This paper develops a simulation estimation algorithm that is particularly useful for estimating dynamic panel data models with unobserved endogenous state variables. The new approach can easily deal with the commonly encountered and widely discussed "initial conditions problem," as well as the more general problem of missing state variables during the sample period. Repeated sampling experiments on dynamic probit models with serially correlated errors indicate that the estimator has good small sample properties. We apply the estimator to a model of married women's labor force participation decisions. The results show that the rarely used Polya model, which is very difficult to estimate given missing data problems, fits the data substantially better than the popular Markov model. The Polya model implies far less state dependence in employment status than the Markov model. It also implies that observed heterogeneity in education, young children and husband income are much more important determinants of participation, while race is much less important.