Dynamic probit models for panel data: A comparison of three methods of estimation

Three different methods have been suggested in the econometrics literature to deal with the initial conditions problem in dynamic Probit models for panel data. Heckman (1981) suggest to approximate the reduced form marginal probability of the initial state with a Probit model and allow free correlation between unobserved individual heterogeneity entering the initial conditions and the main dynamic equations. Alternatively, Wooldridge (2002) suggest to write a dynamic model conditional on the first observation and to specify a distribution for the unobserved individual heterogeneity term conditional on the initial state and any other exogenous explanatory variables. Finally, Orme (1996) introduces a two-step bias corrected procedure that is locally valid when the correlation between unobserved individual heterogeneity determining the initial state and the dynamic Probit equations approximates to zero. Orme suggest that this two-step procedure can perform well even when such correlation is strong. I present some results from a Monte Carlo simulation study comparing the performance of all these three methods using small and medium sample sizes and low and high correlation among unobservables.