Gefang, DeborahHall, Stephen GeorgeTavlas, George S.2025-04-242025-04-242025Deborah Gefang, Stephen G. Hall & George S. Tavlas (17 Apr 2025): Fast two-stage variational Bayesian approach to estimating panel spatial autoregressive models with unrestricted spatial weights matrices, Spatial Economic Analysis, DOI: 10.1080/17421772.2025.2482071.1742-1772 (print)1742-1780 (online)10.1080/17421772.2025.2482071http://hdl.handle.net/2263/102201DATA AVAILABILITY STATEMENT : Data sources are provided in Appendix E in the online supplemental data. The Matlab codes can be found at: https://github.com/DBayesian/GHT2025_HS and https://github.com/DBayesian/GHT2025_DL.We propose a fast two-stage variational Bayesian (VB) algorithm to estimate unrestricted panel spatial autoregressive models. Using Dirichlet–Laplace shrinkage priors, we 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.en© 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http:// creativecommons.org/licenses/by-nc-nd/4.0/).Variational inferenceSpatial panel data modelsSimultaneous equationsLarge datasetsSDG-08: Decent work and economic growthArticle