# NK Model w/ non-linear FOC -- trend inflation and price level

**URL:** https://forum.dynare.org/t/nk-model-w-non-linear-foc-trend-inflation-and-price-level/16255
**Category:** Replication Attempts
**Created:** [14 July 2020 07:02 UTC](https://forum.dynare.org/t/nk-model-w-non-linear-foc-trend-inflation-and-price-level/16255 "2020-07-14T07:02:48Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![jth](https://forum.dynare.org/letter_avatar_proxy/v4/letter/j/67e7ee/32.png) [@jth](https://forum.dynare.org/u/jth)
#### Post date: [14 July 2020 07:02 UTC](https://forum.dynare.org/t/nk-model-w-non-linear-foc-trend-inflation-and-price-level/16255/1 "2020-07-14T07:02:49Z")

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Hi everyone,

I was looking at Johannes Pfeifer’s mod file for the baseline NK model with non-linear first order conditions (github link posted below).

The model has zero steady state inflation and I want to modify it to incorporate trend inflation. I know that this requires modifying some of the FOCs and several equations in the steady state block. My question is in regard to the price level equation

> Pi=P/P(-1);

With no zero steady inflation the static equation will not have a residual equal to zero. I have modified this equation to

> Pi/steady\_state(Pi)=P/P(-1);

where now the static equation has a zero residual. **My question is whether this is correct or there is another way to write this equation when inflation does not equal zero in the steady state?**

Any comments or examples of a small nk model with trend inflation would be much appreciated!

[https://github.com/JohannesPfeifer/DSGE\_mod/blob/master/Gali\_2015/Gali\_2015\_chapter\_3\_nonlinear.mod](https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_3_nonlinear.mod)

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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: [15 July 2020 07:57 UTC](https://forum.dynare.org/t/nk-model-w-non-linear-foc-trend-inflation-and-price-level/16255/2 "2020-07-15T07:57:50Z")

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You need to be careful here. With trend inflation, the price level P will have a unit root with drift so that no steady state exists. For that reason you should only have inflation rates in your model.