# Income process with linear trend

**URL:** <https://forum.dynare.org/t/income-process-with-linear-trend/3803>\
**Category:** Dynare help (legacy posts)\
**Created:** [1 April 2014 15:08 UTC](https://forum.dynare.org/t/income-process-with-linear-trend/3803 "2014-04-01T15:08:19Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![pjg](https://forum.dynare.org/letter_avatar_proxy/v4/letter/p/e5b9ba/32.png) [@pjg](https://forum.dynare.org/u/pjg)\
**Post date:** [1 April 2014 15:08 UTC](https://forum.dynare.org/t/income-process-with-linear-trend/3803/1 "2014-04-01T15:08:19Z")

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Hi All, instead of the standard way to define an exogenous income process as y=exp(w)_y(-1) where w=rho_w(-1) + e , now I need to generate income as y(+1)=exp(alpha\*(TREND+1)+eta(+1)) where eta(+1)=theta\*eta+e(+1).  
I would like to know how I should include this deterministic trend (TREND). What about if the trend is stochastic?.

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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:** [2 April 2014 08:22 UTC](https://forum.dynare.org/t/income-process-with-linear-trend/3803/2 "2014-04-02T08:22:08Z")

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That means your economy has a deterministic growth rate of exp(alpha). Usually it is best to detrend the model by hand. An example is the RBC\_news\_shock\_model.mod on my homepage, where the economy grows at rate gammax. The basic reference would be King/Plosser/Rebelo (1988).

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**Author:** ![pjg](https://forum.dynare.org/letter_avatar_proxy/v4/letter/p/e5b9ba/32.png) [@pjg](https://forum.dynare.org/u/pjg)\
**Post date:** [2 April 2014 13:42 UTC](https://forum.dynare.org/t/income-process-with-linear-trend/3803/3 "2014-04-02T13:42:50Z")

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thank you so much…