IDEAS home Printed from https://ideas.repec.org/p/siu/wpaper/17-2006.html
   My bibliography  Save this paper

Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency

Author

Listed:
  • Kyoo il Kim

    (School of Economics and Social Sciences, Singapore Management University)

Abstract

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equation in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies that at least in terms of the third order stochastic expansion, we cannot improve on the simple one-step bias correction by using the bias correction of moment equations. Though the result in this paper is for a fixed number of parameters, our intuition may extend to the analytical bias correction of the panel data models with individual specific effects. Noting the M-estimation can nest many kinds of estimators including IV, 2SLS, MLE, GMM, and GEL, our finding is a rather strong result.

Suggested Citation

  • Kyoo il Kim, 2006. "Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency," Working Papers 17-2006, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:17-2006
    as

    Download full text from publisher

    File URL: https://mercury.smu.edu.sg/rsrchpubupload/7213/Firth_ES4.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    3. Pfanzagl, J. & Wefelmeyer, W., 1978. "A third-order optimum property of the maximum likelihood estimator," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 1-29, March.
    4. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935, Elsevier.
    5. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    6. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    7. 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.
    8. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    9. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," University of Western Ontario, Departmental Research Report Series 20028, University of Western Ontario, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jinyong Hahn & David W. Hughes & Guido Kuersteiner & Whitney K. Newey, 2024. "Efficient bias correction for cross‐section and panel data," Quantitative Economics, Econometric Society, vol. 15(3), pages 783-816, July.
    2. Michael Creel & Dennis Kristensen, "undated". "Indirect Likelihood Inference," Working Papers 558, Barcelona School of Economics.
    3. Kyoo Il Kim, 2016. "Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency," Econometrics, MDPI, vol. 4(4), pages 1-19, December.
    4. Kundhi, Gubhinder & Rilstone, Paul, 2012. "Edgeworth expansions for GEL estimators," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 118-146.
    5. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    6. Paul Rilstone, 2021. "Higher-Order Stochastic Expansions and Approximate Moments for Non-linear Models with Heterogeneous Observations," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 99-120, December.
    7. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    8. Wilhelm, Daniel, 2015. "Optimal Bandwidth Selection For Robust Generalized Method Of Moments Estimation," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1054-1077, October.
    9. Dennis Kristensen & Bernard Salanié, 2010. "Higher Order Improvements for Approximate Estimators," CAM Working Papers 2010-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    10. Gubhinder Kundhi & Paul Rilstone, 2015. "Saddlepoint expansions for GEL estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 1-24, March.
    11. Grigory Franguridi & Bulat Gafarov & Kaspar Wüthrich, 2021. "Conditional Quantile Estimators: A Small Sample Theory," CESifo Working Paper Series 9046, CESifo.
    12. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    13. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    14. Whitney K. Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    16. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    17. Schumann, Martin & Severini, Thomas A. & Tripathi, Gautam, 2021. "Integrated likelihood based inference for nonlinear panel data models with unobserved effects," Journal of Econometrics, Elsevier, vol. 223(1), pages 73-95.
    18. Pakel, Cavit, 2019. "Bias reduction in nonlinear and dynamic panels in the presence of cross-section dependence," Journal of Econometrics, Elsevier, vol. 213(2), pages 459-492.
    19. 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.
    20. Amor Keziou & Aida Toma, 2021. "A Robust Version of the Empirical Likelihood Estimator," Mathematics, MDPI, vol. 9(8), pages 1-19, April.

    More about this item

    Keywords

    Third-order Stochastic Expansion; Bias Correction; M-estimation;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:siu:wpaper:17-2006. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: QL THor (email available below). General contact details of provider: https://edirc.repec.org/data/sesmusg.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.