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Generalized Reduced Rank Tests using the Singular Value Decomposition

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  • Frank Kleibergen

    ()
    (Faculty of Economics and Econometrics, University of Amsterdam)

  • Richard Paap

    ()
    (Faculty of Economics, Erasmus University Rotterdam)

Abstract

We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson [Annals of Mathematical Statistics (1951), 22, 327–351] sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald [Journal of the American Statistical Association (1996), 91, 1301–1309] and Gill and Lewbel [Journal of the American Statistical Association (1992), 87, 766–776] a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith [Econometric Theory (2000), 16, 151–175] usage of numerical optimization for the objective function statistic of Cragg and Donald [Journal of Econometrics (1997), 76, 223–250] and ignoring the non-negativity restriction on the singular values in Ratsimalahelo [2002, Rank test based on matrix perturbation theory. Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté]. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic. This discussion paper has resulted in a publication in the Journal of Econometrics , 2006, 133(1), 97-126.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-003/4.

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Date of creation: 09 Jan 2003
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Handle: RePEc:dgr:uvatin:20030003

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Keywords: stochastic discount factor model; cointegration; GMM;

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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 111(2), pages 223-249, December.
  3. Kenneth D. West, 1995. "Another Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0183, National Bureau of Economic Research, Inc.
  4. Wright, Jonathan H., 2003. "Detecting Lack Of Identification In Gmm," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 322-330, April.
  5. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 932, Cowles Foundation for Research in Economics, Yale University.
  6. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  7. Jagannathan, Ravi & Skoulakis, Georgios & Wang, Zhenyu, 2002. "Generalized Method of Moments: Applications in Finance," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(4), pages 470-81, October.
  8. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 9(02), pages 222-240, April.
  9. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  10. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198774501, October.
  11. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 3(03), pages 348-358, June.
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  13. Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, Elsevier, vol. 63(1), pages 61-103, July.
  14. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, Elsevier, vol. 76(1-2), pages 223-250.
  15. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 251-76, March.
  16. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(02), pages 151-175, April.
  17. Pentti Saikkonen, 1999. "Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(3), pages 235-257.
  18. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  19. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 711-30, May.
  20. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, Elsevier, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  21. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
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