Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression

Abstract

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix. To address these complications new local and global rotation techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under regularity conditions we derive asymptotic results that differ substantially from existing kernel regression asymptotics, leading to new limit theory under multiple convergence rates. For the practically important case of endogenous nonstationary regressors we propose a fully-modified kernel estimator whose limit distribution theory corresponds to the prototypical pure cointegration case (i.e., with exogenous covariates), thereby facilitating inference using a generalized Wald-type test statistic. These results substantially generalize econometric estimation and testing techniques in the cointegration literature to accommodate time variation and complications of co-moving regressors. Finally, Monte-Carlo simulation studies as well as an empirical illustration to aggregate US data on consumption, income, and interest rates are provided to illustrate the methodology and evaluate the numerical performance of the proposed methods in finite samples.