Item-Unit-Month Level Frequency Percent Non-Missing 133,566 25 Missing 402,036 75 Total 535,602 100 Table A3 is at the item-unit level. There will be a high proportion of missing data at this level as we do not expect to find items being sold in all unit of measurement across all markets in all periods. For example, it is highly likely that some unit of measurements will be more prevalent in certain parts of the country than others. If we shift focus to the item level i.e., those missing all prices in all item-unit combinations in the market in a particular month, we can examine the proportion of missing data at the item-month level. At the item-month level, missing data represents the non-availability of this item in any unit in the market in that month. Table A4 presents the proportion of missing data at the item-month level. Table A4 Total Frequency and Proportion of Missing Data at the Item-Month Level Status at Item-Month Level Frequency Percent Non-Missing 49,228 36 Missing 89,186 64 Total 138,414 100 Around 64 percent of data from the market survey prices are missing at the item-month level. Some of the missing data here will reflect seasonality and the non-availability of these items in particular times when they were visited. Tables A5 and A6 present the temporal and spatial distribution of the item-month-level availability. Table A5 shows that the highest proportion of missing data comes from the southern region while the northern region has the lowest proportion of missing data. Table A5 Frequency and Proportion of Missing Data at the Item-Region-Month Level Status at Item-Region-Month Level North Central South Total Non-missing 9,280 17,799 22,149 49,228 Missing 12,248 32,709 44,229 89,186 Proportion Missing 57% 65% 67% 64% Total 21,528 50,508 66,378 138,414 Note. Frequency and proportion of missing data at the item-region-month level over all data collection periods Table A6 shows that the lowest proportions of missing data were at the initial months of the survey from April-September. This period coincides with the harvest season in Malawi, and it is not surprising 39 to find fewer missing data over this period. The final months of the actual data collection (from February 2020 to April 2020) have the highest proportion of missing data, with April 2020 (the last month of actual data collection) having the highest proportion of missing data at 71 percent. Table A6 Monthly Frequency and Proportion of Missing Data at the Item-Month Level Status at Item-Month Level Non-Missing Missing Total Proportion Missing April 2019 2,492 3,166 5,658 56% May 2019 4,667 7,615 12,282 62% June 2019 3,811 6,815 10,626 64% July 2019 3,808 6,404 10,212 63% August 2019 5,363 8,713 14,076 62% September 2019 4,122 7,470 11,592 64% October 2019 3,883 7,295 11,178 65% November 2019 4,551 8,697 13,248 66% December 2019 2,339 4,837 7,176 67% January 2020 5,293 9,749 15,042 65% February 2020 3,397 6,815 10,212 67% March 2020 4,154 8,266 12,420 67% April 2020 1,348 3,344 4,692 71% Total 49,228 89,186 138,414 64% Imputation of Missing Data Given the proportion of missing data, we take a cascading median approach to imputing missing prices. We perform the imputation at the item-unit-month level using the following approach: If the price of an item-unit ( ) is missing in market ( ) at month ( ℎ ), we replace it with the median price of the item-unit combination in the associated traditional authority ( TA ), if the item-unit combination is missing at the TA-level, we replace it with the median of the item-unit combination in the district. This approach is illustrated below: |ℎ if |ℎ is not missing ⎡ ⎤ [ | , ℎ] if | ℎ is missing =⎢ ⎢[ | , ℎ] ⎥ ⎥ (10) ⎢ if [ |, ℎ] is missing ⎥ ⎣ [ | , ℎ] ⎦ Tables A7 and A8 present the spatial and temporal distribution of observations at the market level after the imputation process. 40 Table A7 Frequency and Proportion of Missing Data at Item-Region-Month Level after Imputation Status at Item-Region-Month North Central South Total Prop. of Level After Imputation Total Actual Survey (Raw) 9,280 17,799 22,149 49,228 36% Imputed 3,153 9,587 9,296 22,036 16% Missing 9,095 23,122 34,933 67,150 49% Total 21,528 50,508 66,378 138,414 Prop. missing post-imputation 42% 46% 53% 49% The imputation provides 16 percent more observations, thus reducing the proportion of missing observations from 64 percent of total observations to 49 percent at the item level. Table A8 Frequency and Proportion of Missing Data at Item-Month Level after Imputation Status at item-month level Prop. missing after imputation Actual (Raw) Imputed Missing Total post-imputation April 2019 2,492 448 2,718 5,658 48% May 2019 4,667 2,334 5,281 12,282 43% June 2019 3,811 1,676 5,139 10,626 48% July 2019 3,808 1,614 4,790 10,212 47% August 2019 5,363 2,510 6,203 14,076 44% September 2019 4,122 1,831 5,639 11,592 49% October 2019 3,883 1,531 5,764 11,178 52% November 2019 4,551 2,171 6,526 13,248 49% December 2019 2,339 931 3,906 7,176 54% January 2020 5,293 2,953 6,796 15,042 45% February 2020 3,397 1,403 5,412 10,212 53% March 2020 4,154 2,013 6,253 12,420 50% April 2020 1,348 621 2,723 4,692 58% Total 49,228 22,036 67,150 138,414 49% This imputed data set is the base price dataset for all our analysis. We calculate district prices for all items in each month from this base dataset. This district prices are the median prices across all markets in a particular district in each month. For the poverty re-estimation presented in Section 4, we harmonize the IHS5 data with the market price data. The prices of items gathered from the market survey is allocated to each household at the district-month level, i.e., if household A in District 101 is visited in April, then the household is allocated the market prices for District 101 in April from the market survey. Our poverty re-estimation thus compares the sensitivity of poverty and inequality estimates based on unit value (as a proxy for prices) with an alternative based on measures of price coming from the market survey. 41 Please note that in cases where there is no market price for a particular item in a district for a particular month, we adopt a second-round imputation process such that: If the median price of an item ( ) is missing in district ( ) at month ( ℎ ), we replace it with the median price of the item at the region level for that month, and if missing at the region level for that month, we replace with the median price for all that region level in all periods. If missing at the region level in all periods, we replace with the national median price for that item. The second-round imputation process is summarized in Equation 11 below. The price of item ( ) for household ( ℎ ) in IHS5 living in district ( ) is: ℎ, = [ |ℎ] if |ℎ is not missing ⎡ ⎤ ⎢ [ | , ℎ] if | ℎ is missing ⎥ ⎢ [ | ] (11) ⎢ if [ | , ℎ] is missing⎥ ⎥ ⎣ [[ ] [ | ] ⎦ This second-round imputation approach is the same as the approach used to deal with missing values in the traditional poverty estimation method based on unit value as a proxy for price. Once our price data has been harmonized with the IHS5 data, we follow all the steps in the traditional unit value- based analysis to estimate welfare measures (poverty and inequality). This ensures that the only difference between our market price approach and the unit value approach is our price data. 42 Appendix 2: Food Groups and Elementary Specifications in the Market Survey Table A9 Breakdown of Food Groups and Elementary Specifications in the Market Survey Food Group in the Corresponding Elementary Goods Included 1:1 Correspondence to an IH5 Food Consumption Module in the Market Survey Item in the IHS5 Food Consumption Module? Maize (Ufa) Normal Flour Yes Refined (Fine Flour) Yes Bran Flour, Processed No Bran Flour, Unprocessed No Maize, Yellow Flour No Rice Rice, 25% Broken, White No Medium Grain Rice No Short Grain Rice No Bread Brown Bread No White Bread No Buns, scones Buns, Scones, White No Buns, Scones, Yellow No Cassava tubers Cassava Tubers Yes Dried Cassava Makaka No Irish Potato Irish Potato (Local) No Irish Potato (Hybrid) No Pigeon pea (Nandolo) Pigeon pea (Nandolo) Yes Pigeon pea (Nandolo), Fresh No Beans Beans, Demetta No Beans, Kenyata No Bean, Spotted No Onion Onion (White) No Onion (Red) No Chinese cabbage Chinese Cabbage, Fresh No Chinese Cabbage, Wilt No Eggs Eggs Local No Eggs Hybrid No Beef Beef With Bones No Beef Without Bones No Beef, Ham No Beef, Liver No Beef, Minced No Beef, Prepacked No Beef, Rump Steak No Beef, Fillet No Pork Pork, Fillet No Pork, Shoulder No Chicken Chicken (Frozen), Whole No Chicken (Traditionally), Bred Live No Chicken Breast Without Skin No Chicken Legs No Chicken Wings No Banana Banana, Short No Banana, Long No Fresh milk Fresh Milk, Unskimmed No Fresh Milk, Low Fat No Sugar Sugar, White No Sugar, Brown No 43 Appendix 3: Number and proportion of individuals in each quintile: Unit value vs Market Price Approach Table A10 Number of Individuals in Aggregate per Capita Expenditure Quintile Group: Unit Value vs Market Price Approach (Unit Value Approach classification is used as the base) Unit Value Quintile Market Price Quintile 1 2 3 4 5 Total 1 3,096,647 522,509 7,355 1,528 - 3,628,039 2 496,042 2,554,360 568,236 7,410 - 3,626,049 3 34,348 522,693 2,589,416 482,945 - 3,629,402 4 - 27,332 458,562 2,860,190 278,081 3,624,164 5 - - 4,322 273,605 3,348,521 3,626,449 Total 3,627,038 3,626,894 3,627,892 3,625,678 3,626,602 18,134,103 Table A11 Number of Individuals in Aggregate per Capita Expenditure Quintile Group: Unit Value vs Market Price Approach (Market Price Approach Classification is used as the base) Market Price Quintile Unit Value Quintile 1 2 3 4 5 Total 1 3,096,647 496,042 34,348 - - 3,627,038 2 522,509 2,554,360 522,693 27,332 - 3,626,894 3 7,355 568,236 2,589,416 458,562 4,322 3,627,892 4 1,528 7,410 482,945 2,860,190 273,605 3,625,678 5 - - - 278,081 3,348,521 3,626,602 Total 3,628,039 3,626,049 3,629,402 3,624,164 3,626,449 18,134,103 44 Table A12 Proportion of Individuals in Aggregate per Capita Real Expenditure Quintile Group: Unit Value vs Market Price (Unit Value Approach Classification is used as the base) Unit Value Quintile Market Price Quintile 1 2 3 4 5 Total 1 85.4% 14.4% 0.2% - - 3,628,039 2 13.7% 70.4% 15.7% 0.2% - 3,626,049 3 0.9% 14.4% 71.4% 13.3% - 3,629,402 4 - 0.8% 12.6% 78.9% 7.7% 3,624,164 5 - - 0.1% 7.5% 92.3% 3,626,449 Total 3,627,038 3,626,894 3,627,892 3,625,678 3,626,602 18,134,103 100% 100% 100% 100% 100% % Ranked Within 99.1% 99.2% 99.7% 99.8% 100.0% One Quintile Table A13 Proportion of Individuals in Aggregate per Capita Real Expenditure Quintile Group: Unit Value vs Market Price (Market Price Approach Classification is used as the base) Market Price Quintile Unit Value Quintile 1 2 3 4 5 Total 1 85.4% 13.7% 0.9% - - 3,627,038 2 14.4% 70.4% 14.4% 0.8% - 3,626,894 3 0.2% 15.7% 71.3% 12.7% 0.1% 3,627,892 4 - 0.2% 13.3% 78.9% 7.5% 3,625,678 5 - - - 7.7% 92.3% 3,626,602 Total 1,814,803 1,812,235 1,813,296 1,813,597 1,816,537 18,134,103 100% 100% 100% 100% 100% % Ranked Within 99.8% 99.8% 99.1% 99.2% 99.9% One Quintile 45 Appendix 4: Sensitivity of Poverty Lines to the Choice of Calorie Requirement and Reference Group Table A14 Sensitivity of Market Price Derived Food and Total Poverty Lines (in Malawian Kwacha) to Calorie Requirements Calorie Req. Food Poverty Total Poverty Reference Group Lines Lines 2215 413.0 679.2 Deciles 5 and 6 2315 431.6 708.9 Deciles 5 and 6 2415 450.3 738.6 Deciles 5 and 6 2515 468.9 768.2 Deciles 5 and 6 2615 487.5 797.8 Deciles 5 and 6 2715 506.2 827.4 Deciles 5 and 6 2815 524.8 856.9 Deciles 5 and 6 Table A15 Sensitivity of Market Price Derived Food and Total Poverty Lines (in Malawian Kwacha) to Reference Group Food Poverty line Total Poverty line Reference Group 393.9 585.2 Deciles 4 and 5 413.0 679.2 Deciles 5 and 6 420.2 563.0 Deciles 6 and 7 428.8 417.6 Deciles 7 and 8 46 Appendix 5: Sensitivity of Poverty Lines to Item Coverage in Market Survey Table A16 Sensitivity of Poverty Lines to Item Coverage in Market Survey Calorie Reference-group Unit Value Complete Market Price Survey Req. Deciles Item Coverage in Food Poverty Total Poverty Non-food Food Poverty Total Poverty Non-food Market Price Survey Line Line share Line Line Share Full item Coverage 2215 Deciles 5 and 6 277.5 454.4 0.64 413.0 679.2 0.64 90 2215 Deciles 5 and 6 412.2 641.2 0.56 80 2215 Deciles 5 and 6 412.2 613.8 0.49 70 2215 Deciles 5 and 6 409.4 644.0 0.57 60 2215 Deciles 5 and 6 410.3 609.2 0.48 50 2215 Deciles 5 and 6 406.7 623.2 0.53 Note. These estimates are based on calorie requirement of 2215 Kcal and reference group of 5th and 6th deciles of aggregate real household consumption. 47 Appendix 6: Validation of Poverty and Consumption Estimates with Night Lights at Territorial Area and Enumeration Area Levels. Results in Appendix Table A17 and A18 confirms a stronger association between poverty rates derived through the market price approach and the night lights measured at the traditional authority- and enumeration area-levels. Table A17: Relationship between Poverty rates and Nightlights at Territorial Area (TA) level: Comparison of unit value and market price approaches Log TA CBN Log TA CBN Log TA Food Log TA Food TA CBN TA CBN TA Food Poverty TA Food Poverty Poverty Rates Poverty Rates Poverty Rates Poverty Rates Poverty Rates Poverty Rates Rates (Unit Rates (Market (Unit Value) (Market Price) (Unit Value) (Market Price) (Unit Value) (Market Price) Value) Price) Log TA Average Night Lights -0.339*** -0.316*** -0.350*** -0.384*** (0.0221) (0.0174) (0.0388) (0.0322) TA Average Night Lights -6.897*** -7.955*** -3.298*** -4.915*** (0.466) (0.457) (0.349) (0.451) Constant 3.385*** 3.697*** 2.455*** 2.831*** 54.81*** 69.27*** 21.70*** 34.45*** (0.0352) (0.0277) (0.0622) (0.0511) (1.178) (1.154) (0.883) (1.139) Observations 317 322 256 287 328 328 328 328 R-squared 0.427 0.508 0.243 0.334 0.402 0.482 0.215 0.267 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table A18: Relationship between Poverty rates and Nightlights at Enumeration Area (EA) level: Comparison of unit value and market price approaches Log EA CBN Log EA CBN Log EA Food Log EA Food EA CBN EA CBN EA Food EA Food Poverty Rates Poverty Rates Poverty Rates Poverty Rates Poverty Rates Poverty Rates Poverty Rates Poverty Rates (Unit Value) (Market Price) (Unit Value) (Market Price) (Unit Value) (Market Price) (Unit Value) (Market Price) Log EA Average Night Lights -0.244*** -0.254*** -0.154*** -0.169*** (0.0152) (0.0124) (0.0266) (0.0226) EA Average Night Lights -6.474*** -7.488*** -3.047*** -4.528*** (0.376) (0.365) (0.291) (0.365) Constant 3.437*** 3.696*** 2.779*** 3.094*** 53.32*** 67.94*** 20.87*** 33.22*** (0.0277) (0.0226) (0.0500) (0.0422) (0.874) (0.848) (0.675) (0.847) Observations 672 693 499 586 717 717 717 717 R-squared 0.278 0.379 0.063 0.088 0.293 0.370 0.133 0.177 Standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1 48 Appendix 7: Distribution of Markets at Reduced Market Coverage Scenario. Appendix Table A19 presents the distribution of the number of markets in each level of market coverage scenario in the reduced market coverage scenarios. Please note that due to differences in the number of markets visited per district with some districts having fewer than 10 markets visited, the differences in the number of markets visited in each sensitivity analysis scenario will not exactly be different by 10 percent i.e., the 90 percent market coverage will not have exactly 10 percent less markets than the complete market coverage. In addition, one district (Likoma Island) had only one market visited in the complete survey. We have included this single market in all scenarios to prevent a situation where there is no information to represent market prices in this area in the sensitivity scenarios. Compared to complete coverage where prices were collected from 377 markets across Malawi. Market coverage for the sensitivity scenarios ranged from 184 markets in the top 50 percent market coverage scenario to 325 markets in the top 90 percent coverage scenario. Appendix Table A19 Number of markets in each level of market coverage Top 50% Top 60% Top 70% Top 80% Top 90% Complete Market Market Market Market Market Market Coverage Coverage Coverage Coverage Coverage Coverage Urban 52 58 59 66 70 75 Rural North 20 25 30 35 40 47 Rural Center 49 61 71 83 95 113 Rural South 63 74 94 105 120 142 National 184 218 254 289 325 377 49 Appendix 8: Additional inequality Statistics: Comparison of Unit Value and Market Price Approach Appendix Table A20 Comparison of Inequality Statistics According to Unit Value versus Market Price Approach Decile Ratios MLD CoV 90-10 80-20 90-50 50-10 Unit Market Unit Market Unit Market Unit Market Unit Market Unit Market Value Price Value Price Value Price Value Price Value Price Value Price Urban 0.2528 0.2350 1.13 1.07 5.55 5.14 3.17 3.02 2.52 2.38 2.21 2.15 Rural-North 0.1680 0.1457 0.70 0.63 4.03 3.83 2.44 2.31 2.10 2.02 1.91 1.89 Rural-Center 0.1741 0.1778 0.71 0.70 4.25 4.42 2.55 2.58 2.11 2.12 2.01 2.09 Rural-South 0.1742 0.1716 0.76 0.73 3.97 4.08 2.46 2.46 2.10 2.10 1.89 1.94 National 0.2367 0.2264 1.06 0.99 5.02 4.93 2.82 2.79 2.43 2.35 2.06 2.10 50