IDEAS home Printed from
   My bibliography  Save this article

Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions


  • Dufour, Jean-Marie
  • Khalaf, Lynda


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, outperforms the likelihood-based MC tests. The tests are applied to data used by Fischer (1993) to analyze the macroeconomic determinants of growth.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions," Journal of Econometrics, Elsevier, vol. 106(1), pages 143-170, January.
  • Handle: RePEc:eee:econom:v:106:y:2002:i:1:p:143-170

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    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)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Dufour, Jean-Marie & Khalaf, Lynda & Bernard, Jean-Thomas & Genest, Ian, 2004. "Simulation-based finite-sample tests for heteroskedasticity and ARCH effects," Journal of Econometrics, Elsevier, vol. 122(2), pages 317-347, October.
    2. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2003. "Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-Fit in Multivariate Regressions with Application to Asset Pricing Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 891-906, December.
    3. Marie-Claude BEAULIEU & Jean-Marie DUFOUR & Lynda KHALAF, 2002. "Testing Mean-Variance Efficiency In Capm With Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach," Cahiers de recherche 17-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
    5. Badi Baltagi & Chihwa Kao & Fa wang, 2016. "Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model," Center for Policy Research Working Papers 189, Center for Policy Research, Maxwell School, Syracuse University.
    6. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2010. "Multivariate residual-based finite-sample tests for serial dependence and ARCH effects with applications to asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 263-285.
    7. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2003. "Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models," CIRANO Working Papers 2003s-34, CIRANO.
    8. Khalaf, Lynda & Kichian, Maral, 2005. "Exact tests of the stability of the Phillips curve: the Canadian case," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 445-460, April.
    9. Khalaf, Lynda & Kichian, Maral, 2007. "Exact test for breaks in covariance in multivariate regressions," Economics Letters, Elsevier, vol. 95(2), pages 241-246, May.
    10. BEAULIEU, Marie-Claude & DUFOUR, Jean-Marie & KHALAF, Lynda, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," Cahiers de recherche 2005-04, Universite de Montreal, Departement de sciences economiques.
    11. Khalaf, Lynda & Saphores, Jean-Daniel & Bilodeau, Jean-Francois, 2003. "Simulation-based exact jump tests in models with conditional heteroskedasticity," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 531-553, December.
    12. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.
    13. repec:zbw:rwirep:0084 is not listed on IDEAS
    14. Björn Alecke & Timo Mitze & Gerhard Untiedt, 2010. "Internal migration, regional labour market dynamics and implications for German East-West disparities: results from a Panel VAR," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 30(2), pages 159-189, September.
    15. Timo Mitze & Björn Alecke & Gerhard Untiedt, 2009. "Trade-FDI Linkages in a System of Gravity Equations for German Regional Data," Ruhr Economic Papers 0084, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    16. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2006. "Inflation dynamics and the New Keynesian Phillips Curve: An identification robust econometric analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1707-1727.
    17. Alexander Chudik & M. Hashem Pesaran, 2013. "Large Panel Data Models with Cross-Sectional Dependence: A Survey," CESifo Working Paper Series 4371, CESifo Group Munich.
    18. Mitze, Timo & Alecke, Björn & Untiedt, Gerhard, 2008. "Trade, FDI and Cross-Variable Linkages: A German (Macro-)Regional Perspective," MPRA Paper 12245, University Library of Munich, Germany.
    19. Wiertz Caroline & Ruyter Ko de & Streukens Sandra, 2003. "On The Role Of Normative Influences In Commercial Virtual Communities," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. repec:eee:stapro:v:126:y:2017:i:c:p:119-126 is not listed on IDEAS
    21. Tsay, Wen-Jen, 2004. "Testing for contemporaneous correlation of disturbances in seemingly unrelated regressions with serial dependence," Economics Letters, Elsevier, vol. 83(1), pages 69-76, April.

    More about this item

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:106:y:2002:i:1:p:143-170. 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: (Dana Niculescu). General contact details of provider: .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.