Near-VAR with sign restrictions

[TomDoan]

If you were to use a Cholesky factor with the three global variables first in the order, then the first three shocks would indeed account for 100% of the total variance. (It wouldn't show as exactly 100% since medians aren't linear, but it would probably be close). You're not doing that. What remains after the three sign-restricted shocks obviously includes a rather substantial amount of contribution to the three global variables.

The HD graphs look fine to me (though what you posted doesn't run as it doesn't define depvar).

[Yashodha]

Dear Tom,

I am confused now - I have set-up my system of equations like this in my TOT_setup file.

system(model=foreign)
variables EXPR IMPR FORGDP
lags 1 to 2
determ constant gfc{0}
end(system)
system(model=domestic)
variables GDP CPI INT REER TB
lags 1 to 2
determ constant EXPR{1 to 2} IMPR{1 to 2} FORGDP{1 to 2} gfc{0}
end(system)
compute varmodel=foreign+domestic

Then, I would get the foreign variables before the domestic variables in the Cholesky order, wouldn't I? And I defined the depar in the TOT_setup file.

[TomDoan]

You're not doing Cholesky factors to identify the shocks. You're doing sign restrictions. They are about as polar opposite as one can get.

[Yashodha]

Dear Tom,

So if I want to have no effect from the domestic shocks on the foreign variables in the contemporaneous period, do I have to specify all domestic variable shocks with sign restriction+zero restriction?

For example, for my first domestic shock should I have something like this?

compute forcedcols=i1~i2~i3
@forcedfactor(force=column) sigmad forcedcols ffactor
compute r4=inv(sigmap)*%xsubmat(ffactor,1,nvar,%cols(forcedcols)+1,nvar)
compute [vector] v4=%zeros(3,2,1)~~r4*%ransphere(%cols(r4))
if UhligAccept(v4,KMIN,KMAX,||+4||)==0
goto reject
compute i4=sigmap*v4

[TomDoan]

No. First of all, you can't really do that. Also, the percentage FEVD on your first identified shocks are independent of the choice of the remaining shocks. (That's why you can ignore them).

[Yashodha]

Dear Tom,

Then how can we restrict the domestic variables affecting the foreign variables in the contemporaneous period? I want show how the three foreign shocks are affecting the three foreign variables through FEVD.

[TomDoan]

You can't have both the sign restrictions and the global/domestic blocking. You have to decide which is most important.

[Yashodha]

Dear Tom,

This is with regard to my previous question on the restriction of domestic shocks affecting the foreign variables. I understand it is not possible to identify all my domestic shocks with zero restrictions using sign restriction technique. But is it possible to combine sign restrictions with short-run restrictions so that I can restrict the effect of domestic shocks on foreign variables? If this is possible, could you explain how I should do it.

Thanking you in advance.

[TomDoan]

That's covered in the VAR course. Note, however, that you will be severely limited in what you can do. If you pick shocks with zero impacts on the three global variables, then there are only two degrees of freedom for the first shock, one for the second (and none for the third). You might have a hard time hitting more than relatively basic restrictions.

[Yashodha]

Dear Tom,

Need another clarification. In Uhlig JME (2005) and Mountford and Uhlig JME(2009) (in replication files), the number of shocks identified is less than the total number of shocks in the model. So, is Cholesky decomposition used to identify the shocks that are not identified by the sign restrictions in these examples? If they are not identified at all, we will have the issue of 'multiple shocks' problem since there is no guarantee that the unidentified shocks are not similar to the shocks identified by sign restrictions. I don't know whether this is a silly question but please bear with me since I am a layman to sign restriction technique.

[TomDoan]

The precise set of other shocks don't matter. They just have to be from a space orthogonal to the shocks you've chosen. (In general, you never even need to compute them).

[Yashodha]

Dear Tim,

But does the orthogonality of other shocks guarantee that they would not generate impulse responses that have same direction as in the sign restricted shocks. For example, can we guarantee none of the unidentified shocks have 'signs' similar to my world demand shock?

[TomDoan]

No. But if there are very different shocks which generate the same types of sign restrictions, then you'll get very wide bands and your results won't be very interesting.