MONTENEARSVAR.RPF does Monte Carlo integration for an overidentified structural covariance model with a near-VAR. This is based upon the six-variable model from Sims and Zha, Econometrica 1999 with the adjustment that the equation for investment excludes all the other variables. The use of a near-VAR (rather than a flat prior full VAR) complicates the Monte Carlo integration because the marginal likelihood of the covariance matrix depends upon the observed covariance matrix of the residuals at the current draws for the lag coefficients rather than the observed covariance matrix at the OLS estimates only. This uses random walk Metropolis for the structural VAR coefficients, then draws the lag coefficients using the procedures from the SURGibbsSetup file.
Detailed description
There is quite a bit more calculation involved in this than there is for a flat prior full VAR; basically it requires a full system estimate for the SUR model at each sweep. This model has 130 coefficients in the near-VAR and takes about five minutes to do 12000 sweeps. The computational burden goes up roughly with the cube of the number of coefficients, so a 1000 coefficient model will take about 400 times as long. The Cushman and Zha JME 1997 example shows the use of a more complicated but much more efficient sampler which can be used for larger models with a special structure.