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.
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