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Nonlinear and Complex Dynamics in Economics

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  • William Barnett

    (Department of Economics, The University of Kansas)

  • Apostolos Serletis

    (Department of Economics, University of Calgary)

  • Demitre Serletis

    (Neurological Institute, Epilepsy Center)

Abstract

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 specific applications in microeconomics, macroeconomics, and finance, and discuss the policy relevancy of chaos.

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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201238.

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Length: 37 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Handle: RePEc:kan:wpaper:201238

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Keywords: Complexity; Chaos; Endogenous business cycles;

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References

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  1. Serletis, Apostolos & Gogas, Periklis, 1997. "Chaos in East European black market exchange rates," Research in Economics, Elsevier, Elsevier, vol. 51(4), pages 359-385, December.
  2. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, American Finance Association, vol. 25(2), pages 383-417, May.
  3. William Barnett & Apostolos Serletis & Demitre Serletis, 2012. "Nonlinear and Complex Dynamics in Economics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201238, University of Kansas, Department of Economics, revised Sep 2012.
  4. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, Elsevier, vol. 40(1), pages 89-102, October.
  5. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, Elsevier, vol. 10(2), pages 139-162.
  6. Frank, Murray & Gencay, Ramazan & Stengos, Thanasis, 1988. "International chaos?," European Economic Review, Elsevier, Elsevier, vol. 32(8), pages 1569-1584, October.
  7. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1361-1401, November.
  8. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 62(3), pages 311-37, July.
  9. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
  10. Sanjibani Banerjee & William Barnett & Evgeniya Duzhak & Ramu Gopalan, 2011. "Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201102, University of Kansas, Department of Economics, revised Apr 2011.
  11. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(5), pages 893-920, October.
  12. Abhyankar, A & Copeland, L S & Wong, W, 1997. "Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 15(1), pages 1-14, January.
  13. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521484619.
  14. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 995-1045, September.
  15. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
  16. repec:fth:calaec:13-89 is not listed on IDEAS
  17. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 391-407, March.
  18. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 200510, University of Kansas, Department of Economics, revised Mar 2005.
  19. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  20. William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201219, University of Kansas, Department of Economics, revised Sep 2012.
  21. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 979, Cowles Foundation for Research in Economics, Yale University.
  22. Ramsey, J.B. & Sayers, C.L. & Rothman, P., 1988. "The Statistical Properties Of Dimension Calculations Using Small Data Sets: Some Economic Applications," Papers, Houston - Department of Economics 15, Houston - Department of Economics.
  23. Baumol, William J. & Benhabib, Jess, 1987. "Chaos: Significance, Mechanism, and Economic Applications," Working Papers, C.V. Starr Center for Applied Economics, New York University 87-16, C.V. Starr Center for Applied Economics, New York University.
  24. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, American Finance Association, vol. 41(3), pages 591-601, July.
  25. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, Elsevier, vol. 27(6), pages 1345-1354, November.
  26. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, Elsevier, vol. 22(1), pages 71-90, July.
  27. Reichlin Pietro, 1997. "Endogenous Cycles in Competitive Models: An Overview," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 1(4), pages 1-13, January.
  28. Kiminori Matsuyama, 1988. "Endogenous Price Fluctuations in an Optimizing Model of a Monetary Economy," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 813, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  29. LeRoy, Stephen F, 1989. "Efficient Capital Markets and Martingales," Journal of Economic Literature, American Economic Association, American Economic Association, vol. 27(4), pages 1583-1621, December.
  30. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, Elsevier, vol. 22(1), pages 27-59, October.
  31. repec:fth:guelph:1988-15 is not listed on IDEAS
  32. Abhyankar, A & Copeland, L S & Wong, W, 1995. "Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the United Kingdom," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 105(431), pages 864-80, July.
  33. Brock, W.A., 1988. "Nonlinearity And Complex Dynamics In Economics And Finance," Working papers, Wisconsin Madison - Social Systems 360, Wisconsin Madison - Social Systems.
  34. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers, UCLA Department of Economics 464, UCLA Department of Economics.
  35. Barnett, William A. & Ronald Gallant, A. & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1995. "Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 27(2), pages 301-320, July.
  36. Frank, Murray Z. & Stengos, Thanasis, 1988. "Some evidence concerning macroeconomic chaos," Journal of Monetary Economics, Elsevier, Elsevier, vol. 22(3), pages 423-438.
  37. Bullard, James & Butler, Alison, 1993. "Nonlinearity and Chaos in Economic Models: Implications for Policy Decisions," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 103(419), pages 849-67, July.
  38. Frank, Murray & Stengos, Thanasis, 1989. "Measuring the Strangeness of Gold and Silver Rates of Return," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(4), pages 553-67, October.
  39. Benhabib, Jess & Day, Richard H, 1981. "Rational Choice and Erratic Behaviour," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 48(3), pages 459-71, July.
  40. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, Elsevier, vol. 56(3), pages 269-290, April.
  41. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, Elsevier, vol. 40(1), pages 128-137, October.
  42. Ramsey, James B & Rothman, Philip, 1994. "Nonlinear Monetary Dynamics: Comment," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(1), pages 135-36, January.
  43. Nishimura Kazuo & Sorger Gerhard, 1996. "Optimal Cycles and Chaos: A Survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 1(1), pages 1-20, April.
  44. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521551861.
  45. Serletis, Apostolos, 1995. "Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 13(4), pages 453-58, October.
  46. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 5-59, July.
  47. Scheinkman, Jose A, 1990. "Nonlinearities in Economic Dynamics," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 100(400), pages 33-48, Supplemen.
  48. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(2), pages 246-73, April.
  49. DeCoster, Gregory P & Mitchell, Douglas W, 1991. "Nonlinear Monetary Dynamics," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 9(4), pages 455-61, October.
  50. Barnett,William A. & Kirman,Alan P. & Salmon,Mark, 1997. "Nonlinear Dynamics and Economics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521471411.
  51. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, American Finance Association, vol. 46(5), pages 1839-77, December.
  52. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, American Economic Association, vol. 72(3), pages 406-14, June.
  53. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 36, pages 394.
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Citations

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Cited by:
  1. Gomes, Orlando, 2012. "Information stickiness in general equilibrium and endogenous cycles," Economics Discussion Papers 2012-46, Kiel Institute for the World Economy.
  2. Vivaldo M. Mendes & Diana A. Mendes, 2006. "Active Interest Rate Rules and the Role of Stabilization Policy R&D Tax Credits," Working Papers Series 1, ISCTE-IUL, Business Research Unit (BRU-IUL) ercwp0208, ISCTE-IUL, Business Research Unit (BRU-IUL).
  3. William Barnett & Yijun He, 2012. "Center Manifold, Stability, and Bifurcations in Continuous Time Macroeconometric Systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201227, University of Kansas, Department of Economics, revised Sep 2012.
  4. Vivaldo M. Mendes & Diana A. Mendes, 2007. "Controlling Endogenous Cycles in an OLG Economy by the OGY Method," Working Papers Series 1, ISCTE-IUL, Business Research Unit (BRU-IUL) ercwp0808, ISCTE-IUL, Business Research Unit (BRU-IUL).
  5. William A. Barnett & Alfredo Medio & Apostolos Serletis, 1997. "Nonlinear and Complex Dynamics in Economics," Econometrics, EconWPA 9709001, EconWPA.
  6. Orlando Gomes, 2006. "Routes to chaos in macroeconomic theory," Journal of Economic Studies, Emerald Group Publishing, Emerald Group Publishing, vol. 33(6), pages 437-468, November.
  7. Orlando Gomes, 2006. "Endogenous Business Cycles in the Ramsey Growth Model," Zagreb International Review of Economics and Business, Faculty of Economics and Business, University of Zagreb, Faculty of Economics and Business, University of Zagreb, vol. 9(2), pages 13-36, November.
  8. Haider, Adnan & Hanif, Muhammad Nadeem, 2007. "Inflation Forecasting in Pakistan using Artificial Neural Networks," MPRA Paper 14645, University Library of Munich, Germany.
  9. Nakamura, Emi, 2005. "Inflation forecasting using a neural network," Economics Letters, Elsevier, Elsevier, vol. 86(3), pages 373-378, March.

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