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      Newcomb–Benford law and the detection of frauds in international trade

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          Significance

          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.

          Abstract

          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.

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          Most cited references28

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          Large-Scale Inference

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            A Statistical Derivation of the Significant-Digit Law

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              Trade Liberalization, Quality, and Export Prices

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                Author and article information

                Journal
                Proc Natl Acad Sci U S A
                Proc. Natl. Acad. Sci. U.S.A
                pnas
                pnas
                PNAS
                Proceedings of the National Academy of Sciences of the United States of America
                National Academy of Sciences
                0027-8424
                1091-6490
                2 January 2019
                10 December 2018
                10 December 2018
                : 116
                : 1
                : 106-115
                Affiliations
                [1] aDepartment of Economics and Management, University of Parma, 43125 Parma, Italy;
                [2] bDepartment of Economics and Statistics, University of Siena, 53100 Siena, Italy;
                [3] cEuropean Commission, Joint Research Centre , 21027 Ispra, Italy
                Author notes
                1To whom correspondence may be addressed. Email: andrea.cerioli@ 123456unipr.it or domenico.perrotta@ 123456ec.europa.eu .

                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)

                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.

                Author information
                http://orcid.org/0000-0002-2485-5674
                Article
                201806617
                10.1073/pnas.1806617115
                6320519
                30530688
                593b9831-8add-4cac-a76c-b5a4384ffc9e
                Copyright © 2019 the Author(s). Published by PNAS.

                This open access article is distributed under Creative Commons Attribution License 4.0 (CC BY).

                History
                Page count
                Pages: 10
                Funding
                Funded by: EC | Joint Research Centre (JRC) 501100000900
                Award ID: 2014-2020 Work Programme
                Award Recipient : Andrea Cerioli Award Recipient : Lucio Barabesi Award Recipient : Andrea Cerasa Award Recipient : Domenico Perrotta
                Categories
                PNAS Plus
                Physical Sciences
                Statistics
                Social Sciences
                Political Sciences
                From the Cover
                PNAS Plus

                statistical antifraud analysis,newcomb–benford law,customs fraud,customs valuation,anomaly detection

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