Fit of model based on log data density


Just a quick question.
I’m trying to estimate an open economy model for a Central Eastern Country and the Euro Area. Among the data used in estimation I use domestic inflation, domestic CPI, domestic investment prices, domestic interest rate as well as foreign (EA) inflation and foreign interest rate.
When I use demeaned domestic and EA data in estimating some parameters I get a log data density of -2670,60
When I use only demean in domestic data and no demean in EA data I get a log data density of -2643,151

Does this mean that during estimation I have to use domestic demeaned data and no demean EA data because it better fits the model ?

Thank you!

I am not sure I can follow your question. However, whether you have to detrend or not depends on your model formulation and the observation equation. Unless your observation equation differs between domestic and foreign variables, you have to treat them equally. Say for example you do not detrend foreign ouput and it has a mean deviation from steady state of +1%. Then your shocks have to be estimated to explain this positive 1% deviation. The implications of wrong detrending/observation equations go beyond the simple model fit.

Note also that you can use the log data density for model comparison. But that is for given data. Here you change the data.

Thank you jpfeifer for your quick answear. Seeing a lower log data density made me wonder. I will treat all the series the same.