Yt = a1 Yt-1 + a2 Xt-1 +a3 Zt-1

Xt = a4 Yt-1 + a5 Xt-1 +a6 Zt-1

Zt = a7 Yt-1 + a8 Xt-1 +a9 Zt-1

Suppose further that Y is a macro variable from, say, the US, whilst X and Y are macro variables from Mexico. I would like to assume that Y affects X and W, but is not affected by X, and Y. Thus, what I need to do is to restrict a2 = a3:

Yt = a1 Yt-1

Xt = a4 Yt-1 + a5 Xt-1 +a6 Zt-1

Zt = a7 Yt-1 + a8 Xt-1 +a9 Zt-1

Therefore, Y has its own AR equation. This is not exactly an exogenous variables as defined in the GRETL VAR command. At most, what I can do with GRETL command is:

Xt = a4 Yt-1 + a5 Xt-1 +a6 Zt-1

Zt = a7 Yt-1 + a8 Xt-1 +a9 Zt-1

But then I lose Y's equation. I could estimate separately the first equation and then the other two in a regular VAR, but I was wondering if I can directly estimate the VAR with the three variables and restrict two specific parameters, as in the first set of equations. My final goal is to estimate the IRF Yt -> Xt. Is this feasible in GRETL?

Thanks in advance.

Friendly,

D.