Confusion about the practical application of temporary and permanent shocks

Stochastic simulations
1

Hello everyone,

I would like to ask a question regarding the choice between temporary and permanent shocks. If I am studying the impact of a macroeconomic policy that can essentially be considered a permanent increase in fiscal spending, should I use a permanent shock in a deterministic simulation, or a temporary shock (with a high persistence parameter) instead? I may not have read enough papers, but it seems rare to see permanent shocks used to analyze macroeconomic policies. Most of the analyses I’ve seen use impulse response functions from stochastic simulations, with the persistence parameter set at 0.9 or even higher. Are such papers actually presenting the effects of a temporary policy (albeit with a long duration) or the effects of a permanent policy on the economy?
Sincerely asking for your help to resolve this confusion. Thank you.

2

A different way of framing the problem of a permanent shock is studying transitions to a new steady state. That is regularly done in the literature.

3

So if I set the parameter representing impact persistence to 0.9 or higher, can I use pulse images in random simulations to study permanent impacts? I have another question: When I use the permanent shock in the deterministic simulation, output increases a lot and then falls back, but the final steady state is slightly lower than the original steady state. Should I pay attention to the growth during the shock or should I pay more attention to the decline in output under the new steady state?

4
  1. No, you cannot. Permanent means a unit root, i.e., an AR coefficient of 1. 0.9 is not even close to permanent.
  2. You describe a trade-off between short- and long-run effects. You may need a welfare measure to decide on whether the overall effect is positive or negative.
5

“Thank you very much for your help. If I want to analyze a permanent increase in government spending as a policy, do I have to use a permanent shock in deterministic simulations? What should I do if I want to use a permanent shock in stochastic simulations?”

6

See

7

So as long as the persistence parameter of the shock is set to 1, it’s a permanent shock in a stochastic simulation, right? Would the impulse response graphs of a permanent shock in a stochastic simulation differ significantly from those in a deterministic simulation? Or would they be almost identical?

8
  1. Yes, a unit root means a permanent shock.
  2. That depends on the degree of nonlinearity and the order of approximation.
9

Thank you very much. I guess if I take the first-order Taylor expansion, the impulse response graphs for permanent shocks in deterministic simulations and stochastic simulations would be almost identical. In other words, if I want to use permanent shocks in my paper, it is not necessary to set up a model without stochastic terms. I can directly set the AR(1) coefficient of the shock to 1 for analysis. Is my understanding correct? However, I have never seen such an article before, so I am not sure how to start writing it. Have you seen any classic literature similar to this?

10

Yes, you can directly set the AR coefficient to 1. This is such an obvious solution that it is often not explicitly mentioned in papers.

11

Thank you very much for your guidance. I have benefited greatly from it.

12

Mr. Jpfeifer, sorry to bother you again. I would like to ask an additional question: In a macroeconomic model that includes government debt and a tax rule that adjusts with changes in debt, how should I implement a permanent shock to the tax rate? (Simply setting the AR coefficient of the tax rate to 1 either violates the Blanchard-Kahn condition or makes the impulse response function highly unstable.)

13

If you have fiscal rules reacting to deviations from steady states, you need to account for the shift in steady states as well.

14

Sorry, I don’t quite understand what you mean. Specifically, how should we consider the shift in steady states

15

How exactly did you specify the fiscal rules?

16

For the equation

log(tau/tauss)=0.9*log(tau(-1)/tauss)+(1-0.9)*(0.5*log(y/yss)+0.5*log(aabb/aabbss))+a_tau

how should I implement a permanent shock to the tax rate?

17

That is tricky because you would need to shock tauss, which may alter yss as well.