Estimating smooth structural change in cointegration models
Estimating smooth structural change in cointegration models
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.
Cointegration, Endogeneity, Kernel degeneracy, Nonparametric regression, Super-consistency, Time varying coefficients
180-195
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Li, Degui
e341f702-23cd-4c1a-91a8-3b7aa3dfda15
Gao, Jiti
fb907009-eef0-4e30-aca7-b484324f4955
January 2017
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Li, Degui
e341f702-23cd-4c1a-91a8-3b7aa3dfda15
Gao, Jiti
fb907009-eef0-4e30-aca7-b484324f4955
Phillips, Peter C.B., Li, Degui and Gao, Jiti
(2017)
Estimating smooth structural change in cointegration models.
Journal of Econometrics, 196 (1), .
(doi:10.1016/j.jeconom.2016.09.013).
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.
Text
PLGJE2014196-June-03-2016B
- Accepted Manuscript
More information
Accepted/In Press date: 6 September 2016
e-pub ahead of print date: 8 October 2016
Published date: January 2017
Keywords:
Cointegration, Endogeneity, Kernel degeneracy, Nonparametric regression, Super-consistency, Time varying coefficients
Organisations:
Economics
Identifiers
Local EPrints ID: 409660
URI: http://eprints.soton.ac.uk/id/eprint/409660
ISSN: 0304-4076
PURE UUID: 2e901a7e-95da-4246-870a-84fa4d1f239c
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Date deposited: 01 Jun 2017 04:04
Last modified: 16 Mar 2024 05:24
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Author:
Degui Li
Author:
Jiti Gao
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