In this paper I develop a practical extension of McFadden's method of
simulated moments estimator for limited dependent variable models to t
he panel data case. The method is based on a factorization of the MSM
first order condition into transition probabilities, along with the de
velopment of a new highly accurate method for similating these transit
ion probabilities. A series of Monte-Carlo tests show that this MSM es
timator performs quite well relative to quadrature-based ML estimators
, even when large numbers of quadrature points are employed. The estim
ator also performs well relative to simulated ML, even when a highly a
ccurate method is used to simulate the choice probabilities. In terms
of computational speed, complex panel data models involving random eff
ects and ARMA errors may be estimated via MSM in times similar to thos
e necessary for estimation of simple random effects models via ML-quad
rature.