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Testing for Threshold Effects in Regression Models

Author

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  • Lee, Sokbae
  • Seo, Myung Hwan
  • Shin, Youngki

Abstract

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online.
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Suggested Citation

  • 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.
  • Handle: RePEc:bes:jnlasa:v:106:i:493:y:2011:p:220-231
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    File URL: http://pubs.amstat.org/doi/abs/10.1198/jasa.2011.tm09800
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    References listed on IDEAS

    as
    1. David Card & Alexandre Mas & Jesse Rothstein, 2008. "Tipping and the Dynamics of Segregation," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 177-218.
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    Citations

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    Cited by:

    1. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2016. "Oracle Estimation of a Change Point in High Dimensional Quantile Regression," Papers 1603.00235, arXiv.org, revised Dec 2016.
    2. Javier Hidalgo & Jungyoon Lee & Myung Hwan Seo, 2017. "Robust Inference and Testing of Continuity in Threshold Regression Models," STICERD - Econometrics Paper Series 590, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Liwen Zhang & Huixia Judy Wang & Zhongyi Zhu, 2017. "Composite change point estimation for bent line quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 145-168, February.
    4. Le-Yu Chen & Sokbae Lee, 2016. "Best Subset Binary Prediction," Papers 1610.02738, arXiv.org, revised May 2018.
    5. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. repec:eee:ecolet:v:157:y:2017:i:c:p:116-121 is not listed on IDEAS
    7. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    8. Tang, Yanlin & Song, Xinyuan & Zhu, Zhongyi, 2015. "Threshold effect test in censored quantile regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 149-156.
    9. 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.
    10. Sokbae Lee & Hyunmin Park & Myung Hwan Seo & Youngki Shin, 2014. "A contribution to the Reinhart and Rogoff debate: not 90 percent but maybe 30 percent," CeMMAP working papers CWP39/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    12. Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.
    13. repec:bla:biomet:v:73:y:2017:i:2:p:452-462 is not listed on IDEAS
    14. Rothfelder, Mario & Boldea, Otilia, 2016. "Testing for a Threshold in Models with Endogenous Regressors," Discussion Paper 2016-029, Tilburg University, Center for Economic Research.
    15. repec:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-017-0711-9 is not listed on IDEAS
    16. repec:cep:stiecm:/2014/577 is not listed on IDEAS
    17. repec:eee:csdana:v:116:y:2017:i:c:p:49-66 is not listed on IDEAS
    18. repec:bla:jtsera:v:38:y:2017:i:1:p:99-119 is not listed on IDEAS
    19. Gabriela Ciuperca & Zahraa Salloum, 2015. "Empirical likelihood test in a posteriori change-point nonlinear model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 919-952, November.

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