Tail forecasts of inflation using time-varying parameter quantile regressions

This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regression (QR) models. We use data augmentation schemes to facilitate the conditional likelihood, and render the model conditionally Gaussian to develop an efficient Gibbs sampling algorithm. Regularization of the high-dimensional parameter space is achieved via flexible dynamic shrinkage priors. A simple version of the TVP-QR based on an unobserved component (UC) model is applied to dynamically trace the quantiles of the distribution of inflation in the United States (US), the United Kingdom (UK) and the euro area (EA). We conduct an out-of-sample inflation forecasting exercise to assess predictive accuracy of the proposed framework versus several benchmarks using metrics to capture performance in different parts of the distribution. The proposed model is competitive and performs particularly well for higher-order and tail forecasts. We analyze the resulting predictive distributions and find that they are often skewed and feature heavier than normal tails.