Optimal reserve supply caps at 15 percent of bank assets
A Bank of England working paper by William Pagel finds that the optimal long-run central bank balance sheet supplies reserves up to demand satiation at roughly 15 percent of banking assets. Expanding supply further causes welfare losses through capital misallocation.
Balancing run risks against misallocated capital
The general equilibrium framework evaluates the trade-off between liquidity insurance and capital misallocation.
Supplying central bank reserves curbs the probability of bank runs, but backing them requires purchasing a narrow set of eligible securities, which distorts private investment.
Under full information, welfare is maximized when reserve supply reaches demand satiation at roughly 15 percent of bank assets, where the convenience yield drops close to zero.
Expanding beyond this threshold reduces output without offering additional stability.
Calibrated to pre-crisis data, moving from a 3 percent scarce supply to the ample optimum delivers a welfare gain of 0.15 percentage points of consumption.
Asymmetric risks favor modest buffers
Evaluating 484 admissible parameterizations shows that under-supplying reserves is 1.6 times more costly than over-supplying them.
To insure against parameter uncertainty, the model prescribes a precautionary buffer of at most 2.4 percentage points of bank assets above the 15.6 percent baseline, even under extreme risk aversion.
Furthermore, the paper demonstrates that broadening the set of securities eligible for central bank purchase reduces capital misallocation and lowers the overall welfare cost of reserve supply.
Restraint over open-ended abundance
The analysis establishes a rigorous theoretical limit against claims that oversized balance sheets are costless.
By quantifying capital misallocation, it demonstrates that expanding reserves beyond satiation actively destroys economic welfare.
Central banks can no longer invoke uncertainty to defend open-ended balance sheet expansion.