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Indeterminacy in stochastic overlapping generations models: real effects in the long run

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  • Zhigang Feng

    (University of Illinois at Urbana–Champaign)

  • Matthew Hoelle

    (Purdue University)

Abstract

Indeterminate equilibria are known to exist for overlapping generations models, though recent research has been limited to deterministic settings in which all equilibria converge to a steady state in the long run. This paper analyzes stochastic overlapping generations models with three-period-lived representative consumers and adopts a novel computational algorithm to numerically approximate the entire set of competitive equilibria. In a stochastic setting with incomplete markets, indeterminacy has real effects in the long run. Our numerical simulations reveal that indeterminacy is an order of magnitude more important than endowment shocks in explaining long-run consumption and asset price volatility.

Suggested Citation

  • Zhigang Feng & Matthew Hoelle, 2017. "Indeterminacy in stochastic overlapping generations models: real effects in the long run," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 559-585, February.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:2:d:10.1007_s00199-015-0947-y
    DOI: 10.1007/s00199-015-0947-y
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    1. Galor, Oded & Ryder, Harl E., 1989. "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital," Journal of Economic Theory, Elsevier, vol. 49(2), pages 360-375, December.
    2. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    3. Gomis-Porqueras, Pere & Haro, Alex, 2003. "Global dynamics in macroeconomics: an overlapping generations example," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 1941-1959, September.
    4. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    5. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    6. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Post-Print hal-00537071, HAL.
    7. Kehoe, Timothy J. & Levine, David K., 1990. "The economics of indeterminacy in overlapping generations models," Journal of Public Economics, Elsevier, vol. 42(2), pages 219-243, July.
    8. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    9. Gabrielle Demange, 2002. "On optimality in intergenerational risk sharing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 1-27.
    10. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    11. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    12. Galor, Oded, 1992. "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System," Econometrica, Econometric Society, vol. 60(6), pages 1351-1386, November.
    13. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    14. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    15. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    16. Wang Yong, 1993. "Stationary Equilibria in an Overlapping Generations Economy with Stochastic Production," Journal of Economic Theory, Elsevier, vol. 61(2), pages 423-435, December.
    17. Auerbach, Alan J & Kotlikoff, Laurence J, 1987. "Evaluating Fiscal Policy with a Dynamic Simulation Model," American Economic Review, American Economic Association, vol. 77(2), pages 49-55, May.
    18. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 83-110, February.
    19. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    20. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December.
    21. Gomis-Porqueras, Pere & Haro, Alex, 2007. "Global bifurcations, credit rationing and recurrent hyperinflations," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 473-491, February.
    22. Spear, Stephen E. & Srivastava, Sanjay & Woodford, Michael, 1990. "Indeterminacy of stationary equilibrium in stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 50(2), pages 265-284, April.
    23. 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.
    24. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    25. Dirk Krueger & Fabrizio Perri, 2006. "Does Income Inequality Lead to Consumption Inequality? Evidence and Theory -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 163-193.
    26. N. Gregory Mankiw & Julio J. Rotemberg & Lawrence H. Summers, 1985. "Intertemporal Substitution in Macroeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(1), pages 225-251.
    27. Alessandro Citanna & Paolo Siconolfi, 2010. "Recursive Equilibrium in Stochastic Overlapping-Generations Economies," Econometrica, Econometric Society, vol. 78(1), pages 309-347, January.
    28. Roger E.A. Farmer, 2015. "Global Sunspots and Asset Prices in a Monetary Economy," NBER Working Papers 20831, National Bureau of Economic Research, Inc.
    29. 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.
    30. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June.
    31. Michael Magill & Martine Quinzii, 2003. "Indeterminacy of equilibrium in stochastic OLG models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 435-454, March.
    32. Farmer, Roger E.A. & Woodford, Michael, 1997. "Self-Fulfilling Prophecies And The Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 1(4), pages 740-769, December.
    33. Zhigang Feng, 2013. "Tackling indeterminacy in overlapping generations models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 445-457, June.
    34. 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.
    35. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-574, May.
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    More about this item

    Keywords

    OLG; Indeterminacy; Markov Equilibrium; Computation; Simulation;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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