Under a federal-state cooperative program, the U.S. Bureau of Labor Statistics (BLS) publishes monthly unemployment rate estimates for its 50 states and the District of Columbia. The primary source of data for this estimation problem is the Current Population Survey (CPS). However, the CPS state unemployment rate estimates are unreliable, because the survey provides relatively few observations per state. Various federal agencies use state-level unemployment rate estimates for policy making and fund allocation. Thus it is important to improve on the CPS estimates. For this, we propose a hierarchical Bayes (HB) method using a time series generalization of a widely used cross-sectional model in small-area estimation. The proposed method is compared 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 implement for these data; the resulting estimates are very unstable and not meaningful. If we ignore some important factors from this model, then the reduced model can be fit, but the resulting model is found to be less than adequate. Gibbs sampling is used to obtain the posterior means and variances of the state unemployment rates. Based on some diagnostic tools recently developed for hierarchical models, our proposed model emerges as the best. The coefficients of variation of the proposed HB estimates are considerably lower than those of the rival estimates.