Log-linearization of Habit Persistence Preferences in a DSGE Model

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).

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

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.

Thank you very much for your advise