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Structural Threshold Regression

Author

Listed:
  • Kourtellos, Andros
  • Stengos, Thanasis
  • Tan, Chih Ming
Abstract
This paper introduces the structural threshold regression (STR) model that allows for an endogenous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000, Econometrica 68, 575–603) and Caner and Hansen (2004, Econometric Theory 20, 813–843) to allow for the endogeneity of the threshold variable and regime-specific heteroskedasticity. Our estimation of the threshold parameter is based on a two-stage concentrated least squares method that involves an inverse Mills ratio bias correction term in each regime. We derive its asymptotic distribution and propose a method to construct confidence intervals. We also provide inference for the slope parameters based on a generalized method of moments. Finally, we investigate the performance of the asymptotic approximations using a Monte Carlo simulation, which shows the applicability of the method in finite samples.

Suggested Citation

  • Kourtellos, Andros & Stengos, Thanasis & Tan, Chih Ming, 2016. "Structural Threshold Regression," Econometric Theory, Cambridge University Press, vol. 32(4), pages 827-860, August.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:04:p:827-860_00
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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. Papageorgiou, Chris, 2002. "Trade as a threshold variable for multiple regimes," Economics Letters, Elsevier, vol. 77(1), pages 85-91, September.
    3. 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.
    4. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    5. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(5), pages 813-843, October.
    6. Papageorgiou, Chris, 2006. "Trade as a threshold variable for multiple regimes: Reply," Economics Letters, Elsevier, vol. 91(3), pages 460-461, June.
    7. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    8. Li, Qi & Wooldridge, Jeffrey M., 2002. "Semiparametric Estimation Of Partially Linear Models For Dependent Data With Generated Regressors," Econometric Theory, Cambridge University Press, vol. 18(3), pages 625-645, June.
    9. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
    10. Stryhn, Henrik, 1996. "The location of the maximum of asymmetric two-sided Brownian motion with triangular drift," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 279-284, September.
    11. Easterly, William & Levine, Ross, 2003. "Tropics, germs, and crops: how endowments influence economic development," Journal of Monetary Economics, Elsevier, vol. 50(1), pages 3-39, January.
    12. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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