eprintid: 682
rev_number: 16
eprint_status: archive
userid: 2
dir: disk0/00/00/06/82
datestamp: 2011-06-30 14:21:56
lastmod: 2014-12-18 15:42:26
status_changed: 2011-06-30 14:21:56
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Podobnik, Boris
creators_name: Wang, Fengzhong
creators_name: Pammolli, Fabio
creators_name: Stanley, H. Eugene
creators_name: Grosse, I.
creators_id: 
creators_id: 
creators_id: f.pammolli@imtlucca.it
creators_id: 
creators_id: 
title: Size-dependent standard deviation for growth rates: empirical results and theoretical modeling
ispublished: pub
subjects: HB
subjects: QC
divisions: EIC
full_text_status: public
keywords: PACS: 89.65.Gh, 89.65.−s, 82.20.Uv, 02.50.Ey
note: © 2008 American Physical Society

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 σ(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 σ(R) on the average value of the wages with a scaling exponent β≈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 σ(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 σ(R) on the average payroll with a scaling exponent β≈−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) the standard deviation of the logarithmic growth rate depends algebraically on the average size of the stochastic variable.
date: 2008
date_type: published
publication: Physical Review E
volume: 77
number: 5
publisher: American Physical Society
pagerange: 056102
id_number: 10.1103/PhysRevE.77.056102
refereed: TRUE
issn: 1539-3755
official_url: http://link.aps.org/doi/10.1103/PhysRevE.77.056102
citation:   Podobnik, Boris and Wang, Fengzhong and Pammolli, Fabio and Stanley, H. Eugene and Grosse, I.  Size-dependent standard deviation for growth rates: empirical results and theoretical modeling.  Physical Review E, 77 (5).  056102.  ISSN 1539-3755      (2008)  
document_url: http://eprints.imtlucca.it/682/1/PhysRevE.Pammolli_2008.pdf