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Lecture 6 Stephen G Hall MULTIVARIATE COINTEGRATION

IF WE WRITE OUT A MODEL IT WILL GENERALLY CONTAIN MANY COINTEGRATING VECTORS (MAYBE ONE FOR EACH EQUATION).

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Lecture 6 Stephen G Hall MULTIVARIATE COINTEGRATION

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    1. Lecture 6 Stephen G Hall MULTIVARIATE COINTEGRATION

    12. SINGLE EQUATION TECHNIQUES CAN NEVER SATISFACTORILY ANSWER THESE POINTS. JOHANSEN PROVIDES THE ANSWER

    13. ESTIMATING MANY COINTEGRATING VECTORS Johansen (1988) proposed a general framework for considering the possibility of multiple cointegrating vectors and this framework also allows questions of causality and general hypothesis tests to be carried out in a more satisfactory way. Begin by defining a VAR of a set of variables X as

    24. THEN A VALID COINTEGRATING VECTOR WILL PRODUCE A SIGNIFICANTLY NON-ZERO EIGENVALUE AND THE ESTIMATE OF THE COINTEGRATING VECTOR WILL BE GIVEN BY THE CORRESPONDING EIGENVECTOR.

    25. THE COINTEGRATING SPACE THE MATRIX OF EIGENVECTORS IS SAID TO SPAN THE COINTEGRATING SPACE THIS IS BECAUSE THEY ARE NOT THE SAME THING AS THE TARGET RELATIONSHIPS. THE COINTEGRATING VECTORS MAY BE ANY LINEAR COMBINATION OF THE UNDERLYING TARGET RELATIONS. WE HAVE IN EFFECT ESTIMATED AN UNIDENTIFIED SYSTEM AND ALL WE REALLY KNOW ABOUT IS THE BOUNDARIES OF THE SPACE THAT THE TARGET RELATIONSHIPS MUST LIE WITHIN.

    43. Conclusion

    44. Example The Long Run Determination of the UK Monetary Aggregates Hall, Henry and Wilcox Bank of England Study

    54. Similar results A similar set of results showing that log versions of the financial innovation variables also failed to cointegrate

    55. So where now? Practitioners explain the result by financial innovation. What drives this? Interest rates! But summed over time because of learning

    58. Seems to work! Cumulated interest rates seem to pick up the trend movement in velocity

    59. Dynamic Model So we can go on and estimate a standard ECM based on this long run relationship

    62. conclusion A parsimonious and very stable dynamic model Cointegration has made an important missing effect very obvious Fixing this improves things enormously

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