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Identifying, estimating and testing restricted cointegrated systems: An overview

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  • H. Peter Boswijk
  • Jurgen A. Doornik

Abstract

The notion of cointegration has led to a renewed interest in the identification and estimation of structural relations among economic time series. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over‐identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so‐called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:58:y:2004:i:4:p:440-465
    DOI: 10.1111/j.1467-9574.2004.00270.x
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    1. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    2. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    3. Elliott, Graham, 1999. "Estimating Restricted Cointegrating Vectors," University of California at San Diego, Economics Working Paper Series qt5sr55716, Department of Economics, UC San Diego.
    4. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    5. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
    6. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    7. Johansen, Soren, 2006. "Statistical analysis of hypotheses on the cointegrating relations in the I(2) model," Journal of Econometrics, Elsevier, vol. 132(1), pages 81-115, May.
    8. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    9. Hendry, David F. & Ericsson, Neil R., 1991. "Modeling the demand for narrow money in the United Kingdom and the United States," European Economic Review, Elsevier, vol. 35(4), pages 833-881, May.
    10. Omtzigt Pieter & Fachin Stefano, 2002. "Bootstrapping and Bartlett corrections in the cointegrated VAR model," Economics and Quantitative Methods qf0212, Department of Economics, University of Insubria.
    11. repec:bla:jecsur:v:12:y:1998:i:5:p:533-72 is not listed on IDEAS
    12. Johansen, Soren & Juselius, Katarina, 1994. "Identification of the long-run and the short-run structure an application to the ISLM model," Journal of Econometrics, Elsevier, vol. 63(1), pages 7-36, July.
    13. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    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, February.
    15. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-160, April.
    16. Peter Hansen, 2002. "Generalized Reduced Rank Regression," Working Papers 2002-02, Brown University, Department of Economics.
    17. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    18. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    19. Boswijk, H. Peter, 2000. "Mixed Normality And Ancillarity In I(2) Systems," Econometric Theory, Cambridge University Press, vol. 16(6), pages 878-904, December.
    20. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
    21. repec:cup:etheor:v:11:y:1995:i:5:p:888-911 is not listed on IDEAS
    22. 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.
    23. Davidson, James E H, et al, 1978. "Econometric Modelling of the Aggregate Time-Series Relationship between Consumers' Expenditure and Income in the United Kingdom," Economic Journal, Royal Economic Society, vol. 88(352), pages 661-692, December.
    24. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    25. 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.
    26. 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.
    27. Elliott, Graham, 2000. "Estimating Restricted Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 91-99, January.
    28. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(5), pages 888-911, October.
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