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Approximate recursive equilibrium with minimal state space

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  • Raad, Rodrigo Jardim

Abstract

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

Suggested Citation

  • Raad, Rodrigo Jardim, 2013. "Approximate recursive equilibrium with minimal state space," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 737, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:epgewp:737
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    References listed on IDEAS

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    1. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. Felix Kubler & Karl Schmedders, 2005. "Approximate versus Exact Equilibria in Dynamic Economies," Econometrica, Econometric Society, vol. 73(4), pages 1205-1235, July.
    5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    6. 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.
    7. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    8. Jordan, J S, 1977. "The Continuity of Optimal Dynamic Decision Rules," Econometrica, Econometric Society, vol. 45(6), pages 1365-1376, September.
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