TY - JOUR
T1 - Estimating Smooth Structural Change in Cointegration Models
AU - Phillips, Peter C. B.
AU - Li, Degui
AU - Gao, Jiti
N1 - Â© 2016 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the publisherâ€™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 -