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On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models

Published online by Cambridge University Press:  18 October 2010

Lung-Fei Lee
Affiliation:
University of Michigan

Abstract

This article considers methods of simulated moments for estimation of discrete response models. It is possible to use the same set of random numbers to simulate the choice probabilities for each individual in the sample. In addition to the method of simulated moments of McFadden, we have considered also maximum simulated likelihood estimation methods. An asymptotic theory for such procedures is provided. The estimators are shown to be consistent and asymptotically normal by the theory of generalized U-statistics. Asymptotic efficiency is discussed. Monte Carlo experiments on the finite sample performance of the estimators are reported.

Type
Articles
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

1.Amemiya, T.Advanced Econometrics. Cambridge; Harvard University Press, 1985.Google Scholar
2.Berkovec, J. & Stern, S.. Job exit behavior of older men. Econometrica 59 (1991): 189210.CrossRefGoogle Scholar
3.Chung, K.L.A Course in Probability Theory, 2nd ed. New York: Academic Press, 1974.Google Scholar
4.Geweke, J.Bayesian inference in econometric models with Monte Carlo integration. Econometrica 51 (1989): 13171339.CrossRefGoogle Scholar
5.Hajivassiliou, V. & McFadden, D.. The debt repayment crisis LDC's: Estimation by the method of simulated moments. Yale University, Working paper, 1987.Google Scholar
6.Ichimura, H. & Lee, L.F.. Semiparametric estimation of multiple index models: Single equation estimation. In Barnett, W.A., Powell, J., and Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, Chapter 1 and pp. 349. New York: Cambridge University Press, 1991.Google Scholar
7.Keanse, M.P. A computationally practical simulation estimator for panel data, with applications to labor supply and real wage movement over the business cycle. Discussion Paper No. 16, Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis, 1989.CrossRefGoogle Scholar
8.Lee, A.J.U-Statistics: Theory and Practice. New York: Marcel Dekker, 1990.Google Scholar
9.Lee, L.F. Semiparametric maximum profile likelihood estimation of polytomous and sequential choice models. Discussion Paper No. 253, Center for Economic Research, Department of Economics, University of Minnesota, 1989.Google Scholar
10.Lee, B.S. & Ingram, B.F.. Simulation estimation of time series models. Journal of Econometrics 47 (1991): 197205.CrossRefGoogle Scholar
11.Lehmann, E.L.Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden Day, 1966.Google Scholar
12.Lerman, S. & Manski, C.. On the use of simulated frequencies to approximate choice probabilities. In Manski, C. and McFadden, D. (ed.), Structural Analysis of Discrete Data with Econometric Applications, Chapter 7 and pp. 305319. Cambridge: MIT Press, 1981.Google Scholar
13.McFadden, D.A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57 (1989): 9951026.CrossRefGoogle Scholar
14.Nolan, D. & Pollard, D.. U-processes: Rates of convergence. The Annals of Statistics 15 (1987): 780799.CrossRefGoogle Scholar
15.Nolan, D. & Pollard, D.. Functional limit theorems for U-processes. The Annals of Probability 16 (1988): 12911298.CrossRefGoogle Scholar
16.Pakes, A.Patents as options: Some estimates of the value of holding European patent stocks. Econometrica 54 (1986): 755785.CrossRefGoogle Scholar
17.Pakes, A. & Pollard, D.. Simulation and the asymptotics of optimization estimators. Econometrica 57 (1989): 10271057.CrossRefGoogle Scholar
18.Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T.. Numerical Recipes. New York: Cambridge University Press, 1986.Google Scholar
19.Royden, H.L.Real Analysis. New York: MacMillan, 1963.Google Scholar
20.Serfling, R.J.Approximation Theorems of Mathematical Statistics. New York: Wiley, 1980.CrossRefGoogle Scholar
21.Stern, S. A method for smoothing simulated moments of discrete probabilities in multinomial probit models. Manuscript, Department of Economics, University of Virginia, 1987.Google Scholar