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

Bayesian FAVARs with Agnostic Identification 39
Before presenting the main results such as the plots for the impulse responses I provide
the plots that show whether the chains of the single factors of the Gibbs iteration converge
or not. There are several convergence criteria that can be applied to check the convergence
of the algorithm for different starting values. To assure convergence of the Gibbs algorithm
I also imposed on the one hand, the proper priors BBE imposed. They are reported in
section (5.3) on Inference. The task of convergence diagnostics is an important one, but
its formal implementation would have gone beyond the scope of this thesis. I decided to
choose a less formal method where the first half of the median of the Gibbs sampling draws,
of a single factor, are plotted against the second half after having discarded sufficient initial
draws of Gibbs sampler in order to avoid the influence of the initial conditions. If the
second half does not deviate too much from the first half, one might conclude as a first
check that this single chain has converged. It is straight-forward that the convergence
of the Gibbs chains should be checked for different starting values in order to assure the
convergence of the respective Gibbs iteration with the respective specifications such as
the number of factors, the number of draws, the number of initial draws to be discarded
and so forth. Convergence has been tested for different starting values. The Figure 1-3
provide provide the results for the single chains and the single factors.