Fused LASSO as Non-Crossing Quantile Regression

Growth-at-Risk is vital for empirical macroeconomics but is often suspect to quantile crossing due to data limitations. While existing literature addresses this through post-processing of the fitted quantiles, these methods do not correct the estimated coefficients. We advocate for imposing non-crossing constraints during estimation and demonstrate their equivalence to fused LASSO with quantile-specific shrinkage parameters. By re-examining Growth-at-Risk through an interquantile shrinkage lens, we achieve improved left-tail forecasts and better identification of variables that drive quantile variation. We show that these improvements have ramifications for policy tools such as Expected Shortfall and Quantile Local Projections.