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ON THE EVOLUTIONARY STABILITY OF RATIONAL EXPECTATIONS

Published online by Cambridge University Press:  18 June 2013

William R. Parke  and
George A. Waters
William R. Parke
Affiliation:
University of North Carolina
George A. Waters*
Affiliation:
Illinois State University
*
Address correspondence to: George A. Waters, Department of Economics, Illinois State University, Normal, IL 61790-4200, USA; e-mail: [email protected].
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Abstract

Evolutionary game theory provides a fresh perspective on the prospect that agents with heterogeneous expectations might eventually come to agree on a single expectation corresponding to the efficient markets hypothesis. We establish conditions under which agreement on a unique forecast is stable, but also show that persistent heterogeneous expectations can arise if those conditions do not hold. The critical element is the degree of curvature in the payoff weighting functions agents use to value forecasting performance. We illustrate our results in the context of an asset pricing model where a martingale solution competes with the fundamental solution for agents' attention.

Keywords

Rational ExpectationsHeterogeneous ExpectationsEvolutionary Game TheoryAsset PricingEfficient Markets Hypothesis
Type
Articles
Information
Macroeconomic Dynamics , Volume 18 , Issue 7 , October 2014 , pp. 1581 - 1606
Copyright
Copyright © Cambridge University Press 2013 

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References

REFERENCES

Anufriev, Mikhail and Hommes, Cars H. (2012a) Evolution of market heuristics. Knowledge of Engineering Review 27, 255–271.Google Scholar
Anufriev, Mikhail and Hommes, Cars H. (2012b) Evolutionary selection of individual expectations and aggregate outcomes. American Economic Review—Micro 4, 35–64.Google Scholar
Bates, J.M. and Clive, W.J. Granger (1969) The combination of forecasts. Operations Research Quarterly 20, 451–468.Google Scholar
Binmore, Kenneth, Gale, John, and Samuelson, Lawrence (1995) Learning to be imperfect: The ultimatum game. Games and Economic Behavior 8, 56–90.Google Scholar
Blanchard, Olivier (1979) Backward and forward solutions for economies with rational expectations. American Economic Review 69 (2), 114–118.Google Scholar
Blume, Lawrence E. and Easley, David (1992) Evolution and market behavior. Journal of Economic Theory 58, 9–40.CrossRefGoogle Scholar
Box, George E.P. and Jenkins, Gwilym M. (1970) Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.Google Scholar
Branch, William and Evans, George (2007) Model uncertainty and endogenous volatility. Review of Economic Dynamics 10, 207–237.Google Scholar
Branch, William and Evans, George (2011) Learning about risk and return: A simple model of bubbles and crashes. American Economic Review: Macroeconomics 3 (1), 159–191.Google Scholar
Branch, W. and McGough, B. (2004) Multiple equilibria in heterogeneous expectations models. Contributions to Macroeconomics 4 (1), Article 12.Google Scholar
Branch, William and McGough, Bruce (2008) Replicator dynamics in a cobweb model with rationally heterogeneous agents. Journal of Economic Behavior and Organization 65 (2), 224–244.Google Scholar
Brock, William A. and Hommes, Cars H. (1997) A rational route to randomness. Econometrica 65, 1059–1095.Google Scholar
Brock, William A. and Hommes, Cars H. (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control 22, 1235–1274.Google Scholar
Charemza, Wojciech and Deadman, Derek (1995) Speculative bubbles with stochastic explosive roots: The failure of unit root testing. Journal of Empirical Finance 2, 153–163.CrossRefGoogle Scholar
Cochrane, John (2001) Asset Pricing. Princeton, NJ: Princeton University Press.Google Scholar
Constanides, George M. and Duffie, Darrel (1996) Asset pricing with heterogeneous consumers. Journal of Political Economy 104, 219–240.Google Scholar
Covel, Michael W. (2004) Trend Following: How Great Traders Make Millions in Up or Down Markets. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Elliot, Graham and Timmerman, Allan (2008) Economic forecasting. Journal of Economic Literature, 46 (1), 3–56.Google Scholar
Engle, Charles (2001) GARCH 101: The use of ARCH/GARCH models in applied econometrics. Journal of Economic Perspectives 15 (4), 157–168.Google Scholar
Evans, George (1991) Pitfalls in testing for explosive bubbles in asset prices. American Economic Review 81 (4), 922–930.Google Scholar
Evans, George and Guesnerie, Roger (2005) Coordination on saddle path solutions: The eductive viewpoint—linear multivariate models. Journal of Economic Theory 124, 202–229.Google Scholar
Evans, George, Honkapohja, Seppo, and Williams, Noah (2005) Generalized Stochastic Gradient Learning. NBER Working Paper 0317.CrossRefGoogle Scholar
Fama, Eugene F. (1991) Efficient markets II. Journal of Finance 46 (5), 1575–1617.Google Scholar
Fama, Eugene F. and French, Kenneth R. (1989) Business condition and the expected returns on stocks and bonds. Journal of Financial Economics 25 (1), 23–49.Google Scholar
Föllmer, Hans, Horst, Ulrich, and Kirman, Alan (2005) Equilibria in financial markets with heterogeneous agents: A probabilistic perspective. Journal of Mathematical Economics 41, 123–155.Google Scholar
Granger, Clive W.J. and Ramanathan, Ramu (1984) Improved methods of combining forecasts. Journal of Forecasting 3, 197–204.Google Scholar
Guse, Eran (2010) Heterogeneous expectations, adaptive learning and evolutionary dynamics. Journal of Economic Behavior and Organization 74, 42–57.Google Scholar
Hens, Thorsten and Schenk-Hoppé, Klaus R. (2009) Handbook of Financial Markets: Dynamics and Evolution. Amsterdam: North Holland.Google Scholar
Hofbauer, Josef and Sandholm, William (2007) Evolution in games with randomly disturbed payoffs. Journal of Economic Theory 132, 47–69.Google Scholar
Hofbauer, Josef and Sigmund, Karl (1988) The Theory of Evolution and Dynamical Systems. Cambridge, UK: Cambridge University Press.Google Scholar
Hofbauer, Josef and Weibull, Jorgen (1996) Evolutionary selection against dominated strategies. Journal of Economic Theory 71, 558–573.CrossRefGoogle Scholar
Hommes, Cars H. (2001) Financial markets as nonlinear adaptive evolutionary systems. Quantitative Finance 1, 149–167.Google Scholar
Hommes, Cars H. (2006) Heterogeneous agent models in economics and finance. In Tesfatsion, L. and Judd, K.I. (eds.), Agent-Based Computational Economics, Handbook of Computational Economics, vol. 2, pp. 1109–1186. Amsterdam: Elsevier Science BV.Google Scholar
Horst, Ulrich and Wenzelburger, Jan (2008) On nonergodic asset prices. Economic Theory 34, 207–234.Google Scholar
Kandori, Michihiro, Mailath, George J., and Rob, Rafael (1993) Learning, mutation and long run equilibria in games. Econometrica 61 (1), 29–56.Google Scholar
Lakshmikantham, V. and Trigiante, D. (2002) Theory of Difference Equations: Numerical Methods and Applications. New York: Marcel Dekker.Google Scholar
Marcet, Albert and Sargent, Thomas (1989a) Convergence of least squares learning in an environment with hidden state variables and private information. Journal of Political Economy 97 (6), 1306–1322.Google Scholar
Marcet, Albert and Sargent, Thomas (1989b) Convergence of least squares learning mechanisms in self-referential linear stochastic models. Journal of Economic Theory 48, 337–368.Google Scholar
McCallum, Bennett T. (1983) On nonuniqueness in rational expectations models: An attempt at perspective. Journal of Monetary Economics 11, 139–168.Google Scholar
McCallum, Bennett T. (1997) The role of the minimum state variables criterion in rational expectations models. International Journal of Tax and Finance 6 (4), 621–639.Google Scholar
Parke, William R. and George A. Waters (2007) An evolutionary game theory explanation of arch effects. Journal of Economic Dynamics and Control 31 (7), 2234–2262.Google Scholar
Pesaran, Hashem (1987) The Limits of Rational Expectations. Oxford, UK: Blackwell Publishing.Google Scholar
Samuelson, Lawrence (1997) Evolutionary games and equilibrium selection. Cambridge, MA: MIT Press.Google Scholar
Sandholm, William (2011) Population Games and Evolutionary Dynamics. Cambridge, MA: MIT Press.Google Scholar
Sethi, Rajiv and Franke, Reiner (1995) Behavioural heterogeneity under evolutionary pressure: Macroeconomics implications of costly optimization. Economics Journal 105, 583–600.Google Scholar
Shiller, Robert J. (1981) Do stock prices move too much to be justified by subsequent changes in dividends? American Economics Review 71 (3), 421–436.Google Scholar
Stock, James H. and Watson, Mark W. (1999) A comparison of linear and nonlinear models for forecasting macroeconomic time series. In Engle, R.F. and White, H. (eds.), Cointegration, Causality and Forecasting: A Festschrift in Honor of Clive W. Granger, pp. 1–44. Oxford, UK: Oxford University Press.Google Scholar
Waters, George A. (2009) Chaos in the cobweb model with a new learning dynamic. Journal of Economic Dynamics and Control 33 (6), 1201–1216.Google Scholar
Weibull, Jorgen (1997) Evolutionary Game Theory. Cambridge, MA: MIT Press.Google Scholar