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Goodness-of-Fit Testing for the Newcomb-Benford Law With Application to the Detection of Customs Fraud

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  • Lucio Barabesi
  • Andrea Cerasa
  • Andrea Cerioli
  • Domenico Perrotta

Abstract

The Newcomb-Benford law for digit sequences has recently attracted interest in antifraud analysis. However, most of its applications rely either on diagnostic checks of the data, or on informal decision rules. We suggest a new way of testing the Newcomb-Benford law that turns out to be particularly attractive for the detection of frauds in customs data collected from international trade. Our approach has two major advantages. The first one is that we control the rate of false rejections at each stage of the procedure, as required in antifraud applications. The second improvement is that our testing procedure leads to exact significance levels and does not rely on large-sample approximations. Another contribution of our work is the derivation of a simple expression for the digit distribution when the Newcomb-Benford law is violated, and a bound for a chi-squared type of distance between the actual digit distribution and the Newcomb-Benford one.

Suggested Citation

  • Lucio Barabesi & Andrea Cerasa & Andrea Cerioli & Domenico Perrotta, 2018. "Goodness-of-Fit Testing for the Newcomb-Benford Law With Application to the Detection of Customs Fraud," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 346-358, April.
    • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:2:p:346-358
    DOI: 10.1080/07350015.2016.1172014
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    Cited by:

    1. Demir, Banu & Javorcik, Beata, 2020. "Trade policy changes, tax evasion and Benford's law," Journal of Development Economics, Elsevier, vol. 144(C).
    2. Barabesi, Lucio & Pratelli, Luca, 2020. "On the Generalized Benford law," Statistics & Probability Letters, Elsevier, vol. 160(C).
    3. Lucio Barabesi & Andrea Cerioli & Domenico Perrotta, 2021. "Forum on Benford’s law and statistical methods for the detection of frauds," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 767-778, September.
    4. Huang, Yasheng & Niu, Zhiyong & Yang, Clair, 2020. "Testing firm-level data quality in China against Benford’s Law," Economics Letters, Elsevier, vol. 192(C).
    5. Wang, Delu & Chen, Fan & Mao, Jinqi & Liu, Nannan & Rong, Fangyu, 2022. "Are the official national data credible? Empirical evidence from statistics quality evaluation of China's coal and its downstream industries," Energy Economics, Elsevier, vol. 114(C).
    6. Lee, Kang-Bok & Han, Sumin & Jeong, Yeasung, 2020. "COVID-19, flattening the curve, and Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    7. Liu, Renliang & Sheng, Liugang & Wang, Jian, 2023. "Faking trade for capital control evasion: Evidence from dual exchange rate arbitrage in China," Journal of International Money and Finance, Elsevier, vol. 138(C).

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