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Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions

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  • Jean-Marie Dufour
  • Lynda Khalaf

Abstract

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.

Suggested Citation

  • Jean-Marie Dufour & Lynda Khalaf, 2000. "Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions," CIRANO Working Papers 2000s-16, CIRANO.
  • Handle: RePEc:cir:cirwor:2000s-16
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    References listed on IDEAS

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    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.
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    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.
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    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. 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.
    3. 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.
    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. 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.
    6. Badi H. Baltagi & Chihwa Kao & Fa Wang, 2017. "Asymptotic power of the sphericity test under weak and strong factors in a fixed effects panel data model," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 853-882, October.
    7. DUFOUR, Jean-Marie & KHALAF, Lynda & BEAULIEU, Marie-Claude, 2003. "Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models," Cahiers de recherche 2003-08, Universite de Montreal, Departement de sciences economiques.
    8. Alexander Chudik & M. Hashem Pesaran, 2013. "Large Panel Data Models with Cross-Sectional Dependence: A Survey," CESifo Working Paper Series 4371, CESifo Group Munich.
    9. 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.
    10. 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.
    11. Khalaf, Lynda & Kichian, Maral, 2007. "Exact test for breaks in covariance in multivariate regressions," Economics Letters, Elsevier, vol. 95(2), pages 241-246, May.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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).
    17. repec:zbw:rwirep:0084 is not listed on IDEAS
    18. repec:eee:stapro:v:126:y:2017:i:c:p:119-126 is not listed on IDEAS
    19. 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.
    20. 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.
    21. 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.

    More about this item

    Keywords

    Seemingly unrelated regressions; SURE system; multivariate linear regression; contemporaneous correlation; exact test; finite-sample test; Monte Carlo test; bootstrap; induced test; LM test; likelihood ratio test; specification test; macroeconomics; growth; Régressions empilées; système SURE; test d'indépendance; régression linéaire multivariée; corrélation contemporaine; test exact; test à distance finie; test de Monte Carlo; bootstrap; test induit; test LM; quotient de vraisemblance; test de spécification; macroéconomie; croissance;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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