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On learning and the stability of cycles

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  • James B. Bullard
  • John Duffy

Abstract

We study a general equilibrium model where the multiplicity of stationary periodic perfect foresight equilibria is pervasive. We investigate the extent of which agents can learn to coordinate on stationary perfect foresight cycles. The example economy, taken from Grandmont (1985), is an endowment overlapping generations model with fiat money, where consumption in the first and second periods of life are not necessarily gross substitutes. Depending on the value of a preference parameter, the limiting backward (direction of time reversed) perfect foresight dynamics are characterized by steady state, periodic, or chaotic trajectories for real money balances. We relax the perfect foresight assumption and examine how a population of artificial, heterogeneous adaptive agents might learn in such an environment. These artificial agents optimize given their forecasts of future prices, and they use forecast rules that are consistent with steady state or periodic trajectories for prices. The agents' forecast rules are updated by a genetic algorithm. We find that the population of artificial adaptive agents is able to eventually coordinate on steady state and low-order cycles, but not on the higher-order periodic equilibria that exist under the perfect foresight assumption.

Suggested Citation

  • James B. Bullard & John Duffy, 1995. "On learning and the stability of cycles," Working Papers 1995-006, Federal Reserve Bank of St. Louis.
  • Handle: RePEc:fip:fedlwp:1995-006
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    References listed on IDEAS

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    1. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
    2. Arifovic, Jasmina, 1995. "Genetic algorithms and inflationary economies," Journal of Monetary Economics, Elsevier, vol. 36(1), pages 219-243, August.
    3. Andreoni James & Miller John H., 1995. "Auctions with Artificial Adaptive Agents," Games and Economic Behavior, Elsevier, vol. 10(1), pages 39-64, July.
    4. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-541, June.
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    Cited by:

    1. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    2. Stefano Eusepi, 2005. "Comparing forecast-based and backward-looking Taylor rules: a "global" analysis," Staff Reports 198, Federal Reserve Bank of New York.
    3. Bullard, James & Duffy, John, 1999. "Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs," Computational Economics, Springer;Society for Computational Economics, vol. 13(1), pages 41-60, February.
    4. Richard C. Barnett & Joydeep Bhattacharya & Helle Bunzel, 2007. "Resurrecting Equilibria Through Cycles," Economics Working Papers 2007-12, Department of Economics and Business Economics, Aarhus University.
    5. James B. Bullard & Jasmina Arifovic & John Duffy, 1995. "Learning in a model of economic growth and development," Working Papers 1995-017, Federal Reserve Bank of St. Louis.
    6. Negroni, Giorgio, 2005. "Eductive expectations coordination on deterministic cycles in an economy with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 931-952, May.
    7. Barnett, Richard C. & Bhattacharya, Joydeep & Bunzel, Helle, 2007. "Minimum Consumption Requirements and Cycles in an Overlapping Generations Model of Money," Staff General Research Papers Archive 12834, Iowa State University, Department of Economics.
    8. 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.
    9. Shu-Heng Chen & Chia-Hsuan Yeh, 1999. "Evolving Traders and the Faculty of the Business School: A New Architecture of the Artificial Stock Market," Computing in Economics and Finance 1999 613, Society for Computational Economics.

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    Keywords

    Business cycles;

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