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A Monetary Theory with Non-degenerate Distributions

Author

Listed:
  • Guido Menzio
  • Shouyong Shi
  • Hongfei Sun

Abstract

We construct and analyze a tractable search model of money with a non-degenerate distribution of money holdings. Analytical tractability comes from modeling decentralized exchange as directed search, which makes the monetary steady state block recursive. 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 and provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate. Moreover, we analyze the properties of this distribution.

Suggested Citation

  • Guido Menzio & Shouyong Shi & Hongfei Sun, 2013. "A Monetary Theory with Non-degenerate Distributions," Working Papers tecipa-495, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-495
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    1. Aleksander Berentsen & Gabriele Camera & C hristopher W aller, 2005. "The Distribution Of Money Balances And The Nonneutrality Of Money," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(2), pages 465-487, May.
    2. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    3. Menzio, Guido & Shi, Shouyong, 2010. "Block recursive equilibria for stochastic models of search on the job," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1453-1494, July.
    4. Edward J. Green & Ruilin Zhou, "undated". ""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.
    5. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October.
    6. 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, August.
    7. 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.
    8. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    9. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    10. 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.
    11. Francisco M. Gonzalez & Shouyong Shi, 2010. "An Equilibrium Theory of Learning, Search, and Wages," Econometrica, Econometric Society, vol. 78(2), pages 509-537, March.
    12. 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.
    13. Julien, BenoI^t & Kennes, John & King, Ian, 2008. "Bidding for money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 196-217, September.
    14. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
    15. William J. Baumol, 1952. "The Transactions Demand for Cash: An Inventory Theoretic Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 66(4), pages 545-556.
    16. 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.
    17. Aleksander Berentsen & Gabriele Camera & Christopher Waller, 2006. "The distribution of money and prices in an equilibrium with lotteries," Studies in Economic Theory, in: Charalambos D. Aliprantis & Nicholas C. Yannelis & Gabriele Camera (ed.), Recent Developments on Money and Finance, pages 173-193, Springer.
    18. Guillaume Rocheteau & Randall Wright, 2005. "Money in Search Equilibrium, in Competitive Equilibrium, and in Competitive Search Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 175-202, January.
    19. Zhu, Tao, 2005. "Existence of a monetary steady state in a matching model: divisible money," Journal of Economic Theory, Elsevier, vol. 123(2), pages 135-160, August.
    20. Jonathan Chiu & Miguel Molico, 2011. "Uncertainty, Inflation, and Welfare," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43, pages 487-512, October.
    21. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    22. Zhou, Ruilin, 1999. "Individual and Aggregate Real Balances in a Random-Matching Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 1009-1038, November.
    23. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    24. Jovanovic, Boyan, 1982. "Inflation and Welfare in the Steady State," Journal of Political Economy, University of Chicago Press, vol. 90(3), pages 561-577, June.
    25. Ricardo Lagos & Guillaume Rocheteau, 2005. "Inflation, Output, And Welfare," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(2), pages 495-522, May.
    26. Benoit Julien & John Kennes & Ian King, 2000. "Bidding for Labor," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 619-649, October.
    27. Rotemberg, Julio J, 1984. "A Monetary Equilibrium Model with Transactions Costs," Journal of Political Economy, University of Chicago Press, vol. 92(1), pages 40-58, February.
    28. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    29. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, vol. 65(1), pages 75-102, January.
    30. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-1127, September.
    31. Shi Shougong, 1995. "Money and Prices: A Model of Search and Bargaining," Journal of Economic Theory, Elsevier, vol. 67(2), pages 467-496, December.
    32. Galenianos, Manolis & Kircher, Philipp, 2008. "A model of money with multilateral matching," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1054-1066, September.
    33. Trejos, Alberto & Wright, Randall, 1995. "Search, Bargaining, Money, and Prices," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 118-141, February.
    34. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    35. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    36. 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, May.
    37. 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.
    38. Clausen, Andrew & Strub, Carlo, 2013. "A General and Intuitive Envelope Theorem," SIRE Discussion Papers 2015-43, Scottish Institute for Research in Economics (SIRE).
    39. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, vol. 71(3), pages 731-756, May.
    40. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
    41. Faig, Miquel, 2008. "Endogenous buyer-seller choice and divisible money in search equilibrium," Journal of Economic Theory, Elsevier, vol. 141(1), pages 184-199, July.
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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:

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    2. 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.
    3. 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.
    4. Beverly Lapham & Ayman Mnasri, 2019. "Exchange Rate Pass-Through: A Competitive Search Approach," Working Paper 1418, Economics Department, Queen's University.
    5. Maurizio Iacopetta, 2014. "Dynamics of assets liquidity and inequality in economies with decentralized markets," Sciences Po publications info:hdl:2441/2029nqlehl8, Sciences Po.
    6. 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.
    7. Yashar Blouri & Maximilian von Ehrlich, 2017. "On the Optimal Design of Place-Based Policies: A Structural Evaluation of EU Regional Transfers," CESifo Working Paper Series 6742, CESifo.
    8. Baughman, Garth & Rabinovich, Stanislav, 2019. "Self-confirming price dispersion in monetary economies," Journal of Economic Theory, Elsevier, vol. 183(C), pages 284-311.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Chao Gu & Randall Wright, 2016. "Monetary Mechanisms," Working Papers 1601, Department of Economics, University of Missouri.
    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. Randall Wright & Philipp Kircher & Benoit Julîen & Veronica Guerrieri, 2017. "Directed Search: A Guided Tour," NBER Working Papers 23884, National Bureau of Economic Research, Inc.
    17. 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.
    18. Gu, Chao & Wright, Randall, 2016. "Monetary mechanisms," Journal of Economic Theory, Elsevier, vol. 163(C), pages 644-657.
    19. Pablo Ottonello, 2015. "Capital Unemployment, Financial Shocks, and Investment Slumps," 2015 Meeting Papers 1153, Society for Economic Dynamics.
    20. 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.
    21. 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.
    22. 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).
    23. Davoodalhosseini, Seyed Mohammadreza, 2019. "Constrained efficiency with adverse selection and directed search," Journal of Economic Theory, Elsevier, vol. 183(C), pages 568-593.
    24. Mahmoudi, Babak, 2013. "Open-Market Operations, Asset Distributions, and Endogenous Market Segmentation," MPRA Paper 50089, University Library of Munich, Germany.
    25. Zeno Enders, 2017. "Heterogeneous Consumers, Segmented Asset Markets, and the Real Effects of Monetary Policy," CESifo Working Paper Series 6467, CESifo.

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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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