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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 lead to a renewed interest in the identification and estimation of structural relations among economic time series, a field to which Henri Theil has made many pioneering contributions. 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.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Netherlands Society for Statistics and Operations Research in its journal Statistica Neerlandica.

Volume (Year): 58 (2004)
Issue (Month): 4 ()
Pages: 440-465

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Handle: RePEc:bla:stanee:v:58:y:2004:i:4:p:440-465

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References

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  1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  2. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(05), pages 888-911, October.
  3. 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.
  4. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  5. Elliott, Graham, 2000. "Estimating Restricted Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 91-99, January.
  6. M Pesaran & Yongcheol Shin, 2004. "Long-Run Structural Modelling," ESE Discussion Papers 44, Edinburgh School of Economics, University of Edinburgh.
  7. 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.
  8. David F. Hendry & Neil R. Ericsson, 1990. "Modeling the demand for narrow money in the United Kingdom and the United States," International Finance Discussion Papers 383, Board of Governors of the Federal Reserve System (U.S.).
  9. 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.
  10. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
  11. 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.
  12. Jurgen A. Doornik & David F. Hendry & Bent Nielsen, 1998. "Inference in Cointegrating Models: UK M1 Revisited," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 533-572, December.
  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. 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.
  15. Johansen, S. & Schaumburg, E., 1997. "Likelihood Analysis of Seasonal Cointegration," Economics Working Papers eco97/16, European University Institute.
  16. 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.
  17. Boswijk, H. Peter, 2000. "Mixed Normality And Ancillarity In I(2) Systems," Econometric Theory, Cambridge University Press, vol. 16(06), pages 878-904, December.
  18. 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.
  19. 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.
  20. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
  21. Peter Hansen, 2002. "Generalized Reduced Rank Regression," Working Papers 2002-02, Brown University, Department of Economics.
  22. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  23. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  24. 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 661-92, December.
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  26. repec:cup:etheor:v:11:y:1995:i:5:p:888-911 is not listed on IDEAS
  27. Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-60, April.
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Citations

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Cited by:
  1. Paruolo Paolo, 2004. "The likelihood ratio test for the rank of a cointegration submatrix," Economics and Quantitative Methods qf04024, Department of Economics, University of Insubria.
  2. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
  3. H. Peter Boswijk & Giuseppe Cavaliere & Anders Rahbek & A.M. Robert Taylor, 2013. "Inference on Co-integration Parameters in Heteroskedastic Vector Autoregressions," Discussion Papers 13-13, University of Copenhagen. Department of Economics.
  4. Abdul Qayyum, 2005. "Modelling the Demand for Money in Pakistan," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 44(3), pages 233-252.
  5. Mosconi, Rocco & Paruolo, Paolo, 2014. "Rank and order conditions for identification in simultaneous system of cointegrating equations with integrated variables of order two," MPRA Paper 53589, University Library of Munich, Germany.
  6. Zavkidjon Zavkiev, 2005. "Estimating A Model Of Inflation In Tajikistan," CAMA Working Papers 2005-27, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  7. Jennifer Castle & David Hendry & Nicholas W.P. Fawcett, 2008. "Forecasting with Equilibrium-correction Models during Structural Breaks," Economics Series Working Papers 408, University of Oxford, Department of Economics.
  8. David Hendry & Carlos Santos, 2010. "An Automatic Test of Super Exogeneity," Economics Series Working Papers 476, University of Oxford, Department of Economics.
  9. 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.
  10. H. Peter Boswijk & Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2013. "Inference on Co-integration Parameters in Heteroskedastic Vector Autoregressions," Tinbergen Institute Discussion Papers 13-187/III, Tinbergen Institute.

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