Spatial Panel Data Model with Error Dependence: A Bayesian Separable Covariance Approach

Abstract

A hierarchical Bayesian model for spatial panel data is proposed. The idea behind the proposed method is to analyze spatially dependent panel data by means of a separable covariance matrix. Let us indicate the observations as $y_{it}$, in $i=1,\dots ,N$ regions and at $t=1,\dots ,T$ times, and suppose the covariance matrix of $\mathbf{y}$, given a set of regressors, is written as a Kronecker product of a purely spatial and a purely temporal covariance. On the one hand, the structure of separable covariances dramatically reduces the number of parameters, while on the other hand, the lack of a structured pattern for spatial and temporal covariances permits capturing possible unknown dependencies (both in time and space). The use of the Bayesian approach allows one to overcome some of the difficulties of the classical (MLE or GMM based) approach. We present two illustrative examples: the estimation of cigarette price elasticity and of the determinants of the house price in 120 municipalities in the Province of Rome.