Small Area Estimation Methods for Producing Poverty Maps

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Small Area Estimation Methods for Producing
Poverty Maps

• Berk Özler
• Development Research Group, World Bank
• Washington, DC

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Example Ecuador Poverty Map

• Provinces

Regions
Cantons
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Example Eastern Cape Poverty Map
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What are Poverty Maps?

• Not necessarily Maps rather,
• highly disaggregated databases of poverty and
  inequality.
• disaggregation need not be spatial

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Why is there demand?

• Policy
• Geographic targeting of public policies
• Decentralization (fiscal, community
  decision-making and implementation, etc.)
• Research
• Political economy of local decision-making
• Within-country determinants of welfare outcomes.
• Impact maps

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How to obtain a Poverty Map?

• Basic 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.

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How to obtain a Poverty Map?

• Options
• 1.Collect household data at highly disaggregated
  levels
• 2.Produce Basic Needs Index from census (and
  other data sources)
• 3.Apply small area estimation methods to combine
  survey and census data.

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Collecting Disaggregated Data

• Costly
• Time-consuming
• Quantity-Quality tradeoff
• Difficult to maintain comparability

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Producing a Basic Needs Index

• Ad-hoc
• Often disputed (multiple maps)
• Interpretation? (povertylow income?)

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Small Area Estimation Methods

• Combine Census and Survey Data
• Impute a measure of welfare from household survey
  into census, using statistical prediction
  methods.
• Produces readily interpretable estimates
• Statistical precision can be gauged
• Encouraging results to date
• But, non-negligible data requirements

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Methodology

• Detailed description in Elbers et al. (2003),
  Econometrica.
• Data pre-requisites
• high quality household sample survey and census
  data are available for the same time period. Need
  good measure of welfare (e.g. real per capita
  consumption)
• Census and household survey have a number of
  variables in common (household demographics,
  education levels, etc.)

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Methodology

• Three Stages
• zero stage establish comparability of data
  sources identify common variables understand
  sampling strategy.
• First stage estimate model of consumption in
  the household survey based on common variables.
• second stage take parameter estimates to census,
  predict consumption, and estimate poverty and
  inequality.

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Methodology

• Zero Stage
• make or break can the exercise proceed?
• painstaking and very time consuming.
• not conceptually difficult.
• this cannot be done carefully enough-- you will
  keep coming back to this stage.

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Methodology

• First Stage
• We estimate
• ln yh xhß uh
• Where necessary we use cluster weights.
• Estimate separate regressions per stratum.
• For the disturbances, uh , we allow
• intra-cluster correlation (location effects)
• heteroskedasticity (household component of the
  error)
• non-normality
• (i.e. challenge uh ? (0, ?2), i.i.d.)

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Methodology

• Second Stage
• Now, using census data, calculate...
• Xhß (draw ß from the VarCov (ß) )
• Add error components for the cluster and the
  household (by drawing both errors from the
  appropriate distribution) to calculate...
• Xhß ?c eh
• Using the above, calculate desired welfare
  measures

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Methodology

• Second Stage
• Repeat this N (e.g. N 100) times.
• The mean over N simulations gives the point
  estimate for the desired welfare measure, while
  the standard deviation is the standard error of
  that point estimate.

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Methodology

• Standard Errors
• Difference between u, our estimator of the
  expected value of W for the village, and the
  actual level of welfare for the village may be
  written as
• W u (W-u) (u-û) (û- u)
• first component is idiosyncratic error.
• second component is model error.
• third component is computation error.

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Methodology

• Second Stage
• 2 principal sources of error in the welfare
  measure estimates produced by this method
• model error is due to the fact that the
  parameters from the first-stage equation are
  estimated.
• idiosyncratic error, is associated with the
  disturbance term in the same model, which implies
  that households actual expenditures deviate from
  their expected values.

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Methodology

• Second Stage
• While population size in a location does not
  affect the model error, the idiosyncratic error
  increases as the number of households in a target
  population decreases.
• A third potential source of error is associated
  with computation methods. Elbers et al. found
  this component to be negligible.

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Experience

• Growing experience with method in IFPRI, WFP,
  academia, The World Bank
• Completed Maps
• Ecuador (2), Panama, Nicaragua, Guatemala,
  Kenya, South Africa, Madagascar, Mozambique,
  Malawi, Uganda, Cambodia, Vietnam.
• Maps Underway
• Bolivia, Mexico, Zambia, Bulgaria, Albania,
  Thailand, Indonesia, Papua New Guinea, Laos,
  China.

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How Low Can We Go?
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Applications

• Targeting localities
• Overlay poverty distributions against other
  indicators (deforestation, crime, cholera)
• Survey to survey imputations
• Nutritional mapping (Cambodia)
• Within-country growth regressions (Kuznets type
  analysis) using Panel poverty maps
• Impact mapping

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Cross Cutting Issues

• Emphasis on Process
• in-country work
• transfer of technique
• offers an entry-point for information based
  policy making (e.g. Panama, Guatemala, South
  Africa).
• Squeezing more out of existing data
• Snap-shot dynamics pose additional challenges.
• Validation is needed