Bayesian Methods for Completing Data in Spatial Models

Completing data sets that are collected in heterogeneous units is a quite frequent problem. Chow and Lin (1971) were the first to develop a unified framework for the three problems (interpolation, extrapolation and distribution) of predicting times series by related series (the 'indicators'). This paper develops a spatial Chow-Lin procedure for cross-sectional data and compares the classical and Bayesian estimation methods. We outline the error co- variance structure in a spatial context and derive the BLUE for ML and Bayesian MCMC estimation. In an example, we apply the procedure to Spanish regional GDP data between 2000 and 2004. We assume that only NUTS-2 GDP is known and predict GDP at NUTS-3 level by using socio-economic and spatial information available at NUTS-3. The spatial neighborhood is defined by either km distance, travel time, contiguity or trade relation- ships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted values with the observed ones.