The RATS Software Forum

Question about Impulse Response of "GROUP Y" to Shock in "GROUP X"

Dear Mr.Doan,


I have 17 bank data which are sorted 3 groups by their sizes as below.

Group A = { A1, A2, A3, A4, A5, A6 }
Group B = { B1, B2, B3, B4 }
Group C = { C1, C2, C3, C4, C5, C6, C7 }

My first interest was whether causality relationships among 3 groups exist
or not, and I tested this according to the example of
p.57 in "RATS Programming Manual by Walter Enders"
(I attached the RATS code below my questions).
The result is Group A do granger cause Group B and Group C.

Here is a problem.
I want to get 2 impulse responses, that is, just 2 impulse response graphs,
as below.
(1) Impulse Responses of "Group B" to Shock in "GROUP A"
(2) Impulse Responses of "Group C" to Shock in "GROUP A"

In other words, my goal is just to get 2 impulse reponse functions, not to get
24 series(4 banks in Group B by 6 banks in Group A) and
42 series(7 banks in Group C by 6 banks in Group A)

To get these, first, I thought a way of using averages of each group and
doing granger test with these 3 series - the result was different with grouping
series above and this was not exactly what I wanted to.
Most of all, I think that this is not good
because averaging the all series of elements(banks) in each group
could destroy the characteristics of each element(Am I right?).

The second way that I thought was adding whole or statistically significant
impulse responses in 24 series(4 banks in Group B by 6 banks in Group A)
to get impulse responses of "Group B" to Shock in "GROUP A," and
adding whole or statistically significant impulse responses in
42 series(7 banks in Group C by 6 banks in Group A) to get
impulse responses of "Group C" to Shock in "GROUP A."
Dr.Doan, is this method proper? Somehow, this also looks stupid, I guess...
Would you let me know the best way to get 2 impulse response functions
- "Shock in Group A -> Response of Group B" and
"Shock in Group A -> Response of Group C"?


*******************************************
** test : "Group A -> Group B & Group C"
*******************************************

system(model=unrestricted1)
variables $
B1, B2, B3, B4 $
C1, C2, C3, C4, C5, C6
lags 1 to 1
det constant $
A1, A2, A3, A4, A5, A6
end(system)
estimate(resids=unresids, noprint)
compute ntotal=%nregsystem,mcorr=%nreg,loglunr=%logl
compute logdetunr=%logdet


system(model=restricted1)
variables $
B1, B2, B3, B4 $
C1, C2, C3, C4, C5, C6
lags 1 to 1
det constant
end(system)
estimate(resids=resresids, noprint)
compute loglres=%logl
compute logdetres=%logdet



************** Test Statistics

* (1) Using RATIO
ratio(degrees=ntotal-%nregsystem,mcorr=mcorr, $
title="Group A granger cause Group B & C")
# unresids
# resresids


* (2) Using %LOGL statistics.
* The standard LR test of -2*(L(R)-L(U)) is
* adjusted by multiplying by (T-c)/T to implement the multiplier correction.

compute teststat=-2.0*(%nobs-mcorr)/%nobs*(loglres-loglunr)
cdf(title="Group A granger cause Group B & C") chisqr $
teststat ntotal-%nregsystem


*
* (3) Using %LOGDET statistics:
compute teststat=(%nobs-mcorr)*(logdetres-logdetunr)
cdf(title="Group A granger cause Group B & C") chisqr $
teststat ntotal-%nregsystem

The big problem is figuring out what it means to summarize five shocks with one linear combination of them. The straight average probably is not the best course. You could do principal components on the group A shocks to pick the one shock that explains the most variance of the group A shocks. You could also use canonical correlations (RATS procedure CANCORR) which picks the linear combination of group A shocks that explains the largest proportion of a linear combination of group B shocks. Another approach would be to find the linear combination which explains the highest percentage of group B variance at step N. This is similar to what Faust(1998) did in "The Robustness of Identified VAR Conclusions About Money", Carnegie-Rochester Conference Series on Public Policy, 49, 207-244. See http://www.estima.com/forum/viewtopic.php?f=8&t=1486