Impulse Response Functions deterministic setting non-linear model

Hey everyone,

I am currently trying to compare the linearized solution to the non-linear solution of a model using the impulse responses. The non-linear solution is computed in the deterministic setting and the model is written in the exp() and log() form. I want to convert the Impulse responses from the non-linear deterministic setting to the linearized version. Am I right to assume that I have to substract the steady state from the non-linear impulse responses (which are in log-levels) in order for it to be comparable to the linear solution? Help would be greatly appreciated :slight_smile:

Have a nice weekend

Hey everyone,

I know this may be a stupid question, but I just want to make sure I am on the right track

That very much depends on how you programmed the IRFs for the nonlinear setting. An IRF is in deviation from the initial state. So if you still have to subtract it, you did not compute an IRF, but only a simulation with shock.
The easiest way out is usually to define an auxiliary variable that is defined in deviations from steady state and look at that one:
where y is the log level.

Dear Mr. Pfeiffer,

thanks for your response. As usual you were very helpfull. We defined initially defined the variables as log levels and then ran the perfect foresight simulation. Afterwards we substracted the steady state (which is given in logs due to the exp() notation). Since we substracted the steady state from the log-level the IRFs resulting from that should correspond to percentage deviations from steady state (i.e log differences). It turned out that doing it this way lead to very similar if not exactly similar impulse responses for almost all of our variables when comparing the IRFs for the linear- and non-linear (perfect foresight) model. Only for some variables there are remarkable differences, which are (as far as I know) to be expected since price dispersion and capital adjustment costs are constant to a first order approximation.

I am just asking to make sure, that the deviations we got (i.e a much larger increase in the leverage ratio) are due to the non-linearities of the model and not some misscalculation when calculating the IRFs.

No, what you do sounds right.

Thank you very much. I just wanted to make sure that I did it right and my results are reliable.

Have a good day!