This paper studies the implication of a fraction of the population not responding to the instrument when selecting into treatment. We show that, in general, the presence of non-responders biases the Marginal Treatment Effect (MTE) curve and many of its functionals. We obtain partial identification results for the MTE, the LATE and the MPRTE. Moreover, in a linear-in-covariates model we obtain a testable implication for the presence of non-responders. Simulation results show that our proposed estimators, using the range of the propensity score, work well.
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