Size-dependent standard deviation for growth rates: Empirical results and theoretical modeling

Podobnik, Boris and Horvatić, Davor and Pammolli, Fabio and Wang, Fengzhong and Stanley, H. Eugene and Grosse, I. (2008) Size-dependent standard deviation for growth rates: Empirical results and theoretical modeling. Physical Review E, 77 (5). pp. 56102-8. ISSN 1539-3755

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Abstract

We study annual logarithmic growth rates R of various economic variables such as exports, imports, and foreign debt. For each of these variables we find that the distributions of R can be approximated by double exponential (Laplace) distributions in the central parts and power-law distributions in the tails. For each of these variables we further find a power-law dependence of the standard deviation sigma_R on the average size of the economic variable with a scaling exponent surprisingly close to that found for the gross domestic product (GDP) [Phys. Rev. Lett. 81, 3275 (1998)]. By analyzing annual logarithmic growth rates R of wages of 161 different occupations, we find a power-law dependence of the standard deviation sigma_R on the average value of the wages with a scaling exponent beta~0.14 close to those found for the growth of exports, imports, debt, and the growth of the GDP. In contrast to these findings, we observe for payroll data collected from 50 states of the USA that the standard deviation sigma_R of the annual logarithmic growth rate R increases monotonically with the average value of payroll. However, also in this case we observe a power-law dependence of sigma_R on the average payroll with a scaling exponent beta~− 0.08. Based on these observations we propose a stochastic process for multiple cross-correlated variables where for each variable (i) the distribution of logarithmic growth rates decays exponentially in the central part, (ii) the distribution of the logarithmic growth rate decays algebraically in the far tails, and (iii)Podobnik the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.

Item Type: Article
Keywords: power law, Laplace distribution, growth rates
Date: May 2008
Subjects: NATURAL SCIENCES > Physics
Additional Information: Copyright (2008) by the American Physical Society.
Divisions: Faculty of Science > Department of Physics
Project code: 114-0352827-1370, 119-0982930-1016
Publisher: American Physical Society
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 03 Jun 2014 11:18
Last Modified: 03 Jun 2014 11:26
URI: http://digre.pmf.unizg.hr/id/eprint/1961

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