ABSTRACT
This chapter reviews instrumental variable models of quantile treatment effects. It focuses on models that achieve identification through a monotonicity assumption in the treatment choice equation. The chapter discusses the key conditions, the role of control variables as well as the estimands in detail and review the literature on estimation and inference. It considers extensions to multiple and continuous instruments, to the regression discontinuity design and provide the testability of the assumptions. The chapter also focuses on models that achieve identification through a monotonicity assumption in the treatment choice equation. It explores the particularities of the quantile estimands and their implications for the identification of the effects in setups without and with covariates. The chapter also reviews the literature on estimation and inference. P. Carneiro and S. Lee extend these ideas to the estimation of the quantile analogs, the marginal quantile treatment effects.
