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Exact testing in multivariate regression

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  • 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.

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  • 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
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    1. Stewart, Kenneth G., 1995. "The functional equivalence of the W, LR, and LM statistics," Economics Letters, Elsevier, vol. 49(2), pages 109-112, August.
    2. 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.
    3. 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.
    4. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
    5. 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.
    6. Michael McAleer, 1981. "Exact Tests of a Model Against Non-Nested Alternatives," Working Paper 431, Economics Department, Queen's University.
    7. Shanken, Jay, 1985. "Multivariate tests of the zero-beta CAPM," Journal of Financial Economics, Elsevier, vol. 14(3), pages 327-348, September.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. L. G. Godfrey & M. R. Wickens, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 487-496.
    20. 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.
    21. Fisher, Gordon R., 1983. "Tests for two separate regressions," Journal of Econometrics, Elsevier, vol. 21(1), pages 117-132, January.
    22. Francisco Cribari-Neto & Spyros Zarkos, 1995. "Improved Test Statistics for Multivariate Regression," Econometrics 9506003, University Library of Munich, Germany.
    23. Laitinen, Kenneth, 1978. "Why is demand homogeneity so often rejected?," Economics Letters, Elsevier, vol. 1(3), pages 187-191.
    24. 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.
    25. BARTEN, Anton P., 1969. "Maximum likelihood estimation of a complete system of demand equations," LIDAM Reprints CORE 34, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. Bera, Anil K., 1982. "A note on testing demand homogeneity," Journal of Econometrics, Elsevier, vol. 18(2), pages 291-294, February.
    27. Binder, Jj, 1985. "On The Use Of The Multivariate Regression-Model In Event Studies," Journal of Accounting Research, Wiley Blackwell, vol. 23(1), pages 370-383.
    28. 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.
    29. 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.
    30. 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.
    31. MacKinlay, A. Craig, 1987. "On multivariate tests of the CAPM," Journal of Financial Economics, Elsevier, vol. 18(2), pages 341-371, June.
    32. Evans, G B A & Savin, N E, 1982. "Conflict among the Criteria Revisited: The W, LR and LM Tests," Econometrica, Econometric Society, vol. 50(3), pages 737-748, May.
    33. 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.
    34. Barten, A. P. & Geyskens, E., 1975. "The negativity condition in consumer demand," European Economic Review, Elsevier, vol. 6(3), pages 227-260, July.
    35. 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.
    36. 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.
    37. BARTEN, Anton P. & GEYSKENS, Erik, 1975. "The negativity condition in consumer demand," LIDAM Reprints CORE 223, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    38. 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.
    39. Deaton, Angus S, 1978. "Specification and Testing in Applied Demand Analysis," Economic Journal, Royal Economic Society, vol. 88(351), pages 524-536, September.
    40. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
    41. W.A. Barnett, 2004. "The Minflex Laurent Translog Flexible Functional Form," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 99-110, Emerald Group Publishing Limited.
    42. Schipper, K & Thompson, R, 1985. "The Impact Of Merger-Related Regulations Using Exact Distributions Of Test Statistics," Journal of Accounting Research, Wiley Blackwell, vol. 23(1), pages 408-415.
    43. Cribari-Neto, Francisco & Zarkos, Spyros, 1995. "Improved test statistics for multivariate regression," Economics Letters, Elsevier, vol. 49(2), pages 113-120, August.
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    Cited by:

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    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. 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. 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.
    6. Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 173-191, Springer.
    7. 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.
    8. Dufour, Jean-Marie & Khalaf, Lynda, 2001. "Finite-Sample Simulation-Based Tests in Seemingly Unrelated Regressions," Cahiers de recherche 0111, Université Laval - Département d'économique.
    9. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Paper 1127, Economics Department, Queen's University.
    10. 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.
    11. 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.
    12. 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.

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