Public money as a store of value, heterogeneous beliefs and banks : implications of CBDC

The bulk of cash is held for store of value purposes, with such holdings sharply increasing in times of high economic uncertainty and only a fraction of the population choosing to hoard cash. We develop a Diamond and Dybvig model with public money as a store of value and heterogeneous beliefs about bank stability that accounts for this evidence. Only consumers who are sufficiently pessimistic about bank stability hold cash. The introduction of a central bank digital currency (CBDC) as a store of value lowers the storage cost of public money and induces partial bank disintermediation, which is nevertheless mitigated by an increase in relative maturity transformation. This has heterogeneous welfare consequences across the population. While cash holders always benefit by switching to CBDC, each of all other consumers may be better off or not depending on the probability of a bank run, her (and all others') belief about such probability and the degree of technological superiority of CBDC.