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Summary This paper first reviews some of the approaches that have been taken to estimate the common parameters of binary outcome models with fixed effects. We limit attention to situations in which the researcher has access to a data set with a large number of units (individuals or companies, for example) observed over a number of time periods. We then apply some of the existing approaches to study fixed-effects panel data versions of entry games, like the ones studied in Bresnahan and Reiss (1991) and Tamer (2003). 

It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. The additional structure can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one‐dimensional line segment in the parameter space, and we demonstrate that this line segment can be short in practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. We also provide non‐sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.