Specification choices in quantile regression for empirical macroeconomics

Quantile regression has become widely used in empirical macroeconomics, in particular for estimating and forecasting tail risks to macroeconomic indicators. In this paper we examine various choices in the specification of quantile regressions for macro applications, for example, choices related to how and to what extent to include shrinkage, and whether to apply shrinkage in a classical or Bayesian framework. We focus on forecasting accuracy, using for evaluation both quantile scores and quantile-weighted continuous ranked probability scores at a range of quantiles spanning from the left to right tail. Across a range of applications, we find that shrinkage is generally helpful to quantile forecast accuracy, with Bayesian quantile regression dominating frequentist quantile regression.