Economic Theory

, Volume 63, Issue 2, pp 559–585 | Cite as

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

Research Article

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.

Keywords

OLG Indeterminacy Markov Equilibrium Computation Simulation 

JEL Classification

C63 D52 D91 E21 

References

  1. Allais, M.: Economie et Intérêt. Imprimerie Nationale, Paris (1947)Google Scholar
  2. Auerbach, A.J., Kotlikoff, L.J.: Evaluating fiscal policy with a dynamic simulation model. Am. Econ. Rev. 77, 49–55 (1987)Google Scholar
  3. Backus, D., Chernov, M., Zin, S.E.: Sources of entropy in representative agent models. J. Finance 69, 51–99 (2014)CrossRefGoogle Scholar
  4. Balasko, Y., Shell, K.: The overlapping-generations model: I. The case of pure exchange without money. J. Econ. Theory 23, 281–306 (1980)CrossRefGoogle Scholar
  5. Benhabib, J., Farmer, R.E.A.: Indeterminacy and sunspots in macroeconomics. In: Taylor, J.B., Woodford, M. (eds.) Handbook of Macroeconomics, vol. 1A, pp. 387–448. Elsevier, North-Holland (1999)Google Scholar
  6. Citanna, A., Siconolfi, P.: Recursive equilibria in stochastic overlapping-generations economies. Econometrica 78, 309–348 (2010)CrossRefGoogle Scholar
  7. Demange, G.: On optimality in intergenerational risk sharing. Econ. Theory 20, 1–27 (2002)CrossRefGoogle Scholar
  8. Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A.: Stationary Markov equilibria. Econometrica 62, 745–781 (1994)CrossRefGoogle Scholar
  9. Farmer, R.E.A., Woodford, M.: Self-fulfilling prophecies and the business cycle. Macro Dyn. 1, 740–769 (1997)Google Scholar
  10. Farmer, R.E.A.: Global sunspots and asset prices in a monetary economy. NBER Working Paper No. 20831 (2015)Google Scholar
  11. Feng, Z.: Tackling indeterminacy in the overlapping generations model. Math. Methods Oper. Res. 77, 445–457 (2013)CrossRefGoogle Scholar
  12. Feng, Z., Miao, J., Peralta-Alva, A., Santos, M.: Numerical simulation of nonoptimal dynamic equilibrium models. Inter. Econ. Rev. 55, 83–110 (2014)CrossRefGoogle Scholar
  13. Gale, D.: Pure exchange equilibrium of dynamic economic models. J. Econ. Theory 6, 12–36 (1973)CrossRefGoogle Scholar
  14. Galor, D., Ryder, H.E.: Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital. J. Econ Theory 49, 360–375 (1989)CrossRefGoogle Scholar
  15. Galor, O.: A two-sector overlapping-generations model: a global characterization of the dynamical system. Econometrica 60, 1351–1386 (1992)CrossRefGoogle Scholar
  16. Geanakoplos, J., Polemarchakis, H.: Walrasian indeterminacy and Keynesian macroeconomics. Rev. Econ. Stud. 53, 755–779 (1984)CrossRefGoogle Scholar
  17. Gomis-Porqueras, P., Haro, A.: Global dynamics in macroeconomics: an overlapping generations example. J. Econ. Dyn. Control 27, 1941–1959 (2003)CrossRefGoogle Scholar
  18. Gomis-Porqueras, P., Haro, A.: Global bifurcations, credit rationing and recurrent hyperinflations. J. Econ. Dyn. Control 31, 473–491 (2007)CrossRefGoogle Scholar
  19. Gourinchas, P.O., Parker, J.A.: Consumption over the life cycle. Econometrica 70, 47–89 (2002)CrossRefGoogle Scholar
  20. Hansen, L.P., Jagannathan, R.: Implications of security market data for models of dynamic economies. J. Pol. Econ. 99, 225–262 (1991)CrossRefGoogle Scholar
  21. Henriksen, E., Spear, S.E.: Endogenous market incompleteness without market frictions: dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies. J. Econ. Theory 147, 426–449 (2012)CrossRefGoogle Scholar
  22. Kehoe, T., Levine, D.K.: Regularity in overlapping generations exchange economics. J. Math. Econ. 13, 69–93 (1984)CrossRefGoogle Scholar
  23. Kehoe, T., Levine, D.K.: The economics of indeterminacy in overlapping generations models. J. Public Econ. 42, 219–243 (1990)CrossRefGoogle Scholar
  24. Kehoe, T., Levine, D.K., Mas-Colell, A., Woodford, M.: Gross substitutability in large-square economics. J. Econ. Theory 54, 1–25 (1991)CrossRefGoogle Scholar
  25. Krueger, D., Perri, F.: Does income inequality lead to consumption inequality? Evidence and theory. Rev. Econ. Stud. 73, 163–193 (2006)CrossRefGoogle Scholar
  26. Kubler, F., Polemarchakis, H.: Stationary Markov equilibria for overlapping generations. Econ. Theory 24, 623–643 (2004)CrossRefGoogle Scholar
  27. Kubler, F., Schmedders, K.: Stationary Equilibria in asset-pricing models with incomplete markets and collateral. Econometrica 71, 1767–1793 (2003)CrossRefGoogle Scholar
  28. LeRoy, S.F., Porter, R.D.: The present-value relation: tests based on implied variance bounds. Econometrica 49, 555–574 (1981)CrossRefGoogle Scholar
  29. Limic, N.: Monte Carlo Simulations of Random Variables, Sequences and Processes. Element, Zagreb (2009)Google Scholar
  30. Magill, M., Quinzii, M.: Indeterminacy of equilibrium in stochastic OLG models. Econ. Theory 21, 435–454 (2003)CrossRefGoogle Scholar
  31. Mankiw, N.G., Rotemberg, J.J., Summers, L.H.: Intertemporal substitution in macroeconomics. Quar. J. Econ. 100, 225–251 (1985)CrossRefGoogle Scholar
  32. Mehra, R., Prescott, E.C.: The equity premium: a puzzle. J. Mon. Econ. 15, 145–161 (1985)CrossRefGoogle Scholar
  33. Samuelson, P.: An exact consumption-loan model of interest without the social contrivance of money. J. Pol. Econ. 66, 467–482 (1958)CrossRefGoogle Scholar
  34. Schmachtenberg, R.: Stochastic overlapping generations models with incomplete markets 1: existence of equilibria. University of Mannheim Discussion paper no. 363-88 (1988)Google Scholar
  35. Shiller, R.J.: Do stock prices move too much to be justified by subsequent changes in dividends? Am. Econ. Rev. 71, 421–436 (1981)Google Scholar
  36. Spear, S.E., Srivastava, S., Woodford, M.: Indeterminacy of stationary equilibrium in stochastic overlapping generations models. J. Econ. Theory 50, 265–284 (1990)CrossRefGoogle Scholar
  37. Weil, P.: The equity premium puzzle and the risk-free rate puzzle. J. Mon. Econ. 24, 401–421 (1989)CrossRefGoogle Scholar
  38. Wang, Y.: Stationary equilibria in an overlapping generations economy with stochastic production. J. Econ. Theory 61, 423–435 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Illinois at Urbana–ChampaignUrbanaUSA
  2. 2.Department of EconomicsPurdue UniversityWest LafayetteUSA

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