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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)
• 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
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:
• 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
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.