Conditional vs Unconditional Quantile Regression Models: A Guide to Practitioners

Abstract

This paper analyzes two econometric tools that are used to evaluate distributional effects, condi-tional quantile regression (CQR) and unconditional quantile regression (UQR). Our main objectiveis to shed light on the similarities and differences between these methodologies. An interestingtheoretical derivation to connect CQR and UQR is that, for the effect of a continuous covariate,the UQR is a weighted average of the CQR. This imposes clear bounds on the values that UQRcoefficients can take and provides a way to detect misspecification. The key here is a match be-tween CQR whose predicted values are the closest to the unconditional quantile. For a binarycovariate, however, this relationship is not valid. We illustrate these models using age returns andgender gap in Argentina for 2019 and 2020.