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

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  • Stéphane Bonhomme
  • Kevin Dano
  • Bryan S. Graham

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 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.

Suggested Citation

  • Stéphane Bonhomme & Kevin Dano & Bryan S. Graham, 2023. "Identification in a binary choice panel data model with a predetermined covariate," CeMMAP working papers 17/23, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:17/23
    DOI: 10.47004/wp.cem.2023.1723
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    1. Andrew Chesher & Adam Rosen & Yuanqi Zhang, 2024. "Robust analysis of short panels," IFS Working Papers WCWP01/24, Institute for Fiscal Studies.

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