# Welfare cost of business cycles

**URL:** <https://forum.dynare.org/t/welfare-cost-of-business-cycles/3802>\
**Category:** Optimal Policy\
**Created:** [1 April 2014 09:39 UTC](https://forum.dynare.org/t/welfare-cost-of-business-cycles/3802 "2014-04-01T09:39:55Z")\
**Posts on this page:** 1\
**Showing post:** 12

<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [9 December 2016 11:08 UTC](https://forum.dynare.org/t/welfare-cost-of-business-cycles/3802/12 "2016-12-09T11:08:37Z")

</div>

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\_ss_sigma^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\_ss_sigma^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

```auto
W
```

you need to look at

```auto
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

```auto
POLICY AND TRANSITION FUNCTIONS
```

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