Kernel-Based Inference In Time-Varying Coefficient Cointegrating Regression

Degui Li, Peter Phillips and Jiti Gao

No 2109, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 \textsl{local} and \textsl{global rotation} techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain 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 (i.e., exogenous covariate) cointegration case, 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 an empirical illustration to aggregate US data on consumption, income, and interest rates is provided.

Keywords: Cointegration; FM-kernel estimation; Generalized Wald test; Global rotation; Kernel degeneracy; Local rotation; Super-consistency; Time-varying coefficients (search for similar items in EconPapers)
JEL-codes: C22 C65 (search for similar items in EconPapers)
Pages: 58 pages
Date: 2017-09
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: Includes Supplimental Material
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Journal Article: Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression (2020)
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