3rd order perturbation and volatility of consumptoin

[sfaf]

Thanks a lot, Though, Initial response in consumption is lower at higher risk aversion. But decreasing risk aversion from 2.5 to 2 decrease volatility of consumption by 47%. I think, using pruning option is also adding more persistence. As without pruning option, decreasing the value of risk aversion parameter does not make any significant change in the volatility of consumption. (almost same).

Second question is related to pruning which I discussed earlier.

Basu_Bundick_2017

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.

I want to a bit dig deeper now to see how pruning is creating persistence. How can I do so? I think, starting point would to look into state space model? But which variable I need to look into? How can get access to state space of model in 3rd order.

Thanks a lot.