Identification in a Binary Choice Panel Data Model with a Predetermined Covariate

34 Pages Posted: 15 Mar 2023

See all articles by Stephane Bonhomme

Stephane Bonhomme

University of Chicago

Kevin Dano

University of California, Berkeley

Bryan S. Graham

University of California, Berkeley - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: March 13, 2023

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 is possible even in short panels with feedback.

JEL Classification: C23

Suggested Citation

Bonhomme, Stephane and Dano, Kevin and Graham, Bryan S., Identification in a Binary Choice Panel Data Model with a Predetermined Covariate (March 13, 2023). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2023-35, Available at SSRN: https://ssrn.com/abstract=4389820 or http://dx.doi.org/10.2139/ssrn.4389820

Stephane Bonhomme (Contact Author)

University of Chicago

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United States

Kevin Dano

University of California, Berkeley ( email )

Bryan S. Graham

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

National Bureau of Economic Research (NBER)

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