I doubt that you can restrict the two equations to have the same variance. They will simply be based on the fit of the estimated a1 and a2 coefficients. The reason is that VAR coefficients do not depend on the system's var-cov matrix when maximizing the likelihood function (unless for some reason the restrictions create a dependence -- but I fairly sure they do not). This is generally the consequence of having the same right hand side variables in each equation. In the end, your 'restrict model1' method is probably the easiest way to accomplish what you really want. Alternatively, you could estimate one equation where you stack the observations so the y1 observations have y1(-1) in the first column and the y2 observations have y2(-1) in the same column. Then reverse the case for the second column such that y2(-1) is stacked above y1(-1). It is not clear whether you are using restricted or unrestricted constant terms, but stacked vectors of ones and zeros will accomplish whatever you desire. Then the 'one' equation will have a single estimated standard error, but it will not be 'restricted' in any way.