Money under the mattress: Inflation and lending of last resort

This paper examines whether the two key functions of central banks-ensuring price stability and lending during crises-necessarily conflict. We develop a nominal model of bank runs a la Diamond and Dybvig (1983) in which individuals can store the money they withdraw "under the mattress." In this setting, lending of last resort need not be inflationary. Whether it is depends on the interest rates the central bank charges on its loans. Our results suggest that the central bank must not charge a rate that is too low if it wants to ensure price stability, and must charge a high rate if it wants to robustly attain the ex -ante efficient outcome. These rationales for charging high interest rates on loans during a crisis are distinct from the arguments Bagehot originally relied on to advocate for a similar rule.