Problem with permanent shock

Steady state
1

Dear dynare users,

I have a maybe silly question. I want to implement into my model a permanent shock, which implies a jump from an initial steady-state to a new steady-state. So far so good.

However, the new steady-state (endval) induces a new value of the labor disutility parameter \chi^{n} which is necessary to pin-down the steady-state value of hours worked.

This implies that I have two different values for this parameter, one in the initial steady-state and another in the final steady-state. However, in the model block, I can only pick/use only one value for this parameter. This leads to the problem that the steady-state cannot be found.

PS: The model works perfectly with a temporary shock.

How can I overcome this problem?

2
  1. Why does the labor disutility parameter change in the first place? Usually, it’s hours worked that jumps to a new level.
  2. If the labor disutility parameter is supposed to change, you can define it as a varexo.
3

Thanks for your swift reply.

  1. I am modeling a permanent energy price shock and the number of hours worked is not impacted by the new steady-state since it is set to h_{ss} = 0.33. The new permanent price shifts the steady-state of energy usage, which in turn impacts the steady-state value of consumption (through the aggregate budget constraint) and ultimately the value of MUC. Since Uc_{ss} has changed and w_{ss} and h_{ss} remain constant, \chi^{n} has to change in order to pin down \chi^{n} h_{ss}^{\varphi}=w_{ss}Uc_{ss}. Or am I missing something?

  2. Thanks a lot. I did not know that this was possible, and it worked perfectly.

4

Usually the way to proceed is: you fix h_{ss}^{initial}=0.33 in the initial steady state by setting \chi^n accordingly. Then the shock happens. Because Uc and w change, h_{ss}^{terminal} must also permanently change to satisfy the FOC.

5

Ok, thanks. That explains why the simulations were so weird.

For now, my strategy to calculate the steady-state was to normalize Y_{ss} to 1 and to calculate the remaining steady-state variables from this point. I guess that I should change this so that all the variables permanently change.

thanks a lot.

6

Yes, indeed.