Instrumental Variable Quantile Regression * †

Quantile regression is an increasingly important tool that estimates the conditional quantiles of a response Y given a vector of regressors D. It usefully generalizes Laplace’s median regression and can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. For the linear quantile model defined by Y = D′γ(U) where D′γ(U) is strictly increasing in U and U is a standard uniform variable independent of D, quantile regression allows estimation of quantile specific covariate effects γ(τ) for τ ∈ (0, 1). In this paper, we propose an instrumental variable quantile regression estimator that appropriately modifies the conventional quantile regression and recovers quantile-specific covariate effects in an instrumental variables model defined by Y = D′α(U) where D′α(U) is strictly increasing in U and U is a uniform variable that may depend onD but is independent of a set of instrumental variables Z. The proposed estimator and inferential procedures are computationally convenient in typical applications and can be carried out using software available for conventional quantile regression. In addition, the proposed estimation procedure gives rise to a convenient inferential procedure that is naturally robust to weak identification. The use of the proposed estimator and testing procedure is illustrated through two empirical examples.