2023/01/13 by Stéphane Bonhomme, Bonhomme, Stéphane, Kevin Dano +3 · 1 citation
Economics, Econometrics and Finance · #Econometrics (econ.EM) #Economic and Environmental Valuation #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Housing Market and Economics #Methodology (stat.ME) #Spatial and Panel Data Analysis #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2301.05733
openalex publication_date 2023/01/13 · openalex created_date 2023/01/19 · openalex updated_date 2026/07/28
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.