Generalized Reduced Rank Tests using the Singular Value Decomposition

Frank Kleibergen and Richard Paap

No 03-003/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

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 Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté].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 resulted in a publication in the Journal of Econometrics , 2006, 133(1), 97-126.

Keywords: stochastic discount factor model; cointegration; GMM (search for similar items in EconPapers)
JEL-codes: C12 C13 C30 (search for similar items in EconPapers)
Date: 2003-01-09
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Generalized reduced rank tests using the singular value decomposition (2006)
Working Paper: Generalized Reduced Rank Tests using the Singular Value Decomposition (2004)
Working Paper: Generalized Reduced Rank Tests using the Singular Value Decomposition (2003)
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