The Failure of Orthogonality under Nonstationarity: Should We Care About It?
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, acknowle...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/329870 |
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| Summary: | 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. |
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| ISSN: | 1687-952X 1687-9538 |