Publication Type

Journal Article

Publication Date

1-2017

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 reorient 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. (C) 2016 Elsevier B.V. All rights reserved.

Keywords

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

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

196

Issue

1

First Page

180

Last Page

195

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2016.09.013

Publisher

Elsevier

Copyright Owner and License

Authors

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://doi.org/10.1016/j.jeconom.2016.09.013

Included in

Econometrics Commons

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