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New critical values for likelihood ratio inference of threshold regression

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  • Yu, Ping

Abstract

This paper shows that the critical values for likelihood ratio inference of the threshold point in Hansen (2000) are too large if we restrict the confidence set as an interval, which can partially explain why Hansen’s confidence interval is conservative when the threshold effect is not too small. We provide appropriate critical values and show that different from conventional critical values, these new critical values are invariant to the structural change in the error and covariate distributions.

Suggested Citation

  • Yu, Ping, 2026. "New critical values for likelihood ratio inference of threshold regression," Economics Letters, Elsevier, vol. 259(C).
    • Handle: RePEc:eee:ecolet:v:259:y:2026:i:c:s0165176525006287
    DOI: 10.1016/j.econlet.2025.112791
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    References listed on IDEAS

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    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    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. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    5. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    6. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    7. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    8. Bruce E. Hansen, 2017. "Regression Kink With an Unknown Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 228-240, April.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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