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Bayesian FAVARs with Agnostic Identification 19
the statement that more data necessarily means more information and hence better for
the analysis seems not to be the end of the story.
The dynamics of the ”informational” variables is assumed to be like the following:
X ′ t = Λ f F ′
t + Λ y Y ′
t + e ′ t
(5)
et ∼ N(0, R) (6)
Here Λ f denotes the matrix of factor loadings with dimension [N × K] and Λ y is
[N × M]. The error term is et with mean 0 and covariance R. Note that et and vt are
independent and that R is diagonal which means that the error terms of the observable
variables are mutually uncorrelated. At this point one has to make a clear stand which
assumption one follows when it comes to the issue of error correlation. One can think
of the error terms to be weakly correlated or completely uncorrelated. We had this
previously in the discussion of exact or approximate dynamic factor models. The standard
assumptions in the literature with respect to dynamic factor models has been introduced
in the previous section. As we follow the Bayesian likelihood-based approach we decide to
set the assumption of uncorrelated error terms. Hence we model an exact dynamic factor
model in the vein of Sargent and Sims [1977]. The distinction between the observation
equations of the DFMs we have seen so far and (1) is that there, the dynamics of the data
are supposed to be driven by Ft and Yt which in fact can be correlated. Here Xt only
depends on the current and not lagged values of Ft. BBE state that this implication is
not restrictive in practice as the factors can be interpreted as including arbitrary lags of
the fundamental factors.
4.2 FAVAR Identification
Identifying restrictions have to be set, in order to distinguish the idiosyncratic from the
common component. Additionally one can set further identifying assumptions in order to