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A new estimator of the Box-Cox transformation model using moment conditions

Author

Listed:
  • Kazumitsu Nawata

    (University of Tokyo)

Abstract

The maximum likelihood estimator (MLE) under the normality assumption of error terms is widely used to estimate the Box-Cox transformation model. However, since the error terms cannot be normally distributed, it is not a proper estimator. In other words, the estimator is inconsistent. In this paper, I propose a new estimator of the Box-Cox transformation model that modifies the MLE in key ways. I demonstrate that the estimator is consistent, and that an asymptotic distribution is obtained. The results of Monte Carlo experiments are also presented.

Suggested Citation

  • Kazumitsu Nawata, 2013. "A new estimator of the Box-Cox transformation model using moment conditions," Economics Bulletin, AccessEcon, vol. 33(3), pages 2287-2297.
    • Handle: RePEc:ebl:ecbull:eb-12-00807
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2013/Volume33/EB-13-V33-I3-P214.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Khazzoom, J. Daniel, 1989. "A note on the application of the nonlinear two-stage least-squares estimator to a Box-Cox-transformed model," Journal of Econometrics, Elsevier, vol. 42(3), pages 377-379, November.
    3. Amemiya, Takeshi & Powell, James L., 1981. "A comparison of the Box-Cox maximum likelihood estimator and the non-linear two-stage least squares estimator," Journal of Econometrics, Elsevier, vol. 17(3), pages 351-381, December.
    4. Nawata, Kazumitsu, 1994. "Estimation of sample selection bias models by the maximum likelihood estimator and Heckman's two-step estimator," Economics Letters, Elsevier, vol. 45(1), pages 33-40, May.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    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. 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.
    3. 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.

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    More about this item

    Keywords

    Box-Cox transformation; consistent estimator; moment condition;
    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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