Public works audit and Benford's Law

the case of Expresso DF Sul in the Brazilian Federal District

Authors

DOI:

https://doi.org/10.21874/rsp.v72i2.4570

Keywords:

Benford’s Law, public works audit, fraud detection technologies, Expresso DF Sul

Abstract

A country’s development requires major works, a task often undertaken by the government. Courts of Accounts carry out audits on public works, seeking to ensure efficient use of limited public resources. This paper shows how Benford's Law can be used in the selection of the sample for auditing a public work, focusing on the specific case of a transport corridor in the Brazilian Federal District known as Expresso DF Sul or VLP. The methodology is based on a version of the algorithm by Bugarin and Ceccato (2015) for prioritizing the audit of items with greater statistical evidence of overpricing in the budget spreadsheet. A comparison with the audit actually performed based on the ABC curve shows that there is an important potential benefit of using Benford’s Law. Indeed, the new methodology exposed 73.40% of the overbilling indicated by the Federal District Audit Court, while auditing only 38.17% of the total value of the work.

Downloads

Download data is not yet available.

Author Biographies

Renata Motta Café, University of Brasilia

Current PhD, Fundação Getúlio Vargas (EPGE/FGV). Master’s Degree, Fundação Getúlio Vargas (EPGE / FGV ). Economist, University of Brasília (UnB)

Maurício Soares Bugarin, Escola Brasileira de Economia e Finanças (PGE/FGV), Rio de Janeiro – RJ, Brasil

Full professor at the Department of Economics at the University of Brasilia (UnB) and  currently Leader of the Economics and Politics Research Group (EPRG).

Adriana Cuoco Portugal, Brazilian Federal District Court of Accounts

Civil engineer and PhD in Economics from the University of Brasília (UnB). External control auditor at the Federal District Court of Accounts (TCDF) and Technical Director of the Brazilian Public Works Audit Institute (IBRAOP).

References

ARIS, N. A.; OTHMAN, R.; BUKHORI, M. A. M.; ARIF, S. M. M.; MALEK, M. A. A. Detecting accounting anomalies using Benford’s Law: evidence from the Malaysian public sector. Management and Accounting Review (MAR), v. 16, n. 2, p. 73-100, 2017.

AZEVEDO, C. DA S.; GONÇALVES, R. F.; GAVA, V. L.;DE MESQUITA SPINOLA, M. A Benford’s Law based methodology for fraud detection in social welfare programs: Bolsa Familia analysis. Physica A: Statistical Mechanics and its Applications, v. 567, 125626, 2021.

BENFORD, F. The law of anomalous numbers. Proceedings of the American Philosophical Society, v. 78, p. 551-572, 1938.

BOYLE, J. An application of Fourier series to the most significant digit problem. American Mathematical Monthly, v. 101, p. 879-886, 1994.

BUGARIN, M. COVID-19 e a inevitável Lei dos Números Anômalos: resultados preliminares. Revista Conceito Jurídico, v. 4, n. 46, p. 90-93, 2020.

BUGARIN, M.; CUNHA, F. A didactic note on the use of Benford's Law in public works auditing, with an application to the construction of Brazilian Amazon Arena 2014 World Cup soccer stadium. Economia (Yokohama), v. 66, p. 23-55, 2015.

BUGARIN, M.; CUNHA, F. Lei de Benford aplicada à auditoria da reforma do Aeroporto Internacional de Minas Gerais. Revista do Setor Público, v. 68, n. 4, p. 915-940, 2017.

CARSLAW, C. Anomalies in income numbers: evidence from goal oriented behaviour. The Accounting Review, v. 63, p. 321-327, 1988.

CELLA, R. S.; ZANOLLA, E. A Lei de Benford e a transparência: uma análise das despesas públicas municipais.” Brazilian Business Review, v. 15, n. 4, p. 331-347, 2018.

CORACIONI, A. T. Testing of published information on greenhouse gas emissions. Conformity analysis with the Benford's Law Method. Audit Financiar, v. 18, n. 4, p. 821-830, 2020.

CUNHA, F.; BUGARIN, M. (Benford Law for audit of public works: an analysis of overpricing in Maracanã soccer arena’s renovation. Economics Bulletin, v. 35, p. 120-129, 2015a.

CUNHA, F.; BUGARIN, M. Lei de Benford para a auditoria de obras públicas: análise de sobrepreço na construção da arena da Amazônia. Boletim de Licitações e Contratos (BLC/NDJ), v. 28, n. 8, p. 841-857, 2015b.

CUNHA, F.; BUGARIN, M. Aplicações da Lei Newcomb-Benford às planilhas orçamentárias de obras públicas. In: SECRETARIA DE ORÇAMENTO FEDERAL. (Org.). Orçamento Público: VII Prêmio SOF de Monografias: coletânea. Brasília: Esaf, 2015c. p. 229-318.

CUNHA, F. C. R. Aplicações da Lei Newcomb-Benford à auditoria de obras públicas. Dissertação (Mestrado em Regulação e Gestão de Negócios) – Universidade de Brasília, Brasília, 2013.

COSTA, J. I. DE F.; HENRIQUES, D. B. B.; MELO, S. DE B.; DOS SANTOS, J. Análise de métodos contabilométricos para determinação de conformidade da Lei de Newcomb-Benford aplicados à auditoria contábil. Revista Gestão Pública: Prática e Desafios, v. 3, n. 2, p. 292-314, 2012.

DURTSCHI, C.; HILLISON, W.; PACINI, C. The effective use of Benford’s Law to assist in detecting fraud in accounting data. Journal of Forensic Accounting, v. 5, p. 17-34, 2004.

HILL, T. Base-invariance implies Benford's Law. Proceedings of the American Mathematical Society, v. 123, p. 887-895, 1995.

JAMAIN, A. Benford’s Law. Dissertação – Departamento de Matemática, Imperial College of London, Reino Unido, 2001.

LEEMIS, L.; SCHMEISER B.; EVANS, D. Survival distributions satisfying Benford’s Law. American Statistician, v. 54, p. 236–241, 2000.

MEBANE, W. R. Comment on “Benford's Law and the detection of election fraud”. Political Analysis, v. 19, n. 3, p. 269-272, 2011.

MEBANE JR, W. R.; KALININ, K. Electoral fraud in Russia: vote counts analysis using second-digit mean tests. In: Annual Meeting of the Midwest Political Science Association, Chicago, IL, April (Vol. 20), 2010.

MENEZES, R. O. Aplicação da Lei de Benford nos números de casos confirmados de COVID-19 em diferentes países. REMAT: Revista Eletrônica da Matemática, v. 7, n. 1, p. e3005, 2021.

MILANI FILHO, M. A. F. A confiabilidade dos dados financeiros de hospitais filantrópicos canadenses: um estudo empírico baseado na Lei de Benford. Sociedade, Contabilidade e Gestão, v. 8, n. 2, p. 47-63, 2013.

MUELLER, D. Public choice III. 3. ed. Cambridge University Press, 2003.

NEWCOMB, S. (Note on the frequency of the different digits in natural numbers. The American Journal of Mathematics, v. 4, p. 39-40, 1881.

NIGRINI, M. Benford’s Law. Applications for forensic accounting auditing, and fraud detection. New Jersey: John Wiley & Sons, 2012.

NIGRINI, M. J.; MILLER, S. J. Data diagnostics using second‐order tests of Benford's Law. Auditing: A Journal of Practice & Theory, v. 28, n. 2, p. 305-324, 2009.

NIGRINI, M. J.; MITTERMAIER, L. J. The use of Benford's law as an aid in analytical procedures. Auditing, v. 16, n. 2, p. 52-67, 1997.

PINKHAM, R. (On the distribution of first significant digits. The Annals of Mathematical Statistics, v. 32, p. 1223-1230, 1961.

RAIMI, R. The first digit problem. American Mathematical Monthly, v. 83, p. 521-538, 1976.

SAHU, S. K.; JAVA, A.; SHAIKH, A. On the connection of Benford's Law and neural networks. arXiv e-prints, arXiv-2102, 2021.

SALLABERRY, D. J.; FLACH, J.; CODESSO, M. M.; RODRIGUES, F. L. Sinalização de inconsistências a partir do patrimônio declarado de políticos no Brasil: aplicação da Lei de Newcomb-Benford. Revista Evidenciação Contábil & Finanças, v. 7, n. 3, p. 39-59, 2019.

SPIER, L. Uso da Lei de Benford para identificar inserção de dados fictícios em requerimentos de seguro-desemprego. Revista da Escola Nacional da Inspeção do Trabalho, v. 3, p. 273-292, 2019.

THOMAS, J. Unusual patterns in reported earnings. The Accounting Review, v. 64, p. 773-787, 1989.

VAN CANEGHEM, T. NPO financial statement quality: an empirical analysis based on Benford’s Law. Voluntas, v. 27, p. 2685-2708, 2016.

Published

2021-06-30

How to Cite

Motta Café, R. ., Soares Bugarin, M. ., & Cuoco Portugal, A. . (2021). Public works audit and Benford’s Law: the case of Expresso DF Sul in the Brazilian Federal District. Revista Do Serviço Público, 72(2), 360 - 399. https://doi.org/10.21874/rsp.v72i2.4570

Issue

Section

Artigos