IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/24483.html
   My bibliography  Save this paper

Some Simple Bitcoin Economics

Author

Listed:
  • Linda Schilling
  • Harald Uhlig

Abstract

In a novel model of an endowment economy, we analyze coexistence and competition between traditional fiat money (Dollar) and another intrinsically worthless medium of exchange, not controlled by a central bank, such as Bitcoin. Agents can trade consumption goods in either currency or hold on to currency for speculative purposes. A central bank ensures a Dollar inflation target, while Bitcoin mining is decentralized via proof-of-work. We analyze Bitcoin price evolution and interaction between the Bitcoin price and monetary policy which targets the Dollar. We obtain a fundamental pricing equation, which in its simplest form implies that Bitcoin prices form a martingale. We derive conditions, under which Bitcoin speculation cannot happen, and the fundamental pricing equation must hold. We show that the block rewards are not a tax on Bitcoin holders: they are financed by Dollar taxes imposed by the Dollar central bank. We discuss monetary policy implications and characterize the range of equilibria.

Suggested Citation

  • Linda Schilling & Harald Uhlig, 2018. "Some Simple Bitcoin Economics," NBER Working Papers 24483, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:24483
    Note: AP EFG IFM ME
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w24483.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Guerrieri, V. & Uhlig, H., 2016. "Housing and Credit Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1427-1496, Elsevier.
    2. Wilko Bolt & Maarten R.C. Van Oordt, 2020. "On the Value of Virtual Currencies," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 52(4), pages 835-862, June.
    3. Fernández-Villaverde, Jesús & Sanches, Daniel, 2019. "Can currency competition work?," Journal of Monetary Economics, Elsevier, vol. 106(C), pages 1-15.
    4. Julien Prat & Benjamin Walter, 2021. "An Equilibrium Model of the Market for Bitcoin Mining," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2415-2452.
    5. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    6. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    7. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    8. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 2016. "Understanding Booms and Busts in Housing Markets," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 1088-1147.
    9. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2016. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. I," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 44, pages 5-24.
    10. John Kareken & Neil Wallace, 1981. "On the Indeterminacy of Equilibrium Exchange Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 96(2), pages 207-222.
    11. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 2011. "Carry Trade and Momentum in Currency Markets," Annual Review of Financial Economics, Annual Reviews, vol. 3(1), pages 511-535, December.
    12. Morten Linnemann Bech & Rodney Garratt, 2017. "Central bank cryptocurrencies," BIS Quarterly Review, Bank for International Settlements, September.
    13. repec:zbw:bofrdp:2017_027 is not listed on IDEAS
    14. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-1181, September.
    15. Lin William Cong & Zhiguo He, 2019. "Blockchain Disruption and Smart Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 32(5), pages 1754-1797.
    16. Anton Badev & Matthew Chen, 2014. "Bitcoin: Technical Background and Data Analysis," Finance and Economics Discussion Series 2014-104, Board of Governors of the Federal Reserve System (U.S.).
    17. J. B. Taylor & Harald Uhlig (ed.), 2016. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 2, number 2.
    18. Manuelli, Rodolfo E & Peck, James, 1990. "Exchange Rate Volatility in an Equilibrium Asset Pricing Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 559-574, August.
    19. Sean Foley & Jonathan R Karlsen & Tālis J Putniņš, 2019. "Sex, Drugs, and Bitcoin: How Much Illegal Activity Is Financed through Cryptocurrencies?," The Review of Financial Studies, Society for Financial Studies, vol. 32(5), pages 1798-1853.
    20. Bewley, Truman, 1977. "The permanent income hypothesis: A theoretical formulation," Journal of Economic Theory, Elsevier, vol. 16(2), pages 252-292, December.
    21. Huberman, Gur & Leshno, Jacob & Moallemi, Ciamac C., 2017. "Monopoly Without a Monopolist: An Economic Analysis of the Bitcoin Payment System," CEPR Discussion Papers 12322, C.E.P.R. Discussion Papers.
    22. Härdle, Wolfgang Karl & Trimborn, Simon, 2015. "CRIX or evaluating blockchain based currencies," SFB 649 Discussion Papers 2015-048, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    23. Isabel Schnabel & Hyun Song Shin, 2018. "Money and trust: lessons from the 1620s for money in the digital age," BIS Working Papers 698, Bank for International Settlements.
    24. Jose A. Scheinkman & Wei Xiong, 2003. "Overconfidence and Speculative Bubbles," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1183-1219, December.
    25. Emanuele Borgonovo & Stefano Caselli & Alessandra Cillo & Donato Masciandaro, 2017. "Beyond Bitcoin And Cash: Do We Like A Central Bank Digital Currency? A Financial And Political Economics Approach," BAFFI CAREFIN Working Papers 1765, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    26. Beat Weber, 2016. "Bitcoin and the legitimacy crisis of money," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 40(1), pages 17-41.
    27. Rainer Böhme & Nicolas Christin & Benjamin Edelman & Tyler Moore, 2015. "Bitcoin: Economics, Technology, and Governance," Journal of Economic Perspectives, American Economic Association, vol. 29(2), pages 213-238, Spring.
    28. Linda M. Schilling & Harald Uhlig, 2019. "Currency Substitution under Transaction Costs," AEA Papers and Proceedings, American Economic Association, vol. 109, pages 83-87, May.
    29. Brandvold, Morten & Molnár, Peter & Vagstad, Kristian & Andreas Valstad, Ole Christian, 2015. "Price discovery on Bitcoin exchanges," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 36(C), pages 18-35.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Benigno, Pierpaolo & Schilling, Linda M. & Uhlig, Harald, 2022. "Cryptocurrencies, currency competition, and the impossible trinity," Journal of International Economics, Elsevier, vol. 136(C).
    2. Bruno Biais & Christophe Bisière & Matthieu Bouvard & Catherine Casamatta & Albert J. Menkveld, 2023. "Equilibrium Bitcoin Pricing," Journal of Finance, American Finance Association, vol. 78(2), pages 967-1014, April.
    3. Raphael Auer, 2019. "Beyond the doomsday economics of "proof-of-work" in cryptocurrencies," BIS Working Papers 765, Bank for International Settlements.
    4. Schilling, Linda & Fernández-Villaverde, Jesús & Uhlig, Harald, 2024. "Central bank digital currency: When price and bank stability collide," Journal of Monetary Economics, Elsevier, vol. 145(C).
    5. Marcelo A. T. Aragão, 2021. "A Few Things You Wanted to Know about the Economics of CBDCs, but were Afraid to Model: a survey of what we can learn from who has done," Working Papers Series 554, Central Bank of Brazil, Research Department.
    6. Julien Prat & Benjamin Walter, 2021. "An Equilibrium Model of the Market for Bitcoin Mining," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2415-2452.
    7. Marchiori, Luca, 2021. "Monetary theory reversed: Virtual currency issuance and the inflation tax," Journal of International Money and Finance, Elsevier, vol. 117(C).
    8. Matteo Benetton & Giovanni Compiani, 2024. "Investors’ Beliefs and Cryptocurrency Prices," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 14(2), pages 197-236.
    9. Feng Dong & Zhiwei Xu & Yu Zhang, 2022. "Bubbly Bitcoin," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 973-1015, October.
    10. Stylianos Asimakopoulos & Marco Lorusso & Francesco Ravazzolo, 2019. "A New Economic Framework: A DSGE Model with Cryptocurrency," Working Papers No 07/2019, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    11. Julián A. Parra & Carlos Arango - Joaquín Bernal & José E. Gómez - Javier Gómez & Carlos León - Clara Machado & Daniel Osorio - Daniel Rojas & Nicolás Suárez - Eduardo Yanquen, 2019. "Criptoactivos: análisis y revisión de literatura," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República, issue 92, pages 1-37, November.
    12. Grym, Aleksi, 2018. "The great illusion of digital currencies," BoF Economics Review 1/2018, Bank of Finland.
    13. Emanuele Borgonovo & Stefano Caselli & Alessandra Cillo & Donato Masciandaro & Giovanno Rabitti, 2018. "Cryptocurrencies, central bank digital cash, traditional money: does privacy matter?," BAFFI CAREFIN Working Papers 1895, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    14. Matteo Benetton & Giovanni Compiani, 2020. "Investors’ Beliefs and Asset Prices: A Structural Model of Cryptocurrency Demand," Working Papers 2020-107, Becker Friedman Institute for Research In Economics.
    15. Donato Masciandaro, 2018. "Central Bank Digital Cash and Cryptocurrencies: Insights from a New Baumol–Friedman Demand for Money," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 51(4), pages 540-550, December.
    16. Choi, Michael & Rocheteau, Guillaume, 2022. "Money mining and price dynamics: The case of divisible currencies," Journal of Economic Dynamics and Control, Elsevier, vol. 142(C).
    17. Gilles Hilary & Laura Xiaolei Liu, 2021. "Blockchain and Other Distributed Ledger Technologies in Finance," Springer Books, in: Raghavendra Rau & Robert Wardrop & Luigi Zingales (ed.), The Palgrave Handbook of Technological Finance, pages 243-268, Springer.
    18. Radwanski, Juliusz, 2020. "On the Purchasing Power of Money in an Exchange Economy," MPRA Paper 104244, University Library of Munich, Germany.
    19. Harald Uhlig & Taojun Xie, 2020. "Parallel Digital Currencies and Sticky Prices," Working Papers 2020-188, Becker Friedman Institute for Research In Economics.
    20. Alexis Derviz, 2019. "Coexistence of Physical and Crypto Assets in a Stochastic Endogenous Growth Model," Working Papers 2019/7, Czech National Bank.

    More about this item

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • E40 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - General
    • E42 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Monetary Sytsems; Standards; Regimes; Government and the Monetary System
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:24483. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.