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Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models

Published online by Cambridge University Press:  11 February 2009

Lung-Fei Lee
Lung-Fei Lee
Affiliation:
The University of Michigan and Hong Kong University of Science and Technology
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Abstract

In this article, we investigate a bias in an asymptotic expansion of the simulated maximum likelihood estimator introduced by Lerman and Manski (pp. 305–319 in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, Cambridge: MIT Press, 1981) for the estimation of discrete choice models. This bias occurs due to the nonlinearity of the derivatives of the log likelihood function and the statistically independent simulation errors of the choice probabilities across observations. This bias can be the dominating bias in an asymptotic expansion of the simulated maximum likelihood estimator when the number of simulated random variables per observation does not increase at least as fast as the sample size. The properly normalized simulated maximum likelihood estimator even has an asymptotic bias in its limiting distribution if the number of simulated random variables increases only as fast as the square root of the sample size. A bias-adjustment is introduced that can reduce the bias. Some Monte Carlo experiments have demonstrated the usefulness of the bias-adjustment procedure.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 3 , June 1995 , pp. 437 - 483
Copyright
Copyright © Cambridge University Press 1995

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