Alright! Thank you

*I'm not sure this is what I'm looking for. If I correctly understood, here
you are adding "extra" restrictions in*
*the standard Cholesky approach, right? Instead, what I would like to have
is an estimate of the following system:*

*Y1,t = a11 Y1,t-1 + u1t*
*Y2,t = a21 Y1,t-1 + a22 Y2,t-1 + a23 Y3,t-1 + u2t*

*Y3,t = a31 Y1,t-1 + a32 Y2,t-1 + a33 Y3,t-1 + u3t*

*Does the SVAR function allow one to estimate it?*

What you're describing is not a SVAR at all (unless you also have extra assumptions on the disturbances): it's simply a restricted VAR, which can be handled quite easily via SUR estimation: set up a system an you'll be ok.
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