Identification of cointegration vectors

[Tiona]

I am empirically testing the Monetary Approach to Exchange Rate Determination model w.r.t UK's nominal exchange rate, and using US as the foreign country. In accordance with Johansen's cointegration rank test, 2 possible cointegrating vectors were discovered. I attempted to identify the two equations based on economic theory. The first Cointegration Vector (CV) is of course normalised w.r.t exchange rate, and the second CV (which I am not interested in but I am aware it still has to make economic sense since it impacts on the first CV's coefficients) is normalised w.r.t to money demand (while restricting exchange rate to equal zero). Now, with the identification, literature suggests imposing restrictions on the proportionality between relative monies and exchange rate, as well as the symmetry (equal and opposite signs) of the domestic and foreign outputs and interest rate. This is where I am having problems with. I do not wish to impose these restrictions since they will force the coefficients to be the same for the domestic and foreign variables. However, I want to have unique coefficients for the individual variables.
So my question is, what other restrictions can I make in order to satisfy both the order and rank conditions for identification? I have tried to impose weak exogeneity on both CVs but Eviews will not give me t-statistics, reporting that one of the CV is not properly identified. It could be that my numerical restrictions are wrong (see below), I don’t know. Interestingly however, Eviews produces t-statistics (meaning it believes the CVs are identified) when weak exogeneity is imposed on the second CV only. Below is my estimating equation and the restrictions I imposed.

My model is as follows:

Z=(e,m,m*,y,y*,i,i*) denoting nominal exchange rate, UK (domesic) money supply, US (foreign) money supply, UK output, US output, UK interest rate, US interest rate – respectively.

Normalisation and Restrictions (weak exogeneity) used:
B(1,1)=1
B(2,1)=0
B(2,2)=1
A(3,1)=0,A(5,1)=0,A(7,1)=0,A(3,2)=0,A(5,2)=0,A(7,2)=0
Imposing the above restrictions does not produce t-statistics. However, the following does, but I do not understand the intuition, since there are no restrictions on CV 1.
B(1,1)=1
B(2,1)=0
B(2,2)=1
A(3,2)=0,A(5,2)=0,A(7,2)=0

Thanks for your assistance.

[dakila]

Could you post the results?

[Tiona]

The results are in the attached file. The first set of VECM output - which reported un-identified CEs - is from imposing weak exogeneity on both CEs (and normalisation). The second set - with identified CEs - is from imposing weak exogeneity on the second CE only, while there is no restriction on the first CE.

As an additional question, would it make economics sense to impose a zero restriction on the first CE's constant?

Thanks

[dakila]

The first restrictions is totally unacceptable. That is why Eviews did not estimate t statistics.
1. On the forum you posted B(2,2)=1, but you actually imposed zero restriction.
2. The convergence is not achieved (max iteration is reached)
3. LR test for binding restriction is rejected.

[Tiona]

Thanks for taking time to look through my problem and sorry that was not the correct one. I have now attached the VECM output I intended to post (with B(2,2)=1) which is still not binding.

[dakila]

My suggestions:
1. If the second cointegration vector is money demand then you try to restrict foreign variables to zero.
2. Carefully impose the weak exogeneity restrictions.

[Tiona]

I tried these restrictions:

B(1,1)=1,B(2,1)=0,B(2,2)=1,A(3,1)=0,A(5,1)=0,A(7,1)=0,A(3,2)=0,A(5,2)=0,A(7,2)=0,B(2,3)=0,B(2,5)=0,B(2,7)=0

and also this combination:

B(1,1)=1,B(2,1)=0,B(2,2)=1,A(3,1)=0,A(5,1)=0,A(7,1)=0,B(2,3)=0,B(2,5)=0,B(2,7)=0

Both didn't work.

[dakila]

First, do not impose the weak exogeneity restrictions, just impose the restrictions on the cointegration vectors based on the theory.
Second, if these restrictions is accepted then impose the weak exogeneity restrictions sequentially.

[Tiona]

No luck either