Unconditional Quantile Regressions Under Endogeneity

Abstract

This paper proposes an extension of the Unconditional Quantile Regression approach under strict exogeneity restriction (Firpo et al. (2009)) and allowing endogenous regressors in a nonseparable model (Rothe (2010)) by developing the asymptotic properties of the Unconditional Quantile Partial Effect (UQPE) estimator and the RIF (Re-centered Influence Function) regression function using the control variable approach in a triangular nonseparable model. Further, we show the robust inference procedure of the UQPE estimator. These results are not specific for only nonseparable model, but also apply to both linear and nonlinear additive separable models. Two empirical applications of estimating demand elasticity of fish and heterogeneous returns to education illustrate the usefulness of the UQPE estimator.

Keywords: Re-centered influence function, control variable, unconditional quantile partial effects, RIF regression, nonseparable triangular model

JEL Classification: C13, C14