1. Mapping Poverty and Inequality: A Small Area Estimation Approach Peter Lanjouw, DECRG, The World Bank Washington D.C., January 25, 2007

2. Introduction Project within World Bank’s research department in collaboration with Chris Elbers (Free University, Amsterdam) and Jean Lanjouw (UC Berkeley) Numerous other collaborators. Goal is to produce (and use) estimators of welfare that are accurate and easily calculated. Termed “poverty maps”.

3. What are Poverty Maps? Not necessarily “Maps”; rather, highly disaggregated databases of welfare Poverty Inequality Calorie intake Under-nutrition Other indicators (health outcomes? life- expectancy?) disaggregation may, but need not, be spatial Poverty of “statistically invisible” groups

4. Example: Yunnan Province (China)

5. 2%-6% 6%-12% 12%-18% 18%-30%>30% County Level Poverty Incidence Estimates >30% <2%

6. Example: Yunnan Province (China) Township-level poverty

7. Why is there demand for these? Geographic targeting of anti- poverty programs Decentralization and Public Policy (fiscal, evidence-based policy) Political economy of local decision- making Within-country determinants of welfare outcomes.

8. What is the problem? Main source of information on distributional outcomes - household surveys - permit only limited disaggregation. Very large data sources (e.g. census) typically collect very limited information on welfare outcomes.

9. What are the options? 1.Collect larger samples - expensive - some kind of data compromise 2.Combine the limited information available in data sources like the census, into some proxy of welfare (e.g. “basic needs index”) - ad-hoc - often widely disputed (multiple maps) - limited usually to a notion of poverty - how to interpret? (poverty=low income?)

10. Options, continued 3.Impute a preferred measure of welfare (e.g. comprehensive real consumption) from household survey into census, using statistical prediction methods Small Area Estimation Approach developed by a DECRG team

11. Our Solution: Combine Census and Survey Impute a measure of welfare from household survey into census, using statistical prediction methods. Produces readily interpretable estimates: Works with exactly the same concept of welfare as traditional survey-based analysis. Statistical precision can be gauged Encouraging results to date But, non-negligible data requirements

12. Methodology ELL (2002, 2003) Estimate a model of, for example, per-capita consumption, y h, using sample survey data. Restrict explanatory variables to those that can be linked to households in survey and census. Estimate expected level of poverty or inequality for a target population using its census-based characteristics and the estimates from the model of y.

13. Three Basic Stages Zero stage: establish comparability of data sources; identify/merge common variables; understand sampling strategy. First stage: estimate model of consumption. Second stage: take parameter estimates to census, predict consumption, and estimate poverty and inequality.

14. Methodology Let W(m, y) be a welfare measure based on a vector of household per-capita expenditures, y, and household sizes, m. We want to estimate W for a target population (say a village, v) where y is unknown. Typical Estimations to date have used a log-linear model of consumption: where η c is a cluster random effect allowing for a locational influence on consumption. (Can be more than one level.)

15. Estimation Details Estimate separate regressions per stratum Use cluster weights where significant Allow for non-normality of disturbances (parametric/non-parametric), and Heteroskedasticity in individual-specific component of disturbances. Logistic model of the variance of ε ch conditional on z ch, bounding the prediction between zero and a maximum, A, set equal to (1.05)*max{e ch ²}:

16. Simulation of Welfare Measures We are interested in estimating W(m, Z, ζ, u) where m, Z, and u are conformable arrays of household size, observables and disturbances. The expected value of W is: where ζ is the vector of model parameters We replace the unknown vector ζ with consistent estimators from the first stage, and use simulation to obtain our estimator,

17. Prediction Error The error in the estimator can be decomposed as: Idiosyncratic error – increases with smaller populations. Model error – not related to size of target population. Other elements can include: Computation error – part of model error, can be negligible. Sample error – when large dataset is also a sample vs. census.

18. Albania Poverty Map

19. Validation In Mexico, PROGRESA is a rural health, education and nutrition project. As part of the PROGRESA evaluation, a census was taken of all households in 496 rural communities in 1998. 20,544 households were covered This census included detailed information on consumption expenditures.

20. Testing the Poverty Mapping Methodology A random sample of 50 communities was drawn from the full 496 communities. From each of the 50 communities, 10 households were randomly sampled. The data from these households serve as a “pseudo” survey.

21. Testing the Poverty Mapping Methodology 20 “target populations” were constructed from the full set of 496 localities, by grouping together 24-25 localities at a time. Each target population covers about 1000 households. Central Question: How well does poverty mapping methodology applied to the “pseudo survey” predict poverty in the target populations?

25. Precision of estimates

26. Caveats Mexican localities do not vary much in terms of poverty. Haven’t been able to test the methodology in a setting where localities vary dramatically from each other. Test is almost a laboratory set-up: Survey and census refer explicitly to exactly the same time period Variables are fully comparable, by construction. The fact that results are good in Mexico does not mean they will be good everywhere. Mexican experience shows that method matters.

27. Countries Being Mapped Latin America: Mexico, Guatemala, Honduras, Nicaragua, Panama, Ecuador, Bolivia Asia: China, Indonesia, Papua New Guinea, Laos, Cambodia, Vietnam, Thailand, Philippines, Bangladesh, Sri Lanka, India. Africa: South Africa, Mozambique, Madagascar, Kenya, Uganda, Zambia, Malawi, Morocco Eastern Europe and FSU: Albania, Azerbaijan, Bulgaria, Kazakhstan

28. What have we learned so far? The exercise itself can have a huge impact on the debate on poverty within a country and the Bank’s relationship with the client government (e.g. Kenya, Morocco, among many others) Methods borrowed from ‘poverty mapping’ can improve the quality of the debate and inform policy.

29. What have we learned so far? There should be no presumption that small, poor, rural villages are homogenous in terms of income or consumption

30. What have we learned so far? Geographic targeting of transfers can generate very large gains for poverty reduction

31. What have we learned so far? Inequality is negatively correlated with many social outcomes we care about. It can also influence the functioning of projects at the local level.

32. Research and Future Directions Research and Future Directions: Methodology Mapping other indicators (e.g. nutrition) Survey to Survey Updating Poverty maps Research Should we target using maps? How? “Impact” Mapping (ex-ante policy impact analysis) Small area analysis of poverty, inequality and: Growth Environment Crime Health Infrastructure City size Electoral Participation

33. Cambodia Stunting Map

34. Poverty and Stunting in Cambodia

35. Survey to Survey Application: Introduction India in the 1990s: Acceleration of economic growth Economic reforms and liberalization What has happened to Poverty? Has poverty reduction accelerated?

36. Survey to Survey cont. Poverty Trends Analysis has traditionally been based on National Sample Survey (NSS) data. Two “ thick ” rounds in the 1990s: 1993/4 (50th) and 1999/0 (55th) “ Thick ” rounds are designed to be representative at the state and even, sub- state, level (NSS-regions).

37. Survey to Survey, cont. At first glance analysis of NSS data suggest impressive declines in poverty: “ Official ” headcounts (published by Planning Commission) 1987/8 1993/41999/0 Rural India: 39.4 37.3 27.1 Urban India: 39.1 32.4 23.6 These trends suggest an acceleration of poverty decline

38. Survey to Survey, cont. Are these estimates credible? Serious concern regarding comparability of the 50th and 55th round NSS consumption data 55th round applies different recall periods across expenditure items, while 50th applies only one (30 days). –7-day recall period for frequency items like food, 365-day recall period for low-frequency items Households might try to reconcile their answer to questions that refer to different recall periods, it is likely to boost the expenditure estimates based on 30-day recall data.

39. Survey to Survey : Methodology Based on Elbers, Lanjouw, Lanjouw (2001, 2003) We estimate in the 50th round: ln y h = x h β + ε h y h : per capita exp for household h, x: 30-day exp, or a set of observed household characteristics, ε: disturbance term Model is estimated with weights. We estimate separate regressions per state and again per region. We allow for: intra-cluster correlation in disturbances heteroskedasticity in individual-specific component of disturbances. non-normal and non-parametric disturbances report estimated standard errors alongside point estimates.

40. Adjustment Methodologies Deaton and Dreze (2002)identify one consumption component in 55th round questionnaire which has not been altered. 30-day “ intermediate goods ” consumption Comprises fuel and light, rent, non-institutional medical miscellaneous goods and services. Assess the relationship between 30-day comparable consumption and probability of being poor in 50th round, and then predict 55 th round headcounts Key Assumptions: (1) reported 30-day expenditure are unaffected by the changes in questionnaire elsewhere (2) relationship between 30-day consumption and full consumption is much the same in 55 th as in 50 th round.

41. Adjustment Methodologies Deaton and Dreze find a slightly less rapid decline in rural poverty during the 90s. Kijima and Lanjouw worry about some of the regional patterns emerging from Deaton and Dreze results. Is it possible that “ comparable ” 30-day expenditure has been contaminated by questionnaire changes elsewhere? Does the stability assumption underpinning D&D fail to hold in places?

42. Adjustment Methodologies Kijima and Lanjouw propose another specification: model replaces 30-day intermediate goods consumption with a set of other household variables that have clearly not been redefined between 50th and 55th rounds: “ multivariate model ” Assumption: relationship between household ’ s characteristics and log per capita expenditure is stable in each region between 1993/4 and 1999/0 How reasonable? Note: we side-step inflation adjustments

43. Selected Region-Level Results Rural 50 th 55 th (single) 55 th (multiple) Andhra South 22% 32%22%(3.1) Bihar Southern53% 44%46%(2.5) Gujarat Dry Areas38% 23%35%(4.9) Karnataka Eastern22% 6%15%(3.3) Karnataka Southern40%22%30%(2.9) MP Central46%20%37%(4.7) MP Western65%52%66%(3.7) Maharashtra North53%38%47%(3.7) Tamil Nadu Southern42%21%37%(2.6) UP Southern: 51%16%45%(5.8) Note: Standard errors are not small Partly sampling, and partly prediction error

44. Adjusted Rural Poverty Estimates % point decline 50 th -55 th Rounds RuralIndia UNADJUSTED 10 Sundaram and Tendulkar (2003a) 9 Deaton and Dreze (2002) 7 Sundaram and Tendulkar (2003b) 5 Datt, Kozel, and Ravallion (2003) 4 Sen and Himanshu (2004) 3 Kijima and Lanjouw (2003) 3 Kijima and Lanjouw (2005) 2 Note: different poverty lines! Rate of poverty decline depends on adjustment method

45. Concluding remarks “Poverty Mapping” has been widely implemented. As “snap shots” become more common, demand is shifting increasingly towards updates. Poverty monitoring at the local level is a, key, policy imperative in many countries. Critical step is to validate methods outlined here