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The Likelihood Ratio Test for the Rank of a Cointegration Submatrix

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  • Paolo Paruolo

Abstract

This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent-transitory decompositions and of subhypotheses related to neutrality and long-run Granger noncausality. The proposed test has a chi-squared limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable. Copyright 2006 Blackwell Publishing Ltd.

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  • Paolo Paruolo, 2006. "The Likelihood Ratio Test for the Rank of a Cointegration Submatrix," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 921-948, December.
  • Handle: RePEc:bla:obuest:v:68:y:2006:i:s1:p:921-948
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    Cited by:

    1. Bertocco Giancarlo, 2006. "Are banks special? A note on Tobin’s theory of financial intermediaries," Economics and Quantitative Methods qf0605, Department of Economics, University of Insubria.
    2. Johansen, Søren, 2010. "Some identification problems in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 158(2), pages 262-273, October.
    3. Fanelli, Luca & Paruolo, Paolo, 2010. "Speed of adjustment in cointegrated systems," Journal of Econometrics, Elsevier, vol. 158(1), pages 130-141, September.
    4. Emerson Fernandes Marçal & Priscila Fernandes Ribeiro, 2011. "Levado pelos Fundamentos? Estimando o Desalinhamento Cambial Norte-Americano a partir de Técnicas de Cointegração," Discussion Papers 1674, Instituto de Pesquisa Econômica Aplicada - IPEA.
    5. Emerson Fernandes Marçal & Fernando Barbi, 2010. "“Quo Vadis Real? Estimating the Brazilian Real Exchange Rate Misalignment in Vector Error Correction Model with Structural Change”," Working Papers 10-2010, Universidade de São Paulo, Faculdade de Economia, Administração e Contabilidade de Ribeirão Preto.
    6. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.

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