Is this how a structual VAR works ?

#1
Hello everyone,

I'm currently working on a research project for which I need to estimate parameters on a structural VAR model (a VAR including contemporaneous terms). I have read quite a lot lately but I'm still unsure how to estimate the coefficients under Cholesky identification (slides 15-17).

To put things in context, I'll start by explaining what I understood and how I think it works. Let's take the exemple of a trivariate VAR(2) including contemporaneous terms:
y1,t = a1,t + b11y2,t + b12y3,t + g11y1,t-1 + g12y2,t-1 + g13y3,t-1 + d11y1,t-2 + d12y2,t-2 + d13y3,t-2 + u1,t
y2,t = a2,t + b21y1,t + b22y3,t + g21y1,t-1 + g22y2,t-1 + g23y3,t-1 + d21y1,t-2 + d22y2,t-2 + d23y3,t-2 + u2,t
y3,t = a3,t + b31y1,t + b32y2,t + g31y1,t-1 + g32y2,t-1 + g33y3,t-1 + d31y1,t-2 + d32y2,t-2 + d33y3,t-2 + u3,t

a = constants, b = coefficients for variables at time t, g = coefficients for variables at time t-1, d = coefficients for variables at time t-2

Now, we can write this:
A y,t = a + g y,t-1 + d y,t-2 + u,t

Where: (please correct me if I'm wrong)
Capture.JPG
However, we need to set restrictions to A otherwise the VAR is not identified. So assume we set
1547554260887.png
My question is now the following:
Having set the restrictions, can I simply estimate my parameters by running the following 3 regressions individually ?

y1,t = a1,t + g11y1,t-1 + g12y2,t-1 + g13y3,t-1 + d11y1,t-2 + d12y2,t-2 + d13y3,t-2 + u1,t
y2,t = a2,t + b21y1,t + g21y1,t-1 + g22y2,t-1 + g23y3,t-1 + d21y1,t-2 + d22y2,t-2 + d23y3,t-2 + u2,t
y3,t = a3,t + b31y1,t + b32y2,t + g31y1,t-1 + g32y2,t-1 + g33y3,t-1 + d31y1,t-2 + d32y2,t-2 + d33y3,t-2 + u3,t


I sincerely hope you can help me!
 
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