  This paper revisits the identification and estimation of a class of
semiparametric (distribution-free) panel data binary choice models with lagged
dependent variables, exogenous covariates, and entity fixed effects. We provide
a novel identification strategy, using an "identification at infinity"
argument. In contrast with the celebrated Honore 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 Household, Income and Labour Dynamics in Australia (HILDA)
Survey data.
