Barnett, William A. and Serletis, Apostolos and Serletis, Demitre (2012): Nonlinear and Complex Dynamics in Economics.
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This paper is an up-to-date survey of the state-of-the-art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and �finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specifi�c applications in microeconomics, macroeconomics, and �finance, and discuss the policy relevancy of chaos.
|Item Type:||MPRA Paper|
|Original Title:||Nonlinear and Complex Dynamics in Economics|
|Keywords:||Complexity; chaos; endogenous business cycles|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C30 - General
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
|Depositing User:||William A. Barnett|
|Date Deposited:||12. Sep 2012 12:32|
|Last Modified:||12. Feb 2013 21:10|
 Azariadis, Costas (1993) Intertemporal Macroeconomics. Blackwell Publishers.
 Barnett, William A. and Ping Chen (1988) �The Aggregation-Theoretic Monetary Aggregates are Chaotic and Have Strange Attractors: An Econometric Application of Mathematical Chaos.� In William A. Barnett, Ernst R. Berndt, and Halbert White (eds.), Dynamic Econometric Modeling, pp. 199-246. Cambridge: Cambridge University Press.
 Barnett, William A. and Evgeniya A. Duzhak (2007) �Hopf Bifurcation within New Keynesian Functional Structure.� In William A. Barnett and Apostolos Serletis (eds.), Functional Structure Inference, pp. 257-275. Elsevier.
 Barnett, William A. and Evgeniya A. Duzhak (2010) Empirical Assessment of Bifurcation Regions within New Keynesian Models.� Economic Theory 45, 99-128.
 Barnett, William A. and Susan He (2010) �Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right.� Economic Modelling 27, 1345-1354.
 Barnett, William A. and Melvin J. Hinich (1992) �Empirical Chaotic Dynamics in Economics. �Annals of Operations Research 37, 1-15.
 Barnett, William A. and Apostolos Serletis (2000) �Martingales, Nonlinearity, and Chaos.� Journal of Economic Dynamics and Control 24, 703-724.
 Barnett, William A., Alfredo Medio, and Apostolos Serletis (1997) �Nonlinear and Complex Dynamics in Economics.� Working Paper.
 Barnett, William A., Sanjibani Banerjee, Evgeniya Duzhak, and Ramu Gopalan (2011) Bifurcation Analysis of Zellner�'s Marshallian Macro Model.� Journal of Economic Dynamics and Control 35, 1577-1585.
 Barnett, William A., A. Ronald Gallant, Melvin J. Hinich, Joschen Jungeilges, Daniel Kaplan, and Mark J. Jensen (1995) �Robustness of Nonlinearity and Chaos Tests to Measurement Error, Inference Method, and Sample Size. �Journal of Economic Behavior and Organization 27, 301-320.
 Barnett, William A., A. Ronald Gallant, Melvin J. Hinich, Joschen Jungeilges, Daniel Kaplan, and Mark J. Jensen (1997) �A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos.� Journal of Econometrics 82, 157-192.
 Barnett, William A., A. Ronald Gallant, Melvin J. Hinich, Joschen Jungeilges, Daniel Kaplan, and Mark J. Jensen (1996) �An Experimental Design to Compare Tests of Nonlinearity and Chaos.� In William A. Barnett, Alan Kirman, and Mark Salmon (eds.), Nonlinear Dynamics in Economics, pp. 163-190. Cambridge: Cambridge University Press.
 Baumol, William and Jess Benhabib (1989) �Chaos: Signi�ficance, Mechanism, and Economic Applications.� Journal of Economic Perspectives 3, 77-106.
 Benhabib, Jess and Richard H. Day (1981) �Rational Choice and Erratic Behavior.� Review of Economic Studies 48, 459-471.
 Bollerslev, Tim (1986) �Generalized Autoregressive Conditional Heteroscedasticity.� Journal of Econometrics 31, 307-27.
 Brock, William A. (1988) �Nonlinearity and Complex Dynamics in Economics and Finance.� In Philip W. Anderson, Kenneth J. Arrow, and David Pines (eds.), The Economy as an Evolving Complex System, pp. 77-97. Addison Wesley.
 Brock, William A., W. Davis Dechert, Blake LeBaron, and José A. Scheinkmam (1996) A Test for Independence Based on the Correlation Dimension.� Econometric Reviews 15, 197-235.
 Bullard, James and Alison Butler (1993) �Nonlinearity and Chaos in Economic Models: Implications for Policy Decisions.� Economic Journal 103, 849-867.
 Day, Richard H. (1982) �Irregular Growth Cycles.� American Economic Review 72, 406-414.
 Engle, Robert F. (1982) �Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of U.K. In�ation.�Econometrica 50, 987-�1008.
 Engle, Robert F., David M. Lilien, and Russell P. Robins (1987) �Estimating Time Varying Risk Premia in the Term Structure.�Econometrica 55, 391-407.
 Fama, Eugene F. (1965) �The Behavior of Stock Market Prices.� Journal of Business 38, 34-105.
 Fama, Eugene F. (1970) �Efficient Capital Markets: A Review of Theory and Empirical Work.� Journal of Finance 25, 383-417.
 Feigenbaum, Mitchell J. (1978) �Quantitative Universality for a Class of Nonlinear Transformations. �Journal of Statistical Physics 19, 25-52.
 Goodwin, Richard M. (1951) �The Non-linear Accelerator and the Persistence of Business Cycles. �Econometrica 19, 1-17.
 Grandmont, Jean-Michel (1985) �On Endogenous Competitive Business Cycles. �Econometrica 53, 995-1045.
 Grassberger, Peter and Itamar Procaccia (1983) �Characterization of Strange Attractors. �Physical Review Letters 50, 346-349.
 Guckenheimer, John and Philip Holmes (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer Verlag.
 LeRoy, Stephen F. (1989) �Efficient Capital Markets and Martingales. �Journal of Economic Literature 27, 1583-1621.
 Li, Tien-Yien and James A. Yorke (1975) �Period Three Implies Chaos.� American Mathematical Monthly 82, 985-992.
 Lucas, Robert E. Jr. (2009) �In Defence of the Dismal Science.� The Economist. August 6th.
 Mandelbrot, Benoit B. (1963) �The Variation of Certain Speculative Stock Prices.� Journal of Business 36, 394-419.
 Mandelbrot, Benoit B. (1985) �Self-Affine Fractals and Fractal Dimension.� Physica Scripta 32, 257-260.
 Matsuyama, Kiminori (1991) �Endogenous Price Fluctuations in an Optimizing Model of a Monetary Economy.� Econometrica 59, 1617-1631.
 Medio, Alfredo (1992) Chaotic Dynamics. Theory and Applications to Economics. Cambridge: Cambridge University Press.
 Nelson, Daniel B. (1991) �Conditional Heteroscedasticity in Asset Returns.� Econometrica 59, 347-370.
 Samuelson, Paul A. (1965) �Proof that Properly Anticipated Prices Fluctuate Randomly. �Industrial Management Review 6, 41-49.
 Sidrauski, Miguel (1967) �Rational Choice and Patterns of Growth in a Monetary Economy. �American Economic Review 57, 534-544.
 Solow, Robert M. (1956) �A Contribution to the Theory of Economic Growth.� Quarterly Journal of Economics 70, 65-94.
 Summers, Laurence H. (1986) �Does the Stock Market Rationally Refl�ect Fundamental Values.� Journal of Finance 41, 591-601.
 Woodford, Michael (1989) �Imperfect Financial Intermediation and Complex Dynamics. �In William A. Barnett, John Geweke, and Karl Shell (eds.), Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity, pp. 309-338. Cambridge: Cambridge University Press.