IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v16y1997i3p321-352.html
   My bibliography  Save this article

Exact testing in multivariate regression

Author

Listed:
  • Kenneth Stewart

Abstract

An F statistic due to Rao (1951,1973) tests uniform mixed linear restrictions in the multivariateregression model. In combination with a generalization of the Bera-Evans-Savin exact functional relationship between the W, LR, and LM statistics, Rao's F serves to unify a number of exact test procedures commonly applied in disparate empirical literatures. Examples in demand analysis and asset pricing are provided. The availability of exact tests of restrictions in certain nonlinear models when the model is linear under the null, originally explored by Milliken-Graybill (1970), is extended to multivariate regression. Generalized RESET, J-, and Hausman-Wu tests are resented. As an extension of Dufour (1989), bounds tests exist for nonlinear and inequality restrictions. Applications include conservative bound tests for symmetry or negativity of the substitution matrix in demand systems.

Suggested Citation

  • Kenneth Stewart, 1997. "Exact testing in multivariate regression," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 321-352.
  • Handle: RePEc:taf:emetrv:v:16:y:1997:i:3:p:321-352
    DOI: 10.1080/07474939708800390
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/07474939708800390
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    as
    1. Laitinen, Kenneth, 1978. "Why is demand homogeneity so often rejected?," Economics Letters, Elsevier, vol. 1(3), pages 187-191.
    2. Stewart, Kenneth G., 1995. "The functional equivalence of the W, LR, and LM statistics," Economics Letters, Elsevier, vol. 49(2), pages 109-112, August.
    3. Stambaugh, Robert F., 1982. "On the exclusion of assets from tests of the two-parameter model : A sensitivity analysis," Journal of Financial Economics, Elsevier, vol. 10(3), pages 237-268, November.
    4. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
    5. Anderson, G J & Blundell, R W, 1982. "Estimation and Hypothesis Testing in Dynamic Singular Equation Systems," Econometrica, Econometric Society, vol. 50(6), pages 1559-1571, November.
    6. BARTEN, Anton P., 1969. "Maximum likelihood estimation of a complete system of demand equations," CORE Discussion Papers RP 34, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
    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. Bera, Anil K., 1982. "A note on testing demand homogeneity," Journal of Econometrics, Elsevier, vol. 18(2), pages 291-294, February.
    10. repec:bla:joares:v:23:y:1985:i:1:p:370-383 is not listed on IDEAS
    11. Shanken, Jay, 1985. "Multivariate tests of the zero-beta CAPM," Journal of Financial Economics, Elsevier, vol. 14(3), pages 327-348, September.
    12. Jayatissa, W A, 1977. "Tests of Equality between Sets of Coefficients in Two Linear Regressions when Disturbance Variances Are Unequal," Econometrica, Econometric Society, vol. 45(5), pages 1291-1292, July.
    13. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-365, March.
    14. Bera, A. K. & Byron, R. P. & Jarque, C. M., 1981. "Further evidence on asymptotic tests for homogeneity and symmetry in large demand systems," Economics Letters, Elsevier, vol. 8(2), pages 101-105.
    15. Caves, Douglas W & Christensen, Laurits R & Tretheway, Michael W, 1980. "Flexible Cost Functions for Multiproduct Firms," The Review of Economics and Statistics, MIT Press, vol. 62(3), pages 477-481, August.
    16. Meisner, James F., 1979. "The sad fate of the asymptotic Slutsky symmetry test for large systems," Economics Letters, Elsevier, vol. 2(3), pages 231-233.
    17. Handa, Puneet & Kothari, S P & Wasley, Charles, 1993. " Sensitivity of Multivariate Tests of the Capital Asset-Pricing Model to the Return Measurement Interval," Journal of Finance, American Finance Association, vol. 48(4), pages 1543-1551, September.
    18. MacKinlay, A. Craig, 1987. "On multivariate tests of the CAPM," Journal of Financial Economics, Elsevier, vol. 18(2), pages 341-371, June.
    19. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
    20. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 16(1), pages 103-119, May.
    21. Kodde, David A & Palm, Franz C, 1987. "A Parametric Test of the Negativity of the Substitution Matrix," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 2(3), pages 227-235, July.
    22. 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.
    23. Amsler, Christine E. & Schmidt, Peter, 1985. "A Monte Carlo investigation of the accuracy of multivariate CAPM tests," Journal of Financial Economics, Elsevier, vol. 14(3), pages 359-375, September.
    24. Barten, A. P. & Geyskens, E., 1975. "The negativity condition in consumer demand," European Economic Review, Elsevier, vol. 6(3), pages 227-260, July.
    25. Berndt, Ernst R & Wood, David O, 1975. "Technology, Prices, and the Derived Demand for Energy," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 259-268, August.
    26. Hashimoto, Noriko & Ohtani, Kazuhiro, 1990. "An exact test for linear restrictions in seemingly unrelated regressions with the same regressors," Economics Letters, Elsevier, vol. 32(3), pages 243-246, March.
    27. MacKinlay, A. Craig, 1995. "Multifactor models do not explain deviations from the CAPM," Journal of Financial Economics, Elsevier, vol. 38(1), pages 3-28, May.
    28. BARTEN, Anton P. & GEYSKENS, Erik, 1975. "The negativity condition in consumer demand," CORE Discussion Papers RP 223, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    29. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    30. Bera, Anvil K & McAleer, Michael, 1983. "Some Exact Tests for Model Specification," The Review of Economics and Statistics, MIT Press, vol. 65(2), pages 351-354, May.
    31. Deaton, Angus S, 1978. "Specification and Testing in Applied Demand Analysis," Economic Journal, Royal Economic Society, vol. 88(351), pages 524-536, September.
    32. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
    33. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    34. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-1248, September.
    35. Jobson, John D, 1982. " A Multivariate Linear Regression Test for the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 37(4), pages 1037-1042, September.
    36. L. G. Godfrey & M. R. Wickens, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," Review of Economic Studies, Oxford University Press, vol. 48(3), pages 487-496.
    37. repec:bla:joares:v:23:y:1985:i:1:p:408-415 is not listed on IDEAS
    38. Fisher, Gordon R., 1983. "Tests for two separate regressions," Journal of Econometrics, Elsevier, vol. 21(1), pages 117-132, January.
    39. Barnett, William A., 1985. "The minflex-laurent translog flexible functional form," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 33-44.
    40. Cribari-Neto, Francisco & Zarkos, Spyros, 1995. "Improved test statistics for multivariate regression," Economics Letters, Elsevier, vol. 49(2), pages 113-120, August.
    41. Francisco Cribari-Neto & Spyros Zarkos, 1995. "Improved Test Statistics for Multivariate Regression," Econometrics 9506003, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. Sermin Gungor & Richard Luger, 2016. "Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 161-175, April.
    6. 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.
    7. 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.
    8. 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.
    9. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    10. Surajit Ray & N. E. Savin, 2008. "The performance of heteroskedasticity and autocorrelation robust tests: a Monte Carlo study with an application to the three-factor Fama-French asset-pricing model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 91-109.
    11. Dufour, Jean-Marie & Khalaf, Lynda, 2001. "Finite-Sample Simulation-Based Tests in Seemingly Unrelated Regressions," Cahiers de recherche 0111, Université Laval - Département d'économique.
    12. MacKinnon, James, 2007. "Bootstrap Hypothesis Testing," Queen's Economics Department Working Papers 273603, Queen's University - Department of Economics.

    More about this item

    Keywords

    exact test; multivariate regression;

    Statistics

    Access and download statistics

    Corrections

    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:taf:emetrv:v:16:y:1997:i:3:p:321-352. 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: (). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.