Economics on the edge of chaos: Some pitfalls of linearizing complex systems

We discuss some issues and challenges facing economic modellers when confronted with data generated within a non-linear world. The pitfalls associated with the linearisation of inherently non-linear models are raised and the concept of robustness defined and proposed as a necessary property of scientifically valid models. The existence of chaos in economic time series is discussed and an example, using financial data, presented.

[1]  Frederic L. Pryor Economic Evolution And Structure: The Impact Of Complexity On The U.S. Economic System , 1995 .

[2]  Les Oxley,et al.  Linear saddlepoint dynamics ‘on their head’. the scientific content of the new orthodoxy in macrodynamics , 1994 .

[3]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[4]  J. Barkley Rosser,et al.  Chaos theory and Post Walrasian macroeconomics , 1996 .

[5]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[6]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[7]  Philip Rothman,et al.  The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications , 1990 .

[8]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[9]  Walter G. Rosen,et al.  The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age , 1996 .

[10]  I. Prigogine,et al.  Exploring Complexity: An Introduction , 1989 .

[11]  Richard H. Day,et al.  Complex economic dynamics , 1994 .

[12]  J. Geweke,et al.  Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity , 1992 .

[13]  W. Brock,et al.  Is the business cycle characterized by deterministic chaos , 1988 .

[14]  Lawrence J. Christiano,et al.  Money Growth Monitoring and the Taylor Rule , 2001 .

[15]  W. Arthur,et al.  Increasing Returns and Path Dependence in the Economy , 1996 .

[16]  Robert G. Harrison,et al.  Non-linear noise reduction and detecting chaos: some evidence from the S&P composite price index , 1999 .

[17]  Les Oxley,et al.  Robustness and Local Linearisation in Economic Models , 1999 .

[18]  B. LeBaron,et al.  Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence , 1991 .

[19]  Bruce Hannon,et al.  Modeling Dynamic Economic Systems , 1997, Modeling Dynamic Systems.

[20]  James Stodder The Evolution of Complexity in Primitive Exchange: Theory , 1995 .

[21]  William A. Barnett,et al.  Dynamic econometric modeling: The aggregation-theoretic monetary aggregates are chaotic and have strange attractors: an econometric application of mathematical chaos , 1988 .

[22]  William A. Brock,et al.  PATHWAYS TO RANDOMNESS IN THE ECONOMY: EMERGENT NONLINEARITY AND CHAOS IN ECONOMICS AND FINANCE , 1993 .

[23]  W. Davis Dechert Chaos theory in economics : methods, models and evidence , 1996 .

[24]  C. Sparrow The Fractal Geometry of Nature , 1984 .

[25]  William A. Barnett,et al.  A single-blind controlled competition among tests for nonlinearity and chaos , 1996 .

[26]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[27]  J. Barkley Rosser,et al.  From Catastrophe to Chaos: A General Theory of Economic Discontinuities , 1991 .

[28]  J. Stodder,et al.  Complexity Aversion: Simplification in the Herrnstein and Allais Behaviors , 1997 .

[29]  Ping Chen,et al.  A Random Walk or Color Chaos on the Stock Market? Time-Frequency Analysis of S&P Indexes , 1996 .

[30]  William A. Barnett,et al.  The Aggregation-Theoretic Monetary Aggregates Are Chaotic and Have Strange Attractors: An Econometric Application of Mathematical Chaos , 2004 .

[31]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[32]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[33]  Peter Nijkamp,et al.  Non-linear Evolution of Dynamic Spatial Systems: The Relevance of Chaos and Ecologically-based Models , 1995 .

[34]  Stephanie Schmitt-Grohé,et al.  The Perils of Taylor Rules , 1999, J. Econ. Theory.

[35]  Elise Couper,et al.  Potential Consequences of Linear Approximation in Economics , 2003 .

[36]  William Rand,et al.  Agent-based and analytical modeling to evaluate the effectiveness of greenbelts , 2004, Environ. Model. Softw..

[37]  T. Puu Nonlinear economic dynamics , 1989 .

[38]  H. Lorenz Nonlinear Dynamical Economics and Chaotic Motion , 1989 .

[39]  H. White,et al.  An additional hidden unit test for neglected nonlinearity in multilayer feedforward networks , 1989, International 1989 Joint Conference on Neural Networks.

[40]  David Colander Beyond microfoundations: The Post Walrasian macroeconomic vision , 1996 .

[41]  Roy Jeffrey Rotheim,et al.  New Keynesian economics/post Keynesian alternatives , 1998 .

[42]  Wei-Bin Zhang,et al.  Synergetic Economics: Time and Change in Nonlinear Economics , 1991 .

[43]  Richard Hollis Day,et al.  An introduction to dynamical systems and market mechanisms , 1994 .

[44]  R. Palmer,et al.  Asset Pricing Under Endogenous Expectations in an Artificial Stock Market , 1996 .

[45]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[46]  H. Halkin Necessary conditions for optimal control problems with infinite horizons , 1974 .

[47]  Edwin Burmeister,et al.  Mathematical Theories of Economic Growth , 1971 .

[48]  David A. Starrett,et al.  Mathematical Theories of Economic Growth , 1971 .

[49]  Stephen J. Guastello,et al.  Chaos, Catastrophe, and Human Affairs: Applications of Nonlinear Dynamics To Work, Organizations, and Social Evolution , 1995 .

[50]  T. Koopmans Three Essays on the State of Economic Science , 1958 .

[51]  Peter E. Rossi,et al.  Nonlinear dynamic structures , 1993 .

[52]  William J. Baumol,et al.  Topology of Second Order Linear Difference Equations with Constant Coefficients , 1958 .

[53]  Stuart A. Kauffman,et al.  The origins of order , 1993 .