This paper exposits and relates two distinct approaches to bounding the average treatment effect. One approach, based on instrumental variables, is due to Manski (1990, 1994), who derives tight bounds on the average treatment effect under a mean independence form of the instrumental variables...

This paper considers the use of instrumental variables to estimate the mean effect of treatment on the treated. It reviews previous work on this topic by Heckman and Robb (1985, 1986) and demonstrates that (a) unless the effect of treatment is the same for everyone (conditional on observables),...