Bayesian methods for completing data in space-time panel 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 united 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 and panel data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for the ML and Bayesian MCMC estimation. Finally, we apply the procedure to Spanish regional GDP data between 2000-2004. We assume that only NUTS-2 GDP is known and predict GDPat 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 and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted with the observed values.