3rd order perturbation closing devices Uribe

Hello Pfeifer ,

I am trying to do 3rd order perturbation on Schmitt-Grohe and Uribe (2003), closing devices by using your dynare codes. I have basic level of clarification.
on this link “Time varying volatility” you mentioned that “You need to enter a fully nonlinear model and in stoch_simul you must put order=3.” My question is, do I need to remove all exp() on the model before applying 3rd perturbation. What about steady state? do I need to remove log as well.

Thanks in Advance,


No, you can keep the exp(). The simply means you are approximating in percentages. Note that I tried the SGU 2003 model with third-order perturbation. It turns out that the approximation order hardly matters, because the original model is quite close to linear. Thus, you will get almost the same results as the original paper.

Thank you so much Professor Johannes pfeifer for clarification. so we simply can add stoch_simul(order=3, periods, irf=0, pruning); to your codes. As you mentioned at another place that " Theoretical moments are currently only reported up to order=2. If we want moments at order > 2 you need to use simulated moments". What is exactly the numbers of periods that we will get same second moments as theoretical moments of SGU 2003. I need a little guidance to find out mean and variance using simulation for SGU using 3rd order.

Have you posted your codes for third-order perturbation for SUG 2003 anywhere.? I am trying to learn 3rd order using dynare.I am thankful to you for this lovely forum of learning.

Thanks, Professor Johannes pfeifer I have been able to apply now 3rd order perturbation on SGU 2003, Yes, it gives the same second moments as 1st order as you have already mentioned in your note to me.

Hello Professor Johannes,
You mentioned in the following note that SGU 2003 model with 3rd order perturbation produce second moments similar to 1st order perturbation. My Question is, if some one apply 3rd order perturbation to SGU 2003 using different set parameters and calibration as done by Seoane 2005 [https://econpapers.repec.org/article/eeedyncon/v_3a53_3ay_3a2015_3ai_3ac_3ap_3a37-46.htm]. Is moving from 3rd perturbation to 1st order perturbation shall also produce similar second moments? As we know from original version of SGU 2003 1st and 3rd order approximately produce same seconds?

No, for those models it matters.

Thanks, I want to confirm again if I understood it correctly. If SGU 2003 is calibrated to any emerging countries data. where Business cycle characteristics are different than the developed countries. So Do you mean to say that then 1st order perturbation and 3rd order shall not produce similar second moments using SGU 2003 models. Is it so?

Or it is only suitable to move from 1st order to 3 order perturbation. and vice versa is not possible i.e. from 3rd order to 1st order.

I don’t get your point. All I am saying is: if your model is close to linear, then using a higher order approximation will not do anything. If your model is nonlinear, then the higher order approximation will matter. In the original SGU version, we are in a case where the model is close to linear.

Yes, Seoane applied 3rd on the original SGU version (which is close to linear). I mean he did not change anything in the model only value of parameters and calibration for emerging countries. So it means that (keeping in mind that original model is close to linear). Now, if we move or we change the 3rd order to 1st order perturbation that both should produce same second moments.

But It is not the in the case Seoane(2015).When I apply 1st order using exactly his parameters I get the very different moments than his 3rd order.
While, When apply 3rd order on SGU 2003 using his parameters exactly the same, we get the same moments for 1st and 3rd order.

Why we get different moments in the case of Seoane.? if we switch from 3rd to 1st order. That, s why I asked that Or it is only suitable to move from 1st order to 3 order perturbation. and vice versa is not possible i.e. from 3rd order to 1st order.

Whether a model is close to linear of course depends on the parameters. The calibration you are talking about is a highly nonlinear one.

Thanks you so much. I got the point now. But I am a bit confused about what kind of calibration will make the model non-linear. Can you please explain a bit? Can you please provide me any example? Or will you refer me to any book or material to be able to understand this point.

Just have a look at the first order conditions. You will see which parts are not linear and what governs the degree of nonlinearity. Take the Euler equation. There you often have c_t^{-\sigma}. Here it clearly is \sigma.

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Thank you so much Professor Johannes for your detail note. Now, It is clear to me.

Hi Johannes,

I have been reading about pruning in others discussion at this forum. Though, I got some basic idea about it. I am using portfolio adjustment model from SGU 2003 and calibrating the model for emerging countries. With 3rd order perturbation and standard deviation of productivity is 0.0214. And without pruning option moments are better matched with empirical. Can I remove pruning option why and why not.?

Pruning is a technical fix to prevent explosive simulations. If your simulations do not explode, you can remove it.

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Thanks a lot. Yes Simulation in PAC model do not explode,

stoch_simul(order=3,periods = 500000, drop= 200, irf=50)

Similarly Internal discount factor without internalization discount factor(IDF) and External discount factor without internalization(EDF) do not explode too.

However, Debt elastic models(both, External Debt Elastic Interest Rate Model (EDEIR) and Internal Elastic Interest Rate Model (IDEIR)) are exploding I get NaN ….

I could not find reason why there is difference. I am using the same parameters values across these models.

Those are different models. If you want to stay comparable across models, you should use pruning.

Thanks, I found the solution, I play around for a while, with the debt friction value for IDEIR and EDEIR model. They both work well without pruning too. I don’t get the explosive in simulation and also GIRFs are fine too.

@jpfeifer how do you explain this closeness of the model to linearity in SGU2003?

I am using different values of parameters than SGU2003. so model is non-linear and 1st order and 3rd order perturbation give different moments. 3rd order give better moments than 1st.