Simulated maximum likelihood estimation for discrete choices using transformed simulated frequencies

Abstract

Many existing methods of simulated likelihood for discrete choice models require additive errors that have normal or extreme value distributions. This paper focuses on a situation where the model does not admit such additive errors so that the popular method of GHK or logit estimation is not applicable. This paper proposes a new method of simulated likelihood that is free from simulation bias for each finite number of simulations, and yet flexible enough to accommodate various model specifications beyond those of additive normal or logit errors. The method begins with the likelihood function involving simulated frequencies and finds a transform of the likelihood function that identifies the true parameter for each finite simulation number. The transform is explicit, containing no unknowns that demand an additional step of estimation. The estimator achieves the efficiency of MLE when the simulation number increases fast enough. This paper presents and discusses results from Monte Carlo simulation studies of the new method.