Dear Johannes,
In my DSGE model, I have a sentiment/mood shock with a prior mean size of 0.1 while the remaining shocks sizes’ prior mean are all set to 0.01, because this sentiment/mood shock is highly volatile. I have also formulated a DSGE-VAR model derived from the DSGE model (utilizing the artificial observations from the DSGE model to formulate priors for VAR model), I have generated impulse responses from the VAR model, my question is in interpreting the impulse responses of the sentiment/mood shock in the DSGE-VAR model, does the sentiment/mood shock in the DSGE-VAR model should also have much larger variances (e.g. around 0.1) in comparison with other structural shock in the DSGE-VAR model?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse
I am not sure I understand the question. You seem to be asking about the posterior variance of the shocks in the DSGE-VAR. That will be a combination of the prior and the likelihood of the data. So unless the prior is completely driven out by the data, you would expect the prior to exert a role. Moreover, if you prior captures actual information on the shock, it should not be too different from what the data tells you. So yes, the variance should be larger for that one shock.
Dear Johannes,
The sentiment/mood shock in the underlying DSGE model has a prior variance of 0.1, which is 10 times larger than prior variance size 0.01 of other structural shocks, and also a larger posterior variance for sentiment/mood shock, does this information of larger variance of sentiment/mood shock be captured by artificial observations? So could the DSGE-VAR prior based on artificial observations reflect the information of larger variance of sentiment/mood shock? And in turn generate impulse responses where standard deviation of sentiment/mood shock is about 10 times larger than the variance size of other structural shock in the DSGE-VAR model?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse
This has nothing to do with the DSGE-VAR setup. If priors are informative (regardless of where they come from), they will still affect the posterior (unless there are infinitely many observations).
If prior and posterior are almost identical, it can mean that i) the prior very well reflected the truth or ii) that the data is not very informative.