Should the euro zone also adopt the "overheating theory", like the United States?

The "overheating theory" describes the positive effects of maintaining a significant demand-stimulating policy when the economy has returned to the full employment. The idea is that if companies are faced with both stimulation of demand and major hiring difficulties, they have to organise themselves better to be able to meet demand: efficiency gains, hiring of less employable people . This theory is currently being applied in the United States with expansionary fiscal and monetary policies at full employment, which seems to have led to an upturn in labour productivity and the participation rate and therefore in potential growth. While monetary policy is expansionary in the euro zone, this is not the case with fiscal policy. Does this rejection of the "overheating theory" in the euro zone explain why productivity gains are declin ing instead of increasing in the zone?