What are main reasons a typical DSGE model is called non-linear? Why are these non-linearities important? Is a non-linear model inherently less stable than a linear model? Why?
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They are called non-linear because they often consist of non linear equations (although linearized approximations exist).
No matter what kind of empirical research you are doing it is important to avoid misspecification. If relationships are non-linear it’s not appropriate to try to fit an linear model which identifying assumption requires linearity. If you would do so your parameter estimates would be biased.
There is nothing inherently unstable about non linear processes. In the context of DSGE models dynamic stability implies there should be no unit root in the modeled series. There is no reason why non-linear series would be more prone to have unit root than linear one.
answered Mar 16, 2020 at 23:07
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$\begingroup$ Thanks for your answer! However, In Carl Hommes 2015 book on Expectations, it seems he considers DSGE models (being it either RBC DSGE or New Keynesian DSGE) to be linear, or (log)linearized models, on page 3 of the introduction. He is making a distinction between the non-linear view and the random exogeneous shocks view (with a linear economic model), with both DSGE models and old Tinbergen models being examples of the latter, if I read his paragraph correctly. What are your thoughs about this? $\endgroup$ Commented Mar 20, 2020 at 13:51
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$\begingroup$ @BeckBatucada as mentioned in my answer linearized approximation exist. Non-linear models also assume often random exogenous shocks so I am not really sure exactly what you mean by that I would have to read the whole passage. Both RBC and New Keynesian non-linear versions exists as well. $\endgroup$– 1muflon1 ♦Commented Mar 20, 2020 at 14:12
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$\begingroup$ yes exactly what I though: exo shocks are combined with non-linear models in DSGE approach maybe I'm misreading Hommes writings $\endgroup$ Commented Mar 20, 2020 at 14:25