VEC and single-equation error-correction model

[jomike]

Dear all,

I have a small question concerning the procedure, when reducing a VEC-model to a single-equation error-correction model. To fix ideas, here a concrete example:
In a VEC-model with four included variables (lags 1 to 7), with one cointegrating equation, I find that the loading coefficients of three of the four variables are insignificant, i.e. these variables weakly exogenous to the system. Then, Johansen (1992) found, a single-equation error-correction model can be fitted instead of the VEC-model.
Thus, I reduce the VEC-model via the options: "Proc" -> "make system" -> "by variable" ->throwing out all insignificant loading coefficients and the lags reported below in the EViews-output -> "estimate" to a single-equation error-correction model.
I was told, that this reduction in parameters should change the coefficents of the error-correction terms, i.e. of the long-run relation. But they don't change, regardless of which model I use to achieve this change. The I read somewhere, that this reduction doesn't change the long-run coefficents (which sounds plausible to me, after the confirmation that the other loading coefficents are weakly exogenous).

I would appreciate a lot if someone could answer my question!

Many Greetings,

jomike