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Instrumental Variable Interpretation Of Cointegration With Inference Results For Fractional Cointegration


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  • Marmol, Francesc
  • Escribano, Alvaro
  • Aparicio, Felipe M.


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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 03 (June)
Pages: 646-672

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Handle: RePEc:cup:etheor:v:18:y:2002:i:03:p:646-672_18

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Cited by:
  1. M. Gerolimetto & Peter M Robinson, 2006. "Instrumental Variables Estimation of Stationaryand Nonstationary Cointegrating Regressions," STICERD - Econometrics Paper Series /2006/500, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Peter M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and nonstationary cointegrating regressions," LSE Research Online Documents on Economics 4539, London School of Economics and Political Science, LSE Library.
  3. Alvaro Escribano & M. Santos & Ana Sipols, 2008. "Testing for cointegration using induced-order statistics," Computational Statistics, Springer, vol. 23(1), pages 131-151, January.
  4. Mauro Costantini & Roy Cerqueti, 2007. "Non parametric Fractional Cointegration Analysis," ISAE Working Papers 78, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).


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