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A Monetary Theory with Non-Degenerate Distributions

Author

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  • Guido Menzio

    (Department of Economics, University of Pennsylvania)

  • Shouyong Shi

    (Department of Economics, University of Toronto)

  • Hongfei Sun

    (Department of Economics, Queens University)

Abstract

Dispersion of money balances among individuals is the basis for a range of policies but it has been abstracted from in monetary theory for tractability reasons. In this paper, we fill in this gap by constructing a tractable search model of money with a non-degenerate distribution of money holdings. We assume search to be directed in the sense that buyers know the terms of trade before visiting particular sellers. Directed search makes the monetary steady state block recursive in the sense that individuals’ policy functions, value functions and the market tightness function are all independent of the distribution of individuals over money balances, although the distribution affects the aggregate activity by itself. Block recursivity enables us to characterize the equilibrium analytically. By adapting lattice-theoretic techniques, we characterize individuals’ policy and value functions, and show that these functions satisfy the standard conditions of optimization. We prove that a unique monetary steady state exists. Moreover, we provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate and analyze the properties of this distribution.

Suggested Citation

  • Guido Menzio & Shouyong Shi & Hongfei Sun, 2011. "A Monetary Theory with Non-Degenerate Distributions," PIER Working Paper Archive 11-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:11-009
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. A Monetary Theory with Non-degenerate Distributions
      by Christian Zimmermann in NEP-DGE blog on 2013-09-09 05:45:08
    2. A Monetary Theory with Non-Degenerate Distributions
      by Christian Zimmermann in NEP-DGE blog on 2011-04-11 07:44:40

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    Cited by:

    1. Guillaume Rocheteau & Pierre-Olivier Weill & Tsz-Nga Wong, 2015. "Working through the Distribution: Money in the Short and Long Run," NBER Working Papers 21779, National Bureau of Economic Research, Inc.
    2. Rocheteau, Guillaume & Weill, Pierre-Olivier & Wong, Tsz-Nga, 2021. "An heterogeneous-agent New-Monetarist model with an application to unemployment," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 64-90.
    3. Rocheteau, Guillaume & Weill, Pierre-Olivier & Wong, Russell, 2018. "A tractable model of monetary exchange with ex-post heterogeneity," Theoretical Economics, Econometric Society, vol. 13(3), September.
    4. Rincón-Zapatero, Juan Pablo & Jerez, Belén & Díaz, Antonia, 2019. "Housing Prices and Credit Constraints in Competitive Search," UC3M Working papers. Economics 28874, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Pablo Ottonello, 2015. "Capital Unemployment, Financial Shocks, and Investment Slumps," 2015 Meeting Papers 1153, Society for Economic Dynamics.
    6. Davoodalhosseini, Seyed Mohammadreza, 2019. "Constrained efficiency with adverse selection and directed search," Journal of Economic Theory, Elsevier, vol. 183(C), pages 568-593.
    7. Williamson, Stephen & Wright, Randall, 2010. "New Monetarist Economics: Models," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 2, pages 25-96, Elsevier.
    8. Kubota, So, 2019. "Market Structure and Indeterminacy of Stationary Equilibria in a Decentralized Monetary Economy," Discussion paper series HIAS-E-84, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    9. Baughman, Garth & Rabinovich, Stanislav, 2019. "Self-confirming price dispersion in monetary economies," Journal of Economic Theory, Elsevier, vol. 183(C), pages 284-311.
    10. Burdett, Kenneth & Trejos, Alberto & Wright, Randall, 2017. "A new suggestion for simplifying the theory of money," Journal of Economic Theory, Elsevier, vol. 172(C), pages 423-450.
    11. Jonathan Chiu & Miguel Molico, . "Short-Run Dynamics in a Search-Theoretic Model of Monetary Exchange," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.
    12. Blouri, Yashar & Ehrlich, Maximilian V., 2020. "On the optimal design of place-based policies: A structural evaluation of EU regional transfers," Journal of International Economics, Elsevier, vol. 125(C).
    13. Chao Gu & Randall Wright, 2016. "Monetary Mechanisms," Working Papers 1601, Department of Economics, University of Missouri.
    14. Zeno Enders, 2020. "Heterogeneous Consumers, Segmented Asset Markets and the Real Effects of Monetary Policy," Economic Journal, Royal Economic Society, vol. 130(628), pages 1031-1056.
    15. Enders, Zeno, 2010. "Heterogeneous consumers, segmented asset markets, and the effects of monetary policy," Bonn Econ Discussion Papers 08/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    16. Beverly Lapham & Ayman Mnasri, 2019. "Exchange Rate Pass-Through: A Competitive Search Approach," Working Paper 1418, Economics Department, Queen's University.
    17. Randall Wright & Philipp Kircher & Benoit Julîen & Veronica Guerrieri, 2017. "Directed Search: A Guided Tour," NBER Working Papers 23884, National Bureau of Economic Research, Inc.
    18. Maurizio Iacopetta, 2014. "Dynamics of assets liquidity and inequality in economies with decentralized markets," Sciences Po publications info:hdl:2441/2029nqlehl8, Sciences Po.
    19. Jung, Kuk Mo, 2018. "Uncertainty-induced dynamic inefficiency and the optimal inflation rate," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 486-506.
    20. Mahmoudi, Babak, 2013. "Open-Market Operations, Asset Distributions, and Endogenous Market Segmentation," MPRA Paper 50089, University Library of Munich, Germany.
    21. Tsz-Nga Wong & Pierre-Olivier Weill & Guillaume Rocheteau, 2015. "Long-Run and Short-Run Effects of Money Injections," 2015 Meeting Papers 793, Society for Economic Dynamics.
    22. Jonathan Chiu & Miguel Molico, . "Short-Run Dynamics in a Search-Theoretic Model of Monetary Exchange," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.
    23. Gu, Chao & Wright, Randall, 2016. "Monetary mechanisms," Journal of Economic Theory, Elsevier, vol. 163(C), pages 644-657.

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    More about this item

    Keywords

    Money; Distribution; Search; Lattice-Theoretic;
    All these keywords.

    JEL classification:

    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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