Shock in exogenous variables in a SVAR

[torresgc]

Hello. I could help. How I can generate shocks of 1% in the exogenous variables in a SVAR program?
Thanks for any help! (e-mail address: torresgc@bccr.fi.cr)

[TomDoan]

Hello. I could help. How I can generate shocks of 1% in the exogenous variables in a SVAR program?
Thanks for any help! (e-mail address: torresgc@bccr.fi.cr)

This may be a bit more than you need (it does MC integration for the response), but it shows the general idea. You create a placeholder equation which has the exogenous variable as its dependent variable, and shock that using the SHOCKS option on IMPULSE. To get 1%, you would use the option
shocks=.01*%unitv(%nvar+1,%nvar+1)

Code: Select all

*
* Monte Carlo integration with shock to "exogenous" variable
*
compute lags=4            ;*Number of lags
compute nstep=16         ;*Number of response steps
compute ndraws=10000      ;*Number of keeper draws
*
open data haversample.rat
cal(q) 1959
data(format=rats) 1959:1 2006:4 ftb3 gdph ih cbhm
*
set loggdp = log(gdph)
set loginv = log(ih)
set logc   = log(cbhm)
*
* T-Bill rate is treated as exogenous
*
system(model=varmodel)
variables loggdp loginv logc
lags 1 to lags
det constant ftb3{1 to 4}
end(system)
*
* Define placeholder equation to allow shock to T-bills.
*
equation(empty) rateeq ftb3
*
******************************************************************
estimate
compute nshocks=1
compute nvar   =%nvar
compute fxx    =%decomp(%xx)
compute fwish  =%decomp(inv(%nobs*%sigma))
compute wishdof=%nobs-%nreg
compute betaols=%modelgetcoeffs(varmodel)
*
declare vect[rect] %%responses(ndraws)
declare rect[series] impulses(nvar,nvar)

infobox(action=define,progress,lower=1,upper=ndraws) "Monte Carlo Integration"
do draw=1,ndraws
   *
   * On the odd values for <<draw>>, a draw is made from the inverse Wishart
   * distribution for the covariance matrix. This assumes use of the
   * Jeffrey's prior |S|^-(n+1)/2 where n is the number of equations in
   * the VAR. The posterior for S with that prior is inverse Wishart with
   * T-p d.f. (p = number of explanatory variables per equation) and
   * covariance matrix inv(T(S-hat)).
   *
   * Given the draw for S, a draw is made for the coefficients by adding
   * the mean from the least squares estimate to a draw from a
   * multivariate Normal with  (factor of) covariance matrix as the
   * Kroneker product of the factor of the draw for S and a factor of
   * the X'X^-1 from OLS.
   *
   * On even draws, the S is kept at the previous value, and the
   * coefficient draw is reflected through the mean.
   *
   if %clock(draw,2)==1 {
      compute sigmad  =%ranwisharti(fwish,wishdof)
      compute fsigma  =%decomp(sigmad)
      compute betau   =%ranmvkron(fsigma,fxx)
      compute betadraw=betaols+betau
   }
   else
      compute betadraw=betaols-betau
   *
   * Push the draw for the coefficient back into the model.
   *
   compute %modelsetcoeffs(varmodel,betadraw)
   *
   * Shock the combination of the VAR + the placeholder equation with a
   * unit shock to the placeholder.
   *
   impulse(noprint,model=varmodel+rateeq,shocks=%unitv(%nvar+1,%nvar+1),$
     result=impulses,steps=nstep)
   *
   * Save the impulse responses
   *
   dim %%responses(draw)(nvar*nshocks,nstep)
   ewise %%responses(draw)(i,j)=ix=%vec(%xt(impulses,j)),ix(i)
   infobox(current=draw)
end do draw
infobox(action=remove)
*
@mcgraphirf(model=varmodel,shocklabels=||"To Interest Rate"||)


[Ozmando]

Hi Everyone. I need more help with this code please. Is there a way to modify the code so that the impulse response functions graph only the response to the exogenous shocks? Thanks. Oz

[TomDoan]

That's what this does. The only shock analyzed is to the variable treated as exogenous.

[Ozmando]

That's what this does. The only shock analyzed is to the variable treated as exogenous.

TomDan thanks. However, I notice that the IFR of LOGC do not correspond to the estimates of the coefficients of FTB(?) They appear to be fine for other variables.

[TomDoan]

Look fine to me. LOGC is the only equation that has a negative coefficient on lag one of FTB3. Beyond lag one, it's very hard to tell what will happen just by eyeballing the coefficients.

[Ozmando]

Tom, thanks. Will have another look again.
Oz

[Ozmando]

More query please: if I read the data into rats into a panel format and I introduce country dummies as exogenous variables. Can that be treated as a panel SVAR? If not is there a way to estimate panel SVAR in the context of exogenous shocks?
Thanks
oz

[TomDoan]

In your panel SVAR, what's heterogeneous and what's homogeneous? What you're describing would seem to have only the intercepts being heterogeneous, which is a rather strong assumption, generally only appropriate if you have a limited amount of data per country. And if you have that, then the small-sample bias in the fixed effects estimator could be quite severe.

[Ozmando]

That's what this does. The only shock analyzed is to the variable treated as exogenous.

Hi Tom,
Sorry to bother again: If I am right the coefficients obtained are the mean response? is there away to also obtain the cumulative response (let's say after 3 period) and their confidence band?
Thanks
Oz

[TomDoan]

Use the ACCUMULATE instruction. See, for instance, what the BQDODRAWS procedure does.

[Ozmando]

Use the ACCUMULATE instruction. See, for instance, what the BQDODRAWS procedure does.

Thanks Tom for prompt reply and guidance.
best wishes,
Oz

[wfirew]

I am estimating a vector error correction model (vecm) and a shock to the exogenous variable as described above does not work. Any suggestion?
Best,

[TomDoan]

I am estimating a vector error correction model (vecm) and a shock to the exogenous variable as described above does not work. Any suggestion?
Best,

Why not?

[wfirew]

It works fine for VAR. Then, I have modified the code as follow for vecm (leaving the MC part). When I run it, the programs freezes prompting me to close the program.

Code: Select all

*
* Monte Carlo integration with shock to "exogenous" variable
*
compute lags=4            ;*Number of lags
compute nstep=16         ;*Number of response steps

*
open data haversample.rat
cal(q) 1959
data(format=rats) 1959:1 2006:4 ftb3 gdph ih cbhm
*
set loggdp = log(gdph)
set loginv = log(ih)
set logc   = log(cbhm)
*
* T-Bill rate is treated as exogenous
*
setset dftb3  = ftb3 - ftb3{1}
equation(coeffs=||1.0,0.3,0.3,0.3||) ect1
# loggdp loginv logc ftb3

system(model=vecmmodel)
variables loggdp loginv logc
lags 1 to lags
ect ect1
det constant dftb3{0 to 3}
end(system)
*
* Define placeholder equation to allow shock to T-bills.
*
equation(empty) rateeq ftb3
*
******************************************************************
estimate

impulse(noprint,model=vecmmodel+rateeq,shocks=%unitv(%nvar+1,%nvar+1),$
     result=impulses,steps=nstep)


I have one more concern that is dftb3 is just another exogenous variable instead of the difference of ftb3. But I want the difference of ftb3 outside the co-integrating vector as an exogenous while ftb3 is in the cointegrating vector.