Correction term of the constant in the simulations

Stochastic simulations
1

Hi everyone, I have a question regarding the correction term of the constant that is printed in POLICY AND TRANSITION FUNCTIONS and stored in oo_.dr.ghs2 after using the stoch_simul command. I have coded a simple new Keynesian model and computed IRFs for inflation. I would have 2 main questions:

  1. The steady state of inflation in my model is 0.005, as also correctly stated under STEADY STATE RESULTS. In a first simulation I get Constant=0.004869 and (correction)=-0.000131. Now, in my understanding from reading the manual, to build the policy function I should sum these two elements (in other words, sum the constant and what is stored in oo_.dr.ghs2 divided by 2). However, if I did Constant minus correction, I would get exactly the steady state of 0.005. Therefore my question is: to build a policy function for inflation, should I do Constant + correction (which would get me further away from the true steady state) or Constant - correction?

  2. I did two stoch_simul: in the first one I have
    shocks;
    var eps_a = SIGMA_A^20.25^2;
    var eps_v = SIGMA_V^2    0.25^2;
    end;

In the second one I have instead:
shocks;
var eps_a = SIGMA_A^2;
var eps_v = SIGMA_V^2;
end;

Now, under POLICY AND TRANSITION FUNCTIONS, I get two different things for the two stoch_simuls in the Constant and (correction) terms. All the other coefficients are the same. For the first stoch_simul, I get:
Constant=0.004869
(correction)=-0.000131

For the second one I get:
Constant: 0.002901
(correction): -0.002099

Now Constant minus correction gives me 0.005 for both. Why do I get different constant and correction terms for different variance specifications?

Hope the qeustions are clear and thanks a lot in advance.

2

The constant is the overall sum

oo_.dr.ys+0.5*oo_.dr.ghs2

while the correction is just 0.5*oo_.dr.ghs2. Thus,
constant+correction=steady state

If you change the shock variance, that will affect ghs2 and therefore both the correction and the constant, but not the steady state.

3

Thank you, this is clearer now! One quick follow-up question. When I compute the policy function (meaning I want to know the value of an endogenous variable for different combinations of the state variables), I use the constant (i.e. steady state + correction) + coefficients * state variables… This is according to the latest issue of the manual.

This means that the level (not slope) of the policy functions can depend (heavily sometimes) on the variance of the shocks. Is that right?

4

Yes, that is correct. That’s why the stochastic steady state is sometimes very different from the deterministic one.