metadata: authors: 0: author: Schady,Norbert Rudiger
count: Peru
docna: 0: docna: Picking the poor : indicators for geographic
            targeting in Peru
docty: Policy Research Working Paper
subtopic: Reproductive Health,Early Child and Children's Health,Nutrition,Energy Policies & Economics,Hydrology,Inequality
teratopic: Poverty Reduction
abstracts: cdata!: Geographic targeting is perhaps the most
            popular mechanism used to direct social programs to the poor
            in Latin America. The author empirically compares geographic
            targeting indicators available in Peru. He combines
            household-level information from the 1994 and 1997 Peru
            Living Standards Measurement Surveys and district-level
            information from the 1993 Peru Population and Housing
            Census. He then conducts a series of simulations that
            estimate leakage rates; concentration curves; the impact of
            transfers on poverty as measured by the headcount index,
            poverty gap, and [poverty] measures of the
            Foster-Greer-Thorbecke family; and nonparametric (kernal)
            densities when transfers are based on alternative
            indicators. He concludes that there is substantial potential
            for geographic targeting in Peru. The differences in
            outcomes across geographic targeting indicators are small
            and not statistically significant.
geo_reg_key: 119228,517191
repnme: repnme: Picking the poor : indicators for
            geographic targeting in Peru
display_title: Picking the poor : indicators for
            geographic targeting in Peru
listing_relative_url: /research/2000/11/717451/picking-poor-indicators-geographic-targeting-peru
topicv3: Water m1326522 137,Infant and Child Mortality m1326544 1446,Poverty m1326687 695,Power and Electricity Sector m1327094 515,Malnutrition m1627088 4737
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Poverty Reduction
origu: Poverty, Gender and Equity Group (LCSPP)
no_of_pages: 28
author_keys: 0: author_key: 321084
model_extractions: I POLIcY RESEARCH WORKING PAPER 2477

# Summary findings

Geographic targeting is perhaps the most popular mechanism used to direct social programs to the poor in Latin America.

Schady empirically compares geographic targeting indicators available in Peru. He combines householdlevel information from the 1994 and 1997 Peru Living Standards Measurement Surveys and district-level information from the 1993 Peru Population and Housing Census.

He then conducts a series of simulations that estimate leakage rates; concentration curves; the impact of transfers on poverty as measured by the headcount index, poverty gap, and PI measures of the Foster-GreerThorbecke family; and nonparametric (kernel) densities when transfers are based on alternative indicators.

He concludes that there is substantial potential for geographic targeting in Peru. The differences in outcomes across geographic targeting indicators are small and not statistically significant.

This paper-a product of the Poverty Sector Unit, Latin America and the Caribbean Region-is part of a larger effort in the region to explore the potential of geographic targeting. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contactTania Gomez, room 18-102, telephone 202-473-2127, fax 202522-0054, email address tgomez@worldbank.org. Policy Research Working Papers are also posted on the Web at www.worldbank.org/research/workingpapers. The author may be contacted at nschady@worldbank.org. November 2000. (23 pages)

> _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 he cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank. its Executive Directors, or the comntries they represent._

Produced by the Policy Research Dissemination Center
# Picking the Poor: Indicators for Geographic Targeting in Peru

Norbert R. Schady World Bank* I thank particularly Christina Paxson for much helpful advice. I have also benefited from comments made by Greg Felker, Francisco Ferreira, Jesko Hentschel, John Waterbury, and participants at a seminar held at the World Bank. I am indebted to Marcos Robles for help obtaining the necessary data from INEI, and to Vajeera Dorabawila for help with the consumption aggregates for the 1994 and 1997 LSMS. Please address correspondence to Norbert R. Schady, The World Bank, 1818 H Street N.W., Washington, DC 20433 (nschady@worldbank.org).
# 1. **Introduction**

Lack of information is a serious constraint<sup>to targeting social programs effectively,</sup> especially in Less Developed Countries (LDCs)<sup>(Besley 1993; Ravallion 1993). Targeting social</sup> programs involves making distinctions between<sup>"deserving" (poor) and "undeserving" (non-poor)</sup> applicants. But this is no simple matter in countries<sup>where household characteristics such as</sup> income are rarely known. In such circumstances, policy-makers<sup>intent on targeting are forced to</sup> choose among imperfect solutions. They can rely<sup>on observable household characteristics, such</sup> as land ownership, the ratio of working age-adults to<sup>dependents, or ownership of durable goods</sup> that seem likely to separate poor from non-poor households.<sup>They can "self-target" programs by</sup> designing them so that they appeal mainly<sup>to the poor--perhaps by offering employment at below-</sup> market wages, or subsidizing foodstuffs consumed<sup>primarily by the poor. Or they can use</sup> "geographic targeting" to direct resources to<sup>areas in which, on average, poverty appears to be</sup> greatest (Akerlof 1978; Besley and Kanbur 1990;<sup>Grosh 1992).</sup> Geographic targeting is appealing because<sup>it is comparatively simple to administer.</sup> Different parts of a country--regions, provinces, districts,<sup>even city blocks--are ranked by some</sup> measure of deprivation. This measure could be income-based<sup>poverty or, more commonly, an</sup> indicator of health, educational or nutritional<sup>status, or access to basic services, such as electricity</sup> or running water. Resources are then allocated in<sup>inverse proportion to average welfare, so that</sup> poor regions receive higher per capita transfers than<sup>rich ones. Alternatively, rich areas can be</sup> excluded from the program altogether. The simplicity<sup>of geographic targeting is an important</sup> advantage when lack of information or administrative<sup>capacity is a serious concern.</sup> This paper compares a number of geographic<sup>targeting indicators that have been discussed</sup> by policy-makers in Peru. These include the infant<sup>mortality rate, which is used to target the</sup> Municipal Compensation Fund, the main block<sup>grant from the central government to local</sup> governments in Peru; a composite "poverty" index<sup>developed by the Peruvian Social Fund</sup> (FONCODES), which FONCODES uses to target its<sup>projects; and an estimate of "imputed"</sup> poverty which combines census and survey data in<sup>an attempt to approximate money-based</sup> measures of welfare.

To test the potential impact on poverty of targeting<sup>with alternative indicators, I conduct a</sup> series of simulations which combine information<sup>on household expenditures from the 1994 and</sup> 1997 Peru Living Standards Measurement<sup>Surveys (LSMS) with district-level averages of various</sup> welfare measures. I use the results of the simulations<sup>to compare leakage rates, trace out</sup> concentration curves, estimate the impact on various<sup>poverty measures of the Foster-Greer-</sup> Thorbecke (FGT) family, and graph non-parametric<sup>(kernel) density estimates of the log of per</sup> capita expenditures (PCE) when transfers are made<sup>on the basis of alternative indicators.</sup> 2
The results show that geographic targeting with any of the indicators is a significant improvement over an untargeted regime in which resources are distributed equally across all districts. There is, therefore, substantial potential for geographic targeting in Peru. However, targeting outcomes are quite similar for all of the targeting indicators I consider, and differences in outcomes between indicators are not significant at conventional levels of significance.

The rest of the paper proceeds as follows. Section 2 briefly describes alternative geographic targeting indicators available in Peru. Section 3 describes the methodology I use to compare indicators. It also describes altemative performance measures, identifies formulas that can be used to allocate resources to districts, describes data requirements, and states the assumptions made for the simulation exercise. Section 4 summarizes the results of the analysis. Section 5 draws conclusions.

# **2. Geographic targeting indicators in Peru**

In 1997 there were 13 administrative regions, 24 departments, 194 provinces, and 1812 districts in Peru (Webb and Fernandez Baca 1997, p. 112). Recent discussion about the geographic targeting of government programs has focused on the use of district-level averages. Districts can be quite small in Peru: According to the 1993 Population and Housing Census, the average district population was about 12,600 inhabitants, but some, predominantly rural districts had less than 200 inhabitants.

# _Infant mortality_

The infant mortality rate measures the fraction of children ever born who do not reach the first year of age. In Peru, as in many other developing countries, one would be loathe to estimate infant mortality on the basis of seriously incomplete death registries. To address this problem, demographers have developed indirect methods to estimate mortality at early ages (Hill, Zlotnik and Trussell 1983; Brass and Macrae 1984 and 1985; Trussell and Menken 1984). The Peruvian National Statistical Institute (INEI) used one such method--the preceding births technique--to estimate infant mortality in Peru.

The preceding births technique requires women to report the total number of children ever born and surviving at two different points in time. This information was available in Peru from the 1981 and 1993 population censuses. However, because the population of many districts is very small, applying the preceding births technique to individual districts would have produced highly uncertain results. INEI therefore followed a two-stage procedure. First, it estimated the infant mortality rate in every department, where the sample size was large enough. In addition, INEI regressed its estimate of the infant mortality rate in every department on some of its 3
correlates--indicators such as women's average education level, household characteristics, and place of residence on which inforrnation had been gathered in the 1993 census. In the second stage, the coefficients from these departmental regressions were applied to district-level data from the 1993 census to estimate district-level infant mortality rates (INEI 1997).

# _The FONCODES index_

Peru has a long history of developing "poverty maps" based on composite indices of unmet basic needs. The first of these maps was constructed by Webb with information from the 1961 population census (Webb 1977). This poverty map was updated with new censuses conducted in 1972, 1981, and 1993 (Amat y Le6n n.d.; Banco Central de Reserva 1981; INEI 1994). FONCODES, in turn, has developed composite poverty maps since its creation in 1991, often with technical assistance from the Inter-American Development Bank, the World Bank, and the German development agency GTZ.

The current district-level poverty map was developed by FONCODES and the Ministry of the Presidency. It is based on eight indicators--the rate of chronic malnutrition, illiteracy, schoolaged children not in school, overcrowded housing, inadequate roofing, and the proportion of the population without access to water, sewerage, and electricity. All of these indicators except the rate of chronic malnutrition were estimated with data from the 1993 population census. The rate of chronic malnutrition was estimated from a census of height and weight among school-aged children, also conducted in 1993 (FONCODES 1995 and 1996).

Composite indices invariably involve some arbitrary weighting of individual indicators. The 1996 index standardized each indicator by dividing it by its minimum value, multiplied the rate of chronic malnutrition by seven, and then added all of the individual indicators' For ease of interpretation, FONCODES then standardized the index by dividing all values by the lowest value. The resulting index ranges from a value of 1 to 36.38.

# _Imputed poverty and income_

In Peru, there are no survey-based estimates of income or expenditures at a level more disaggregated than the department: for example, household surveys conducted by INEI, which generally have sample sizes of 15,000 to 20,000 households, can only be used to compare income i This procedure had the unintended consequence that the greatest weight was given to those indicators with the greatest variance. Thus, while the intended weights were 50% for the rate of chronic malnutrition, and 7.14% each for the seven other measures, the actual weights in the index turned out to be 15.3% for the rate of chronic malnutrition, and 3.4%, 2.2%, 3.0%, 38.3%, 8.8%, 7.4%, and 21.6% for the measures of illiteracy, school attendance, overcrowding, inadequate roofing, and access to water, sewerage and electricity, respectively (World Bank 1996, p. 7).

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across "natural regions" and departments.2 But INEI has combined variables which are common to both the 1993 census and one such survey conducted in 1995 to develop imputed district-level measures of income and poverty (INEI 1996).

This procedure is conceptually similar to that used to estimate infant mortality at the district level. INEI estimated income in 1995 on the basis of the household survey, and then regressed income in every department on its correlates--household composition, education levels, access to basic services such as water, sewerage and electricity, ownership of durable goods, such as television, radio and refrigerator, and other variables included in both the census and the survey. The coefficients from the 24 department-level regressions were then used to impute average income in every district, and the fraction of the population in each district below an income-based poverty line.

# **3. The analytic framework**

# _Measures ofperformance_

The simplest measure of targeting focuses on leakage and undercoverage rates (Grosh, pp. 16-17; Baker and Grosh 1994). A poverty line is chosen to separate "poor" from "non-poor". Leakage rates are then defined as the fraction of total program resources which go to the nonpoor, and undercoverage rates as the fraction of the poor who do _not_ benefit from the program. By this measure, better geographic targeting indicators result in lower leakage and lower undercoverage rates.

A second approach simply ranks individuals by an indicator of welfare-say, per capita expenditures-and then cumulates the fraction of households and the fraction of resources transferred by different indicators. The results are often presented in terms of so-called "concentration curves" (see, for example, Milanovic 1995), and I follow this practice below. By this measure, the best targeting indicator is that whose concentration curve is above all others at every point. The concentration curve method does not require use of a poverty line, which may be an advantage given the fact that setting poverty lines can be contentious.

Alternatively, one might want to compare the changes in various poverty measures which are likely to result when transfers are based on alternative targeting indicators (Chaudhuri and Ravallion 1994). This is an exercise in comparative statics: what is total poverty before and

> 2 These natural regions are Lima, and the urban and rural areas of the coast, sierra (highlands), and selva (3ungle), respectively. Natural regions do not, in general, correspond to the administrative regions mentioned before.

3 The methodology applied by INEI for these imputations is similar in spirit to that proposed in Hentschel et. al (2000).

5
immediately after the transfer? By this measure, the preferred geographic targeting indicator directs limited resources to areas where they would have the greatest short-term impact on poverty. More complex formulations, which might model the expected long-term returns<sup>from</sup> transfers to different districts, are beyond the scope of this paper (see the comments by Binswanger 1989, cited in Ravallion 1993).

In what follows I use three poverty measures from the Foster-Greer-Thorbecke (FGT) family--the headcount index, the poverty gap, and the P2 measure (Foster, Greer, and Thorbecke 1984). The FGT family of poverty measures follows the general formulation below: where y is income, z the poverty line, and a is a parameter which represents the aversion to inequality. When a=O, Po corresponds to the headcount index--the number of people below the poverty line; when oa= 1, P1 corresponds to the poverty gap--a sum of the individual shortfalls in income for those below the poverty line, as a fraction of the poverty line itself. As a increases, the measure gives a greater weight to the poorest poor, and at very high values of a P,, approaches a "Rawlsian" measure of welfare which gives weight only to the poorest household. The P2 measure corresponds to a value of a=2.

Finally, one could look at changes in the entire distribution of log PCE, rather than just at changes for those below the poverty line. I use non-parametric (kernel) density estimates for this purpose.

# _Allocationformulas_

When there is no targeting, districts are simply allocated resources according to their share of the total population in the country, and everyone is assumed to receive the same per capita transfer. This no-targeting scenario serves as a benchmark to measure additional reductions in poverty that could be achieved when geographic targeting is conducted on the basis of some welfare indicator.

To compare targeting indicators, one must develop a formula which allocates resources across districts. I consider one such formula, which is relevant for Peru because it has been<sup>the</sup> basis of targeting by FONCODES, the program which made the most significant early advances developing targeting indicators in Peru. FONCODES ranks all districts by its poverty index. It then allocates resources to each district according to the following formula: 6
(2) _Allocation, (Index, * Population,)_ The "FONCODES method" thus makes all districts in the country eligible for benefits, but weights the population of each one by its poverty index. For example, Coronel<sup>Castaffeda, the</sup> district with the highest value of the FONCODES index (36.38),<sup>and a population of 607</sup> inhabitants, would be allocated (36.38*607)/346,201,217 = .0064%<sup>of the total budget for that</sup> year. By contrast, Pacocha, the district with the lowest value<sup>of the FONCODES index (1.00),</sup> and a population of 6500, would be allocated (1*6,500)/346,201,217<sup>= .0019% of the total budget</sup> for that year. Per capita allocations to inhabitants of Coronel<sup>Castafieda Castaiieda would</sup> therefore be almost 37 times per capita allocations to inhabitants of Pacocha<sup>4Note that if the</sup> index is a poverty rate, allocations to district i simply correspond to the fraction<sup>of the poor who</sup> live in district i. I adapt the "FONCODES method" to other indicators by substituting<sup>the infant</sup> mortality rates and the imputed poverty measure for the FONCODES index<sup>in equation (2)</sup> above, and compute the corresponding district-level allocations.

The simulations in this paper make a number of assumptions. The most<sup>important</sup> assumption is that there is no targeting of program resources _within_<sup>a given district. This is</sup> clearly unrealistic: Paxson and Schady (1999) use non-parametric<sup>regressions to estimate the</sup> probability of benefiting from social programs as a function of the number<sup>of standard deviations</sup> a given household's income is above or below mean district income.<sup>Their results show that the</sup> within-district distribution of investments made by FONCODES<sup>and the food distribution</sup> program PRONAA is hump-shaped, peaking at about one-standard<sup>deviation above mean district</sup> income, while the within-district distribution of investments made by the school<sup>construction</sup> program INFES is regressive, rising with household income. A<sup>more plausible assumption for</sup> the simulations in this paper is that the degree of within-district<sup>targeting is independent of the</sup> 4 In actual fact, FONCODES' allocation mechanism is a little more complicated<sup>than this. FONCODES</sup> first allocates 60% of resources to rural areas and 40% to urban areas. The<sup>final allocation to each district</sup> is then the sum of the rural and urban allocations--standardized toadd up to 100%, Ad hoc adjustments are also made to privilege border areas, to coordinate investments with other<sup>public sector programs, and to</sup> ensure that each of FONCODES' regional offices (which correspond roughly<sup>to individual departments)</sup> has a minimum operating budget. I do not take these "refinements" into account<sup>in the simulations below.</sup> **5** Of course, this is only one of a potentially infinitely large number<sup>of fortnulas which could be used. For</sup> example, the Technical Team of the Ministry of the Presidency has<sup>proposed an allocation formula which</sup> makes a distinction between districts with a high _proportion_ of poor<sup>people (as measured by the</sup> FONCODES index) and districts with a large _number_ of poor people<sup>(as measured by the product of the</sup> FONCODES index and population). Proposed investments would then be<sup>directed to 262 districts with the</sup> highest proportion of the population in poverty and 232 districts with<sup>the highest number of people in</sup> poverty. The final count is 419 of Peru's 1812 districts, because<sup>some districts have a high value of the</sup> FONCODES index and a high value of the product of the index and population.

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choice of welfare indicator which is used to distribute resources _across_ districts. Under this assumption, which seems quite reasonable, the actual estimates of changes in poverty under different targeting regimes will be biased (up, if there is positive intra-district targeting, down if the converse is true), but the preferred rank-order of the indicators used to assign resources _across_ districts should be unaffected.

The simulations assume that benefits from program investments in a district accrue entirely to the residents of that district. This might not hold, say, if beneficiaries of a food distribution program implemented in one district are residents of a different district. But intra-district spillovers are unlikely to be systematic--that is, they should not consistently favor residents of one kind of district over residents of another. Intra-district spill-overs should therefore not affect the rank order of indicators either.

Some additional assumptions have to be made about the impact of transfers on various poverty measures. Poverty in Peru has generally been defined as an individual's inability to meet a specified level of expenditures-the poverty line-when individual expenditures are approximated by total household expenditures divided by the number of eligible household members.<sup>6</sup> We must therefore translate expenditures by social programs into household expenditures--by first translating program expenditures into changes in household income, and then estimating the proportion of additional disposable income that is spent. As a matter of convenience, I have assumed that all program expenditures translate into additional household income and that all of this additional income is spent7 Finally, the simulations assume that the cost of administering programs is constant across regions, and ignore the effects of transfers on behavior such as migration towards districts which 6 The 1995 and 1996 INEI household surveys, which used income to measure poverty, are exceptions. 7Two points are worth noting here. First, many social programs in Peru are involved with the construction of small-scale infrastructure. The wages paid to laborers in these projects are only a fraction of the total cost, and other benefits--say, of having an additional classroom--are unlikely to have a short-term impact on household income. We can easily relax the assumption of a one-for-one equivalence between changes in program expenditures and changes in household income, however, if we simply model a smaller budget. For example, if only 50% of the expenditures on poverty alleviation programs translate into short-term increases in income, the "relevant" budget would be only half the actual budget. Second, households typically do not spend all of an increase in income. Assuming that all households spend a fixed fraction of additional income is not entirely satisfactory either, because the marginal propensity to save is likely to differ _systematically_ across households. For example, if the fraction of income that is saved is higher in rich districts than in poor districts, simulations based on a constant marginal propensity to save might under-estimate the short-term impact of program investments in poor districts relative to rich districts, and under-estimate the relative performance of targeting indicators which assign a higher share of their resources to the poorest districts. One potential solution would be to estimate marginal propensities to save for households from the LSMS itself. The simplest way to do this would be to convert measures of income and expenditures into current prices, and then take the difference between them as a measure of savings (see especially Paxson 1992). By this measure, however, almost two-thirds (61%) of households in the 1994 LSMS _dissaved._ This seems unreasonable and suggests that income in these surveys is seriously underestimated vis-a-vis expenditures.

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receive large per capita transfers, offsetting reductions in private intra-household transfers or employment, and the impact of taxes needed to finance poverty alleviation programs.

# _The data set_

For all of the estimations below, I combine information from two sources: district-level averages of the infant mortality rate, the FONCODES index, and the measure of imputed poverty, and household-level data on expenditures. District-level averages are available from INEI, and household-level data can be estimated from the 1994 and 1997 LSMS, both of which were executed by the Peruvian think-tank Cuanto.

District-level data can be used to estimate the proportion of total funds that would be allocated to every district under alternative targeting regimes. Further dividing this fraction by the total population of the district in question allows us to calculate the proportion of funds that would be allocated to every individual. Finally, multiplying this proportion by the total budget available for poverty alleviation programs, we can estimate per capita transfers.

The LSMS can be used to estimate the expenditures of the households in the sample (3,558 for 1994, and 3,840 for 1997) and, dividing total household expenditures by household size, for household members (18,362 for 1994 and 19,562 for 1997). These estimates can be combined with information on poverty lines to calculate the headcount index, poverty gap, and P2 measure at a national level before any transfers take place.8 The 1994 and 1997 Peru LSMS drew households from 364 and 397 clusters, respectively, and the accompanying literature lists the districts from which each one of these clusters was drawn. Observations in the LSMS can be coded manually with district identifiers which match those used by INEI, and district-level and household-level data can then be merged. Having done this, we keep only those observations for which there are matching codes for place of residence in both data sets--in effect, discarding the district-level information for all but the 199 and 238 districts which were sampled in the 1994 and 1997 LSMS, respectively.<sup>9</sup> The new, composite s Note that regional price deflators available from Cuanto and INEI are used throughou **t** he paper to deflate _both_ household expenditures and simulated transfers.

9 In theory, the first step in the FGT approach implemented in the simulations in this paper would divide a given budget amongst the 1812 districts in Peru. How much gets allocated to each district would then depend on the targeting indicator and the allocation formula in question. But the fact that households in the 1994 and 1997 LSMS were only drawn from 199 and 238 districts across the country, respectively, raises a potential problem: since every targeting indicator allocates a different amount to each district, the total budget for this sample of districts would _not_ be constant across indicators. For example, the proportion of the total budget allocated to the 199 districts in the 1994 LSMS would be smaller by the FONCODES index than by the measure of imputed poverty. As a result, the total amount transferred to the 3,558 households in the survey would be smaller when we use the FONCODES index than when we use the imputed poverty measure, even after each household in the survey is weighted by its expansion factor. At the heart of the problem is the fact that the LSMS draws a nationally-representative sample of households 9
data set is representative in exactly the same way as the original LSMS data set, and can be used to make reasonable simulations about changes in expenditures and poverty at the national level. .

# **4. Results**

What is the effect of geographic targeting with alternative indicators in Peru? As a first step towards answering this question, I present estimates of poverty and allocations of funds by region. About two-thirds of the population of Peru lives in urban areas, and well over a third of these urban residents live in the capital city, Lima. Table 1 decomposes poverty measures and allocations by alternative geographic targeting indicators into three categories: Lima, other urban, and rural. The values in each cell correspond to the proportion of total poverty or the proportion of total allocations by region, so that every row sums to 100%. Here, and for all of the results presented in the paper, individuals in the household surveys are weighted with the appropriate expansion factors.

Since the no targeting scenario makes an equal transfer to every Peruvian, regional allocations when there is no targeting correspond exactly to the fraction of the population living in each region. A comparison of these allocations with the various poverty measures shows that poverty in urban areas is below average: about 29% of the population lives in Lima, but only 14% to 22% of total poverty was found there in 1994, and 13% to 20% in 1997. Other urban areas account for about 36% of the population, and about one-third of poverty. Poverty in rural areas, by contrast, is well above average: just over one-third of the population lives in rural areas, but between 44% and 55% of poverty was found there in 1994, and as much as 47% to 57% in 1997.

Table 1 suggests that geographic targeting using any of the indicators under consideration appears to approximate the distribution of poverty reasonably well. When any of these indicators is used for geographic targeting, about one-half of all resources are transferred to rural areas, and about two-thirds of the remaining resources to urban areas outside Lima. Comparing the three indicators, the FONCODES index transfers more to Lima than the measures of infant mortality and imputed poverty, while the measure of infant mortality makes the largest transfers to rural areas.

irrespective of the district in which these households live. If a number of samples were drawn, on average, the total budget would be the same across indicators, but this does not hold for any one sample. I have corrected for this problem by normalizing the budget-in effect, summing equation (2) above only over the sample of districts in the LSMS. Note that this is not an issue with the concentration curve approach because concentration curves graph out the _proportion_ of a given budget that is allocated to each household

**10**
# _Leakage rates_

Table 2 presents leakage rates by targeting indicator. The leakage rate when there is no targeting (46.50 in 1994, and 51.15 in 1997) corresponds exactly to the fraction of the population which is not in poverty. Table 2 shows that leakage rates would be minimized with geographic targeting by the infant mortality rate (according to the 1994 LSMS) or the FONCODES index (according to the 1997 LSMS). Bootstrapped standard errors (not reported, but available from the author upon request) suggest that geographic targeting with any of the indicators in question is a significant improvement on the no targeting scenario, while the differences in outcomes across indicators are not significant.

# _Concentration curves_

Initial simulations show that the concentration curves for the FONCODES index, the infant mortality rate, and the imputed poverty rate are so close to each other as to be virtually indistinguishable from each other on a graph. For the sake of clarity, I therefore graph the _difference_ between each of the concentration curves and the no targeting baseline case in Figures 1.1 and 1.2. (The "concentration curve" for the no targeting scenario is a straight, forty-five degree line: every individual receives the same transfer, so the cumulative fraction of the transfer equals the cumulative fraction of the population at every point). Figure 1.1 shows that this difference is positive throughout for all three curves: no matter where we take the cut-off between "poor" and "non-poor" to be, the poor receive a larger share of transfers when these are made on the basis of the infant mortality rate, the FONCODES index, or the measure of imputed poverty than when transfers are not targeted. Figures 1 .1 and 1.2 also show that no single concentration curve lies everywhere above all others, although the FONCODES index curve always transfers more resources to poor households than the imputed poverty measure. This is noteworthy given that much recent effort has gone into developing these kinds of measures, in Peru and elsewhere.

# _Changes in poverty_

Figures 2.1 and 2.2 consider the impact of alternative geographic targeting regimes on poverty at various budget levels between 10 million soles and 5 billion soles (for a similar approach see Chaudhuri and Ravallion 1994, and Jalan and Ravallion 1998). As a point of reference, the Ministry of the Presidency, the single largest implementing agency of social in the survey-weighted, once again, by the appropriate expansion factors. Because concentration curves are mean-normalized in this way, the results are budget-independent.

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programs in Peru, spent 2.2 billion soles on programs which could be targeted in 1995.10 For the sake of parsimony, I present graphs only for the poverty gap measure. Results for the headcount index and the P2 measure, which are available from the author upon request, are very similar." Once again, because targeting outcomes with different indicators are very similar to each other but are clearly superior to the no targeting regime, I graph the _differences_ in poverty gaps. One way to understand the graphs is therefore as a double-difference: the first difference is the change in the poverty gap when a given budget is transferred-separately, for the no targeting scenario, and for geographic targeting using the FONCODES index, the infant mortality rate, and the measure of imputed poverty. The second difference is the difference between the change in the poverty gap under the no targeting scenario, on the one hand, and the changes in the poverty gap when there is targeting by a given indicator. The value of the y-axis at any given budget and for any given curve is therefore the additional increase in the poverty gap which could be attained from switching from no targeting to targeting with the indicator in question.

Impact on povet: Like the concentration curve analysis, Figures 2.1 and 2.2 show that targeting with any one of the indicators in question is clearly preferable to no geographic targeting: all of the curves are above zero throughout. Figures 2.1 and 2.2 also show that none of the indicators clearly outperforms the others, although transfers based on imputed poverty appear to result in smaller decreases in poverty than the corresponding transfers made on the basis of infant mortality or the FONCODES index.<sup>12</sup> Budget savings: Table 3 presents the same information from a different angle: it considers the impact on the headcount index, poverty gap, and P2 measures of spending the 2.2 billion sol reference budget without geographic targeting, and estimates the budget that would be necessary to achieve this same reduction in poverty when geographic targeting is conducted by the infant mortality rate, imputed poverty, or FONCODES index, respectively. The results show that the '° These expenditures included programs in housing (Banco de Materiales, ENACE), potable water, sanitation, and electricity (UTE-FONAVI), educational infrastructure (INFES), food and nutrition (PRONAA), social services (INABIF), and numerous multi-sectoral programs (FONCODES, COOPOP, INADE) (World Bank 1996).

**'** The curves for the headcount index tend to be much more choppy. The reason for this is that transfers will not reduce the headcount index unless at least one person in the country (or, in this case, one person in the survey) is bumped over the poverty line. This need not happen, for example, if resources are spent on those who are well below the poverty line. An increase in expenditures on the poor will always reduce poverty, however, if poverty is measured by the poverty gap or P2 measures.

12 Once again, bootstrapped standard errors suggest that the differences between, on the one hand, the no targeting case and, on the other hand, the measures of imputed poverty, infant mortality, and FONCODES index are statistically significant at the 1% level or better. The differences between the infant mortality rate, FONCODES index and imputed poverty are not significant (estimates available from the author upon request).

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headcount index could be reduced by the same amount with a budget which is 159 million to 361 million soles smaller; the poverty gap could be reduced by the same amount with a budget which is between 288 million and 353 million soles smaller; while the P2 measure, finally, could be reduced by the same amount with a budget which is 309 to 397 million soles smaller. Clearly, substantial savings can be achieved with geographic targeting in Peru.

## _Non-parametric density estimates_

Figure 3. 1, finally, graphs the non-parametric (kernel) density estimates of the log of PCE _after_ hypothetical transfers totaling 2.2 billion soles have been made to households in the 1997 LSMS. I do not show the comparable picture for 1994 because it is very similar indeed. To avoid cluttering the picture, and because outcomes are so similar across indicators, I present density estimates for the FONCODES index and the no targeting scenario only. A vertical line which corresponds to the log of PCE at the poverty line is also included. Figure 3.1 clearly shows that the left tail of the distribution for the no targeting scenario has more mass than the corresponding distribution for the FONCODES index: that is, the fraction of people with very low levels of income would be higher had transfers to districts been based simply on population rather than on the FONCODES index. By contrast, more mass is concentrated around the middle of the distribution when transfers are made using the FONCODES index. The cumulative density functions of log PCE (not presented, but available from the author upon request) show that the distribution corresponding to the FONCODES index first-order stochastically dominates the no targeting distribution up to the poverty line (the two distributions intersect at about the poverty line).

# **5. Conclusion**

Geographic targeting of social programs has become increasingly important in Peru. Expenditures in basic health, primary education, nutrition programs, and basic justice conducted by the regular line ministries through the Basic Social Expenditure Improvement Plan have generally been directed towards the poorest departments. The Municipal Compensation Fund, the main block grant from the central governmen **t** o local governments in Peru, is allocated with a formula which takes into account the population, infant mortality rate, and proportion rural in each district. FONCODES has used its own poverty maps since 1992, and other programs in the Ministry of the Presidency have been encouraged to prioritize investments in a sub-sample of districts.

In this context, it is important to see how well different targeting indicators perform in practice. This paper evaluates alternative indicators for geographic targeting available at the 13
district level in Peru. I use a number of outcome measures to compare geographic targeting indicators: leakage rates; concentration curve analysis; the impact of transfers on poverty as measured by the headcount index, poverty gap and FGT P2 measure; and non-parametric density estimates of the log of per capita expenditures when transfers are made on the basis of competing indicators. The results in this paper suggest that there are large potential pay-offs to geographic targeting in Peru. But differences between geographic targeting indicators-the FONCODES index, the infant mortality rate, and the measure of imputed poverty-are small.

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