Time stable empirical best predictors under a unit-level model

Abstract

Comparability as well as stability over time are highly desirable properties of regularly published statistics, specially when they are related to important issues such as people’s living conditions. For instance, poverty statistics displaying drastic changes from one period to the next for the same area have low credibility. In fact, longitudinal surveys that collect information on the same phenomena at several time points are indeed very popular, specially because they allow analyzing changes over time. Data coming from those surveys are likely to present correlation over time, which should be accounted for by the considered statistical procedures, and methods that account for it are expected to yield more stable estimates over time. A unit-level temporal linear mixed model is considered for small area estimation using historical information. The proposed model includes random time effects nested within the usual area effects, following an autoregressive process of order 1, AR(1). Based on the proposed model, empirical best predictors (EBPs) of small area parameters that are comparable for different time points and are expected to be more stable are derived. Explicit expressions are provided for the EBPs of some common poverty indicators. A parametric bootstrap method is also proposed for estimation of the mean square errors under the model. The proposed methods are studied through different simulation experiments, and are illustrated in an application to poverty mapping in Spanish provinces using survey data on living conditions from years 2004–2006.