Estimation of Median Household Income for Small Areas : A Bayesian Semiparametric Approach

Abstract Estimation of median income of small areas is one of the principal targets of inference of the U.S Bureau of Census. These estimates play an important role in the formulation of various governmental decisions and policies. Since these estimates are collected over time, they often possess an inherent longitudinal pattern. Taking proper account of this time varying pattern may result in better estimates for the current or future median household incomes for a particular state or county. In this study, we put forward a semiparametric modeling procedure for estimating the median household income for all the U.S states. Our models include a nonparametric functional part for accommodating any unspecified time varying income pattern and also a state specific random effect to account for the within-state correlation of the income observations. Model fitting and parameter estimation is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo (MCMC) methodology. It is seen that the semiparametric model estimates can be superior to both the direct estimates and the Census Bureau estimates. Overall, our study indicates that proper modeling of the underlying longitudinal income profiles can improve the performance of model based estimates of household median income of small areas.