Hierarchical Bayes estimation of unemployment rates for the states of the US

Under a federal-state cooperative program, the U.S. Bureau of Labor Statist ics (BLS) publishes monthly unemployment rate estimates for its 50 states a nd the District of Columbia. The primary source of data for this estimation problem is the Current Population Survey (CPS). However, the CPS state une mployment rate estimates are unreliable, because the survey provides relati vely few observations per state. Various federal agencies use state-level u nemployment rate estimates for policy making and fund allocation. Thus it i s important to improve on the CPS estimates. For this, we propose a hierarc hical Bayes (HB) method using a time series generalization of a widely used cross-sectional model in small-area estimation. The proposed method is com pared in detail with the corresponding HB method, which uses the HB analog of the well-known Fay-Herriot cross-sectional model. A third model based on a time series approach to repetitive surveys is found to be very hard to i mplement for these data; the resulting estimates are very unstable and not meaningful. If we ignore some important factors from this model, then the r educed model can be fit, but the resulting model is found to be less than a dequate. Gibbs sampling is used to obtain the posterior means and variances of the state unemployment rates. Based on some diagnostic tools recently d eveloped for hierarchical models, our proposed model emerges as the best. T he coefficients of variation of the proposed HB estimates are considerably lower than those of the rival estimates.