Bayesian VAR (n=14) by Musso, Neri and Stracca (JBF, 2011)

[KOBE24]

Dear Tom,

I am reading the paper "Housing, consumption and monetary policy:
how different are the U.S. and the euro area?"
by Musso, Neri and Stracca (2011, Journal of Banking and Finance, vol. 35(11), pages 3019-3041, November).

In particular, I am interested in understanding how to replicate some results using their framework.
Having a look at their graphs I bet that they're using RATS, and I am tryng to figure how to implement their
Bayesian VAR in RATS 7.0.They even have a 14 variables specification

I focused on the instruction SPECIFY, section 10.9 of the manual, but I could not solve the puzzle of getting such tight confidence bands
with such a high size of the system.

Could you please have a look and suggest some possible way to develop a code for sign restrictions
using this model and the instruction specify?

In the meanwhile, I will go on and try to figure a solution, but I doubt I will be able to do without your help.

Thanks in advance,

KOBE

[TomDoan]

Unless the published paper is completely different from the working paper, they don't do a 14 variable system---they just compare two 7 variable systems. And they don't do sign restrictions, from what I can tell, they're doing Choleski factorizations in the order given and simply computing the typical signs of the responses. Although they don't give any details on the settings for the Minnesota prior, there's no reason that it couldn't produce IRF's that look like those.

[KOBE24]

To qualify my post above, I put here the VAR setup I am trying with


system(model=JBF)
var y prx houprx resinv ffunds m2 spread loans eay eahicp eahouprx earesinv euribor m3 easpread ealoans
lags 1 to 2
det constant trend
SPECIFY(type=symmetric,lagtype=harmonic, tight=.1,decay=5.0) .2
end(system)
estimate(noprint) 1999:1 2011:4

it makes 52 data points and I have 16 variables I don't know if this is feasible..
Anyway, it would be sufficient have ten variables for my main analysis (if the former proves to be unfeasible, which I fear)
I chose a stroger degree of overall tightness (tight) than normally suggested and only .2 for correlation among variables. Dont'know if I can strenghten the decay or improve the setup in some way.
Basically, the sign restrictions code work, but produces very large bands, I mean not significant and too large, impossible to show.

Hope it hepls, and thank you again!

[KOBE24]

Dear Tom,

thanks for your quick (as usual!) answer . I was writing while you were posting, so I didn't see your reply.
I understand your point on Cholesky, I'll rephrase this: I would like to implement sign restrictions on this system, or on a system of at least n=10 variables.
Do you think it is feasible, considering that data start in 1999Q1?
As for the size of the system, unless I don't understand , at page 20 they mention n= 14 variables.

http://www.bancaditalia.it/pubblicazion ... ma_807.pdf

sorry for not being clearer before.

[KOBE24]

For what I understand from their settings on the prior, theimpose a Minnesota prior on the reduced coefficients of the VAR model, and a diffuse prior on the covariance matrix.
In particular, (see page 15 of the Bank of Italy Working Paper I posted above, which coincides with the final published article) they state:

- overall thightness theta_0 = 0.1
- relative tightness of other variables theta_1 = 0.2
- relative tightness of exogenous variables theta_2 = 10^5

I was wondering if the proper way to translate this in RATS is the following


SPECIFY(type=symmetric,lagtype=harmonic, tight=.1,decay=100000) .2

When I try this, I het an error message like this

## MAT14. Non-invertible Matrix. Using Generalized Inverse for SYMMETRIC.
## EQ4. Equation %MODELEQN(JBF,1) Has At Least One Undefined or NA Coefficient

could you please help me with these settings?

Thanks in advance.

KOBE

[KOBE24]

Sorry Tom,

probably I asked too many questions in a silly and uncorrect way.

My bad.

If I continue to struggle with my 10 variables specification from 1999Q1 TO 2011Q4 I will go back to you and I will do my best to be as clear as possible.

Thanks,

KOBE

[TomDoan]

What they are using is the techniques from the GIBBSVAR.RPF example program. They are using exactly the same as the TIGHT=.1 and OTHER=.5 used there. However, this:

compute minnprec((j-1)*lags+l,i)=olssee(j)/olssee(i)*%if(i==j,1.0/tight,1.0/(other*tight))

needs to be adjusted because they are using a linear increase in the precision. If this were done using the RATS VAR system, that would be LAGDECAY=HARMONIC,DECAY=.5. Done the way GIBBSVAR does it, you would want

compute minnprec((j-1)*lags+l,i)=olssee(j)/olssee(i)*sqrt(lags)*%if(i==j,1.0/tight,1.0/(other*tight))

(This is computing the square root of the precision, so it goes up with the square root of the lag). The 10^5 on the other variables is effectively an infinite variance/zero precision, which is what this is doing.

[KOBE24]

Dear Tom,

thank you so much for clarifying this.

I will study your instructions and try to implement this in my system.

Your help is nothing less than essential to me and to my understanding of RATS and Bayesian econometrics!

Best,

Kobe