Parameter estimation graphs

[gologan]

Hi everyone,

I got some questions about the graphs resulting from the parameter estimation in Dynare:

1. Mode check plots. What can you tell about this graphs? What I see is that the green line corresponds to the log-lik kernel, so it is informative about the importance of the data in the parameter estimation, however, how do I know how much important the data is? Is it related with how the green line fits the blue one (log-post)? The vertical line appears to be the posterior mode, can I tell something else about it?

2. MCMC univariate convergence diagnostics. The red line corresponds to the within chain measure and the blue one to the between chain measure, if parameter estimation went right they are expected to converge at the final iterations. Whats the specific difference between these two kind of measures? Am I missing something important from the graph?

3. Priors and posteriors. I expect that posterior distribution (black line) shows a normal distribution shape and to be different from prior distribution (gray line); also, posterior mode (green line) should be right in the middle of the posterior distribution. What if something of the previous is not happening?

Thank you very much!

[jpfeifer]

A detailed description of these graphs is available in Pfeifer (2014): An Introduction to Graphs in Dynare at https://sites.google.com/site/pfeiferecon/dynare

1. The curvature of the likelihood kernel tells you about the informativeness of the data. If it is completely flat, your parameter is not identified from the data. The difference between the posterior and the likelihood tells you how strongly your prior affects the results.

2. Please have a look at the original Brooks/Gelman article. Looking at within an between chain variances has to do with using overdispersed initial draws, allowing to study whether the different chains converge to sampling the "same posterior".

3. Yes, the shape should be "approximately normal" and the line for the posterior mode should be at the mode. If any of this is not happening, it is often a sign of convergence issues in your chain and/or that you did not start your estimation at the mode. The latter is not a problem if your chain had enough time to converge to the true posterior distribution.

[gologan]

Dear Johannes,

Thank you very much for your response, really clear and helpful.