Identification in a Binary Choice Panel Data Model with a Predetermined Covariate /
Stéphane Bonhomme, Kevin Dano, Bryan S. Graham.
- Cambridge, Mass. National Bureau of Economic Research 2023.
- 1 online resource: illustrations (black and white);
- NBER working paper series no. w31027 .
- Working Paper Series (National Bureau of Economic Research) no. w31027. .
March 2023.
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 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 is possible even in short panels with feedback.
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