Measuring the Effects of a Shock to Monetary Policy - Humboldt ...

16 Bayesian FAVARs with Agnostic Identification
4 The Econometric Framework
4.1 FAVARs
As already stated, the idea behind the FAVARs is to combine the standard structural
VAR analysis with the recent developed and advanced features of dynamic factor models
estimating a joint VAR that contains factors extracted from large panel of informational
data and in addition perfectly observable time series that have pervasive effects on the
economy such as the short-term interest rate set by the central. Therefore BBE labeled
the model in a straight forward manner ”factor-augmented VAR”. This approach is well
suited for structural analysis such as impulse response analysis and variance decomposi-
tion (in particular for the problem at hand). For the estimation procedure the model has
to be cast into a state-space representation. For the rest of the thesis I will mostly follow
the approach and notation of BBE otherwise explicitly stated.
The model consists of the two equations (1) and (2) introduced in the previous section.
The FAVAR equation (2) already has the form to build the state equation to which one
also refers often to as the transition equation. Equation (2) represents the joint dynamics
of factors and the observable pervasive variables (Ft, Yt).
⎡
⎢
⎣ Ft
Yt
⎤
⎡
⎥ ⎢
⎦ = Φ(L) ⎣ Ft−1
Yt−1
⎤
⎥
⎦ + vt
(3)
vt ∼ N(0, Q) (4)
Here the variable Yt denotes the [M × 1] vector of observable economic variables
that having pervasive effects throughout the economy. The index t = 1, ..., T represents
the time the term Φ(L) represents a conformable lag polynomial of order d. In our
specification that follows BBE Yt is assumed to represent the policy instrument,e.g. the