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

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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.
40 Bayesian FAVARs with Agnostic Identification Figure 1: Here the convergence is checked for the 2 factors specification. It is obvious that each of the factors have converged as the second half of the median of the factors generated does not deviate from the first half. This can be considered as an indication that the empirical distribution has approximated the marginal distribution of the factors sufficiently accurate.
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