Fast Two-Stage Variational Bayesian Approach to Estimating Panel Spatial Autoregressive Models with Unrestricted Spatial Weights Matrices

TL;DR

This paper introduces a fast two-stage variational Bayesian method for estimating unrestricted panel spatial autoregressive models, effectively capturing complex spatial relationships without prior restrictions.

Contribution

It develops the first VB approach for large covariance matrices with unrestricted sparsity, applicable to models like Bayesian vector autoregressions.

Findings

Effective estimation for both long and short panels.

Uncovered distinct spillover behaviors in euro area countries.

First VB method for unrestricted large covariance matrices.

Abstract

This paper proposes a fast two-stage variational Bayesian (VB) algorithm to estimate unrestricted panel spatial autoregressive models. Using Dirichlet-Laplace priors, we are able to uncover the spatial relationships between cross-sectional units without imposing any a priori restrictions. Monte Carlo experiments show that our approach works well for both long and short panels. We are also the first in the literature to develop VB methods to estimate large covariance matrices with unrestricted sparsity patterns, which are useful for popular large data models such as Bayesian vector autoregressions. In empirical applications, we examine the spatial interdependence between euro area sovereign bond ratings and spreads. We find marked differences between the spillover behaviours of the northern euro area countries and those of the south.