A Simulation Estimator for Dynamic Models of Discrete Choice

This paper extends the recent work of Hotz and Miller (1991) on the use of conditional choice probabilities to represent the valuation functions in the estimation of dynamic, discrete choice models. They derive a N1/2 consistent and asymptotically normal estimator of the structural parameters of agents' optimal decision rules that relies on nonparametric estimates of the conditional choice probabilities of future choices. This paper extends their work by deriving a related estimator that does not require the estimation of the conditional choice probabilities of all future paths associated with a current action, but rather only those associated with a simulated path or paths. This estimator is also shown to be N1/2 consistent and asymptotically normal. The derivation of our estimator's asymptotic properties makes use of recent results in Pakes and Pollard (1989). By reducing the number of conditional choice probabilities that must be estimated, this new estimator allows the consideration of models with large numbers of alternative choices. We report results from a Monte Carlo study comparing several versions of our estimator with the maximum likelihood estimator in the context of Rust's (1989) model of bus engine replacement. We also discuss the implications of the Monte Carlo evidence regarding the actual implementation of the estimator.