On Identification of Dynamic Binary Response. Models using Data from Repeated Cross Sections

Abstract

We examine what can be learned about the coefficients of a single index dynamic binary response models with individual effects when repeated cross sections instead of genuine panel data are available. Unlike the existing literature, we allow for time varying variables among the regressors. We show that the coefficients of interest are point identified under the assumptions that: (i) The individual effect and the idiosyncratic disturbance are, conditional on the regressors, independent each other and over time; (ii) There is a continuous regressor which is, conditional on the other regressors, independent of the individual effect, the idiosyncratic disturbance, and the lagged value of the response variable; and (iii) There is a time invariant regressor whose support has at least as many points as number of coefficients of interest, and the idiosyncratic disturbance is mean independent of it. Maintaining the point identification assumptions, we propose a sieve minimum distance estimator of the coefficients of interest and explore its asymptotic properties. An empirical example concerning child labor supply illustrates our results.