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Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation

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  • Koenker, Roger
  • Machado, José A.F.
  • Skeels, Christopher L.
  • Welsh, Alan H.

Abstract

This paper explores the robustness of minimum distance (GMM) estimators focusing particularly on the effect of intermediate covariance matrix estimation on final estimator performance. Asymptotic expansions to order Op(n−3/2) are employed to construct O(n−2) expansions for the variance of estimators constructed from preliminary least-squares and general M-estimators. In the former case, there is a rather curious robustifying effect due to estimation of the Eicker-White covariance matrix for error distributions with sufficiently large kurtosis.

Suggested Citation

  • Koenker, Roger & Machado, José A.F. & Skeels, Christopher L. & Welsh, Alan H., 1994. "Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation," Econometric Theory, Cambridge University Press, vol. 10(1), pages 172-197, March.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:01:p:172-197_00
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    Cited by:

    1. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
    2. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    3. Marsh, Thomas L. & Mittelhammer, Ronald C., 2001. "Adaptive Truncated Estimaton Applied To Maximum Entropy," 2001 Annual Meeting, July 8-11, 2001, Logan, Utah 36169, Western Agricultural Economics Association.
    4. Castro, Luciano de & Galvao, Antonio F. & Kim, Jeong Yeol & Montes-Rojas, Gabriel & Olmo, Jose, 2022. "Experiments on portfolio selection: A comparison between quantile preferences and expected utility decision models," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    5. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    6. Koenker, Roger & Machado, Jose A. F., 1998. "The Falstaff estimator," Economics Letters, Elsevier, vol. 61(1), pages 23-28, October.
    7. Myoung-jae Lee & Yasushi Kondo, 2002. "Nonparametric Derivative Estimation for Related-Effect Panel Data," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 A5-1, International Conferences on Panel Data.
    8. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
    9. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    10. Joel L. Horowitz, 1996. "Bootstrap Methods For Covariance Structures," Econometrics 9610003, University Library of Munich, Germany.
    11. Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Carrasco, Marine & Kotchoni, Rachidi, 2017. "Efficient Estimation Using The Characteristic Function," Econometric Theory, Cambridge University Press, vol. 33(2), pages 479-526, April.
    13. Galvao, Antonio F. & Wang, Liang, 2015. "Efficient minimum distance estimator for quantile regression fixed effects panel data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 1-26.
    14. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
    15. Richard H Spady, 1996. "Nonparametric inference by quasi-likelihood methods'/A>Size-v0: 198,000," Economics Papers 19. & 111., Economics Group, Nuffield College, University of Oxford.
    16. Beum-Jo Park, 2009. "Risk-return relationship in equity markets: using a robust GMM estimator for GARCH-M models," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 93-104.
    17. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    18. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    19. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    20. Windmeijer, Frank, 2005. "A finite sample correction for the variance of linear efficient two-step GMM estimators," Journal of Econometrics, Elsevier, vol. 126(1), pages 25-51, May.

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