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. 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. 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.
    5. 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.
    6. Daron Acemoglu & Robert Shimer, 1999. "Efficient Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 893-928, October.
    7. 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.
    8. 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.
    9. 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.
    10. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    11. 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.
    12. Francisco M. Gonzalez & Shouyong Shi, 2010. "An Equilibrium Theory of Learning, Search, and Wages," Econometrica, Econometric Society, vol. 78(2), pages 509-537, March.
    13. 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.
    14. Julien, BenoI^t & Kennes, John & King, Ian, 2008. "Bidding for money," Journal of Economic Theory, Elsevier, vol. 142(1), pages 196-217, September.
    15. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
    16. 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.
    17. 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.
    18. Aleksander Berentsen & Gabriele Camera & Christopher Waller, 2004. "The distribution of money and prices in an equilibrium with lotteries," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(4), pages 887-906, November.
    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. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    28. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, vol. 65(1), pages 75-102, January.
    29. Peters, Michael, 1984. "Bertrand Equilibrium with Capacity Constraints and Restricted Mobility," Econometrica, Econometric Society, vol. 52(5), pages 1117-1127, September.
    30. Shi Shougong, 1995. "Money and Prices: A Model of Search and Bargaining," Journal of Economic Theory, Elsevier, vol. 67(2), pages 467-496, December.
    31. Galenianos, Manolis & Kircher, Philipp, 2008. "A model of money with multilateral matching," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1054-1066, September.
    32. Jonathan Chiu & Miguel Molico, 2011. "Uncertainty, Inflation, and Welfare," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43, pages 487-512, October.
    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. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, vol. 71(3), pages 731-756, May.
    39. Lucas, Robert Jr., 1990. "Liquidity and interest rates," Journal of Economic Theory, Elsevier, vol. 50(2), pages 237-264, April.
    40. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Pablo Ottonello, 2015. "Capital Unemployment, Financial Shocks, and Investment Slumps," 2015 Meeting Papers 1153, Society for Economic Dynamics.
    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. repec:eee:jetheo:v:172:y:2017:i:c:p:423-450 is not listed on IDEAS
    4. Guillaume Rocheteau & Pierre-Olivier Weill & Tsz-Nga Wong, 2015. "A Tractable Model of Monetary Exchange with Ex-post Heterogeneity," NBER Working Papers 21179, National Bureau of Economic Research, Inc.
    5. Enders, Zeno, 2012. "Heterogeneous consumers, segmented asset markets, and the effects of monetary policy," Working Papers 0537, University of Heidelberg, Department of Economics.
    6. Maurizio Iacopetta, 2014. "Dynamics of assets liquidity and inequality in economies with decentralized markets," Sciences Po publications info:hdl:2441/2029nqlehl8, Sciences Po.
    7. Jung, Kuk Mo, 2016. "Uncertainty-Induced Dynamic Inefficiency and the Optimal Inflation Rate," MPRA Paper 69715, University Library of Munich, Germany.
    8. 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.
    9. Zeno Enders, 2010. "Heterogeneous consumers, segmented asset markets,and the effects of monetary policy," Bonn Econ Discussion Papers bgse08_2010, University of Bonn, Germany.
    10. Guerrieri, Veronica & Julien, Benoit & Kircher, Philipp & Wright, Randall, 2017. "Directed Search: A Guided Tour," CEPR Discussion Papers 12315, C.E.P.R. Discussion Papers.
    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. Mohammad Davoodalhosseini, 2017. "Constrained Efficiency with Adverse Selection and Directed Search," Staff Working Papers 17-15, Bank of Canada.
    13. Chao Gu & Randall Wright, 2016. "Monetary Mechanisms," Working Papers 1601, Department of Economics, University of Missouri.
    14. Zeno Enders, 2017. "Heterogeneous Consumers, Segmented Asset Markets, and the Real Effects of Monetary Policy," CESifo Working Paper Series 6467, CESifo Group Munich.
    15. Mahmoudi, Babak, 2013. "Open-Market Operations, Asset Distributions, and Endogenous Market Segmentation," MPRA Paper 50089, University Library of Munich, Germany.
    16. Gu, Chao & Wright, Randall, 2016. "Monetary mechanisms," Journal of Economic Theory, Elsevier, vol. 163(C), pages 644-657.

    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: http://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.