Can we do welfare analysis after log_linearizing?

[zhanshuo]

Dear all ,I have learned that we can do welfare analysis using a recursive definition of welfare like Welfare = Util + beta*Welfare(+1).
But this is based on the first order condition of the model, without log-linearizing it.
But it is often hard to calculate steady-state values of all the endogenous variables and log-linearizing it will make it easy.
Here comes the question, Can we do welfare analysis after log_linearizing?
If could, would you give us some example papers?
Thanks

[jpfeifer]

The general answer is no, you cannot do this. Due to certainty equivalence, stochastics will not affect the welfare ranking. In some cases, you can do a naive linear-quadratic approach, but generally, full second order is required. See Woodford (2002): "Inflation Stabilization and Welfare" for a thorough discussion