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How did Bernanke et al obtained IRFs of variables not included in their baseline FAVAR model?

Economics Asked on July 15, 2021

In the original FAVAR paper by Bernanke et al, how did the authors obtain the IRFs of industrial production (IP) and CPI in their baseline model (as shown in figure 1)? Their ‘preferred’ baseline FAVAR model include only one observed variable $Y_t$ (i.e., FFR) and three unobserved factors. They write their baseline model as follows: Baseline (Y = FFR, k = 3).

If I have data on FFR and the three factors and I estimate a standard VAR with these 4 variables, ordering FFR last. How is it possible to get IRFs of IP and CPI which are not explicitly included in the model?. I guess I am missing something which I cannot see.

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