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Endogeneity in Semiparametric Threshold Regression

Author

Listed:
  • Andros Kourtellos

    () (Department of Economics, University of Cyprus, Cyprus; The Rimini Centre for Economic Analysis)

  • Thanasis Stengos

    () (Department of Economics and Finance, University of Guelph, Canada; The Rimini Centre for Economic Analysis)

  • Yiguo Sun

    () (Department of Economics and Finance, University of Guelph, Canada)

Abstract

In this paper, we investigate semiparametric threshold regression models with endogenous threshold variables based on a nonparametric control function approach. Using a series approximation we propose a two-step estimation method for the threshold parameter. For the regression coefficients we consider least-squares estimation in the case of exogenous regressors and two-stage least-squares estimation in the case of endogenous regressors. We show that our estimators are consistent and derive their asymptotic distribution for weakly dependent data. Furthermore, we propose a test for the endogeneity of the threshold variable, which is valid regardless of whether the threshold effect is zero or not. Finally, we assess the performance of our methods using a Monte Carlo simulation.

Suggested Citation

  • Andros Kourtellos & Thanasis Stengos & Yiguo Sun, 2017. "Endogeneity in Semiparametric Threshold Regression," Working Paper series 17-13, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:17-13
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    References listed on IDEAS

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    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(05), pages 813-843, October.
    3. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    4. Durlauf, Steven N, 1996. "A Theory of Persistent Income Inequality," Journal of Economic Growth, Springer, vol. 1(1), pages 75-93, March.
    5. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    6. Oded Galor & Joseph Zeira, 1993. "Income Distribution and Macroeconomics," Review of Economic Studies, Oxford University Press, vol. 60(1), pages 35-52.
    7. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    8. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    9. Deniz Ozabaci & Daniel J. Henderson & Liangjun Su, 2014. "Additive Nonparametric Regression in the Presence of Endogenous Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 555-575, October.
    10. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
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    12. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    13. Andros Kourtellos & Thanasis Stengos & Yiguo Sun, 2017. "Endogeneity in Semiparametric Threshold Regression," Working Paper series 17-13, Rimini Centre for Economic Analysis.
    14. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    15. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. Andros Kourtellos & Thanasis Stengos & Yiguo Sun, 2017. "Endogeneity in Semiparametric Threshold Regression," University of Cyprus Working Papers in Economics 10-2017, University of Cyprus Department of Economics.
    2. Christopoulos, Dimitris & McAdam, Peter & Tzavalis, Elias, 2018. "Dealing with endogeneity in threshold models using copulas: an illustration to the foreign trade multiplier," Working Paper Series 2136, European Central Bank.
    3. Daniel J. Henderson & Christopher F. Parmeter & Liangjun Su, 2017. "M-Estimation of a Nonparametric Threshold Regression Model," Working Papers 2017-15, University of Miami, Department of Economics.

    More about this item

    Keywords

    control function; series estimation; threshold regression;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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