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Testing for threshold effects in regression models

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  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and Seoul National University)

  • Myung Hwan Seo
  • Youngki Shin

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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File URL: http://cemmap.ifs.org.uk/wps/cwp3610.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP36/10.

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Date of creation: Dec 2010
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Handle: RePEc:ifs:cemmap:36/10

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  1. David Card & Alexandre Mas & Jesse Rothstein, 2007. "Tipping and the Dynamics of Segregation," NBER Working Papers 13052, National Bureau of Economic Research, Inc.
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Cited by:
  1. 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.
  2. 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.
  3. 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, vol. 66(2), pages 413-439, April.

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