Use of Small Area Estimation Method: Case of Ethiopia

Arun Srivastava

Small AreasWhat is a small area?Sub - populationDomainThe Domain need not necessarily be

geographical. Examples

Geographical Subpopulations – districts as small areas

Small domains- group of people with specific age, sex, race types of classifications.

Small Areas – Contd.How small should be the domain to be

considered as Small Area?

Purcell and Kish (1979)Major Domains (1/10 of the pop. or more)Minor Domains ( Between 1/10 and 1/100)Mini Domains (Between 1/100 and

1/10,000)Rare Domains (Less than 1/10,000)

What is SAE Problem?Sample surveys are often designed to

produce estimates at higher levels such as Country, State or sometimes even for Districts

For micro-level planning, estimates needed at smaller levels

Direct estimates for large domains or subpopulations can be improved through standard sample survey techniques (such as ratio or regression methods)

What is SAE Problem? – Contd.For smaller domains the problem

becomes more acuteThe sample sizes available at SA level are

sometimes too small to be used for developing direct estimates

The standard techniques of estimation based on direct estimation do not work

Indirect methods of SAE techniques developed

What is SAE Problem? – Contd.• Important Features

– Use of information from other sources, such as official records, registers etc

– Borrows strength from related or similar areas through implicit and explicit models

– Cost – effectiveness, sample sizes need not be increased

SOME CLASSICAL SAE METHODSPurcell and Kish (1979-80)

Symptomatic Accounting Techniques (SAT)

Regression Symptomatic MethodSample-Regression MethodSynthetic Estimation MethodSynthetic Regression MethodBase Unit MethodStructure Preservation Method (SPREE)

Synthetic method of estimation• National Center for Health Statistics (1968). • Gonzalez (1973)

– An unbiased estimate is obtained from a sample survey for a larger area. When this estimate is used to derive estimates for sub areas

having the same characteristics as the larger area, these estimates are identified as synthetic estimates.

11N hN1 HN1 .N1

1qN qhN qHN .qN

1QN QhN QHN .QN

1.N hN. HN. N

GroupsSmall domains

1 …. h …… H Total

1 ……

 

             

q    

             

Q    

Total    

Synthetic estimation (Contd.)

Y qhY ˆ Nq.

NqhH

1=h ˆ

q.

hYh

Y .ˆ

H

1 qX

qhX

= .q

ˆ

H

1=hY.

hX

qhX

= Y . hq

Synthetic estimation (Contd.)Synthetic method and all other traditional

methods are based on assumptions and models are implicit in the assumptions

Subsequently, SAE methods based on explicit statistical models have been developed

Some of the models are described as follows:

Small Area Models• Two types of models

– Only area-specific auxiliary data

available and the parameters of interest are

assumed to be related to

( Type A models)

T)xipxi1(Xi

iiX

iiiTii evbXˆ

– Element-specific auxiliary data are available for the population elements, and the variable of interest, y, is assumed to be related to through a nested error regression model:

j = 1,------, Ni ; i = 1,--------,m

( Type B models)

ijiTijij evXy

Small Area Models (Contd.)1. Empirical Best Linear Unbiased Predictor

(EBLUP)

2. Empirical Bayes Approach (EB)

3. Hierarchical Bayes Approach (HB)

Basic Area Level (Type A) model with EBLUP method was used in the Ethiopian context

Reference: J.N.K. Rao (2003) Small area Estimation, Wiley Series in Survey Methodology

SAE Application in Ethiopia Background – (2008-09)Ministry of Agriculture (MoARD) Central Statistical Agency (CSA)Both the agencies were estimating area and

production of crops through different approaches

MoARD – Aggregative approachCSA – Integrated Sample survey approach

SAE Application – contd.CSA was providing estimates for more than

50 crops at Zone levelsGrowing demand for woreda level estimatesOne major limitation of CSA results was that

woreda level estimates could not be providedSAE approach was tried on CSA results to

develop woreda level estimates for 6 important crops

Model UsedFay and Herriot model (Basic area level Type

A model) usedEBLUP estimates were developedA software was developed for the procedure

at CSA The method requires woreda level auxiliary

variables to be used as input data in the model

Crops chosen6 major crops chosen for SAE applicationTeff, barley, maize, sorghum, wheat and

fingermillet (2007-08)Criteria for choosing the crops was the the

coverage of crops and CVs for the estimated crop areas at Region level

These crops had less than 4 to 5% CV at region levels

Only good estimates can be scaled down to SA levels through SAE techniques

Input Data UsedBefore EBLUP model was fitted, a regression

analysis was done on the input data availableCSA crop area estimates at woreda level as

obtained in Annual survey results – dependent variable in the linear model

Agricultural Census (2001) results – independent variable

MoARD estimates (2007-08) – independent variable

SAE EstimatesNot all woredas had good direct estimatesBut the EBLUP model could provide improved

estimates for all woredasEBLUP estimates at woreda levels were done

for Tigray, Amhara, Oromiya, Benishangul Gumuz and SNNP regions

Estimates for Affar, Somalie and Gambela were not done

Hareri and Diredawa SAE estimates not needed as there were only one woreda in these regions

Diagnostics For assessing accuracy, validity and

consistency of SAE estimatesA bias test – plotting the SAE estimates with

the direct estimatesComparing the results with available

estimates at Regional and National levelsComparison of MSE and CVs of EBLUP and

Direct estimates at woreda levelsLocal knowledge and expert advice

Some Other ApplicationsSmall Area Estimates of School Age Children

in Poverty in USANational Academy Press 2000USDE uses estimates of school age children

in poverty to allocate federal fundsEarlier allocations based on number and

proportion from decennial census

School Age Children in Poverty1994- authorization of census bureau for

updating of estimates every two years (1993 estimates in 1996 and 1995 estimates in 1998)

The SAE approach developed being used regularly

Concluding RemarksSAE approach is feasible and cost effectiveAlternative methods availableAvailability of auxiliary data is a constraint

sometimesJudicious choice of variables and models

neededA word of caution

What can be done and what can not be done through SAE techniques should be kept in mind.

Visibility of estimates at SA levels demands more credibility of results.

THANKS