Optimal CBDC design: A model with two access mechanisms and the role of anonymity

This paper analyzes the optimal design of central bank digital currencies (CBDCs). To this end, we build a model in which households freely choose among four types of money — cash, deposits, and two forms of CBDC (account-based and token-based) differing in their degrees of anonymity and remuneration. Users are heterogeneous in their preferences for privacy and security, giving rise to trade-offs in CBDC design. We derive closed-form expressions for the optimal CBDC design parameters and characterize the resulting equilibrium. Our results show that when the central bank distributes both types of CBDC directly, it is optimal to set their remuneration to zero and differentiate them solely by their position along the anonymity-security spectrum. A higher value added from bank intermediation leads the central bank to design CBDCs with greater anonymity to limit deposit disintermediation. We also consider an alternative scenario where the account-based CBDC is managed by commercial banks and used for lending and find that only a modest degree of bank intermediation value is needed for this arrangement to improve welfare. Our findings provide policy-relevant insights into how to design and implement CBDCs that preserve financial stability while accommodating users’ heterogeneous preferences.