Accounting for Uncertainty About Variances in Small Area Estimation

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Introduction

This paper considers different approaches to dealing with uncertainty in the context of a particular application: estimating annual poverty rates of school-aged (5-17) children for the states of the U.S. using data from the Current Population Survey (CPS). For this problem Fay and Train (1997) developed a Fay-Herriot model for each year where, for each of m=51 “states” i (including the District of Columbia as a “state”), y is the direct CPS estimate, Y the true poverty rate, and x includes a constant term and three variables derived from administrative sources. (Actually, ratios differing slightly from true poverty rates were modeled.) U.S. Internal Revenue Service income tax return files supplied two variables: an analogue to state child poverty rates and also state rates of nonfiling for income taxes. Data from the U.S. Department of Agriculture were used to develop a variable reflecting state participation rates in the food stamp poverty assistance program.

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