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European Journal of Economics, Finance and Administrative Sciences

ISSN 1450-2275 Issue 59 August, 2013

http://www.EuropeanJournalofEconomicsFinanceandAdministrativeSciences.com

Detection of Earnings Management by Applying Benford's

Law in Selected Accounts: Evidence from Quarterly Financial

Statements of Turkish Public Companies

Çiğdem Özarı

Assistant Prof Economics and Finance, Faculty of Economics and Administrative Science

Istanbul Aydın University, Istanbul, Turkey

Beşyol Mah.Inönü Cad.No: 38, Sefaköy-Küçükçekmece / İSTANBUL

E-mail: cigdemozari@aydin.edu.tr

Tel: +90-212-4441428 Fax: +90-212-425575

Murat Ocak

Ph.d in Business Administration

E-mail: ocak.mrt@gmail.com

Abstract

This paper investigates the occurence of earnings management by applying Benford's Law

in selected accounts. We find that some numbers are manipulated in third and fourth digits

of the selected accounts. However, we find no evidence that managers engaged to manage

earnings upward (downward); because, we did not observe high (low) significance

freguency of number zero and low (high) significance of number nine in second, third,

fourth digits of net profit, sales revenues and we did not observe high (low) significance

freguency of number nine and low (high) significance of number zero in second, third,

fourth digits of cost of goods sold and operating expenses.

Keywords: Benford's Law, Earnings Management

1. Introduction

While earnings is used by company's related parties to make decisions on various issues, earnings

figures should be qualified. Earnings quality refers to the degree to which reported earnings capture a

company’s economic reality.

1

Thus, bad earnings quality does not reflect company's economic reality.

Earnings management induces to bad earnings quality.

It is toilsome to find a standard accepted defination for earnings management. According to

Healy and Wahlen

2

who offered the most popular definition, "earnings management occurs when

manager use judgment in financial reporting and in structuring transactions to alter financial reports to

either mislead some stakeholder about the underlying economic performance of the company or to

influence contractual outcomes that depend of reported accounting numbers".Katherine Schipper

3

defined earnings management as "a disclosure management in the sense of a purposeful intervention in

the external financial reporting process, with the intent of obtaining some private gain."

1

Gopal V. Krishnan, Linda M. Parsons, “Getting to Bottom Line: An Exploration of Gender and Earnings Quality”,

Journal of Business Ethics, 2008, Vol:78, Issue:1/2, pp.65

2

Paul N. Healy, James M. Wahlen, “A Review of The Earnings Management Literature and Its Implications for Standards

Settings”, Accounting Horizons, Vol: 13, No:4, 1999, pp.368

3

Katherine Schipper, “Commentary on Earnings Management”, Accounting Horizons, Vol:3 No:4-5,1989, pp.92-93

38 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Prior studies show that there are various incentives for earnings management. Managers

manage earnings to maximize their profit based bonus

4

or manage earnings to maximize equity based

compensation such as stock options

5

. After a change in management, new manager reduces earnings by

recording big charges in his/her first year to increase next year earnings

6

7

. Important indicator of

manager's failure is company's poor earnings performance and dismissal is associated to company's

poor earnings performance. So managers manage earnings to minimize possibility of dismissal

8

.

Another incentives to manage earnings are meeting or beating analysts' expectations, avoiding losses

and earnings decreases

9

. Initial and second public offerings are incentives to manage earnings. Because

managing earnings before initial and second public offering leads to high share price

10

11

. In order to

reduce purchase price during management buy-out practises is another incentive of earnings

management.

12

Managers can manage earnings to maintain company's market values

13

. Avoiding

violation of debt covenants or ensuring the terms of debt covenants are other incentives.

14

Political and

regulatory requirments

15

and minimizing the information asymmetry between company and related

parties

16

are induce manager to manage earnings.

There are two basic techniques to manage earnings. Managers use accruals and real transaction

to manage earnings upward or downward. While "switching method for amortisation or

depreciation"

17

, "changing amortisation or depreciation life"

18

are example of accruals based earnings

management techniques; "timing operating expense"

19

, "making higher discount

in year-end"

20

are example of real transaction based earnings management techniques.

4

Paul N. Healy, “The Impact of Bonus Schemes on Accounting Choices”, Journal of Accounting and Economics ,7,

1985, pp.92.

5

Quiang Cheng, Terry D. Warfield, “Equity Incentives and Earnings Management”, The Accounting Review, Vol:80,

No:2, 2005, pp.441-475.

6

Michael R. Moore, “Management Changes and Discretionary Accounting Decisions”, Journal of Accounting Research,

1973, pp.100-107.

7

Joshua Ronen, Varda Lewinstein Varda, Earnings Management: Emerging Insight in Theory, Practise and

Resource, Springer Science and Business Media, 2008, pp.100

8

Susan Pourciau,“Earnings Management and Nonroutine Executive Exchange”, Journal of Accounting and Economics,

Vol:16, No:1-3, 1993, pp.317-336

9

David C. Burgstahler, Ilia Dichev, “Earnings Management to Avoid Losses and Earnings Decreases, Journal of

Accounting and Economics, Vol:24, 1997, pp.99-126

10

Siew Hong Teoh, T.J. Wong, Gita R. Rao, “Are Accruals During Initial Public Offerings Opportunistic”, Review of

Accounting Studies, 1998, pp.175-179

11

Siew Hong Teoh, Ivo Welch, T.J Wong, “Earnings Management and The Underperformance of Seasoned Public

Offering”, Journal of Financial Economics, Vol:50, 1998, pp.63-99

12

Y.Woody Wu, “Management Buyouts and Earnings Management”, Journal of Accounting, Auditing&Finance,

Vol:12, No:2, 1997, pp.373-389

13

Larry N. Bitner, Robert C. Dolan, “Assessing The Relationship Between Income Smoothing and The Value of The

Firm”, Quarterly Journal of Business and Economics, Vol:35, Iss:1, 1996, pp.16-35

14

Brooke W. Stanley, Vikram I. Sharma, “To Cheat Or Not To Cheat: How Bank Debt Influences The Decision To

Misreport”, Journal of Accounting, Auditing&Finance, Vol: 26, No:2, 2011, pp.383-414

15

In Mu Haw, Daqing QI, Donghui Wu, Woody Wo, “Market Consequences of Earnings Management in Response to

Security Regulations in China”, Contemporary Accounting Research, Vol: 22, No:1, 2005, pp.110-130

16

Mandira Roy Sankar, K.R. Subramanyam, “Reporting Discretion and Private Information Comminication Through

Earnings”, Journal of Accounting Research, Vol:39, No:2, 2001, pp.365-386

17

Meng Yanqiong, “Earnings Management Incentives and Techniques in China's Listed Companies: A Case Study”,

Proceedings of /th International Conference on Innovation and Management, 2010,

http://www.pucsp.br/icim/ingles/downloads/papers_2010/part_5/96_Earnings%20Management%20Incentives%20and%2

0Techniques.pdf

18

Marquerite L. Bishop, Elizabeth A. Eccher, “Do Markets Remember Accounting Changes? An Examination of

Subsequent Years?” http://papers.ssrn.com/sol3/papers.cfm?abstract_id=218448

19

William R. Baber, Patricia M. Fairfield, James A. Haggard, "The Effect of Corcern About Reported Income on

Discretionary Spending Decisions: The Case of Research and Development, The Accounting Review, Vol:66, No:4,

1991, pp.818-829

20

Scott B. Jackson, William E. Wilcox, “Do Managers Grant Sales Price Reductions to Avoid Loses and Declines in

Earnings and Sales?” QJBI, Vol: 39, No:4, Auntumn 2000, pp.3-20

39 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Many model for detection of two types of earnings management techniques are developed by

academicians. Healy

21

, Deangelo

22

, Jones

23

, Dechow et al

24

, Kothari

25

developed main models to detect

accruals based earnings management. Roychowdhury

26

,Jackson&Wilcox

27

and

Herrmann&Inoue&Thomas

28

also developed to detect real transaction based earnings management.

Accruals and real transactions based detection models help to measure how much quantity of

earnings managed. There are different models to detect managed earnings out of the above-mentioned.

These are distribution approach

29

and Benford's Law

30

. Both models only investigate the possibility of

earnings management in financial reports. This paper focus on Benford's Law.

The remaining sections of this study include, second prior literature of Benford's Law as a

detection method of earnings management, third hypotheses developed, fourth samples and statistics

are described, fifth testing methodology are discussed, and last section present conclusions.

2. Prior Literature on Benford's Law as Earnings Management Detection Method

Simon Newcomb observed that books of logorithms were considerably more worn in the beginings

pages which dealt with low digits and progressively worn on the pages dealing with higher digits. He

conclude that numbers which started with number one more often than those starting with two, three, ...

, nine. Then Newcomb calculated expected frequency of a number in the first digit.

31

In 1996, Nigrini used Newcomb's formula and calculated expected frequencies of a number for

the digits in the first, second, third and fourth positions. His findings of the expected digit frequencies

are shown in table 2.1

32

21

Paul N. Healy, “The Impact of Bonus Schemes on Accounting Choices”, Journal of Accounting and Economics ,7,

1985, pp. 85-107

22

Linda Elizabeth Deangelo, “Accounting Numbers as Market Valuation Substitutes: A Study of Management Buyouts of

Public Shareholders”, The Accounting Review, Vol: LX1, No:3, 1986, pp.400-420

23

Jennifer Jones, “Earnings Management During Import Relief Investigations”, Journal of Accounting Research, Vol:29,

No:2, 1991pp.193-228.

24

Patricia M. Dechow, Richard G. Sloan, Amy P. Sweeney, “Detecting Earnings Management”, The Accounting Review,

Vol:70, No:2, 1995 pp.193-225

25

S.P. Kothari, Andrew J. Leone, Chales E. Wasley, “Performance-Matched Discretionary Accruals”,Journal of

Accounting and Economics, Vol. 39, 2005, pp.163-197

26

S. Roychowdhury, “Earnings Management Through Real Activities Manipulation”, Journal of Accounting and

Economics, Vol:42, 2006,, pp.335-370.

27

Scott B. Jackson, William E. Wilcox, “Do Managers Grant Sales Price Reductions to Avoid Loses and Declines in

Earnings and Sales?” QJBI, Vol: 39, No:4, Auntumn 2000, pp.3-20 , pp.3-20

28

Don Herrmann, Tatsuo Inoue, Wayne B.Thomas, "The Sales of Assets to Manage Earnings in Japan", Journal of

Accounting Research, Vol:41, Issue:1, 2003, pp.89-108

29

David C. Burgstahler, Ilia Dichev, “Earnings Management to Avoid Losses and Earnings Decreases, Journal of

Accounting and Economics, Vol:24, 1997, pp.99-126.

30

Mark J. Nigrini, Forensic Analytics: Methods and Techniques for Forensic Accounting Investigation, John

Wiley&Sons Inc, 2011, pp.85.

31

Cindy Durtschi, William Hillison, Carl Pacini, "The Effective Use of Benford's Law to Assist in Detecting Fraud in

Accounting Data", Journal of Forensic Accounting, Vol:V(2004), pp.17-34.

32

Mark J. Nigrini, Forensic Analytics: Methods and Techniques for Forensic Accounting Investigation, John

Wiley&Sons Inc, 2011, pp.88.

40 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Table 2.1: Expected Digit Frequencies of Benford's Law

Digit Position in Number

First Second Third Fourth

0 0.00000 0.11968 0.10178 0.10018

1 0.30103 0.11389 0.10138 0.10014

2 0.17609 0.10882 0.10097 0.10010

3 0.12494 0.10433 0.10057 0.10006

4 0.09691 0.10031 0.10018 0.10002

5 0.07918 0.09668 0.09979 0.09998

6 0.06695 0.09337 0.09940 0.09994

7 0.05799 0.09035 0.09902 0.09990

8 0.05115 0.08757 0.09864 0.09986

9 0.04576 0.08500 0.09827 0.09982

Source: Mark J. Nigrini, Forensic Analytics: Methods and Techniques for Forensic Accounting Investigation, John

Wiley&Sons Inc, 2011, p.88.

Probability that the digit d, is encountered as the n

th

digit is calculated with the following

equation.

Pn(d)

∑

k

=

10

n−2

10

n

−

1

−1

log10

(

1+1

(10k +d)

)

where d is a number 1, 2, 3, ..., 9 and P is the probability.

Nigrini state that Benford's Law is applicable method to detect manipulation in financial

statements.

33

As mentioned above, managers have various incentives to manage earnings upward or

downward. Earnings management practises as a type of manipulation may be detected by using

Benford's Law.

According to Nigrini, detection of irregular numbers in financial statements would be much

easier by Benford's Law. It analyse digits of accounts in financial statements by testing whether the

observed digits frequencies differs from expected digits frequencies of Benford's Law. If there is a

nonconformity in a financial statement account, it indicates that account is misstated.

34

However,

variability in the data, no requirment of minimum-maximum or often-repeated numbers, large sample

size, result of standard transactions of calculations are certain criteria to perform Benford's Law.

35

36

Limited reseaches used Benford's Law to detect earnings management in literature. While Niskanen

et al.(2000)

37

, Kinnunen et al. (2003)

38

, Caneghem (2004)

39

, Skousen et al. (2004)

40

, Johnson (2009)

41

,

33

Mark J. Nigrini, Forensic Analytics: Methods and Techniques for Forensic Accounting Investigation, John

Wiley&Sons Inc, 2011, pp.388-389.

34

Wiley&Sons Inc, 2011, pp.388-389.

35

http://www.exceluser.com/tools/benford_xl11.htm

36

Cristi Tilden, Troy Janes, "Empirical Evidence of Financial Statement Manipulation During Economic Recession",

Journal of Finance and Accountancy, pp.3.

37

Jyrki Niskanen, Matti Keloharju, “Earnings Cosmetics in Tax-Deriven Accounting Environment: Evidence From Finnish

Public Firms”, The European Accounting Review, Vol:9:3, 2000, pp.443-452.

38

Juha Kinnunen, Markku Koskela, “Who is Miss World in Cosmetic Earnings Management? A Cross-National

Comparison of Small Upward Rounding of Net Income Numbers Among Eighteen Countries”, Journal of International

Accounting Reseach, Vol:2, 2003, pp.39-68.

39

Tom Van Caneghem, “The Impact of Audit Quality on Earnings Rounding-up Behaviour: Some UK Evidence”,

European Accounting Review, Vol:13, No:4, 2004, pp.771-786.

40

Christopher J. Skousen, Liming Guan, T. Sterling Wetzel, “Anomalies and Unusual Patterns in Reported Earnings:

Japanese Manager Round Earnings”, Journal of International Financial Management and Accounting, Vol:15:3,

2004, pp.212-234.

41

Gary C. Johnson, “Using Benford's Law to Determine If Selected Company Characteristics are Red Flags For Earnings

Management”, Journal of Forensic Studies in Accounting and Business, 2009, pp.39-65.

41 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Lin et al. (2011)

42

, Zgela et al. (2011)

43

, Wilson et al (2012)

44

, Tilden et al. (2012)

45

used different

earnings variables such as net profit, net loss, or absolute value of net income in Benford's Law

analyses to detect earnings management, Kinnunen et al. (2003)

46

, Jordan et al.(2009)

47

, Wilson et al

(2012)

48

, Tilden et al. (2012)

49

used different control variables such as net sales, inventory, allowance

for doubtful, total assets. Reseachs generally tested second digits of selected accounts. The following

table 2.2 summurize used sample, period, used accounts, tested digits, main findings of prior studies

about Benford's Law as earnings management detection method.

Table 2.2: Prior Literature on Benford's Law as Earning Management Detection Method

Study Sample Period Accounts Digits Main Findings

Niskanen et

al.(2000) 1637 Comp. 1953

1997 Positive Net Income 2

nd

Companies tend to adjust the second

digit of Positive Net Income

Kinnunen et

al. (2003) 21662 Comp. 1995-1999

Net

Sales,Positive/Negative

Net Income

2

nd

Main findings suggest that there are

systematic differences across

countries in the specific (cosmetic)

type of earnings management

Caneghem

(2004) 1256 Comp. 1998 Pre-Tax Income 2

nd

Big Five auditors constraining

earnings management practices

Skousen et al.

(2004) 37900 Data 1974

1997 Net Income,Net Loss

1

th

, 2

nd

, 3

th

,

4

th

Japanese companies tend to round

earnings numbers to achieve key

reference points.

Johnson

(2009)

576CompQuart

erly Data

1999

2004

Net Income, Earnings

Per Share

1

th

Low market capitalization

companies, High insider trading

companies,New publicly traded

companies represent an increased risk

of earnings management

Jordan et

al.(2009) 1002 Comp/ 2006 Sales Revenues,Total

Assets

2

nd

An unusually high frequency of zeros

in the second digital position of sales

indicates that sales revenue is

manipulated

Lin et al.

(2011)

29,459

Monthly

1992

2007 Positive Earnings

1

th

, 2

nd

First-Two

Companies attempted to report

earnings that have 5 in the second

place.

Zgela et al

(2011)

1500

Comp'Years

2007

2009

Profit, Losses, Absolute

Net Income

1

th

Net income amounts follow

Benford's Law first digit distribution

Wilson et al

(2012) 5989 Comp/ 2009 Net Sales, Net

Profit/Loss

2

th

No statistically significant evidence

Tilden et

al.(2012) No Info. 1950

2006

Net Sales, Net Income,

Inventory, Allowance for

Doubtful

1

th

The presence of manipulated data in

allowance for doubtful accounts and

net income.

42

Fengyi Lin, Liming Guan, Wenchang Fang, “Heaping in Reported Earnings: Evidence From Monthly, Financial Reports

of Taiwanese Firms”, Emerging Markets Finance&Trade, Vol:47, No:2, 2011, pp.62-73.

43

Mario Zgela, Jasminka Dobsa, “Analysis of Top 500 Central and East European Companies Net Income Using Benford's

Law”, Journal of Information and Organizational Sciences, Vol:35, No:2, 2011, pp.215-228.

44

Thomas E. Wilson Jr., “Further Evidence on The Extend of Cosmetic Earnings Management By U.S Firms”, Academy

of Accounting and Financial Studies Journal, Vol:16, No:3, 2012, pp.57-64.

45

Cristi Tilden, Troy Janes, "Empirical Evidence of Financial Statement Manipulation During Economic Recession",

Journal of Finance and Accountancy

46

Juha Kinnunen, Markku Koskela, “Who is Miss World in Cosmetic Earnings Management? A Cross-National

Comparison of Small Upward Rounding of Net Income Numbers Among Eighteen Countries”, Journal of International

Accounting Reseach, Vol:2, 2003, pp.39-68.

47

Charles E. Jordan, Stanley J. Clark, Charlotte Hames, “Manipulating Sales Revenue to Achieve Cognitive Reference

Point: An Examination of Large U.S Public Companies, The Journal of Applied Business Research, Vol:25, No:2,

2009, pp. 95-103.

48

Thomas E. Wilson Jr., “Further Evidence on The Extend of Cosmetic Earnings Management By U.S Firms”, Academy

of Accounting and Financial Studies Journal, Vol:16, No:3, 2012, pp.57-64

49

Cristi Tilden, Troy Janes, "Empirical Evidence of Financial Statement Manipulation During Economic Recession",

Journal of Finance and Accountancy

42 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

3. Hypotheses Development

We used net income as earnings variable and then divided net income sample into positive (net profit)

and negative (net loss) and we denote this account by NP, NL. Besides we analysis sales revenues

which is denoted by SR, cost of goods sold accounts which is denoted by COGS and operating expense

which is denoted by OPEX. Because, we consider as menditoned by Roychowdhury

50

that managers

can adjust sales revenues by accelerating the timing of sales and or generating additional unsustainable

sales through increased price discount or more lenient credit terms and can adjust cost of goods sold by

increasing/decreasing production, and can adjust timing of operating expenses such as advertising,

R&D expenses when they manage net profit and net loss. So we suppose that sales revenues, cost of

goods sold and operating expenses takes on an important role on earnings management practices

performed by managers.

We observed first, second, third, fourth digit in net profit (NP), sales revenues (SR), cost of

goods sold (COGS), operating expenses (OPEX) for companies that reported a profit, in net loss (NL),

sales revenues (SR), cost of goods sold (COGS), operating expenses (OPEX) for companies that

reported a loss. We compared the observed digits frequencies of selected accounts differs from

expected digits frequencies of Benford's Law. Chi-Square and Z-score tests are used for conformity. If

there is a nonconformity in selected accounts, it indicates that accounts are misstated.

Then, we compared significance freguency of number zero and significance of number nine to

test tendency of earnings management. As discussed in prior studies such as Kinnunen et al.

51

, Skousen

et al.

52

if managers engaged to manage earnings upward (downward), we expected to observe

high(low) significance freguency of number zero and low (high) significance of number nine in

second, third, fourth digits of net profit, sales revenues. On the contrary, if managers engaged to

manage earnings upward (downward), we expected to observe high (low) significance freguency of

number nine and low (high) significance of number zero in second, third, fourth digits of cost of goods

sold and operating expenses.

4. Dataset and Descriptive Statistics

In this study, we are examining the quarterly financial report of the the Istanbul Stock Exchange

companies between 2005-2010. Sample include five industries, 181 companies, 6 years, 4 quarters for

each year. The detailed information about our sample is shown in table 4.1

Table 4.1: Dataset Classification

Sector Total Data Company Year Period

Electricity 48 2 2005/2010 4

Manufacturing 3552 148 2005/2010 4

Transport 72 3 2005/2010 4

Technology 336 14 2005/2010 4

Trade 336 14 2005/2010 4

Total 4344 181 6 24

We tested four accounts of income statements in Benford's Law analysis to detect earnings

management practices. Accounts are sales, cost of goods sold, operating expenses and net income.

50

S. Roychowdhury, “Earnings Management Through Real Activities Manipulation”, Journal of Accounting and

Economics, Vol:42, 2006,, pp.335-370., pp.335-370

51

Juha Kinnunen, Markku Koskela, “Who is Miss World in Cosmetic Earnings Management? A Cross-National

Comparison of Small Upward Rounding of Net Income Numbers Among Eighteen Countries”, Journal of International

Accounting Reseach, Vol:2, 2003, pp.39-68.

52

Christopher J. Skousen, Liming Guan, T. Sterling Wetzel, “Anomalies and Unusual Patterns in Reported Earnings:

Japanese Manager Round Earnings”, Journal of International Financial Management and Accounting, Vol:15:3,

2004, pp.212-234.

43 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

When we divide our sample into companies that reported a profit and reported a loss; net profit, sales

revenues, cost of goods sold, operating expense consists of 2837 data for companies that reported a

profit and net loss, sales revenues, cost of goods sold, operating expenses consists of 1507 data for

companies that reported a loss. Descriptive statistics about accounts for each classification are shown

in table 4.2

Table 4.2: Descriptive Statistics

Companies Report a Profit

Statistics Net Profit Sales Revenues Cost of Goods Sold Operating Expenses

Mean 4,692,131,159 65,820,960,674 53,584,931,171 6,835,288,646

Median 889,300,000 12,648,918,000 9,146,949,700 1,483,517,700

Maximum 219,160,900,000 3,045,639,900,000 2,855,699,900,000 215,578,700,000

Minimum 8500 89,492 49,568 47,512

Std. Dev. 14,149,988,236 190,863,523,339 168,914,626,860 18,296,832,347

Skewness 7 7 8 6

Observation

2837 2837 2837 2837

Companies Report a Loss

Statistics Net Loss (Absolute) Sales Revenues Cost of Goods Sold Operating Expense

Mean 1.069.905.857 15,775,370,753 13,668,754,949 2,227,727,730

Median 301.293.400 3,660,059,700 3,005,774,100 615,095,900

Maximum 39.952.200.000 1,614,067,615,500 1,532,819,237,700 69,495,600,000

Minimum 3.996 2290 1,013 9140

Std. Dev. 2.478.144,058 60,060,871,603 55,588,146,991 5,105,467,565

Skewness 7 16 17 6

Observation

1507 1507 1507 1507

There are quantitative indicators whether Benford's Law can be applied to our dataset. First, the

mean of observed digits should be larger than the median, second the skewness value should be

positive.

53

For companies that reported a profit/loss, data's mean is larger than our whole data's median

for all selected accounts and skewness value is positive for all selected accounts. So, data for

companies that reported a profit/loss is approptiate dataset to apply Benford's Law.

5. Testing Methodology

Testing methodology was performed in three stages.

First stage, we used Chi-square test to determine whether there ise a significance difference

between the expected frequencies and the observed frequencies in one or more categories. In our case,

for the Benford's law, we compare the expected distribution of over all digits with the observed

distribution.

In this analysis, we compare p-value of the observed distribution with the significance level.

The p-value is the probability that chi-square random variable with degrees of freedom eight (9-1) is

smaller than the calculated chi-square random variable, which we denote by

χ

(calc)

2

.

χ

(calc)

2

=N

∑

k=1

9

[p(k)− b(k)]

2

b

k

where

χ

2

:

the chi-square value

p

(

k

)

:

proportion of the original data

b

(

k

)

:

proportion of the Benford's Law

N

:

sum of the frequencies

53

Klaus Henselmann, Elisabeth Scherr, Dominik Ditter, “Applying Benford's Law to Individual Financial Report: An

Empirical Investigation on the Basis of SEC XBRL Fillings”, Working Papers in Accounting Valuation Auditing;

No:2012-1, pp.8-9, http://hdl.handle.net/10419/55146.

44 European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

If this p-value is smaller than the level of significance we rejected that there is no difference

betwwen the sample population's value (observed data) and the underlying population's value

(Benford's); If this p-value is larger than the level of significance we accepted that there is difference

betwwen the sample population's value (observed data) and the underlying population's value

(Benford's);

Second stage include to test each of the nine proportions for first digit (ten proportions for

second, third, fourth digits) separately. In other words, the normal-distribution approximation to the

binomial distribution is used to test each of the nine proportions for first digit (ten proportions for

second, third, fourth digits) separately. To do this, we first calculate the z-scores for each observed

proportion, against the Benford proportions, using following formula.

score

p(k) b(k)

Z

(b(k) (1 b(k))

N

−

=

− −

The process of reducing the level of significance used in each of the nine tests for first digit (ten

proportions for second, third, fourth digits) for the z-scores is based on Bonferroni’s inequality54. In

other words, each p-value is compared with the value of

0.05

/

9

55, which is equal to 0.0056. Since

probability of absolute value of standart normal distribution greater than 2.77 is equal to 0.0056. If we

change the confidence interval %96 to %90, each p-value is compared with the value of

0.1

/

9

, which

is equal to 0.0111, any z-score greater in absolute value than

α

, where

α

is a number between 2.53

and 2.54.

Third stage include to test earnings management behavior. If managers engaged to manage

earnings upward (downward), we expected to observe high(low) significance z-score of number zero

and low (high) significance z-score of number nine in second, third, fourth digits of net profit, sales

revenues. On the contrary, if managers engaged to manage earnings upward (downward), we expected

to observe high (low) significance z-score of number nine and low (high) significance z-score of

number zero in second, third, fourth digits of cost of goods sold and operating expenses.

5.1. First Digit Analysis

In our study, we initially determine the value of the digit in the first digit position and derive the

frequency of values between one and nine. We rename these frequencies as the actual values of the

accounts; SR, COGS, OPEX, NI; SR, COGS, OPEX, companies that reported a NP and SR, COGS,

OPEX, companies that reported a NL. As we mentioned before, we make the first digit analysis in two

parts. You can find the first part of the analysis in table 5.1.1, which illustrates first digit analysis for

companies that reported a NP (contains 2837 examinable observations) and table 5.1.2 illustrates first

digit analysis for companies that reported a NL (contains 1507 examinable observations).

In table 5.1.1, table 5.1.2 , freguencies, z-scores and p-values of all accounts for the first digit

analysis are given. In table 5.1.1 sample consists of companies that reported a NP and in table 5.1.2

sample consists of companies that reported a NL.

54

Robert V. Hogg, Joseph W. McKean, Allen T. Craig, Introduction to Mathematical Statistics, Pearson Education,

Sixth Edition, 2005, pp. 14, 481.

55

%95 Confidence interval.

45

European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Table 5.1.1: First Digit Analysis for Companies That Reported a NP

First

Digit

SR

Actual

SR Z-

Score

COGS

Actual

COGS

Z-Score

OPEX

Actual

OPEX

Z-Score

NP

Actual

NP Z-

Score Expected Benford

1 850 -0.1646 802 -2.13 867 0.5436 830 -0.9832 853.72 30.10%

2 467 -1.6054 509 0.4648 511 0.5721 486 -0.6689 499.39 17.61%

3 357 0.1447 373 1.0532 351 -0.1889 361 0.3718 354.33 12.49%

4 283 0.5119 278 0.1946 281 0.3912 277 0.1311 274.84 9.69%

5 242 1.2072 234 0.6510 213 -0.8038 232 0.5119 224.56 7.92%

6 206 1.2073 193 0.2308 191 0.0856 213 1.7332 189.86 6.69%

7 157 -0.6043 171 0.5203 155 -0.794 154 -0.8453 164.47 5.80%

8 160 1.2681 136 -0.7772 141 0.0794 166 1.7794 145.07 5.12%

9 115 -1.3310 141 1.0050 121 -0.7880 118 -1.0615 129.77 4.58%

Sum 2837 2837 2837 2837 2837 100%

P-Value 0.3718 0.5821 0.9666 0.3442

Since p-values of all accounts for the companies that reported a NP are greater than significance

level (0.05 and 0.1), the distribution of the accounts are same with Benford distribution.

As the value of the z-scores in table 5.1.2 are all small, absolute value of z-scores are below

2.54, that the first digits of the all parameters (1, 2, 3, …, 9) follow Benford's Law.

Table 5.1.2: First Digit Analysis for Companies That Reported a NL

First

Digit

SR

Actual

SR Z-

Score

COGS

Actual

COGS

Z-Score

OPEX

Actual

OPEX

Z-Score

NL

Actual

NL Z-

Score Expected Benford

1 432 -1.2159 461 0.4126 446 -0.4297 446 -0.427 453.65 30.10%

2 303 2.54 277 0.7866 291 1.7334 273 0.5160 265.37 17.61%

3 188 -0.0220 191 0.2117 196 0.6012 179 -0.7232 188.28 12.49%

4 139 -0.6133 136 -0.8745 134 -1.0487 141 -0.4392 146.04 9.69%

5 123 0.3505 123 0.3505 127 0.7321 127 0.7321 119.33 7.92%

6 86 -1.5346 105 0.4237 101 0.0115 96 -0.5039 100.89 6.69%

7 89 0.1770 86 -0.1536 75 -1.3660 101 1.4996 87.39 5.80%

8 71 -0.7117 62 -1.7640 78 0.1068 75 -0.2440 77.09 5.12%

9 76 0.8683 66 -0.3645 59 -1.2274 69 0.0054 68.96 4.58%

Sum 1507 1507 1507 1507 1507 100%

P-Value 0.2479 0.7849 0.4721 0.8673

Since p-values of all accounts are greater than significance level (0.05 and 0.1), the distribution

of the observed accounts are same with Benford distribution.

5.2. Second Digit Analysis

In table 5.2.1, table 5.2.2, freguencies, z-scores and p-values of all accounts for the second digit

analysis are given. Table 5.2.1 and 5.2.2 illustrate second digit analysis for all accounts for companies

that reported a NP and for companies that reported a NP, respectively.

Table 5.2.1: Second Digit Analysis- Companies That Reported NP

Second

Digit

SR

Actual

SR Z-

Score

COGS

Actual

COGS Z-

Score

OPEX

Actual

OPEX Z-

Score

NP

Actual

NP Z-

Score Expected Benford

1 311 -0.7155 335 0.7029 332 0.5256 326 0.1710 323.11

11.39%

2 332 1.4034 305 -0.2244 303 -0.3450 311 0.1373 308.72

10.88%

3 287 -0.5518 282 -0.8589 276 -1.2274 273 -1.4116 295.98

10.43%

4 264 -1.2861 304 1.2137 282 -0.1612 284 -0.0362 284.58

10.03%

5 269 -0.3355 303 1.8245 266 -0.5261 268 0.6523 274.28

9.67%

6 264 -0.0575 267 0.1361 240 -1.6062 275 0.9612 264.89

9.34%

7 272 1.0267 258 0.1098 253 -0.2176 271 0.9612 256.32

9.04%

8 256 0.5024 214 -2.29 260 0.7681 208 -1.6857 248.44

8.76%

9 220 -1.4235 227 -0.9523 267 1.7406 249 0.5288 241.15

8.50%

0 362 1.2996 342 0.1427 358 1.0682 37 1.8780 339.53

11.97%

Sum

2837 2837 2837 2837 2837 100%

P-Value 0.4746 0.2673 0.4682 0.1563

46

European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Table 5.2.3: Second Digit Analysis- Companies That Reported a NL

Second

Digit

SR

Actual

SR Z-

Score

COGS

Actual

COGS

Z-Score

OPEX

Actual

OPEX

Z-Score

NL

Actual

NL Z-

Score Expected Benford

1 161 -0.8621 173 0.1109 186 1.1651 164 -0.6189 171.63 11.39%

2 165 0.0834 170 0.4970 146 -1.4883 166 0.1661 163.99 10.88%

3 174 1.4136 146 -0.9459 174 1.4136 187 2.51 157.23 10.43%

4 161 0.8431 137 -1.2148 154 0.2429 157 0.5002 151.17 10.03%

5 146 0.0264 170 2.1185 135 -0.9324 140 -0.4966 145.7 9.67%

6 129 -1.0366 149 0.7341 144 0.2914 149 0.7341 140.71 9.34%

7 131 -0.4634 128 -0.7330 122 -1.2721 124 -1.0924 136.16 9.04%

8 130 -0.1793 131 -0.0882 147 1.3699 142 0.9142 131.97 8.76%

9 120 -0.7477 140 1.0996 126 -0.1935 120 -0.7477 128.1 8.50%

0 190 0.7652 163 -1.3775 173 -0.5839 158 -1.7744 180.36 11.97%

Sum 1507 1507 1507 1507 1507 100%

P-Value 0.8055 0.3365 0.4012 0.2094

Since p-values of all accounts in table 5.2.1, table 5.2.2 are greater than significance level (0.05

and 0.1), the distributions of the observed accounts for second digits are same with Benford

distribution.

As the value of the z-scores in table 5.2.1 are all small, absolute value of z-scores are below

2.54, that the second digits of all parameters follow Benford's Law.

When we test to for tendency of managing earnings upward (downward), we expected to

observe high(low) significance z-score of number zero and low (high) significance z-score of number

nine in seccond digit of net profit, sales revenues in table 5.2.1, table 5.2.2, On the contrary, if

managers engaged to manage earnings upward (downward), we expected to observe high (low)

significance z-score of number nine and low (high) significance z-score of number zero in second digit

of cost of goods sold and operating expenses in table 5.2.1, table 5.2.2 . But, observation did not

happen in accordance with our expectation.

5.3. Third Digit Analysis

In table 5.3.1, table 5.3.2, freguencies, z-scores and p-values of all accounts for the third digit analysis

are given.

Table 5.3.1: Third Digit Analysis for Companies That Reported a NP

Third

Digit

SR

Actual

SR

Z-Score

COGS

Actual

COGS

Z-Score

OPEX

Actual

OPEX

Z-Score

NP

Actual

NP

Z-Score Expected Benford

1 285 -0.1662 295 0.4558 266 -1.3479 298 0.6424 287.67 10.14%

2 299 0.7819 282 -0.2774 249 -2.3338 319 2.03 286.45 10.10%

3 291 0.3548 287 0.1051 279 -0.3943 284 -0.0822 285.32 10.06%

4 281 -0.2008 303 1.1749 262 -1.3889 281 -0.2008 284.21 10.02%

5 305 1.3716 290 0.4320 280 -0.1945 295 0.7452 283.1 9.98%

6 263 -1.1921 272 -0.6274 290 0.5021 258 -1.5059 282 9.94%

7 296 0.9479 251 -1.8807 305 1.5136 259 -1.3778 280.92 9.90%

8 298 1.1433 252 -1.7530 270 -0.6197 254 -1.6271 279.84 9.86%

9 253 -1.6267 310 1.9683 301 1.4007 281 0.1393 278.79 9.83%

0 266 -1.4126 295 0.3881 335 2.8718* 308 1.1953 288.75 10.18%

Sum 2837 2837 2837 2837 2837 100%

P-Value 0.3616 0.2358 0.0164* 0.2104

For the OPEX variable, p-value is smaller than significance level (0.05), the distributions of the

observed account OPEX for third digit are not same with Benford distribution. For this account, the

number 0 has z-score greater than 2.54, thus we concluded that the observed frequencies for OPEX

account do not follow a Benford distribution for number zero. The actual versus expected distributions

for the OPEX account for companies that reported a NP are plotted below in Figure 1.

47

European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Although the observed frequencies for OPEX account do not follow a Benford distribution for

digit zero, there ise no evidence that managers engaged to manage earnings upward (downward),

because, we did not observe high (low) significance z-score of number nine and low (high)

significance z-score of number zero in third digit of operating expenses.

Figure 1: Third Digit Analysis for OPEX (Companies That Reported A NP)

Table 5.3.2: Third Digit Analysis for Companies That Reported a NL

Third

Digit

SR

Actual

SR

Z-Score

COGS

Actual

COGS

Z-Score

OPEX

Actual

OPEX

Z-Score

NL

Actual

NL

Z-Score Expected Benford

1 146 -0.5811 151 -0.1544 132 -1.7759 168 1.2963 152.81 10.14%

2 174 1.8671 151 -0.0993 145 -0.6123 147 -0.4413 152.16 10.10%

3 149 -0.2192 147 -0.3905 166 1.2369 147 -0.3905 151.56 10.06%

4 168 1.4610 157 0.5173 175 2.0616 156 0.4315 150.97 10.02%

5 148 -0.2049 147 -0.2908 153 0.2249 161 0.9124 150.38 9.98%

6 156 0.5342 144 -0.4990 153 1.2759 160 0.8785 149.8 9.94%

7 124 -2.18 140 -0.7954 126 -2.0028 148 -0.1055 149.22 9.90%

8 144 -0.4018 162 1.1533 172 2.0172 141 -0.6609 148.65 9.86%

9 146 -0.1811 148 -0.0080 139 -0.7869 137 -0.9599 148.09 9.83%

0 152 -0.1178 160 0.5638 146 -0.6290 142 -0.9697 153.38 10.18%

Sum 1507 1507 1507 1507 1507 100%

P-Value 0.3387 0.9730 0.0540** 0.7874

Table 5.3.2 provides information for companies that reported a NL. From this table, OPEX is

the only account which has p-value smaller than 0.1 (90 percent confidence). According to this

information for 90 percent confidence, we can say that OPEX account has distribution different from

Benford's distribution. Figure 2 illustrates the third digit analysis for the OPEX account for companies

that reported a NL.

For this account, z-score of all numbers smaller than 2.54, thus we concluded that the observed

frequencies for OPEX account follow a Benford distribution for parameters (0, 1, 2, ..., 9).

However, there ise no evidence that managers engaged to manage earnings upward

(downward), because, we did not observe high (low) significance z-score of number nine and low

(high) significance z-score of number zero in third digit of operating expenses.

1 2 3 4 5 6 7 8 9 0

0

50

100

150

200

250

300

350

400

Actual Expected

48

European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Figure 2: Third Digit Analysis for OPEX (Companies That Reported a NL)

5.4. Fourth Digit Analysis

In table 5.4.1 and table 5.4.2 freguencies, z-scores and p-values of all accounts for the fourth digit

analysis are given.

Table 5.4.1: Fourth Digit Analysis for Companies That Reported a NP

Fourth

Digit

SR

Actual

SR Z-

Score

COGS

Actual

COGS

Z_Score

OPEX

Actual

OPEX

Z-Score

NP

Actual

NP

Z-Score Expected Benford

1 310 1.6127 273 -0.7010 298 0.8623 284 -0.0132 284.21 10.000%

2 303 1.1822 294 0.6194 235 -3.0707* 278 -0.3813 284.1 10.014%

3 263 -1.3126 317 2.0653 260 -1.5003 283 -0.0615 283.98 10.010%

4 290 0.3835 289 0.3209 285 0.0707 282 -0.1170 283.87 10.006%

5 248 -2.2375 292 0.5158 254 -1.8621 292 0.5158 283.76 10.002%

6 289 0.3353 269 -0.9165 321 2.3381 296 0.7734 283.64 9.998%

7 275 -0.5340 297 0.8432 284 0.0294 288 0.2798 283.53 9.994%

8 274 -0.5896 287 0.2244 299 0.9757 282 -0.0887 283.42 9.990%

9 284 0.0437 247 -2.2733 292 0.5446 260 -1.4592 283.3 9.986%

0 301 1.1155 272 -0.7008 309 1.6166 292 0.5518 283.19 9.820%

Sum 2837 2837 2837 2837 2837 100.000%

P-Value 0.2381 0.2434 0.0069* 0.9562

Table 5.4.I provides information for companies that reported a NP. From this table, OPEX is

the only account which has p-value smaller than 0.1 (90 percent confidence). According to this

information for 90 percent confidence, we can say that OPEX account has distribution different from

Benford's distribution. Figure 3 illustrates the fourth digit analysis for the OPEX account for

companies that reported a NP.

Since the absolute value of the z-score for OPEX account is bigger than 2.54, we conclude that

the observed frequencies for OPEX account do not follow a Benford distribution for number two. The

actual versus expected distributions are plotted below in Figure 3.

Although the observed frequencies for OPEX account do not follow a Benford distribution for

number two, there ise no evidence that managers engaged to manage earnings upward (downward),

because, we did not observe high (low) significance z-score of number nine and low (high)

significance z-score of number zero in fourth digit of operating expenses.

1 2 3 4 5 6 7 8 9 0

0

20

40

60

80

100

120

140

160

180

200

Ac tual Expected

49

European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

Figure 3: Fourth Digit Analysis of OPEX(Companies That Reported a NP)

Table 5.4.2: Fourth Digit Analysis for Companies That Reported a NL

Fourth

Digit

SR

Actual

SR

Z-Score

COGS

Actual

COGS

Z_Score

OPEX

Actual

OPEX

Z-Score

NL

Actual

NL

Z-Score Expected Benford

1 159 0.6888 159 0.6888 147 -0.3407 135 -1.3703 150.97 10.018%

2 150 -0.0782 136 -1.2796 147 -0.3356 142 -0.7647 150.91 10.014%

3 180 2.5018 176 2.1585 168 1.4719 172 1.8152 150.85 10.010%

4 139 -1.0121 154 0.2755 146 -0.4112 129 -1.8706 150.79 10.006%

5 141 -0.8354 139 -1.0071 150 -0.0627 148 -0.2344 150.73 10.002%

6 148 -0.2293 157 0.5436 146 -0.4010 179 2.4328 150.67 9.998%

7 123 -2.3714 159 0.7206 149 -0.1382 156 0.4630 150.61 9.994%

8 170 1.6709 166 1.3273 154 0.2964 151 0.0387 150.55 9.990%

9 148 -0.2139 129 -1.8463 152 0.1298 157 0.5594 150.49 9.986%

0 149 -0.1228 132 -1.5837 148 -0.2087 138 -1.0681 150.43 9.820%

Sum 1507 1507 1507 1507 1507 100.000%

P-Value 0.0832** 0.0989** 0.9779 0.0854**

Table 5.4.2 provides information for companies that reported a NL. From this table, NL, SR,

COGS are accounts which have p-value smaller than 0.1 (90 percent confidence). According to this

information for 90 percent confidence, we can say that NL, SR, COGS accounts have distribution

different from Benford's distribution.

For NL, SR, COGS z-score of all parameters (0, 1, 2, 3, ..., 9) smaller than 2.54, thus we

concluded that the observed frequencies for NL, SR, COGS accounts follow Benford distribution for

all parameters.

However, there ise no evidence that managers engaged to manage earnings upward

(downward), because, we did not observe high (low) significance z-score of number nine and low

(high) significance z-score of number zero in fourth digit of NL, SR, COGS.

6. Conclusion

We are examining the quarterly financial report of the the Istanbul Stock Exchange companies between

2005-2010. Sample include five industries, 181 companies, 6 years, 4 quarters for each year. We used

companies that reported a profit and reported a loss; net profit, sales revenues, cost of goods sold,

operating expense consists of 2837 data for companies that reported a profit and net loss, sales

revenues, cost of goods sold, operating expenses consists of 1507 data for companies that reported a

loss.

We find no evidence that any parameters are manipulated in first and second digits to manage

earnings. We find evidence that number 0 ( number two) are manipulated in third digit (fourth digit) of

OPEX for companies that reported a NP.

1 2 3 4 5 6 7 8 9 0

0

50

100

150

200

250

300

350

Actual Expected

50

European Journal of Economics Finance and Administrative Sciences - Issue 59 (2013)

We find no evidence for tendency of managing earnings upward (downward), If managers

engaged to manage earnings upward (downward), we expected to observe high(low) significance z-

score of number zero and low (high) significance z-score of number nine in second, third, fourth digits

of net profit, sales revenues. On the contrary, if managers engaged to manage earnings upward

(downward), we expected to observe high (low) significance z-score of number nine and low (high)

significance z-score of number zero in second, third, fourth digits of cost of goods sold and operating

expenses. However, observation did not happen in accordance with our expectation.

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