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Sunspot Fluctuations: A Way Out of a Development Trap?

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  • Sergey Slobodyan

    () (Washington University)

Abstract

In dynamic general-equilibrium economic models, equilibrium may be indeterminate, so a continuum of equilibrium trajectories may converge to the same steady state. Often, those mechanisms leading to indeterminacy, like increasing returns to scale, may also lead to multiple steady states and possible underdevelopment traps. But indeterminacy often allows construction of rational sunspot equilibrium as a randomization over different equilibrium trajectories or equilibria. This paper studies "rescuing" an economy from a development trap through sunspot-driven self-fulfilling expectations. The problem is stated as stochastic stability of a system of stochastic differential equations with white noise perturbations from sunspot-driven self-fulfilling expectations. The framework of, Benhabib and Farmer (1994) is used. This deterministic continuous-time model with infinitely lived agents is characterized by increasing social returns to scale due to an imperceived externality in the production function. There are two steady states. One has zero capital and zero consumption (the origin); the other has positive capital and consumption. For some parameter values, both steady states are indeterminate, and the parameter space is separated into two regions of attraction. The region of attraction at the origin is a development trap. If the economy starts in the development trap, it is possible to select a level of consumption to push the system into the positive steady-state region of attraction. However, no individual agent has an incentive to experiment, and everyone coordinates on a trajectory leading to the origin. This could be corrected if agents could form expectations corresponding to a trajectory converging to a positive steady state. Agents are unaware of such a trajectory because the externality is assumed to be unknown. If a sunspot variable - white noise - is added to the model, agents could take it into account when making their decisions. Coordinating on a sunspot white noise allows exploring new regions of the state space and can eventually move the trajectory of the system out of the trap. This happens if a zero steady state is stochastically unstable under sunspot fluctuations or if an initial condition lies outside a region of stochastic stability that may not coincide with the development trap of a deterministic system. When the economy eventually leaves the trap, it is possible to calculate the expected first-exit times from the region of attraction to a zero steady state depending on the initial conditions and magnitude of a sunspot process. This paper uses numerical simulations of stochastic differential equations to calculate the expected times of escape. Boundaries of the stochastic stability region are calculated using a stochastic averaging method. The question of asymptotic stochastic stability is studied by the Lyapunov method.

Suggested Citation

  • Sergey Slobodyan, 1999. "Sunspot Fluctuations: A Way Out of a Development Trap?," Computing in Economics and Finance 1999 922, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:922
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    1. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    2. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    3. Jordi Gali & Fabrizio Zilibotti, 1995. "Endogenous Growth and Poverty Traps in a Cournotian Model," Annals of Economics and Statistics, GENES, issue 37-38, pages 197-213.
    4. Burguet, Roberto & Fernandez-Ruiz, Jorge, 1998. "Growth through taxes or borrowing? A model of development traps with public capital," European Journal of Political Economy, Elsevier, vol. 14(2), pages 327-344, May.
    5. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages 401-426, October.
    6. Baland, Jean-Marie & Francois, Patrick, 1996. "Innovation, monopolies and the poverty trap," Journal of Development Economics, Elsevier, vol. 49(1), pages 151-178, April.
    7. Spear, Stephen E., 1991. "Growth, externalities, and sunspots," Journal of Economic Theory, Elsevier, vol. 54(1), pages 215-223, June.
    8. Drugeon, Jean-Pierre & Wigniolle, Bertrand, 1996. "Continuous-Time Sunspot Equilibria and Dynamics in a Model of Growth," Journal of Economic Theory, Elsevier, vol. 69(1), pages 24-52, April.
    9. Ciccone, Antonio & Matsuyama, Kiminori, 1996. "Start-up costs and pecuniary externalities as barriers to economic development," Journal of Development Economics, Elsevier, pages 33-59.
    10. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
    11. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    12. Gali, Jordi, 1994. "Monopolistic competition, endogenous markups, and growth," European Economic Review, Elsevier, vol. 38(3-4), pages 748-756, April.
    13. Mendoza, Enrique G, 1995. "The Terms of Trade, the Real Exchange Rate, and Economic Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(1), pages 101-137, February.
    14. Kiminori Matsuyama, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, Oxford University Press, vol. 106(2), pages 617-650.
    15. Evans, George W. & Honkapohja, Seppo & Honkapohja, Seppo, 1994. "Learning, convergence, and stability with multiple rational expectations equilibria," European Economic Review, Elsevier, vol. 38(5), pages 1071-1098, May.
    16. Salyer, Kevin D. & Sheffrin, Steven M., 1998. "Spotting sunspots: Some evidence in support of models with self-fulfilling prophecies," Journal of Monetary Economics, Elsevier, vol. 42(3), pages 511-523, October.
    17. Costas Azariadis & Allan Drazen, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 501-526.
    18. 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.
    19. Grandmont, Jean-Michel, 1986. "Stabilizing competitive business cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 57-76, October.
    20. Lee, Jaewoo, 1996. "Financial development by learning," Journal of Development Economics, Elsevier, vol. 50(1), pages 147-164, June.
    21. Arifovic, Jasmina & Bullard, James & Duffy, John, 1997. "The Transition from Stagnation to Growth: An Adaptive Learning Approach," Journal of Economic Growth, Springer, vol. 2(2), pages 185-209, July.
    22. Gans, Joshua S., 1998. "Time Lags and Indicative Planning in a Dynamic Model of Industrialization," Journal of the Japanese and International Economies, Elsevier, vol. 12(2), pages 103-130, June.
    23. Duffy John, 1994. "On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money," Journal of Economic Theory, Elsevier, vol. 64(2), pages 541-553, December.
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