Local quantile treatment effects

This chapter reviews instrumental variable models of quantile treatment effects. We focus on models that achieve identification through a monotonicity assumption in the treatment choice equation. We discuss the key conditions, the role of control variables as well as the estimands in detail and review the literature on estimation and inference. Then we consider extensions to multiple and continuous instruments, to the regression discontinuity design, and discuss the testability of the assumptions. Finally, we compare this approach to the alternative instrumental variable approach reviewed by Chernozhukov et al. (2016). Two open research problems are highlighted in the conclusion.