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Applying Negishi's method to stochastic models with overlapping generations

  • Felix Kubler

    (University of Zurich and SFI)

  • Johannes Brumm

    (University of Zurich)

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

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Date of creation: 2013
Date of revision:
Handle: RePEc:red:sed013:1352
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Society for Economic Dynamics Marina Azzimonti Department of Economics Stonybrook University 10 Nicolls Road Stonybrook NY 11790 USA

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  1. Timothy J. Kehoe & David K. Levine & Paul M. Romer, 1990. "On characterizing equilibria of economies with externalities and taxes as solutions to optimization problems," Working Papers 436, Federal Reserve Bank of Minneapolis.
  2. 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.
  3. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manuel S. Santos, . "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," Boston University - Department of Economics - Working Papers Series wp2009-013, Boston University - Department of Economics.
  4. 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.
  5. 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.
  6. Felix Kubler & Karl Schmedders, 2005. "Approximate versus Exact Equilibria in Dynamic Economies," Econometrica, Econometric Society, vol. 73(4), pages 1205-1235, 07.
  7. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June.
  8. 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.
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