Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2003-01-09 Number: 03-003/4 Author-Name: Frank Kleibergen Author-Email: f.r.kleibergen@uva.nl Author-Workplace-Name: Faculty of Economics and Econometrics, University of Amsterdam Author-Name: Richard Paap Author-Email: paap@few.eur.nl Author-Workplace-Name: Faculty of Economics, Erasmus University Rotterdam Title: Generalized Reduced Rank Tests using the Singular Value Decomposition 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 Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté].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. Classification-JEL: C12; C13; C30 Keywords: stochastic discount factor model; cointegration; GMM File-Url: https://papers.tinbergen.nl/03003.pdf File-Format: application/pdf File-Size: 332221 bytes Handle: RePEc:tin:wpaper:20030003