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Panel kink regression with an unknown threshold

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  • Zhang, Yonghui
  • Zhou, Qiankun
  • Jiang, Li

Abstract

In this paper, we extend the kink regression model with an unknown threshold in Hansen (2017) to the panel data framework, where the cross-sectional dimension (N) goes to infinity and the time period (T) is fixed. Following the literature of threshold regressions, we propose an estimator based on the within-group transformation. Under fixed threshold effect assumption, we establish that the slope and threshold estimators are jointly normally distributed with the same convergence rate OpN−1∕2 and a non-zero asymptotic covariance. We also suggest a sup-Wald test for the presence of kink effect, and derive its limiting distribution. A bootstrap procedure is proposed to obtain the bootstrap p-values to improve the finite sample performance of the test. Monte Carlo simulations show that the FE estimator and the sup-Wald test perform quite well in estimating the unknown parameters and testing for kink effect, respectively.

Suggested Citation

  • Zhang, Yonghui & Zhou, Qiankun & Jiang, Li, 2017. "Panel kink regression with an unknown threshold," Economics Letters, Elsevier, vol. 157(C), pages 116-121.
    • Handle: RePEc:eee:ecolet:v:157:y:2017:i:c:p:116-121
    DOI: 10.1016/j.econlet.2017.05.033
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    References listed on IDEAS

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    1. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. 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.
    4. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
    5. Alexander Chudik & Kamiar Mohaddes & M. Hashem Pesaran & Mehdi Raissi, 2017. "Is There a Debt-Threshold Effect on Output Growth?," The Review of Economics and Statistics, MIT Press, vol. 99(1), pages 135-150, March.
    6. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
    7. Masulis, Ronald W, 1983. "The Impact of Capital Structure Change on Firm Value: Some Estimates," Journal of Finance, American Finance Association, vol. 38(1), pages 107-126, March.
    8. Carmen M. Reinhart & Kenneth S. Rogoff, 2011. "From Financial Crash to Debt Crisis," American Economic Review, American Economic Association, vol. 101(5), pages 1676-1706, August.
    9. 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.
    10. 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.
    11. Savvides, Andreas & Stengos, Thanasis, 2000. "Income inequality and economic development: evidence from the threshold regression model," Economics Letters, Elsevier, vol. 69(2), pages 207-212, November.
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    Cited by:

    1. Klaus Moeltner & A. Ford Ramsey & Clinton L. Neill, 2021. "Bayesian Kinked Regression with Unobserved Thresholds: An Application to the von Liebig Hypothesis," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(5), pages 1832-1856, October.
    2. V., Ernesto Guerra & H., Eugenio Bobenrieth & H., Juan Bobenrieth & Wright, Brian D., 2023. "Endogenous thresholds in energy prices: Modeling and empirical estimation," Energy Economics, Elsevier, vol. 121(C).
    3. Nutnaree Maneejuk & Sutthipat Ratchakom & Paravee Maneejuk & Woraphon Yamaka, 2020. "Does the Environmental Kuznets Curve Exist? An International Study," Sustainability, MDPI, vol. 12(21), pages 1-22, November.
    4. Myung Hwan Seo & Sueyoul Kim & Young-Joo Kim, 2019. "Estimation of dynamic panel threshold model using Stata," Stata Journal, StataCorp LP, vol. 19(3), pages 685-697, September.
    5. Bolarinwa, Segun Thompson & Akinlo, Anthony Enisan, 2021. "Is there a nonlinear relationship between financial development and income inequality in Africa? Evidence from dynamic panel threshold," The Journal of Economic Asymmetries, Elsevier, vol. 24(C).
    6. Sun, Yan & Wan, Chuang & Zhang, Wenyang & Zhong, Wei, 2024. "A Multi-Kink quantile regression model with common structure for panel data analysis," Journal of Econometrics, Elsevier, vol. 239(2).
    7. Maneejuk, Paravee & Yamaka, Woraphon, 2020. "An analysis of the impacts of telecommunications technology and innovation on economic growth," Telecommunications Policy, Elsevier, vol. 44(10).
    8. Paravee Maneejuk & Woraphon Yamaka & Wilawan Srichaikul, 2022. "Tourism Development and Economic Growth in Southeast Asian Countries under the Presence of Structural Break: Panel Kink with GME Estimator," Mathematics, MDPI, vol. 10(5), pages 1-17, February.

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    More about this item

    Keywords

    Panel data; Fixed effects; Kink regression; Unknown threshold; Testing for kink effect;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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