| With the advent of the era of information audit, advanced technology and methods can enable CPAs to use much more scientific audit means to identify financial reports’authenticity, thus improving audit efficiency and guaranteeing the quality of audit. And the analysis of financial data quality can not only be the starting point for CPAs to look for fraud, it can also provide direct evidences to ascertain the doubtful data.Finance evaluation index system and mathematical statistic methods are two of the usual analytic techniques of financial data quality. The former utilizes logical relationship between financial data to look for the outliers, while the latter analyze the data from the point of view of Statistics. The perfection and development of mathematical science allow the application of mathematical rules to other fields. Benford’s Law is just such an interesting and marvelous mathematical rule. In1935, American physical scientist Frank-Benford found that as long as there were enough data, the number1occurs as the leading digit of a data is not1/9,but it is about30.1%. And the number2occurs as the leading digit of a data is17.6%, while larger numbers occur in that position with less frequency:9as the first digit less than5%, that’s4.6%.This result has been found to apply to a wide variety of data sets that are totally different from each other in property, including statistics of baseball, physical and mathematical constants, death rates, population numbers. Frank named the law after his name Benford. From then on, many scholars studied the Benford’s Law, and applied it to various industries. Research in the financial field proved the law’s applicability in fraud audit. It reminded us that Benford’s law can be introduced to analyze the quality of financial data.However, there are limitations to the application of Benford’s Law. First of all, data that can be applied to Benford’s Law should satisfy some conditions; Second, it can not be certain that the data have not any quality issues if they conform to the frequency distribution of Benford’s Law; Third, for those data that are in large scale and large sample, Benford’s Law can not provide the exact "location", that is where the problem data are. Forth, the application of Benford’s Law can only provide "doubtful data" for CPAs, not being able to prove its fraud.In the mathematical statistics, the panel data refers to the data that can be observed by N different objects in T periods. The panel model can combine the longitudinal section and cross section synthetically. It can determine the relationship between the dependent variables and independent variables by setting models and proper regression methods. If the model setting is good, those points that deviate from the model can be fraudulent, and they should be analyzed further to determine whether there are quality problems.Based on the recognition of Benford’s Law and Panel Model, the paper uses both of them to inspect those abnormal data. Meanwhile, according to the actual situation, the paper confirms the applicability and reliability of this method in finding fraudulent and illegal accounting data. It can not only solve the Law’s limitations in a large part, but can create a much effective method to find fraudulent financial data.The paper’s meanings are:In theory, analysis of mathematical statistics on financial data quality at home focuses on the application of Benford’s law, not yet combining it with other statistical methods. However, comprehensive application of Benford’s law and the panel model can improve the reliability of the results of data quality test. If the study of this paper can explore a practical and effective method, it will contribute to the theoretical fields by broadening and perfecting relative research.In practice, auditors can use Benford’s law to inspect and analyze financial data, but he can only get limited degree of assurance, being unable to determine the data’s quality problem. What’s more, for those tests with large samples, auditors in many times need to know the specific location of the doubtful data. Therefore, comprehensive application of Benford’s law and the panel model provides a much more reliable and accurate proof method to inspect the data quality. From this point of the view, this paper’s research has a certain guiding significance in the development of the practical field of audit work.The paper’s main frame and content is as following: The first part is an introduction, mainly expounding the background of the selected topic and research meanings. It also introduces the paper’s overall framework synoptically, illustrating research ideas and methods. In addition, this part points out its innovation and defects.The second part is literature review. Based on relative literature and information on Benford’s Law and financial data’s quality characteristics both at home and abroad, the paper reviews current research status, providing theoretical accordance for subsequent inquiry.The third part is an illustration of the basic theory and ideas of Benford’s Law and the panel modeling. For the former, the paper expounds its historical findings, formulas, mathematical demonstration, application area and limitations; for the latter, it explains its application ideas and how to combine it with Benford’s law to find "doubtful" financial data. The main research procedure is:(1) testing all the financial indicators in the samples based on Benford’s law to get the frequency distribution of the first digit;(2) comparing the frequency distribution with Benford’s law by statistical tests to find the "doubtful" financial indicators;(3) constructing a panel modeling to analyze the "doubtful" data which can find the specific location of the data;(4) by referring to related websites, such as securities regulatory commission and the Ministry of Finance, compare the specific and doubtful companies with the actual situations. If the company really did some illegal accounting incidents or frauds in the measured periods, it can be validated that the method is reasonable and effective. Otherwise, courses should be reflected.The forth part is the empirical test of the study. The study tests the first digit’s frequency of ten main financial indicators from companies that are listed in Shenzhen and Shanghai Stock Exchange issuing A shares. They are total assets, net account receivable, taxes payable, total owners’equity, selling expenses, overhead expenses, net profit, total profit, operating revenue, operating cost. The results show that:the frequency distribution of the first digit of financial indicators from the annual financial reports of the listed companies in our country conforms to Benford’s law in the overall; the frequency distributions of the first digit of financial indicators are different from each other, whereas their relevance to Benford’s law are also different; the frequency distributions of the first digit of a financial indicator in different years are different from each other, whereas they are different from Benford’s law. Next, test the frequency distributions of the first digits with Benford’s law using Pearson correlation coefficient, Chi-square test, T teat and K-S teat. The result shows that total asset, total owners’equity may have quality problems. And total owners’equity shows the most probability in quality problem. Then, choose total owners’equity as the dependent variable and total profits as independent variable to set the panel model. After deleting the unqualified samples, the model’s goodness of fit is0.9351, indicating a pretty good overall fitting effect. Based on this, test the model with residual analysis to find the abnormal points. Analysis results show that, at the95%confidence level, a total number of349samples, amounting to100enterprises, may have financial data quality problems.Further reference on the regulators and media reports shows that:(1) without considering the specific location,55out of100companies did illegal accounting incidents or had fraudulent behaviors;(2) If specific location is considered,33out of349samples had illegal records in the corresponding year where27companies are involved. The results show that comprehensive application of Benford’s law and the Panel model can find listed companies that did illegal accounting incidents effectively if the specific location is not considered. Otherwise, the empirical results do not match with the actual situation very well. Reasons coursing such results may be:(1) Because of the long periods, too many samples are included. Except for the major fraud cases, companies’financial information in the early years are unable to be found, resulting in some omissions.(2) If a company has fraudulent motivation, it would last for a long time, not focusing on a single year. Before and after the exacting year that is found out, fraudulent or illegal behaviors can exist. Manipulation of money involved varies in nature and amounts. In those concealed years that companies manipulate a smaller amount with a lighter nature, mathematical statistics method would not find them.(3) The results of this paper depend totally on the10financial indicators selected. But in reality, companies in different natures and scales will choose different financial indicators to abuse. The10financial indicators may not be the most suitable data adopted to study the illegal behaviors.The last part of the paper is the results and defects of the research as well as the future improved direction. In the improved direction, the paper puts forward four points:(1) testing the second and third digits of the financial indictors according to Benford’s Law;(2) selecting more appropriate financial indictors and more accurate models to fit, aiming a precise predicting result. One of the available methods is adopting financial data according to industry samples;(3) Varying-coefficient model or some other much more reasonable and appropriate models can be considered to improve the accuracy;(4) some foreign scholars point out that the variance of Benford’s Law is much more beneficial to the findings of fraud financial data. So we can also test the conclusion by using our country’s financial data;The paper’s innovations are:(1) From the topic and contents, combination of the panel model and Benford’s law is a new mathematical and statistical method which is not yet used before to explore illegal or fraudulent financial information data. So the paper has strong and pioneering exploration significance.(2) From the research direction and depth, the paper puts forward meaningful and further improvements, providing innovative directions to perfect the method.The shortcomings of the paper are:(1) there are not too much theoretical elaborations on fraud auditing. The thesis just introduces theories that are related to results, resulting in an inadequate theoretical introduction;(2) verification of the results mainly refers to the domestic related websites and some financial securities regulators. For those samples in early years, the paper can not find all the details of financial information of the "doubtful companies", leading to the omissions of some information and errors in analysis;(3) although referring to relative literatures, the selection of indictors are some subjective and random, without considering the results. It is also one of the paper’s improvements. |
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