Semiparametric Estimation of Dynamic Binary Choice Panel Data Models

We propose a new approach to the semiparametric analysis of panel data binary choice models with fixed effects and dynamics (lagged dependent variables). The model we consider has the same random utility framework as in Honoré and Kyriazidou (2000). We demonstrate that, with additional serial dependence conditions on the process of deterministic utility and tail restrictions on the error distribution, the (point) identification of the model can proceed in two steps, and only requires matching the value of an index function of explanatory variables over time, as opposed to that of each explanatory variable. Our identification approach motivates an easily implementable, two-step maximum score (2SMS) procedure – producing estimators whose rates of convergence, in contrast to Honoré and Kyriazidou’s (2000) methods, are independent of the model dimension. We then derive the asymptotic properties of the 2SMS procedure and propose bootstrap-based distributional approximations for inference. Monte Carlo evidence indicates that our procedure performs adequately in finite samples. We then apply the proposed estimators to study labor market dependence and the effects of health shocks, using data from the Household, Income and Labor Dynamics in Australia (HILDA) survey.