The Great Recession and the resulting European debt crisis revived a debate about deeper fiscal integration in the Eurozone. We discuss different alternatives how an unemployment insurance system for the euro area could be designed and run counterfactual simulations based on micro data to analyze the effectiveness of a basic scheme to act as an insurance device in the presence of asymmetric macroeconomic shocks. We find that such a scheme could be implemented with a relatively small annual budget of roughly 61 billion euros over the period 2008-2013. Net benefits would have stabilized incomes in particular in Cyprus, Estonia, Greece, Ireland, Portugal and Spain whereas Austria, Germany and the Netherlands would have been the largest net contributors. With a predicted increase in output of only up to 0.2 per cent relative to a situation with existing pre-crisis national unemployment insurance systems, our results suggest that a basic euro area unemployment insurance scheme would have had only moderate growth-enhancing effects at the euro area level.