I am running a Bayesian estimation of my model with a wide range of shocks (initially I wanted to only calibrate the model so everything was OK). Afterwards, with the estimated parameters, I’d like to perform a second order approximation the model where the latter will be “calibrated” with the posterior mode parameter values. And I am basically coming across the issue of cost-push shocks. Since I am using them in the estimation procedure, I presume I’ll have to include them also in any subsequent welfare analysis. However, the NK Phillips curves (both price and wage ones) cannot be really derived in a non-linear form with time-varying markups from what I see on this forum due to the infinite sum story.
My question is then whether it would be a huge sin if I skip these shocks in the subsequent welfare analysis (I am putting them only for the purposes of estimation, otherwise I don’t really need them and the focus of what I’m doing is by far not on them).
I know it would be great if I can estimate a full non-linear model and have the welfare variable in the code during estimation but that would lead to estimation with a particle filter which I’d like to avoid for now.