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Inflationary Equilibrium in a Stochastic Economy with Independent Agents

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We argue that even when macroeconomic variables are constant, underlying microeconomic uncertainty and borrowing constraints generate inflation. We study stochastic economies with fiat money, a central bank, one nondurable commodity, countably many time periods, and a continuum of agents. The aggregate amount of the commodity remains constant, but the endowments of individual agents fluctuate "independently" in a random fashion from period to period. Agents hold money and, prior to bidding in the commodity market each period, can either borrow from or deposit in a central bank at a fixed rate of interest. If the interest rate is strictly positive, then typically there will not exist an equilibrium with a stationary wealth distribution and a fixed price for the commodity. Consequently, we investigate stationary equilibria with inflation, in which aggregate wealth and prices rise deterministically and at the same rate. Such an equilibrium does exist under appropriate bounds on the interest rate set by the central bank and on the amount of borrowing by the agents. If there is no uncertainty, or if the stationary strategies of the agents select actions in the interior of their action sets in equilibrium, then the classical Fisher equation for the rate of inflation continues to hold and the real rate of interest is equal to the common discount rate of the agents. However, with genuine uncertainty in the endowments and with convex marginal utilities, no interior equilibrium can exist. The equilibrium inflation must then be higher than that predicted by the Fisher equation, and the equilibrium real rate of interest underestimates the discount rate of the agents.

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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d17/d1708.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1708.

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Length: 30 pages
Date of creation: Jun 2009
Publication status: Published in Journal of Mathematical Economics (May 2014), 52: 1-11
Handle: RePEc:cwl:cwldpp:1708
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  1. Huggett, Mark, 1997. "The one-sector growth model with idiosyncratic shocks: Steady states and dynamics," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 385-403, August.
  2. Karatzas, Ioannis & Shubik, Martin & Sudderth, William D., 1997. "A strategic market game with secured lending," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 207-247, September.
  3. Laitner, John, 1992. "Random earnings differences, lifetime liquidity constraints, and altruistic intergenerational transfers," Journal of Economic Theory, Elsevier, vol. 58(2), pages 135-170, December.
  4. Laitner, John P, 1979. "Bequests, Golden-age Capital Accumulation and Government Debt," Economica, London School of Economics and Political Science, vol. 46(184), pages 403-414, November.
  5. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
  6. Geanakoplos, J. & Karatzas, I. & Shubik, M. & Sudderth, W., 2000. "A strategic market game with active bankruptcy," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 359-396, November.
  7. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1992. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Cowles Foundation Discussion Papers 1033, Cowles Foundation for Research in Economics, Yale University.
  8. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
  9. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  10. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 807-835, 08.
  11. Ioannis Karatzas & Martin Shubik & William Sudderth & John Geanakoplos, 2006. "The inflationary bias of real uncertainty and the harmonic Fisher equation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 481-512, 08.
  12. Clarida, Richard H, 1990. "International Lending and Borrowing in a Stochastic, Stationary Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 543-558, August.
  13. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
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