Spatial microsimulation: A method for small area level estimation
An Overview of Small Area Estimation
-
Upload
essp2 -
Category
Technology
-
view
360 -
download
3
description
Transcript of An Overview of Small Area Estimation
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