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

Bayesian FAVARs with Agnostic Identification 13
procedures. Stock and Watson [1989,1991,1991,2001,2003,2005], study a static version of
the DFM estimated via principal component analysis. In the proceeding papers they
consider a two-step estimation procedure. Forni,Hallin,Lippi and Reichlin (2001), provide
a dynamic version of the PCA which is known as the generalized dynamic factor model
(henceforth GDFM). Some refer to it also as the dynamic principal component analysis
(DPCA) where the model is considered in the frequency domain. Kim and Nelson (1998),
Otrok and Whiteman (1998) tackle the model estimation from a Bayesian perspective
via Markov chain Monte Carlo (MCMC) simulation methods, in particular applying the
Gibbs sampler. This will be the approach I apply in my thesis in order to extract the
factors and do inference on the models parameters. One of the most recent advances
have been the so-called factor augmented vector autoregression (FAVAR) which has been
introduced by Bernanke and Boivin [2003], and advanced in Bernanke, Boivin and Eliasz
[2005], a framework in which the advantages of DFMs are combined with the analysis of
SVARs. The various model specifications and estimation procedures of large data sets on
which the FAVAR builds are briefly explained in the following subsection where I provide
an overview of the most important and influencing ones and briefly explain the different
approaches.
Dynamic factor models can be considered either in the frequency domain representa-
tion or in the state-space representation depending on the estimation approach desired.
The model cast in the frequency domain representation are introduced and explained
in several papers by Forni,Hallin,Lippi and Reichlin. They use an approximate DFM,
and compute the eigenvector-eigenvalue decomposition of the spectral density matrix fre-
quency by frequency and inverse-Fourier transform the eigenvectors to create polynomials
in the lag operator which when applied to the observables, yields estimates of the dynamic
principal components (DPCA).
The latter is a generalization that captures all time series models, such as the au-
toregressive integrated moving average model (ARIMA), and consists of one observation