Instrumental Variable Quantile Regression

Abstract

This chapter reviews the instrumental variable quantile regression model of Chernozhukov and Hansen. It discusses the key conditions used for identification of structural quantile effects within this model which include the availability of instruments and a restriction on the ranks of structural disturbances. The chapter outlines several approaches to obtaining point estimates and performing statistical inference for model parameters. It also discusses the approach by Imbens and Newey and compares it to the framework. Endogeneity of covariates renders conventional quantile regression inconsistent for estimating the causal effects of variables on the quantiles of outcomes of interest. The chapter focuses on the instrumental variable quantile regression model developed in Chernozhukov and Hansen. The instrumental variable quantile regression model is developed within the conventional potential outcome framework. Extending the discussion to allow for nonlinear parametric specifications of the potential outcome quantile functions or to estimation at a small number of quantile indices that are widely spaced is straightforward.