Exploration of dynamic fixed effects logit models from a traditional angle

This paper proposes the transformations for the dynamic fixed effects logit models. Firstly, the transformations construct the valid moment conditions (including the stationarity moment conditions) for the case without explanatory variable. Combining portions of the valid moment conditions gives just the first-order condition of the conditional MLE proposed by Chamberlain (1985). Next, the valid moment conditions are constructed by using the transformations for the case with strictly exogenous continuous explanatory variables, when the number of time periods is greater than or equal to four. This implies that for the dynamic fixed effects logit model with strictly exogenous continuous explanatory variables, the estimators can be constructed which are consistent and asymptotically normal and whose convergence rates equal the inverse of the square root of the cross-sectional sample size. In addition, the small sample properties of the GMM estimators using these moment conditions are investigated by using Monte Carlo experiments.