A Simple Approach to Simultaneous Quantile Regression under Partial Homogeneity Constraints

Abstract Quantile regression is one of the most important methods to estimate heterogeneous effects on a variable of interest. In many applications there is a subset of covariates of interest, while the rest operate as controls in the regression equation. This work presents a straightforward empirical strategy for situations in which the control variables have a homogeneous effect on the conditional distribution. We develop the asymptotic theory for the proposed estimator and the corresponding inference procedures. An application using environmental pollution data illustrates the method by estimating the Environmental Kuznets Curve.