Sharp IV bounds on average treatment effects under endogeneity and noncompliance
In the presence of an endogenous treatment and a valid instrument, causal effects are (nonparametrically) point identified only for the subpopulation of compliers, given that the treatment is monotone in the instrument. Further populations of likely policy interest have been widely ignored in econometrics. Therefore, we use treatment monotonicity and/or stochastic dominance assumptions to derive sharp bounds on the average treatment effects of the treated population, the entire population, the compliers, the always takers, and the never takers. We also provide an application to labor market data and briefly discuss testable implications of the instrumental exclusion restriction and stochastic dominance.
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