How to choose the best DSGE model

Dear all:
I consturct several DSGE models, each one use different fiscal policy rule or monetary policy rule, and I want to know which policy rule is the best for this economy, in other words, I need to choose one model which can fit the economy data best, how to choose?
When I read papers, I found someone choose the model according to “marginal data density” this index, but I don’t know how to get this index from the dynare run results, or how to compute this index.
Hope for your reply. Thank you very much!

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You need to choose an objective function according to which you judge the performance of your model. If you want to use the marginal data density, you need to estimate your model using Bayesian techniques.

Thank you for your reply! Acoording to Bayesian estimation results, I can get the " Log data density" value, is this value the same as marginal data density?
Looking forward to your reply!

Thé log data density is the log of the marginal data density. Since the logarithmic functtion is stricly increasing, the rankings are the same.


I see, this really helps me a lot, thank you very much!

Note that there two ways to compute it: via a Laplace approximation and via the modified harmonic mean. Ideally, the ranking should be the same regardless of the method you use.
Note also that the data needs to be the same across models compared and that the prior needs to integrate to 1 (see e.g. Model Comparison Bayesian Estimation (again))

Thank you very much !