INSTRUMENTAL VARIABLE INTERPRETATION OF COINTEGRATION WITH INFERENCE RESULTS FOR FRACTIONAL COINTEGRATION

Francesc Marmol, Alvaro Escribano () and Felipe M. Aparicio

Econometric Theory, 2002, vol. 18, issue 03, pages 646-672

Abstract: In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that, in the I(1) case, with a semiparametric correction simpler than the one required for the fully modified ordinary least squares (FM-OLS), our fully modified instrumental variables (FM-IV) estimator is median-unbiased, a mixture of normals, and asymptotically efficient. As a consequence, standard inference can be conducted with this new FM-IV estimator of the cointegrating parameter. We show by the use of Monte Carlo simulations that the small sample gains with the new IV estimator over OLS are remarkable.

Date: 2002
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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:18:y:2002:i:03:p:646-672_18

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