Comparison two models of DSGEs

Is it significant to compare marginal data densities of two dsge models with very different specification? Of course on the exactly same data (time series).

One model has 13 variables(doesnt have government and monetary policy) and another has 30 variables that includes government & monetary policy section.

Yes, the marginal data density is supposed to compare the empirical fit of different models on the same data.

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How about comparing models with different features in a DSGE-VAR environment? We can still use marginal data density and model_comparison command? Or we need to do something like this (in the attached figure) as in Del Negro and Frank Schorfheide?

My understanding is that the marginal data density of the dsge_var is the correct one as used here, i.e. not only the one of the DSGE-model. @stepan-a should know for sure
Regarding \lambda: it depends on whether you want to consider it as a fixed hyperparameter. If yes, there is no point in checking its effect.

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