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Dear all,

I have a linearized Smets&Wouters'07 model estimated on a few undemeaned observed variables, which are coded as (in the case of output):

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dy=y-y(-1)+ctrend;

where dy is not demeaned first difference of log GDP times 100, and ctrend is its long-run growth.

When estimating the model, the smoothed dy is shifted down by a constant 'ctrend', thus it does not coincide with the observed dy.

My question:
1) is that lack of long-run growth in the smoothed variables an expected result?

If 'yes', my concern is that the smoothed y, in contrast to the observed one, is not trending anymore and thus
2) I'm wondering whether the 'output gap = y - y_flexible' is correctly estimated/smoothed (as a difference between two trending variables).
3) Also, shock_decomposition decomposes the variables without constants, so how to decompose the missing constant growth?

shock_decomposition shows the decomposition of the variables around their steady state. As the steady state includes the constant, it is expected that the smoother does not show a trend. Note also that the trend is a constant and does not need to be decomposed as you wrote.