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Scale invariant properties of public debt growth

Author

Listed:
  • Alexander M. Petersen
  • Boris Podobnik
  • Davor Horvatic
  • H. Eugene Stanley

Abstract

Public debt is one of the important economic variables that quantitatively describes a nation's economy. Because bankruptcy is a risk faced even by institutions as large as governments (e.g. Iceland), national debt should be strictly controlled with respect to national wealth. Also, the problem of eliminating extreme poverty in the world is closely connected to the study of extremely poor debtor nations. We analyze the time evolution of national public debt and find "convergence": initially less-indebted countries increase their debt more quickly than initially more-indebted countries. We also analyze the public debt-to-GDP ratio R, a proxy for default risk, and approximate the probability density function P(R) with a Gamma distribution, which can be used to establish thresholds for sustainable debt. We also observe "convergence" in R: countries with initially small R increase their R more quickly than countries with initially large R. The scaling relationships for debt and R have practical applications, e.g. the Maastricht Treaty requires members of the European Monetary Union to maintain R

Suggested Citation

  • Alexander M. Petersen & Boris Podobnik & Davor Horvatic & H. Eugene Stanley, 2010. "Scale invariant properties of public debt growth," Papers 1002.2491, arXiv.org.
  • Handle: RePEc:arx:papers:1002.2491
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    References listed on IDEAS

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    Cited by:

    1. Chen, Yanguang, 2012. "The rank-size scaling law and entropy-maximizing principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 767-778.
    2. Chen, Yanguang & Wang, Jiejing, 2014. "Recursive subdivision of urban space and Zipf’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 392-404.
    3. Chen, Yanguang, 2012. "The mathematical relationship between Zipf’s law and the hierarchical scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3285-3299.
    4. Hu, Lunchao & Tian, Kailan & Wang, Xin & Zhang, Jiang, 2012. "The “S” curve relationship between export diversity and economic size of countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 731-739.
    5. Pokrovskii, Vladimir N., 2011. "Pulsation of the growth rate of output and technology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4347-4354.
    6. Tunali, Çiǧdem Börke & Yilanci, Veli, 2010. "Are per capita incomes of MENA countries converging or diverging?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4855-4862.
    7. Wu, Yajing & Guo, Jinzhong & Chen, Qinghua & Wang, Yougui, 2011. "Socioeconomic implications of donation distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4325-4331.

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