Bayesian quantile vector autoregression: (un)certainty through tail-specific shocks

Abstract

I propose a Bayesian quantile vector autoregression framework. My Metropolis-within-Gibbs sampler successfully recovers the joint distribution of random variables – similar to recursive approaches that rely on equation-by-equation estimation, but without requiring a recursive structure. I leverage this framework to identify and analyze uncertainty shocks as tail shocks, unifying Bloom’s (2009) two-step identification into a single approach. Among others, my framework uncovers that right-tail shocks to stock market volatility – uncertainty shocks – and left-tail shocks, which I term certainty shocks, are distinct, asymmetric macroeconomic shocks rather than mere opposites in sign.

Keywords: Bayesian quantile VAR, uncertainty shocks, tail risks, irrational exuberance

JEL Classification: C32, E44, G01