I am teaching myself econometrics and I am having trouble understanding how the cointegrating equation in VECM is derived.

Lets say we have two variables, Consumption and Income. As I understand it, to derive the long run equation I would run OLS on the equation: log(Consumption) = log(Income). However, when I run the two variable VECM in Eviews, I get different coefficients than when I estimate the aforementioned equation by itself, using the same data. I understand that the signs need to be reversed but the values are also different. Can someone please what I am doing wrong?

EDIT: On the left side is the equation estimated by itself. On the right side is the VECM enter image description here

  • $\begingroup$ Can you show the estimates in each case? $\endgroup$ – The Laconic Apr 9 at 1:12
  • $\begingroup$ Hi, I have added them to the original post. Thank you $\endgroup$ – wincelzy Apr 9 at 1:46
  • $\begingroup$ VECM does not imply logs. So if you apply vecm estimated in level to running regression in logs you will of course see different results $\endgroup$ – user1587692 Apr 9 at 8:27
  • $\begingroup$ Understood. However that's not what I've done - I've estimated both equations using logs(I downloaded the data as logs). I think that I am misspecifying something which is what I'm hoping someone can help with $\endgroup$ – wincelzy Apr 9 at 13:51

The VECM estimation probably uses the Johansen MLE procedure, which can give quite different results than OLS even though they are both super-consistent. See Gonzalo: Five alternative methods of estimating long-run equilibrium relationships.

  • $\begingroup$ That makes sense. Thank you $\endgroup$ – wincelzy Apr 10 at 16:26

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