Central Bank Digital Currency with Collateral-Constrained Banks
What this paper finds — and why it matters
The paper analyzes the implications of introducing a retail central bank digital currency (CBDC) that competes with commercial bank deposits for household liquidity, in a model where banks must post government bonds as collateral to access central bank lending. The authors revisit Niepelt’s (2022) “equivalence of payment systems” result and find that equivalence survives even under a collateral constraint: the central bank can still offer loans to banks that replicate the no-CBDC equilibrium allocation, but at a lending rate lower than Niepelt’s unconstrained rate, because tighter terms are needed to incentivize sufficient loan uptake when banks must redirect portfolio holdings toward government bonds to qualify. A structural cost remains: banks must hold government bonds as collateral at the expense of extending credit to firms, so equivalence in allocation does not imply full neutrality — banks’ business models and the government’s intermediation role change even when aggregate output and prices are unchanged. In the dynamic extension where the central bank does not sterilize the CBDC introduction, banks respond by narrowing deposit spreads to attract inflows, with the result that a CBDC ramp-up to 5 percent of steady-state output expands rather than contracts bank credit to firms.
Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Q1. What is the equivalence of payment systems result and how does the collateral constraint change it?
Brunnermeier and Niepelt (2019) and Niepelt (2022) established that the central bank can neutralize the real effects of CBDC introduction by lending to banks at an appropriate rate to replace lost deposit funding, a result the present paper revisits by adding a collateral requirement on central bank lending — specifically, that banks must hold eligible government bonds up to a fraction θb of their central bank loan value. Under this constraint, Proposition 1 shows that equivalence survives: there exists a central bank lending rate that replicates the no-CBDC equilibrium allocation and price system. However, this lending rate is lower than Niepelt’s unconstrained rate by a factor increasing in the restrictiveness of the constraint (lower θb requires a lower lending rate), because when banks are collateral-constrained, cheaper terms are needed to induce them to borrow enough from the central bank to offset deposit outflows.
Q2. What is Corollary 1 and why does “full neutrality” fail?
Corollary 1 states that even when the central bank achieves allocation equivalence by setting the appropriate lending rate, banks must redirect portfolio holdings from firm loans to government bonds to meet the collateral requirement — crowding out bank credit to firms by an amount equal to the bond uptake, with the crowding-out diminishing as the collateral constraint becomes less restrictive (higher θb). This is the sense in which “full neutrality” fails under the collateral constraint: aggregate output and prices are unchanged, but the composition of credit changes — banks extend less to firms and hold more government bonds — and the government or household sector must absorb the gap in firm financing. In the limiting case where CBDC and deposits are equally valuable to households (λ = 1), the government alone compensates for the reduction in bank loans, effectively expanding its own intermediation role.
Q3. What does the dynamic extension show about bank disintermediation?
Simulating a gradual and near-permanent increase in CBDC to 5 percent of steady-state output without central bank sterilization, the paper finds that banks respond by narrowing their deposit interest spread to attract deposit inflows, such that total deposits do not fall and bank loans to firms expand rather than contract — the opposite of the disintermediation hypothesis. The mechanism relies on the assumption that banks have market power in their regional deposit markets (each bank is a monopsonist): in response to CBDC competition, the bank voluntarily reduces the rent it extracts on deposits (the spread between the risk-free rate and the deposit rate), attracting more deposit inflows. This deposit inflow, combined with central bank loan uptake, expands the bank’s balance sheet and increases credit extension to firms. The result stands in contrast to models with competitive deposit markets, where banks cannot respond to CBDC competition through deposit pricing.
Q4. What changes even if credit is not reduced?
Even when the dynamic model shows credit expansion rather than contraction, the paper establishes that CBDC introduction alters banks’ balance sheet composition and business model: banks shift toward holding more government bonds and away from firm loans, the government assumes a larger credit intermediation role, and the aggregate distribution of capital ownership changes — constituting the form of non-neutrality that survives even when total credit is unchanged. This is what Corollary 1 calls the failure of “full neutrality”: the real allocation equivalence holds at the aggregate level, but the sectoral distribution of who provides credit to firms shifts from the banking sector toward the public sector. The paper interprets this as a structural consequence of the collateral requirement on central bank lending that is absent in the frictionless equivalence benchmark.
Key concepts
equivalence of payment systems : the theoretical result (from Brunnermeier-Niepelt 2019 and Niepelt 2022) that the central bank can ensure the same equilibrium allocation whether or not CBDC exists, by adjusting its lending terms to banks; this paper revisits and extends the result to environments with a collateral constraint.
collateral constraint (θb) : the requirement in this model that banks hold eligible government bonds as a fraction of the central bank loans they take on; adding this friction to Niepelt’s framework preserves equivalence in allocation but requires a lower central bank lending rate and crowds out bank loans to firms.
disintermediation : the concern that CBDC adoption would cause households to shift en masse from bank deposits to CBDC, reducing bank funding and contracting bank credit; the paper finds this does not occur in either the equivalence analysis or the dynamic extension.
monopsony in deposits : the market structure assumption that each regional bank is the sole deposit provider in its region, giving it pricing power over deposit rates; this is what enables banks in the dynamic model to narrow the deposit spread in response to CBDC competition, generating deposit inflows rather than outflows.
full neutrality : a stronger invariance result requiring that not only the equilibrium allocation but also banks’ balance sheet composition and business model are unchanged by CBDC introduction; the paper shows this fails under the collateral constraint even when allocation equivalence holds.