A first-stage representation for instrumental variables quantile regression

Summary This paper develops a first-stage linear regression representation for an instrumental variables (IV) quantile (QR) model. The first stage is analogous to the least-squares case, i.e., projection of endogenous on instruments and other exogenous covariates, with difference that QR case weighted projection. weights are given by conditional density function innovation term in structural model, at quantile. We also show required Jacobian identification conditions IVQR models embedded stage. then suggest procedures evaluate validity evaluating their statistical significance using representation. Monte Carlo experiments provide numerical evidence proposed tests work as expected terms empirical size power. An application illustrates methods.