Small area estimation of poverty indicators under bivariate Fay–Herriot model with correlated time effects

This paper presents an area-level temporal bivariate linear mixed model, incorporating correlated time effects for estimating socioeconomic indicators in small areas. The model is applied through the residual maximum likelihood method, leading to the derivation of empirical best linear unbiased predictors for these indicators. Additionally, an approximation of the mean square error matrix (MSE) is provided and four MSE estimators are proposed. The first estimator involves a plug-in approach to the MSE approximation, while the remaining estimators are based on parametric bootstrap procedures. To assess the performance of the fitting algorithm, predictors, and MSE estimators, three simulation experiments are carried out. An application to real data from the 2016 to 2022 Spanish Living Conditions Survey is conducted. The focus is on estimating poverty proportions and gaps for the year 2022, categorized by provinces and sex.