A Simple Model of a Central Bank Digital Currency

We develop a general equilibrium model that highlights the trade-offs between physical and digital forms of retail central bank money. The key differences between cash and central bank digital currency (CBDC) include transaction efficiency, possibilities for tax evasion, and, potentially, nominal rates of return. We establish conditions under which cash and CBDC can co-exist and show how government policies can influence relative holdings of cash, CBDC, and other assets. We illustrate how a CBDC can facilitate negative nominal interest rates and helicopter drops, and also how a CBDC can be structured to prevent capital flight from other assets.