Identification of Dynamic Panel Binary Response Models

We analyze identification in dynamic econometric models of binary choice with fixed effects under general conditions. This class of models is often used in the literature to distinguish between state dependence (invariably referred to in the recent literature as switching costs, inertia or stickiness) and heterogeneity. We first characterize the sharp set for parameters in a dynamic panel of binary choice under conditional stationarity. The identified set can be characterized by a union of convex polyhedrons. We conduct the same exercise under the stronger assumption of conditional exchangeability, and establish its incremental identifying power. We extend our identification approach to study models with more time periods as well. We also provide sufficient conditions for point identification. For inference in cases with discrete regressors, we provide an approach to constructing confidence sets for the identified sets using a linear program that is simple to implement. The paper then provides simulation based evidence on the size and shape of the identified sets in varying designs to illustrate the informational content of different assumptions. We also illustrate the inference approach using a data set on women’s labor supply decisions.