HP-Filtered simulation of log-linearized model

[cmarchionatti]

Hello. I am using a calibrated log-linearized model and comparing its moments to HP-filtered log data.

The model steady states are all set to zero.

I wonder if should we apply the HP-filter to the simulations of the model or not, since they are already log deviations from the steady state?

Or the need of HP-filter the simulation series is for log-linearized model with steady states different from zero?

Thanks!

[cmarch]

Hi cmarchionatti,

See @jpfeifer’s explanations in the following thread

Comparing model with data after log-linearization

Why do you get zeros? For the mean, that is expected. If it happens for the standard deviations, there is something wrong/odd. To compare model variables in percentage deviations to the data, you need to obtain empirical data in percentage deviations from a trend. The easiest way is using the theoretical HP filter on the loglinearized model variables and comparing them to HP-filtered logged empircal data (see Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE…

[cmarchionatti]

Hello cmarch!

I saw it already, however I did not understand why to HP-filter the log-linearized model simulations, since they are log-deviations from the steady state values (which are all zero in my model).

Perhaps it is just for log-linearized models that have non-zero steady states… what do you think?

I will wait for Professor Pfeifer answer to be sure as well.

Thanks a lot!

[jpfeifer]

It’s not about the mean, but the frequency components. If you consider your model to be the data generating process that created the empirical data, then a meaningful comparison involves using the same filter for both the model and the data.
But there is an alternative approach that wants the DGSE model to just replicate the filtered data.
See e.g.

One side HP-filter and model fit to real data

This is clearly not my preference, but you can estimate your model on HP-filtered data. In that case, you treat your DSGE model as the data generating process of the filtered data. It is not supposed to reproduce the characteristics of the original unfiltered data.