Hi,
I am trying to replicate Bernanke, Boivin, Eliasz's (2005) FAVAR model but with factors extracted by principal components.
When treating the federal funds rate as an observable factor and identifying the monetary policy shock recursively, BBE run a regression of the factors extracted from all informational variables on factors extracted from slow-moving variables and the federal funds rate (Rt). The factors extracted from the slow-moving variables represent an estimate of all the common components other than the FFR.
Why does this have to be included in this regression? I do not fully understand footnote 20:
"Note that the other common factors will in general be correlated with Rt. For instance, in terms of our illustration in Section II, the policy instrument Rt is correlated with the other variable of the model, i.e., (Pi_t y_t y^n_t s_t), which could all be unobserved. As a result, the residuals from a regression of Cˆ(Ft,Yt) on Rt would not be appropriate." (Yt includes Rt only in their baseline specification)
Especially the last sentence confuses me because the slow-moving variables are assumed to react to the Rtwith a lag only. If I understand it correctly, subtracting the Rt part from Cˆ(Ft,Yt) should yield the space spanned by both Ft and Yt minus the marginal effect of Yt corrected for its correlation with the slow-moving variables. But why does this matter if the slow-moving factors react with a lag anyway?
Any help to get my head around this intuitively would be very much appreciated. Thanks in advance!