Comparing model to real data


I am new to the DSGE models literature and Dynare, so probaly my question is trivial. My aim is to compare the Smets and Wouters (2007) model to real data in terms of correlations among variables. Now, to my understanding, the simulated data from the model are log-linearized- real-world data,instead, are in levels. How do I make the two datasets homogeneous for comparison? My idea is to take the log of real-world data and filter them with a band-pass filter (and filter the simulated data as well). The problem arises when I have to take the log of the inflation rate and the real interest rate that in many cases are negative. Maybe I could try to reconstruct the model’s variables in levels, but this looks quite complicated, if not infeasible. If you could suggest a solution to this issue, I would be very grateful.

Thank you a lot.

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The Smets/Wouters uses first differences for estimation. So the best approach is to use the same filter, i.e. compare growth rates in the data to growth rates in the model. The exception are stationary variables like inflation and the interest rate. Here, you don’t need a filter at all. Also note that SW use net inflation and interest rates, so the result is already in percent. There is no point in logging them.

Thank you , I think I understand now.
Best regards