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I am attending a time series econometrics course and I am working on VECM models.

We have learnt that to estimate a VECM model we should use Engle-Granger two-step procedure but I have not understood why checking for the significance of the adjustment parameter to study cointegration among the two time series.

Engle-Granger representation theorem said that if there exist a well represented VECM model of two series, the two are cointegrated; so why checking after have estimated the model?

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  • $\begingroup$ I think VECM is more suitable than ECM here (so you could perhaps edit and replace ECM with VECM). ECM can refer to univariate models, while here you seem to have a multivariate model and cointegration. $\endgroup$ – Richard Hardy May 19 '15 at 17:50
  • $\begingroup$ Ok I'll try editing with VECM $\endgroup$ – PhDing May 20 '15 at 11:16
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I guess you are speaking about two different types of

  • The cointegrating $\beta$ parameter: indicate how in the "equilibrium" variables are related
  • The adjustment parameters $\alpha$ : how deviations from the equilibrium are adjusted

But you are right that, after an Engle-Granger test, one would not need to test again for cointegration: one can test merely what is the strength of the adjustment, and whether only one variable adjusts to the other (what cannot be detected with a Engle-Granger test).

Hope this helps

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  • $\begingroup$ So what is the point in testing for the adjustment paramenter significativity? Does it mean something? $\endgroup$ – PhDing May 19 '15 at 7:06
  • $\begingroup$ If the Engle-Granger test shows that the time series are cointegrated while the vector error correction model shows that there is no adjustment towards equilibrium (cannot reject the hypothesis that $\alpha=0$) that would be a contradiction worth exploring. This should not happen in theory if the model is well specified etc., but it could in principle happen in practice. That would indicate something is wrong, and you would have to figure out what exactly. Thus it could still make sense to check $\alpha$ as a means of double checking that "everything is alright". $\endgroup$ – Richard Hardy May 19 '15 at 17:47
  • $\begingroup$ Besides double-checking, checking for the adjustment parameter can tell you whether one variable adjusts to the other, and at which speed. This has a clear economic interepretation, that oyu do not get from the simple EG test. Typically, you can have that one variable adjusts to the second, while the second does not adjust to the first. $\endgroup$ – Matifou May 20 '15 at 1:00
  • $\begingroup$ Thank you to both of you! You have been very clear and kind $\endgroup$ – PhDing May 20 '15 at 11:15

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