Small‐area estimation by combining time‐series and cross‐sectional data

Abstract

A model involving autocorrelated random effects and sampling errors is proposed for small‐area estimation, using both time‐series and cross‐sectional data. The sampling errors are assumed to have a known block‐diagonal covariance matrix. This model is an extension of a well‐known model, due to Fay and Herriot (1979), for cross‐sectional data. A two‐stage estimator of a small‐area mean for the current period is obtained under the proposed model with known autocorrelation, by first deriving the best linear unbiased prediction estimator assuming known variance components, and then replacing them with their consistent estimators. Extending the approach of Prasad and Rao (1986, 1990) for the Fay‐Herriot model, an estimator of mean squared error (MSE) of the two‐stage estimator, correct to a second‐order approximation for a small or moderate number of time points, T, and a large number of small areas, m, is obtained. The case of unknown autocorrelation is also considered. Limited simulation results on the efficiency of two‐stage estimators and the accuracy of the proposed estimator of MSE are présentés.