Optimal monetary policy and liquidity with heterogeneous households

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. (C) 2020 Elsevier Inc. All rights reserved.