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Statistical ensembles for money and debt

Author

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  • Stefano Viaggiu
  • Andrea Lionetto
  • Leonardo Bargigli
  • Michele Longo

Abstract

We build a statistical ensemble representation of two economic models describing respectively, in simplified terms, a payment system and a credit market. To this purpose we adopt the Boltzmann-Gibbs distribution where the role of the Hamiltonian is taken by the total money supply (i.e. including money created from debt) of a set of interacting economic agents. As a result, we can read the main thermodynamic quantities in terms of monetary ones. In particular, we define for the credit market model a work term which is related to the impact of monetary policy on credit creation. Furthermore, with our formalism we recover and extend some results concerning the temperature of an economic system, previously presented in the literature by considering only the monetary base as conserved quantity. Finally, we study the statistical ensemble for the Pareto distribution.

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  • Stefano Viaggiu & Andrea Lionetto & Leonardo Bargigli & Michele Longo, 2011. "Statistical ensembles for money and debt," Papers 1109.0891, arXiv.org, revised Jul 2012.
    • Handle: RePEc:arx:papers:1109.0891
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    References listed on IDEAS

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    1. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406.
    2. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096.
    3. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    4. Aoki,Masanao & Yoshikawa,Hiroshi, 2011. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9781107634206.
    5. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Statistical theories of income and wealth distribution," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-31.
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    Cited by:

    1. Leonardo Bargigli & Giovanni di Iasio & Luigi Infante & Fabrizio Lillo & Federico Pierobon, 2015. "Interbank markets and multiplex networks: centrality measures and statistical null models," Papers 1501.05751, arXiv.org.
    2. Leonardo Bargigli, 2013. "Statistical Equilibrium Models for Sparse Economic Networks," Working Papers - Economics wp2013_25.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    3. Leonardo Bargigli & Renato Giannetti, 2015. "The Italian Corporate System: SOEs, Private Firms and Institutions in a Network Perspective (1952-1983)," Working Papers - Economics wp2015_01.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    4. Bicci, Alberto, 2016. "Limit order book and its modeling in terms of Gibbs Grand-Canonical Ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 516-524.
    5. Alberto Bicci, 2016. "Limit Order Book and its modelling in terms of Gibbs Grand-Canonical Ensemble," Papers 1602.06968, arXiv.org, revised Feb 2016.

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