The Optimum Quantity of Central Bank Reserves

This paper analyzes the optimal quantity of central bank reserves in an economy where reserves and other financial assets provide liquidity benefits. Using a static model, I derive a constrained Friedman rule that characterizes the socially optimal level of reserves, demonstrating that this quantity is neither necessarily large nor small but depends on the marginal benefits of reserves relative to alternative safe assets. The model highlights how the supply of government and private-sector liquid assets influences demand for reserves and the size of a central bank balance sheet. I calibrate and estimate the model to determine the optimal amount of central bank holdings in the United States. I extend the analysis to account for shadow banking, where non-bank intermediaries create short-term liquid assets but generate monitoring costs and externalities. The presence of shadow banking alters the optimal balance of reserves and other assets, potentially constraining optimal balance sheet policy. The results offer new insights into the debate over the size of central bank balance sheets and the interaction between public and private liquidity provision.