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Journal of Probability and Statistics
Volume 2011, Article ID 329870, 15 pages
Research Article

The Failure of Orthogonality under Nonstationarity: Should We Care About It?

1Banco de México, Dirección General de Investigación Económica, 5 de Mayo No. 18, Col. Centro, 06059 Mexico City, Mexico
2Departamento de Economía y Finanzas, Universidad de Guanajuato, Campus Guanajuato, Sede Marfil, Col. El Establo, DCEA, 36250 Guanajuato, Gto., Mexico

Received 23 August 2010; Revised 26 November 2010; Accepted 17 January 2011

Academic Editor: Kelvin K. W. Yau

Copyright © 2011 Jose A. Campillo-García and Daniel Ventosa-Santaulària. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider two well-known facts in econometrics: (i) the failure of the orthogonality assumption (i.e., no independence between the regressors and the error term), which implies biased and inconsistent Least Squares (LS) estimates and (ii) the consequences of using nonstationary variables, acknowledged since the seventies; LS might yield spurious estimates when the variables do have a trend component, whether stochastic or deterministic. In this work, an optimistic corollary is provided: it is proven that the LS regression, employed in nonstationary and cointegrated variables where the orthogonality assumption is not satisfied, provides estimates that converge to their true values. Monte Carlo evidence suggests that this property is maintained in samples of a practical size.