In the case that the dependent variable is (0 1), the traditional model, such as sys-GMM can not be used directly, while the xtprobit or xtlogit may be considered.

For dynamic probit or logit, see:

Carro, J., 2007, Estimating dynamic panel data discrete choice models with fixed effects, Journal of Econometrics, 140 (2): 503-528.

Wooldridge, J., 2005, Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity, JOURNAL OF APPLIED ECONOMETRICS, 20 (1): 39-54.

Really? But I have found some papers used sys_GMM for binary dependent variable. I feel puzzled now. Thanks for explanations.