Bounds on policy relevant parameters with discrete policy variation

When estimating policy parameters, also known as treatment effects, the assignment to treatment mechanism almost always causes endogeneity and thus bias many of these policy parameters estimates. Additionally, heterogeneity in program impacts is more likely to be the norm than the exception for most social programs. In situations where these issues are present, the Marginal Treatment Effect (MTE) parameter estimation makes use of an instrument to avoid assignment bias and simultaneously to account for heterogeneous effects throughout individuals. Although this parameter is point identified in the literature, the assumptions required for identification may be strong. Given that, we use weaker assumptions in order to partially identify the MTE, i.e. to stablish a methodology for MTE bounds estimation, implementing it computationally and showing results from Monte Carlo simulations. The partial identification we perfom requires the MTE to be a monotone function over the propensity score, which is a reasonable assumption on several economics' examples, and the simulation results shows it is possible to get informative even in restricted cases where point identification is lost. Additionally, in situations where estimated bounds are not informative and the traditional point identification is lost, we suggest a more generic method to point estimate MTE using the Moore-Penrose Pseudo-Invese Matrix, achieving better results than traditional methods.