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The likelihood ratio test for the rank of a cointegration submatrix

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  • Paruolo Paolo

    ()
    (Department of Economics, University of Insubria, Italy)

Abstract

This paper proposes a likelihood ratio test for rank-dficiency of a sub- matrix 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 neu- trality and long run Granger noncausality. The proposed test has x2 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.

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File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2004_35.pdf
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Bibliographic Info

Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf04024.

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Length: 25 pages
Date of creation: Dec 2004
Date of revision:
Handle: RePEc:ins:quaeco:qf04024

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References

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  1. Paruolo, Paolo, 2001. " The Power of Lambda Max," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(3), pages 395-403, July.
  2. H. Peter Boswijk & Jurgen Doornik, 2003. "Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview," Economics Papers 2003-W10, Economics Group, Nuffield College, University of Oxford.
  3. Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September.
  4. Yamamoto, Taku & Kurozumi, Eiji, 2003. "Tests for Long-Run Granger Non-Causality in Cointegrated Systems," Discussion Papers 2003-12, Graduate School of Economics, Hitotsubashi University.
  5. C. Bruneau & E. Jondeau, 1997. "Long-run causality, with an application to international links between long-term interest rates," THEMA Working Papers 97-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Luukkonen, Ritva & Ripatti, Antti & Saikkonen, Pentti, 1999. "Testing for a Valid Normalization of Cointegrating Vectors in Vector Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 195-204, April.
  7. Gonzalo, J. & Granger, C., 1992. "Estimation of Common Long-Memory Components in Cointegrated Systems," Papers 4, Boston University - Department of Economics.
  8. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-93, November.
  9. Omtzigt Pieter & Paruolo Paolo, 2002. "Impact factors," Economics and Quantitative Methods qf0203, Department of Economics, University of Insubria.
  10. Kurozumi, Eiji, 2005. "The Rank Of A Submatrix Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(02), pages 299-325, April.
  11. Paruolo, Paolo, 1997. "Asymptotic Inference on the Moving Average Impact Matrix in Cointegrated 1(1) VAR Systems," Econometric Theory, Cambridge University Press, vol. 13(01), pages 79-118, February.
  12. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-60, April.
  13. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-99, October.
  14. Søren Johansen, 2005. "Interpretation of Cointegrating Coefficients in the Cointegrated Vector Autoregressive Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 93-104, 02.
  15. repec:cup:etheor:v:13:y:1997:i:1:p:79-118 is not listed on IDEAS
  16. Andrews, Donald W K, 1996. "Admissibility of the Likelihood Ratio Test When the Parameter Space Is Restricted under the Alternative," Econometrica, Econometric Society, vol. 64(3), pages 705-18, May.
  17. Pentti Saikkonen, 1999. "Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes," Econometric Reviews, 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, vol. 59(6), pages 1551-80, November.
  19. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
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Citations

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Cited by:
  1. Fanelli, Luca & Paruolo, Paolo, 2007. "Speed of Adjustment in Cointegrated Systems," MPRA Paper 9174, University Library of Munich, Germany.
  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. 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.
  4. 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.
  5. 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.

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