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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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    1. Stephanie Schmitt-Groh√ & Mart√Çn Uribe, 2012. "Foreign Demand for Domestic Currency and the Optimal Rate of Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(6), pages 1207-1224, September.
    2. Smith, A. Lee & Valcarcel, Victor J., 2023. "The financial market effects of unwinding the Federal Reserve’s balance sheet," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    3. Gara Afonso & Roc Armenter & Benjamin Lester, 2019. "A Model of the Federal Funds Market: Yesterday, Today, and Tomorrow," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 33, pages 177-204, July.
    4. Arvind Krishnamurthy & Annette Vissing-Jorgensen, 2012. "The Aggregate Demand for Treasury Debt," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 233-267.
    5. Jeremy C. Stein & Anil K. Kashyap, 2000. "What Do a Million Observations on Banks Say about the Transmission of Monetary Policy?," American Economic Review, American Economic Association, vol. 90(3), pages 407-428, June.
    6. Chari, V. V. & Christiano, Lawrence J. & Kehoe, Patrick J., 1996. "Optimality of the Friedman rule in economies with distorting taxes," Journal of Monetary Economics, Elsevier, vol. 37(2-3), pages 203-223, April.
    7. Roc Armenter & Benjamin Lester, 2017. "Excess Reserves and Monetary Policy Implementation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 212-235, January.
    8. Wallace, Neil, 1981. "A Modigliani-Miller Theorem for Open-Market Operations," American Economic Review, American Economic Association, vol. 71(3), pages 267-274, June.
    9. Adam Copeland & Darrell Duffie & Yilin (David) Yang, 2025. "Reserves Were Not So Ample After All," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 140(1), pages 239-281.
    10. Itamar Drechsler & Alexi Savov & Philipp Schnabl, 2017. "The Deposits Channel of Monetary Policy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1819-1876.
    11. Ryan Bush & Adam Kirk & Antoine Martin & Phillip Weed & Patricia Zobel, 2019. "Stressed Outflows and the Supply of Central Bank Reserves," Liberty Street Economics 20190220, Federal Reserve Bank of New York.
    12. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Optimal fiscal and monetary policy under sticky prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 198-230, February.
    13. Williamson, Stephen D., 2019. "Interest on reserves, interbank lending, and monetary policy," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 14-30.
    14. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Optimal fiscal and monetary policy under imperfect competition," Journal of Macroeconomics, Elsevier, vol. 26(2), pages 183-209, June.
    15. Cúrdia, Vasco & Woodford, Michael, 2011. "The central-bank balance sheet as an instrument of monetarypolicy," Journal of Monetary Economics, Elsevier, vol. 58(1), pages 54-79, January.
    16. Ennis, Huberto M., 2018. "A simple general equilibrium model of large excess reserves," Journal of Monetary Economics, Elsevier, vol. 98(C), pages 50-65.
    17. Ricardo Lagos & Gaston Navarro, 2019. "Monetary Operating Procedures in the Fed Funds Market: Theory and Policy Analysis," 2019 Meeting Papers 1521, Society for Economic Dynamics.
    18. Gary Gorton & Tyler Muir, 2016. "Mobile collateral versus immobile collateral," BIS Working Papers 561, Bank for International Settlements.
    19. Andrew Lee Smith, 2019. "Do Changes in Reserve Balances Still Influence the Federal Funds Rate?," Economic Review, Federal Reserve Bank of Kansas City, issue Q I, pages 5-34.
    20. Banegas, Ayelen & Tase, Manjola, 2020. "Reserve balances, the federal funds market and arbitrage in the new regulatory framework," Journal of Banking & Finance, Elsevier, vol. 118(C).
    21. Michael D. Bordo & Andrew T. Levin, 2017. "Central Bank Digital Currency and the Future of Monetary Policy," NBER Working Papers 23711, National Bureau of Economic Research, Inc.
    22. Williamson, Stephen D., 2016. "Scarce collateral, the term premium, and quantitative easing," Journal of Economic Theory, Elsevier, vol. 164(C), pages 136-165.
    23. Gary Gorton & Tyler Muir, 2016. "Mobile Collateral versus Immobile Collateral," NBER Working Papers 22619, National Bureau of Economic Research, Inc.
    24. Joseph E. Gagnon & Brian Sack, 2014. "Monetary Policy with Abundant Liquidity: A New Operating Framework for the Fed," Policy Briefs PB14-4, Peterson Institute for International Economics.
    25. Adam Ashcraft & James Mcandrews & David Skeie, 2011. "Precautionary Reserves and the Interbank Market," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(s2), pages 311-348, October.
    26. Arvind Krishnamurthy & Wenhao Li, 2023. "The Demand for Money, Near-Money, and Treasury Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 36(5), pages 2091-2130.
    27. Stefan Nagel, 2016. "The Liquidity Premium of Near-Money Assets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1927-1971.
    28. Kimbrough, Kent P, 1986. "Inflation, Employment, and Welfare in the Presence of Transactions Costs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 18(2), pages 127-140, May.
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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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