Bayesian estimation of median household income for small areas with some longitudinal pattern

Abstract

One of the main objectives of the U.S. Census Bureau is the proper estimation of median household income for small areas. These estimates have an important role in the formulation of various governmental decisions and policies. Since direct survey estimates are available annually for each state or county, it is desirable to exploit the longitudinal trend in income observations in the estimation procedure. In this study, we consider Fay-Herriot type small area models which include time-specific random effect to accommodate any unspecified time varying income pattern. Analysis is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo methodology. We have evaluated our estimates by comparing those with the corresponding census estimates of 1999 using some commonly used comparison measures. It turns out that among three types of time-specific random effects the small area model with a time series random walk component provides estimates which are superior to both direct estimates and the Census Bureau estimates.

Simultaneous modeling of mean and variance in small area estimation

“…Model fitting and parameter estimations are carried out in a hierarchical Bayesian framework. A hierarchical Bayesian model for median household income of four-person families has recently been considered in Bhadra, Ghosh and Kim (2012), Goo and Kim (2013) and Lee and Kim (2013). To overcome calculation problems, we perform the Gibbs sampler and the grid method to generate some parameters from non-standard posterior distributions.…”

A comparative study in Bayesian semiparametric approach to small area estimation

“…In this sense, the demand for small area estimation has greatly increased. A study on the small area estimation is related to Ghosh and Rao (1994), Ghosh, Nangia and Kim (1996) and Lee and Kim (2015). These estimates play an important role in formulating policies and programs, in the allocation of government funds and in regional planning.…”