Long- versus medium-run identification in fractionally integrated VAR models

- Fractional VAR with integration orders < 1: long-run identification lacks interpretation.
- Consider medium-run information to obtain identified shocks.
- Three such approaches are presented.
- Asymptotic equivalence to long-run restriction shown for large horizons.

We state that long-run restrictions that identify structural shocks in VAR models with unit roots lose their original interpretation if the fractional integration order of the affected variable is below one. For such fractionally integrated models we consider a medium-run approach that employs restrictions on variance contributions over finite horizons. We show for alternative identification schemes that letting the horizon tend to infinity is equivalent to imposing the restriction of Blanchard and Quah (1989) introduced for the unit-root case.