Central Bank Digital Currency with Collateral-constrained Banks

We analyze the risks to bank intermediation following the introduction of a central bank digital currency (CBDC). The CBDC competes with commercial bank deposits as the household's source of liquidity. We revisit the result in the literature regarding the equivalence of payment systems by introducing a collateral constraint for banks when borrowing from the central bank. When comparing two equilibria with and without the CBDC, the central bank can ensure the same equilibrium allocation and price system by offering loans to banks. However, to access loans, banks must hold collateral at the expense of extending credit to firms, and the central bank assumes part of the credit-extension role. Thus, in the equivalence analysis, while the CBDC introduction has no real effects on the economy, it does not guarantee full neutrality as it affects banks' business models. In a dynamic model extension, we analyze the effects of an increase in the CBDC and show that the CBDC not only does not cause bank disintermediation or crowd out of deposits but may foster an expansion of bank credit to firms.