A welfare analysis of the central bank balance sheet

What is the socially optimal long-run size of the central bank balance sheet, once interest rates are away from the effective lower bound and the balance sheet is no longer needed for monetary stimulus? I introduce a central bank into a model in which banks are liquidity mismatched and prone to sudden ‘bank runs’. Supplying central bank reserves reduces the likelihood and severity of runs, but comes at a cost: constraints on the set of securities the central bank can hold mean a larger balance sheet crowds out private investment and misallocates capital. I calibrate the model to pre-financial crisis conditions and empirical estimates of the non-linear reserve demand curve, and compute optimal policy. Under full information, it is optimal to expand reserve supply to the point where reserve demand is satiated, but no further. However, because under-supplying reserves is more costly than over-supplying them, robustness to parameter uncertainty calls for an additional buffer in reserve supply. But even for high degrees of robustness, the buffer needed is no larger than two and a half percentage points of bank assets. The policy prescription remains restrained: robustness moves the balance sheet modestly beyond satiation, but fails to justify an open-ended provision of abundant reserves.