Sign Restrictions - Identification using ratios of responses

[KOBE24]

Dear Tom,

I have a question on how to impose sign restrictions on the ratio between two variables.
I clarify my objective in what follows.

I am interesting in replicating a paper by Furlanetto, Ravazzolo and Seneca (2014), which I post here in the WP version (Table 3, page 22).

http://www.norges-bank.no/en/Published/ ... s/2014/09/

They disentangle credit from uncertainty shocks by imposing sign restrictions on the ratio of some variables responses (a financial stress indicator and a volatility indicator).
They do not include the ratio of variables, to my understanding: they retain the draw if and only if the ratio between their responses of a couple of variables has the desired sign.
I am wondering whether one can do in the Mountford - Uhlig (2009) framework, by using elements of the v(jj) or i(jj) vectors for jj = 1, 2, nshocks.
Should I nest a further loop after the first if UhligAccept?
Do you have any recommendations or suggestions?

Thanks a lot!

do subdraw=1,n2
************************************************
* First in Order - Financial shock
************************************************
compute [vector] v1=%zeros(3,1)~~%ransphere(5)
if UhligAccept(v1,KMIN,KMAX,||-4,-5,+6,+8||)==0
goto reject
compute i1=p*v1

[TomDoan]

The description isn't that clear, but I think you're misinterpreting what they're doing. Investment and output are in the model (presumably in log form) and so log(investment/output) is log(investment)-log(output). If the response of log(investment) is less than that of log(output), then the ratio goes down---instead of being a sign restriction on a specific response, it's a sign restriction on a linear combination of them. It's not the ratio of responses, it's the response of the ratio.

[KOBE24]

Dear Tom,

thanks a lot for your reply.
This was also my first view, but then I contacted the authors and they told me that they are restricting the responses.
For now, I have included the ratio in the endogeunous variables vector Y_t, after having standardized the two variables of interest, to take care of the different volatility. This looks consistent with your reply.

The other option which comes to my mind would be using the linear constraints which you were mentioning. But I am left with a further question.
How can I impose that one variabe react more to one shock, without making an explicit quantitative guess on the impact?

Suppose that I am interested in the 7th and 8th variable (uncertainty and financial stress), which are raised by a financial stress shock.
The idea would be to establish a relation such that a< b (or vice versa for the uncertainty shock).
is it sufficient to define a and b on a set of values before starting the loop?

Thanks for your precious help.
best

do subdraw=1,n2
************************************************
* First in Order - Financial shock
************************************************
compute p=%decomp(s)
compute rperp = %perp(||0.0,0.0,0.0,0.0,0.0,0.0, a, b||*p)
compute [vector] v1=%zeros(3,1)~~%ransphere(5)
if UhligAccept(v1,KMIN,KMAX,||-4,-5,+6,+7,+8||)==0
goto reject
compute i1=p*v1

[TomDoan]

Dear Tom,

thanks a lot for your reply.
This was also my first view, but then I contacted the authors and they told me that they are restricting the responses.
For now, I have included the ratio in the endogeunous variables vector Y_t, after having standardized the two variables of interest, to take care of the different volatility. This looks consistent with your reply.

No. Absolutely not. That has to be wrong. If output and investment are in the model, investment/output can't be included as a separate endogenous variable. The only reason you don't get a singular regression is that they are linked by a non-linear rather than linear identity. Again, while the description could be (much) clearer, I'm fairly sure that they are looking at the response of log(investment)-log(output), which can be computed by adding an identity to the model and then just using the standard UhligAccept function.

[KOBE24]

Dear Tom,

I apologize, I wans not clear neither.
I included
6 variables (GDP, prices, policy rate, exchange rate, loans and loan rate)
the financial stress indicator
the ratio between fin.stress and VIX (standardized)

in this sense, it looks consistent with including output and inv/output, not the three of them.
Am I wrong on this?

Also, how could I augment the VAR with the identity in the sign restrictions approach?
I have never done it before. Perhaps creating a system of the VAR and the identity and then applying UhligFuncs to this new system?

Thanks again, sorry for the misunderstanding.

[TomDoan]

There's no question about the fact that the authors include output and investment in the model. (Aside those being in the list, they're also in the graphic output). What they're doing that's different is instead of sign-constraining output and investment, they're sign-constraining output and investment/output. You can either run the model on log Y, log I and sign-constrain the response of log I-log Y, or you can run the model on log Y, log(I/Y) and then derive the response of log I as response of log I = response of log(I/Y) + response of log Y. It's about the same amount of work either way.

To define an identity for log(i/y), you do something like:

equation(identity,coeffs=||1.0,-1.0||) ioveryid logiovery
# logi logy

adjusted for your actual variable, then change the IMPULSE instruction to

impulse(noprint,model=varmodel+ioveryid,factor=sigmap,results=impulses,steps=nstep)

[TomDoan]

One of the authors has confirmed that they did as I describe.

[KOBE24]

Dear Tom,

thanks a lot for your help!
I am working on the code and it seems to produce the expected effect: I should be able in disentangling the effects of "investment and output shocks" adjusted to my specification.

I was wondering whether the same trick could be applied to the historical decomposition.
If I run the model on log Y, log(I/Y), can I derive the contribution of log I as contr( log I) = contr of log(I/Y) + contr of log Y?

Thanks a lot: your help is already gratefully acknowledged in my project, for what is worth.

[TomDoan]

I think you have that backwards. It's not the contribution of I that you can get from Y and I/Y, but the decomposition. But yes. Historical decompositions are linear calculations, so they can be used on any linear combination of the variables in the model.