A Bayesian approach for the estimation of weight matrices in spatial autoregressive models

Abstract

We develop a Bayesian approach to estimate weight matrices in spatial autoregressive (or spatial lag) models. Datasets in regional economic literature are typically characterized by a limited number of time periods (Formula presented.) relative to spatial units (Formula presented.). When the spatial weight matrix is subject to estimation severe problems of over-parametrization are likely. To make estimation feasible, our approach focusses on spatial weight matrices which are binary prior to row-standardization. We discuss the use of hierarchical priors which impose sparsity in the spatial weight matrix. Monte Carlo simulations show that these priors perform very well where the number of unknown parameters is large relative to the observations. The virtues of our approach are demonstrated using global data from the early phase of the COVID-19 pandemic.