Question on Liu,Wang and Zha(2013) and shock_decompostion

Hi Prof,
I’m trying to replicate Liu, Wang and Zha (2013, Econometrica). But I don’t quite understand Figure 5 in their paper. How are the two lines obtained?

  1. In their paper, the black solid lines are observables. So we can easily get them in dataset. But What if black solid lines are non-observables, say GDP or interest rate? Should I use smoothed variables?

  2. How are the red thin lines obtained? Through shock_decomposition command or some other options?

  3. If these lines are obtained through shock_decomposition, then why they start at the same point in 2006Q1?

Thanks in advance!
Here are Figure 5.

and the paper LWZpaper-2013-Econometrica.pdf (497.9 KB)

  1. The black lines are the smoothed objects. If the variable is observable, it will coincide with actual values.
  2. The red lines are the result of a model simulation with all shocks turned off except for one. The shock_decomposition-command should give you this if you consider only the contribution of one shock.
  3. It may be a coincidence that the starting point matches (or a normalization). Without seeing the codes it is impossible to tell.

Thank you so much, Prof!