Interpretation of Bayesian DSGE mode check plot / posterior graph

Estimation ML/Bayesian estimation
1

Dear All,

See attached two figures from my Bayesian estimation of a fairly simple DSGE model. The model is estimated on data simulated from the model, and all the parameters seem to be estimated pretty well, with the exception of rhob. For the first figure, mode_check, I have one question:

(1) For the alpha and tp parameters, I don’t see the log-posterior. Is this because the log posterior is exactly on top of the log-likelihood?

For the second figure, spike_alpha, I have two questions:

(1) Is it worrying that there is such a large spike in the posterior of alpha? The spike is exactly at the actual value of alpha (remember this is using simulated data), but still it seems a little strange to me.

spike_alpha

mode_check
mode_check.png1106×836 45.6 KB

I have also attached the dynare code that generates these graphs.

All the best and thanks,
Jake

testy.mod (5.7 KB)

2
  1. Yes the posterior is on top of the likelihood.
  2. No, the strong peak for alpha is no reason to worry. It simply shows the parameter is well-identified in the data.
  3. There is a problem with rhob. You can see the likelihood is flat. That means the parameter is not identified. This explains why prior and posterior are the same.
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