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.

More on this topic

BFI Working Paper·Jul 11, 2024

Identifying Agglomeration Shadows: Long-run Evidence from Ancient Ports

Richard Hornbeck, Guy Michaels and Ferdinand Rauch
Topics: Uncategorized
BFI Working Paper·Jul 8, 2024

Firms’ Perceived Cost of Capital

Niels Gormsen and Kilian Huber
Topics: Uncategorized
BFI Working Paper·Mar 11, 2024

On Recoding Ordered Treatments as Binary Indicators

Evan K. Rose and Yotam Shem-Tov
Topics: Uncategorized