Working Paper

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

Authors

Stéphane Bonhomme, Kevin Dano, Bryan S. Graham

Published Date

26 July 2023

Type

Working Paper (CWP17/23)

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.


Previous version

Identification in a binary choice panel data model with a predetermined covariate
Stéphane Bonhomme, Kevin Dano, Bryan S. Graham
CWP01/23