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Estimating Smooth Structural Change in Cointegration Models

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  • Peter C. B. Phillips

    ()

  • Degui Li

    ()

  • Jiti Gao

    ()

Abstract

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.

Suggested Citation

  • Peter C. B. Phillips & Degui Li & Jiti Gao, 2013. "Estimating Smooth Structural Change in Cointegration Models," Monash Econometrics and Business Statistics Working Papers 22/13, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2013-22
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp22-13.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Harris, A.R. & Rogers, Michelle Marinich & Miller, Carol J. & McElmurry, Shawn P. & Wang, Caisheng, 2015. "Residential emissions reductions through variable timing of electricity consumption," Applied Energy, Elsevier, vol. 158(C), pages 484-489.
    2. Isabel Casas & Xiuping Mao & Helena Veiga, 0503. "Reexamining financial and economic predictability with new estimators of realized variance and variance risk premium," CREATES Research Papers 2018-10, Department of Economics and Business Economics, Aarhus University.
    3. Li, Degui & Phillips, Peter C. B. & Gao, Jiti, 2016. "Uniform Consistency Of Nonstationary Kernel-Weighted Sample Covariances For Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 32(03), pages 655-685, June.
    4. Isabel Casas & Eva Ferreira & Susan Orbe, 0310. "Time-varying coefficient estimation in SURE models. Application to portfolio management," CREATES Research Papers 2017-33, Department of Economics and Business Economics, Aarhus University.
    5. Kunpeng Li & Degui Li & Zhongwen Liang & Cheng Hsiao, 2017. "Estimation of semi-varying coefficient models with nonstationary regressors," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 354-369, March.

    More about this item

    Keywords

    Cointegration; Endogeneity; Kernel degeneracy; Nonparametric regression; Super-consistency; Time varying coefficients;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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