Small area estimation in the presence of correlated random area effects

This article is a contribution to the discussion on the utility of spatial models in the context of Small Area Estimation (SAE) (see Cressie 1991; Pfeffermann 2002; Saei and Chambers 2003, 2005; Singh et al. 2005; Pratesi and Salvati 2008). The attention is on the Fay–Herriot model and its Mean Squared Error (MSE) when a common autocorrelation parameter among small areas is included. Firstly, we discuss the extent to which the spatial effects in data used for SAE motivate the introduction of an autocorrelation parameter in the Fay–Herriot model. Secondly, the performance of MSE estimators is discussed through a simulation study where the joint effect of the area level sampling variance and of the parameter estimation is shown. The importance of the strength of spatial autocorrelation among small areas is confirmed. The results are tenable for different sampling variance patterns. A case study with spatial dependence in the data is presented and estimates at small area level are provided.