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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| Format: | Article |
| Language: | English |
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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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| author | Jose A. Campillo-García Daniel Ventosa-Santaulària |
| author_facet | Jose A. Campillo-García Daniel Ventosa-Santaulària |
| author_sort | Jose A. Campillo-García |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-27e676a5049842e5822de22093ee6d18 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-27e676a5049842e5822de22093ee6d182025-02-03T05:52:40ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/329870329870The Failure of Orthogonality under Nonstationarity: Should We Care About It?Jose A. Campillo-García0Daniel Ventosa-Santaulària1Banco de México, Dirección General de Investigación Económica, 5 de Mayo No. 18, Col. Centro, 06059 Mexico City, MexicoDepartamento de Economía y Finanzas, Universidad de Guanajuato, Campus Guanajuato, Sede Marfil, Col. El Establo, DCEA, 36250 Guanajuato, Gto., MexicoWe 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.http://dx.doi.org/10.1155/2011/329870 |
| spellingShingle | Jose A. Campillo-García Daniel Ventosa-Santaulària The Failure of Orthogonality under Nonstationarity: Should We Care About It? Journal of Probability and Statistics |
| title | The Failure of Orthogonality under Nonstationarity: Should We Care About It? |
| title_full | The Failure of Orthogonality under Nonstationarity: Should We Care About It? |
| title_fullStr | The Failure of Orthogonality under Nonstationarity: Should We Care About It? |
| title_full_unstemmed | The Failure of Orthogonality under Nonstationarity: Should We Care About It? |
| title_short | The Failure of Orthogonality under Nonstationarity: Should We Care About It? |
| title_sort | failure of orthogonality under nonstationarity should we care about it |
| url | http://dx.doi.org/10.1155/2011/329870 |
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