Number of observables much less than number of shocks

Estimation ML/Bayesian estimation
1

Dear Johannes,
First thank you for your previous guidance, I am grateful.
I have a question in estimating DSGE models, I know the general rule is that the number of observables should be smaller than or equal to the number of structural shocks. I would like to know that if the number of observables is 8 and the number of structural shocks is 12, the dynare program can be run, but do you think there will be identification or inefficiency problems? is there any general rule about the minimum number of observables to identify structural shocks?
Thank you and look forward to hearing from you.
Best regards,
Jesse

2

Hello Jesse,

in general I do not see a problem in doing what you have described. Unfortunately there is no rule, at least that I am aware of, for the ratio of observables to shocks. You would have to check identification (with the identification-command) for the parameters you are interested in and potentially adjust the number observables in case of poor identification.
If, as you say, it runs and you can identify all parameters of interest you should be fine.

Best

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3

@DoubleBass is correct. There are two technical restrictions:

  1. You must have a sufficient number of shocks to prevent stochastic singularity.
  2. All processes you add need to be identified (which you can check in Dynare).

Weak identification is more tricky as there is only so much you can do about it.

But generally I would approach this from an economic instead of a technical perspective. You have a particular model at hand including a given number of structural shocks. Now you want to estimate the parameters. Usually, you want to use as much data as possible as this will provide the most accurate information. For that reason, you may want to avoid using the “minimum number of observables”.

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