How to set welfare loss function in OSR?

[litmuszhu]

I build a model who contains two production sectors. Then I want to use OSR to find some optimal monetary policy. I have to derive the welfare function which contains output gap and inflation. Because I have two production sectors. It is so complex to derive the output gaps and inflation dispersion. But I set log consumption in utility function. So in second order approximation the welfare function contains only variance of labors. I wonder if I could just put variance of labor in the welfare loss function in OSR instead of deriving deriving complex output gaps and inflation dispersion. Thank you!

[jpfeifer]

Your welfare function just needs to be correct. It does not need to be in terms of output gap and inflation. This is often just a convenient and intuitive representation.