IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-14-00592.html
   My bibliography  Save this article

Robust estimation based on the third-moment restriction of the error terms for the Box-Cox transformation model: An estimator consistent under heteroscedasticity

Author

Listed:
  • Kazumitsu Nawata

    (University of Tokyo)

Abstract

The Box-Cox (1964) transformation model is widely used in various fields of econometrics and statistics. Generally, the maximum likelihood estimator under the normality assumption (BC MLE) is used. However, the BC MLE is not consistent under heteroscedasticity, even if the “small sigma†assumption is satisfied.　Here I propose a new robust estimator of the Box-Cox transformation model. The estimator is based on only the first- and third-moment restrictions of the error terms, and it is consistent even under heteroscedasticity. Moreover, it can be easily calculated by the least-squares and scanning methods. The asymptotic distribution of the proposed estimator was obtained, and the results of Monte Carlo experiments are presented.

Suggested Citation

  • Kazumitsu Nawata, 2015. "Robust estimation based on the third-moment restriction of the error terms for the Box-Cox transformation model: An estimator consistent under heteroscedasticity," Economics Bulletin, AccessEcon, vol. 35(2), pages 1056-1064.
    • Handle: RePEc:ebl:ecbull:eb-14-00592
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2015/Volume35/EB-15-V35-I2-P107.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nawata, Kazumitsu & McAleer, Michael, 2014. "The maximum number of parameters for the Hausman test when the estimators are from different sets of equations," Economics Letters, Elsevier, vol. 123(3), pages 291-294.
    2. Wooldridge, Jeffrey M, 1992. "Some Alternatives to the Box-Cox Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 935-955, November.
    3. Showalter, Mark H, 1994. "A Monte Carlo Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative," The Review of Economics and Statistics, MIT Press, vol. 76(3), pages 560-570, August.
    4. Kazumitsu Nawata & Koichi Kawabuchi, 2014. "A new test for the Box-Cox transformation model: An analysis of length of hospital stay for diabetes patients in Japan," Economics Bulletin, AccessEcon, vol. 34(1), pages 324-332.
    5. Kazumitsu Nawata, 2013. "A new estimator of the Box-Cox transformation model using moment conditions," Economics Bulletin, AccessEcon, vol. 33(3), pages 2287-2297.
    6. Powell, James L., 1996. "Rescaled methods-of-moments estimation for the Box-Cox regression model," Economics Letters, Elsevier, vol. 51(3), pages 259-265, June.
    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. Daniel Becker & Alois Kneip & Valentin Patilea, 2021. "Semiparametric inference for partially linear regressions with Box-Cox transformation," Papers 2106.10723, arXiv.org.
    2. Jason Abrevaya, 2002. "Computing Marginal Effects In The Box-Cox Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 383-393.
    3. Kazumitsu Nawata, 2013. "A new estimator of the Box-Cox transformation model using moment conditions," Economics Bulletin, AccessEcon, vol. 33(3), pages 2287-2297.
    4. Marcus Asplund, 2000. "What Fraction of a Capital Investment is Sunk Costs?," Journal of Industrial Economics, Wiley Blackwell, vol. 48(3), pages 287-304, September.
    5. Daniel, Vanessa E. & Florax, Raymond J.G.M. & Rietveld, Piet, 2009. "Flooding risk and housing values: An economic assessment of environmental hazard," Ecological Economics, Elsevier, vol. 69(2), pages 355-365, December.
    6. J. M. C. Santos Silva & Silvana Tenreyro, 2022. "The Log of Gravity at 15," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 423-437, September.
    7. Nawata, K. & Kawabuchi, K., 2013. "Evaluation of the DPC-based inclusive payment system in Japan for cataract operations by a new model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 76-85.
    8. Brant Abbott & Giovanni Gallipoli, 2022. "Permanent‐income inequality," Quantitative Economics, Econometric Society, vol. 13(3), pages 1023-1060, July.
    9. Komunjer, Ivana, 2009. "Global identification of the semiparametric Box-Cox model," Economics Letters, Elsevier, vol. 104(2), pages 53-56, August.
    10. Anirban Basu & Bhakti V. Arondekar & Paul J. Rathouz, 2006. "Scale of interest versus scale of estimation: comparing alternative estimators for the incremental costs of a comorbidity," Health Economics, John Wiley & Sons, Ltd., vol. 15(10), pages 1091-1107, October.
    11. Nawata, Kazumitsu & McAleer, Michael, 2014. "The maximum number of parameters for the Hausman test when the estimators are from different sets of equations," Economics Letters, Elsevier, vol. 123(3), pages 291-294.
    12. Stefan Boes, 2007. "Count Data Models with Unobserved Heterogeneity: An Empirical Likelihood Approach," SOI - Working Papers 0704, Socioeconomic Institute - University of Zurich.
    13. Ciani Emanuele & Fisher Paul, 2019. "Dif-in-Dif Estimators of Multiplicative Treatment Effects," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-10, January.
    14. Sara Amoroso & Mafini Dosso & Pietro Moncada-Paterno-Castello, 2015. "The impact of skill endowments and collective bargaining on knowledge-intensive greenfield FDI," JRC Working Papers on Corporate R&D and Innovation 2015-08, Joint Research Centre.
    15. Gormley, Fionnuala M. & Meade, Nigel, 2007. "The utility of cash flow forecasts in the management of corporate cash balances," European Journal of Operational Research, Elsevier, vol. 182(2), pages 923-935, October.
    16. Blackburn, McKinley L., 2007. "Estimating wage differentials without logarithms," Labour Economics, Elsevier, vol. 14(1), pages 73-98, January.
    17. James Bugden, 2013. "Renovations and the Repeat-Sales House Price Index," Working Papers 2013.08, School of Economics, La Trobe University.
    18. Kazumitsu Nawata & Koichi Kawabuchi, 2014. "A new test for the Box-Cox transformation model: An analysis of length of hospital stay for diabetes patients in Japan," Economics Bulletin, AccessEcon, vol. 34(1), pages 324-332.
    19. Terza, Joseph V. & Basu, Anirban & Rathouz, Paul J., 2008. "Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling," Journal of Health Economics, Elsevier, vol. 27(3), pages 531-543, May.
    20. Boris Kaiser, 2016. "Decomposing differences in arithmetic means: a doubly robust estimation approach," Empirical Economics, Springer, vol. 50(3), pages 873-899, May.

    More about this item

    Keywords

    Box-Cox transformation; heteroscedasticity; robust estimator; moment restriction;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

    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:ebl:ecbull:eb-14-00592. 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: John P. Conley (email available below). General contact details of provider: .

    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.