Nonlinear Dynamical Systems in Economics pp 131-164 | Cite as
Heterogeneous Agent Models: two simple examples
- 3 Citations
- 613 Downloads
Abstract
These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and Hommes (1998). Agents are boundedly rational and switch endogenously between different trading strategies, based upon an evolutionary fitness measure given by realized past profits. Evolutionary switching creates a nonlinearity in the dynamic models. Rational routes to randomness, that is, bifurcation routes to complicated dynamical behavior occur when agents become more sensitive to differences in evolutionary fitness.
Keywords
Unstable Manifold Trading Strategy Rational Expectation Risky Asset Asset Price ModelPreview
Unable to display preview. Download preview PDF.
Bibliography
- [1]Anderson, S., de Palma, A. and Thisse, J., (1993), Discrete choice theory of product differentiation, MIT Press, Cambridge.Google Scholar
- [2]Arthur, W.B., Holland, J.H., LeBaron, B., Palmer, R. and Taylor, P., (1997) Asset pricing under endogenous expectations in an artificial stock market, in Arthur, W., Lane, D. and Durlauf, S., (eds.) The economy as an evolving complex system II, Addison-Wesley.Google Scholar
- [3]Baak, S.J. (1999), Tests for bounded rationality with a linear dynamic model distorted by heterogeneous expectations, Journal of Economic Dynamics and Control 23, 1517–1543.zbMATHCrossRefMathSciNetGoogle Scholar
- [4]Brock, W.A., (1993) Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance, Estudios Económicos 8, 3–55.Google Scholar
- [5]Brock, W.A., (1997), Asset Price Behavior in Complex Environments, in: Arthur, W.B., Durlauf, S.N., and Lane, D.A., eds., The Economy as an Evolving Complex System II, Addison-Wesley, Reading, MA, 385–423.Google Scholar
- [6]Brock, W.A., and Hommes, C.H., (1997a) A rational route to randomness, Econometrica 65, 1059–1095.zbMATHCrossRefMathSciNetGoogle Scholar
- [7]Brock, W.A., and Hommes, C.H., (1997b) Models of complexity in economics and finance, In: Hey, C. et al. (eds.), System Dynamics in Economic and Financial Models, Chapter 1, Wiley PubL, pp. 3–41.Google Scholar
- [8]Brock, W.A., and Hommes, C.H., (1998), Heterogeneous beliefs and routes to chaos in a simple asset pricing model, Journal of Economic Dynamics and Control 22, 1235–1274.zbMATHCrossRefMathSciNetGoogle Scholar
- [9]Brock, W.A., and Hommes, C.H., (1999), Rational Animal Spirits, In: Herings, P.J.J., Laan, van der G. and Talman, A.J.J. eds., The Theory of Markets, North-Holland, Amsterdam, 109–137.Google Scholar
- [10]Brock, W.A., Hommes, C.H., and Wagener, F.O.O. (2004), Evolutionary dynamics in markets with many trader types, Journal of Mathematical Economics, forthcoming.Google Scholar
- [11]Brock, W.A. and LeBaron, (1996), A structural model for stock return volatility and trading volume, Review of Economics and Statistics 78, 94–110.CrossRefGoogle Scholar
- [12]Chavas, J.P., (2000) On information and market dynamics: The case of the U.S. beef market, Journal of Economic Dynamics and Control, 24, 833–853.zbMATHCrossRefGoogle Scholar
- [13]Chiarella, C, (1992), The dynamics of speculative behaviour, Annals of Operations Research 37, 101–123.zbMATHCrossRefMathSciNetGoogle Scholar
- [14]Chiarella, C. and He, T. (2000), Heterogeneous beliefs, risk and learning in a simple asset pricing model, Computational Economics, forthcoming.Google Scholar
- [15]Dacorogna, M.M., Müller, U.A., Jost, C, Pictet, O.V., Olsen, R.B. and Ward, J.R., (1995), Heterogeneous real-time trading strategies in the foreign exchange market, European Journal of Finance 1, 383–403.CrossRefGoogle Scholar
- [16]Day, R.H. and Huang, W. (1990) Bulls, bears and market sheep, Journal of Economic Behavior and Organization 14, 299–329.CrossRefGoogle Scholar
- [17]DeGrauwe, P., DeWachter, H. and Embrechts, M., (1993) Exchange rate theory. Chaotic models of foreign exchange markets, Blackwell.Google Scholar
- [18]De Long, J.B., Shleifer, A., Summers, L.H. and Waldmann, R.J., (1990a) Noise trader risk in financial markets, Journal of Political Economy 98, 703–738.CrossRefGoogle Scholar
- [19]De Long, J.B., Shleifer, A., Summers, L.H. and Waldmann, R.J., (1990b) Positive feedback investment strategies and destabilizing rational speculation, Journal of Finance 45, 379–395.CrossRefGoogle Scholar
- [20]Fama, E.F., (1970) Efficient capital markets: a review of theory and empirical work, Journal of Finance 25, 383–423.CrossRefGoogle Scholar
- [21]Farmer, J.D., (1998), Market force, ecology, and evolution, Santa Fe Institute working paper 98-12-117.Google Scholar
- [22]Farmer, J.D. and Joshi, S., (2002), The price dynamics of common trading strategies, Journal of Economic Behaviour and Organization 49, 149–171.CrossRefGoogle Scholar
- [23]de Fontnouvelle, P., (2000), Information dynamics in financial markets, Macroeconomic Dynamics 4, 139–169.zbMATHCrossRefGoogle Scholar
- [24]Frankel, J.A. and Froot, K.A., (1988) Chartists, Fundamentalists and the Demand for Dollars, Greek Economic Review 10, 49–102.Google Scholar
- [25]Friedman, M., (1953) The case of flexible exchange rates, In: Essays in positive economics, Univ. Chicago Press.Google Scholar
- [26]Gaunersdorfer, A., (2000) Endogenous fluctuations in a simple asset pricing model with heterogeneous beliefs, Journal of Economic Dynamics and Control 24, 799–831.zbMATHCrossRefGoogle Scholar
- [27]Gaunersdorfer, A. and Hommes, C.H., (2000), A nonlinear structural model for volatility clustering, CeNDEF working paper 00-02, University of Amsterdam.Google Scholar
- [28]Gaunersdorfer, A., Hommes, C.H., and Wagener, F.O.J., (2000) Bifurcation routes to volatility clustering, CeNDEF working paper 00-04, University of Amsterdam.Google Scholar
- [29]Goeree, J.K. and Hommes, C.H., (2000), Heterogeneous beliefs and the non-linear cobweb model, Journal of Economic Dynamics and Control 24, 761–798.zbMATHCrossRefMathSciNetGoogle Scholar
- [30]Hommes, C.H., (1994) Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand, Journal of Economic Behavior & Organization 24, 315–335.CrossRefGoogle Scholar
- [31]Hommes, C. H., (1998) On the Consistency of Backward-Looking Expectations: The Case of the Cobweb, Journal of Economic Behavior and Organization, 33, 333–362.CrossRefGoogle Scholar
- [32]Hommes, C.H., (2001), Financial markets as nonlinear adaptive evolutionary systems, Quantitative Finance 1, 149–167.CrossRefMathSciNetGoogle Scholar
- [33]Kantz and Schreiber (1997), Nonlinear time series analysis, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
- [34]Keynes, J.M., (1936) The general theory of unemployment, interest and money, Harcourt, Brace and World.Google Scholar
- [35]Kirman, A., (1991) Epidemics of opinion and speculative bubbles in financial markets, In M. Taylor (ed.), Money and financial markets, Macmillan.Google Scholar
- [36]Kirman, A. and Teyssiere, G., (2002), Microeconomic models for long memory in the volatility of financial time series, Studies in Nonlinear Dynamics & Econometrics, 5, 281–302.CrossRefGoogle Scholar
- [37]Kurz, M., (ed.) (1997), Endogenous economic fluctuations, Springer Verlag.Google Scholar
- [38]LeBaron, B., (2000), Agent based computational finance: suggested readings and early research, Journal of Economic Dynamics and Control 24, 679–702.zbMATHCrossRefGoogle Scholar
- [39]LeBaron, B., Arthur, W.B. and Palmer, R. (1999) Time series properties of an artificial stock market, Journal of Economic Dynamics and Control 23, 1487–1516.zbMATHCrossRefGoogle Scholar
- [40]Lucas, R.E., (1971) Econometric testing of the natural rate hypothesis, In: O. Eckstein (ed.) The econometrics of price determination Conference. Board of Governors of the Federal Reserve System and Social Science Research Council.Google Scholar
- [41]Lux, T., (1995) Herd Behavior, Bubbles and Crashes, The Economic Journal 105, 881–896.CrossRefGoogle Scholar
- [42]Lux, T., (1997) Time variation of second moments from a noise trader/infection model, Journal of Economic Dynamics and Control 22, 1–38.zbMATHCrossRefMathSciNetGoogle Scholar
- [43]Lux, T. and Marchesi, M. (1999) Scaling and criticality in a stochastic multi-agent model of a financial market, Nature Vol. 397, February 1999, 498–500.CrossRefADSGoogle Scholar
- [44]Lux, T. and Marchesi, M. (2000) Volatility clustering in financial markets: a microsimulation of interacting agents, International Journal of Theoretical and Applied Finance, 3, 675–702.zbMATHCrossRefMathSciNetGoogle Scholar
- [45]Manski, C. and McFadden, D., (1981), Structural analysis of discrete data with econometric applications, MIT Press, Cambridge.zbMATHGoogle Scholar
- [46]Muth, J.F., (1961) Rational expectations and the theory of price movements, Econometrica 29, 315–335.CrossRefGoogle Scholar
- [47]Palis, J. and Takens, F., (1993) Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press.Google Scholar
- [48]Poincaré, H. (1890) “Sur le Problème des Trois Corps et les Equations de la Dynamique” Mémoire couronné du prise de S.M. le roi Oscar II de Surde), Act a Mathematica 13, 1–270.Google Scholar
- [49]Sargent, Thomas J., (1999) The Conquest of American Inflation, Princeton: Princeton University Press.Google Scholar
- [50]Wang, J., (1994), A model of competitive stock trading volume, Journal of Political Economy 102, 127–168.CrossRefGoogle Scholar
- [51]Zeeman, E.C., (1974) The unstable behavior of stock exchange, Journal of Mathematical Economics 1, 39–49.zbMATHCrossRefMathSciNetGoogle Scholar