A HANK2 model of monetary unions

How does a monetary union alter the impact of business cycle shocks at the household level? We develop a Heterogeneous Agent New Keynesian model of two countries (HANK${}^2$) and show in closed form that a monetary union shifts the adjustment to a shock horizontally across countries, within the brackets of the union-wide wealth distribution, rather than vertically, that is, across the brackets of the union-wide wealth distribution. Calibrating the model to the euro area reveals that a monetary union alters the impact of shocks most strongly in the tails of the wealth distribution but leaves the middle class almost unaffected.