*
* MONTEEXOGVAR.RPF
* 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
*
* These are transformed to 100*log(x) so responses can be interpreted as
* percentage changes (at annual rate, since the data are in annual
* rates).
*
set loggdp = 100.0*log(gdph)
set loginv = 100.0*log(ih)
set logc = 100.0*log(cbhm)
*
* T-Bill rate is treated as exogenous, with current and lagged values
* included in the VAR equation.
*
system(model=varmodel)
variables loggdp loginv logc
lags 1 to lags
det constant ftb3{0 to lags}
end(system)
*
* Define placeholder equation to allow shock to T-bills. Note that the
* combined model will have no dynamics for the exogenous variable, so a
* unit shock will be a +1 at impact followed by zero for the remaining
* periods.
*
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)
*
infobox(action=define,progress,lower=1,upper=ndraws) "Monte Carlo Integration"
do draw=1,ndraws
*
* On the odd values for <>, 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. Save into %%responses(draw)
*
impulse(noprint,model=varmodel+rateeq,shocks=%unitv(%nvar+1,%nvar+1),$
flatten=%%responses(draw),steps=nstep)
infobox(current=draw)
end do draw
infobox(action=remove)
*
@mcgraphirf(model=varmodel,footer="Response to Rate Shock",$
shocklabels=||"Rate Shock"||)