# Filtered data

Hi all,

I am measuring output gap using standard methodologies (e.g. imf.org/external/pubs/ft/wp/2015/wp1579.pdf). The method (in the most simple form, with a simple filtration) separate the output gap from potential and actual output. However, the gap is given by the difference between potential and filtered values of actual, not the ones I supplied.

I was wondering what is the standard practice here - should I follow this or just take the Dynare values for potential output and then use the real values?

Sorry, but I don’t understand your question. What exactly is the problem and what do you mean with “filtered”?

Thanks Johannes,

By filtered I mean the values coming out of the Kalman filtering procedure, specifically those stored in oo_.SmoothedVariables or oo_.UpdatedVariables (which are identical in my case). I am attaching the mod and data file to make things more clear.
turkey_15.mod (3.86 KB)
turkey_15.m (10.5 KB)

I see. But what exactly is your question?

I want to extract the potential output growth (DY_bar in the code) and the output gap (y in the code). Dynare stores in oo_.Smoothed/UpdatedVariables the product of the Kalman smoother/filter for DY_bar, as expected. As y is defined as y=y(-1)+DY_bar+DY, where DY is actual growth (it is observable), I need both DY_bar and DY to back-out y.

However, in calculating this, Dynare does not use the observed data for DY, but the filtered data (i.e. those stored in oo_.UpdatedVariables) - and the divergence is quite large. Put another way, the problem is that Dynare filters the measured variable excessively. So my question is: should I just take the value for potential growth (DY_bar) as provided by Dynare and backout the output gap (y) using the observable data on actual growth (DY)?

Ok. Now I am totally lost. The “filtered” variable in Dynare is the best estimate given the data up to this point. What do you mean with

?
If you observe the variable, what is the point of using a structural model to extract it from other data? Essentially, you are using a completely different method to reestimate an already observed variable.

I am not explaining myself clearly. Say there are just 3 variables, DY, DY_bar, and y. I have data on DY, and want to estimate the latent variables DY_bar and y using the Kalman filter. The relationship is (roughly) y=DY-DY_bar. However, when giving me the estimate for y, Dynare uses oo_.UpdatedVariables.DY, not the observable DY, which are different (unless steady state growth is set to zero).

Am I doing something wrong regarding estimation? I thought I was supposed to set the observed variables as endogenous.

For observed variables, the UpdatedVariables should be identical to the data as they are perfectly observed and E_t(y_t) is thus known.