I was conducting a model comparison using Dynare. I am following the same comparison analysis proposed by An and Schorfheide (2007). Hence, I am trying to compare different models using the log of the marginal data density (for example, as reported in Tables 4,5, and 6). Using the estimation command in Dynare, I get (after the posterior maximization) this result:
Log data density [Laplace approximation] is -825.875694
This one is the marginal data density (The marginal data density is calculated as the integral of the likelihood function with respect to the prior density of the parameters), isn’t it?
Is it calculated as the one reported in formula (47) of An and Schorfheide (2007)? Or is it given by a different formula?

Hi,
I actually have the same doubt. Is the log data density computed by Dynare the same as the marginal data density? The latter is obtained by integrating the product of the likelihood function and the prior density over the parameters, i.e. p(Y) = \int L(theta|Y)p(theta)dtheta.