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Threshold Regression With a Threshold Boundary

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  • Ping Yu
  • Xiaodong Fan

Abstract

This article studies computation, estimation, inference, and testing for linearity in threshold regression with a threshold boundary. We first put forward a new algorithm to ease the computation of the threshold boundary, and develop the asymptotics for the least squares estimator in both the fixed-threshold-effect framework and the small-threshold-effect framework. We also show that the inverting-likelihood-ratio method is not suitable to construct confidence sets for the threshold parameters, while the nonparametric posterior interval is still applicable. We then propose a new score-type test to test for the existence of threshold effects. Comparing with the usual Wald-type test, it is computationally less intensive, and its critical values are easier to obtain by the simulation method. Simulation studies corroborate the theoretical results. We finally conduct two empirical applications in labor economics to illustrate the nonconstancy of thresholds.

Suggested Citation

  • Ping Yu & Xiaodong Fan, 2021. "Threshold Regression With a Threshold Boundary," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 953-971, October.
    • Handle: RePEc:taf:jnlbes:v:39:y:2021:i:4:p:953-971
    DOI: 10.1080/07350015.2020.1740712
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    Cited by:

    1. Ping Yu & Shengjie Hong & Peter C. B. Phillips, 2022. "Panel Threshold Regression with Unobserved Individual-Specific Threshold Effects," Cowles Foundation Discussion Papers 2352, Cowles Foundation for Research in Economics, Yale University.
    2. Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.
    3. Lixiong Yang, 2023. "Variable selection in threshold model with a covariate-dependent threshold," Empirical Economics, Springer, vol. 65(1), pages 189-202, July.
    4. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.

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