We study the application of approximate mean field variational inference algorithms to Bayesian panel VAR models in which an exchangeable prior is placed on the dynamic parameters and the residuals follow either a Gaussian or a Student-t distribution. This reduces the estimation time of possibly several hours using conventional MCMC methods to less than a minute using variational inference algorithms. Next to considerable speed improvements, our results show that the approximations accurately capture the dynamic effects of macroeconomic shocks as well as overall parameter uncertainty. The application with Student-t residuals shows that it is computationally easy to include the COVID-19 observations in Bayesian panel VARs, thus offering a fast way to estimate such models.
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