Below is a typical output from a 5 variable VECM model with 4 cointegrating vectors with $r-1$ restrictions on each equation. Therefore, the top part of the output is a diagonal matrix by default. For instance, $ect1$ is $x_1=-0.5574268x_4+21.07965$ and $ect2$ is $x_2=-0.4633047x_4+4.424252$ etc as seen in the output. Let's now say the theory suggests I should model $x_1$ as $$x_1=\beta_1x_2+\beta_2x_3-\beta_3x_4-\beta_4x_5$$ Let's also say I want to give economic meaning to the $\beta's$ as long-run 'elasticities' as the $x's$ are in log form. How will I be able to obtain this equation while accounting for other CVs i.e. $ect2$, $ect3$ and $ect4$.
ect1 ect2 ect3 ect4 X1 1.000000e+00 0.000000e+00 0.00000000 0.000000e+00 X2 0.000000e+00 1.000000e+00 0.00000000 0.000000e+00 X3 0.000000e+00 0.000000e+00 1.00000000 0.000000e+00 X4 0.000000e+00 0.000000e+00 0.00000000 1.000000e+00 X5 5.574268e-01 -4.633047e-01 0.25466051 2.523022e-02 constant -2.107965e+01 -4.424252e+00 -4.92108590 -2.599895e+00
Can you please advise what sort of restrictions matrix I should create? I guess, I will do overidentifying restrictions for this, but any suggestion is welcome.