Approximate Versus Exact Equilibria

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• K.Schmedders
• F.Kubler
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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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Handle: RePEc:sce:scecf4:46

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Keywords: error analysis; incomplete markets;

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• C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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References

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1. 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 105-11, February.
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Cited by:
1. D'Agata, Antonio, 2012. "Existence of an exact Walrasian equilibrium in nonconvex economies," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 6(12), pages 1-16.

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