Estimation of Median Household Income for Small Areas

Abstract

Estimation of median income of small areas is one of the important targets of inference of the U.S. Bureau of Census. These estimates play a critical role in the formulation of various governmental decisions and policies. In this study, we propose and compare some modeling procedures for estimating the median household income for all the U.S. states for a particular year, when the income observations for each state are available over time (years). Our models include the simple linear regression model (SLR), the random intercept model (RIM) as well as the random intercept and slope model (RISM), with the last two taking care of the dependence of the state-specific income observations over time. Model fitting is carried out with the mean and median income observations obtained from IRS returns as covariates. On applying our models to the dataset, it is seen that the RIM model with irsmean as the explanatory variable performs optimally, in terms of providing estimates (of median income) closest to the actual (true) census values. In fact, the estimates obtained from our proposed model seems to be superior to those formulated by the Census Bureau.