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) competing with commercial bank deposits as households' source of liquidity. We revisit the result in the literature regarding the equivalence of payment systems introducing a collateral constraint on banks borrowing from the central bank. Comparing two equilibria with and without the CBDC, we find that even with this constraint, 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. Thus, 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 examine the effects of an increase in the CBDC and show that the CBDC does not cause bank disintermediation or crowd out deposits but may foster an expansion of bank credit to firms.