Modeling tail risks of inflation using unobserved component quantile regressions

Abstract

This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regressions (QRs) featuring conditional heteroskedasticity. I use data augmentation schemes to render the model conditionally Gaussian and develop an efficient sampling algorithm. Regularization of the high-dimensional parameter space is achieved via dynamic shrinkage priors. The merits of the proposed approach are illustrated in a simulation study, and a simple version of TVP-QR based on an unobserved components model is applied to dynamically trace the quantiles of inflation in the United States, the United Kingdom and the euro area. In an out-of-sample forecast exercise, I find the proposed model to be competitive and perform particularly well for higher-order and tail forecasts. A detailed analysis of the resulting predictive distributions reveals that they are sometimes skewed and occasionally feature heavy tails.