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Regularized Bayesian estimation in generalized threshold regression models

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Author Info

  • Friederike Greb

    (Georg-August-University Göttingen)

  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

  • Axel Munk

    (Georg-August-University Göttingen)

  • Stephan von Cramon-Taubadel

    (Georg-August-University Göttingen)

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    Abstract

    Estimation of threshold parameters in (generalized) threshold regression models is typically performed by maximizing the corresponding pro file likelihood function. Also, certain Bayesian techniques based on non-informative priors are developed and widely used. This article draws attention to settings (not rare in practice) in which these standard estimators either perform poorly or even fail. In particular, if estimation of the regression coeffcients is associated with high uncertainty, the pro file likelihood for the threshold parameters and thus the corresponding estimator can be highly aff ected. We suggest an alternative estimation method employing the empirical Bayes paradigm, which allows to circumvent defi ciencies of standard estimators. The new estimator is completely data-driven and induces little additional numerical e ffort compared with the old one. Simulation results show that our estimator outperforms commonly used estimators and produces excellent results even if the latter show poor performance. The practical relevance of our approach is illustrated by a real-data example; we follow up the anlysis of cross-country growth behavior detailed in Hansen (2000).

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    File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_99.pdf
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    Bibliographic Info

    Paper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 99.

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    Date of creation: 07 Oct 2011
    Date of revision: 18 Oct 2012
    Handle: RePEc:got:gotcrc:099

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    Web page: http://www.uni-goettingen.de/en/82144.html

    Related research

    Keywords: threshold estimation; nuisance parameters; empirical Bayes;

    This paper has been announced in the following NEP Reports:

    References

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    1. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 821-56, July.
    2. Lee, Sokbae & Seo, Myung Hwan & Shin, Youngki, 2011. "Testing for Threshold Effects in Regression Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 106(493), pages 220-231.
    3. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 66(1), pages 165-185.
    4. Noelle I. Samia & Kung-Sik Chan, 2011. "Maximum likelihood estimation of a generalized threshold stochastic regression model," Biometrika, Biometrika Trust, Biometrika Trust, vol. 98(2), pages 433-448.
    5. repec:att:wimass:9419 is not listed on IDEAS
    6. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 575-604, May.
    7. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 10(4), pages 365-84, Oct.-Dec..
    8. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, Elsevier, vol. 110(2), pages 293-318, October.
    9. Noelle I. Samia & Kung-Sik Chan & Nils Chr. Stenseth, 2007. "A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan," Biometrika, Biometrika Trust, Biometrika Trust, vol. 94(1), pages 101-118.
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