Identification of Multi-Index Sample Selection Models

This paper derives conditions for identification of a general class of sample selection models that allows for selection based on, for example, game-theoretic models. The conditions apply to models with binary or continuous outcome variables and generalize the conditions for the standard Heckman sample selection model. For illustration, the results are applied to selection in a two-sided matching market, which is not captured by the standard model. In this market the characteristics of other agents can provide the identifying variation, and no explicit instrument is required