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The Optimum Quantity of Central Bank Reserves

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  • Jonathan Witmer

Abstract

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.

Suggested Citation

  • Jonathan Witmer, 2025. "The Optimum Quantity of Central Bank Reserves," Staff Working Papers 25-15, Bank of Canada.
  • Handle: RePEc:bca:bocawp:25-15
    DOI: 10.34989/swp-2025-15
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    More about this item

    Keywords

    Monetary policy implementation; Financial institutions; Financial markets; Financial system regulation and policies;
    All these keywords.

    JEL classification:

    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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