Deterministic and stochastic shocks in the same model

Perfect foresight simulations
1

Dear Johannes,

Is there a way to have stochastic shocks together with deterministic shocks in the same model?

I have read the code for RBC_news_shock_model.mod, which seems to be able to do that, however I have some questions:

  1. By defining
    z=rhoz*z(-1)+eps_z_surprise + eps_z_news(-8);

shocks;
var eps_z_news=1; //8 period anticipated TFP news shock
var eps_z_surprise=1; //TFP surprise shock
end;

you’re assuming that both shocks are stochastic after period 8, right?

Then having eps_z_news(-8) makes this part of the shock deterministic (then known)?

  1. In the second part, with

shock_matrix(1,strmatch(‘eps_z_news’,M_.exo_names,‘exact’)) = 1;
shock_matrix(1+8,strmatch(‘eps_z_surprise’,M_.exo_names,‘exact’)) = -1;

you are assuming that the deterministic shock only hits in period 1, then in period 9 the stochastic hits with value -1.

If I wanted to assume that the deterministic shock is 1 in each period from 1 to 8, then I should simply do this

shock_matrix(2,strmatch(‘eps_z_news’,M_.exo_names,‘exact’)) = 1;
shock_matrix(3,strmatch(‘eps_z_news’,M_.exo_names,‘exact’)) = 1;
etc…

right ?

  1. Let’s say I want to do the same thing but assuming that there are two different exogenous variables: one with 8 known values (z1 in the labor FOC), and the other a pure stochastic (z2 in the production function).

exp(z1)*psi*exp(c)^{sigma}*1/(1-exp(l))=exp(w);
exp(y)=exp(z2)*exp(k(-1))^{alpha}*exp(l)^{(1-alpha)};

z1=rhoz1*z1(-1)+eps_z1;
z2=eps_z2;

shocks;
var eps_z1=1; //8 period anticipated labor supply shock
var eps_z2=1; //TFP surprise TFP shock
end;

This code should work and assume that z1 shock is deterministic until period 8, after period 8, this becomes a stochastic shock without persistance, while z2 is stochastic from period 0 and persistant with rhoz1 right?

Thanks for your answer!

Verónica

2

Please have a look at Problems with mixing shocks?

What exactly is the information structure you have in mind?

3

Will do thanks.

What do you mean by “information structure”?

4

When are agents supposed to know what happens? Do they know the actual values and persistence? Or only the distribution? Are they supposed to react to potentially stochastic shocks via e.g. precautionary behavior? Or is certainty equivalence OK.

5

Agents are suppose to know the actual values for one of the shocks (z1) until period 8, but they only know persistance and distribution of the other (z2).

So knowing the exact value of occurence of z1, agents are supposed to react to potentially stochastic shocks z2.

6

But what happens with z1 after period 8? It becomes 0 forever and agents know that as well?

7

That was part of my first question. I would like to know if the formulation I propose translates that after the 8 period the shock become stochastic or in the contrary that it becomes 0 forever deterministic.

8

Under certainty equivalence (order=1), that distinction is not really meaningful. Stochastic shocks can happen all the time, but the distribution does not affect the decision rules.