Household Heterogeneity across Countries and Optimal Monetary Policy in a Monetary Union

The financial situation of households differs substantially across countries, but the implications of this heterogeneity are still vastly understudied. We examine the implications of this asymmetry for optimal monetary policy in a currency union. We build a two-country monetary union model with heterogeneous households leading to inequality due to imperfect insurance. Money is introduced through central bank digital currency (CBDC) as a liquid asset to self-insure against idiosyncratic risk. CBDC is a new instrument which allows the central bank to target heterogeneity within a monetary union. We derive a welfare function with two additional objectives, consumption inequality within and across countries. The more heterogeneous households are, the less important inflation stabilization becomes in favor of stabilizing consumption inequality through providing money. Our research provides important policy implications as we show that it is beneficial for a monetary union to have a country-specific instrument to compensate for country differentials.