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Robust Estimation and Inference for Threshold Models with Integrated Regressors

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  • Haiqiang Chen
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    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.

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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2013-034.

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    Length: 39 pages
    Date of creation: Jul 2013
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    Handle: RePEc:hum:wpaper:sfb649dp2013-034

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

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    1. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2010. "Regime specific predictability in predictive regressions," Discussion Paper Series In Economics And Econometrics 0916, Economics Division, School of Social Sciences, University of Southampton.
    2. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series, Institute of Economic Research, Seoul National University no6, Institute of Economic Research, Seoul National University.
    3. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 943, Cowles Foundation for Research in Economics, Yale University.
    4. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 783-820, July.
    5. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
    6. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, Elsevier, vol. 110(2), pages 319-352, October.
    7. Andrews, Donald W K & McDermott, C John, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 62(3), pages 343-60, July.
    8. 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, American Statistical Association, vol. 27(3), pages 369-396.
    9. Phillips, Peter C.B. & Hodgson, Douglas J., 1994. "Spurious Regression and Generalized Least Squares," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(05), pages 967-968, December.
    10. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(1), pages 99-125, January.
    11. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics, Boston College Department of Economics 319., Boston College Department of Economics, revised 12 May 1998.
    12. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 119-43, January.
    13. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 10(4), pages 365-84, Oct.-Dec..
    14. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 274-294.
    15. Oliver Linton & Myunghwan Seo, 2005. "A smoothed least squares estimator for threshold regression models," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 4434, London School of Economics and Political Science, LSE Library.
    16. John Y. Campbell & Motohiro Yogo, 2002. "Efficient Tests of Stock Return Predictability," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1972, Harvard - Institute of Economic Research.
    17. Gonzalo, J. & Pitarakis, J., 2005. "Threshold effects in cointegrating relationships," Discussion Paper Series In Economics And Econometrics 0506, Economics Division, School of Social Sciences, University of Southampton.
    18. Choi, In & Saikkonen, Pentti, 2010. "Tests For Nonlinear Cointegration," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 26(03), pages 682-709, June.
    19. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers, UCLA Department of Economics 693, UCLA Department of Economics.
    20. Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics, EconWPA 0503002, EconWPA, revised 15 Dec 2005.
    21. Choi, Chi-Young & Hu, Ling & Ogaki, Masao, 2008. "Robust estimation for structural spurious regressions and a Hausman-type cointegration test," Journal of Econometrics, Elsevier, Elsevier, vol. 142(1), pages 327-351, January.
    22. Bruce E. Hansen & Mehmet Caner, 1997. "Threshold Autoregressions with a Unit Root," Boston College Working Papers in Economics, Boston College Department of Economics 381, Boston College Department of Economics.
    23. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(05), pages 1373-1403, October.
    24. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 240-253.
    25. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, Elsevier, vol. 152(2), pages 81-92, October.
    26. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(4), pages 473-95, August.
    27. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 26(05), pages 1453-1490, October.
    28. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, Econometric Society, vol. 64(2), pages 413-30, March.
    29. Park, Joon Y. & Hahn, Sang B., 1999. "Cointegrating Regressions With Time Varying Coefficients," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 15(05), pages 664-703, October.
    30. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, Elsevier, vol. 148(2), pages 101-113, February.
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