A Nonparametric Simulated Maximum Likelihood Estimation Method

Existing simulation-based estimation methods are either general purpose but asymptotically inefficient or asymptotically efficient but only suitable for restricted classes of models. This paper studies a simulated maximum likelihood method that rests on estimating the likelihood nonparametrically on a simulated sample. We prove that this method, which can be used on very general models, is consistent and asymptotically efficient for static models. We then propose an extension to dynamic models and give some Monte-Carlo simulation results on a dynamic Tobit model.We thank Jean-Pierre Florens, Arnoldo Frigessi, Christian Gouriéroux, Jim Heckman, Guy Laroque, Oliver Linton, Nour Meddahi, Alain Monfort, Eric Renault, Christian Robert, Neil Shephard, and two referees for their comments. Remaining errors and imperfections are ours. Parts of this paper were written while Bernard Salanié was visiting the University of Chicago, which he thanks for its hospitality.