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Consistent Pseudo-Maximum Likelihood Estimators and Groups of Transformations

Author

Listed:
  • Christian Gouriéroux

    (University of Toronto, TSE and PSL)

  • Alain Monfort

    (CREST)

  • Jean-Michel Zakoian

    (CREST; University of Lille)

Abstract

In a transformation model yt = c[a(xt, ß),ut], where the errors ut are i.i.d and independent of the explanatory variables xt, the parameters can be estimated by a pseudo-maximum likelihood (PML) method, that is, by using a misspecified distribution of the errors, but the PML estimator of ß is in general not consistent. We explain in this paper how to nest the initial model in an identified augmented model with more parameters in order to derive consistent PML estimators of appropriate functions of parameter ß. The usefulness of the consistency result is illustrated by examples of systems of nonlinear equations, conditionally heteroskedastic models, stochastic volatility, or models with spatial interactions.

Suggested Citation

  • Christian Gouriéroux & Alain Monfort & Jean-Michel Zakoian, 2018. "Consistent Pseudo-Maximum Likelihood Estimators and Groups of Transformations," Working Papers 2018-08, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2018-08
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    3. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373, July.
    4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    5. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 531-542.
    6. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    7. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444.
    8. Fiorentini, Gabriele & Sentana, Enrique, 2019. "Consistent non-Gaussian pseudo maximum likelihood estimators," Journal of Econometrics, Elsevier, vol. 213(2), pages 321-358.
    9. Paul Goldsmith-Pinkham & Guido W. Imbens, 2013. "Social Networks and the Identification of Peer Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 253-264, July.
    10. Piotr Zwiernik & Caroline Uhler & Donald Richards, 2017. "Maximum likelihood estimation for linear Gaussian covariance models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1269-1292, September.
    11. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    12. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(2), pages 251-280, April.
    13. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    14. Ying Yuan & Hongtu Zhu & Weili Lin & J. S. Marron, 2012. "Local polynomial regression for symmetric positive definite matrices," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 697-719, September.
    15. Francq, Christian & Lepage, Guillaume & Zakoïan, Jean-Michel, 2011. "Two-stage non Gaussian QML estimation of GARCH models and testing the efficiency of the Gaussian QMLE," Journal of Econometrics, Elsevier, vol. 165(2), pages 246-257.
    16. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Gourieroux, Christian & Lu, Yang, 2019. "Least impulse response estimator for stress test exercises," Journal of Banking & Finance, Elsevier, vol. 103(C), pages 62-77.

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    More about this item

    Keywords

    Pseudo-Maximum Likelihood; Transformation Model; Identification; Consistency; Stochastic Volatility; Conditional Heteroskedasticity; Spatial Interactions;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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