Revisiting Panel Data Discrete Choice Models with Lagged Dependent Variables

Abstract

This paper revisits the identification and estimation of a class of semiparametric (distributionfree) panel data binary choice models with lagged dependent variables, exogenous covariates, and entity fixed effects. Using an "identification at infinity" argument, we show that the model is point identified in the presence of a free-varying continuous covariate. In contrast with the celebrated Honoré and Kyriazidou (2000), our method permits time trends of any form and does not suffer from the "curse of dimensionality". We propose an easily implementable conditional maximum score estimator. The asymptotic properties of the proposed estimator are fully characterized. A small-scale Monte Carlo study demonstrates that our approach performs satisfactorily in finite samples. We illustrate the usefulness of our method by presenting an empirical application to enrollment in private hospital insurance using the HILDA survey data.

Robust analysis of short panels

“…There are many papers studying panel models of binary outcomes and multiple discrete choice under conditional stationarity restrictions on the distribution of the time varying latent variables introduced in Manski (1987). These papers include Chernozhukov, Fernandez-Val, Hahn, and Newey (2013), Shi, Shum, and Song (2018), Gao and Li (2020), Khan, Ouyang, and Tamer (2021), Pakes, Porter, Shepard, and Calder-Wang (2021), Pakes and Porter (2022), Dobronyi, Ouyang, and Yang (2023), Tamer (2023), andMbakop (2023).…”