Optimal policy in a model with stochastic volatility shocks

Dear all,

I’m working on a model with one stochastic volatility shock and I have a doubt about it. I would like to know if -in this context- is possible to run a simple and implementable optimal policy analysis, like Schmitt-Grohé and Uribe. In other words, getting the best simple monetary policy rule under the volatility shock using consumer’s welfare criteria.

I’m not sure if I should to asses the model with the welfare function using just a second-order expansion (like is common) or with the third order, necessary for getting the impact of this kind of shocks on the economy.

Do you have any ideas or, maybe, a paper about this kind of analysis? I will appreciate any help.



I haven’t seen a formal proof of this, but a second order approximation should not give you the correct welfare ranking as the effects in the laws of motion are already of second order. Third order seems to be the minimum requirement, but you may need to go even higher. Have you searched for papers already doing this?