IDEAS home Printed from https://ideas.repec.org/p/red/sed009/172.html
   My bibliography  Save this paper

Monetary Theory with Non-degenerate Distributions

Author

Listed:
  • 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.

Suggested Citation

  • Shouyong Shi & Hongfei Sun & Guido Menzio, 2009. "Monetary Theory with Non-degenerate Distributions," 2009 Meeting Papers 172, Society for Economic Dynamics.
  • Handle: RePEc:red:sed009:172
    as

    Download full text from publisher

    File URL: https://economicdynamics.org/meetpapers/2009/paper_172.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    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. 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. 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.
    6. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, vol. 65(1), pages 75-102, January.
    7. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
    8. Edward J. Green & Ruilin Zhou, "undated". "A Rudimentary Model of Search with Divisible Money and Prices," Penn CARESS Working Papers 2772f94306e08ef7292945588, Penn Economics Department.
    9. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    10. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-1127, September.
    11. Shi Shougong, 1995. "Money and Prices: A Model of Search and Bargaining," Journal of Economic Theory, Elsevier, vol. 67(2), pages 467-496, December.
    12. 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.
    13. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October.
    14. 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.
    15. 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.
    16. 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.
    17. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    18. Francisco M. Gonzalez & Shouyong Shi, 2010. "An Equilibrium Theory of Learning, Search, and Wages," Econometrica, Econometric Society, vol. 78(2), pages 509-537, March.
    19. 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.
    20. 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.
    21. Galenianos, Manolis & Kircher, Philipp, 2008. "A model of money with multilateral matching," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1054-1066, September.
    22. Jonathan Chiu & Miguel Molico, 2011. "Uncertainty, Inflation, and Welfare," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43, pages 487-512, October.
    23. 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.
    24. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    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. 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.
    27. 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.
    28. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    29. 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.
    30. 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.
    31. 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.
    32. 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.
    33. Clausen, Andrew & Strub, Carlo, 2013. "A General and Intuitive Envelope Theorem," SIRE Discussion Papers 2015-43, Scottish Institute for Research in Economics (SIRE).
    34. 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.
    35. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, vol. 71(3), pages 731-756, May.
    36. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
    37. 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.
    38. 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.
    39. 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.
    40. 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.
    41. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Pablo Ottonello, 2015. "Capital Unemployment, Financial Shocks, and Investment Slumps," 2015 Meeting Papers 1153, Society for Economic Dynamics.
    3. 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.
    4. 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.
    5. Baughman, Garth & Rabinovich, Stanislav, 2019. "Self-confirming price dispersion in monetary economies," Journal of Economic Theory, Elsevier, vol. 183(C), pages 284-311.
    6. 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.
    7. 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.
    8. Yashar Blouri, Maximilian von Ehrlich, 2017. "On the optimal design of place-based policies: A structural evaluation of EU regional transfers," Diskussionsschriften credresearchpaper17, Universitaet Bern, Departement Volkswirtschaft - CRED.
    9. 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.
    10. 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).
    11. Beverly Lapham & Ayman Mnasri, 2019. "Exchange Rate Pass-Through: A Competitive Search Approach," Working Paper 1418, Economics Department, Queen's University.
    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. Maurizio Iacopetta, 2014. "Dynamics of assets liquidity and inequality in economies with decentralized markets," Sciences Po publications info:hdl:2441/2029nqlehl8, Sciences Po.
    14. 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.
    15. 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.
    16. Guerrieri, Veronica & Julien, Benoit & Kircher, Philipp & Wright, Randall, 2017. "Directed Search: A Guided Tour," CEPR Discussion Papers 12315, C.E.P.R. Discussion Papers.
    17. 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.
    18. Guillaume Rocheteau & Pierre-Olivier Weill & Tsz-Nga Wong, 2018. "An Heterogeneous-Agent New-Monetarist Model with an Application to Unemployment," NBER Working Papers 25220, National Bureau of Economic Research, Inc.
    19. 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.
    20. Davoodalhosseini, Seyed Mohammadreza, 2019. "Constrained efficiency with adverse selection and directed search," Journal of Economic Theory, Elsevier, vol. 183(C), pages 568-593.
    21. Chao Gu & Randall Wright, 2016. "Monetary Mechanisms," Working Papers 1601, Department of Economics, University of Missouri.
    22. Mahmoudi, Babak, 2013. "Open-Market Operations, Asset Distributions, and Endogenous Market Segmentation," MPRA Paper 50089, University Library of Munich, Germany.
    23. 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.
    24. Gu, Chao & Wright, Randall, 2016. "Monetary mechanisms," Journal of Economic Theory, Elsevier, vol. 163(C), pages 644-657.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stephen D. Williamson & Randall Wright, 2010. "New monetarist economics: methods," Review, Federal Reserve Bank of St. Louis, vol. 92(May), pages 265-302.
    2. 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.
    3. Mahmoudi, Babak, 2013. "Open-Market Operations, Asset Distributions, and Endogenous Market Segmentation," MPRA Paper 50089, University Library of Munich, Germany.
    4. Shouyong Shi, 2006. "A Microfoundation of Monetary Economics," Working Papers tecipa-211, University of Toronto, Department of Economics.
    5. Aleksander Berentsen & Guido Menzio & Randall Wright, 2011. "Inflation and Unemployment in the Long Run," American Economic Review, American Economic Association, vol. 101(1), pages 371-398, February.
    6. Richard Dutu & Benoit Julien & Ian King, 2009. "Liquidity Constrained Competing Auctions," Department of Economics - Working Papers Series 1068, The University of Melbourne.
    7. Aleksander Berentsen & Guillaume Rocheteau & Shouyong Shi, 2007. "Friedman Meets Hosios: Efficiency in Search Models of Money," Economic Journal, Royal Economic Society, vol. 117(516), pages 174-195, January.
    8. 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.
    9. Han, Han & Julien, Benoît & Petursdottir, Asgerdur & Wang, Liang, 2016. "Equilibrium using credit or money with indivisible goods," Journal of Economic Theory, Elsevier, vol. 166(C), pages 152-163.
    10. Randall Wright, 2005. "Introduction to \\"Models of Monetary Economies II: The Next Generation\\"," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 29(Oct), pages 2-9.
    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, Russell, 2018. "A tractable model of monetary exchange with ex-post heterogeneity," Theoretical Economics, Econometric Society, vol. 13(3), September.
    13. Rocheteau, Guillaume & Rupert, Peter & Shell, Karl & Wright, Randall, 2008. "General equilibrium with nonconvexities and money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 294-317, September.
    14. Scott J. Dressler, 2011. "Money Holdings, Inflation, And Welfare In A Competitive Market," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(2), pages 407-423, May.
    15. Shi, Shouyong, 2016. "Customer relationship and sales," Journal of Economic Theory, Elsevier, vol. 166(C), pages 483-516.
    16. Jean, Kasie & Rabinovich, Stanislav & Wright, Randall, 2010. "On the multiplicity of monetary equilibria: Green-Zhou meets Lagos-Wright," Journal of Economic Theory, Elsevier, vol. 145(1), pages 392-401, January.
    17. Anbarci, Nejat & Dutu, Richard & Feltovich, Nick, 2015. "Inflation tax in the lab: a theoretical and experimental study of competitive search equilibrium with inflation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 17-33.
    18. Rocheteau, Guillaume & Rupert, Peter & Wright, Randall, 2007. "Inflation and Unemployment in General Equilibrium," University of California at Santa Barbara, Economics Working Paper Series qt2fq1855f, Department of Economics, UC Santa Barbara.
    19. Rocheteau, Guillaume & Rupert, Peter & Shell, Karl & Wright, Randall, 2005. "General Equilibrium with Nonconvexities, Sunspots, and Money," Working Papers 05-16, Cornell University, Center for Analytic Economics.
    20. Shouyong Shi, 2006. "Viewpoint: A microfoundation of monetary economics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 39(3), pages 643-688, August.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:red:sed009:172. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christian Zimmermann). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.