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Applying Negishi's method to stochastic models with overlapping generations

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  • Felix Kubler

    (University of Zurich and SFI)

  • Johannes Brumm

    (University of Zurich)

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    Abstract

    In this paper we develop a Negishi approach to characterize recursive equilibria in stochastic models with overlapping generations. When competitive equilibria are Pareto-optimal, using Negishi-weights as a co-state variable has three major computational advantages over the standard approach of using the natural state: First, the endogenous state space is a unit simplex and thus easy to handle. Second, the number of unknown functions characterizing equilibrium dynamics is orders of magnitude smaller. Third, approximation errors have a compelling economic interpretation. Our main contribution is to show that the Negishi approach extends naturally to models with borrowing-constraints and incomplete financial markets where the welfare theorems fail. Many of the computational advantages carry over to this setting. We derive sufficient conditions for the existence of Markov equilibria in the complete markets model as well as for models with incomplete markets and borrowing constraints.

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    Bibliographic Info

    Paper provided by Society for Economic Dynamics in its series 2013 Meeting Papers with number 1352.

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    Date of creation: 2013
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    Handle: RePEc:red:sed013:1352

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    1. Yili Chien & Harold Cole & Hanno Lustig, 2011. "A Multiplier Approach to Understanding the Macro Implications of Household Finance," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 199-234.
    2. David Cass, 2006. "Musings on the Cass Trick," PIER Working Paper Archive 06-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manual Santos, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," Working Papers 0912, University of Miami, Department of Economics.
    4. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer, vol. 24(3), pages 623-643, October.
    5. Hanno Lustig & Yi-Li Chien, 2005. "The Market Price of Aggregate Risk and the Wealth Distribution," NBER Working Papers 11132, National Bureau of Economic Research, Inc.
    6. Kjetil Storesletten & Chris Telmer & Amir Yaron, 1996. "Asset pricing with idiosyncratic risk and overlapping generations," Economics Working Papers 405, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1999.
    7. Kehoe, Timothy J & Levine, David K & Romer, Paul M, 1992. "On Characterizing Equilibria of Economies with Externalities and Taxes as Solutions to Optimization Problems," Economic Theory, Springer, vol. 2(1), pages 43-68, January.
    8. Bernard Dumas & Andrew Lyasoff, 2012. "Incomplete-Market Equilibria Solved Recursively on an Event Tree," Journal of Finance, American Finance Association, vol. 67(5), pages 1897-1941, October.
    9. Felix Kubler & Karl Schmedders, 2005. "Approximate versus Exact Equilibria in Dynamic Economies," Econometrica, Econometric Society, vol. 73(4), pages 1205-1235, 07.
    10. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-57, July.
    11. Huffman, Gregory W, 1987. "A Dynamic Equilibrium Model of Asset Prices and Transaction Volume," Journal of Political Economy, University of Chicago Press, vol. 95(1), pages 138-59, February.
    12. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
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    Cited by:
    1. Jose-Victor Rios Rull & Jonathan Heathcote & Dirk Krueger & Andy Glover, 2011. "Intergenerational Redistribution in the Great Recession," 2011 Meeting Papers 141, Society for Economic Dynamics.

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