Time stable small area estimates of general parameters under a unit-level model

Longitudinal surveys collecting information on certain phenomena at several time points are very popular because they allow to analyze the changes over time. Data coming from those surveys often present correlation over time that should be accounted for by the considered statistical procedures. In fact, methods that account for the existing time correlation are expected to yield more stable small area estimates over time. Temporal stability is a desirable property of statistics that are published regularly, specially in certain applications like in poverty mapping, where poverty estimates for the same area with big jumps from one period to the next are rarely credible. This paper considers a unit-level temporal linear mixed model for small area estimation that includes random time effects nested within the usual area effects, following an autoregressive process of order 1, AR(1). Based on the proposed model, we obtain empirical best predictors of general area parameters, giving explicit expressions for some common poverty indicators. We also propose a parametric bootstrap method for estimating their mean square errors under the model. The proposed methods are studied through simulation experiments and illustrated with an application to poverty mapping in Spanish provinces using survey data from 2004-2006.