Welfare analysis, logs-exp() and pruning


I have a model expressed in logs (using exp()) instead of levels and it is initially estimated in 1st order and it works properly.

The thing is that because i wan’t to make a welfare analysis, from what i have read, i need a 2nd order approximation to both the equilibrium condotion and the welfare criterion, so i try to proceed with 2nd order approximation.

Is it correct to apply it even in logs (leaving the exp()) in each variable or do i need to remove them and have the variables appearing in levels, recalculate the stady state and proceed with the 2nd order approximation?

Finally, in case i apply 2nd order approx. in log variables {exp()} and then because the IRFs are explosive, use Pruning would that be wrong for welfare analysis? My point is that whether Pruning is compatible with welfare analysis.

Kind regards

Doing the approximation in logs for welfare analysis is actually standard and not a problem. Pruning is a different issue. I am not aware of any analysis comparing welfare in a pruned and a non-pruned state space.There is indeed some tension when doing welfare analysis in a non-pruned state space and then turning on pruning for IRFs. But my reading of the literature is that this is quite standard.


Thank you very much for your help.