Prediction in a spatial nested error components panel data model

This paper derives the Best Linear Unbiased Predictor (BLUP) for a spatial nested error components panel data model. This predictor is useful for panel data applications that exhibit spatial dependence and a nested (hierarchical) structure. The predictor allows for unbalancedness in the number of observations in the nested groups. One application includes forecasting average housing prices located in a county nested in a state. When deriving the BLUP, we take into account the spatial correlation across counties, as well as the unbalancedness due to observing different numbers of counties nested in each state. Ignoring the nested spatial structure leads to inefficiency and inferior forecasts. Using Monte Carlo simulations, we show that our feasible predictor is better in root mean square error performance than the usual fixed and random effects panel predictors which ignore the spatial nested structure of the data.