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Testing for threshold effects in regression models

Author

Listed:
  • Sokbae (Simon) Lee

    (Institute for Fiscal Studies and Columbia University)

  • Myung Hwan Seo

    (Institute for Fiscal Studies)

  • Youngki Shin

    (Institute for Fiscal Studies)

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.

Suggested Citation

  • Sokbae (Simon) Lee & Myung Hwan Seo & Youngki Shin, 2010. "Testing for threshold effects in regression models," CeMMAP working papers CWP36/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:36/10
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    File URL: http://cemmap.ifs.org.uk/wps/cwp3610.pdf
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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, President and Fellows of Harvard College, vol. 123(1), pages 177-218.
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    regression; econometrics;

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