Prof. H.E. Stanley（Boston Univerisyt）

Scale Invariance and Universality in Economic Phenomena

Abstract: In recent years, statistical physicists have determined that physical systems consisting of a large number of interacting particles obey scaling laws that are ``universal'' in the sense that they are independent of many details of the system under study. Since economic systems also consist of a large number of interacting units, it is plausible that universal scaling laws abound in economics. To test this possibility [1] using realistic data sets, we have begun analyzing economic data using methods of statistical physics [2-4]. We have found evidence for scaling and data collapse in various quantities. For example, in one study [5-8], we analyze the Computstat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find the fluctuations in the growth rates--measured by the width of this distribution---scale as a power law characterized by an exponent which takes the same value within the error bars, 0.2, for several measures of the company size, and for different sectors of the economy. Surprisingly, we find the same scaling laws describe a number of other complex organizations, such as country GDP, university research budgets, and bird populations [9]. We also describe applications of physics methods, such as random matrix theory, to practical problems such as risk quantification and portfolio construction [10-13]. Finally, we discuss models that may lead to some insight into these phenomena [7,14]. These results will be discussed, as well as the overall rationale for why one might expect scaling principles to hold for complex economic systems.

This work on which this talk is based is supported by NSF, and was carried out in collaboration with S. V. Buldyrev, D. Canning, P. Cizeau, S. Havlin, T. A. Keitt, Y. Lee, Y. Liu, P. Maass, M. Meyer, C.-K. Peng, and M. H. R. Stanley.

[1] B. Mandelbrot, ``The Variation of Certain Speculative Prices,'' J. Business 36, 394--419 (1963); this and other work is reviewed in R. N. Mantegna and H. E. Stanley, Introduction to Econophysics: Correlations Complexity in Finance (Cambridge University Press, Cambridge, 1999).

[2] R. N. Mantegna and H. E. Stanley, ``Stochastic Process with Ultra-Slow Convergence to a Gaussian: The Truncated L Flight,'' Phys. Rev. Lett. 73, 2946-2949 (1994); R. N. Mantegna and H. E. Stanley, ``Scaling Behaviour in the Dynamics of an Economic Index,'' Nature 376, 46-49 (1995); A. Timmermann, Nature 376, 18-19 (1995).

[3] R. N. Mantegna and H. E. Stanley, ``Turbulence and Exchange Markets,'' Nature (Scientific Correspondence) 383, 587-588 (1996); R. N. Mantegna and H. E. Stanley, ``Stock Market Dynamics and Turbulence: Parallel Analysis of Fluctuation Phenomena'' [ Proceedings of the International Conference on Pattern Formation in Fluids and Materials ], Physica A 239, 255-266 (1997).

[4] M. H. R. Stanley, S. V. Buldyrev, S. Havlin, R. N. Mantegna, M. A. Salinger, and H. E. Stanley, ``Zipf Plots and the Size Distribution of Firms,'' Eco. Lett. 49, 453-457 (1995).

[5] M. H. R. Stanley, L. A. N. Amaral, S. V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, and H. E. Stanley, ``Scaling Behavior in the Growth of Companies,'' Nature 379, 804-806 (1996).

[6] L. A. N. Amaral, S. V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, H. E. Stanley, and M. H. R. Stanley, ``Scaling Behavior in Economics: I. Empirical Results for Company Growth,'' J. Phys. I France 7, 621-633 (1997); see also the recent extension: J. Sutton (preprint).

[7] S. V. Buldyrev, L. A. N. Amaral, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, H. E. Stanley, and M. H. R. Stanley, ``Scaling Behavior in Economics: II. Modeling of Company Growth,'' J. Phys. I France 7, 635-650 (1997); L. A. N. Amaral, S. V. Buldyrev, S. Havlin, M. A. Salinger, and H. E. Stanley, ``Power law scaling for a system of interacting units with complex internal structure,'' Phys. Rev. Lett. 80, 1385-1388 (1998).

[8] L. A. N. Amaral, S. V. Buldyrev, S. Havlin, P. Maass, M. A. Salinger, H. E. Stanley, and M. H. R. Stanley, ``Scaling behavior in economics: The problem of quantifying company growth,'' [in B. Widom Festschrift], Physica 244, 1-24 (1997).

[9] Y. Lee, L. A. N. Amaral, D. Canning, M. Meyer, and H. E. Stanley, ``Universal features in the growth dynamics of complex organizations,'' Phys. Rev. Lett. 81 3275-3278 (1998); D. Canning, L. A. N. Amaral, Y. Lee, M. Meyer, and H. E. Stanley, ``A Power Law for Scaling the Volatility of GDP Growth Rates with Country Size,'' Economics Letters 60, 335-341 (1998); V. Plerou, L. A. N. Amaral, P. Gopikrishnan, M. Meyer, and H. E. Stanley, ``Research at Ivory Tower Universities: A Competitive Enterprise?'' Nature 400, 433-437 (1999); T. Keitt and H. E. Stanley, ``Scaling in the Dynamics of North American Breeding-Bird Populations'' Nature 393, 257-259 (1998).

[10] R. N. Mantegna and H. E. Stanley, ``Physics Investigation of Financial Markets,'' in Proceedings of the International School of Physics "Enrico Fermi", Course CXXXIV, edited by F. Mallamace and H.E. Stanley (IOS Press, Amsterdam, 1997); R. N. Mantegna and H. E. Stanley, ``Econophysics: Scaling and Its Breakdown in Finance,'' [Proc. Jancovici Workshop], J. Stat. Phys. 89, 469-479 (1997).

[11] Y. Liu, P. Cizeau, M. Meyer, C.-K. Peng, and H. E. Stanley, ``Quantification of Correlations in Economic Time Series,'' Physica 245, 437-440 (1997); P. Cizeau, Y. Liu, M. Meyer, C.-K. Peng, and H. E. Stanley, ``Volatility distribution in the S&P Stock Index" Physica A 245, 441-445 (1997); Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng, and H. E. Stanley, ``The statistical properties of the volatility of price fluctuations'', Phys. Rev. E 59, 1390-1400 (1999).

[12] P. Gopikrishnan, M. Meyer, L.A.N. Amaral, and H. E. Stanley, ``Inverse Cubic Law for the Probability Distribution of Stock Price Variations,'' European Journal of Physics B: Rapid Communications 3, 139-140 (1998); P. Gopikrishnan, V. Plerou, L. A. N. Amaral, M. Meyer, and H. E. Stanley, ``Scaling of the distributions of fluctuations of financial market indices'', Phys. Rev. E 60 5305 (1999); V. Plerou, P. Gopikrishnan, L. A. N. Amaral, M. Meyer, and H. E. Stanley, ``Scaling of the distribution of price fluctuations of individual companies'' Phys. Rev. E 60 6519-6529 (1999). .

[13] V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. N. Amaral, and H. E. Stanley, ``Universal and Non-Universal Properties of Cross-Correlations in Financial Time Series'' Phys. Rev. Lett. 83, 1471-1474 (1999); P. Gopikrishnan, B. Rosenow, V. Plerou, and H. E. Stanley, ``Identifying Business Sectors from Stock Price Fluctuations'' e-print cond-mat/0011145; V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. N. Amaral, T. Guhr, and H. E. Stanley, ``Applications of Random Matrix Theory in Finance'' submitted to Phys. Rev. E.

[14] V. Plerou, P. Gopikrishnan, L. A. N. Amaral, X. Gabaix, and H. E. Stanley, ``Diffusion and Economic Fluctuations'' Phys. Rev. E (Rapid Communications) 62, 3023-3026 (2000); P. Gopikrishnan, V. Plerou, X. Gabaix, and H. E. Stanley, ``Statistical Properties of Share Volume Traded in Financial Markets'' Phys. Rev. E (Rapid Communications) 62, 4493-4496 (2000).