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I beg your pardon.

1. Say you have some non-stationary real data and you do not HP filter it. You run an SVAR in levels and compute IRFs. Say you want to reproduce these IRFs in a DSGE model. You then model technology with a stochastic drift (unit root+long-run trend+exogenous shock).

Should you normalise the nominal variables to able to properly compare the model IRFs (once the model is solved) with the real data ones or not? It appears to me that you should not, because the real data was kept non-stationary; is that not the case?

2. Is it appropriate to run the real data SVAR in levels rather than in log-levels, since one intends to compare it to a DSGE model which is in percentage deviations (as explained)? Papers seem to have done this. What do you think?

Thank you.

1. I still do not understand what your question is. How do you jump from nominal to real variables? Also, you seem to be confusing stationary IRFs around a long-run nonstationary trend with the nonstationary trend movement itself.

2. No, that is not appropriate and I have never actually seen people run VARs in levels. They all use log-levels (even when they often refer to it colloquially as "levels").

2. OK for the colloquial use of levels; thanks.
1. All I mean is: if you have non-stationary data IRFs are you supposed to de-trend your DSGE model if you want to obtain the same (NS IRFs) there too?

Dear Johannes,

is there any alternative to the use of HP filter when comparing model variables to the data? Is any other transformation practically used?

There are two other filters in practical use

• First differences
• Baxter-King filter

Thanks! Another question, are the lecture slides from your course that you referred to in this topic available somewhere online? Or is it possible to get them from you..?

No. If you send me an email, I can send the respective chapter to you.

@AS90: You need to be more precise. What are

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non-stationary data IRFs?

Are the IRFs to temporary shocks estimated on non-stationary data? Or are the IRFs non-stationary, i.e. they show permanent effects of a temporary shock?

Thanks, sorry for the hiatus.

Yes, the first one you wrote. Non-stationary data IRFs: the IRFs are estimated on non-stationary data.
Hence, is one to de-trend his DSGE model anyways if willing on reproducing said IRFs theoretically?

In that case, you have to work with a detrended model and make sure the data are correctly matched to the stationary model variables. For example, you can use an observation equation with first differences. See Pfeifer(2013): "A Guide to Specifying Observation Equations for the Estimation of DSGE Models" https://sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.

Thank you. That paper is very useful, you had already notified it to me. But, right because of the indications therein, what I asked was: what if you do not want to render the data stationary? That is, what if you wish to reproduce IRFs estimated on non-stationary data: should you still de-trend your DSGE model or not? By logical rigour you shouldn't, right?

In a sense, the data is still non-stationary if you use first differences as you are using an invertible transformation. But if you follow Canova's most recent arguments, you should not be treating your data. However, that massively restricts what you can do in estimation. The reason you need to stationarize your model is that you need to have a well-defined approximation point for log-linearization/Taylor approximation. Thus, you have to use a mapping of the non-stationary data to the stationary model. If you find a way to use a non-stationary model, you might be able to get around this, but I am not aware of any decent way to achieve this.

True and elucidating. Thanks.