Complexity in Economics: Cutting Edge Research pp 205-223 | Cite as

# Why Should Economics Give Chaos Theory Another Chance?

## Abstract

Economic data provide little evidence -if any- of linear, simple dynamics, and of lasting convergence to stationary states or regular cyclical behavior. In spite of this the linear approach absolutely dominates mainstream economics. The problem is that mainstream economics is now in deep crisis. The recent financial crisis clearly showed that orthodox economics was quite unprepared to deal with it. Most mainstream economists not only did not foresee the depth of the current crisis, they not even consider it possible. It is well known since the famous contribution of Mandelbrot (1963) that many economic and financial time series have fat tails, i.e. that the probability of extreme events is higher than if the data-generating process were normal. However, the usual practice among orthodox economists has been to assume-implicitly or explicitly- a normal distribution. Orthodox economists represent the economy as a stable equilibrium system resembling the planetary one. The concept of equilibrium plays a key role in traditional economics. This approach is useful in normal, stable times. However, it is incapable of dealing with unstable, turbulent, chaotic times. The crisis has clearly showed this. Heterodox contributions shed much more light on what happens during these crucial periods in which a good part of the economy is reshaped; they provide powerful insights towards what policies to follow in those extraordinary circumstances. However, they remain as theories mainly suitable for those periods of instability and crisis. The challenge is to arrive at a unified theory valid both for normal and abnormal times. In this respect, the complexity approach with its use of non-linear models offers the advantage that the same model allows to describe stable as well as unstable and even chaotic behaviors. Although the results of chaos tests do not prove so far the existence of chaos in all economic variables they are consistent with its existence. The detection of chaos in economic time series faces three types of difficulties: (1) the limited number of observations such series contain; (2) the high noise level in economic time series; and (3) the high dimension of economic systems. However, topological methods for chaos detection seem to be a highly promising tool. On the other hand, in economics, there are no such things as crucial experiments. Economists seldom practice the falsificationism they preach. Confidence in the implications of economics derives from confidence in its axioms rather than from testing their implications. Therefore, non-linear dynamics and chaos theory should not be subject to more stringent rules than what is usual for the rest of economic theory.

### Keywords

Chaos Determinism Economic methodology Nonlinearity Predictability### References

- Altavilla, C., De Grauwe, P.: Non-linearities in the relation between the exchange rate and its fundamentals. Int. J. Finance Econ.
**15**(1), 1–21 (2010)Google Scholar - Arthur, B.W.: Increasing Returns and Path Dependence in the Economy. The University of Michigan Press, Ann Arbor (1994)Google Scholar
- Arthur, W.B., Durlauf, S.N., Lane, D.A. (eds.): The Economy as an Evolving Complex System II. Addison-Wesley, Reading (1997)Google Scholar
- Arthur, W.B.: Complexity, the Santa Fe approach and nonequilibrium economics. In: Faucci, R., Marchionatti, R. (eds.) History of Economic Ideas. Fabrizio Serra Editore, Rome (2010)Google Scholar
- Bala, V., Majumdar, M., Mitra, T.: Controlling Chaos: Some Analytical Results and Applications to Tattonement. Cornell University, Ithaca Center for Analytic Economics (1996)Google Scholar
- Barnett, W. A., He, Y.: Unsolved econometric problems in nonlinearity, Chaos, and Bifurcation. Working papers series in theoretical and applied economics. University of Kansas, Department of Economics No 201231 (2012)Google Scholar
- Barnett, W. A., Serletis, A.: Martingales, nonlinearity, and chaos. J. Econ. Dyn. Control
**24**(5–7), 703–24 (2000)Google Scholar - Bak, P., Chen, K.: Self-organized criticality. Sci Am.
**264**(1), 46–53 (1991)Google Scholar - Baumol, W., Benhabib, J.: Chaos: significance, mechanism, and economic implications. J. Econ. Perspect.
**3**(1), 77–105 (1989)Google Scholar - Bayar, L.B.: Chaos Theory and its Importance and Applications in Economics. Marmara University, Institute of Social Sciences, Department of Economics, T.C, Istanbul (2005)Google Scholar
- Beker, P.F.: Are inefficient entrepreneurs driven out of the market? J. Econ. Theory
**114**, 329–344 (2004)Google Scholar - Beker, V.A.: Is Economics a Science? A Discussion of Some Methodological Issues (2005). http://ssrn.com/abstract=839307
- Beker, V.A.: Per una teoria economica del non-equilibrio. Note economiche: rivista economica del Monte dei Paschi di Siena
**24**(1), 20–34 (1994)Google Scholar - Beker, V.A.: Non-linear dynamics and Chaos in economics. In: Dahiya, S.B. (ed.) The Current State of Economic Science, vol. 1, pp. 169–193. Spellbound Publications, Rohtak (1999)Google Scholar
- Blume, L., Easley, D.: Evolution and market behavior. J. Econ. Theory
**58**, 9–40 (1992)CrossRefGoogle Scholar - Blume, L., Easley, D.: If you’re so smart, why aren’t you rich? Belief selection in completeand incomplete markets. Econometrica
**74**, 929–966 (2006)Google Scholar - Boldrin, M.: The impact of chaos on economic theory. In: Grebogi, C., Yorke, J. (eds.) Impact of Chaos on Science and Society, pp. 275–297. United Nations University Press. New York (1997)Google Scholar
- Brock, W.: Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance. Estudios Econ.
**8**, 3–55 (1993)Google Scholar - Brock, W.A.: Asset price behavior in complex environments. In: Arthur, W.B., Durlauf, S.N., Lane, D.A. (eds.) The Economy as an Evolving Complex System II, pp. 385–423. Addison-Wesley, Reading (1997)Google Scholar
- Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Lecture Notes No. 61. SIAM, Philadelphia (1992)Google Scholar
- Day, R.H.: Complex Economic Dynamics, An Introduction to Dynamical Systems and Market Mechanisms, vol. I. MIT Press, Cambridge (1994)Google Scholar
- De Grauwe, P., Grimaldi, M.: The Exchange Rate in a Behavioural Finance Framework. Princeton University Press, Princeton (2006)Google Scholar
- De Grauwe, P., Rovira Kaltwasser, P.: Animal spirits in the foreign exchange market. J. Econ. Dyn. Control
**36**(8),1176–1192 (2012)Google Scholar - Faggini, M.: Chaos detection in economics. Metric versus topological tools. MPRA Paper No. 30928. http://mpra.ub.uni-muenchen.de/30928/ (2010)
- Faggini, M.: Chaotic time series analysis in economics: balance and perspectives. Working Paper No. 25. Universitá degli Studi di Torino, Department of Economics and Public Finance. http://web.econ.unito.it/prato/papers/n25.pdf (2011)
- Faggini, M., Parziale, A.: The failure of economic theory. Lessons from chaos theory. Mod. Econ.
**3**, 1–10 (2012). www.scirp.org/journal/PaperDownload.aspx?paperID=16802 - Frankel, J., Froot, K.: Chartists, fundamentalists, and trading in the foreign exchange market. Am. Econ. Rev.
**80**(2), 181–185 (1990)Google Scholar - Friedman, M.: The methodology of positive economics. In: Friedman, M. (ed.) Essays in Positive Economics. University of Chicago Press, Chicago (1953)Google Scholar
- Gao, J., Sultan, H., Hu, J., Tung, W.W.: Denoising nonlinear time series by adaptive filtering and wavelet shrinkage: a comparison. IEEE Signal Proces. Lett.
**17**(3), 127 (2010)Google Scholar - Goldstein, J.: Attractors and Nonlinear Dynamical Systems. Plexus Institute, Bordentown (2011). http://c.ymcdn.com/sites/www.plexusinstitute.org/resource/resmgr/files/deeperlearningspring2011.pdf
- Guégan, D., Hoummiya, K.: Denoising with wavelets method in chaotic time series: application in climatology, energy and finance. In: Abbott, D., Bouchaud, J.P., Gabaix, X., McCaulay, J.L. (eds.) Noise and Fluctuations in Econophysics and Finance. Proceedings of SPIE, vol. 5848, pp. 174–185. (2005)Google Scholar
- Hausman, D.M.: The Inexact and Separate Science of Economics. Cambridge University Press, Cambridge (1992)CrossRefGoogle Scholar
- Hawkins, S.: A Brief History of Time. Bantam Books, London (1988)Google Scholar
- Hommes, C., Manzan, S.: Testing for nonlinear structure and chaos in economic time. A comment. J. Macroecon.
**28**(1), 169–174. Elsevier (2006)Google Scholar - Hommes, C., Wagener, F.: Complex evolutionary systems in behavioral finance. In: Hens, T., Schenk-Hopp, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution. North-Holland, Amsterdam (2008)Google Scholar
- Horgan, J.: From complexity to perplexity. Sci. Am.
**272**(6), 104–109 (1995)Google Scholar - Katz, F.: Methodological Contributions of Chaos Theory to Economic Thought (2002). http://staffnet.kingston.ac.uk/ku32530/PPE/katz.pdf
- Kyrtsou, C., Serletis, A.: Univariate tests for nonlinear structure. J. Macroecon.
**28**(1), 154–168. Elsevier (2006)Google Scholar - LeBaron, B.: Building financial markets with artificial agents: desired goals, and present techniques. In: Karakoulas, G. (ed.) Computational Markets. MIT Press, Cambridge (1999)Google Scholar
- Li, H., Jr, Barkley Rosser: Emergent volatility in asset markets with heterogeneous agents. Discrete Dyn. Nat. Soc.
**6**, 171–180 (2001)CrossRefGoogle Scholar - Lucas, R.E.: Asset prices in an exchange economy. Econometrica
**46**(6), 1429–1445 (1978)Google Scholar - Mandelbrot, B.: The variation of certain speculative prices. J. Bus.
**36**(4), 394–419 (1963)Google Scholar - Martelli, M., Dang, M., Seph, T.: Defining chaos. Math. Mag.
**71**, 112–122 (1998)CrossRefGoogle Scholar - Milgrom, P., Stokey, N.: Information, trade and common knowledge. J. Econ. Theory
**26**, 17–27 (1982)CrossRefGoogle Scholar - North, D.C.: Economic performance through time. Am. Econ. Rev.
**84**(3), 359–368 (1994)Google Scholar - Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett.
**64**, 1196–1199 (1990)CrossRefGoogle Scholar - Rosser, J.B.: On the complexities of complex economic dynamics. J. Econ. Perspect. Fall
**13**(4), 169–192 (1999)Google Scholar - Ruelle, D.: Turbulence, Strange Attractors, and Chaos. World Scientific, Singapore (1994)Google Scholar
- Salzano, M.: The Analysis of Extreme Events - Some Forecasting Approaches. In: Perna, C., Sibillo, M. (eds.) Mathematical and Statistical Methods in Insurance and Finance. Springer, New York (2008)Google Scholar
- Samuelson, P.A.: Foundations of Economic Analysis. Harvard University Press, Cambridge (1983)Google Scholar
- Scheinkmann, J., Woodford, M.: Self-organized criticality and economic fluctuations. Am. Econ. Rev.
**84**(2), 417–421 (1994) (Papers and Proceedings)Google Scholar - Schumpeter, J.A. (1987). History of Economic Analysis. Routledge, LondonGoogle Scholar
- Starrett, J.: Non-strange chaotic attractors equivalent to their templates. Dyn. Sys. Int. J.
**27**(2), 187–196 (2012)CrossRefGoogle Scholar - Tirole, J.: On the possibility of speculation under rational expectations. Econometrica
**50**(5), 1163–1181 (1982)Google Scholar - Vitolo, R., Holland, M.P., Ferro, C.: Robust extremes in chaotic desterministic systems. Chaos
**19**(4), 043127 (2009)Google Scholar