The horseshoe prior for time-varying parameter VARs and Monetary Policy

Time-varying parameter VARs have become the workhorse models in empirical macroeconomics. These models are usually equipped with tightly parametrized prior distributions which favor a small and gradual change in parameters. Do such prior distributions suppress some degree of time variation in the VAR coefficients? We address this question by proposing a flexible global-local prior, namely the horseshoe prior. It turns out that conventional priors may suppress economically relevant patterns of time variation. Using the global-local prior, we observe that parameter change and changes in systematic monetary policy can be abrupt rather than smooth. Furthermore, we provide a comparison of the horseshoe prior with a range of plausible alternatives. Finally, we find that a VAR with a stochastic volatility specification using the horseshoe prior is well suited to modelling the extreme observations due to Covid-19. In contrast, the conventional prior (spuriously) picks up an increase of volatilities even before the Covid crisis.