Unconditional versus conditional Welfare measure

[RaffaelRusso]

But Professor Johannes, isn’t what you just said the same as Valerio said in:

Welfare cost of business cycles

Dear Professor Pfeifer, I read this post and other discussions on this topic but still there is something that is not clear to me. I would like to do a very simple exercise, that is to find the parameter of a policy rule that maximizes conditional expected welfare, defined as Welfare = U + \beta*Welfare(+1) where the condition is being in the deterministic steady state in the first period. Moreover, the parameter has no impact on the deterministic steady-state. I am using a 2nd order approxima…

Back there you said this is a wrong way of computing conditional welfare as we can see in:

Welfare cost of business cycles

Dear Valerio, that would not be correct. Because when you simulate without shocks, you end up at the stochastic steady state, which is different from the deterministic one where you want to evaluate welfare (except for first order). At second order, the policy function for welfare (defined in the model recursively as W_t=U+beta*W(+1) or something similar) will have the form y_t=y_bar + 0.25 g_sssigma^2 + terms that depend on shocks and deviations from steady state (see section 4.13.4 of the man…