Quality & Quantity

, Volume 50, Issue 1, pp 271–281 | Cite as

The leading digit distribution of the worldwide illicit financial flows

  • T. A. MirEmail author


The illicit financial flows (IFFs) exiting the developing countries are frequently discussed as hidden resources which could have been otherwise properly utilized for their development. Further, in the context of overhaul of the global financial system, necessitated by the current financial crisis, the IFFs have generated a lot of media and public interest which in turn has however also triggered a debate on the validity of these estimates. To look for completeness or rather for possible manipulation of financial data, forensic analysts routinely use a statistical tool called Benford’s law which states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. In order to gain some insight on their validity we investigate here the recent data on estimates of IFFs for conformity to Benford’s law. We find the patterns in the distribution of the leading digits in the IFFs data similar as predicted by Benford’s law and thereby establish that the frequency of occurrence of the leading digits in these estimates does closely follow the law.


Benford’s law Developing countries Illicit financial flows 



The author thanks GFI for free access to data and Dev Kar for helpful comments. Suggestions from P. M. Ishtiaq are gratefully acknowledged.


  1. Benford, F.: The law of anomalous numbers. Proc. Am. Philos. Soc. 78, 551–572 (1938)Google Scholar
  2. Berger, A., Hill, T.P.: Benford’s law strikes back: No simple explanation in sight for mathematical gem. Math. Intell. 33(1), 85–91 (2011)CrossRefGoogle Scholar
  3. Durtschi, C., Hillison, W., Pacini, C.: The effective use of Benford’s waw to assist in detecting fraud in accounting data. J. Forensic Account. 1, 17–34 (2004)Google Scholar
  4. Fabre, G.: Prospering on crime: money laundering and financial crisis (2005). Working papers in contemporary Asian studies, availabe at
  5. GFI, Global Financial Integrity,
  6. Giles, D.E.: Benford’s law and naturally occurring prices in certain eBay auctions. Appl. Econ. Lett. 14, 157–161 (2007)CrossRefGoogle Scholar
  7. Gonzalez-Garcia, J., Pastor, G.: Benford’s law and macroeconomic data quality (2009). IMF working paper, WP/09/10, available at
  8. Hill, T.P.: The significant-digit phenomenon. Am. Math. Mon. 102(4), 322–327 (1995)CrossRefGoogle Scholar
  9. Hill, T.P.: The difficulty of faking data. Chance 12(3), 27–31 (1999)CrossRefGoogle Scholar
  10. Judge, G., Schechter, L.: Detecting problems in survey data using Benford’s law. J. Hum. Resour 44, 1–24 (2009)Google Scholar
  11. Kar, D., Cartwright-Smith, D.: Illicit financial flows from developing countries: 2002–2006 (2008). Available at
  12. Kar, D.: Illicit financial flows from the least developed countries: 1990–2008, United Nations Development Program Discussion Paper (2011). Available at
  13. Kar, D., Curcio, K.: Illicit financial flows from developing countries: 2000–2009. Update with a focus on Asia, Global Financial Integrity, Washington DC, (2011). Available at
  14. Kar, D., Freitas, S.: Illicit Financial Flows From Developing Countries Over the Decade Ending 2009. Global Financial Integrity, Washington, D.C (2011)Google Scholar
  15. Ley, E.: On the peculiar distribution of the U.S. stock indexes’ digits. Am. Stat. 50(4), 311–313 (1996)Google Scholar
  16. Maher, M., Akers, M.: Using Benford’s law to detect fraud in insurance industry. Int. Buissness Econ. Res. J. 1(2), 1–12 (2002)Google Scholar
  17. Michalski, T., Stoltz, G.: Do countries falsify economic data strategically? Some evidence that they might. Rev. Econ. Stat. 95(2), 591–616 (2013)CrossRefGoogle Scholar
  18. Minteer, S.: Analysis of Benford’s law applied to 3x+1 Problem (2004). Available at
  19. Mir, T.A.: The law of the leading digits and the world religions. Phys. A: Stat. Mech. Appl. 391, 792–798 (2012)CrossRefGoogle Scholar
  20. Mir, T.A.: The Benford law behavior of religious activity data. Phys. A: Stat. Mech. Appl. 408, 1–9 (2014)CrossRefGoogle Scholar
  21. Mir, T.A., Ausloos, M., Cerqueti, R.: Benford’s law predicted digit distribution of aggregated income taxes: The surprising conformity of Italian cities and regions. Eur. Phys. J. B 87, 261 (2014)Google Scholar
  22. Ndikumana, L., Boyce, J.K.: Measurement of capital flight: Methodology and results for Sub-Saharan African countries. Afr. Dev. Rev. 22(4), 471–481 (2010)CrossRefGoogle Scholar
  23. Newcomb, S.: Note on the frequency of use of the different digits in natural numbers. Am. J. Math. 4, 39–40 (1881)CrossRefGoogle Scholar
  24. Nigrini, M.J.: Taxpayer compliance application of Benford’s law. J. Am Tax. Assoc. 18(1), 72–92 (1996)Google Scholar
  25. Nigrini, M.J., Mittermaier, L.J.: The use of Benford’s law as an aid in analytical procedures. Audit.: J. Pract. Theory 16(2), 52–67 (1997)Google Scholar
  26. Nigrini, M.J.: Benford’s law: Applications for Forensic Accounting, Auditing and Fraud Detection. Wiley Publications, Hoboken (2012)CrossRefGoogle Scholar
  27. Nye, J., Moul, C.: The political economy of numbers: On the application of Benford’s law to international macroeconomic statistics. BE J. Macroecon., 7(1), article 17 (2007).Google Scholar
  28. Pain, J.C.: Benford’s law and complex atomic spectra. Phys. Rev. E 77, 012102 (2008)CrossRefGoogle Scholar
  29. Pietroneroa, L., Tosatti, E., Tosatti, V., Vespignani, A.: Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf. Phys. A: Stat. Mech. Appl. 293, 297–304 (2001)CrossRefGoogle Scholar
  30. Pinkham, R.S.: On the distribution of first signcant digits. Ann. Math. Stat. 32, 1223–1230 (1961)CrossRefGoogle Scholar
  31. Rauch, B., Gottsche, M., Brahler, G., Engel, S.: Fact and fiction in EU-Governmental economic data. Ger. Econ. Rev. 12(3), 243–255 (2011)CrossRefGoogle Scholar
  32. Reuter, P.: Draining development? World Bank available at (2012)
  33. Sambridge, M., Tkali, H., Jackson, A.: Benford’s law in the natural sciences. Geophys. Res. Lett. A 37(L22301), 1–5 (2010)Google Scholar
  34. Sandron, F.: Do populations conform to the law of anomalous numbers? Population 57, 755–761 (2002)CrossRefGoogle Scholar
  35. Shao, L., Ma, B.Q.: First digit distribution of hadron full width. Mod. Phys. Lett. A 24, 3275–3282 (2009)CrossRefGoogle Scholar
  36. Steele, M., Chaseling, J.: Power of discrete goodness-of-fit test statistics for a uniform null against a selection of alternative distributions. Commun. Stat. Simul. Comput. 35, 1067–1075 (2006)CrossRefGoogle Scholar
  37. Tax Havens and development, Official Norwegian Report No. 2009:19. (prepared under Government Commission on Capital Flight from Poor Countries appointed by Royal Decree of June 27, 2008) available at (2009).
  38. UNODC.: Estimating illicit financial flows resulting from drug trafficking and other transnational organized crimes. United Nations Office on Drug and Crime Research Report (2011). available at
  39. Varian, H.: Benford’s law. Am. Stat. 23, 65–66 (1972)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Nuclear Research Laboratory, Astrophysical Sciences DivisionBhabha Atomic Research CentreSrinagarIndia

Personalised recommendations