*
* MONTEVAR.RPF
* Example of Monte Carlo Integration of Impulse Responses
*
* RATS User's Guide, Example from Section 16.5.1.
*
* Note that this is for illustration of the technique. In practice, you
* would use the @MONTEVAR procedure to do the draws.
*
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)
*
system(model=varmodel)
variables loggdp loginv logc ftb3
lags 1 to lags
det constant
end(system)
******************************************************************
estimate
*
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)
*
* Compute the IRF's and "flatten" them into element DRAW of the
* %%RESPONSES array.
*
impulse(noprint,model=varmodel,factor=fsigma,$
results=impulses,steps=nstep,flatten=%%responses(draw))
infobox(current=draw)
end do draw
infobox(action=remove)
*
@mcgraphirf(model=varmodel)