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Robust Estimation and Inference for Threshold Models with Integrated Regressors

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  • Haiqiang Chen

Abstract

This paper studies the robust estimation and inference of threshold models with integrated regres- sors. We derive the asymptotic distribution of the profiled least squares (LS) estimator under the diminishing threshold effect assumption that the size of the threshold effect converges to zero. Depending on how rapidly this sequence converges, the model may be identified or only weakly identified and asymptotic theorems are developed for both cases. As the convergence rate is unknown in practice, a model-selection procedure is applied to determine the model identification strength and to construct robust confidence intervals, which have the correct asymptotic size irrespective of the magnitude of the threshold effect. The model is then generalized to incorporate endogeneity and serial correlation in error terms, under which, we design a Cochrane-Orcutt feasible generalized least squares (FGLS) estimator which enjoys efficiency gains and robustness against different error specifications, including both I(0) and I(1) errors. Based on this FGLS estimator, we further develop a sup-Wald statistic to test for the existence of the threshold effect. Monte Carlo simulations show that our estimators and test statistics perform well.

Suggested Citation

  • Haiqiang Chen, 2013. "Robust Estimation and Inference for Threshold Models with Integrated Regressors," SFB 649 Discussion Papers SFB649DP2013-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2013-034
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    References listed on IDEAS

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    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. 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.
    3. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
    4. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    5. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(04), pages 778-810, August.
    6. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    7. 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..
    8. Jesús Gonzalo & Jean-Yves Pitarakis, 2006. "Threshold Effects in Cointegrating Relationships," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 813-833, December.
    9. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    10. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    11. Jesús Gonzalo & Jean-Yves Pitarakis, 2011. "Regime-Specific Predictability in Predictive Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 229-241, June.
    12. Donald W. K. Andrews & C. John McDermott, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Oxford University Press, vol. 62(3), pages 343-360.
    13. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    14. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    15. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    16. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    17. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    18. 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.
    19. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    20. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    21. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    22. 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.
    23. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    24. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1453-1490, October.
    25. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    26. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    27. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
    28. Choi, Chi-Young & Hu, Ling & Ogaki, Masao, 2008. "Robust estimation for structural spurious regressions and a Hausman-type cointegration test," Journal of Econometrics, Elsevier, vol. 142(1), pages 327-351, January.
    29. Park, Joon Y. & Hahn, Sang B., 1999. "Cointegrating Regressions With Time Varying Coefficients," Econometric Theory, Cambridge University Press, vol. 15(05), pages 664-703, October.
    30. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    31. Phillips, Peter C.B. & Hodgson, Douglas J., 1994. "Spurious Regression and Generalized Least Squares," Econometric Theory, Cambridge University Press, vol. 10(05), pages 967-968, December.
    32. Choi, In & Saikkonen, Pentti, 2010. "Tests For Nonlinear Cointegration," Econometric Theory, Cambridge University Press, vol. 26(03), pages 682-709, June.
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    Cited by:

    1. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(04), pages 778-810, August.
    2. Poeschel, Friedrich, 2012. "Assortative matching through signals," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.

    More about this item

    Keywords

    Threshold effects; Integrated processes; Nonlinear cointegration; Weak identification.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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