Empirica

, Volume 36, Issue 3, pp 273–292 | Cite as

Does Benford’s Law hold in economic research and forecasting?

Original Paper

Abstract

First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford’s law. This phenomenon has been used in business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford’s law holds in economic research and forecasting. First, we examine the distribution of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford’s law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content.

Keywords

Benford’s Law Fraud detection Regression coefficients Standard errors Growth and inflation forecasts Rounding 

JEL Classification

C8  C52  C12 

References

  1. Batchelor R (2001) How useful are the forecasts of intergovernmental agencies? The IMF and OECD versus the consensus. Appl Econom 33:225–235CrossRefGoogle Scholar
  2. Benford F (1938) The law of anomalous numbers. Proc Am Philos Soc 78:551–572Google Scholar
  3. Berlemann M, Nelson F (2005) Forecasting inflation via experimental stock markets: some results from pilot markets. Ifo Working Paper No. 10Google Scholar
  4. Camerer CF (2003) Behavioural game theory: experiments in strategic interaction. Russell Sage Foundation and Princeton University Press, New York, NYGoogle Scholar
  5. Carslaw C (1988) Anomalies in income numbers: Evidence of goal oriented behaviour. Account Rev 63:321–327Google Scholar
  6. De Ceuster MJK, Dhaene G, Schatteman T (1998) On the hypothesis of psychological barriers in stock markets and Benford’s Law. J Empir Finance 5:263–267CrossRefGoogle Scholar
  7. Diekmann A (2007) Not the first digit! Using Benford’s law to detect fraudulent scientific data. J Appl Stat 34:321–329CrossRefGoogle Scholar
  8. Dovern J, Weisser J (2007) Survey expectations in G7 countries: professional forecasts of macroeconomic variables from the consensus data set. The Kiel Institute for the World Economy, MimeoGoogle Scholar
  9. Durtschi C, Hillison W, Pacini C (2004) The effective use of Benford’s law to assist in detecting fraud in accounting data. J Forensic Account 5:17–34Google Scholar
  10. Gallo GM, Granger CWJ, Jeon Y (2002) Copycats and common swings: the impact of the use of forecasts in information sets. IMF Staff Pap 49:4–21Google Scholar
  11. Giles DE (2007) Benford’s law and naturally occurring prices in certain ebaY auctions. Appl Econ Lett 14:157–161CrossRefGoogle Scholar
  12. Hamermesh DS (2007) Viewpoint: replication in economics. Can J Econ 40(3):715–733Google Scholar
  13. Harvey DI, Leybourne SJ, Newbold P (2001) Analysis of a panel of UK macroeconomic forecasts. Econom J 4:37–55CrossRefGoogle Scholar
  14. Hendry DF, Clements MP (2004) Pooling of forecasts. Econom J 7:1–31CrossRefGoogle Scholar
  15. Hill TP (1995) A statistical derivation of the significant-digit law. Stat Sci 10:354–363Google Scholar
  16. Hill TP (1998) The first digit phenomenon. Am Sci 86:358–363Google Scholar
  17. Isiklar G, Lahiri K (2007) How far ahead can we forecast? Evidence from cross-country surveys. Int J Forecast 23:167–187CrossRefGoogle Scholar
  18. Judge G, Schechter L (2007) Detecting problems in survey data using Benford’s Law, November 1, Working Paper. University of California and University of WisconsinGoogle Scholar
  19. Kuiper NH (1959) Alternative proof of a theorem of Birnbaum and Pyke. Ann Math Statis 30:251–252CrossRefGoogle Scholar
  20. Leamer E (1978) Specification searches ad hoc inference with nonexperimental data. John Wiley & Sons, Inc., New YorkGoogle Scholar
  21. Ley E (1996) On the peculiar distribution of the U.S. stock indexes’ digits. Am Stat 50:311–313CrossRefGoogle Scholar
  22. McCullough BD, Vinod HD (2003) Verifying the solution from a nonlinear solver: a case study. Am Econ Rev 93:873–892CrossRefGoogle Scholar
  23. McCullough BD, McGeary KA, Harrison TD (2006) Lessons from the JMCB archive. J Money Credit Bank 38(4):1093–1107CrossRefGoogle Scholar
  24. Mochty L (2002) Die Aufdeckung von Manipulationen im Rechnungswesen–Was leistet das Benford’s Law? Die Wirtschaftsprüfung 14:725–736Google Scholar
  25. Newcomb S (1881) Note on the frequency of use of the different digits in natural numbers. Am J Math 4:39–40CrossRefGoogle Scholar
  26. Nigrini MJ (1996a) A taxpayer compliance application of Benford’s law. J Am Taxpayer Assoc 18:72–91Google Scholar
  27. Nigrini MJ (1996b) Using digital frequencies to detect fraud. The White Paper (April/May) 3–6Google Scholar
  28. Nigrini MJ (1999) Adding value with digital analysis. Intern Auditor 56:21–23Google Scholar
  29. Niskanen J, Keloharju M (2000) Earnings cosmetics in a tax-driven accounting environment: evidence from Finnish public firms. Eur Account Rev 9:443–452CrossRefGoogle Scholar
  30. Osterloh S (2008) Accuracy and properties of German business cycle forecasts. Appl Econ Q 54(1):27–57CrossRefGoogle Scholar
  31. Pinkham RS (1961) On the distribution of first significant digits. Ann Math Stat 32:1223–1230CrossRefGoogle Scholar
  32. Quick R, Wolz M (2003) Benford’s law in deutschen Rechnungslegungsdaten. Betriebswirtschaftliche Forschung und Praxis 208–224Google Scholar
  33. Reulecke A-K (2006) Fälschungen – Zu Autorschaft und Beweis in Wissenschaften und Künsten. Eine Einleitung. In Reulecke A-K, Fälschungen. Suhrkamp Verlag, Frankfurt am Main, pp 7–43Google Scholar
  34. Roberts CJ, Stanley TD (2005) Meta-regression analysis: issues of publication bias in economics. Blackwell Publishing, Oxford, UKGoogle Scholar
  35. Schatte P (1988) On mantissa distributions in computing and Benford’s law. J Inf Process Cybern 24:443–455Google Scholar
  36. Schäfer C, Schräpler JP, Müller KR, Wagner GG (2005) Automatic identification of faked and fraudulent interviews in the German SOEP. Schmollers Jahrbuch—J Appl Soc Sci Stud 125:119–129Google Scholar
  37. Schräpler JP, Wagner GG (2005) Characteristics and impact of faked interviews in surveys. All Stat Arch 89:7–20CrossRefGoogle Scholar
  38. Tam Cho WK, Gaines BJ (2007) Braking the (Benford) law: statistical fraud detection in campaign finance. Am Stat 61(3):218–223CrossRefGoogle Scholar
  39. Thomas JK (1989) Unusual patterns in reported earnings. Account Rev 64:773–787Google Scholar
  40. Tödter K-H (2007) Das Benford-Gesetz und die Anfangsziffern von Aktienkursen. Wirtschaftswissenschaftliches Studium 36(2):93–97Google Scholar
  41. Van Caneghem T (2002) Earnings management induced by cognitive reference points. British Account Rev 34:167–178CrossRefGoogle Scholar
  42. Varian H (1972) Benford’s law. Am Stat 23:65–66Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Research Centre Deutsche BundesbankFrankfurt am MainGermany

Personalised recommendations