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Recursive equilibria in an Aiyagari style economy with permanent income shocks

  • Kuhn, Moritz

In this paper, we prove the existence of a recursive competitive equilibrium (RCE) for an Aiyagari style economy with permanent income shocks and perpetual youth structure. We show that there exist equilibria where borrowing constraints are never binding. This allows us to establish a non-trivial lower bound on the equilibrium interest rate. To solve the individual’s problem, we present a new approach that uses lattices of consumption functions to deal with the non-compact state space and the unbounded utility function. The approach uses only the first order conditions of the problem (Euler equations). The proof is constructive and it serves as a theoretical foundation for the convergence of a policy function iteration procedure.

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File URL: http://mpra.ub.uni-muenchen.de/32323/1/MPRA_paper_32323.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32323.

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Date of creation: 12 Dec 2008
Date of revision: 09 Dec 2009
Handle: RePEc:pra:mprapa:32323
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  1. Carroll, Christopher D. & Samwick, Andrew A., 1997. "The nature of precautionary wealth," Journal of Monetary Economics, Elsevier, vol. 40(1), pages 41-71, September.
  2. Jianjun Miao, 2003. "Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks," Macroeconomics 0310001, EconWPA.
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  4. Cuong Le Van & John Stachurski, 2006. "Parametric Continuity of Stationary Distributions," KIER Working Papers 616, Kyoto University, Institute of Economic Research.
  5. Richard Blundell & Luigi Pistaferri & Ian Preston, 2004. "Consumption inequality and partial insurance," IFS Working Papers W04/28, Institute for Fiscal Studies.
  6. Tom Krebs, 2007. "Job Displacement Risk and the Cost of Business Cycles," American Economic Review, American Economic Association, vol. 97(3), pages 664-686, June.
  7. Christopher D. Carroll, 2004. "Theoretical Foundations of Buffer Stock Saving," Economics Working Paper Archive 517, The Johns Hopkins University,Department of Economics.
  8. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-48, September.
  9. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  10. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
  11. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Consumption and Labor Supply with Partial Insurance: An Analytical Framework," NBER Working Papers 15257, National Bureau of Economic Research, Inc.
  12. Meghir, Costas & Pistaferri, Luigi, 2002. "Income Variance Dynamics and Heterogeneity," CEPR Discussion Papers 3632, C.E.P.R. Discussion Papers.
  13. Telmer, Chris I, 1993. " Asset-Pricing Puzzles and Incomplete Markets," Journal of Finance, American Finance Association, vol. 48(5), pages 1803-32, December.
  14. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-40, April.
  15. Christopher D. Carroll & Miles S. Kimball, 1995. "On the concavity of the consumption function," Finance and Economics Discussion Series 95-10, Board of Governors of the Federal Reserve System (U.S.).
  16. 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.
  17. Rabault, Guillaume, 2002. "When do borrowing constraints bind? Some new results on the income fluctuation problem," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 217-245, February.
  18. Wilbur John Coleman II, 1989. "Equilibrium in a production economy with an income tax," International Finance Discussion Papers 366, Board of Governors of the Federal Reserve System (U.S.).
  19. Tom Krebs, 2004. "Welfare Cost of Business Cycles When Markets Are Incomplete," Working Papers 2004-08, Brown University, Department of Economics.
  20. Huggett, Mark & Ospina, Sandra, 2001. "Aggregate precautionary savings: when is the third derivative irrelevant?," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 373-396, October.
  21. Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
  22. Tom Krebs, 2002. "Non-Existence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete," Working Papers 2002-17, Brown University, Department of Economics.
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