Filtered data

Hi all,

I am measuring output gap using standard methodologies (e.g. 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.