A Guide to Using Prices in Poverty Analysis. John Gibson Department of Economics University of Waikato

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1 A Guide to Using Prices in Poverty Analysis John Gibson Department of Economics University of Waikato The goal of this document is to provide practical guidance to those poverty analysts who need to use price data in their analysis. The relevant issues and choices depend somewhat on the stage at which the analyst has become involved in the project and on the prior information available about poverty in the country. Therefore, after an introductory section that should be read by all users and which outlines the particular poverty analysis tasks that prices can be useful for, the second part of the guide is structured in the following way: Users of the guide should therefore combine Section 1 with one of Sections 2-5, depending on when they enter the project and the extent of previous information. The major division is between those projects where the survey has already finished and where, potentially, the analyst has little connection with the survey agency (Sections 4 and 5) and those where there is a closer integration between survey work and poverty analysis (Sections 2 and 3). The guide is not designed to be read in its entirety because some points are duplicated between sections. Section 1: Which Poverty Analytical Tasks Require Price Data? Most obviously prices are needed to place a monetary value on the food basket for a Cost of Basic Needs (CBN) poverty line. But even methods for constructing a poverty line that seem to rule out the need for prices, such as the Food Energy Intake (FEI) method, prove on further 1

2 examination to require information on prices. 1 Some sort of price index is also needed to calculate the change over time in the cost of reaching a poverty line standard of living. Summarizing across all stages of poverty measurement (including the calculation and crosschecking of household total consumption, which may have been done before the poverty analyst obtains the data), local prices are needed for some or all of the following four tasks (the question of what is local is discussed in Section 2.2): 1. pricing the food basket for the Cost of Basic Needs (CBN) poverty line, 2. forming spatial deflators, so that any ranking of household consumption expenditures is in real rather than nominal terms, 3. imputing values either when the survey only collects quantities or when checking the sensitivity of the consumption estimates to the use of respondent-reported values, and 4. calculating the change over time in the cost of reaching the poverty line. In addition, once poverty estimates have been made there may be an interest in modeling the effect on poverty of price changes for specific items. Examples include changes in the price of commodities that are both key staples and major income sources (Ravallion, 1992), relative price shifts during an economic crisis (Friedman and Levinsohn, 2002) and more general evolution of relative prices over time (Son and Kakwani, 2006). 1.1 Cost of Basic Needs Poverty Lines As the name suggests, a Cost of Basic Needs (CBN) poverty line attempts to estimate the cost of reaching some basic standard of living. Because norms about food energy needs are more widely agreed upon than norms about other needs, and because food is the largest item in the consumption budgets of the poor, these CBN poverty lines are anchored by a food poverty line. Thus, the first task is to calculate the cost of meeting food energy requirements from a diet consisting of the foods that are actually eaten by poor people in the country. The foods to include in this basket, and their relative importance, can be set by looking at the food budgets of a group of poor households. Ideally, this group should not include households ultimately found to be above the poverty line, so that it is the dietary patterns of the poor but no others that count in forming the basket. 2 The identification of this group may thus rely on the use of a spatial price deflator (see Section 1.2 below). Once the list of foods and their relative importance is determined the size of the basket can be scaled up or down (holding calorie budget shares constant within the basket) until it exactly achieves the food energy target (say 2000 calories per person per day). The cost of buying this (scaled) food basket can then be estimated separately for each region and sector, giving a set of food poverty lines. If the survey collects information on food quantities directly, and these are deemed reliable, 1 The FEI method relies on a regression of calorie intakes on a welfare indicator like per capita expenditures. Once a calorie target is set (say, 2000 calories per person per day) the regression is inverted to solve for the required expenditure to meet the calorie target. However there will be a measurement error in this regression if it is carried out in terms of nominal expenditures when there are large price differences between regions. This error will tend to reduce the magnitude of the regression coefficient, causing an overstatement in the level of expenditures required to reach the calorie threshold and hence an overstatement in the value of the poverty line. This error could be reduced if price data were available to calculate real expenditures that reflect regional differences in the cost of living. 2 This may require an iterative approach since an analyst does not know who the poor are in advance. One example of such an approach is Pradhan, Suryahadi, Sumarto and Pritchett (2001). 2

3 the food poverty line basket can be formed in one step from the average consumption quantities for people in the target group. But if quantities are not available they may be derived by dividing recorded consumption expenditure on each food by the local price. 3 The prices are then used again when the basket of goods is priced in each region and sector. In the next step, the food poverty line, z F, is inflated upwards to get the total CBN poverty line by adding to it the typical value of non-food spending by households whose total expenditure just equals z F. This is a somewhat austere non-food allowance because these households displace some required food consumption, given that they don t actually spend their total budget on food (Ravallion, 1992). If the food budget share of households whose total expenditure just equals z F is w L, the CBN poverty line is calculated as: z CBN = z F + z F (1-w L ). This budget share can be found from the following Engel curve: K x w= α + β ln + γ k nk + ε (1) F n z k = 1 where w is the food budget share, x is total expenditure, n is the number of persons, z F is the food poverty line, and n k is the number of people in the k th demographic category. If total expenditure equals the cost of the food poverty line, ln ( ( )) = 0 F L x n z, so w = ˆ α + ˆ γ n k where n k is the mean of the demographic variables for the reference household used to form the poverty line basket of foods. An upper poverty line is also calculated in many analyses, using a non-food allowance that is calculated from the food budget share of those households whose food spending (rather than total spending as in the CBN poverty line) exactly meets the food poverty line, w U. Ravallion (1992) shows how w U can be estimated by putting the estimated parameters from equation (1) into a U F U iterative solution. The upper poverty line is then estimated as: z = z w. 1.2 Spatial price deflators Spatial price deflators are needed because price differences between regions may make betweenhousehold comparisons of nominal consumption expenditures misleading. 4 For example, in the CBN method of setting poverty lines it is typical to base the poverty line basket of foods on the actual consumption pattern of a group of poor households. 5 But in order to identify this group of poor households, some ranking must be used and this needs to control for spatial price variation. Otherwise poor households from regions where prices are high are less likely to be included in the reference group than are poor households in regions where prices are low because those from the higher priced region will have higher nominal expenditures. K k =1 k 3 This of course requires a good match between the items in the price survey and the commodity detail in the food consumption questionnaire. Surprisingly, this basic point is missed by many surveys. 4 Temporal price deflators may also be needed. It is typically assumed that prices do not vary over time within a cross-section but in inflationary environments even a few months between the time of the first and last household being surveyed could cause a difference between nominal and real expenditures. 5 Exactly how many households should be in this group depends on prior notions of the poverty rate. For example, if it was believed that the poverty rate was 0.25 it would be likely that an analyst would use the food consumption patterns of the poorest quarter of households for obtaining the poverty line basket of foods. If this prior estimate of the poverty rate turns out to be quite different than the subsequently calculated one, it may be necessary to revise the calculations, using a different definition of the starting group (Pradhan, Suryahadi, Sumarto and Pritchett, 2001). 3

4 The ideal way to control for spatial differences in the prices facing households is to calculate a true cost-of-living index. This true cost-of-living index is based on the expenditure function, ( ) c = c u, p, which gives the minimum cost, c for a household to reach utility level u when facing the set of prices represented by the vector p. For two, otherwise identical households, one living in the base region and facing prices p 0, and the other living in another region facing prices p 1, the true cost-of-living index is: ( ) True cost - of - living index = cu 1, p 0 cu (, p ) which can be interpreted as the relative price in each region of a fixed level of utility. Although this is the ideal spatial price index, it is not commonly calculated, even in developed countries. Instead the usual approach to controlling for spatial price differences is to use a price index formula that approximates the true cost-of-living index. A common choice is the Laspeyre s index, which calculates the relative cost in each region of buying the base region s basket of goods: L = J Q j= 1 J Q j= 1 kj kj P P ij kj, (2) where k is the base region, i indexes every other region, j indexes each item in the consumption basket, and Q and P are quantities and prices. The Laspeyre s index overstates the cost-of-living in high price regions. It does not allow for households making economising substitutions away from items that are more expensive in their home region than they are in the base region. For example, ocean fish are usually more expensive in the interior of a country than on the coast, so the quantity of fish consumed would typically be lower in the interior than on the coast. But if a coastal region is the base region, the Laspeyre s index calculates the cost of purchasing the coastal level of fish consumption at the high prices prevailing in the interior. Instead, a true cost-of-living index would calculate the cost of obtaining the coastal level of utility when facing the high prices for fish that prevail in the interior, letting the household rearrange its consumption bundle to minimise cost. Another commonly used price index, the Paasche index understates the cost of living in high price regions because it evaluates relative prices using a basket of goods that varies for each of the i regions: P = J Q j = 1 J Q j = 1 ij ij P P ij kj. (3) In other words, the Paasche index takes a weighted average of relative prices, where the weights reflect prior economising substitutions by households. Continuing the above example, the Paasche index weights the high price of fish in the interior with the (low) quantity of fish consumed by interior households. This understates the cost of living disadvantage in the interior 4

5 compared with the coast because it puts a smaller weight on the items with the highest prices relative to other regions. A geometric average of the Laspeyre s and Paasche indexes gives a Fisher index: F = ( L P). This is a superlative price index which will closely approximate a true cost-of-living index. Another superlative price index that is sometimes used is the Törnqvist index: J w kj + wij Pij T = exp ln (4) j = 1 2 Pkj where w ij is the average share that item j has in the consumption basket in region i, and region k is the base region. One practical difficulty with all of these price index formulae is that they require a full set of prices for all items in the consumption basket. Household surveys are typically not able to collect prices for all consumption items (for example, prices for services are hard to measure) so assumptions are needed about the regional pattern of prices for the items that are not observed. One solution to this problem is to derive the spatial price index from the regional poverty lines because poverty lines can be calculated when there are missing non-food prices (see the discussion surrounding equation (1)). A further advantage of deriving the spatial price index from the CBN poverty line is that this ensures consistency between what should be two equivalent methods of calculating poverty statistics (head count, poverty gap, etc): (i) comparing nominal consumption expenditures with poverty lines that vary by region and sector (ii) using the spatial price index to deflate nominal consumption to either national average prices or to the prices in a base region and then comparing these spatially real consumption expenditures with a poverty line that takes a single value. If the spatial price index estimates regional variations in the cost of living that differ from those implied by the CBN poverty line, these two equivalent methods will not give consistent results Spatial price indexes from regional CPIs In cases where information on price levels across regions are lacking for current periods, analysts may be tempted to estimate these regional price levels at a given point in time by applying a local consumer price index (CPI) to some base period when cross-sectional price levels were known (or else were assumed to be equal). For instance, a baseline household survey may enable poverty lines and other deflators to be estimated for each region while subsequent surveys lack a price collection module (or lack quantity information to derive price movements from unit values). But if there is a CPI available for each region (or for key cities within or near to each region) this might be used by a poverty analyst to estimate current price levels across regions. 6 The available evidence suggests that such a procedure is biased. It fails to take into account the inconsistency between price levels involved in comparisons across space and time. The most extensive empirical evidence on the bias involved in this procedure is from Gluschenko (2006) 6 This approach is also common outside of poverty analysis and even in rich countries with extensive data. For example, Hamilton (2001) estimates food Engel curves for the US over several years and in lieu of a variable measuring regional price levels he uses the CPI for each of 25 cities. Cross-country tests of Purchasing Power Parity also rely on approximating local price levels by local CPIs

6 for the case of Russia. Gluschenko uses data from 1997 and 1998 to consider two methods of measuring the relative price level in location r with respect to location s at time t: (i) a direct spatial price index calculated for period t using the local prices for the same period (ii) an indirect spatial price index for period t that is extrapolated from a direct spatial price index for period t 0 with local CPIs used to characterize price changes from t 0 to t In the case of Russia (where biases that may take years to show up elsewhere show up more quickly because of the rapid inflation) the indirect spatial price index had considerable bias. This indirect index implied that regional price levels in 1998 varied from 81 percent to 153 percent of the national price level (a ratio of highest to lowest of 1.9:1). In contrast, the direct spatial price index only varied from 92 percent to 136 percent of the national price level (a ratio of 1.5:1). Gluschenko concludes that the CPI-proxied (indirect) price levels cannot be used adequately to proxy the cross-spatial price levels. The indirect spatial price index is substantially biased and distorts the cross-spatial comparisons in the sense that it tends to overstate cross-spatial differences in price levels. In the context of Russia, this implies that except for occasional periods when a direct spatial price index is able to be calculated (such as in 1997 and 1998) there is no means to get a precise estimate of real incomes (and hence, of real poverty) across regions of the country. Since the methods of construction of the Russian CPI are similar to those in other countries, these pessimistic conclusions may hold more widely. 7 The bias that Gluschenko (2006) reports is likely to become more important in the future, as the demand to combine regional and inter-temporal price indexes rises with the growing availability of nominal data on living standards across time and space. However, this task is much more complicated than it appears. The conceptual problems are discussed below but examples from two developed countries, New Zealand and the UK, may help to reinforce the message. The Consumer Price Index in both countries is constructed according to best practice, especially because it is the indicator used for an explicit inflation target of the central banks. In New Zealand it is calculated and reported for 15 regions. A recent public review of the NZ CPI highlighted a user demand for the statistics agency to produce spatial comparisons of the cost of living in different cities and regions. The statistics office emphasized that this could not be produced from the current CPI and that additional resources would be needed to produce these additional cost of living measures. 8 In the UK, a similar demand for data on spatial price levels caused the Office of National Statistics to field a new survey for 380 goods across 65 towns in year 2000 (Ball and Fenwick, 2004), since it wasn t possible to estimate these spatial price levels from the existing CPI. If technically sophisticated statistics offices in developed countries that place great public policy weight on the CPI cannot extract regional price levels from a CPI it is rather optimistic for a poverty analyst working on developing country data to be able to do this. 7 Indeed, the Russian CPI could be considered best practice in the sense that the expenditure weights are updated for each of 89 regions every year (based on the results of the previous year s Household Budget Survey that surveys 49,000 households every quarter) and prices are gathered each month from 30,000 outlets for 400 representative goods and services in 350 towns and cities. 8 Statistics New Zealand (2005) Report of the Consumers Price Index Revision Advisory Committee,

7 In terms of the conceptual problems, Hill (2004) suggests that it may in general be impossible to construct panel price indexes that are unbiased across both space and time. Bilateral formulae, such as those presented in equations (2)-(4), are unlikely to give transitive results when extended to a multilateral situation. For example, consider a country where a price index is calculated for three regions: the capital city P CC, other urban areas, P OA, and rural areas, P R with base weights that differ in each region. A direct comparison between the rural price level in period t 2 and the capital city price level in period t 0 (say, the base period for the poverty line) will not give the same result as constructing an indirect comparison via the third region in an intermediate time period, t 1: P R2, CC0 PR 2, OA1 POA 1, CC 0 This lack of transitivity is partly due to different consumption patterns causing the weights attached to each commodity to vary across regions. In contrast, a multilateral index is transitive by construction and can be expressed as: PCC0 P R2, CC 0 = PR 2 The most common of the multilateral index methods are (i) average price methods, such as the Geary-Khamis (GK) method that underlies the Penn World Table, (ii) EKS (Eltetö, Köves and Szulc) type methods, (iii) Spanning-Tree Methods and (iv) the Weighted Country-Product Dummy Method (WPCD). 9 The basic idea behind WPCD, as used in the cross-country literature, is that the observed price of commodity n in country k and period t is assumed to be the product n of the PPP price index for the country P kt, the price level of commodity n ( p t ), which is a n country-invariant component, and an error term υ kt. In log form this can be expressed as: n n n n kt ln pkt = ln Pkt + ln pt + lnυkt = πkt + θt + εn (5) If observations are weighted by the expenditure share for each commodity in each country and the parameters of the following regression estimated by weighted least squares: K N n i i n kt = π jt jt + θt t + εkt j= 1 i= 1 (6) ln p C G where C jt and G i t are the country and commodity dummy variables respectively, then the price indexes are obtained by exponentiating the parameter estimates on the country dummies. Advantages of this method are that since it is based on a regression there are standard errors (at least of the logarithms of the price indexes) and it can also be used when there are gaps in the data. 9 Average price methods compare each country (or region) with an artificially constructed average country (or region). They mostly use the Paasche price index formula (including the Geary-Khamis) to make each of these bilateral comparisons, with the artificial country as the base, and tend to suffer from substitution bias because the price vector of the base artificial country is not equally representative of the prices faced by all of the countries in the comparison. EKS methods impose transitivity in the following way: first, make bilateral comparisons between all possible pairs of countries, then take the nth root of the product of all possible Fisher indices between n countries. A spanning tree is a connected graph that does not contain any cycle (i.e. any pair of vertices in the graph are connected by one and only one path of edges) in order to ensure that price indexes are internally consistent. Thus, a multilateral comparison among K countries can be made by chaining together K-1 bilateral comparisons as long as the underlying graph is a spanning tree. The Weighted Country Product Dummy method is explained in detail in the text below. 7

8 These multilateral index methods are widely used in the cross-country literature for calculating Purchasing Power Parity (PPP) exchange rates but very rarely used for multilateral regional and temporal comparisons within countries. One of the few published examples of applying these methods to household survey data to estimate multiregional consumer price index numbers is Coondoo, Majumder and Ray (2004) who adapt the Country-Product Dummy method to using unit value data from the National Sample Survey in India. But even in the cross-country literature where these multilateral indexes are widely used there is controversy about their interpretation and robustness. Hill (2006) shows how it is possible to use Penn World Table data to support either convergence or divergence, depending on which multilateral index is used to compute the per capita income benchmarks. Ackland, Dowrick and Freyens (2006) find that using the EKS method to calculate real income in the Penn World Table raises the global count of people below the PPP$1 per day poverty line by nearly 60 percent, compared with using the standard PWT data that rely on the GK method. Moreover, despite these multilateral indices satisfying transitivity there are other desirable criteria that they fail to meet. These criteria include: temporal fixity the results for an existing time series should be unaffected by the inclusion of a new time period, spatial fixity the results for an existing set of countries (or regions) are unaffected by the inclusion of other countries, temporal consistency temporal results for each country (region) do not depend on the other countries (regions) in the comparison, and spatial consistency spatial results do not depend on the other years in the comparison. In general it is not possible to maintain both temporal and spatial consistency and achieve transitivity. Consequently analysts have to weigh up which violations are least problematic in the particular application they have in mind. Hill (2004) suggests that in many settings (but he does not explicitly consider poverty measurement) most importance will attach to maintaining temporal fixity and consistency. Thus, to conclude this section, poverty analysts should treat the calculation of spatial price levels or indexes from regional CPIs with considerable skepticism. They should also be aware that multilateral indexes also have weaknesses. The sensitivity of cross-country poverty estimates to the particular multilateral index used suggests there may be a similar sensitivity of regional poverty estimates if multilateral indexes are used to calculate regional PPPs. Amongst the class of multilateral indexes, ones based on the Weighted Product-Country Dummy approach show the greatest scope for adapting to household- and regional-level data. 1.3 Using prices to impute the value of consumption Self-produced items, and especially food, are a major component of consumption in rural areas of many developing countries. The monetary values placed on these self-produced items in surveys are often the values that respondents themselves suggest. It is difficult to know how reliable these respondent-reported values are. Many households who produce a food do not buy that same food, so they may not be well informed about prices when they assign a value to their own food production. Moreover, the items available for sale in markets may be of a different quality than their own production so even if they are aware of prices in the market they may not be able to accurately impute a value for their own production. These problems can be particularly acute if a comprehensive measure of consumption is used that attempts to value some of the 8

9 services provided by the environment (eg., firewood and other bush materials are often gathered but rarely sold in rural areas, so valuing these products can be particularly difficult). There are two concerns about relying on respondent-reported values for self-production. First, they introduce an additional, and extraneous, source of inequality into measured consumption because they will vary across respondents who are in the same location and face the same prices. If the poverty line is below the mode of the welfare indicator, this increase in measured inequality will raise the measured poverty rate (see Ravalion, 1988 for a formal treatment). Intuitively, a household might fall below the poverty line just by being too pessimistic when valuing their own food production because they think prices are lower than they truly are. Second, the values applied to self-produced food items could differ, systematically, from market prices. Such discrepancies could drive a wedge between the market prices used to form a CBN food poverty line and the respondent-reported values used to form estimates of consumption. If respondents tend to report values for their self-produced foods that are lower than market prices, estimates of poverty could be inflated, especially in rural areas where subsistence food production is important. There are two alternatives to respondent-reported values, as measures of the value of selfproduced food items. The first is to value self-produced foods with the average of the implicit unit values used by other households living in the same cluster (aka Primary Sampling Unit) as the respondent. These implicit unit values are the ratio of value to quantity reported by each respondent, and are similar to a price except that they may reflect quality variation and also measurement error. Replacing respondent-reported values with a cluster average (medians may be preferred to means, to reduce the effect of measurement error) removes the within-cluster variability in valuations. However, it does not address any discrepancy between these average unit values and market prices which may drive a wedge between the prices used for the poverty line and the implicit prices used when valuing consumption. The second alternative is to value self-produced foods with the average price that was observed during the survey in the market closest to the respondent. In the absence of a market price survey, unit values from the market purchase part of the questionnaire could be used although these may be subject to quality differences between items that are purchased and items that are consumed from own-production. It is notable that both of these alternative ways of valuing self-produced foods switch the cornerstone of consumption measurements from the respondent reports of values to the survey estimates of food production quantities. Poverty analysts may be reluctant to place a lot of faith in quantity measurements depending on the nature of the key food staples (grains are easier to measure than root crops) and their opinions about the thoroughness of the consumption-fromown-production section of the survey (e.g., did the survey agency attempt to weigh items or else use validated conversion factors from traditional units. See Capéau and Dercon (2006)). But unless data on prices in local markets are available it is impossible to know how sensitive the estimates of consumption and poverty are to the various assumptions made when valuing selfproduced items. 9

10 The quality elasticity is one tool that may be useful for poverty analysts facing these issues. This can be estimated from a double-log regression of unit values, v i on household total expenditure x i, various demographic controls z i, and cluster-level dummy variables, δ c : lnv i = α + β ln xi + γ z + δ c + ui (7) The estimated β-coefficient shows how unit values change with respect to household total expenditure, where this change is typically due to an upgrading of quality as households get richer. While equation (7) is typically used with unit values from market purchases, as part of the procedures suggested by Deaton (1989; 1997) for stripping quality effects out of unit values when they are used as proxies for market prices, it could also be applied to the unit values that are implied by reported values and quantities of self-production. If estimated quality elasticities are large, it points to either an inherent variability in the commodity (e.g. tubers are typically less uniform than grains) or else it may reflect the broadness of the commodity category which allows a lot of within-category substitution as households get richer. For example, in Indonesia the quality elasticity for the broad category of meat (from market purchases rather than own-production) is 0.12 but when a finer disaggregation is used the quality elasticity for beef is only 0.05 and for chicken 0.04 (Olivia and Gibson, 2005). For commodities that have a high degree of quality variability, the variation in respondent-reported values may reflect the underlying quality differences rather than measurement error and so there would be a loss of information if respondent-reported values were replaced with some form of cluster average. 1.4 Using prices to update the cost of the poverty lines The cost of the poverty line needs to be recalculated for each year that poverty is being measured, in order that it refers to the same real standard of living. It is impossible to carry out this calculation without some price data, but even with data there are a number of issues that warrant attention Using general purpose deflators The typical approach is to use a general purpose index like the CPI to update a poverty line that has been estimated for a base period using the procedures outlined in Section 1.1 above. Even absent the problems of getting spatial and temporal consistency that are discussed in Section there are other problems with these general purpose deflators. An important practical concern with this procedure is that the change in the cost of living for the group of households below the poverty line could be quite different to the change shown by a general purpose price index. For example, the CPI places greatest weight on the expenditure patterns of households who are in the upper parts of the income distribution. As a result the measured inflation rate from a CPI may be different than the inflation rate facing the poor. There are three sources of this possible difference: 1. the prices for the CPI in many developing countries are collected only from urban areas and the trend in these may be different than the trend in rural prices, especially if the price of transport and other marketing services changes rapidly. Moreover, the base weights for the CPI are also often only for urban households. While using only these households is an (internally) consistent choice, from the point of view of measuring urban inflation, it makes the CPI even less relevant as a poverty line deflator when the majority 10

11 of the poor are in rural areas. For example, even Indonesia, with one of the most comprehensive statistical systems in developing countries and a nation-wide consumption survey fielded every year, carries out its Cost of Living Survey (Survei Biaya Hidup) which provides the base weights for the CPI only in provincial capitals and other large cities. 10 This may have contributed to the discrepancy in estimates of the poverty increase in Indonesia during the Asian economic crisis. The change in the poverty line using the price surveys from the Indonesian Family Life Survey was quite different to the change calculated from applying the official (urban) inflation rates (Beegle, Frankenberg and Thomas, 1999). 2. the price trend for the basic necessities consumed by the poor may not be the same as the trend for items consumed in the upper parts of the income distribution, even if prices were gathered in the same locations, and 3. within a given category of consumption (say, rice) the particular brands, grades, varieties and outlets where rich and poor purchase may differ and may have different price trends. One tool for assessing whether these differences in price trends are likely to be important is the so-called plutocratic gap (Izquierdo, Ley, and Ruiz-Castillo, 2003). The plutocratic gap is the difference between inflation measured using the official CPI and inflation measured using an alternative group index in which all households are weighted equally. To understand this method it is helpful to recall that official CPI calculations weight each commodity by adding up expenditure on that particular item across all households, and calculating the ratio of the total expenditure on the item to the total expenditure on all items. This gives more weight to the rich, who have more total spending, and hence can be considered a plutocratic price index (Prais, 1958). In contrast, another method of calculating the weight for a commodity in the index would be to first calculate budget shares for each household and then average these budget shares across all households. This average of shares approach gives every household the same weight (except for any variation due to household size and sampling weights). Thus it can be considered a democratic price index because a rich household has no more impact on the finally calculated index than does a poor household. This democratic method is more consistent with the approach used with CBN poverty lines. A hypothetical example showing the difference between these two types of averages is presented in Table 1. There are two households, with one having three times the total spending of the other. Only two commodities are available to consume: cassava, which is a necessity and beef, which is a luxury. If the average importance of each commodity is calculated in terms of the shares of total expenditure (the plutocratic method), the resulting price index would put 25 percent of the weight on the price of cassava and 75 percent on the price of beef. This is much closer to the consumption pattern of the rich household than the poor household. But if the democratic average of shares approach was used the weights would be 30 percent on cassava and 70 percent on beef which is halfway between the consumption patterns of the two households. 10 It is sometimes (wrongly) asserted that the base weights for the Indonesian CPI come from the national socioeconomic survey (SUSENAS). For example, see Quinn (2004). The SUSENAS has an abbreviated consumption module every year and a comprehensive consumption module every three years (see Pradhan, 2001 for details) but neither of these are used in the calculation of the CPI. 11

12 Table 1: Example of Two Different Weighting Methods for a Price Index Cassava Beef Total Spending Cassava Share Beef Poor household $40 $60 $ Rich household $60 $240 $ Total $100 $300 Share of total Average of shares Source: Author s example. Consistent with this hypothetical example, in real-world price indexes the consumer whose budget corresponds to the weights in a plutocratic CPI is located well into the upper part of the income distribution. According to calculations by Deaton (1998), in the United States in 1990 this average consumer was at the 75 th percentile of the distribution of household expenditures. Deaton suggests that rising inequality would have raised this position still further since then. Having the representative consumer located so far up the income distribution may not have mattered in the United States in the immediate period prior to 1990 because Deaton suggests that price movements at the 75 th percentile were much the same as for those faced by a median or poor household. However, this may not be the same in other countries, particularly in poor countries where relative price shifts can be expected during the structural changes that occur during development. The sparse international evidence on the size of the plutocratic gap has recently been summarized by Ley (2005). The only developing country with estimates is Argentina, where the plutocratic gap varied in sign over time, ranging from to between (a period when the official annual inflation rate was between 1.2 and 3.3 percentage points). The fact that the sign of the gap varies over time does not mean that this issue can be ignored when choosing a deflator for updating poverty lines under the assumption that the effects cancel over time. For example, in Spain the plutocratic gap averaged 0.06 percentage points during but the average absolute gap was 0.09 percentage points, so the sign reversals only removed a small amount of the effect. One thing that may be helpful for poverty analysts to consider is the characteristics of settings where the plutocratic gap is likely to be larger because these will be where the CPI would be an especially poor deflator for updating poverty lines. Ley (2005) shows that the plutocratic gap will be larger, the greater the expenditure inequality in the country, the more different are the consumption patterns across income groups and the larger the variation in inflation rates for particular consumption items. Hence it is expected to be particularly significant in regions such as Latin America where inequality is high and where high inflation rates may have allowed more differentiated price dynamics across commodities. In addition to the plutocratic gap, a recently developed tool for comparing price changes for the poor with those indicated by a general purpose deflator like the CPI is the Price Index for the Poor (PIP) developed by Son and Kakwani (2006). This index is based on the following thought experiment: the actual change in the price vector over time produces a poverty change with both 12

13 an income component (if all prices rise by 10% it is equivalent to a 10% fall in real income) and a relative price component. The relative price component reflects the fact that some prices move more than others and that some price changes are relatively more important to the poor than are others. The PIP is designed to measure what the percentage change in overall prices would have to be, in order to get the same poverty change that actually occurred (which depends on both the income effect of the change in price and the distribution effect of the price change). The PIP, λ is defined as: m * p η i θ i λ = (8) i= 1 pi ηθ where p i is the price of the i th * (amongst m total) commodity in the initial period, p i is the price in the subsequent period, ηθ i is the elasticity of the poverty measure θ (which is any member of the additive separable class, including the Foster-Greer-Thorbecke measures) with respect to the price of the i th commodity and η θ is the elasticity of the poverty measure if all prices change by one percent, which Son and Kakwani call the total poverty elasticity : 1 z P η θ = x f ( x) dx (9) θ 0 x where for the headcount index, H η = z H f ( x) H, where z is the poverty line and f(x) is the density of income, However, η θ is simply the negative of the elasticity of the poverty measure with respect to mean income (aka the growth elasticity of poverty) since if all prices change by one percent it is equivalent to nominal income falling by one percent. For the change in the price of a single item, the income effect of that price change on poverty is just w iη θ, where w i is the mean budget share for the i th commodity. In contrast, it is the share of the i th commodity at the poverty line, w i (z) that matters for the overall elasticity of the poverty measure with respect to the price of the i th commodity. For example, for the headcount index, H pi z f ( z) wi ( z) η H i = =. (10) pi H H Thus, the PIP is essentially a more elaborate way of contrasting price changes based on the importance of each item at the poverty line and at the mean, and transforming this into an interpretable magnitude what is the equivalent equally distributed price change that would produce the poverty change that actually occurred. In the case of Brazil, prices rose by 59.9 percent between 1999 and 2005 according to a Laspeyres Index with average budget shares as the weights. But the Price Index for the Poor, based on equation (8), household survey data and a set of prices for almost 500 items gathered in 12 regions of Brazil, rose by between 63.8 and 64.4 percent, depending on whether the Headcount, Poverty Gap or Poverty Severity Index is used. Therefore price changes in Brazil appear to have favoured the non-poor over the poor during this period Another factor to note is that the response of poverty to price changes in this framework of Son and Kakwani is based only on first order effects, without allowing for consumers to rearrange their budgets as relative prices change. Welfare estimates based on first-order effects proved to be almost two times as large as those that allowed for substitution responses in the Indonesian crisis (Friedman and Levinsohn, 2002). Analysts wishing to incorporate 13

14 In light of the above discussion of several different ways of highlighting weaknesses in the CPI as a measure of price changes for the poor, poverty analysts should where possible use price indexes calculated specifically for lower income groups. Examples include the CPI for agricultural laborers in India. If such indexes are not already calculated by statistics agencies it provides a further reason for local prices to be collected during poverty-focused household surveys, so that poverty analysts may calculate these deflators themselves. An additional reason for considerable caution in using a published CPI for updating poverty lines is the issue of CPI bias. It is well known that the CPI is a biased measure of changes in the cost of living due not only to the substitution bias discussed above in the spatial context (Section 1.2) but also due to outlet bias (shoppers responding to lower prices by switching outlets while price surveyors do not), and an inability to deal properly with quality change and new goods. Recently, a practical method based on the estimation of food Engel curves has been developed for measuring and correcting this CPI bias and has been applied in several developed and developing countries. This method just requires repeated cross-sections of a household survey with total consumption and food consumption measured consistently over time. In the United States, this method estimates a CPI-bias of roughly one percentage point per year over the 1980s (Hamilton, 2001), which is an estimate very close to that derived by a completely different, and more laborious, method used by the Boskin Commission. In Canada the bias was just over one percentage point per year for (Beatty and Larsen, 2005). In Brazil the CPI bias is estimated as three percentage points per year over 1987/8 to 2002/3 (Filho and Chamon, 2006) while in Russia it is estimated as one percentage points per month from (Gibson, Stillman and Le, 2004). Moreover, in the Brazilian case, the CPI bias appears to be larger for the poor, making the CPI a particularly unreliable index for updating poverty lines that attempt to hold an absolute standard of living constant Recalculating CBN poverty lines each year One seemingly attractive alternative to relying on general purpose deflators is to simply repeat the calculations of a CBN poverty line for each year that survey data are available and poverty estimates required. However, there is a conceptual problem with this approach. While it is possible to re-price the same basket of foods that was identified in the baseline period, there is no easy approach to updating the non-food allowance. Recall from equation (1) that an Engel curve is estimated to calculate the non-food allowance because of two problems: 1. it is hard to get agreement on what to include in the basket of non-foods, compared with using nutritional norms to anchor the food basket. The Engel curve approach gets around this problem by letting the revealed choices of poor households determine the amount (but not the composition) of the non-food allowance, and 2. prices for non-food items are less easily available than they are for foods. Only food prices are needed to calculate the Engel curve in equation (1). However the calculated non-food allowance has both price and quantity components and because these are jointly estimated it is not possible to hold the quantities constant when repeating this calculation in subsequent years. Thus, repeating equation (1) does not hold real living standards these second order effects need either a matrix of demand responses or they can estimate a utility consistent demand model to estimate an equivalent income concept (Ravallion, 1992). 14

15 constant because we cannot rule out quantity changes out, which denote changes in real living standards. An example of the approach of recalculating the CBN poverty line in each year is provided by Meng, Gregory and Wang (2005) who calculate poverty lines for urban China for each year from These authors argue that such recalculation is required because of the rapid changes in the availability of goods, changes in the provision of subsidized services and divergences in the prices of key commodities consumed by the rich and poor. However, these problems could be dealt with by using a more appropriate deflator to adjust the baseline estimate of the non-food allowance for price changes only, keeping the implicit quantity of non-foods the same over time. The one situation where it is appropriate to recalculate an Engel curve for updating the non-food allowance is when measured consumption changes its composition and coverage between surveys. For example, one survey may have rice as an item, but this is broken down in a subsequent survey into basmati rice and plain rice. This greater detail would be expected to raise measured consumption because it prompts respondents to remember some expenditure that they would otherwise forget. In cases such as this, Lanjouw and Lanjouw (2001) show that the bundle of foods in the poverty line should be recalculated, restricting attention just to the subset of items that are common to both surveys, yielding an abbreviated food poverty line z F,subset. This line, which is abbreviated because it excludes items whose definition changed between surveys, is then scaled up to provide a total poverty line. The appropriate nonfood allowance for the U F, subset U scaling up is based on the upper poverty line z = z w rather than having the allowance calculated directly from equation (1). Moreover, in these circumstances, only the headcount measure of poverty maintains its comparability across the two surveys. 15

16 Section 2: No Previous Poverty Lines and Survey Fieldwork Not Yet Complete This section is for those poverty analysts who are in the (increasingly rare) position of working in a country with no previous poverty line and where there has been sufficient forethought to involve the poverty analyst before the survey fieldwork is complete. Obviously there are difficulties if the survey interviewing has already begun but even in that case some amendments can possibly be made in the field. 12 The disruption that this causes could still be worthwhile in order to get good price data. There are three key questions that the poverty analyst and the survey agency should consider: 1. How many prices to collect, in terms of the number of items and the number of individual price observations per item, 2. Where to collect prices, and at what geographical scale to calculate and report any resulting price aggregations such as a spatial price index or food poverty line, and 3. How to collect the price information, in terms of the following four choices: a. Price surveys in community markets, such as those typically done by LSMS surveys, b. Unit values (that is, the ratio of expenditure to quantity) coming typically from a consumption recall but potentially also from individual transaction records in expenditure diaries, c. Surveys of opinions about prices from either sampled households or community leaders, and d. Existing price collection efforts, as might already be occurring for a Consumer Price Index or some sort of rural index like a Farm Cost Index. 2.1 How many prices to collect? The number of items whose prices are needed depends partly on the nature of the consumption module of the survey. If it is an LSMS style survey the consumption recall is likely to have less than 50 categories of food and less than 100 consumption categories in total. In this case, if there is a separate price survey it is sensible to try to obtain the price for at least one item per food category. 13 This matching is especially needed if quantity data are not collected in the consumption recall; otherwise there is no way to derive the required consumption quantities from those food expenditure categories with no matching price. For key foods such as rice and other dominant staples, price surveys often include several specifications (such as high and low quality) although it is not clear how this can help with the calculation of the food poverty line when the expenditure or quantity information is only available for a broader aggregate. 12 For example, midway through the fieldwork in the 1996 Papua New Guinea Household Survey it became apparent that the market price surveys did not cover all items in the food consumption bundle and hence part of the food poverty line basket would have been unpriced. Moreover, some interview teams were less diligent at gathering market prices when produce markets and tradestores were some distance from the selected village (because of the time needed to walk to the markets for the price survey). So additional staff were employed to gather prices for the unpriced commodities and from villages with missing data. While this was more expensive than having the original survey teams gather these data, it was felt to be worthwhile because of the complete absence of other information that could serve as a proxy for these missing prices. 13 If unit values are used there will automatically be a matching between the commodities with expenditure and quantity information and those with prices. 16

17 If the survey uses more consumption recall categories, as would typically occur with a Household Income and Expenditure Survey (HIES) or a Household Budget Survey (HBS), then prices should only be collected for foods that are going to make a significant contribution to the food poverty line. A similar recommendation holds for surveys that use expenditure diaries, because the amount of commodity detail that these allow is almost limitless (eg., such surveys typically use a 4-digit coding scheme, so could have several hundred codes for food items). In these cases it is decisions about which prices to collect which ultimately shape the degree of detail in the poverty line basket of foods. One useful tool in this regard is the concentration curve. If previous survey information on food consumption is available, this curve could be constructed for the foods that could potentially be included in the poverty line basket. After ranking foods according to their importance the concentration curve plots the cumulative contribution to either the total cost or the total calorie content of the poverty line basket. Figure 1 presents an example from Cambodia, where the initial poverty line was calculated from a 1993/94 survey that had 155 separate food items. This detailed food basket was never fully priced in subsequent surveys, which only gathered data on the prices of about 30 foods. In fact this more abbreviated level of price was about an appropriate level of detail for the poverty line food basket. According to Figure 1, a basket with just the 20 of the most important foods would give 73 percent of the total cost and 85 percent of the total calories in the 155-item food poverty line. A basket with 35 items would give 86 percent of the total cost and 94 percent of the calories of the 155-item basket. But because the initial food poverty line in Cambodia had been too detailed, all subsequent updates of that food poverty relied partly on assumptions about price trends for the items that the new surveys had not collected information on. This was an unnecessary source of ambiguity. Figure 1: Concentration curves for poverty line food basket Cost Calories Cumulative % Food items 17

18 While it would not be possible to exactly replicate Figure 1 if there is no previous poverty line, there is likely to be either nutritional of budget information on the importance of various foods. Thus an approximate concentration curve could be constructed to guide the specification of the food price collection effort. In addition to food prices, the prices of key non-foods should also be collected. Even though these are not needed when the CBN method is used to scale the food poverty line up to the total poverty line (see equation (1)) they are useful for at least two other purposes. First, some countries have traditionally based the non-food allowance in the poverty line on the prices of a select group of non-foods that experts have identified as constituting basic needs. This method was especially common in the former Soviet Union. Collecting prices for these items enables some sensitivity analysis by testing that style of poverty line against the CBN line (and may also help in discussions of the social acceptability of the CBN line). Second, the prices of these nonfoods can be used for analytical studies that either look at causes rather than measurement of poverty or else that consider the incidence of social spending. For example, fuel subsidies are important in many countries such as Indonesia so it is necessary to have good estimates of price elasticities of demand to assess their efficiency impacts. In countries with considerable spatial price variation (because of poor infrastructure, difficult topography etc) these elasticities can be estimated cross-sectionally, if the survey has collected the required price data. How many price observations per item If prices are obtained from a market price survey, there is a choice of how many observations to make on the price of each item. The standard in most LSMS surveys is three observations per village (that is, per cluster). It is not clear if a fixed number of observations per item is the best approach, although it does have the advantage of simplicity. A CBN food poverty line is a statistic (essentially a weighted average of a set of average prices) although it is rare to see standard errors reported for poverty lines. This statistic would be more precisely estimated if the prices for the items contributing the most weight (e.g., rice) were based on larger samples than the samples used to measure the price for minor items. The variability across time and space should also be considered when deciding how many observations to take on the price of each item. Some items may be subject to price controls (for example, fuels) so the same price might be observed over all outlets and across short time spans. Other items, and particularly informally marketed foods, may have prices that vary from day to day and from seller to seller, so more observations are required to precisely measure the prices for such items. Some surveys have visited fresh produce markets on two separate days to capture this effect. Some consideration of the lumpiness of the product may also help to inform decisions about the optimal number of observations on market prices. Root crops are lumpier than grains and hence the prices observed in a market are likely to be more variable, especially when they are sold in piles or bundles and where there is no splitting of individual tubers. The greater variability in root crop prices suggests that more observations should be taken of their market prices than for grains, in order to get an equally reliable measure of the mean price. 18

19 Some evidence for this effect comes from market price surveys in Papua New Guinea which looked at intra-seller price variation. Specifically, enumerators selected the seller in each market with the largest number of piles on display and then weighed all piles that were offered at the most common price (e.g., 10-cent piles, one-dollar piles etc). This is a setting where haggling is not the norm (Gibson and Rozelle, 2005) so the posted prices should measure the effective prices paid by consumers. On average, the coefficient of variation for piles offered by the same seller (and at the same listed price) was 0.20 for taro, 0.18 for sweet potato and 0.14 for cassava. At least some of this variability is due to the lumpiness of these foods, because the piles typically have only a few tubers so it is difficult for a seller to exactly equalize the weight of each pile if no tuber is to be split. This implicitly makes it difficult to equalize price across the piles offered by the seller because prices are posted at only certain values (typically 10, 20, 50, 100, and 200). The only product in these markets that approximates a grain is sago, which is a starchy food made from the pith of a palm tree. Sago is sold in bundles of various weights, which can be adjusted, unlike the size of an individual root crop tuber. The average coefficient of variation for the sago bundles was considerably less than for the root crops, at only It would be useful to have evidence on the intra-market and intra-seller variation in prices from other settings to help assess the likely reliability of mean prices calculated from only a few observations in each market. 2.2 Where to collect prices In terms of where to collect prices, the aim should be to observe prices in the markets actually used by the households in the sample. Thus it is worthwhile asking respondents in the consumption questionnaire where they actually buy their items. Otherwise an approach of just visiting the nearest markets and asking vendors the price of particular goods (as was done by the LSMS surveys) can be subject to the criticism that this is possibly the wrong market. Other criticisms of the approach are that prices could be collected for the wrong specification of goods and that the prices quoted may not be the prices actually paid by local residents because of bargaining (Deaton and Grosh, 2000). It is also possible that some prices will need to be collected from larger, more regional, markets because specialized items may not be available in local markets. For example, a 1999 survey in Cambodia tried to obtain prices for 50 food items in 600 villages but data were obtained on less than half of the price-village combinations because of items missing from markets (Gibson, 2000). There are three options for dealing with these missing local prices: Apply the price from a neighboring market (essentially a form of hot deck technique that survey software often applies to missing data) Apply prices that are obtained in larger markets to a whole region, and Use regression to predict the price of missing items, based on the price of some other item more widely available. The logic of the regression approach is that spatial price differences may reflect transport costs, so if goods are coming from a common source (say a port) and moving into the hinterland, prices may tend to move proportionally. 14 Of course if there are more complicated commodity flows, with missing prices reflecting seasonality, environmental constraints (eg., altitudinal limits on coconut) etc, then none of these imputation approaches will be very reliable. 14 Glewwe (1991) used the same logic when taking the price of a can of tomato paste as a proxy for non-food prices in an early LSMS surveys in Côte d Ivoire because the non-food prices that were collected were poorly measured. 19

20 In terms of the geographical scale at which to calculate average prices (as an input to the food poverty lines), most surveys, and the subsequent poverty analyses, report these for only a few major regions despite prices being collected from a far larger number of communities. There are at least three reasons for this aggregation: 15 concern about missing prices at the local level (see above) measurement error because the prices observed in a single village market on a given day are only a snapshot taken with a very small sample. By averaging over prices collected in surrounding markets within the region, the share of the variance due to random measurement error will be reduced, and introduction of temporal variation such that the prices obtained in a village on a given day do not reflect the usual prices facing the households in that community. Regional prices may be more representative because surveys that stagger fieldwork over several months or a year will have price samples within a region that are collected over the entire duration of the fieldwork (unless the survey works entirely in one region and then moves to the next region). But prices in a single village are likely to be collected only once, and so will reflect both spatial and temporal/seasonal variation and it will not be possible for the poverty analyst to identify the purely spatial part, which is needed for setting the regional poverty lines. 16 On the other hand, there are some costs of using regional average prices rather than local prices. Regional prices will overstate the cost of buying the poverty line basket of foods in low-price communities within each region, while understating it for others. Measured poverty will be too high in the low-price communities because these same (high) prices are not used for valuing food consumption. Hence, some households will be above the poverty line if that line is priced using local (i.e., cluster-level) prices, but below the poverty line if regional average prices are used. Bias in the opposite direction (measured poverty too low) will occur in clusters where regional average prices understate the local cost of the poverty line basket of foods. At first glance it would seem that there is no net effect of using regional average prices because the overstatement of poverty in some communities within the region is cancelled out by the understatement in others. This would only be true if the distribution of food prices within each region is symmetric. There is surprisingly little evidence on the distribution of staple food prices within regions to know if this is a reasonable assumption. Some evidence is reported by Gibson and Rozelle (1998) for Papua New Guinea. They find, for example, that for sweet potato (the dominant staple supplying 30 percent of the calories in the food poverty line basket) the hypothesis that the distribution of surveyed prices across clusters in the largest region comes from a Normal distribution is rejected (p<0.01), while the hypothesis of log-normality is not rejected (p<0.50). A similar pattern holds for three-quarters of the combinations of other regions and other foods. 15 Additionally, may also be concerns about estimating the non-food allowance separately for every cluster in the sample, which will introduce a large number of intercepts into equation (1). 16 Surveys with a within-year longitudinal component are an exception. Muller (2002) reports on an example of such a survey from Rwanda, where the same households and villages were revisited four times throughout the year. 20