Identification of dynamic binary response models

Abstract

We consider identification of parameters in dynamic binary response models with panel data under minimal assumptions. This model is prominent in empirical economics as it has been used to infer state dependence in the presence of unobserved heterogeneity. The main results in our paper are characterizations of the identified set under weak assumptions. The results generalize the existing literature in several directions: (1) we do not require any restrictions on the support of the observables; for example, we allow for time trends, time dummies, and/or only discrete covariates; (2) we only maintain that the idiosyncratic error terms are stationary over time conditional on the fixed effect and the covariates (without conditioning on initial conditions) and without imposing a parametric distribution on the distribution of these error terms; (3) we show that it is possible to get point identification in some cases even with T=2 (two time periods). We also construct examples of identified sets in some designs to illustrate the informational content of different assumptions.