Monetary Policy with Reserves and CBDC: Optimality, Equivalence, and Politics

We analyze policy in a two-tiered monetary system. Noncompetitive banks
issue deposits while the central bank issues reserves and a retail CBDC. Monies
differ with respect to operating costs and liquidity. We map the framework into a
baseline business cycle model with “pseudo wedges” and derive optimal policy rules:
Spreads satisfy modified Friedman rules and deposits must be taxed or subsidized.
We generalize the Brunnermeier and Niepelt (2019) result on the macro irrelevance
of CBDC but show that a deposit based payment system requires higher taxes. The
model implies annual implicit subsidies to U.S. banks of up to 0.8 percent of GDP
during the period 1999–2017.