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Estimating Smooth Structural Change in Cointegration Models

  • Peter C. B. Phillips


  • Degui Li


  • Jiti Gao


This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to re-orient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions (or combinations) of the (functional) parameter space. Both rates are faster than the usual (√nh) rate for nonlinear models with smoothly changing coefficients and local stationarity. Hence two types of super-consistency apply in nonparametric kernel estimation of time-varying coefficient cointegration models. The higher rate of convergence (n√h) lies in the direction of the nonstationary regressor vector at the local coordinate point. The lower rate (nh) lies in the degenerate directions but is still super-consistent for nonparametric estimators. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case. Simulations are conducted to explore the finite sample properties of the methods and a practical application is given to examine time varying empirical relationships involving consumption, disposable income, investment and real interest rates.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 22/13.

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Date of creation: 2013
Date of revision:
Handle: RePEc:msh:ebswps:2013-22
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  1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  2. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  3. Peter C.B.Phillips & Jun Yu, 2009. "Dating the Timeline of Financial Bubbles During the Subprime Crisis," Working Papers CoFie-07-2009, Sim Kee Boon Institute for Financial Economics.
  4. Peter C. B. Phillips & Donggyu Sul, 2007. "Transition Modeling and Econometric Convergence Tests," Econometrica, Econometric Society, vol. 75(6), pages 1771-1855, November.
  5. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  6. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(04), pages 888-947, August.
  7. George Athanasopoulos & Osmani T. de C. Guillén & João V. Issler & Farshid Vahid, 2009. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Monash Econometrics and Business Statistics Working Papers 2/09, Monash University, Department of Econometrics and Business Statistics.
  8. Kunpeng Li & Degui Li & Zhongwen Lian & Cheng Hsiao, 2013. "Semiparametric Profile Likelihood Estimation of Varying Coefficient Models with Nonstationary Regressors," Monash Econometrics and Business Statistics Working Papers 2/13, Monash University, Department of Econometrics and Business Statistics.
  9. Campbell, John Y & Mankiw, N Gregory, 1990. "Permanent Income, Current Income, and Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(3), pages 265-79, July.
  10. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
  11. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  12. Jiti Gao & Maxwell King, 2011. "A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors," Monash Econometrics and Business Statistics Working Papers 20/11, Monash University, Department of Econometrics and Business Statistics.
  13. Bin Chen & Yongmiao Hong, 2012. "Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression," Econometrica, Econometric Society, vol. 80(3), pages 1157-1183, 05.
  14. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
  15. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  16. Joon-Ho Hahm & Douglas G. Steigerwald, 1999. "Consumption Adjustment under Time-Varying Income Uncertainty," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 32-40, February.
  17. Gylfason, Thorvaldur, 1981. "Interest Rates, Inflation, and the Aggregate Consumption Function," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 233-45, May.
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