Partial Model Log-Linearization

Dear All,

I have a question that I hope you can help me with. I am new to this literature, so this may be a dumb question.

Is it acceptable to study a model in which only some equations are expressed in log-deviations, while others are not?
In my case this would imply that some variables will be expressed in their levels in some equations and in their log-deviations in other equations (all the equations will be linear though).

To my, very limited, experience I have never encountered a paper doing this but, for what I want to do, it seems to me to be the only solution.

In case the answer is yes, it is possible to implement this in Dynare?

Thank you very much.


Dear Johannes,

thank you for your quick and helpful reply.

Would you be so kind to direct me towards some studies in the literature doing this? For some reasons I could not find any (all the models I have encountered are entirely in levels or in log-deviations).

Specifically, I am working on a NK model (where inflation is linearized around a zero ss), in which I don’t want to loglin the monetary rule:

R_t=A(Pi_t-Pi*) + B(Y_gap)

The reason is that I want to study the model for different values on the CB’s inflation target (Pi*). As this is constant, I’d loose it in the log-lin version of the monetary rule and I won’t be able to study how the system changes by changing Pi*.
The model also contains equations with multiplicative terms that I think is better to log-lin in order to have a linear system of equations.


I don’t understand your problem here. A loglinearized model equation can still contain constant terms. That is not a contradiction. If you don’t linearize by hand, Dynare will do so (of course keeping the constant).
The reason papers don’t talk about this is that in the end, everything is in log-deviations from a steady state. There is no point in stating the approach to get there.


I think the “non linear” monetary rule you have mentioned is actually already linear. The non-linear version of that monetary rule is

R_t = (Pi_t / Pi*)^A times (Y_t/Y*)^B

Take the log of this and you have
ln (R_t) = Aln(Pi_t - Pi) + Bln(Y_t - Y)

If R = 1 + r and Pi = 1 + pi are gross terms with r and pi sufficiently small (less than or equal to 10%), then ln R = r, and ln Pi = pi so that the above is actually

r_t = A*(pi - pi*) + B*yhat.

My guess is that some of the other “non-linear” terms you mention are actually already linear if you look really closely.