IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions

Listed author(s):
  • Jean-Marie Dufour
  • Lynda Khalaf

This paper proposes finite-sample procedures for testing the SURE specification in multi-equation regression models, i.e. whether the disturbances in different equations are contemporaneously uncorrelated or not. We apply the technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] to obtain exact tests based on standard LR and LM zero correlation tests. We also suggest a MC quasi-LR (QLR) test based on feasible generalized least squares (FGLS). We show that the latter statistics are pivotal under the null, which provides the justification for applying MC tests. Furthermore, we extend the exact independence test proposed by Harvey and Phillips (1982) to the multi-equation framework. Specifically, we introduce several induced tests based on a set of simultaneous Harvey/Phillips-type tests and suggest a simulation-based solution to the associated combination problem. The properties of the proposed tests are studied in a Monte Carlo experiment which shows that standard asymptotic tests exhibit important size distortions, while MC tests achieve complete size control and display good power. Moreover, MC-QLR tests performed best in terms of power, a result of interest from the point of view of simulation-based tests. The power of the MC induced tests improves appreciably in comparison to standard Bonferroni tests and in certain cases outperform the likelihood-based MC tests. The tests are applied to data used by Fischer (1993) to analyze the macroeconomic determinants of growth. Cet article propose des procédures exactes pour tester la spécification SURE (régressions empilées) dans le contexte des régressions linéaires multivariées, i.e. si les perturbations des différentes équations sont corrélées ou non. Nous appliquons la technique des tests de Monte Carlo (MC) [Dwass (1957), Barnard (1963)] pour obtenir des tests d'indépendance exacts fondés sur les critères du quotient de vraisemblance (LR) et du multiplicateur de Lagrange (LM). Nous suggérons aussi un critère du type quasi-quotient de vraisemblance (QLR) dérivé sur base des moindres carrés généralisés réalisables (FGLS). Nous démontrons que ces statistiques sont libres de paramètres de nuisance sous l'hypothèse nulle, ce qui justifie l'application des tests de Monte Carlo. Par ailleurs, nous généralisons le test exact proposé par Harvey et Phillips (1982) au contexte des équations multiples. En particulier, nous proposons plusieurs tests induits basés sur des tests de type Harvey-Phillips et nous suggérons une technique basée sur des simulations afin de résoudre le problème de combinaison de tests. Nous évaluons les propriétés des tests que nous proposons dans le cadre d'une étude de Monte Carlo. Nos résultats montrent que les tests asymptotiques usuels présentent de sérieuses distorsions de niveau, alors que les tests de MC contrôlent parfaitement le niveau et ont une bonne puissance. De plus, les tests QLR se comportent bien du point de vue de la puissance; ce résultat est intéressant vu que les tests (multivariés) que nous proposons sont basés sur des simulations. La puissance des tests de MC induits augmente sensiblement par rapport aux tests fondés sur l'inégalité de Bonferroni et, dans certains cas, dépasse la puissance des tests de MC fondés sur la vraisemblance. Nous appliquons les tests sur des données utilisées par Fischer (1993) pour analyser des modèles de croissance.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by CIRANO in its series CIRANO Working Papers with number 2000s-16.

in new window

Length: 35 pages
Date of creation: 01 May 2000
Handle: RePEc:cir:cirwor:2000s-16
Contact details of provider: Postal:
1130 rue Sherbrooke Ouest, suite 1400, Montréal, Quéc, H3A 2M8

Phone: (514) 985-4000
Fax: (514) 985-4039
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  2. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
  3. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-355, March.
  4. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
  5. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
  6. Breusch, Trevor S., 1980. "Useful invariance results for generalized regression models," Journal of Econometrics, Elsevier, vol. 13(3), pages 327-340, August.
  7. Dufour, Jean-Marie & Torres, Olivier, 2000. "Markovian processes, two-sided autoregressions and finite-sample inference for stationary and nonstationary autoregressive processes," Journal of Econometrics, Elsevier, vol. 99(2), pages 255-289, December.
  8. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-1277, July.
  9. Harvey, Andrew C & Phillips, Garry D A, 1982. "Testing for Contemporaneous Correlation of Disturbances in Systems of Regression Equations," Bulletin of Economic Research, Wiley Blackwell, vol. 34(2), pages 79-91, November.
  10. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
  11. Cameron, A Colin & Trivedi, Pravin K, 1993. "Tests of Independence in Parametric Models with Applications and Illustrations," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 29-43, January.
  12. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December.
  13. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
  14. Fischer, Stanley, 1993. "The role of macroeconomic factors in growth," Journal of Monetary Economics, Elsevier, vol. 32(3), pages 485-512, December.
  15. Srivastava, V. K. & Dwivedi, T. D., 1979. "Estimation of seemingly unrelated regression equations : A brief survey," Journal of Econometrics, Elsevier, vol. 10(1), pages 15-32, April.
  16. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879 Elsevier.
  17. Shiba, Tsunemasa & Tsurumi, Hiroki, 1988. "Bayesian and Non-Bayesian Tests of Independence in Seemingly Unrelated Regressions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(2), pages 377-395, May.
  18. Jean-Marie Dufour & Abdeljelil Farhat & Lucien Gardiol & Lynda Khalaf, 1998. "Simulation-based finite sample normality tests in linear regressions," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 154-173.
  19. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-494, March.
  20. Harvey, A C & Phillips, G D A, 1980. "Testing for Serial Correlation in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 48(3), pages 747-759, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2000s-16. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.