Mapping Poverty and Inequality:A Small Area Estimation Approach

Peter Lanjouw,DECRG, The World Bank

Washington D.C., January 25, 2007

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”.

What are Poverty Maps?

Not necessarily “Maps”; rather,highly disaggregated databases of welfare

PovertyInequalityCalorie intakeUnder-nutritionOther indicators (health outcomes? life-expectancy?)

disaggregation may, but need not, be spatial

Poverty of “statistically invisible” groups

Example: Yunnan Province (China)

2%-6%6%-12%

12%-18%18%-30%>30%

County Level Poverty Incidence Estimates

>30%

<2%

Example: Yunnan Province (China)Township-level poverty

Why is there demand for these?Why is there demand for these?

Geographic targeting of anti-poverty programsDecentralization and Public Policy (fiscal, evidence-based policy)Political economy of local decision-makingWithin-country determinants of welfare outcomes.

What is the problem?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.

What are the options?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?)

Options, continuedOptions, continued3. 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

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 gaugedEncouraging results to dateBut, non-negligible data requirements

MethodologyELL (2002, 2003)

Estimate a model of, for example, per-capita consumption, yh, 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.

Three Basic StagesZero 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.

MethodologyLet 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:

ln [ln | ] , Tch ch ch ch ch c chy E y z u z

where ηc is a cluster random effect allowing for a locational influence on consumption. (Can be more than one level.)

Estimation DetailsEstimate separate regressions per stratumUse 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 εch conditional on zch, bounding the prediction between zero and a maximum, A, set equal to (1.05)*max{ech²}:

2Tchch2

ch

eˆln[ ]=z .

A+e chr

Simulation of Welfare MeasuresWe 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:

v v = E[W | m , Z , ], 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, .

Prediction ErrorThe error in the estimator can be decomposed as:

( ) ( ).W W

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.

Albania Poverty Map

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.

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.

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?

Target Population True FGT0 Estimated FGT0 s.e. 1 60.6 58.2 3.7 2 56.8 60.0 3.6 3 57.2 59.8 3.8 4 63.6 61.8 3.8 5 61.6 62.8 3.9 6 64.0 59.2 3.9 7 62.1 59.7 4.1 8 64.7 70.9 3.8 9 61.0 60.3 3.5 10 67.5 65.0 4.0 11 60.3 59.8 3.6 12 56.8 62.7 4.0 13 64.7 64.1 3.4 14 60.4 56.9 4.6 15 57.6 57.8 3.6 16 59.5 58.6 3.6 17 55.3 54.7 4.2 18 58.9 61.5 4.3 19 67.6 65.9 4.2 20 61.3 65.2 3.7

Total 61.1 61.2 2.1

Precision of estimates

Table 4: Relative Frequency of True Target Population Welfare Falling Within 95% Confidence Interval Around Estimated Welfare

Survey Mean Headcount FGT2 GE0 1 1.00 1.00 1.00 1.00 2 0.95 0.95 1.00 1.00 3 0.90 0.85 0.80 0.95 4 0.95 1.00 1.00 0.90 5 1.00 1.00 1.00 0.85 6 0.80 0.90 0.80 0.60 7 0.95 0.95 0.95 1.00 8 0.95 0.95 0.90 0.70 9 0.85 0.85 0.80 0.90 10 0.95 0.90 0.90 0.95 Overall 0.93 0.94 0.92 0.89

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 periodVariables 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.

Countries Being MappedLatin 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

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.

What have we learned so far?

There should be no presumption that small, poor, rural villages are homogenous in terms of income or consumption

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

Table 2: Cost of Reducing Poverty to the same level achieved by Uniform Transfers using the “Optimal” Targeting Scheme

Ecuador

(Rural) Madagascar

(Urban and Rural) Cambodia

(Urban and Rural) Uniform transfer 100 100 100 Optimal Targeting (1st Administrative Level)

76.0 60.7 54.5

Optimal Targeting (2nd Administrative Level)

66.7 46.4 41.4

Optimal Targeting (3rd Administrative Level)

58.4 37.6 30.8

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.

Figure 1: Local Inequality and Probability of FISE Project Receipt

Kernel regression, bw = .02, k = 6

Grid points.051611 .148224

.373049

.615436

Research and Future DirectionsResearch and Future Directions:Methodology

Mapping other indicators (e.g. nutrition)Survey to SurveyUpdating Poverty maps

ResearchShould 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

Cambodia Stunting Map

Poverty and Stunting in Cambodia

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?

Survey to Survey cont.

Poverty TrendsAnalysis 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).

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 27.1Urban India: 39.1 32.4 23.6

These trends suggest an acceleration of poverty decline

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.

Survey to Survey : Methodology

Based on Elbers, Lanjouw, Lanjouw (2001, 2003)We estimate in the 50th round:

ln yh = xhβ + εh

yh: 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 disturbancesheteroskedasticity in individual-specific component of disturbances.non-normal and non-parametric disturbances

report estimated standard errors alongside point

estimates.

Adjustment MethodologiesDeaton 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 55th round headcountsKey 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 55th as in 50th round.

Adjustment MethodologiesDeaton 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?

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

Selected Region-Level Results

Rural 50th 55th (single) 55th (multiple) Andhra South 22% 32% 22% (3.1)Bihar Southern 53% 44% 46% (2.5)Gujarat Dry Areas 38% 23% 35% (4.9)Karnataka Eastern 22% 6% 15% (3.3)Karnataka Southern 40% 22% 30% (2.9)MP Central 46% 20% 37% (4.7)MP Western 65% 52% 66% (3.7)Maharashtra North 53% 38% 47% (3.7)Tamil Nadu Southern 42% 21% 37% (2.6)UP Southern: 51% 16% 45% (5.8)

Note: Standard errors are not smallPartly sampling, and partly prediction error

Adjusted Rural Poverty Estimates% point decline 50th -55th Rounds

Rural IndiaUNADJUSTED 10 Sundaram and Tendulkar (2003a) 9Deaton and Dreze (2002) 7

Sundaram and Tendulkar (2003b) 5Datt, Kozel, and Ravallion (2003) 4 Sen and Himanshu (2004) 3 Kijima and Lanjouw (2003) 3Kijima and Lanjouw (2005) 2

Note: different poverty lines!Rate of poverty decline depends on adjustment method

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