Instrumental Variables Estimation of Quantile Treatment Effects

Abstract

This paper introduces an instrumental variables estimator for the effect of a binary treatment on the quantiles of potential outcomes. The quantile treatment effects (QTE) estimator accommodates exogenous covariates and reduces to quantile regression as a special case when treatment status is exogenous. Asymptotic distribution theory and computational methods are derived. QTE minimizes a piecewise linear objective function for which a local minimum can be obtained using a modified Barrodale-Roberts algorithm. The QTE estimator is illustrated by estimating the effect of childbearing on the distribution of family income.