Identification in a binary choice panel data model with a predetermined covariate

Abstract

We study identification in a binary choice panel data model with a single predetermined binary covariate (i.e., a covariate sequentially exogenous conditional on lagged outcomes and covariates). The choice model is indexed by a scalar parameter theta , whereas the distribution of unit-specific heterogeneity, as well as the feedback process that maps lagged outcomes into future covariate realizations, is left unrestricted. We provide a simple condition under which theta is never point-identified, no matter the number of time periods available. This condition is satisfied in most models, including the logit one. We also characterize the identified set of theta and show how to compute it using linear programming techniques. While theta is not generally point-identified, its identified set is informative in the examples we analyze numerically, suggesting that meaningful learning about theta may be possible even in short panels with feedback. As a complement, we report calculations of identified sets for an average partial effect and find informative sets in this case as well.