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On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production

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  • Acikgoz, Omer

Abstract

I prove existence of stationary recursive competitive equilibrium in Bewley economies with production under specifications in which (i) utility function is allowed to be unbounded, and (ii) the underlying discrete idiosyncratic productivity process can take any form, aside from mild restrictions. Some of the intermediate results provide theoretical basis for assumptions often made in the quantitative macroeconomics literature. By providing an example, I illustrate that equilibrium is not necessarily unique, even under typical specifications of the model, and discuss the underlying reasons for multiplicity.

Suggested Citation

  • Acikgoz, Omer, 2015. "On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production," MPRA Paper 71066, University Library of Munich, Germany, revised 30 Apr 2016.
    • Handle: RePEc:pra:mprapa:71066
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    References listed on IDEAS

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    1. Marcet, Albert & Obiols-Homs, Francesc & Weil, Philippe, 2007. "Incomplete markets, labor supply and capital accumulation," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2621-2635, November.
    2. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 275-298.
    3. Brock, William A. & Gale, David, 1969. "Optimal growth under factor augmenting progress," Journal of Economic Theory, Elsevier, vol. 1(3), pages 229-243, October.
    4. Clarida, Richard H, 1987. "Consumption, Liquidity Constraints and Asset Accumulation in the Presence of Random Income Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 339-351, June.
    5. 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.
    6. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2015. "The wealth distribution in Bewley economies with capital income risk," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 489-515.
    7. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    8. Martin Kaae Jensen, 2018. "Distributional Comparative Statics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 581-610.
    9. Krebs, Tom, 2004. "Non-existence of recursive equilibria on compact state spaces when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 115(1), pages 134-150, March.
    10. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
    11. 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.
    12. repec:hal:wpspec:info:hdl:2441/8623 is not listed on IDEAS
    13. Huggett, Mark & Ospina, Sandra, 2001. "Aggregate precautionary savings: when is the third derivative irrelevant?," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 373-396, October.
    14. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    15. repec:hal:spmain:info:hdl:2441/8623 is not listed on IDEAS
    16. Laitner, John, 1992. "Random earnings differences, lifetime liquidity constraints, and altruistic intergenerational transfers," Journal of Economic Theory, Elsevier, vol. 58(2), pages 135-170, December.
    17. Schechtman, Jack & Escudero, Vera L. S., 1977. "Some results on "an income fluctuation problem"," Journal of Economic Theory, Elsevier, vol. 16(2), pages 151-166, December.
    18. John Laitner, 1979. "Household Bequest Behaviour and the National Distribution of Wealth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(3), pages 467-483.
    19. Rabault, Guillaume, 2002. "When do borrowing constraints bind? Some new results on the income fluctuation problem," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 217-245, February.
    20. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
    21. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 807-835, August.
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    Cited by:

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    2. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    3. Konstantinos Angelopoulos & Spyridon Lazarakis & Jim Malley, 2017. "Wealth Inequality and Externalities from Ex Ante Skill Heterogeneity," CESifo Working Paper Series 6572, CESifo.
    4. Angelos Angelopoulos & Konstantinos Angelopoulos & Spyridon Lazarakis & Apostolis Philippopoulos, 2019. "The Distributional Consequences of Rent Seeking," CESifo Working Paper Series 7835, CESifo.
    5. Angelos Angelopoulos & Konstantinos Angelopoulos & Spyridon Lazarakis & Apostolis Philippopoulos, 2021. "The distributional consequences of rent‐seeking," Economic Inquiry, Western Economic Association International, vol. 59(4), pages 1616-1640, October.
    6. Konstantinos Angelopoulos & Spyridon Lazarakis & Jim Malley, 2019. "Savings externalities and wealth inequality," CESifo Working Paper Series 7619, CESifo.
    7. Konstantinos Angelopoulos & Spyridon Lazarakis & James Malley, 2017. "Wealth inequality and externalities from ex ante skill heterogeneity," Working Papers 2017_07, Business School - Economics, University of Glasgow.
    8. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    9. Bar Light, 2018. "Precautionary Saving in a Markovian Earnings Environment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 138-147, July.

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    More about this item

    Keywords

    Recursive Competitive Equilibrium; Bewley/Huggett/Aiyagari model; Existence; Uniqueness;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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