# Log-linearization of Habit Persistence Preferences in a DSGE Model

**URL:** <https://forum.dynare.org/t/log-linearization-of-habit-persistence-preferences-in-a-dsge-model/11686>\
**Category:** Macroeconomic Model Data Base\
**Created:** [17 April 2018 10:16 UTC](https://forum.dynare.org/t/log-linearization-of-habit-persistence-preferences-in-a-dsge-model/11686 "2018-04-17T10:16:00Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Cybueh](https://forum.dynare.org/letter_avatar_proxy/v4/letter/c/b9e5f3/32.png) [@Cybueh](https://forum.dynare.org/u/Cybueh)\
**Post date:** [17 April 2018 10:16 UTC](https://forum.dynare.org/t/log-linearization-of-habit-persistence-preferences-in-a-dsge-model/11686/1 "2018-04-17T10:16:00Z")

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Hi there,

I’m building my own DSGE model with habit persistence preferences.

After evaluation of the steady state, I now want to log-linearize the FOCs (in particular the Euler equation and the labor-supply equation).

 ![Scan](https://forum.dynare.org/uploads/default/original/2X/d/d9e06c9336edfb8bece11b2219131750418235f0.jpeg)

Are there any tricks to do this? Until now, I was always able to do log-linearization but in this case it becomes a bit more complicated. So far, I have written the model part in the dynare-code in non-linear form.

Thank you in advance

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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:** [21 April 2018 10:15 UTC](https://forum.dynare.org/t/log-linearization-of-habit-persistence-preferences-in-a-dsge-model/11686/2 "2018-04-21T10:15:32Z")

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Simply use a Taylor approximation. If you do not feel up to the task, use the nonlinear model. That is less error-prone.

If you prefer the exp()-trick, you may find Fernandez-Villaverde Rubio-Ramirez (2006) “A Baseline DSGE Model” helpful.

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**Author:** ![Cybueh](https://forum.dynare.org/letter_avatar_proxy/v4/letter/c/b9e5f3/32.png) [@Cybueh](https://forum.dynare.org/u/Cybueh)\
**Post date:** [22 April 2018 11:44 UTC](https://forum.dynare.org/t/log-linearization-of-habit-persistence-preferences-in-a-dsge-model/11686/3 "2018-04-22T11:44:58Z")

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Thank you very much for your advise

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**Author:** ![Tavakoli](https://forum.dynare.org/letter_avatar_proxy/v4/letter/t/e480ec/32.png) [@Tavakoli](https://forum.dynare.org/u/Tavakoli)\
**Post date:** [26 July 2022 09:11 UTC](https://forum.dynare.org/t/log-linearization-of-habit-persistence-preferences-in-a-dsge-model/11686/4 "2022-07-26T09:11:13Z")

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Could you please send the final solution?