Abstract
This chapter discusses some of the similarities between work being done by economists and by physicists seeking to find “patterns” in economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly-discovered scaling results that appear to be “universal”, in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function (PDF), which is a simple power law with exponent α + 1 = 4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈ 0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious “symmetry breaking” for values of Σ above a certain threshold value Σ c ; here Σ is defined to be the local first moment of the probability distribution of demand Ω — the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
V. Pareto: Cours d’Economie Politique ( Rouge, Lausanne and Paris 1897 )
B.B. Mandelbrot: J. Business 36, 394 (1963)
H.E. Stanley: Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford 1971 )
H. Takayasu (Ed.): Empirical Science of Financial Fluctuations: The Advent of Econophysics ( Springer, Berlin 2002 )
H.E. Stanley: Rev. Mod. Phys. 71, S358 (1999)
R.N. Mantegna, H.E. Stanley: An Introduction to Econophysics: Correlations and Complexity in Finance ( Cambridge University Press, Cambridge 2000 )
J.P. Bouchaud: Quantitative Finance 1, 105 (2001)
R.L. Axtell: Science 293, 1818 (2001)
M.H.R. Stanley, S.V. Buldyrev, S. Havlin, R. Mantegna, M.A. Salinger, H.E. Stanley: Econ. Lett. 49, 453 (1996)
M.H.R. Stanley, L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger, H.E. Stanley: Nature 379, 804 (1996)
L. Bachelier: Théorie de la spéculation [Ph.D. thesis in mathematics], Annales Scientifiques de l’Ecole Normale Supérieure III-17, 21 (1900)
R.N. Mantegna, H.E. Stanley: Nature 376, 46 (1995)
Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng, H.E. Stanley: Phys. Rev. E 60, 1390 (1999)
Z. Ding, C.W.J. Granger, R.F. Engle: J. Empirical Finance 1, 83 (1993)
R.N. Mantegna, H.E. Stanley: Phys. Rev. Lett. 73, 2946 (1994)
B. Podobnik, P.C. Ivanov, Y. Lee, A. Chessa, H.E. Stanley: Europhysics Letters 50, 711 (2000)
R.N. Mantegna, H.E. Stanley: `Ultra-Slow Convergence to a Gaussian: The Truncated Lévy Flight’ in Lévy Flights and Related Topics in Physics, Ed. by M.F. Shlesinger, G.M. Zaslaysky, U. Frisch ( Springer, Berlin 1995 ), pp. 300–312
R.N. Mantegna, H.E. Stanley: Physica A 254, 77 (1998)
B. Podobnik, P.C. Ivanov, Y. Lee, H.E. Stanley: Europhysics Letters 52, 491 (2000)
P.C. Ivanov, B. Podobnik, Y. Lee, H.E. Stanley: Physica A 299, 154 (2001)
J.A. Skjeltorp: Physica 283, 486 (2001)
T. Lux: Appl. Finan. Econ. 6, 463 (1996)
P. Gopikrishnan, M. Meyer, L.A.N. Amaral, H.E. Stanley: Eur. Phys. J. B 3, 139 (1998)
V. Plerou, P. Gopikrishnan, L.A.N. Amaral, M. Meyer, H.E. Stanley: Phys. Rev. E 60, 6519 (1999)
P. Gopikrishnan, V. Plerou, L.A.N. Amaral, M. Meyer, H.E. Stanley: Phys. Rev. E 60, 5305 (1999)
B. Gutenberg, C.F. Richter: Seismicity of the Earth and Associated Phenomenon, 2nd Edition ( Princeton University Press, Princeton 1954 )
D.L. Turcotte: Fractals and Chaos in Geology and Geophysics ( Cambridge University Press, Cambridge 1992 )
J.B. Rundle, D.L. Turcotte, W. Klein: Reduction and Predictability of Natural Disasters ( Addison-Wesley, Reading 1996 )
K. Matia, P. Gopikrishnan, V. Plerou, L.A.N. Amaral, S. Goodwin, H.E. Stanley: `Scaling for the Distribution of the Commodity Market Variations’, condmat/0202028
V. Plerou, P. Gopikrishnan, L.A.N. Amaral, X. Gabaix, H.E. Stanley: Phys. Rev. E 62, 3023 (2000)
P. Gopikrishnan, V. Plerou, X. Gabaix, H.E. Stanley: Phys. Rev. E 62, 4–493 (2000)
S. Ghashgaie, W. Breymann, J. Peinke, P. Talkner, Y. Dodge: Nature 381, 767 (1996)
R.N. Mantegna, H.E. Stanley: Nature 383, 587 (1996)
R.N. Mantegna, H.E. Stanley: Physica A 239, 255 (1997)
V. Plerou, P. Gopikrishnan, X. Gabaix, H.E. Stanley: Phys. Rev. E 66 027104 (2002)
V. Plerou, P. Gopikrishnan, H.E. Stanley: `Critical Threshold and Symmetry Breaking in Stock Demand’, cond-mat/0111349
M.L. Mehta: Random Matrices ( Academic Press, Boston 1991 )
T. Guhr, A. Müller-Groeling, H.A. Weidenmüller: Phys. Reports 299, 189 (1998)
E.P. Wigner: Ann. Math. 53, 36 (1951)
E.P. Wigner: Proc Cambridge Philos. Soc. 47, 790 (1951)
E.P. Wigner: `Results and theory of resonance absorption’ in Conference on Neutron Physics by Time-of-flight ( Gatlinburg, Tennessee 1956 ), pp. 59–70
M.L. Mehta, F.J. Dyson: J. Math. Phys. 4, 713 (1963)
F.J. Dyson: Revista Mexicana de Física 20, 231 (1971)
A.M. Sengupta, P.P. Mitra: Phys. Rev. E 60, 3389 (1999)
L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potters: Phys. Rev. Lett. 83, 1469 (1999)
V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley: Phys. Rev. Lett. 83, 1471 (1999)
P. Gopikrishnan, B. Rosenow, V. Plerou, H.E. Stanley: Phys. Rev. E 64, 035106 (2001)
V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, T. Guhr, H.E. Stanley: Phys. Rev. E 65 066136 (2002)
B. Rosenow, V. Plerou, P. Gopikrishnan, H.E. Stanley: Europhys. Lett. 59, 500 (2002)
L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger, H.E. Stanley, M.H.R. Stanley: J. Phys. I France 7, 621 (1997)
S.V. Buldyrev, L.A.N. Amaral, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger, H.E. Stanley, M.H.R. Stanley: J. Phys. I France 7, 635 (1997)
L.A.N. Amaral, S.V. Buldyrev, S. Havlin, M.A. Salinger, H.E. Stanley: Phys. Rev. Lett. 80, 1385 (1998)
J. Sutton: The variance of firm growth rates: the scaling’ puzzle’, working paper, London School of Economics (2001)
G. Bottazzi, G. Dosi, M. Riccaboni, F. Pammolli: `The scaling of growth processes and the dynamics of business firms’ Economics Department at University of Siena and Pisa San’ Anna School of Advanced Studies, working paper (2001)
H.E. Stanley, L.A.N. Amaral, P. Gopikrishnan, V. Plerou, M.A. Salinger: `Scale invariance and universality in economic phenomena’, working paper, based on Invited Talk at the 56th ESEM Econometric Society meeting 26–29 Aug 2001 in Lausanne
H. Takayasu, K. Okuyama: Fractals 6, 67 (1998)
Y. Lee, L.A.N. Amaral, D. Canning, M. Meyer, H.E. Stanley: Phys. Rev. Letters 81, 3275 (1998)
V. Plerou, L.A.N. Amaral, P. Gopikrishnan, M. Meyer, H.E. Stanley: Nature 400, 433 (1999)
T. Keitt, H.E. Stanley: Nature 393, 257 (1998)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Stanley, H.E., Gopikrishnan, P., Plerou, V., Salinger, M.A. (2004). Patterns in Economic Phenomena. In: Wille, L.T. (eds) New Directions in Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08968-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-08968-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07739-5
Online ISBN: 978-3-662-08968-2
eBook Packages: Springer Book Archive