Welfare cost of business cycles

Optimal Policy
12

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 manual)

In the deterministic steady state, these last terms are 0 because shocks are 0 and deviations from steady state are 0. What you are therefore left with is

y_t=y_bar + 0.25 g_sssigma^2

which is related to, but not equal to the stochastic steady state. Thus, what you need to look at in this case is the steady state plus the uncertainty correction. Denoting Welfare with

W

you need to look at

W_pos=strmatch('y',M_.endo_names,'exact');
oo_.dr.ys(W_pos)+0.5*oo_.dr.ghs2(oo_.dr.inv_order_var(W_pos))

which is the Constant
in the display of

POLICY AND TRANSITION FUNCTIONS
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