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On the emergence of a power law in the distribution of COVID-19 cases

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  • Beare, Brendan K
  • Toda, Alexis Akira

Abstract

The first confirmed case of Coronavirus Disease 2019 (COVID-19) in the US was reported on January 21, 2020. By the end of March, 2020, there were more than 180,000 confirmed cases in the US, distributed across more than 2000 counties. We find that the right tail of this distribution exhibits a power law, with Pareto exponent close to one. We investigate whether a simple model of the growth of COVID-19 cases involving Gibrat's law can explain the emergence of this power law. The model is calibrated to match (i) the growth rates of confirmed cases, and (ii) the varying lengths of time during which COVID-19 had been present within each county. Thus calibrated, the model generates a power law with Pareto exponent nearly exactly equal to the exponent estimated directly from the distribution of confirmed cases across counties at the end of March.

Suggested Citation

  • Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt9k5027d0
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    1. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2016. "The Distribution Of Wealth In The Blanchard–Yaari Model," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 466-481, March.
    2. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    3. Miyazima, Sasuke & Lee, Youngki & Nagamine, Tomomasa & Miyajima, Hiroaki, 2000. "Power-law distribution of family names in Japanese societies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 282-288.
    4. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    5. Acemoglu, Daron & Cao, Dan, 2015. "Innovation by entrants and incumbents," Journal of Economic Theory, Elsevier, vol. 157(C), pages 255-294.
    6. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    7. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
    8. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    9. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    10. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    11. William J. Reed, 2002. "On the Rank‐Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17, February.
    12. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 461-504.
    13. Philip Vermeulen, 2018. "How Fat is the Top Tail of the Wealth Distribution?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(2), pages 357-387, June.
    14. Alex Coad, 2010. "The Exponential Age Distribution and the Pareto Firm Size Distribution," Journal of Industry, Competition and Trade, Springer, vol. 10(3), pages 389-395, September.
    15. Costas Arkolakis, 2016. "A Unified Theory of Firm Selection and Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 89-155.
    16. Cramer,J. S., 2011. "Logit Models from Economics and Other Fields," Cambridge Books, Cambridge University Press, number 9780521188036.
    17. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
    18. Toda, Alexis Akira, 2017. "A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1508-1518, September.
    19. Fujiwara, Yoshi & Aoyama, Hideaki & Di Guilmi, Corrado & Souma, Wataru & Gallegati, Mauro, 2004. "Gibrat and Pareto–Zipf revisited with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 112-116.
    20. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    21. Dan Cao & Wenlan Luo, 2017. "Persistent Heterogeneous Returns and Top End Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 301-326, October.
    22. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    23. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    24. Miquel Montero & Axel Masó-Puigdellosas & Javier Villarroel, 2017. "Continuous-time random walks with reset events," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(9), pages 1-10, September.
    25. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    26. Reed, William J. & Hughes, Barry D., 2003. "On the distribution of family names," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 579-590.
    27. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
    28. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    29. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, September.
    30. Zanette, Damián H & Manrubia, Susanna C, 2001. "Vertical transmission of culture and the distribution of family names," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 1-8.
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    5. Sk, Tahajuddin & Biswas, Santosh & Sardar, Tridip, 2022. "The impact of a power law-induced memory effect on the SARS-CoV-2 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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    9. Yekaterina S Pavlova & David Paez-Espino & Andrew Yu Morozov & Ilya S Belalov, 2021. "Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling," PLOS Computational Biology, Public Library of Science, vol. 17(3), pages 1-21, March.

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