Benford’s Law and Public Works Audit: an analysis of overpricing in the maracanã remodeling

Abstract

The pricing analysis in public works audits is a time consuming task and sometimes the auditor spends weeks of his work time doing it, since, in many cases, the budget spreadsheets are long and difficult to analyze. The Newcomb-Benford Law constitutes a data mining tool to be used in conjunction with the ABC curve and is supposed to contribute with a more efficient selection of the services in the spreadsheets for the overpricing analysis. Such law proposes that the frequencies of the leading digits in a multitude of databases are decreasing from 1 to 9; the digit 1 appears in, approximately, 30% of the data, while the digit 9 does not reach 5% of such values. This study aims at demonstrating the application of the Newcomb-Benford Law to the pricing spreadsheets of public works. The methodology consisted of: an introduction to the Newcomb-Benford Law and its main applications; the presentation of the relevant tests of the Law in question; the development and application of such tests to the Maracanã remodeling works; the comparison of the results obtained with the analysis carried out by the Brazilian Federal Court of Accounts (TCU); and the presentation of the results, conclusions and next research. It has been found, in a general way, that the work in question presented a marginal compliance with the Benford Law. However, the tests allowed for the identification of 17 services in the spreadsheet which did not respect the Law and represented 71.54% of the total overpricing found by TCU (R$ 149,972,318.01)