Small-area estimation with state-space models subject to benchmark constraints

Abstract

This article shows how to benchmark small area estimators, produced by fitting separate state-space models within the areas, to aggregates of the survey direct estimators within a group of areas. State-space models are used by the U.S. Bureau of Labor Statistics (BLS) for the production of the monthly Employment and Unemployment State estimates. The computation of the benchmarked estimators and their variances is accomplished by incorporating the benchmark constraints within a joint model of the direct estimators in the different areas, which requires the development of a new filtering algorithm for state-space models with correlated measurement errors. No such algorithm has been developed before. The properties and implications of the use of the benchmarked estimators are discussed and illustrated using BLS unemployment series. The problem of Small Area Estimation is how to produce reliable estimates of area (domain) characteristics, when the sample sizes within the areas are too small to warrant the use of traditional direct survey estimates. This problem is commonly handled by borrowing strength from either neighboring areas and/or from previous surveys, using appropriate cross-sectional/time series models. In order to protect against possible model breakdowns and for consistency in publication, it is often required to benchmark the area model dependent estimates to the direct survey estimate in a group of areas for which the survey estimate is sufficiently accurate. The latter estimate is a weighted sum of the direct estimates in the areas included in the group, so that the benchmarking process defines another way of borrowing strength across the areas