Consistency between loglikelihoods and business cycle statistics for DSGE model comparison

[jpfeifer]

1. It’s not about the log-likelihood, but the marginal data density.
2. The topic has been discussed e.g. at

How to see whether the model fit the real data well?

You still did not grasp the main point: the MDD will incorporate the fit of ALL moments, weighted by the precision they are estimated with. That may imply that the 200th autocorrelation between output and consumption is really well-matched. While that is the most efficient way of estimating parameters, it is often not what researchers care about. We often only care much about the first two to four autocorrelations and cross correlation. Regarding estimated models: you either do that via moment …