Skip to main content

The leading digit distribution of the worldwide illicit financial flows

Abstract

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

References

  • Benford, F.: The law of anomalous numbers. Proc. Am. Philos. Soc. 78, 551–572 (1938)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • Fabre, G.: Prospering on crime: money laundering and financial crisis (2005). Working papers in contemporary Asian studies, availabe at www.ace.lu.se/images/Syd_-och_-sydostasienstudier/working_-papers/Fabre.

  • GFI, Global Financial Integrity, http://www.gfintegrity.org

  • Giles, D.E.: Benford’s law and naturally occurring prices in certain eBay auctions. Appl. Econ. Lett. 14, 157–161 (2007)

    Article  Google Scholar 

  • Gonzalez-Garcia, J., Pastor, G.: Benford’s law and macroeconomic data quality (2009). IMF working paper, WP/09/10, available at http://www.imf.org/external/pubs/ft/wp/2009/wp0910

  • Hill, T.P.: The significant-digit phenomenon. Am. Math. Mon. 102(4), 322–327 (1995)

    Article  Google Scholar 

  • Hill, T.P.: The difficulty of faking data. Chance 12(3), 27–31 (1999)

    Article  Google Scholar 

  • Judge, G., Schechter, L.: Detecting problems in survey data using Benford’s law. J. Hum. Resour 44, 1–24 (2009)

    Google Scholar 

  • Kar, D., Cartwright-Smith, D.: Illicit financial flows from developing countries: 2002–2006 (2008). Available at http://works.bepress.com/dev_kar/2

  • Kar, D.: Illicit financial flows from the least developed countries: 1990–2008, United Nations Development Program Discussion Paper (2011). Available at http://works.bepress.com/dev_kar/3

  • 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 http://econ-jobs.com

  • Kar, D., Freitas, S.: Illicit Financial Flows From Developing Countries Over the Decade Ending 2009. Global Financial Integrity, Washington, D.C (2011)

    Google Scholar 

  • Ley, E.: On the peculiar distribution of the U.S. stock indexes’ digits. Am. Stat. 50(4), 311–313 (1996)

    Google Scholar 

  • 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 

  • Michalski, T., Stoltz, G.: Do countries falsify economic data strategically? Some evidence that they might. Rev. Econ. Stat. 95(2), 591–616 (2013)

    Article  Google Scholar 

  • Minteer, S.: Analysis of Benford’s law applied to 3x+1 Problem (2004). Available at www.math.osu.edu/vigre/ntwg/3x+1/minteer_AnalysisofBenford.doc.

  • Mir, T.A.: The law of the leading digits and the world religions. Phys. A: Stat. Mech. Appl. 391, 792–798 (2012)

    Article  Google Scholar 

  • Mir, T.A.: The Benford law behavior of religious activity data. Phys. A: Stat. Mech. Appl. 408, 1–9 (2014)

    Article  Google Scholar 

  • 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)

  • 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)

    Article  Google Scholar 

  • Newcomb, S.: Note on the frequency of use of the different digits in natural numbers. Am. J. Math. 4, 39–40 (1881)

    Article  Google Scholar 

  • Nigrini, M.J.: Taxpayer compliance application of Benford’s law. J. Am Tax. Assoc. 18(1), 72–92 (1996)

    Google Scholar 

  • 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 

  • Nigrini, M.J.: Benford’s law: Applications for Forensic Accounting, Auditing and Fraud Detection. Wiley Publications, Hoboken (2012)

    Book  Google Scholar 

  • 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).

  • Pain, J.C.: Benford’s law and complex atomic spectra. Phys. Rev. E 77, 012102 (2008)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Pinkham, R.S.: On the distribution of first signcant digits. Ann. Math. Stat. 32, 1223–1230 (1961)

    Article  Google Scholar 

  • Rauch, B., Gottsche, M., Brahler, G., Engel, S.: Fact and fiction in EU-Governmental economic data. Ger. Econ. Rev. 12(3), 243–255 (2011)

    Article  Google Scholar 

  • Reuter, P.: Draining development? World Bank available at http://elibrary.worldbank.org/content/book/9780821388693 (2012)

  • Sambridge, M., Tkali, H., Jackson, A.: Benford’s law in the natural sciences. Geophys. Res. Lett. A 37(L22301), 1–5 (2010)

    Google Scholar 

  • Sandron, F.: Do populations conform to the law of anomalous numbers? Population 57, 755–761 (2002)

    Article  Google Scholar 

  • Shao, L., Ma, B.Q.: First digit distribution of hadron full width. Mod. Phys. Lett. A 24, 3275–3282 (2009)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 www.regjeringen.no/upload/UD/Vedlegg/Utvikling/tax_-report. (2009).

  • 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 www.unodc.org/documents/data_-and_-analysis/Illicit_-financial_-flows_-2011_-web.

  • Varian, H.: Benford’s law. Am. Stat. 23, 65–66 (1972)

    Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. A. Mir.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mir, T.A. The leading digit distribution of the worldwide illicit financial flows. Qual Quant 50, 271–281 (2016). https://doi.org/10.1007/s11135-014-0147-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11135-014-0147-z

Keywords

  • Benford’s law
  • Developing countries
  • Illicit financial flows