Identifying Treatment Effects in the Presence of Confounded Types

In this paper, I consider identification of treatment effects whenthe treatment is endogenous. The use of instrumental variables is a popularsolution to deal with endogeneity, but this may give misleading answers whenthe instrument is invalid. I show that when the instrument is invalid due tocorrelation with the first stage unobserved heterogeneity, a second (alsopossibly invalid) instrument allows to partially identify not only the localaverage treatment effect but also the entire potential outcomes distributionsfor compliers. I exploit the fact that the distribution of the observedoutcome in each group defined by the treatment and the instrument is amixture of the distributions of interest. I write the identified set in theform of conditional moment inequalities, and provide an easily implementableinference procedure. Under some (testable) tail restrictions, the potentialoutcomes distributions are point-identified for compliers. Finally, Iillustrate my methodology on data from the National Longitudinal Survey ofYoung Men to estimate returns to college using college proximity as(potential) instrument. I find that a college degree increases the averagehourly wage of the compliers by 38-79%.