The optimal quantity of CBDC in a bank-based economy

We provide evidence on the estimated effects of digital euro news on bank valuations and lending and find that they depend on deposit reliance and design features aimed at calibrating the quantity of CBDC. Then, we develop a quantitative DSGE model that replicates such evidence and incorporates key selected mechanisms through which CBDC issuance could affect bank intermediation and the economy. Under empirically-relevant assumptions (i.e., central bank collateral requirements and imperfect substitutability across CBDC, cash and deposits), the issuance of CBDC yields non-trivial trade-offs and effects through an expansion of the central bank balance sheet and profits. The issuance of CBDC exerts a smoothing effect on lending and real GDP by stabilizing deposit holdings. Such "stabilization effect" improves the well-known liquidity services/disintermediation trade-off induced by CBDC and permits to rank different types of CBDC rules according to individual and social preferences. Welfare- maximizing CBDC policy rules are effective in mitigating the risk of bank disintermediation and induce significant welfare gains.