Marginal likelihood of model with KNOWN distribution of parameters

Estimation ML/Bayesian estimation
1

Dear all,

I understand dynare calculates and reports the marginal likelihood after Bayesian estimation. However, is there any way it can calculate the marginal likelihood of a model where the distributions of model parameters are known ?

Eg suppose I estimate a simple three-equation model with an IS curve, a Phillips curve and a Taylor, and Dynare reports the marginal likelihood to be 100… How can I calculate the likelihood of a model variant with a different Taylor rule (while keeping the IS and Phillips curves to be exactly the same) WITHOUT re-estimating all the model parameters? Eg example, a variant that allows interest rate to react on inflation only, such that the parameter on output gap is set to zero…

Any advice would be very appreciated. Thank you!

Regards,
Zhirong

2

I am not sure the question makes sense. The marginal data density computes the density of the data, given the model
p(Y|M)
When doing so, it integrates over the prior parameter distribution. What you seem to be after is keeping a posterior distribution fixed, which does not work.

3

Dear Johannes,

Many thanks for your explanation. Yes, it makes a lot of sense now!

Kind regards,
Zhirong