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Approximate Versus Exact Equilibria in Dynamic Economies

In: Computational Aspects of General Equilibrium Theory

Author

Listed:
  • Felix Kubler

    (University of Pennsylvania)

  • Karl Schmedders

    (Northwestern University)

Abstract

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents— first-order conditions are approximately satisfied (“approximate equilibria”), there are few results on h interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close-by economies; that is, for economies with close-by individual endowments and preferences. We present an error analysis for two models that are commonly used in applications, an overlapping generations (OLG) model with stochastic production and an asset pricing model with infinitely lived agents. We provide sufficient conditions that ensure that approximate equilibria are close to exact equilibria of close-by economies. Numerical examples illustrate the analysis.

Suggested Citation

  • Felix Kubler & Karl Schmedders, 2008. "Approximate Versus Exact Equilibria in Dynamic Economies," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 135-163, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-76591-2_10
    DOI: 10.1007/978-3-540-76591-2_10
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    Cited by:

    1. Marco Bassetto & Zhen Huo & José-Víctor Ríos-Rull, 2018. "Organizational Equilibrium with Capital," Working Paper Series WP-2018-20, Federal Reserve Bank of Chicago.
    2. P. Siconolfi & A. Citanna, 2007. "Recursive equilibrium in stochastic OLG economies," 2007 Meeting Papers 777, Society for Economic Dynamics.
    3. D'Agata, Antonio, 2011. "Existence of exact Walrasian equilibria in non convex economies," Economics Discussion Papers 2011-47, Kiel Institute for the World Economy (IfW Kiel).
    4. Rodrigo Raad, 2016. "Recursive equilibrium with Price Perfect Foresight and a minimal state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 1-54, January.
    5. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2017. "Lower Bounds on Approximation Errors to Numerical Solutions of Dynamic Economic Models," Econometrica, Econometric Society, vol. 85, pages 991-1012, May.
    6. Kubler, Felix & Scheidegger, Simon, 2023. "Uniformly self-justified equilibria," Journal of Economic Theory, Elsevier, vol. 212(C).
    7. Dunbar, Geoffrey, 2013. "Returns-to-scale and the equity premium puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1736-1754.
    8. Pascal Gauthier & Timothy J. Kehoe & Erwan Quintin, 2022. "Constructing pure-exchange economies with many equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 541-564, April.
    9. Henriksen, Espen & Spear, Stephen, 2012. "Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies," Journal of Economic Theory, Elsevier, vol. 147(2), pages 426-449.
    10. Felix Kubler & Johannes Brumm, 2013. "Applying Negishi's method to stochastic models with overlapping generations," 2013 Meeting Papers 1352, Society for Economic Dynamics.
    11. D'Agata, Antonio, 2012. "Existence of an exact Walrasian equilibrium in nonconvex economies," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-16.
    12. Yu, Changhua, 2015. "Evaluating international financial integration in a center-periphery economy," Journal of International Economics, Elsevier, vol. 95(1), pages 129-144.
    13. Raad, Rodrigo Jardim, 2013. "Approximate recursive equilibrium with minimal state space," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 737, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    14. Émilien Gouin‐Bonenfant & Alexis Akira Toda, 2023. "Pareto extrapolation: An analytical framework for studying tail inequality," Quantitative Economics, Econometric Society, vol. 14(1), pages 201-233, January.
    15. Leonid Kogan & Indrajit Mitra, 2021. "Near-Rational Equilibria in Heterogeneous-Agent Models: A Verification Method," FRB Atlanta Working Paper 2021-16, Federal Reserve Bank of Atlanta.
    16. Geng, Runjie & Kubler, Felix, 2023. "Stochastic overlapping generations with non-convex budget sets," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    17. Jonen, Benjamin & Scheuring, Simon, 2014. "Time-varying international diversification and the forward premium," Journal of International Money and Finance, Elsevier, vol. 40(C), pages 128-148.
    18. Chakrabarti, Subir K., 2014. "On the robustness of the competitive equilibrium: Utility-improvements and equilibrium points," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 36-47.
    19. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    20. A. Jofré & R. T. Rockafellar & R. J-B. Wets, 2017. "General economic equilibrium with financial markets and retainability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 309-345, January.
    21. Alessandro Citanna & Paolo Siconolfi, 2008. "On the nonexistence of recursive equilibrium in stochastic OLG economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 417-437, December.
    22. Devereux, Michael B. & Saito, Makoto & Yu, Changhua, 2020. "International capital flows, portfolio composition, and the stability of external imbalances," Journal of International Economics, Elsevier, vol. 127(C).

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