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

Author

Listed:
  • Stéphane Bonhomme

    (University of Chicago)

  • Kevin Dano

    (University of California - Berkeley)

  • Bryan S. Graham

    (University of California - Berkeley
    National Bureau of Economic Research)

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 $$\theta $$ θ , 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 $$\theta $$ 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 $$\theta $$ θ and show how to compute it using linear programming techniques. While $$\theta $$ θ is not generally point-identified, its identified set is informative in the examples we analyze numerically, suggesting that meaningful learning about $$\theta $$ 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," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(3), pages 315-351, December.
  • Handle: RePEc:spr:series:v:14:y:2023:i:3:d:10.1007_s13209-023-00290-2
    DOI: 10.1007/s13209-023-00290-2
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    More about this item

    Keywords

    Feedback; Panel data; Incidental parameters; Partial identification;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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