Semiparametric Estimation of Dynamic Binary Choice Panel Data Models

TL;DR

This paper introduces a semiparametric two-step maximum score method for dynamic binary choice panel data models with fixed effects, offering improved convergence rates and practical inference tools.

Contribution

It develops a novel identification strategy and estimation procedure for dynamic binary panel models that overcomes limitations of previous methods like Honore and Kyriazidou (2000).

Findings

Estimation rates are independent of model dimension.

The method performs well in finite-sample simulations.

Provides bootstrap-based inference procedures.

Abstract

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 Honore 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 Honore 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.