Functional Coefficient Nonstationary Regression with Non– and Semi–Parametric Cointegration∗

This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coefficient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and nonstationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960 2009. JEL Classifications: C13, C14, C23. ∗The authors thank participants at many conferences and seminars for comments on earlier versions of this work. Gao acknowledges Australian Research Council Discovery Grants Program support under Grant number: DP1096374. Phillips acknowledges support from the NSF under Grant Nos. SES-0956687 and SES-1258258. †The University of Adelaide & Monash University. ‡Yale University, University of Auckland, University of Southampton, & Singapore Management University.