An Explanation of Universality in Growth Fluctuations

14 Pages Posted: 29 Apr 2010 Last revised: 13 Feb 2011

See all articles by Yonathan Schwarzkopf

Yonathan Schwarzkopf

Lime Brokerage LLC; Santa Fe Institute

Robert Axtell

George Mason University - Department of Computational Social Science; George Mason University - Department of Economics; Santa Fe Institute - Economics

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Date Written: April 28, 2010

Abstract

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, and the scientific output of universities all show unusual but remarkably similar growth fluctuations.

The fluctuations display characteristic features, including heavy tails and anomalous power law scaling of the standard deviation as a function of size. Many theories have now been put forward to explain this, all of them based on modifications and extensions of proportional growth of subunits. We analyze data from bird populations, firms, and mutual funds and show that the growth fluctuations match a Levy distribution very well. This was previously suggested by Wyart and Bouchaud and Gabaix, but until now never tested. However, we show that their theory (and indeed all previous theories) are ruled out, at least for these three data sets, because they require size distributions that are too heavy tailed. We introduce a simple additive replication model, in which groups (such as firms) grow by replacing each of their members by a random number of new members. To demonstrate how the individual growth fluctuations can be heavy-tailed even though the sizes are not, we propose a model based on stochastic influence dynamics over a scale-free contact network, and show that it produces the correct behavior. We generalize the model to the case where some groups are preferred over others, and show that this can lead to a breakdown of the anomalous scaling, which appears to be observed for some other data sets.

Keywords: firm growth, scaling, mutual fund flows

JEL Classification: C21, D21

Suggested Citation

Schwarzkopf, Yonathan and Axtell, Robert and Farmer, J. Doyne, An Explanation of Universality in Growth Fluctuations (April 28, 2010). Available at SSRN: https://ssrn.com/abstract=1597504 or http://dx.doi.org/10.2139/ssrn.1597504

Yonathan Schwarzkopf (Contact Author)

Lime Brokerage LLC ( email )

625 Broadway
New York, NY 10012
United States

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Robert Axtell

George Mason University - Department of Computational Social Science ( email )

4400 University Drive
375 Research Hall
Fairfax, VA 22030
United States

George Mason University - Department of Economics ( email )

4400 University Drive
Fairfax, VA 22030
United States

Santa Fe Institute - Economics ( email )

1399 Hyde Park Rd
Santa Fe, NM 87501
United States

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

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