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

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.
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.