Abstract
Individuals who do not receive treatment in their initial assignment round, often have the option to reapply. The standard approach to analyze such settings is to use the result of the initial assignment round as instrumental variable for eventual receipt of treatment. This approach identifies an average treatment effect for a rather diverse group of compliers and ignores information from subsequent assignment rounds. Based on the notion of principal stratification we develop a framework that distinguishes different complier groups and identifies treatment effects for each of these. We illustrate our framework in an application that uses admission lotteries to estimate returns to enrollment in medical school in the Netherlands. In the standard approach 41 percent of the population are compliers. Our extended framework estimates returns for 70 percent of the population and shows that returns are not very different between different complier groups.