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Benford's law in Deutschen rechnungslegungsdaten

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... Two studies have been presented so far for Germany, which have dealt with the issue of whether this law can be of help to unearth the presence of intentional or inadvertent errors in the financial statements of a company. For this purpose, data pertaining to 1,820 annual financial statements of the largest German private limited companies for the years 1994 to 1998 were analysed in a study conducted by Quick and Wolz, 2003. In the study conducted by Rafeld and Then Bergh, 2007, the corporate data of 694 companies from C-DAX were analysed for the period from 31.01.1999 to 23.11.2004. ...
... This database contained the annual financial statements along with the name of the associated auditor, starting from the year 1996. Only the individual financial statements in conformity with the national accounting principles (HGB) were used, in line with the study conducted by Quick and Wolz, 2003 , p. 214, for the purpose of comparison with respect to the financial reporting standards used as the basis. Since there were 11 companies out of those listed on the German DAX as on 31.12.2006, ...
... The data analysis initially also included, in line with the procedure adopted by Quick and Wolz, 2003, p. 214, the entire annual financial statements, whereby only the individual items were taken into consideration, but no sub-totals and totals, in order to prevent redundancies in the data, which could have distorted and falsified the results. Moreover, independent items of the balance sheet included in the annual financial statements and the annual profit data (net income) of the DAX companies served as an additional basis for centralised analysis. ...
Article
The so-called Benford’s Law describes regularity in the distribution of digits of randomly selected numbers, which states that the relative frequency of the leading digits reduces in a systematic manner from the digit 1 to the digit 9. This distribution hypothesis is being discussed in recent times as an audit instrument in order to gain insights into possible conscious and inadvertent errors in data records. The present paper analyses the closing accounts of 1,373 annual financial statements of companies listed on the German DAX and compares these with the Benford’s distribution hypothesis. It can be seen in the process that data pertaining to financial accounts, which have not been audited by the so-called “Big 4” audit firms, but by smaller external auditors, deviate to a significant extent from the regularity of Benford’s Law, which appears to make the use of Benford’s Law suitable as a benchmark to assess the quality of the audit.
... First, we provide evidence that one group of German firms rounds up net income, whereas a different group rounds up EPS. The German research has used Benford's Law as an analytical audit procedure (Quick & Wolz, 2003), but not to detect rounding up. Second, we use the introduction of the euro to show that rounding up is most likely the result of earnings management. ...
... The German evidence is scarce. Quick and Wolz (2003) investigate single accounts from German firms and find that the data follow Benford's Law, although there are deviations when only balance sheet data are used. However, the authors focus on detecting deviations from Benford's Law in general, and not specifically on providing evidence of rounding up. ...
Article
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We use Benford's Law to provide evidence that German firms round up both their net income and earnings per share. We use the introduction of the euro to show that round earnings numbers are likely the result of earnings management. The incentive to round up comes from stakeholders’ left‐digit bias when processing the information in financial statements. Since round numbers are natural benchmarks, stakeholders perceive the performance metrics directly below such thresholds as abnormally lower. However, rounding up is objectionable only if it involves large‐scale earnings management, but not in cases of negligible “earnings cosmetics.” Because the difference between the pre‐managed and reported earnings is unobservable, we investigate whether the prevalence of rounding up coincides with specific levels of several earnings characteristics and proxies for audit quality. If the rounding up is cosmetic, then it should occur independently of these characteristics. In contrast, if firms use earnings management on a larger scale, then it might not be possible to simultaneously round up and achieve other objectives of earnings management. Our evidence is in line with substantial earnings management. This article is protected by copyright. All rights reserved
... Another mayor indicator mentioned by the authors is the increase in personal drawings by its owners in times of crisis. Quick and Wolz (2003), on the other hand, apply the well-known Benford's Law on accounting data of the largest public limited liability companies according to the Hoppenstedt database between 1994 and 1998. Based on a Chi2-test they find that Benford's Law applies to respective data in terms of volume of assets and the profit and loss account. ...
... Fraud and Forensic Accounting (Services) in Germany -An Overview over Education, Practice, Institutions, and Research Additionally, the authors emphasize that the number of elements of the underlying distribution has to be large enough and that Benford's Law does neither allow for detecting under-nor overvaluations. They further point out that a few large manipulated financial statement items as well as a given manipulation of all data, based on a multiplication of the original data by a constant, will rather stay undetected by Benford's Law (Quick and Wolz 2003). Watrin, Struffert, and Ullmann (2008) A third area of recent German research on forensic accounting consists of state-of-the-art reviews of national practice and international literature. ...
Thesis
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Investment fraud, cybercrime, inconsistencies in health care or the emission scams at the car manufacturers, economic crime (fraud) manifests itself in many facets. For Germany, the cases of FlowTex, Comroad, HRE-Bad-Bank, Holzmann, Volkswagen and the current fraud suspicions at Porsche AG are prominent examples with mostly appalling consequences (Ballwieser and Dobler 2003; Kögler 2015; Meck, Nienhaus, and von Petersdorff 2011; Peemöller and Hofmann 2005). Nevertheless, newspapers without reports on fraud have become scarce. Headlines such as: "Corruption - the daily business" impress hardly anyone, not least because of their certain regularity. The cases revealed publicly are, however, only the tip of the iceberg, as reported by renowned experts (Bundeskriminalamt 2018; LKA 2018). Currently, the State Criminal Police Office (Landeskriminalamt (LKA)) of Baden-Württemberg and its department for economic and environmental crime and corruption is concerned with 72 major proceedings (LKA 2018). However, fraud could be avoided or at least contained by appropriate preventive measures (Bundeskriminalamt 2018; Bussmann 2004; Hlavica, Klapproth, and Hülsberg 2011). Consequently, the pressure on companies and employees to demonstrate compliant and ethical behavior and to meet the demands of stakeholders at all times within their business activities has grown (Buff 2000). This raises the question about which precautionary measures a company can and must implement (Weick and Sutcliffe 2015). Although corporate awareness of this issue has increased, most in-house detection of fraud is accidental, suggesting that companies are still lacking appropriately functioning and systematic (early) detection mechanism (Hlavica et al. 2011). If a company is accused of fraud, this usually has serious repercussions on its corporate reputation. Prior research found that capital market reputation-based penalties for affected companies are on average 7.5 times higher than penalties imposed by the legal system (Karpoff, Lee, and Martin 2008). Furthermore, the accusation of fraud also affects the external auditor’s reputation, since lacking the detection of manipulations in clients’ (financial) reports not only damages public confidence in the accuracy of firms’ financial statements but also in the reliability of the auditor's report. Therefore, it is not surprising that the demand for greater supervision and control of firms’ (financial) reporting as well as for reliable work of statutory auditors continually increases (Herkendell 2007). Although to a lesser extent, this is also the case for the determination of material (accounting) errors within a firm’s financial statements, which are often difficult to distinguish from accounting fraud. According to the International Accounting Standard (IAS) 8.5, published by the International Accounting Standards Board (IASB), errors are omissions and/or misstatements of items that result from the nonapplication or misapplication of trusted information (IASB 2003). Thus, accounting errors and accounting fraud both result in incorrect information of a firm’s financial reports and consequently affect stakeholders’ decision-making. One resulting attempt in counteracting the broad demand for appropriate protective measures was the implementation of a two-stage enforcement system involving the German Financial Reporting Enforcement Panel (Deutsche Prüfstelle für Rechnungslegung (DPR)) as part of the adopted Financial Reporting Enforcement Act (Bilanzkontrollgesetz (BilKoG)) in 2004. The primary objective of the Federal Government's implementation of this mechanism was to strengthen investors' lost confidence in the German capital market, the information content of financial reporting, and Germany as a financial center in the international competition. In addition, the enforcement system serves as a sanctioning instrument for firms in the event of an error detection and subsequent adverse error disclosure via the German federal registry (elektronischer Bundesanzeiger). This adverse error disclosure not only sanctions denounced firms but also questions the quality of the annual financial statement audit and thus the quality of the responsible audit firm. Hence, the often thin line between firms’ unintentional accounting errors, purposive engagement in earnings management, and intentional fraud in particular presents an increasing challenge for the audit profession. The objective of my cumulative dissertation is to provide a comprehensive overview of fraud and forensic accounting as well as insights into the distinct dimensions among the concepts of errors, earnings management and fraud from a German accounting perspective. I aim at achieving this objective in three steps: First (1), by providing an overview of discipline-specific education possibilities, existing forensic accounting practices, institutions, and current developments in research. Second (2), by assessing auditors’ obligations and responsibilities for the detection of irregularities within the scope of the annual financial statement audit and whether including forensic services into the service portfolio of audit firms can help increase their audit quality due to spillover effects. Third (3), by examining firms’ reputation (re-)building management in response to financial violations and how this process is associated with managing multiple (stakeholder) reputations. This dissertation is composed of three individual papers whereby each considers one of the above outlined focus areas
... Currently, a line of development in accounting applies Benford's Law to detect fraud, or the "manufacture" of data, in accounting and financial documents (Beneish, 1999;Durtschi, Hillison and Pacini, 2004;Asllani and Naco, 2014). Quick andWolz (2003), Tam Cho andGaines (2007), Rauch, Göttsche, Brähler, and Engel (2011), and Alali and Romero (2013) constitute other examples. Quick and Wolz (2003) examine data of income and from the balance sheets of various German companies for the years 1994 to 1998 and find that the series of numbers of the first and second digits are, in most cases, adjusted to Benford´s Law. ...
... Quick andWolz (2003), Tam Cho andGaines (2007), Rauch, Göttsche, Brähler, and Engel (2011), and Alali and Romero (2013) constitute other examples. Quick and Wolz (2003) examine data of income and from the balance sheets of various German companies for the years 1994 to 1998 and find that the series of numbers of the first and second digits are, in most cases, adjusted to Benford´s Law. They find these patterns both when the analysis is performed on an annual basis and also when the inspection is carried out for the whole period. ...
Article
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Objectives: This paper is based on the analysis of the database of operations from a macro-case on money laundering orchestrated between a core company and a group of its suppliers, 26 of which had already been identified by the police as fraudulent companies. In the face of a well-founded suspicion that more companies have perpetrated criminal acts and in order to make better use of what are very limited police resources, we aim to construct a tool to detect money laundering criminals. Methods: We combine Benford's Law and machine learning algorithms (logistic regression, decision trees, neural networks, and random forests) to find patterns of money laundering criminals in the context of a real Spanish court case. Results: After mapping each supplier's set of accounting data into a 21-dimensional space using Benford's Law and applying machine learning algorithms, additional companies that could merit further scrutiny are flagged up. Conclusions: A new tool to detect money laundering criminals is proposed in this paper. The tool is tested in the context of a real case.
... His findings indicated that people tend to understate their income to reduce taxation. Quick and Wolz (2003) for instance applied Benford's Law to financial statements of German companies and found that these figures are in line with the expected distribution. Drake and Nigrini (2000) and Durtschi et al. (2004) provided operational descriptions how to implement Benford's law for auditing purposes. ...
Article
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Leading digits often follow a distribution described by Newcomb (1881) and Benford (1938). We apply this phenomenon known as Benford’s Law on cover assets provided by issuers of German covered bonds. The main finding of the empirical analysis is that leading digits of these assets seem to follow the Benford distribution. Standard statistical evidence, however, might be misleading due to effects of large data sets. Consequently, the present paper also provides an example of how to deal with large data sets when a Benford distribution is assumed.
... The additional assumption that fabricated or falsified data are detectable through the deviation of their digits from the Benford distribution has been tested recently in several contexts. For example, some studies have reported success in identifying fraudulent information with a check of digital frequencies in tax or other financial data against the Benford distribution (Carslow, 1988;Berton, 1995;Nigrini, 1996;Quick & Wolz, 2003). Similar results have been reported for fabricated survey interviews (Schraepel & Wagner, 2005;Schäfer et al., 2005). ...
Article
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Digits in statistical data produced by natural or social processes are often distributed in a manner described by 'Benford's law'. Recently, a test against this distribution was used to identify fraudulent accounting data. This test is based on the supposition that first, second, third, and other digits in real data follow the Benford distribution while the digits in fabricated data do not. Is it possible to apply Benford tests to detect fabricated or falsified scientific data as well as fraudulent financial data? We approached this question in two ways. First, we examined the use of the Benford distribution as a standard by checking the frequencies of the nine possible first and ten possible second digits in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). The digits in these experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, both digits of the published regression coefficients were approximately Benford distributed or at least followed a pattern of monotonic decline. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. Surprisingly, first digits of faked data also exhibited a pattern of monotonic decline, while second, third, and fourth digits were distributed less in accordance with Benford's law. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first (i.e. leftmost) and more on later digits.
Article
We investigate whether Benford's Law can be used to differentiate retracted academic papers that have employed fraudulent/manipulated data from other academic papers that have not been retracted. We use the case of Professor James Hunton who had 37 of his articles retracted because there were grave concerns that they contained mis-stated or fabricated datasets. We construct several Benford conformity measures, based on first significant digits contained in the articles, to determine whether Hunton's retracted papers differ significantly from a control group of non-retracted articles by competing authors. Our results clearly indicate that Hunton's retracted papers significantly deviate from Benford Law, relative to the control group of papers. In additional analysis we also find these results are generalisable to other authors with retracted papers. Our findings suggest that potentially both co-authors and journals could consider implementing a data analytical tool which employs Benford Law to highlight potential ‘red flag’ papers, with a view to decreasing the risk of fraudulent activity and thereby enhancing the credibility of academic papers and journals.
Conference Paper
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Jose.A.Alvarez@uv.es Prudencio.Muniz@uv.es Teléfono: 96 382 8428 Fax: 96 382 8415 Área temática: Economía Monetaria y Financiera RESUMEN Diferentes trabajos como el de Eduardo Ley (1996) se han centrado en estudiar el comportamiento del primer dígito de los diferentes mercados bursátiles, como el Down Jones Industrial Average Index (DJIAI) o el Standard & Poor's Index (S&P). El actual trabajo busca encontrar un patrón de comportamiento en las series del rendimiento diario, periodificado y sin periodificar, del Ibex-35. El primer y el segundo dígito de las variables del Ibex-35 analizadas pueden estar de acuerdo con la Ley de Benford, para lo que se utilizará diferentes contrastes de hipótesis basados en otros tantos estadísticos, como son la Chi-cuadrado, Kolmogorov-Smirnov o Kuiper. También se aplicará un contraste sobre la media muestral para aportar el mayor número de evidencias a las conclusiones del trabajo. ABSTRACT Different studies such as Edward Law (1996) have focused on studying the behaviour of the first digit of the various stock markets, as the Down Jones Industrial Average Index (DJIAI) or the Standard & Poor's Index (S & P). The present work aims to find a pattern in the daily performance series, daily and no daily, the Ibex-35. The first and second digit of the Ibex-35 variables analyzed can be consistent with Benford's Law, which will be used for different hypothesis tests based on many other statistics, such as the Chi-square, Kolmogorov-Smirnov or Kuiper. It also applies a contrast on the sample mean to provide the greatest amount of evidence to the conclusions.
Chapter
Nicht allein bei den spektakulären Unternehmenskrisen von Enron (2001) und World Com (2002) in den USA, Parmalat (2003) und Adecco (2004) im europäischen Ausland sowie Flowtex (2000), Philipp Holzmann und Comroad (beide 2002) in Deutschland, sondern im Vorfeld fast aller Unternehmensinsolvenzen sind wirtschaftskriminelle Handlungen zu finden. Außerdem nehmen dolose Handlungen allgemein zu und verfälschen in der Regel die Jahresabschlüsse. Da nach früher üblicher Auffassung Abschlussprüfer sich nicht für die Aufdeckung von Unterschleife verantwortlich zeichneten, wurde das Vertrauen der Öffentlichkeit in geprüfte Jahresabschlüsse wegen der Unsicherheit bzgl. der Auswirkungen von dolosen Handlungen im geprüften Abschluss erschüttert. Indes ist eine Schuldzuweisung an die Abschlussprüfer, wie sie vielfach in der Öffentlichkeit und an den Kapitalmärkten vorgenommen wurde, nicht gerechtfertigt, weil ein Abschlussprüfer nicht so intensiv prüfen soll und kann, dasser jede Unterschleife entdecken könnte. Fraglich ist indes, ob die wesentlichen Erkenntnisse aus forensischen Prüfungen nicht wenigstens zu einer Intensivierung der bisher üblichen Jahresabschlussprüfung führen sollten, so dass man vom Abschlussprüfer eine Aufdeckung von Unterschleife dann erwarten kann, wenn und soweit sie wesentlich und sie mit häufig angewandten Methoden herbeigeführt worden ist.
Article
Financial accounting fraud detection has become an emerging topic for companies, auditors and researchers. Various approaches have been employed to identify data irregularities caused by errors or several fraud schemes. To assist audit practitioners in selecting and efficiently applying forensic data analytics we present an overview of the most common methods and their characteristics and present a framework for systematic risk assessment procedures and related audit responses.
Article
Political parties receive government grants based on their accountability reports provided by the parties themselves. Despite the duty to enforce auditing, a noticeable high amount of fraud within these reports has been detected. In the past years Benford's Law has gained popularity as a digit test to uncover fraud in datasets. Deviations from the expected Benford distribution are possible indicators for manipulations. Consequently, the accountability reports of 15 political parties from 1995 to 2010 have been collected and analyzed. The political party with the highest deviation from Benfords Law are "Graue Panther". The result is remark able as "Graue Panther" were convicted of data manipulation in reality. Therefore, we regard our findings as evidence for the efficiency of the Benford test.
Article
Tax fraud is not only associated with reputational damages of corporations and negative values for investors, it also implies negative consequences for public budgets and economic growth. Therefore, numerous governments have declared the fight against (offshore) tax evasion. Tax authorities as well as accounting research, however, face a huge challenge in identifying tax fraud. This study aims to provide an overview and critical assessment of selected tax fraud detecting methods.
Article
We consider whether Benford’s Law can be used to improve target selection prior to the start of on-site tax audits, thus increasing effectiveness and efficiency of fiscal enforcement. Laboratory experiments are conducted to obtain manipulated data and compare these to data which are known to be unmanipulated. We find that Benford’s Law can be used as a tool for audit selection, but that auditors must be cautious to ensure that Benford’s Law can be expected to apply to unmanipulated data of the prospective audit target. We also find that subjects cannot adapt sufficiently to Benford’s Law during tax fraud activity.
Article
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First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford's law. This phenomenon has been used in many business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford's law holds in economic research and forecasting. First, we examine the distribution of leading digits of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford's law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content.
Article
Introduces a new analytical review procedure that measures the degree to which a data set’s digit distribution deviates from a Benford digit distribution. This deviation can indicate potential manipulation and can be used to signal the need for further audit testing. An artificial neural network is used to distinguish between “normal” and “manipulated” financial data. The results show that if data have been contaminated (at a 10 per cent level or more) a Benford analytical review procedure will detect this 68 per cent of the time. If the data are not contaminated, the test will indicate that the data are “clean” 67 per cent of the time. Because analytical review procedures are not used in isolation, these results probably understate the effectiveness and potential of a digits-based analytical review procedure. This procedure’s fraud detection results compare favorably to traditional analytical review procedures. Importantly, its unique analysis procedure allows it to complement traditional analytical review procedures. A key limitation of this study is that it uses simulated data, rather than actual data. Such an enhancement will be a critical step in future research. This method appears to have potential merit and provides many opportunities for new research.