Papers › Identification in a Binary Choice Panel Data Model with a Predetermined Covariate
Identification in a Binary Choice Panel Data Model with a Predetermined Covariate
Stéphane Bonhomme, Kevin Dano, Bryan S. Graham
We study identification in a binary choice panel data model with a single \emph{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 linear 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 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.
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