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Demand for reliable statistics at a local area (small area) level has greatlyincreased in recent years. Traditional area-specific estimators based onprobability samples are not adequate because of small sample size or even zerosample size in a local area. As a result, methods based on models linking theareas are widely used. World Bank focused on estimating poverty measures, inparticular poverty incidence and poverty gap called FGT measures, using asimulated census method, called ELL, based on a one-fold nested error model fora suitable transformation of the welfare variable. Modified ELL methods leadingto significant gain in efficiency over ELL also have been proposed under theone-fold model. An advantage of ELL and modified ELL methods is thatdistributional assumptions on the random effects in the model are not needed.In this paper, we extend ELL and modified ELL to two-fold nested error modelsto estimate poverty indicators for areas (say a state) and subareas (saycounties within a state). Our simulation results indicate that the modified ELLestimators lead to large efficiency gains over ELL at the area level andsubarea level. Further, modified ELL method retaining both area and subareaestimated effects in the model (called MELL2) performs significantly better interms of mean squared error (MSE) for sampled subareas than the modified ELLretaining only estimated area effect in the model (called MELL1).

Estimation of Poverty Measures for Small Areas Under a Two-Fold Nested Error Linear Regression Model: Comparison of Two Methods