AR(1) shock why log?


That might be a very basic question. For AR(1) shock, why we take log format?
Like in technology shock: log(A)=rhoaA*log(A(-1))+eA;

Thanks for your help!

Hi Fabian

We do it because it is convenient and because that’s how Dynare can run things.
In your example, A_t is a stationary log-normal process, with steady-state equal to 1. And it usually enters a non-linear model multiplying a production function. When you put it in log terms, \log(A) becomes normally distributed with zero steady-state.

In Dynare you have to assume that all shock processes have normal distributions (in your case, e_A is assumed to follow a normal distribution)). Sometimes this normality has to be achieved by means of transformations. As a final comment, when going to 2^{nd} order perturbations, part of this log-normality is preserved.

I would argue it’s not about the computer implementation. Rather A cannot be negative and it is convenient to specify a process in percentage deviations.

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