2023 (20), №3

Assessing Financial Statement Reliability in European Companies Using Benford’s Law

For citation: 

Nazarova, V. V., Churakova, I. Yu., & Kupriyanov, D. A. (2023). Assessing Financial Statement Reliability in European Companies Using Benford’s Law. AlterEconomics, 20(3), 691–711. https://doi.org/10.31063/AlterEconomics/2023.20-3.10


The manipulation of financial reporting and data reliability in statements has become increasingly prevalent since the Enron scandal in 2001, with companies employing various strategies to enhance their stock prices and attract investors, occasionally resorting to unethical practices. Benford’s Law, a mathematical tool dating back to 1938 and popularized by mathematician Nigrini in 1995 for analyzing tax declarations, is employed in this study as a means of identifying potential accounting irregularities. Benford’s Law, also known as the “law of the first digit”, asserts that numbers starting with one are three times more likely to appear in datasets than predicted by a normal distribution, with calculable probabilities. This study aims to validate European companies’ data using Benford’s Law. The paper explores the theoretical underpinnings of Benford’s Law, reviews key research on the subject, and examines methods for assessing the reliability of reporting data. Additionally, the paper contains an analysis of data from European companies. Based on this analysis, an algorithm has been developed, enabling the verification of reporting data and the assessment of their compliance with Benford’s frequencies. This approach proves valuable for examining financial reporting in various industries, countries, and individual companies. The findings help identify which European countries and sectors have the highest occurrences of financial statement falsification or intentional adjustments.

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Varvara V. Nazarova — Cand. Sci. (Econ.), Associate Professor of Department of Finance, St. Petersburg School of Economics and Management, HSE University; https://orcid.org/0000-0002-9127-1644 (16, Soyuza Pechatnikov St., St. Petersburg, 190121, Russian Federation; e-mail: nvarvara@list.ru).

Iya Yu. Churakova — Cand. Sci. (Econ.), Associate Professor of Department of Finance, St. Petersburg School of Economics and Management, HSE University; https://orcid.org/0000-0002-1791-607X (16, Soyuza Pechatnikov St., St. Petersburg, 190121, Russian Federation; e-mail: iychurakova@hse.ru).

Dmitriy A. Kupriyanov — Master in Finance, St. Petersburg School of Economics and Management, HSE University (16, Soyuza Pechatnikov St., St. Petersburg, 190121, Russian Federation).

Adhikari, K., & Sarkar, P. (1968). Distribution of Most Significant Digit in Certain Functions Whose Arguments are Random Variables. Sankhya-The Indian Journal of Statistics Series B, 30, 47–58.

Alali, F., & Romero, S. (2013). Characteristics of Failed U.S. Commercial Banks: An Exploratory Study. Accounting & Finance, 53 (4), 1149–1174. https://doi.org/10.1111/j.1467-629X.2012.00491.x

Álvarez-Jareño, J. A., Badal-Valero, E., & Pavía, J. M. (2017). Using Machine Learning for Financial Fraud Detection in the Accounts of Companies Investigated for Money Laundering. Working Papers 2017/07. Castellón, Spain: Universitat Jaume.

Azevedo, C. da S., Gonçalves, R. F., Gava, V. L., & Spinola, M. de M. (2021). A Benford’s Law Based Methodology for Fraud Detection in Social Welfare Programs: Bolsa Familia Analysis. Physica A: Statistical Mechanics and its Applications, 567, 125626. https://doi.org/10.1016/j.physa.2020.125626

Azevedo, C. da S., Gonçalves, R. F., Gava, V. L., & Spinola, M. M. (2021). A Benford’s Law-Based Method for Fraud Detection using R Library. MethodsX, 8, 101575, 1–10. https://doi.org/10.1016/j.mex.2021.101575

Balashov, V. S., Yan, Y., & Zhu, X. (2021). Who Manipulates Data During Pandemics? Evidence From Newcomb-Benford Law. Preprint from Research Square. https://doi.org/10.21203/rs.3.rs-555372/v1

Barabesi, L., & Pratelli, L. (2020). On the Generalized Benford Law. Statistics & Probability Letters, 160, 108702. https://doi.org/10.1016/j.spl.2020.108702

Barney, B. J., & Schulzke, K. S. (2016). Moderating “Cry Wolf” Events with Excess MAD in Benford’s Law Research and Practice. Journal of Forensic Accounting, 1 (1), A66–A90.

Benford, F. (1938). The Law of Anomalous Numbers. Proceedings of the American Philosophical Society, 78 (4), 551–572.

Bhattacharya, S., Xu, D., & Kumar, K. (2011). An ANN-based Auditor Decision Support System
Using Benford’s Law. Decision Support Systems, 50 (3), 576–584. https://doi.org/10.1016/j.dss.2010.08.011

Druică, E., Oancea, B., & Vâlsan, C. (2018). Benford’s Law and the Limits of Digit Analysis. International Journal of Accounting Information Systems, 31, 75–82. https://doi.org/10.1016/j.accinf.2018.09.004

Furry, W., & Hurwitz, H. (1945). Distribution of Numbers and Distribution of Significant Figures. Nature, 155, 52–53.

Hasan, B. (2002). Assessing data Authenticity with Benford’s law. Information Systems Control Journal, 6, 41–45.

Herteliu, C. Jianu, I., Dragan, I. M., Apostu, S. A., & Luchian, I. (2021). Testing Benford’s Laws (Non)Conformity within Disclosed Companies’ Financial Statements among Hospitality Industry in Romania. Physica A: Statistical Mechanics and its Applications, 582. 126221. https://doi.org/10.1016/j.physa.2021.126221

Hillison, W., Durtschi, C., & Pacini, C. (2004). The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data. Journal of Forensic Accounting, V, 17–34.

Krakar, Z., & Žgela, M. (2009). Application of Benford’s Law in Payment Systems Auditing. Journal of Information and Organizational Sciences, 33 (1), 39–51.

Nigrini, M. (1996). A Taxpayer Compliance Application of Benford’s Law. The Journal of the American Taxation Association, 18 (1), 72–91.

Nigrini, M. (2017). Audit Sampling Using Benford’s Law: A Review of the Literature with Some New Perspectives. Journal of Emerging Technologies in Accounting, 14 (2), 29–46. https://doi.org/10.2308/jeta-51783

Nigrini, M., & Mittermaier, L. (1997). The Use of Benford’s Law as an Aid in Analytical Procedures. Auditing: A Journal of Practice & Theory, 16 (2), 52–67.

Pinkham, R. S. (1961). On the Distribution of First Significant Digits. The Annals of Mathematical Statistics, 32 (4), 1223–1230. https://doi.org/10.1214/aoms/1177704862

Raimi, R. A. (1976). The first digit problem. The American Mathematical Monthly, 83 (7), 521–538. https://doi.org/10.2307/2319349

Silva, W. B. da, Travassos, S. K. de M., & Costa, J. I. de F. (2017). Using the Newcomb-Benford Law as a Deviation Identification Method in Continuous Auditing Environments: A Proposal for Detecting Deviations over Time. Revista Contabilidade & Finanças, 28 (73), 11–26. http://dx.doi.org/10.1590/1808-057×201702690

Torres, D., & Pericchi, L. (2011). Quick Anomaly Detection by the Newcomb—Benford Law, with Applications to Electoral Processes Data from the USA, Puerto Rico and Venezuela. Statistical Science, 26 (4), 502–516. http://dx.doi.org/10.1214/09-STS296

Wallace, W. A. (2002). Assessing the quality of data used for benchmarking and decision-making. The Journal of Government Financial Management, 51 (3), 16–22.

Whitney, R. E. (1972). Initial Digits for the Sequence of Primes. The American Mathematical Monthly, 79 (2), 150–152. https://doi.org/10.2307/2316536

Zverev, E., & Nikiforov, A. (2018). Raspredelenie Benforda: vyyavlenie nestandartnykh elementov v bol’shikh sovokupnostyakh finansovoy informatsii [Benford’s Distribution: Identifying Irregular Elements in Large Sets of Financial Information]. Vnutrenniy kontrol’ v kreditnoy organizatsii [Internal Control in a Credit Institution], 4 (40), 4–18. (In Russ.)