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# Approximate Versus Exact Equilibria

## Author Info

Listed author(s):
• K.Schmedders
• F.Kubler
Registered author(s):

## Abstract

This paper develops theoretical foundations for the computation of competitive equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms which compute prices and allocations for which agents' first order conditions are approximately satisfied (`approximate equilibria'), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. Following Postlewaite and Schmeidler (1981) we interpret approximate equilibria as equilibria for close-by economies, i.e.\ for economies with close-by individual endowments and preferences. In order to conduct an error analysis in dynamic stochastic general equilibrium models, we define an $\epsilon$-equilibrium to be a set of endogenous variables which consists of the finite support of an approximate equilibrium process. Given an $\epsilon$-equilibrium we show how to derive bounds on perturbations in individual endowments and preferences which ensure that the $\epsilon$-equilibrium approximates an exact equilibrium for the perturbed economy.

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## Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 46.

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 Length: Date of creation: 21 Jul 2004 Handle: RePEc:sce:scecf4:46 Contact details of provider: Web page: http://comp-econ.org/Email: More information through EDIRC

## References

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1. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
2. Ingram, Beth Fisher, 1990. "Equilibrium Modeling of Asset Prices: Rationality versus Rules of Thumb," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 115-125, January.
3. John Heaton & Deborah Lucas, 1993. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," NBER Working Papers 4249, National Bureau of Economic Research, Inc.
4. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
5. Felix Kubler & Karl Schmedders, 2001. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Discussion Papers 1319, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
6. Felix Kubler & Herakles Polemarchakis, 2004. "Stationary Markov equilibria for overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 623-643, October.
7. José-Víctor Ríos-Rull, 1996. "Life-Cycle Economies and Aggregate Fluctuations," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 465-489.
8. Mailath,G.J. & Postlewaite,A. & Samuelson,L., 2002. "Contemporaneous perfect Epsilon-equilibria," Working papers 5, Wisconsin Madison - Social Systems.
9. Christopher A. Sims, 1989. "Solving nonlinear stochastic optimization and equilibrium problems backwards," Discussion Paper / Institute for Empirical Macroeconomics 15, Federal Reserve Bank of Minneapolis.
10. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
11. Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 1-27.
12. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
13. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
14. Mas-Colell,Andreu, 1985. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521265140, May.
15. Hellwig, Martin F., 1982. "Rational expectations and the Markov property of temporary equilibrium processes," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 135-144, January.
16. Postlewaite, Andrew & Schmeidler, David, 1981. "Approximate Walrasian Equilibria and Nearby Economies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 105-111, February.
17. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
18. Herbert E. Scarf, 1967. "On the Computation of Equilibrium Prices," Cowles Foundation Discussion Papers 232, Cowles Foundation for Research in Economics, Yale University.
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