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Continuous Markov equilibria with quasi-geometric discounting

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  • Satyajit Chatterjee
  • Burcu Eyigungor

Abstract

We prove that the standard quasi-geometric discounting model used in dynamic consumer theory and political economics does not possess continuous Markov perfect equilibria (MPE) if there is a strictly positive lower bound on wealth. We also show that, at points of discontinuity, the decision maker strictly prefers lotteries over the next period's assets. We then extend the standard model to have lotteries and establish the existence of an MPE with continuous decision rules. The models with and without lotteries are numerically compared, and it is shown that the model with lotteries behaves more in accord with economic intuition.

Suggested Citation

  • Satyajit Chatterjee & Burcu Eyigungor, 2014. "Continuous Markov equilibria with quasi-geometric discounting," Working Papers 14-6, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:14-6
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    2. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2018. "On uniqueness of time-consistent Markov policies for quasi-hyperbolic consumers under uncertainty," Journal of Economic Theory, Elsevier, vol. 176(C), pages 293-310.
    4. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    5. Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    6. Chatterjee, Satyajit & Eyigungor, Burcu, 2019. "Endogenous political turnover and fluctuations in sovereign default risk," Journal of International Economics, Elsevier, vol. 117(C), pages 37-50.
    7. Marco Battaglini, 2021. "Chaos and Unpredictability in Dynamic Social Problems," NBER Working Papers 28347, National Bureau of Economic Research, Inc.
    8. Antonio Cusato Novelli, 2021. "Sovereign default, political instability and political fragmentation," Review of International Economics, Wiley Blackwell, vol. 29(4), pages 732-755, September.
    9. Dan Cao & Iván Werning, 2016. "Dynamic Savings Choices with Disagreements," NBER Working Papers 22007, National Bureau of Economic Research, Inc.
    10. Xie, Zoe & Pei, Yun, 2016. "A Quantitative Theory of Time-Consistent Unemployment Insurance," MPRA Paper 74698, University Library of Munich, Germany.
    11. Dan Cao & Iván Werning, 2018. "Saving and Dissaving With Hyperbolic Discounting," Econometrica, Econometric Society, vol. 86(3), pages 805-857, May.
    12. Jean-Pierre Drugeon & Bertrand Wigniolle, 2021. "On Markovian collective choice with heterogeneous quasi-hyperbolic discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1257-1296, November.
    13. Pei, Yun & Xie, Zoe, 2021. "A quantitative theory of time-consistent unemployment insurance," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 848-870.
    14. Bård Harstad, 2020. "The Conservation Multiplier," CESifo Working Paper Series 8283, CESifo.
    15. Li, Yuan & Yang, Jinqiang & Zhao, Siqi, 2022. "Present-biased government and sovereign debt dynamics," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    16. Arvaniti, Maria & Krishnamurthy, Chandra Kiran B. & Crépin, Anne-Sophie, 2023. "Time-consistent renewable resource management with present bias and regime shifts," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 479-495.

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    More about this item

    Keywords

    Quasi-geometric; Quasi-hyperbolic; Time consistency; Markov Perfect Equilibrium; Debt Limit; Continuous Solutions; Lotteries;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • H63 - Public Economics - - National Budget, Deficit, and Debt - - - Debt; Debt Management; Sovereign Debt
    • P16 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Capitalist Institutions; Welfare State

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