Exclusion restrictions in dynamic binary choice panel data models

In this note we revisit the use of exclusion restrictions in the semiparametric binary choice panel data model introduced in Honore and Lewbel (2002). We show that in a dynamic panel data setting (where one of the pre-determined explanatory variables is the lagged dependent variable), the exclusion restriction in Honore and Lewbel (2002) implicitly re- quires serial independence condition on an observed regressor, that if violated in the data will result in their procedure being inconsistent. We propose a new identification strategy and estimation procedure for the semiparametric binary panel data model under exclusion restrictions that accommodate the serial correlation of observed regressors in a dynamic setting. The new estimator converges at the parametric rate to a limiting normal distribution. This rate is faster than the nonparametric rates of existing alternative estimators for the binary choice panel data model, including the static case in Manski (1987) and the dynamic case in Honore and Kyriazidou (2000).