How to estimate negative impulses & responses for a Bayesian VAR using 'impulse.m' code available in Matlab toolbox

Hi,

I am using Gary Koop's (2010) code (<http://personal.strath.ac.uk/gary.koop/bayes_matlab_code_by_koop_and_korobilis.html>) to estimate a Bayesian VAR and I am trying to pull the IRFs for a 1 std dev shock in the innovations using the 'impulse.m' code available in the Matlab toolbox. At this point, I have managed to obtain good results with the code, not changing anything:

          response=impulse(By,smat,nstep)
          [neq,nvar,nlag]=size(By);
          response=zeros(nvar,neq,nstep);
          response(:,:,1)=smat'; 
          for it=2:nstep
             for ilag=1:min(nlag,it-1)
                response(:,:,it)=response(:,:,it)+By(:,:,ilag)*response(:,:,it-ilag);  %(1)

Where neq = nr of equations of the VAR nvar = nr of variables nstep = nr of lags of the VAR smat = choleski decomposition of the variance-covariance matrix (transposed so as to get the lower triangular side)

The way the code is specified is that shocks are computed the following way:

    shock = chol(SIGMA)';
                d = diag(diag(shock));
                shock = inv(d)*shock

Where SIGMA is the variance-covariance matrix. Based on the above results, when running the program I am receiving the IRFs for a raise with +1 std dev in the innovations for the specified forecast horizon. I am trying to see the responses for a -1 std dev shock for the same specified horizon although I am not sure how should I change the code to get the clear results.

My first guess was to replace (1) with:

response(:,:,it)=response(:,:,it)-By(:,:,ilag)*response(:,:,it-ilag);

but it did not work.

Answer 1

[Uriel Braham]

Hi, hopefully you will receive this. Since the VARs are linear models you can reverse the sign of the shock by just multiplying the whole IRFs with -1.