Higher order Perturbation in dynare (or dynare++)

I wonder if there are papers using higher-order (4th or higher) perturbations in dynare, and more importantly, when that is necessary.

Currently, I have a mod file that can run 1-4 th orders with no problem, and the numerical discrepancy is not large once order >=2.

However, for the 5th order, the dynare does converge but the simulation using its policy function also explodes. Unfortunately, the pruning option does not seem to work for order >=4


That is usually necessary for papers with a lot of curvature, most prominently asset pricing papers. Rudebusch and Swanson have a couple of papers like that, if I remember. One of my own papers also used fourth order as a robustness check: https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Born_Pfeifer_2020

You are right that pruning is not implemented at order>3 yet. See https://git.dynare.org/Dynare/dynare/-/issues/1643

There are papers out there arguing that you don’t even need pruning if the approximation order is high enough.

For a reference on when higher-order solutions are necessary I suggest the introduction of the paper:

Levintal, O. (2017). Fifth-Order Perturbation Solution to DSGE Models. Journal of Economic Dynamics and Control, 80, pp. 1 - 16

In the introduction of this paper, the author gives a quick review of the main cases where higher orders solutions are necessary: welfare concerns, stochastic or time varying volatility, disasters risk and asset pricing (as indicated by Professor J. Pfeifer). Levintal (2017) gives extensive references for each case. Therefore, if your model lies inside in some of these cases or if you are particulary interested in precision you should consider higher order solutions.