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The Interrupted Power Law and The Size of Shadow Banking

  • Davide Fiaschi
  • Imre Kondor
  • Matteo Marsili
  • Valerio Volpati

Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a large body of empirical literature which finds a Pareto distribution for firm sizes both across countries and over time. Pareto distributions are generally traced back to a mechanism of proportional random growth, based on a regime of constant returns to scale. This makes our findings of an ``interrupted'' Pareto distribution all the more puzzling, because we provide evidence that financial firms in our sample should operate in such a regime. We claim that the missing mass from the upper tail of the asset size distribution is a consequence of shadow banking activity and that it provides an (upper) estimate of the size of the shadow banking system. This estimate -- which we propose as a shadow banking index -- compares well with estimates of the Financial Stability Board until 2009, but it shows a sharper rise in shadow banking activity after 2010. Finally, we propose a proportional random growth model that reproduces the observed distribution, thereby providing a quantitative estimate of the intensity of shadow banking activity.

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File URL: http://arxiv.org/pdf/1309.2130
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Paper provided by arXiv.org in its series Papers with number 1309.2130.

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Date of creation: Sep 2013
Date of revision: Apr 2014
Handle: RePEc:arx:papers:1309.2130
Contact details of provider: Web page: http://arxiv.org/

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  1. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
  2. Xavier Gabaix, 2008. "Power Laws in Economics and Finance," NBER Working Papers 14299, National Bureau of Economic Research, Inc.
  3. Tobias Adrian & Daniel Covitz & Nellie Liang, 2013. "Financial stability monitoring," Finance and Economics Discussion Series 2013-21, Board of Governors of the Federal Reserve System (U.S.).
  4. Fujiwara, Yoshi, 2004. "Zipf law in firms bankruptcy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 219-230.
  5. Y. Malevergne & A. Saichev & D. Sornette, 2010. "Zipf's law and maximum sustainable growth," Papers 1012.0199, arXiv.org.
  6. David C. Wheelock & Paul W. Wilson, 2012. "Do Large Banks Have Lower Costs? New Estimates of Returns to Scale for U.S. Banks," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(1), pages 171-199, 02.
  7. Davide Fiaschi - Marzia Romanelli, 2009. "Nonlinear Dynamics in Welfare and the Evolution of World Inequality," Discussion Papers 2009/81, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  8. Pozsar, Zoltan & Adrian, Tobias & Ashcraft, Adam B. & Boesky, Hayley, 2013. "Shadow banking," Economic Policy Review, Federal Reserve Bank of New York, issue Dec, pages 1-16.
    • Zoltan Pozsar & Tobias Adrian & Adam Ashcraft & Hayley Boesky, 2010. "Shadow banking," Staff Reports 458, Federal Reserve Bank of New York.
  9. Andrew G. Haldane & Vasileios Madouros, 2012. "The dog and the frisbee," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 109-159.
  10. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
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