Benford’s Law and Digital Analysis: Application on Turkish Banking Sector

Abstract

Abstract: We investigate the effectiveness of Benford's Law through a digital analysis of the off-balance sheet account disclosures made by Turkish Banks during the 1990-2010. We found that off-balance sheet account disclosures of the fiscal term 1999 doesn't comply with Benford's Law. Our finding is consistent with the Turkish Banks' practices. We also provide evidence on Law of Anomalous Numbers. Our results indicate a link between economic policy and deviation from frequencies of Benford's Law.Keywords: Benford's Law, Digital analysis, Banking sector, Fraud investigationJEL Classification: G21, M42(ProQuest: ... denotes formulae omitted.)1. IntroductionThe purpose of this paper is to investigate effectiveness of Benford's Law in the financial reports of Turkish Banks. Digital Analysis based on the Benford's Law has been used to detect frauds and manipulations and it has been seen that Digital Analysis provide signal in revealing frauds and manipulations.Turkish banks have been chosen since creative accounting applications were frequently realized in the Turkish banking sector especially during the 1990-2001. The investigation has been focused on the off-balance sheet account disclosures because fraud and manipulation methods of Turkish Banks were typically required accounting in the off-balance sheet accounts. In order to accurate assess of Digital Analysis, off-balance sheet account disclosures have been studied for the twenty years period 1990-2010. Looking at twenty years period is required because certain terms provide different expectations regarding frauds and manipulations that are likely to be found in the financial reports.The rest of the paper is arranged as follows. Section 2 reviews literature relating to Benford's law and Digital Analysis. Section 3 describes fraud and manipulation techniques applied by Turkish Banks during the 1990-2001. Section 4 presents our research questions. The method is specified in Section 5. Results are presented and discussed in Section 6. Summary and conclusion are contained in section 7.2. Benford's Law And Digital AnalysisThe Digital Analysis is the comparison of the difference between the expected and observed frequencies of the digits. The difference between the expected and observed frequencies indicates that the data includes systematic error (Nigrini and Mittermaier, 1997). This systematic error may arise from the measurement methods (Hales, Sridharan, Radhakrishnan, Chakravorty and Siha, 2008) or from the frauds and manipulations in the accounting records (Nigrini, 1996).On the other hand, although the Digital Analysis reveals the systematic errors, this is not a final evidence for a fraud or manipulation. The Digital Analysis is a method that shows where to look in order to obtain the best result from the data (Nigrini, 1996; (Hales, Chakravorty and Sridharan, 2009). In other words, the Digital analysis is a method that reveals the doubtful data. This property of the Digital Analysis was first proposed by Varian (1972). According to Varian (1972), the fact that a data set complies with Benford Distribution does not confirm the realness and accurateness of that data set, however, the fact that a data set does not comply with Benford Distribution is enough to be suspicious about that data set.Benford's Law finding a wide application area in the social sciences started in 1881 and spread into a process that has been constituting up to the present day. The first study basis to the Benford's law was published by Simon Newcomb in the American Journal of Mathematics in 1881 with the headline Note on the Frequency of Use of the Different Digits in Natural Numbers. In this article, Newcomb, researched the probability of the 'digits from 1 to 9 being found in the first digit of any number, and explained the Frequency Law stating that these probabilities are not equal. According to Newcomb (1881), the probability of the digits from 1 to 9 being found in the first digit of any number reduces as the digit grows. …