Refering to one of your old comment at forum given. In Basu/Bundick 2017, IRFs are at the stochastic SS/EMAS. Is policy function at 3rd order is also at stochastic steady state. If yes, the how do we interpret?

Last, question is about pruning Haan and wind (2010) found one of the disadvantage of pruning is that it enlarges the state space of the model. you also mentioned at

In Open Economy RBC model, When I used pruning with 3rd order I get very large S.D of second moments and higher persistence(auto-correlation) in output, consumption, trade balance to GDP ratio etc. Without pruning I get better match with empirical moments. Simulations are not explosive as well. My model is highly non-linear. IRFs are also well behaved.

My Question is Is pruning creating very large standard deviation of moments and greater persistence but what is intuition or mechanism?

No, the approximation point for perturbation is still the deterministic steady state.

At third order, you get a term g_{x\sigma\sigma} (in SGU (2004) notation) that affects the eigenvalues of the solution. But under pruning, you prevent this term from affecting the eigenvalues. That can change the persistence of the system.

According to Haan/De Wind(2012) that one of the disadvantage of
pruning is that it enlarges the state space of the model. Add more state variables etc. Furthermore, quoting from their paper section 3.3 "But these problematic features are only relevant when parameter values are such that the generated volatility is much larger than what is observed for aggregate data"

Can we infer from this (â€śgreater volatilityâ€ť than the data. Which I also mentioned in 19 March note (See please in the beginning of this topic) and greater persistence in consumption TBY etc.) that greater volatility and very extreme persistence(unit root) are symptom that we are getting the those problem related to pruning scheme of Andreasen as mentioned by Haan/De Wind(2012).

Lastly, we get these problems if we donâ€™t choose parameter more accurately.

I donâ€™t think so. Den Haan/De Wind are concerned with perturbation introducing explosive solutions that are not present in the true model. Pruning is designed to prevent such explosions.

Thanks for your input. You are right Den Haan/De Wind give solution to the explosiveness in simulations. But how they are organized their paper. 1st they discuss issues related to 2nd order and 2nd order with pruning. Let me give a brief overview of the paper. In some cases, I will directly quote from the paper to retain their original message.

In the 4th paragraph ofIntroduction they highlight the issues related to Kim et; al .(2008) and Lombardo (2010) pruning scheme. In Section 2 They describe economic models. Section 3 Problems related to higher order perturbation Section 4 They present perturbation-plus approximation Section 5 compare results using their alternative methods with others.

Section 3 They discuss Higher-order perturbation in practice in Subsection 3.2 They discuss the Perturbation approximations and the neoclassical growth model. Towards the end of the this subsection they give Summary for the neoclassical growth model. They say "That is, in practice second-order perturbation approximations of the neoclassical growth model do not exhibit the problems we highlighted in the introduction" "It is true that one has to go outside the usual range of parameter values to encounter problems." so far so good. Now in the beginning of subsection 3.3. "But these problematic features are only relevant when parameter values are such that the generated volatility is much larger than what is observed for aggregate data"
This means that those problem that they mentioned in introduction are brings about when we choose parameter values that generated greater volatility than the data. (I experimented this is possible)

In this subsection 3.3, they showed for matching models that â€śThe small increase in the wage rate leads to a minor shift in the policy functionâ€ť" Nevertheless this minor shift has enormous consequences for time paths simulated with the second-order perturbation approximation because the time explodes path for employment, now explodes."
Now in Section 4 They present their Perturbation-plus procedure. Section 5 make comparison between their method and others ", stated that "the pruned second-order approximation performs worse than the regular second-order perturbation approximation."

My conclusion

we can get explosiveness due to change in the range of some parameters of the model.

If standard deviation of shocks is very large.

Very large volatility say in consumption, than the volatility in the data could be one of the symptom that pruning(Kim et al or Andreasen) is creating some problems. Or I am adding to it very high autocorrelation (unit root). This is what he is referring to I think"But these problematic features are only relevant when parameter values are such that the generated volatility is much larger than what is observed for aggregate data"