Estimating Smooth Structural Change in Cointegration Models

Peter Phillips, Degui Li and Jiti Gao

No 1910, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

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)
Pages: 42 pages
Date: 2013-09
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (4)

Published in Journal of Econometrics (January 2017)

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Related works:
Journal Article: Estimating smooth structural change in cointegration models (2017)
Working Paper: Estimating Smooth Structural Change in Cointegration Models (2013)
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