THERE HAS BEEN MUCH INTEREST over the years in estimating discrete choice models. However, with the exception of multinomial logit models, agents have been restricted to few choices so that multivariate integrals could be feasibly integrated numerically.2 Pakes and Pollard (1989) and McFadden (1989) have independently developed the method of simulated moments (MSM) to deal with estimating a wide class of models of which high order discrete choice models are a subset. One of the problems a researcher must handle when using MSM for a discrete choice model is how to smooth the discrete simulated random variables. This is necessary to keep small the number of draws required to simulate derivatives and to simulate variation in the data. Geweke (1989) and McFadden (1989) have suggested importance sampling methods (and other methods) to smooth the simulated variables for general error structures. In this paper, I present a factor analytic smoothing method that can be applied to probit problems. Although it is not as general as the methods Geweke and McFadden suggest, it is easy to use and has clear intuition. Furthermore, simulated probabilities will be unbiased, will be bounded between zero and unity, and will have smaller variances than unsmoothed probabilities always and smaller variances than importance sampling estimates for a large class of probabilities. The second section of this paper develops notation, defines the problem, and presents the smoothing method and an algorithm to employ it. The last section presents Monte Carlo comparisons of the smoothing method to the importance sampling method.

A dynamic programming model of job exit behavior and retirement is constructed and estimated using the method of simulated moments. The model and estimation method allow for both unobserved individual effects and unobserved job-specific "match" effects. The model is estimated using two different assumptions about individual discount factors. First, a static model, with the discount factor equal to zero, is estimated. Then a dynamic model, with the discount factor equal to .95 is estimated. In both models, it is found that bad health, age, and lack of education increase the probability of retirement. The dynamic model performs better than the static model and has different implications for retirement behavior. The job-specific effects are an important source of unobserved heterogeneity. Copyright 1991 by The Econometric Society.