Shock to standard deviation

General DSGE Modeling
1

Is there a way to model a shock to the standard deviation?

Like, what are the responses of each variable, when standard deviation of a technology process moved from 0.01 to 0.02?

2

Maybe just change the standard deviation from 0.01 to 0.02 if you are interested only in the responses of the variables (i.e., IRFs) after a one-period shock.

3

There is a huge literature on uncertainty shocks, see e.g. https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Born_Pfeifer_2014

4

So, in the code; you had a shock on the level and also a shock on the volatility.

Is it possible to have a shock only on the volatility? So,
var u_tb; stderr 0
var u_sigma_tb; stderr 1

5

Not really. In that case the shock, whose standard deviation you are increasing would not exist.

6

So, if I want to study the effect of a volatility shock to TFP, I would do;

Am I getting this right?

y = exp(z) * k^theta * n^(1-theta)

z = rho * z(-1) + e * sigma;
sigma = eta * sigma(-1) + eps * size;

shocks;
var e; stderr 1;
var eps; stderr 1;
end;

stoch_simul(order=3, periods=500, irf=300, pruning, replic=50000);
7

Mostly yes. But

  1. You are using a log-log-specification, whose moments do not exist. See Andreasen (2010)
  2. I would recommend against GIRFs. See https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Basu_Bundick_2017/Basu_Bundick_2017.mod for an alternative.