State-space modeling with correlated measurements with application to small area estimation under benchmark constraints

The problem of Small Area Estimation is how to produce reliable estimates of area (domain) characteristics, when the sizes within the areas are too small to warrant the use of traditional direct survey estimates. This problem is commonly tackled by borrowing information from either neighboring areas and/or from previous surveys, using appropriate time series/cross-sectional models. In order to protect against possible model breakdowns and for other reasons, it is often required to benchmark the model dependent estimates to the corresponding direct survey estimates in larger areas, for which the survey estimates are sufficiently accurate. The benchmarking process defines another way of borrowing information across the areas.This article shows how benchmarking can be implemented with the state-space models used by the Bureau of Labor Statistics in the U.S. for the production of the monthly employment and unemployment estimates at the state level. The computation of valid estimators for the variances of the benchmarked estimators requires joint modeling of the direct estimators in several states, which in turn requires the development of a filtering algorithm for state-space models with correlated measurement errors. No such algorithm has been developed so far. The application of the proposed procedure is illustrated using real unemployment series.