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

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  • 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
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    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.
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    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

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