  We analyze the risks to financial stability 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 government bonds as 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. We also analyze the dynamics
of an increase in the CBDC and show that the CBDC not only does not cause bank
disintermediation and financial instability but may foster an expansion of bank
credit to firms.
