Central Bank Digital Currency (CBDC) and Financial Fragility under Capacity-Constrained Credit Policy

The financial stability implications of a retail CBDC depend on how it is integrated into the central bank’s crisis-response framework. This paper studies CBDC-based credit policy in a dynamic macro-banking model with anticipated risk of bank runs. The key friction is that the credit policy is capacity-constrained: following an adverse productivity shock, the central bank may be unable to extend the necessary emergency lending immediately, restoring intervention only gradually. The model shows that this constraint can make self-fulfilling runs feasible. Nevertheless, limited central bank lending partially reduces the anticipation of a bank run risk, improves resilience, and raises net expected output relative to an economy with a CBDC but no credit-policy channel. Additionally, higher steady-state CBDC balances can eliminate post-shock run risk under the benchmark calibration by increasing the non-runnable central bank funding available to banks before the shock. On the other hand, allowing banks to hold central bank reserves can eliminate the run equilibrium by raising depositor recovery, but may crowd out productive capital. However, highly pledgeable reserves can encourage deposit-financed balance-sheet expansion when not accompanied by sufficient bank equity, which reintroduces the risk of bank runs. The reserve policy needs to be designed jointly with equity and leverage regulations.