Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

While modern day economics, and broadly social science research, is often faced with high dimensional estimation problems in which the number of potential explanatory variables is large, often larger than the number of sample observations, the extant literature for high dimensional methods has focused developments mainly on for conditional mean models. Moving beyond the conditional mean, by estimating quantile regression on the other hand, allows to gauge potentially heterogeneous effects of variables directly across the conditional response distribution. While highly influential in the risk-management and finance literature in calculating risk measures such as VaR (i.e., the loss a portfolio's value incurs at a specific probability level), quantile regression has experienced a recent surge in popularity within the macroeconomic literature to quantify risks and vulnerabilities of output growth in response to summary measures of financial health, aptly named growth-at-risk (GaR) (Adrian et al., 2019; Figueres and Jarociński, 2020; Adams et al., 2020). As an important distinction to literature that focuses on forecasting crisis periods directly such as through Markov-switching models (Hubrich and Tetlow, 2015; Guérin and Marcellino, 2013) or probit models (McCracken et al., 2021), GaR instead gives information about the accumulation of risks facing an economy. Since sources of risk can be numerous, high dimensional quantile problems are becoming ever more pertinent to policy makers and practitioners alike which has spurned methods that deal with variable selection and shrinkage for the quantile regression problem (Chernozhukov et al., 2010; Kohns and Szendrei, 2020; Hasenzagl et al., 2020).