Small area estimation of poverty indicators

Abstract

We propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains.Keywords: Empirical best estimator; Parametric bootstrap; Poverty mapping; Small area estimation. AbstractWe propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains.

A Comparison of Small Area Estimation Methods for Poverty Mapping

“…The EB method of Molina and Rao (2010) assumes that the population variables Y di follow the nested error model (9) with normality of random effects u d and errors e di . Under that model, the area vectors…”

“…where v (a) d and (a) dr are independent and satisfy Molina and Rao (2010). Using model (14), instead of generating a multivariate normal vector (14) using as means, the corresponding elements µ di|s of µ dr|s given by (11).…”

“…In particular, to estimate the FGT poverty indicator given in (1), Molina and Rao (2010) assumed that Y di = T (E di ) follow the nested error model (9), where E di are variables measuring welfare and T (·) is a one-to-one transformation. In terms of the vector of transformed variables…”

“…• In terms of model MSE, ELL estimates perform poorly and can even perform worse than direct estimators when unexplained between-area variation is significant, see Molina and Rao (2010). In fact, for the estimation of domain means, ELL estimates are basically equal to regression-synthetic estimators, which assume the regression model without further between-area variation.…”

“…Here we review the main small area estimation methods for poverty mapping. In particular, we consider direct estimation, the Fay-Herriot area level model, the method of Elbers, Lanjouw and Lanjouw (2003) used by the World Bank, the empirical Best/Bayes (EB) method of Molina and Rao (2010) and its extension, the Census EB, and finally the hierarchical Bayes proposal of Molina, Nandram and Rao (2014). We put ourselves in the point of view of a practitioner and discuss, as objectively as possible, the benefits and drawbacks of each method, illustrating some of them through simulation studies.…”