[Gretl-users] Re: Can I estimate a VAR-X in GRETL?
On Sun, 4 Oct 2020, Daniel Ventosa-Santaulària wrote:
Hello everyone,
I am being asked to estimate a VAR-X; I would like to do it in GRETL, but I
don´t really know how.
My understanding of a VAR-X is the following: Suppose 3 variables, X, Y,
and Z, to be included in a VAR(1).
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?
Yes. You can cast the VAR as a system and use the "system" command block.
In the following example, first the VAR estimation is replicated; then,
some restrictions are imposed so that you get what I think you want.
<hansl>
set verbose off
open AWM18.gdt --quiet
y = log(YER)
c = log(PCR)
i = log(GCR)
list X = y c i
var 1 X
# re-do VAR as a system
system name=foo
equation y const X(-1)
equation c const X(-1)
equation i const X(-1)
end system
estimate foo method=sur
# estimate VAR with constraints
system name=foo
equation y const y(-1)
equation c const X(-1)
equation i const X(-1)
end system
estimate foo method=sur
</hansl>
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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