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 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 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 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 and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted values with the observed ones.Interpolation, Spatial panel econometrics, MCMC, Spatial

Chow-Lin Methods in Spatial Mixed Models

Missing data in dynamic panel models occur quite often since detailed recording of the dependent variable is often not possible at all observation points in time and space. In this paper we develop classical and Bayesian methods to complete missing data in panel models. The Chow-Lin (1971) method is a classical method for completing dependent disaggregated data and is successfully applied in economics to disaggregate aggregated time series. We will extend the space-time panel model in a new way to include cross-sectional and spatially correlated data. The missing disaggregated data will be obtained either by point prediction or by a numerical (posterior) predictive density. Furthermore, we point out that the approach can be extended to more complex models, like ow data or systems of panel data. The panel Chow-Lin approach will be demonstrated with examples involving regional growth for Spanish regions.Space-time interpolation, Spatial panel econometrics, MCMC, Spatial Chow-Lin, missing regional data, Spanish provinces, MCMC, NUTS: nomenclature of territorial units for statistics