10 Simulation-Assisted Estimation Motivation So far we have examined how to simulate choice probabilities but have not investigated the properties of the parameter estimators that are based on these simulated probabilities. In the applications we have presented, we simply inserted the simulated probabilities | P1 GEM IKJ P2 GEM IKJ QC GEM ABE T1 GEM August 20 2002 13 43 Char Count 0 CB495-10DRV CB495 Train KEYBOARDED 10 Simulation-Assisted Estimation Motivation So far we have examined how to simulate choice probabilities but have not investigated the properties of the parameter estimators that are based on these simulated probabilities. In the applications we have presented we simply inserted the simulated probabilities into the log-likelihood function and maximized this function the same as if the probabilities were exact. This procedure seems intuitively reasonable. However we have not actually shown at least so far that the resulting estimator has any desirable properties such as consistency asymptotic normality or efficiency. We have also not explored the possibility that other forms of estimation might perhaps be preferable when simulation is used rather than exact probabilities. The purpose of this chapter is to examine various methods of estimation in the context of simulation. We derive the properties of these estimators and show the conditions under which each estimator is consistent and asymptotically equivalent to the estimator that would arise with exact values rather than simulation. These conditions provide guidance to the researcher on how the simulation needs to be performed to obtain desirable properties of the resultant estimator. The analysis also illuminates the advantages and limitations of each form of estimation thereby facilitating the researcher s choice among methods. We consider three methods of estimation 1. Maximum Simulated Likelihood MSL. This procedure is the same as maximum likelihood ML except that simulated probabilities are used in lieu of the exact probabilities. The properties of MSL have been derived by for example Gourieroux and Monfort 1993 Lee 1995 and Hajivassiliou and Ruud 1994 . 2. Method of Simulated Moments MSM. This procedure suggested by McFadden 1989 is a simulated analog to the traditional method of moments MOM . .
