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 θ, whereas the distribution of unit-speciﬁc heterogeneity, as well as the feedback process that maps lagged outcomes into future covariate realizations, are left unrestricted. We provide a simple condition under which θ 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 θ and show how to compute it using lin-ear programming techniques. While θ is not generally point-identiﬁed, its identiﬁed set is informative in the examples we analyze numerically, suggesting that meaningful learning about θ is possible even in short panels with feedback.
Identification in a binary choice panel data model with a predetermined covariate
18 January 2023
Working Paper (CWP01/23)