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This paper extends the idea of decoupling shrinkage and sparsity forcontinuous priors to Bayesian Quantile Regression (BQR). The procedure followstwo steps: In the first step, we shrink the quantile regression posteriorthrough state of the art continuous priors and in the second step, we sparsifythe posterior through an efficient variant of the adaptive lasso, the signaladaptive variable selection (SAVS) algorithm. We propose a new variant of theSAVS which automates the choice of penalisation through quantile specificloss-functions that are valid in high dimensions. We show in large scalesimulations that our selection procedure decreases bias irrespective of thetrue underlying degree of sparsity in the data, compared to the un-sparsifiedregression posterior. We apply our two-step approach to a high dimensionalgrowth-at-risk (GaR) exercise. The prediction accuracy of the un-sparsifiedposterior is retained while yielding interpretable quantile specific variableselection results. Our procedure can be used to communicate to policymakerswhich variables drive downside risk to the macro economy.

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression