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Stochastic stability of monotone economies in regenerative environments

Author

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  • Foss, Sergey
  • Shneer, Vsevolod
  • Thomas, Jonathan P.
  • Worrall, Tim

Abstract

We introduce and analyze a new class of monotone stochastic recursions in a regenerative environment which is essentially broader than that of Markov chains. We prove stability theorems and apply our results to three canonical models in recursive economics, generalizing some known stability results to the cases when driving sequences are not independent and identically distributed.

Suggested Citation

  • Foss, Sergey & Shneer, Vsevolod & Thomas, Jonathan P. & Worrall, Tim, 2018. "Stochastic stability of monotone economies in regenerative environments," Journal of Economic Theory, Elsevier, vol. 173(C), pages 334-360.
    • Handle: RePEc:eee:jetheo:v:173:y:2018:i:c:p:334-360
    DOI: 10.1016/j.jet.2017.11.004
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    1. Jonathan Thomas & Tim Worrall, 1988. "Self-Enforcing Wage Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 541-554.
    2. Donaldson, John B. & Mehra, Rajnish, 1983. "Stochastic growth with correlated production shocks," Journal of Economic Theory, Elsevier, vol. 29(2), pages 282-312, April.
    3. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    4. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    5. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    6. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2002. "Informal Insurance Arrangements with Limited Commitment: Theory and Evidence from Village Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 209-244.
    7. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
    8. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    9. Alvarez, Fernando & Jermann, Urban J, 2001. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1117-1151.
    10. Mitra, Tapan & Roy, Santanu, 2012. "Sustained positive consumption in a model of stochastic growth: The role of risk aversion," Journal of Economic Theory, Elsevier, vol. 147(2), pages 850-880.
    11. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    12. Santanu Roy & Itzhak Zilcha, 2012. "Stochastic growth with short-run prediction of shocks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 539-580, November.
    13. Tobias Broer & Tessa Bold, 2015. "Risk-Sharing in Village Economies Revisited," 2015 Meeting Papers 1232, Society for Economic Dynamics.
    14. Kamihigashi, Takashi & Stachurski, John, 2015. "Perfect simulation for models of industry dynamics," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 9-14.
    15. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658, October.
    16. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    17. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 595-609.
    18. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    19. Kaymak, Barış & Poschke, Markus, 2016. "The evolution of wealth inequality over half a century: The role of taxes, transfers and technology," Journal of Monetary Economics, Elsevier, vol. 77(C), pages 1-25.
    20. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723, October.
    21. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
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    Cited by:

    1. Bar Light, 2019. "General equilibrium in a heterogeneous-agent incomplete-market economy with many consumption goods and a risk-free bond," Papers 1906.06810, arXiv.org, revised Mar 2021.
    2. Thomas, Jonathan P. & Worrall, Tim, 2018. "Dynamic relational contracts under complete information," Journal of Economic Theory, Elsevier, vol. 175(C), pages 624-651.
    3. Fuh, Cheng-Der, 2021. "Asymptotic behavior for Markovian iterated function systems," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 186-211.
    4. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    5. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    6. Onno Boxma & Andreas Löpker & Michel Mandjes & Zbigniew Palmowski, 2021. "A multiplicative version of the Lindley recursion," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 225-245, August.
    7. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    Monotone economy; Stochastic recursion; Stochastic stability; One sector stochastic growth model; Bewley–Imrohoroglu–Huggett–Aiyagari model; Risk-sharing model;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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