Optimal Monetary Policy and Liquidity with Heterogeneous Households

Abstract A liquidity-insurance motive for monetary policy operates when heterogeneous households use government-provided liquidity (“money”) to insure idiosyncratic risk. In our tractable sticky-price model this changes the central bank's trade-off by adding a linear benefit of insurance in the second-order approximation to aggregate welfare. Inflation volatility hinders the consumption volatility of constrained households as a side-effect of liquidity-insuring them; but price stability has quantitatively significant welfare costs only when monopolistic rents are also large, which indicates a complementarity between imperfect-insurance and New-Keynesian distortions. Helicopter drops are welfare-superior to open-market operations to achieve insurance, but quantitatively their benefit is surprisingly small.