Further Results on MSFE Encompassing

We show that the standard condition for MSFE encompassing is no longer valid when the forecasts to be compared are biased. We propose a simple modification of such a condition and of tests for its validity. The relationship between these tests, pooling regressions and tests for non-nested hypotheses is also analysed, together with their multivariate versions. The teoretical results are illustrated by an empirical example on inflation and deficit forecasts, key variables for the formulation of monetary and fiscal policy.