# Second order approximation Schmitt-Grohe, Uribe (2004)

**URL:** <https://forum.dynare.org/t/second-order-approximation-schmitt-grohe-uribe-2004/4619>\
**Category:** Dynare help (legacy posts)\
**Created:** [11 April 2015 18:11 UTC](https://forum.dynare.org/t/second-order-approximation-schmitt-grohe-uribe-2004/4619 "2015-04-11T18:11:14Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![bayes](https://forum.dynare.org/letter_avatar_proxy/v4/letter/b/aca169/32.png) [@bayes](https://forum.dynare.org/u/bayes)\
**Post date:** [11 April 2015 18:11 UTC](https://forum.dynare.org/t/second-order-approximation-schmitt-grohe-uribe-2004/4619/1 "2015-04-11T18:11:14Z")

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Hi! I would like to use the second-order approximation to solve the model and then evaluate welfare using this solution as in Schmitt-Grohe and Uribe (2004). Are there Dynare codes available that replicate results of this paper? I found this page - [dynare.org/DynareWiki/OrderTwo](http://www.dynare.org/DynareWiki/OrderTwo) , however, both mod-files there don’t function.  
I’ve never done welfare evaluation in Dynare and now not sure how I should proceed…

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**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:** [12 April 2015 08:11 UTC](https://forum.dynare.org/t/second-order-approximation-schmitt-grohe-uribe-2004/4619/2 "2015-04-12T08:11:44Z")

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Please be more precise. Which Schmitt-Grohé/Uribe (2004)-paper are you talking about? They have been immensely productive and it’s impossible to identify papers just by the year.

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**Author:** ![bayes](https://forum.dynare.org/letter_avatar_proxy/v4/letter/b/aca169/32.png) [@bayes](https://forum.dynare.org/u/bayes)\
**Post date:** [12 April 2015 15:39 UTC](https://forum.dynare.org/t/second-order-approximation-schmitt-grohe-uribe-2004/4619/3 "2015-04-12T15:39:29Z")

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I was referring to the paper “Optimal Simple and Implementable Monetary and Fiscal rules” [columbia.edu/~mu2166/optimal … panded.pdf](http://www.columbia.edu/~mu2166/optimal_simple_rules/jme_revision_expanded.pdf)

I want to calculate conditional welfare measure - conditional on the initial state being the non stochasic steady state. How could I do this in Dynare in the same way as it is done in the paper I attached, for example.  
Should I then, first, do second order approximation and calculate conditional welfare as welfare = utility + beta\*welfare(+1)?  
If my model is in log-deviations from steadystate, then I would calculate welfare deviations from steady state?

My goal is to compare conditional welfare under different policy rules. Could you please give me some advice on this issue?  
[welfare calculation.pdf](https://forum.dynare.org/uploads/default/original/2X/6/69df4451ea4692be3cbed195810a9db3580c18e2.pdf) (257 KB)

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**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:** [13 April 2015 06:35 UTC](https://forum.dynare.org/t/second-order-approximation-schmitt-grohe-uribe-2004/4619/4 "2015-04-13T06:35:28Z")

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This paper is on my replication list, but still months away. For now, I can only refer you to [[Welfare cost of business cycles](https://forum.dynare.org/t/welfare-cost-of-business-cycles/3802/1))