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A Note on Bootstrapping Generalized Method of Moments Estimators

Published online by Cambridge University Press:  11 February 2009

Jinyong Hahn
Jinyong Hahn
Affiliation:
University of Pennsylvania
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Abstract

Recently, Arcones and Giné (1992, pp. 13–47, in R. LePage & L. Billard [eds.], Exploring the Limits of Bootstrap, New York: Wiley) established that the bootstrap distribution of the M-estimator converges weakly to the limit distribution of the estimator in probability. In contrast, Brown and Newey (1992, Bootstrapping for GMM, Seminar note) discovered that the bootstrap distribution of the GMM overidentification test statistic does not converge weakly to the x2 distribution. In this paper, it is shown that the bootstrap distribution of the GMM estimator converges weakly to the limit distribution of the estimator in probability. Asymptotic coverage probabilities of the confidence intervals based on the bootstrap percentile method are thus equal to their nominal coverage probability.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 1 , March 1996 , pp. 187 - 197
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

Amemiya, T. (1985) Advanced Econometrics. Cambridge: Harvard University Press.Google Scholar
Arcones, M. & Gine, E. (1992) On the bootstrap of M-estimators and other statistical functionals. In LePage, R. & Billard, L. (eds.), Exploring the Limits of Bootstrap, pp. 13–47. New York: Wiley.Google Scholar
Babu, G.J. (1986) A note on bootstrapping the variance of sample quantile. Annals of the Institute of Statistical Mathematics 38 (A), 439–443.Google Scholar
Bickel, P.J. & Freedman, D.A. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196–1217.Google Scholar
Brown, W. & Newey, W. (1992) Bootstrapping for GMM. Seminar note. Massachusetts Institute of Technology.Google Scholar
Gine, E. & Zinn, J. (1990) Bootstrapping general empirical measures. Annals of Probability 18, 851–869.CrossRefGoogle Scholar
Hahn, J. (1993) Three Essays in Econometrics. Ph.D. Dissertation, Harvard University.Google Scholar
Hall, P. (1986) On the bootstrap and confident intervals. Annals of Statistics 14, 1431–1452.CrossRefGoogle Scholar
Hall, P. (1992) The Bootstrap and Edgewonh Expansion. New York: Springer-Verlag.CrossRefGoogle Scholar
Harisen, L. (1982) Large sample properties of generalized method of moments estimators. EcOn- omelhca 50, 1029–1054.Google Scholar
Pakes, A. & Pollard, D. (1986) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.CrossRefGoogle Scholar
Phillips, P. (1991) A shortcut to LAD estimator asymptotics. Econometric Theory 7, 450–463.CrossRefGoogle Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. New York: Springer-Verlag.CrossRefGoogle Scholar