I have several macroeconomic models (eg two DSGEs and a VAR). They each produce forecasts for GDP, inflation and unemployment, and I have data to test them on, going back years.
How can I say which model has the "best" overall performance?
I realise this is vague, so here's more detail:
Assume that model X performs better than model Y on GDP, but worse on inflation.
If I'm just looking at GDP, I could just ask something like "which model has the smallest mean square error?" (predicted GDP - actual GDP, squared) Similarly, if I only care about inflation, I could do the same thing.
But I actually care about forecast accuracy over all three variables (GDP/inf/unemployment).
Is there a way to assess accuracy over all three variables, without just assigning weights to each MSE value and adding them up?
Thanks for your help!