Title

Structural Nonparametric Cointegrating Regression

Publication Type

Journal Article

Publication Date

11-2009

Abstract

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated or near-integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Instead, simple nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving straightforward asymptotics that are useable in practical work. It is further shown that use of augmented regression, as is common in linear cointegration modeling to address endogeneity, does not lead to bias reduction in nonparametric regression, but there is an asymptotic gain in variance reduction. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series when there is a single integrated or near-integrated regressor. The methods may be applied to a range of empirical models where functional estimation of cointegrating relations is required.

Keywords

Brownian local time, Cointegration, Functional regression, Gaussian process, Integrated process, Kernel estimate, Near integration, Nonlinear functional, Nonparametric regression, Structural estimation, Unit root

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometrica

Volume

77

Issue

6

First Page

1901

Last Page

1948

ISSN

0012-9682

Identifier

10.3982/ECTA7732

Publisher

Econometric Society: Econometrica

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