Simulated MLE for Discrete Choices using Transformed Simulated Frequencies1

Many existing methods of simulated likelihood for discrete choice models require additive errors that have normal or extreme value distributions, with the prominent exception of the original simulated frequency method of Lerman and Manski (1981). This paper proposes a new method of simulated likelihood that is free from simulation bias for each …nite number of simulation, and yet ‡exible enough to accommodate various model speci…cations beyond those of additive normal or logit errors. The method is ‡exible in the sense that it applies to almost any discrete choice model where individual choices can be simulated. The method begins with the likelihood function involving simulated frequencies and …nds a transform of the likelihood function that identi…es the true parameter for each …nite simulation number. The transform is explicit, containing no unknowns that demand an additional step of estimation. The estimator achieves the e¢ ciency of MLE as the simulation number increases fast enough. This paper presents and discusses results from Monte Carlo simulation studies of the new method. Key words: Simulated MLE, Discrete Choice Models, Simulation Bias, Simulated Frequencies, Cube-Root Asymptotics JEL Classi…cations: C12, C14, C52. 1A prevoius version was titled, "A Consistent SMLE When the Simulation Number was Finite." We are indebted to Sean D. Campbell, Joel Horowitz, and Eugene Savin for their valuable comments and inputs. We are also grateful to the seminar participants at Cemmap Seminar at University College London, Columbia University, Econometric Society Meeting, Greater New York Econometrics Colloquium, Lehigh University, University of Iowa, University of Rochester, and New York University for useful comments. The views expressed in this paper are those of the authors and do not necessarily re‡ect the views of the Federal Reserve Bank of New York or the Federal Reserve System. 2Federal Reserve Bank of New York, 33 Liberty Street, New York, NY, 10045. 3Department of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC, Canada, V6T 1Z1.