Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints

This paper explores semi-monotonicity constraints in the distribution of potential outcomes, first, conditional on an instrument, and second, in terms of the response function. The imposed assumptions are strictly weaker than traditional instrumental variables assumptions and can be gainfully employed to bound the counterfactual distributions, even though point identification is only achieved in special cases. The bounds have a simple analytical form and thus have much practical relevance in all instances when strong exogeneity assumptions cannot be credibly invoked. The bounding strategy is illustrated in a simulated data example and applied to the effect of education on smoking.