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

12 Bayesian FAVARs with Agnostic Identification
among others). In the next subsections I am first going to explain DFMs on which the
FAVAR methodology grounds. Then I explain the FAVAR and the required identification
assumptions in order to identify the factors and factor loading separately. The last sub-
section elaborates on the estimation procedures and in particular on the likelihood-based
joint estimation.
The classical (static) factor model applied only to cross-sectional data, was first set in
a dynamic setting and introduced to economics by the seminal work of Sargent and Sims
[1977] and Geweke [1977]. Sargent and Sims [1977] applied DFM to a low dimensional set
of macroeconomic variables in order to explain the mutual comovements. The dynamic
factors parsimoniously summarize the dynamics and information of a large panel of data.
Due to the small dimensionality of the data the estimation could be accomplished by
maximum likelihood estimation methods (MLE). The MLE will soon arrive at its limits
with increasing number of time series. Quah and Sargent [1993] apply the EM algorithm
for a set of 60 variables which is the biggest application considered in a MLE framework.
Due to the complicated nature of the shape of the likelihood in a high dimensional case
it becomes soon infeasible to apply ML methods. Stock and Watson [1998,2001] show
that factor 14 extracted from eight 15 macroeconomic variables, improve the forecasting ac-
curacy of inflation. Their results outperform the standard AR approach but only in a
supportive manner for the real variables except for employment. Since then DFMs have
gained an increasing attention in the academic world of empirical macroeconomics and
seem to become an important alternative to the VAR, which is still the ”workhorse” in
empirical macroeconomics and most widely applied.
Important extensions and advances have been achieved especially w.r.t. the estimation
14 The authors sometimes refer to the factors as diffusion indexes that summarize the inherent risk of
the variables considered
15 In their first paper the consider four variables and extend there data and variables in Stock and
Watson [2001]