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Uniformly self-justified equilibria

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  • Kubler, Felix
  • Scheidegger, Simon

Abstract

We consider dynamic stochastic economies with heterogeneous agents and introduce the concept of uniformly self-justified equilibria (USJE)—temporary equilibria for which expectations satisfy the following rationality requirements: i) individuals' forecasting functions for the next period's endogenous variables are assumed to lie in a compact, finite-dimensional set of functions, and ii) the forecasts constitute the best uniform approximation to a selection of the equilibrium correspondence. We show that in contrast to rational expectations equilibria, USJE always exist, and we develop a simple algorithm to compute them. As an application, we discuss a stochastic overlapping generations exchange economy. We give an example where recursive (rational expectations) equilibria fail to exist and explain how to construct USJE for that example. In addition, we provide numerical examples to illustrate our computational method.

Suggested Citation

  • Kubler, Felix & Scheidegger, Simon, 2023. "Uniformly self-justified equilibria," Journal of Economic Theory, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:jetheo:v:212:y:2023:i:c:s0022053123001035
    DOI: 10.1016/j.jet.2023.105707
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    1. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    2. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    3. Kollmann, Robert & Maliar, Serguei & Malin, Benjamin A. & Pichler, Paul, 2011. "Comparison of solutions to the multi-country Real Business Cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 186-202, February.
    4. Blume, Lawrence E. & Easley, David, 1982. "Learning to be rational," Journal of Economic Theory, Elsevier, vol. 26(2), pages 340-351, April.
    5. Krueger, D. & Mitman, K. & Perri, F., 2016. "Macroeconomics and Household Heterogeneity," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 843-921, Elsevier.
    6. Jordan, J. S., 1976. "Temporary competitive equilibrium and the existence of self-fulfilling expectations," Journal of Economic Theory, Elsevier, vol. 12(3), pages 455-471, June.
    7. 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.
    8. Hellwig, Martin F., 1983. "A note on the implementation of rational expectations equilibria," Economics Letters, Elsevier, vol. 11(1-2), pages 1-8.
    9. Marlon Azinovic & Luca Gaegauf & Simon Scheidegger, 2022. "Deep Equilibrium Nets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1471-1525, November.
    10. Klaus Adam & Albert Marcet & Juan Pablo Nicolini, 2016. "Stock Market Volatility and Learning," Journal of Finance, American Finance Association, vol. 71(1), pages 33-82, February.
    11. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    12. Xavier Gabaix, 2014. "A Sparsity-Based Model of Bounded Rationality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1661-1710.
    13. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Econometrica, Econometric Society, vol. 78(1), pages 309-347, January.
    14. Felix Kubler & Karl Schmedders, 2003. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Econometrica, Econometric Society, vol. 71(6), pages 1767-1793, November.
    15. 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.
    16. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(2), pages 284-306, April.
    17. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    18. Michael Woodford, 2013. "Macroeconomic Analysis Without the Rational Expectations Hypothesis," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 303-346, May.
    19. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
    20. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695.
    21. Aryan Eftekhari & Simon Scheidegger, 2022. "High-Dimensional Dynamic Stochastic Model Representation," Papers 2202.06555, arXiv.org.
    22. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    23. Felix Kubler & Simon Scheidegger, 2018. "Self-justi ed equilibria: Existence and computation," 2018 Meeting Papers 694, Society for Economic Dynamics.
    24. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    25. Johannes Brumm & Dominika Kryczka & Felix Kubler, 2017. "Recursive Equilibria in Dynamic Economies With Stochastic Production," Econometrica, Econometric Society, vol. 85, pages 1467-1499, September.
    26. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    27. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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    More about this item

    Keywords

    Dynamic general equilibrium; Dynamically simple equilibrium;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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