IDEAS home Printed from https://ideas.repec.org/a/bla/obuest/v68y2006is1p921-948.html

The Likelihood Ratio Test for the Rank of a Cointegration Submatrix

Author

Listed:
  • 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.

Suggested Citation

  • 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
    DOI: 10.1111/j.1468-0084.2006.00463.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1468-0084.2006.00463.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1468-0084.2006.00463.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    2. repec:cup:etheor:v:13:y:1997:i:1:p:79-118 is not listed on IDEAS
    3. Omtzigt, Pieter & Paruolo, Paolo, 2005. "Impact factors," Journal of Econometrics, Elsevier, vol. 128(1), pages 31-68, September.
    4. 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 388-399, October.
    5. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-160, April.
    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. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    8. Kasa, Kenneth, 1992. "Common stochastic trends in international stock markets," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 95-124, February.
    9. Paolo Paruolo, 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.
    10. 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.
    11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    12. Paruolo, Paolo, 2002. "Asymptotic Inference On The Moving Average Impact Matrix In Cointegrated I (2) Var Systems," Econometric Theory, Cambridge University Press, vol. 18(3), pages 673-690, June.
    13. 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.
    14. 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, November.
    15. Kurozumi, Eiji, 2005. "The Rank Of A Submatrix Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(2), pages 299-325, April.
    16. Catherine Bruneau & Eric Jondeau, 1999. "Long‐run Causality, with an Application to International Links Between Long‐term Interest Rates," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 545-568, November.
    17. 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, September.
    18. repec:bla:obuest:v:61:y:1999:i:4:p:545-68 is not listed on IDEAS
    19. 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, February.
    20. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    21. 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 705-718, May.
    22. 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.
    23. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Cubadda, Gianluca, 2007. "A unifying framework for analysing common cyclical features in cointegrated time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 896-906, October.
    4. Fanelli, Luca & Paruolo, Paolo, 2010. "Speed of adjustment in cointegrated systems," Journal of Econometrics, Elsevier, vol. 158(1), pages 130-141, September.
    5. 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.
    6. Kurita, Takamitsu, 2020. "Normalising cointegrating relationships subject to long-run exclusion," Economics Letters, Elsevier, vol. 192(C).
    7. 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.
    8. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.
    2. Norman J. Morin, 2006. "Likelihood ratio tests on cointegrating vectors, disequilibrium adjustment vectors, and their orthogonal complements," Finance and Economics Discussion Series 2006-21, Board of Governors of the Federal Reserve System (U.S.).
    3. 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, November.
    4. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    5. Massimo Franchi & Paolo Paruolo, 2019. "A general inversion theorem for cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1176-1201, November.
    6. Masih, Abul M. M. & Masih, Rumi, 1999. "Are Asian stock market fluctuations due mainly to intra-regional contagion effects? Evidence based on Asian emerging stock markets," Pacific-Basin Finance Journal, Elsevier, vol. 7(3-4), pages 251-282, August.
    7. 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.
    8. Kerry Patterson & Michael A. Thornton, 2013. "A review of econometric concepts and methods for empirical macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 2, pages 4-42, Edward Elgar Publishing.
    9. Masih, Rumi & Masih, Abul M. M., 2001. "Long and short term dynamic causal transmission amongst international stock markets," Journal of International Money and Finance, Elsevier, vol. 20(4), pages 563-587, August.
    10. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
    11. 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.
    12. Christophe Rault, 2007. "Une synthèse de l'exogénéité dans les modèles vectoriels à correction d'erreurs," Post-Print halshs-00202651, HAL.
    13. Qizilbash, M., 1995. "Egalitarian justice, capability and well-being prospects," Discussion Paper Series In Economics And Econometrics 9516, Economics Division, School of Social Sciences, University of Southampton.
    14. Yasser Abdih & Charalambos Tsangarides, 2010. "FEER for the CFA franc," Applied Economics, Taylor & Francis Journals, vol. 42(16), pages 2009-2029.
    15. Diamandis, Panayiotis F., 2009. "International stock market linkages: Evidence from Latin America," Global Finance Journal, Elsevier, vol. 20(1), pages 13-30.
    16. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    17. Gonzalo, Jesus & Ng, Serena, 2001. "A systematic framework for analyzing the dynamic effects of permanent and transitory shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1527-1546, October.
    18. Hall, Stephen & Mizon, Grayham E. & Welfe, Aleksander, 2000. "Modelling economies in transition: an introduction," Economic Modelling, Elsevier, vol. 17(3), pages 339-357, August.
    19. Jorg Breitung, 2005. "A Parametric approach to the Estimation of Cointegration Vectors in Panel Data," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 151-173.
    20. Kouretas, Georgios P. & Zarangas, Leonidas P., 2000. "Wage Setting, Taxes, and Demand for Labor in Greece: A Multivariate Analysis of Cointegrating Relationships," Journal of Policy Modeling, Elsevier, vol. 22(2), pages 171-195, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:obuest:v:68:y:2006:i:s1:p:921-948. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/sfeixuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.