I have coded a DSGE model with several real frictions and government distortionary taxation. I have introduced volatility shocks in the government sector and I get totally different results depending on whether I change the order of the shocks in the VAREXO section w.r.t the volatility shocks in the government instruments! It is very strange and I don’t understand why. The level shocks remain the same but the volatility ones change. Someone, please, can tell me why is this happening?

Sorry, my mistake. I forgot to say that I was talking about the IRF´s when considering the volatility shocks. For instance, the following ordering in the VAREXO section for these four shocks: e_a, e_s_a, e_g, e_s_g, provides totally different IRF´s (ONLY for the volatility ones) as this ordering: e_s_a, e_a, e_s_g, e_g. Where the letter “s” stands for the volatility shocks and “a” for TFP shock and “g” for government consumption.

No, this is the issue, for that reason I don’t understand why. It is true that the IRFs for the volatility shocks are odd (the reason is well explained by you in other posts) but the thing is that with a particular ordering you get negative responses for output, consumption… to a volatility shock (the correct answer) but with another ordering, dynare gives me positive responses for output, consumption… for the same volatility shock…

Moreover, I have introduced volatility shocks to some old codes that I have and the pattern is the same. The ordering in the VAREXO section matters for the IRFs but only for the responses to the volatility shocks, the level shocks don’t change.

This is the file of a RBC with capital utilization, trend on TFP and volatility shock. At least, in my computer, when I change the ordering of the 3 shocks that I have, the IRFs for the volatility shock change.

I am not sure you are doing proper fiscal policy volatility shocks. The shock you have is not mean preserving as it has a an effect at second order. Essentially you are relying on log-normality to change the mean.

Your problem is that you are using GIRFs that are very sensitive to the particular shocks drawn and therefore require many replications. When increasing

to 5000 the responses become consistent regardless of ordering.

Thanks a lot for your response Johannes. I really appreciate it. The code RBC.mod is not for fiscal policy, it was one of my old codes with only SV to the technology process. The problem now is that applying your solution and putting replic=5000, I get positive responses to the SV shock when I should get negative ones.

In the paper of Fernandez-Villaverde et. al (Fiscal Volatility Shocks and Economic Activity) or in your paper (Policy Risk and the Business Cycle), you show that an increase in uncertainty in the fiscal instruments has negative effects on output and consumption among other variables. In the case of my fiscal policy DSGE (please find attached), I get positive responses…

If you read the papers carefully, you will see that
i) the contractionary effect of uncertainty relies on the presence of sticky prices and wages. In RBC models like yours uncertainty is generally expansionary (unless capital adjustment costs are really large). This has been pointed out by Basu/Bundick.
ii) that you require a third order approximation for uncertainty shocks. As your model exhibits effects at second order, you cannot be studying the same type of shocks. Rather, you must have a mean effect on the level (maybe coming from e.g. a log-normal distribution that should not be there). Depending on the direction of this mean effect, you will also see a positive output response.

Thank you very much for your response. You are right with the first point. For the second point, I have to mention that I have also run the code for order=3 with the same identical results in terms of SV shock. What do you suggest to me in order to fix the problem when you say: “The shock you have is not mean preserving as it has a an effect at second order. Essentially you are relying on log-normality to change the mean.”

That is not comforting. At order=2 there should be no effect at all, only at order=3. What you should do is start with your small model and specify the shocks as in Basu/Bundick:

//Shock processes
a=(1-rho_a)*a_bar+rho_a*a(-1)+sigma_a*eps_a;
sigma_a=(1-rho_sigma_a)*sigma_a_bar+rho_sigma_a*sigma_a(-1)+sigma_sigma_a*eps_sigma_a;
where a is the level of the variable. That way you avoid any Jensen’s Inequality effect coming from log-normal distributions.

Thanks a lot for the advise. Regarding the order=2 or order=3, it is true that I get the same IRF’s in both simulations. I am going to follow your advise and start adding the SV shock as you proposed to me and see what happens.