First-stage analysis for instrumental-variables quantile regression

Abstract

In this article, we develop a first-stage linear regression command, fsivqreg, for an instrumental-variables quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, that is, a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, at a given quantile. An empirical application illustrates its implementation.