# Confusion about the practical application of temporary and permanent shocks
**URL:** https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318
**Category:** Stochastic simulations
**Created:** [25 August 2024 19:49 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318 "2024-08-25T19:49:39Z")
**Posts on this page:** 18
**Page:** 1
### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [25 August 2024 19:49 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/1 "2024-08-25T19:49:39Z")
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.
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [26 August 2024 08:47 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/2 "2024-08-26T08:47:58Z")
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.
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [26 August 2024 09:00 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/3 "2024-08-26T09:00:57Z")
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?
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [26 August 2024 09:07 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/4 "2024-08-26T09:07:26Z")
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.
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [26 August 2024 20:00 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/5 "2024-08-26T20:00:11Z")
“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?”
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [27 August 2024 06:57 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/6 "2024-08-27T06:57:34Z")
See
> [@Basic rbc model with temporary and permanent shocks](https://forum.dynare.org/t/basic-rbc-model-with-temporary-and-permanent-shocks/4798/6):
>
> An alternative is to have both a stationary and a unit root shock in an undetrended model: var y, c, k, a, h, a\_temp, a\_perm; varexo e, u; parameters beta, rho, alpha, delta, theta, psi, tau; alpha = 0.36; rho = 0.95; tau = 0.025; beta = 0.99; delta = 0.025; psi = 0; theta = 2.95; phi = 0.1; model; c\*theta\*h^(1+psi)=(1-alpha)\*y; k = beta\*(c/c(+1))\*(alpha\*y(+1)+(1-delta)\*k); y = exp(a)\*(k(-1)^alpha)\*(h^(1-alpha)); k = (y-c)+(1-delta)\*k(-1); a = a\_temp+a\_perm; a\_temp=rho\*a\_temp(-1) +…
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [27 August 2024 18:46 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/7 "2024-08-27T18:46:07Z")
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?
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [27 August 2024 19:17 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/8 "2024-08-27T19:17:30Z")
1. Yes, a unit root means a permanent shock.
2. That depends on the degree of nonlinearity and the order of approximation.
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [27 August 2024 21:12 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/9 "2024-08-27T21:12:46Z")
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?
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [28 August 2024 06:48 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/10 "2024-08-28T06:48:16Z")
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.
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [29 August 2024 11:34 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/11 "2024-08-29T11:34:35Z")
Thank you very much for your guidance. I have benefited greatly from it.
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [31 August 2024 20:43 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/12 "2024-08-31T20:43:08Z")
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.)
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [1 September 2024 07:35 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/13 "2024-09-01T07:35:19Z")
If you have fiscal rules reacting to deviations from steady states, you need to account for the shift in steady states as well.
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [1 September 2024 09:12 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/14 "2024-09-01T09:12:39Z")
Sorry, I don’t quite understand what you mean. Specifically, how should we consider the shift in steady states
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [1 September 2024 09:40 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/15 "2024-09-01T09:40:27Z")
How exactly did you specify the fiscal rules?
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### Author:  [@wenzhuo](https://forum.dynare.org/u/wenzhuo)
#### Post date: [1 September 2024 11:06 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/16 "2024-09-01T11:06:19Z")
For the equation
```auto
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?
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### Author:  [@jpfeifer](https://forum.dynare.org/u/jpfeifer)
#### Post date: [2 September 2024 06:45 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/17 "2024-09-02T06:45:34Z")
> [@wenzhuo](#):
>
> to
That is tricky because you would need to shock `tauss`, which may alter `yss` as well.
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### Author:  [@Priyadarshini\_Roy](https://forum.dynare.org/u/Priyadarshini_Roy)
#### Post date: [29 March 2026 11:49 UTC](https://forum.dynare.org/t/confusion-about-the-practical-application-of-temporary-and-permanent-shocks/26318/18 "2026-03-29T11:49:43Z")
Hello, Sir. This is my very first message on the forum. I am working a three-agent NK model (3 household groups) with consumption taxes and labor income taxes for my dissertation. Motivated by the GST Reforms 2.0 and Income Tax Act 2025 in India, I am trying to incorporate differential tax shocks (tax rate reduction of different magnitudes to each household group). I have been using unit root processes for the tax rates as I am viewing these reforms as permanent shocks to tax rates. In similar lines with the above discussion, would it be right to directly set AR coefficient to 1 in the stochastic setting? (doing this, I have been able to obtain the IRFs). I am seeking a confirmation on the same. My objective is to study the impact of such reforms on the consumption of different household groups and the effect on consumption inequality both in the short-run and long-run. I sincerely apologize if I am making any mistakes, please pardon me for the same. Thanks!