Edited by Alex Kossovsky, University of Panama, Panama City, Panama, and accepted by Editorial Board Member Donald B. Rubin October 30, 2018 (received for review April 17, 2018)
The detection of frauds is one of the most prominent applications of the Newcomb–Benford law for significant digits. However, no general theory can exactly anticipate whether this law provides a valid model for genuine, that is, nonfraudulent, empirical observations, whose generating process cannot be known with certainty. Our first aim is then to establish conditions for the validity of the Newcomb–Benford law in the field of international trade data, where frauds typically involve huge amounts of money and constitute a major threat for national budgets. We also provide approximations to the distribution of test statistics when the Newcomb–Benford law does not hold, thus opening the door to the development of statistical procedures with good inferential properties and wide applicability.
The contrast of fraud in international trade is a crucial task of modern economic regulations. We develop statistical tools for the detection of frauds in customs declarations that rely on the Newcomb–Benford law for significant digits. Our first contribution is to show the features, in the context of a European Union market, of the traders for which the law should hold in the absence of fraudulent data manipulation. Our results shed light on a relevant and debated question, since no general known theory can exactly predict validity of the law for genuine empirical data. We also provide approximations to the distribution of test statistics when the Newcomb–Benford law does not hold. These approximations open the door to the development of modified goodness-of-fit procedures with wide applicability and good inferential properties.
Author contributions: A. Cerioli, L.B., A. Cerasa, and D.P. designed research; M.M. contributed the study of economic implications of research; A. Cerioli, L.B., A. Cerasa, and D.P. performed research; A. Cerioli, L.B., A. Cerasa, and D.P. contributed new analytic tools; A. Cerioli, L.B., A. Cerasa, and D.P. analyzed data; and A. Cerioli, L.B., M.M., and D.P. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. A.K. is a guest editor invited by the Editorial Board.
Data deposition: The available pseudo-data files have been deposited at the Athena repository maintained by the Joint Research Centre (JRC). SI Appendix, section 3 provides details on how to access them.
See Commentary on page 11.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1806617115/-/DCSupplemental.
This open access article is distributed under Creative Commons Attribution License 4.0 (CC BY).
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