Small Area Estimation of Poverty Incidence with Sampling Error Variances Through Generalized Variance Function

Abstract

Small area estimation based on area level models, particularly the EBLUP method, typically assumes that sampling error variances of the direct survey small area estimates are known. In practice, the sampling error variances are unknown. This paper generates EBLUP estimates of poverty incidence when the sampling error variances are estimated using the generalized variance function (GVF) approach. The precision of the EBLUP estimates is determined using a modified version of the Prasad-Rao MSPE estimator. The modification is made by adding an extra term that would account the uncertainty associated with estimating the sampling error variances. The performance of the modified Prasad-Rao estimator relative to the commonly used Prasad-Rao estimator is evaluated through a simulation study. Results have shown that the modified Prasad-Rao MSPE estimator has relatively greater bias than the commonly used Prasad-Rao MSPE estimator, particularly for small samples. A slight gain in precision is observed when using the modified PR MSPE estimator, especially for large samples. Moreover, the findings imply that estimating sampling error variances using GVF models can be a very useful strategy in the application of EBLUP small area estimation, most particularly in poverty incidence estimation.