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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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Bibliographic Info

Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 68 (2006)
Issue (Month): s1 (December)
Pages: 921-948

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Handle: RePEc:bla:obuest:v:68:y:2006:i:s1:p:921-948

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  1. Omtzigt Pieter & Paruolo Paolo, 2002. "Impact factors," Economics and Quantitative Methods qf0203, Department of Economics, University of Insubria.
  2. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality," Cowles Foundation Discussion Papers 977, Cowles Foundation for Research in Economics, Yale University.
  3. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
  4. Taku Yamamoto & Eiji Kurozumi, 2006. "Tests for Long-Run Granger Non-Causality in Cointegrated Systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 703-723, 09.
  5. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465.
  6. 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.
  7. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-60, April.
  8. 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.
  9. Kurozumi, Eiji, 2003. "The Rank of a Sub-Matrix of Cointegration," Discussion Papers 2002-15, Graduate School of Economics, Hitotsubashi University.
  10. Paruolo Paolo, . "The power of lambda max," Economics and Quantitative Methods qf0004, Department of Economics, University of Insubria.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. repec:cup:etheor:v:13:y:1997:i:1:p:79-118 is not listed on IDEAS
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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. Søren Johansen, 2007. "Some identification problems in the cointegrated vector autoregressive model," CREATES Research Papers 2007-32, School of Economics and Management, University of Aarhus.
  3. 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.
  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. 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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