Location-Scale and Compensated Effects in Unconditional Quantile Regressions

Abstract

This paper proposes an extension of the unconditional quantile regression analysis to (i) location-scale shifts, and (ii) compensated shifts. The first case is intended to study a counterfactual policy analysis aimed at increasing not only the mean or location of a covariate but also its dispersion or scale. The compensated shift refers to a situation where a shift in a covariate is compensated at a certain rate by another covariate. Not accounting for these possible scale or compensated effects will result in an incorrect assessment of the potential policy effects on the quantiles of an outcome variable. More general interventions and compensated shifts are also considered. The unconditional policy parameters are estimated with simple semiparametric estimators, for which asymptotic properties are studied. Monte Carlo simulations are implemented to study their finite sample performances, and the proposed approach is applied to a Mincer equation to study the effects of a location-scale shift in education on the unconditional quantiles of wages.