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A Monetary Theory with Non-Degenerate Distributions

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 11-009.

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Length: 57 pages
Date of creation: 11 Mar 2011
Date of revision:
Handle: RePEc:pen:papers:11-009

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Keywords: Money; Distribution; Search; Lattice-Theoretic;

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References

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  1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  2. Guido Menzio & Shouyong Shi, 2009. "Block Recursive Equilibria for Stochastic Models of Search on the Job," Working Papers tecipa-347, University of Toronto, Department of Economics.
  3. Guido Menzio & Shouyong Shi, 2011. "Efficient Search on the Job and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 468 - 510.
  4. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, vol. 65(1), pages 75-102, January.
  5. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  6. Edward J. Green & Ruilin Zhou, . ""A Rudimentary Model of Search with Divisible Money and Prices''," CARESS Working Papres 95-17, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  7. Shouyong Shi, 2006. "Directed Search for Equilibrium Wage-Tenure Contracts," Working Papers tecipa-260, University of Toronto, Department of Economics.
  8. Randall Wright & Guillame Rocheteau, 2003. "Money in Search Equilibrium, in Competitive Equilibrium, and in Competitive Search Equilibrium," Levine's Bibliography 666156000000000302, UCLA Department of Economics.
  9. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-27, September.
  10. Shouyong Shi, 1995. "Money and Prices: A Model of Search and Bargaining," Working Papers 916, Queen's University, Department of Economics.
  11. Miguel Molico, 2006. "The Distribution Of Money And Prices In Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 701-722, 08.
  12. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
  13. Francisco M. Gonzalez & Shouyong Shi, 2008. "An Equilibrium Theory of Learning, Search and Wages," Working Papers tecipa-328, University of Toronto, Department of Economics.
  14. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
  15. Jonathan Chiu & Miguel Molico, 2008. "Uncertainty, Inflation, and Welfare," Working Papers 08-13, Bank of Canada.
  16. Trejos, Alberto & Wright, Randall, 1995. "Search, Bargaining, Money, and Prices," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 118-41, February.
  17. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-54, September.
  18. Julien, BenoI^t & Kennes, John & King, Ian, 2008. "Bidding for money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 196-217, September.
  19. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-54, August.
  20. Moen, E.R., 1995. "Competitive Search Equilibrium," Memorandum 37/1995, Oslo University, Department of Economics.
  21. Alain Delacroix & Shouyong Shi, 2006. "Directed Search On The Job And The Wage Ladder," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 651-699, 05.
  22. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  23. Zhu, Tao, 2003. "Existence of a monetary steady state in a matching model: indivisible money," Journal of Economic Theory, Elsevier, vol. 112(2), pages 307-324, October.
  24. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, vol. 71(3), pages 731-756, 05.
  25. Galenianos, Manolis & Kircher, Philipp, 2008. "A model of money with multilateral matching," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1054-1066, September.
  26. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
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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 2011-04-11 02:44:40
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Cited by:
  1. Williamson, Stephen D. & Wright, Randall, 2010. "New Monetarist Economics: Models," MPRA Paper 21030, University Library of Munich, Germany.
  2. Enders, Zeno, 2012. "Heterogeneous consumers, segmented asset markets, and the effects of monetary policy," Working Papers 0537, University of Heidelberg, Department of Economics.

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