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A Monetary Theory with Non-Degenerate Distributions

Author

Listed:
  • Guido Menzio

    (Department of Economics, University of Pennsylvania)

  • Shouyong Shi

    (Department of Economics, University of Toronto)

  • Hongfei Sun

    (Department of Economics, Queens University)

Abstract

Dispersion of money balances among individuals is the basis for a range of policies but it has been abstracted from in monetary theory for tractability reasons. In this paper, we fill in this gap by constructing a tractable search model of money with a non-degenerate distribution of money holdings. We assume search to be directed in the sense that buyers know the terms of trade before visiting particular sellers. Directed search makes the monetary steady state block recursive in the sense that individuals’ policy functions, value functions and the market tightness function are all independent of the distribution of individuals over money balances, although the distribution affects the aggregate activity by itself. Block recursivity enables us to characterize the equilibrium analytically. 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. Moreover, we provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate and analyze the properties of this distribution.

Suggested Citation

  • Guido Menzio & Shouyong Shi & Hongfei Sun, 2011. "A Monetary Theory with Non-Degenerate Distributions," PIER Working Paper Archive 11-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:11-009
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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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