An Overview of Small Area Estimation (aka Poverty Mapping)

David Stifel Lafayette College IFPRI Addis Ababa

Central Statistical AgencyAddis Ababa, 29 May 2012

1

• To understand the spatial distribution of poverty in a country / region.

What is the goal?

• Main source of information on distributional outcomes (e.g. household surveys) permit only limited disaggregation

o e.g. HICES/WMS – urban/rural within region

• Very large data sources (e.g. census) typically collect very limited information on welfare outcomes

o Usually no data on income or consumption at all

What is the problem?

1. Collect larger samples• Expensive

• There is a quantity-quality trade-off

2. Combine limited information in census into some sort of proxy of welfare (e.g. “basic needs index”, factor analysis asset index, etc)

• ad hoc

• disputed

• interpretation?

How to solve this problem?

3. Use statistical, small-area estimation (SAE) techniques

• Readily interpretable results

Uses exactly the same concept of welfare as traditional survey-based analysis

• Statistical precision can be gauged

• Encouraging results to date

How to solve this problem?

• Brainchild of…o Peter Lanjuow (World Bank)

o Jean Lanjuow (UC Berkeley, deceased)

o Chris Elbers (Free University, Amsterdam)

o Jesko Hentschel (World Bank)

SAE Poverty Maps

Goal: To produce disaggregated estimates of welfare that are accurate and easily calculated

• Called “Poverty Maps”, but not necessarily maps

• Highly disaggregated databases of welfare• Poverty

• Inequality

• Average consumption

SAE Poverty Maps

Terminology: Map

• Mathematical term Map from one set to another

• Geographical term Graphically represent data using a map

We use both terms here.

SAE Poverty Maps

• Nationally or regionally representative household budget survey

Does include household consumption

• National census Does NOT include household consumption

• Comparable correlates of HH consumption in both survey and census (causality does not matter)

• External data can also be merged with survey & census (e.g. GPS recordings – meteorological data)

Data Requirements

1. Identify explanatory variables common to both expenditure survey & census (Stage 0)

2. Estimate model of pc (or per AE) expenditures using expenditure survey at the lowest level of representation – stepwise regression (Stage 1)

3. Predict pc expenditures at household level in target data using the parameters from Stage 1 (Stage 2)

4. Calculate poverty (and/or) inequality measures at desired level of disaggregation

Poverty Mapping - Basics

Estimate the following model in the sample (stepwise)…

(Stage 1)

Using the estimated parameters, predict in the population…

(Stage 2)

Poverty Mapping - Basics

cisurveycici uXc

ln

cicensuscici uXc ˆˆˆln

Use predicted values of expenditure (c) to predict poverty measures (e.g. FGT measures)…

Run 100 simulations (draws from the error term and β distributions), and report average poverty measure & standard errors.

Poverty Estimates

cin

i

ci czz

cz

nP ˆ1

ˆ1ˆ1

• Because explains only a portion of the observed consumption.

• This may be due to: Unobserved factors which also explain the variation in the

observed consumption, but which are not included in the model

Model misspecification

Measurement error in the observed consumption

To account for the first two factors, an estimate of the error term is added to the predicted consumption.

Why include the predicted error?̂X

Actual vs. Predicted Expenditures

0 10,000 20,000 30,000 40,0000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Actual

Predicted

Annual Per AE Consumption

Shar

e of

Pop

ulati

on

z z

Location component (c): Allows for spatial correlation

Household component (ci): Allows for individual differences in the error term (heteroskedasticity)

These error components are drawn from distributions, the variances of which are functions of the data.

So… although the heteroskedastic functional form is assumed constant, the actual distribution is a function of the data.

Error Term

cicciu

Stage 2 – Repeated simulations for different draws from the distributions of β and distribution of…

To get multiple distributions of predicted consumption…

For each simulation, calculate welfare indicators...

Poverty Mapping - Basics

cicensuscici uXc ˆˆˆln

cicciu

Sample

Poverty Mapping – A VisualSample - Poverty

Sample

Poverty Mapping – A VisualCensus - Poverty

Stage 2 – Repeated simulations for different draws from the distributions of β and distribution of…

To get a distribution of predicted consumption…

For each simulation, calculate welfare indicators...

Poverty Mapping - Basics

cicensuscici uXc ˆˆˆln

cicciu

1. Idiosyncratic Error

vs. Larger target sample smaller error

Better prediction from xci smaller error

2. Model Error

vs. Careful specification of the model smaller error

Sources of Error

)];,,([ zuxPE )];([ zcPE

)];ˆ,ˆ,([ zuxPE )];,,([ zuxPE

3. Computation Error

Simulations generate computation error More simulations smaller error

Sources of Error

1. Identify explanatory variables common to both expenditure survey & census (Stage 0)

2. Estimate model of pc expenditures using expenditure survey at the lowest level of representation (Stage 1)

3. Predict pc expenditures at household level in target data using the parameters from Stage 1 (Stage 2)

4. Calculate poverty (and/or) inequality measures at desired level of disaggregation

Review of Poverty Mapping Basics