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

TL;DR

This paper introduces a Bayesian method for estimating sparse, binary spatial weight matrices in spatial autoregressive models, effectively handling over-parametrization issues in limited data scenarios.

Contribution

It proposes hierarchical priors for binary spatial weight matrices, improving estimation in models with many parameters relative to observations.

Findings

Hierarchical priors perform well with high parameter-to-observation ratios.

The approach effectively estimates spatial weights in COVID-19 data.

Simulation results demonstrate robustness of the Bayesian method.

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 T relative to spatial units N. 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.