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

Stéphane Bonhomme (), Kevin Dano () and Bryan S. Graham ()
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Stéphane Bonhomme: University of Chicago
Kevin Dano: University of California - Berkeley
Bryan S. Graham: University of California - Berkeley

SERIEs: Journal of the Spanish Economic Association, 2023, vol. 14, issue 3, No 5, 315-351

Abstract: 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.

Keywords: Feedback; Panel data; Incidental parameters; Partial identification (search for similar items in EconPapers)
JEL-codes: C23 C33 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13209-023-00290-2

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