Setting size of stochastic shock

wulx · February 4, 2018, 11:23pm

A simple question: how to set size for a stochastic shock instead of default option, which is one std. dev.?

No clue in Dynare reference manual and guide.

I found an out-dated topic for the same question, but it’s not answered correctly.

I also managed to find some example codes by Prof. Johannes Pfeifer, which seems relevant. But I have a hard time understanding contents starting on line 130. I ran this code with different values on line 138, but didn’t see any difference.

github.com

JohannesPfeifer/DSGE_mod/blob/master/RBC_news_shock_model/RBC_news_shock_model.mod

/*
 * This file implements a simple RBC model with additively separable utility and TFP news calibrated to US data. It shows how 
 * to generate IRFs to a "pure" news shock where an 8 period anticipated news shock does not materialize at time 0. 
 * This is the type of policy experiment that is for example performed in Beaudry Portier (2004): An exploration  
 * into Pigou�s theory of cycles, Journal of Monetary Economics 51, pp. 1183�1216.
 *
 * This is done using Dynare's simult_ function, which can be used to simulate time series given the decision rules. This capability
 * can be useful if user's want to use a particular shock series (e.g. truncated normal, historical smoothed shocks etc.)
 * 
 * Note that having two exactly offsetting shocks from continuous distributions to keep the exogenous variable constant 
 * is a 0 probability event for the agents of the model. 
 * 
 * Moreover, this mod-file shows how to use Dynare's capacities to generate TeX-files of the model equations. If you want to see the model
 * equations belonging to this mod-file, run it using Dynare and then use a TeX-editor to compile the TeX-files generated.
 *
 * This implementation was written by Johannes Pfeifer. In case you spot mistakes,
 * email me at jpfeifer@gmx.de
 *
 * This mod-file uses variable substitution to perform a log-linearization of the model. All variables,
 * except for the interest rate (which is already in percent), are put in exp() for this purpose.

This file has been truncated. show original

jpfeifer · February 5, 2018, 10:43am

It depends what you are trying to do. If you work with a linear(ized) model, you can simply set the standard deviation of the shocks to the value desired. Due to certainty equivalence, that is a valid way. At higher order, you indeed need to follow the approach outlined in my mod-file.

wulx · February 5, 2018, 1:17pm

Hi jpfeifer,

Thanks for your reply. I’m working with a simple log-linearized RBC model.

I can’t simply set the deviation of the shock to the value desired, because it affects the expectation in intertemporal Euler equation. Specifically, I want a very large realization of the stochastic shock at the beginning followed by a series of zero deviations to investigate how the economy goes back to steady states depending on the size of the shock with the std. dev. the same. Again, std. dev. of innovation enters into play by affecting the expectation in intertemporal Euler. You could take a look of my codes here, which is really short.https://github.com/wulxGH/2010d/blob/master/PS2Q1.mod I want the shock realize 5*sigmaA rather than sigmaA.

Is there any way to set the size of the shock?

jpfeifer · February 5, 2018, 1:29pm

You need to rethink your exercise. In a linear model certainty equivalence holds. In a linear model, there are no Jensen’s Inequality effects coming from the expectation operator,
The IRF to 5 standard deviation shock is simply the IRF to a 1 standard deviation shock multiplied by 5.

wulx · February 5, 2018, 3:24pm

Thanks! It didn’t occur to me when I raised the question.

But what if I want a series of shocks of different size?

jpfeifer · February 6, 2018, 5:56am

Again, in a linear model, there are not interaction or size effects. The IRF to a series of shocks is simply the linear combination of the IRFs to a single shock.
If you want to consider the effects of different shock sizes or interactions between shocks, you need a nonlinear model.

wulx · February 6, 2018, 1:54pm

Yes I agree. I’m thinking about applying different shocks at different time periods and see their linear combination directly rather than doing a series of experiments and adding them myself. But maybe it’s not very meaningful. Anyway, thanks very much for your patient explanations!

jpfeifer · February 6, 2018, 3:06pm

Then please see

wulx · February 7, 2018, 1:10pm

Great. Thanks! I’ll try that.

mxw · November 24, 2020, 1:40pm

Hi Johannes,

I would like to set the size of a stochastic shock, with the goal of changing another variable. For example, a TFP shock to increase Y by 20%, how to set the size of the TFP shock? linearized first?

My question comes from the codes of Iacoviello (2017). They attempt to demonstrate the asymmetric responses, the sizes of a positive shock and a negative shock are different in magnitude, but they increase or decrease another variable (house price) by 20%, I’m a bit confused how to set the size of these shocks.

Many thanks!

jpfeifer · November 25, 2020, 8:11pm

If I understand your question correctly, you are looking for a shock to make a given endogenous variable move by a pre-specified amount. There is no standard routine available for that. If you only have to do this once, I would simply use trial and error.

Note that linearization is not recommended. In that case, the model would become symmetric.

If you have to do this in an automated way, you could use a solver, but that is quite complicated.

mxw · November 25, 2020, 8:28pm

Many thanks for your response. I’ll make some trials.