Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors

Journal of Econometrics Volume 149 Issue 2 Page 118-135 published_at 2009-04
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Title ( eng )
Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors
Creator
Kurozumi Eiji
Source Title
Journal of Econometrics
Volume 149
Issue 2
Start Page 118
End Page 135
Abstract
In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen's [Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125] fully modified OLS estimator, Park's [Park, J.Y., 1992. Canonical cointegrating regressions. Econometrica 60, 119–143] canonical cointegrating regression estimator, and Saikkonen's [Saikkonen, P., 1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21] dynamic OLS estimator. We consider the case where the regression errors are moderately serially correlated and the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T, where T represents the sample size. We derive the limiting distributions of the efficient estimators under this system and find that they depend on the approaching rate of the AR coefficient. If the rate is slow enough, efficiency is established for the three estimators; however, if the approaching rate is relatively faster, the estimators will have the same limiting distribution as the OLS estimator. For the intermediate case, the second-order bias of the OLS estimator is partially eliminated by the efficient methods.

This result explains why, in finite samples, the effect of the efficient methods diminishes as the serial correlation in the regression errors becomes stronger. We also propose to modify the existing efficient estimators in order to eliminate the second-order bias, which possibly remains in the efficient estimators. Using Monte Carlo simulations, we demonstrate that our modification is effective when the regression errors are moderately serially correlated and the simultaneous correlation is relatively strong.
Keywords
cointegration
second-order bias
fully modified regressions
canonical cointegrating regressions
dynamic ordinary least squares regressions
NDC
Economics [ 330 ]
Language
eng
Resource Type journal article
Publisher
Elsevier B.V.
Date of Issued 2009-04
Rights
Copyright (c) 2008 Elsevier B.V.
Publish Type Author’s Original
Access Rights open access
Source Identifier
[ISSN] 0304-4076
[DOI] 10.1016/j.jeconom.2008.11.003
[NCID] AA00251673
[DOI] http://dx.doi.org/10.1016/j.jeconom.2008.11.003 isVersionOf