Estimating smooth structural change in cointegration models

Peter Phillips, Degui Li and Jiti Gao

Journal of Econometrics, 2017, vol. 196, issue 1, 180-195

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 (search for similar items in EconPapers)
JEL-codes: C13 C14 C32 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (42)

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Related works:
Working Paper: Estimating Smooth Structural Change in Cointegration Models (2013)
Working Paper: Estimating Smooth Structural Change in Cointegration Models (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:196:y:2017:i:1:p:180-195

DOI: 10.1016/j.jeconom.2016.09.013

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