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Estimating Smooth Structural Change in Cointegration Models

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Estimating Smooth Structural Change in Cointegration Models. / Phillips, Peter C. B.; Li, Degui; Gao, Jiti .

In: Journal of Econometrics, Vol. 196, No. 1, 01.2017, p. 180-195.

Research output: Contribution to journalArticlepeer-review

Harvard

Phillips, PCB, Li, D & Gao, J 2017, 'Estimating Smooth Structural Change in Cointegration Models', Journal of Econometrics, vol. 196, no. 1, pp. 180-195. https://doi.org/10.1016/j.jeconom.2016.09.013

APA

Phillips, P. C. B., Li, D., & Gao, J. (2017). Estimating Smooth Structural Change in Cointegration Models. Journal of Econometrics, 196(1), 180-195. https://doi.org/10.1016/j.jeconom.2016.09.013

Vancouver

Phillips PCB, Li D, Gao J. Estimating Smooth Structural Change in Cointegration Models. Journal of Econometrics. 2017 Jan;196(1):180-195. https://doi.org/10.1016/j.jeconom.2016.09.013

Author

Phillips, Peter C. B. ; Li, Degui ; Gao, Jiti . / Estimating Smooth Structural Change in Cointegration Models. In: Journal of Econometrics. 2017 ; Vol. 196, No. 1. pp. 180-195.

Bibtex - Download

@article{93e27e04aeac4e428ea9c326d17d6491,
title = "Estimating Smooth Structural Change in Cointegration Models",
abstract = "This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated 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 of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. 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, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression.",
keywords = "Cointegration, Endogeneity, Kernel degeneracy, Nonparametric regression, Super-consistency, Time varying coefficients",
author = "Phillips, {Peter C. B.} and Degui Li and Jiti Gao",
note = "{\textcopyright} 2016 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details.",
year = "2017",
month = jan,
doi = "10.1016/j.jeconom.2016.09.013",
language = "English",
volume = "196",
pages = "180--195",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "1",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Estimating Smooth Structural Change in Cointegration Models

AU - Phillips, Peter C. B.

AU - Li, Degui

AU - Gao, Jiti

N1 - © 2016 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2017/1

Y1 - 2017/1

N2 - This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated 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 of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. 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, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression.

AB - This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated 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 of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. 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, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression.

KW - Cointegration

KW - Endogeneity

KW - Kernel degeneracy

KW - Nonparametric regression

KW - Super-consistency

KW - Time varying coefficients

U2 - 10.1016/j.jeconom.2016.09.013

DO - 10.1016/j.jeconom.2016.09.013

M3 - Article

VL - 196

SP - 180

EP - 195

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -