Semiparametric distribution regression with instruments and monotonicity

Abstract

This paper proposes IV-based estimators for the semiparametric distribution regression model in the presence of an endogenous regressor, which are based on an extension of IV probit estimators and the idea of control functions. We discuss the causal interpretation of the estimators and two methods (monotone rearrangement and isotonic regression) to ensure a monotonically increasing distribution function. Asymptotic properties and simulation evidence are provided. An application to income equations with German SOEP data reveals statistically significant and heterogeneous differences to the inconsistent non-IV-based estimator.