Arun Srivastava

Small Areas What is a small area? Sub - population Domain The 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 acute The 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 METHODS Purcell and Kish ( ) Symptomatic Accounting Techniques (SAT) Regression Symptomatic Method Sample-Regression Method Synthetic Estimation Method Synthetic Regression Method Base Unit Method Structure 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.

Groups Small domains 1….h……HTotal 1… q Q

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)

–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)

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 – ( ) Ministry of Agriculture (MoARD) Central Statistical Agency (CSA) Both the agencies were estimating area and production of crops through different approaches MoARD – Aggregative approach CSA – Integrated Sample survey approach

SAE Application – contd. CSA was providing estimates for more than 50 crops at Zone levels Growing demand for woreda level estimates One major limitation of CSA results was that woreda level estimates could not be provided SAE approach was tried on CSA results to develop woreda level estimates for 6 important crops

Model Used Fay and Herriot model (Basic area level Type A model) used EBLUP estimates were developed A 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 chosen 6 major crops chosen for SAE application Teff, barley, maize, sorghum, wheat and fingermillet ( ) 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 Used Before EBLUP model was fitted, a regression analysis was done on the input data available CSA 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 ( ) – independent variable

SAE Estimates Not all woredas had good direct estimates But the EBLUP model could provide improved estimates for all woredas EBLUP 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 estimates A bias test – plotting the SAE estimates with the direct estimates Comparing the results with available estimates at Regional and National levels Comparison of MSE and CVs of EBLUP and Direct estimates at woreda levels Local knowledge and expert advice

Some Other Applications Small Area Estimates of School Age Children in Poverty in USA National Academy Press 2000 USDE uses estimates of school age children in poverty to allocate federal funds Earlier allocations based on number and proportion from decennial census

School Age Children in Poverty 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 Remarks SAE approach is feasible and cost effective Alternative methods available Availability of auxiliary data is a constraint sometimes Judicious choice of variables and models needed A 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.

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