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Regularized Bayesian estimation in generalized threshold regression models


  • 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)


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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  • Friederike Greb & Tatyana Krivobokova & Axel Munk & Stephan von Cramon-Taubadel, 2011. "Regularized Bayesian estimation in generalized threshold regression models," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 99, Courant Research Centre PEG, revised 18 Oct 2012.
  • Handle: RePEc:got:gotcrc:099

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    References listed on IDEAS

    1. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    2. Noelle I. Samia & Kung-Sik Chan, 2011. "Maximum likelihood estimation of a generalized threshold stochastic regression model," Biometrika, Biometrika Trust, vol. 98(2), pages 433-448.
    3. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 365-384, Oct.-Dec..
    4. 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, vol. 94(1), pages 101-118.
    5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    6. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    7. Lee, Sokbae & Seo, Myung Hwan & Shin, Youngki, 2011. "Testing for Threshold Effects in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 220-231.
    8. 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, vol. 66(1), pages 165-185.
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    threshold estimation; nuisance parameters; empirical Bayes;

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