IRF 2nd order approx with shocks of different sizes

javiergc · October 21, 2022, 1:58pm

As I understood from Dynare’s documentation, if you are using a 2nd order of approximation IRFs are computed by simulation (as explained in IrFs - DynareWiki). There it says that the IRF being calculated is to a shock of size equal to 1 StdDev. However, under non-linear solutions, IRFs can vary depending on the size of the shock, so it might be of interest to see the IRF to a larger shock. Is there an option to change the size of the shock for the IRF? An imperfect possible fix is to calibrate the StdDev of the shock to a larger value, and thus Dynare will be computing the IRF to a larger shock. But I think this is imperfect precisely because the size of the variance matters for non-linear solution. I’ll appreciate any feedback on this!

jpfeifer · October 22, 2022, 10:34am

That feature is on our to-do-list but not yet implemented. You would need to program your GIRFs using the simult_-function. See e.g.

github.com

JohannesPfeifer/DSGE_mod/blob/master/RBC_state_dependent_GIRF/RBC_state_dependent_GIRF.mod

/*
 * This file uses a basic RBC model with government spending and TFP shocks to
 * demonstrate how to compute Generalized Impulse Response Functions using 
 * Dynare's simult_-function. The model is solved up to second order to allow 
 * for non-linearities.
 * 
 * Two exercises are considered:
 *      1. A comparison of the absolute output response to a 1% of GDP shock that is either 
 *          positive or negative. The positive/negative shock is imposed at the ergodic mean.
 *          It shows that in nonlinear models, the sign of the shock matters.
 *      2. A comparison of the absolute output response to a positive 1% of GDP 
 *          shock at the ergodic mean and when capital is 10% below the steady state.
 *          It shows that in nonlinear models, the point in the state space where the shock happens 
 *          matters.
 *
* 
 * Notes:
 * - This implementation has been tested with Dynare 5.2
 *
 * This implementation was written by Johannes Pfeifer.

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javiergc · October 22, 2022, 3:42pm

Great. Thank you for the reference!

javiergc · October 24, 2022, 2:53pm

In case this is useful for someone, a simple modification of the file ‘stoch_simul.m’ in dynare’s matlab folder allows you to compute IRF for different sizes. In particular, you need to do 2 things

In ‘stoch_simul.m’, replace lines 250 and 251 by

                if isfield(options_,'shock_size')==1
                    y=irf(M_, options_, oo_.dr,cs(M_.exo_names_orig_ord,i)*options_.shock_size, options_.irf, options_.drop, ...
                          options_.replic, options_.order);
                else
                    y=irf(M_, options_, oo_.dr,cs(M_.exo_names_orig_ord,i), options_.irf, options_.drop, ...
                      options_.replic, options_.order);
                end

In the mod-file, before specifying the stoch_simul command, add the line

options_.shock_size=N;

where N is the size of the shock, expressed in terms of multiples of the standard deviation of the exogenous shock (i.e. is the shock’ standard deviation is S, this will produce the IRF to a shock of size N*S)