Hi

I would not say that the ECT terms have to be between 0 and -1. it was not clear to me whether you are referring to the cointegrating parameters (the betas) or the speed adjustment (alphas)? For the betas, the values from these vectors can take any value, but need to be normalised for identification purpose.

For the alphas, the expected sign depends precisely on the corresponding value in the cointegrating vector. The reasoning in the bi-variate case can be simply extended to the k-variate. Taking a vector: y= b1 x - b2z, (with b1 and b2 positive):

With a positive shocks, so that y > b1 x - b2z, if variables are "error correcting" you expect:
-y to have negative alpha coefficient (should decrease the y to "reduce" the inequality by reducing the left)
-x to have a positive coefficient (should increase the x in order to  "reduce" the inequality by increasing the right)
-z to have a negative coefficient (should increase the z in order to  "reduce" the inequality by increasing the right)

So I do not think one can say that the values should be bezween 0 and -1.

Best

Matthieu


2012/10/15 Claudio Shikida (敷田治誠　クラウジオ) <cdshikida@gmail.com>
Dear Asongu,

In Vinod, H.D. (2008)'s "Hands-on Intermediate Econometrics Using R", in sections 3.4.2 to 3.4.5 I've found some hints for your question. The author uses a bivariate ECM. If you consider no a priori knowledge for the relationship between, say, x and y, so we have a system of two equations, both with ECM's. 

In this case, says the author: "If the equilibrium error experienced by economic agent at time t-1 is positive, in inequality (yt-1 > bxt-1) must hold. During the current period t decreasing the left-hand side (yt < yt-1 or deltayt < 0) and increasing the right-hand side (bxt > bxt-1, deltaxt > 0, since b >0) of the inequality reduces the equilibrium error. If the agent learns from past errors in predictable ways, we have seen that this implications on the signs of coefficients in [number of equation] implying nonrejection of two hypothesis, gama1 > 0 and gama2 <0".

Gama1 and 2 are, respectively, the coefficients of the long-run relationship in t-1 (as usual in VECM). The gama 1 is for delta xt's equation and the gama 2 for the delta yt's one). 

So, in this case, you should expect a positive coefficient for the coefficient. Is that what you asked? Hope to have helped you.

Best Wishes,

Claudio D. Shikida
http://www.shikida.net  and http://works.bepress.com/claudio_shikida/

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On Sat, Oct 13, 2012 at 8:31 AM, Anutechia Asongu <simplice_peace@yahoo.com> wrote:

Hi All,
           I understand within a bivariate VECM framework, the Error Correction Terms(ECTs) have to be negative and situated within the interval: 0 and -1. Does this principle on sign and interval apply to a multivariate VECM framework?
           Cheers
  

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