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Monetary Theory with Non-degenerate Distributions

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  • Shouyong Shi

    (University of Toronto)

  • Hongfei Sun

    (Queen's University)

  • Guido Menzio

    (University of Pennsylvania)

Abstract

In this paper, we construct a tractable search model of money with a non-degenerate distribution of money holdings. We model search as a directed process in the sense that buyers know the terms of trade before visiting particular sellers, as opposed to undirected search that has dominated the literature. Directed search implies that the buyers who differ in money holdings will optimally choose to visit sellers who offer different terms of trade. With such endogenous separation of buyers, we show that the distribution of money holdings affects individual agents' decisions not directly, but rather indirectly only through a one-dimension variable – the seller's future marginal value of money. This result drastically reduces the state space of individual agents' decisions and makes the model tractable despite that the distribution of money holdings among agents is non-degenerate. We analytically characterize the monetary equilibrium and prove existence of a unique monetary steady state, using lattice-theoretic techniques. We also show that the non-degenerate distribution of money has desirable properties. Finally, we provide a calibrated example to illustrate the quantitative features of the steady state.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2009 Meeting Papers with number 172.

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Date of creation: 2009
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Handle: RePEc:red:sed009:172

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  1. 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.
  2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  3. 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.
  4. 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.
  5. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, vol. 71(3), pages 731-756, 05.
  6. Galenianos, Manolis & Kircher, Philipp, 2008. "A model of money with multilateral matching," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1054-1066, September.
  7. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, vol. 65(1), pages 75-102, January.
  8. Jonathan Chiu & Miguel Molico, 2011. "Uncertainty, Inflation, and Welfare," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43, pages 487-512, October.
  9. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  10. 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.
  11. Shouyong Shi, 2006. "Directed Search for Equilibrium Wage-Tenure Contracts," Working Papers tecipa-260, University of Toronto, Department of Economics.
  12. 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.
  13. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-27, September.
  14. Shouyong Shi, 1995. "Money and Prices: A Model of Search and Bargaining," Working Papers 916, Queen's University, Department of Economics.
  15. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
  16. Alain Delacroix & Shouyong Shi, 2003. "Directed Search On the Job and the Wage Ladder," Working Papers shouyong-03-04, University of Toronto, Department of Economics.
  17. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
  18. 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.
  19. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
  20. Francisco M. Gonzalez & Shouyong Shi, 2008. "An Equilibrium Theory of Learning, Search and Wages," Working Papers tecipa-328, University of Toronto, Department of Economics.
  21. 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.
  22. 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.
  23. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-54, September.
  24. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
  25. Julien, BenoI^t & Kennes, John & King, Ian, 2008. "Bidding for money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 196-217, September.
  26. 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.
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  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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