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 examines the correlated random coefficient model. It extends the analysis of Swamy (1971, 1974), who pioneered the uncorrelated random coefficient model in economics. We develop the properties of the correlated random coefficient model and derive a new representation of the variance...

The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing...

This paper discusses how randomized social experiments operate as an instrumental variable. For two types of randomization schemes, the fundamental experimental estimation equations are derived from the principle that experiments equate bias in control and experimental samples. Using...