In this paper I develop a practical extension of McFadden's method of simulated moments estimator for limited dependent variable models to the panel data case. The method is based on a factorization of the MSM first order condition into transition probabilities, along with the development of a new highly accurate method for simulating these transition probabilities. A series of Monte-Carlo tests show that this MSM estimator performs quite well relative to quadrature-based ML estimators, even when large numbers of quadrature points are employed. The estimator also performs well relative to simulated ML, even when a highly accurate method is used to simulate the choice probabilities. In terms of computational speed, complex panel data models involving random effects and ARMA errors may be estimated via MSM in times similar to those necessary for estimation of simple random effects models via ML-quadrature.