Benford's Law and Earnings Management Detection: The Case of REITs

Abstract

Benford’s Law has been employed by auditors to identify suspicious financial data and by researchers to investigate whether financial data has been manipulated in various industries, but the present study is the first to apply the concept to Real Estate Investment Trusts (REITs). Researchers using other investigative techniques report that REITs have systematically practiced earnings management. In the present study, a Benford test is conducted on quarterly REIT net income, collected for the years 2009 through 2014 and the results are analyzed using the Mean Absolute Deviation. For the full sample, no earnings management is detected; the distribution of both the first and second digits of net income conforms to a Benford’s distribution, but we cannot be certain whether this means the REITs in our sample did not manage earnings or that they did and the test failed to detect it. Tests on subsamples of the data provide different results. Combined with the results for the full sample, the latter finding is consistent with an issue critics of Benford’s Law find troublesome.

Full text

Journal of Forensic & Investigative Accounting
Volume 9: Issue 2, July–December, 2017
779
∗The author is Professor at Department of Finance and Financial Services at Wright State University.
Benford’s Law and Earnings Management Detection: The Case of REITs
James E. Larsen*
Introduction
A mathematical property, which has become known as Benford’s Law, was discovered independently by Newcomb
(1881) and Benford (1938). Benford’s Law holds that, contrary to intuition, the digits in large sets of positive-valued,
naturally occurring numbers that range over many orders of scale are not uniformly distributed. Instead, they often (but
not always) follow a logarithmic distribution such that numbers beginning with smaller digits appear more frequently than
those beginning with larger ones. Because manipulated, unrelated, or created numbers usually do not follow a Benford
distribution, Benford’s Law has been used to identify suspicious data in a variety of settings. Financial auditors, for
example, routinely check individual firm data for compliance with Benford’s Law (Kumar and Bhattacharya, 2007), and
researchers have used Benford’s Law to investigate whether financial data has been manipulated for a group of firms or an
entire industry.
A growing body of empirical evidence suggests that data omissions, errors, biases, misstatements, or fraud may be a
possibility when data deviates from the Benford distribution. Not everyone, however, is convinced of the power of
Benford’s Law to detect suspicious data. Diekmann and Jann (2010), for example, assert that it is doubtful that Benford
tests are necessarily an appropriate tool to discriminate between manipulated and nonmanipulated data and may produce
false positives (i.e., incorrectly indicate a data set contains manipulated data). Others suggest that Benford tests may
result in false negatives (i.e., fail to indicate a problem when the data set contains manipulated data). Varian (1972), for
example, opined that a data sets’ conformity with Benford’s Law does not necessarily imply authenticity.
Researchers have employed other statistical tests and concluded that earnings management has occurred routinely in
American corporations in general and REITs in particular.1 The purpose of this study is to determine whether or not
recent REIT earnings data conforms to a Benford’s distribution. Quarterly net income collected for the years 2009
through 2014 for equity and mortgage REITs listed on either the NYSE or NASDAQ is evaluated by calculating and
analyzing the Mean Absolute Deviation of both the first and second digits of REIT net income. For the entire sample, the
results indicate that the data conforms to Benford’s Law. This result is consistent with one of the following possibilities:
1) REITs no longer systematically manage earnings; or 2) the Benford test provides a false negative for the industry.
When the sample is bifurcated by REIT classification (equity vs. mortgage), or by the exchange on which the REITs’
shares are traded, nonconformance with Benford’s Law is detected. This finding is consistent with another issue critics of
Benford’s Law find troublesome.
The remainder of this article is organized as follows. In the next section, a brief explanation of Benford’s Law is
presented. The third section contains a literature review. The data and methodology are presented in the fourth section,
and the results are presented in the fifth section. The last section contains a summary and our conclusions.
Benford’s Law
According to Benford’s Law the expected occurrence, or proportion, of a given number (a) as the first digit in a number
set (P1a) can be calculated using equation (1).
P1a = log10 (a + 1) – log10 (a) (1)
Further, the expected proportion of a given number (a) as the first digit and the number (b) as the second digit (P1a2b) can
be calculated using equation (2).
 = log  +
   log  +
 (2)

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And equation (3), which sums equation (2) over all possible a values for a particular b value yields an overall expected
proportion for b as the second digit.
 = (  +
     +
)

 (3)
The expected proportion of each number in the third, and all subsequent, digits can be similarly derived. Table I shows
the proportion of each number in the first through fourth digits as predicted by Bedford’s Law. Note that the proportions
shown in Table I are skewed towards one for the first digit (because zero cannot be a first digit) and towards zero for
subsequent digits.
Table I: Expected Proportions Based on Benford’s Law
Number 1st digit 2nd digit 3rd digit 4th digit
0 .11968 .10178 .10018
1 .30103 .11389 .10138 .10014
2 .17609 .10882 .10097 .10010
3 .12494 .10433 .10057 .10006
4 .09691 .10031 .10018 .10002
5 .07918 .09668 .09979 .09998
6 .06695 .09337 .09940 .09994
7 .05799 .09035 .09902 .09990
8 .05115 .08757 .09864 .09986
9 .04576 .08500 .09827 .09982
Source: Nigrini (1996)
Literature Review
Benford’s Law
A mathematical discovery made by Simon Newcomb (1881) was ignored for nearly six decades until Benford (1938)
rediscovered it, and for another six decades after its rediscovery published empirical applications of Benford’s Law were
sparse. In recent years, however, empirical studies have mushroomed. A variety of data has been shown to follow a
Benford distribution including, among others, aggregated data reported to American (Nigrini, 1996) and Italian (Mir, et al,
2014) taxing agencies, prices in various stock markets (Ley, 1996) and eBay auctions (Giles 2007).2
Financial auditors now routinely check data for compliance with Benford’s Law.3 For example, McGinty (2014) relates
the results an audit of a national call center. Several hundred call center operators were authorized to issue refunds up to
fifty dollars (anything larger required the permission of a supervisor), and each operator had processed more than 10,000
refunds over several years. Auditors decided to check whether the first digit of each operator’s refunds was consistent
with Benford’s Law. For most operators, no discrepancy was discovered, but for a small group there was a large spike in
the four categories indicating that many refunds just below the fifty-dollar threshold were being issued. Further
investigation revealed that these operators had issued thousands of dollars in fraudulent refunds to themselves, family, and
friends.
Deviations from a Benford distribution are not necessarily a result of fraud. McGinty (2014a) describes another case in
which auditors ran a Benford test on three types of a client’s expense accounts. Two ended up exactly as predicted by
Benford’s Law. For the third, auto and truck expenses, nine’s were overrepresented, and one’s were underrepresented.
Further investigation, however, indicated the discrepancies were not fraudulent as many employees were simply following
company policy, which allowed them to expense gas purchases and to combine expenses if the combined amount did not
exceed $100. The price of a tank of gas had effectively eliminated one’s from the equation, and combining expenses
increased the frequency of nine’s.

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Because Benford’s Law works best with large data sets, many researchers using Benford’s Law to analyze the private
sector use data from an entire industry or groups of companies rather than focusing on a particular company; a procedure
followed in the present study. Some of these studies report small irregularities or data that conformed to the Bedford
distribution. Alali and Romero (2013) conducted tests on a variety of accounts from financial statements of American
banks that failed between October 2000 and February 2012. First, they compared the distribution of the first digit in the
accounts to Benford’s theoretical distribution. They also computed what Nigrini (1996) coined the distortion factor model
which equals the difference in the mean of the observed first two digits compared to the expected mean according to
Benford’s Law. They report no significant anomalies.
Özer and Babacan (2013) examine the first digit in annual off-balance sheet disclosures of Turkish Banks over the period
1990–2010 and report significant deviations between the distribution of the reported numbers and a Benford distribution
for only one year: 1999. Gava and Vitiello (2014) compared the distribution of the first digit of asset accounts for
fourteen Brazilian companies over the time period 1986 through 2009 to the Benford distribution. Their study period
contained periods of high and low inflation, and they found that the data from the low-inflation period fit better to
Benford’s Law than data from the high-inflation period, and suggest that high inflation increases the possibility of fraud.
Other researchers report suspicious data. Johnson (2009) used Benford’s Law to analyze the first digit of quarterly net
income and earnings per share data for twenty-four randomly selected publicly traded American companies for fiscal
years 1999 through 2004 to identify firm characteristics that may be associated with earnings management. He identified
several firm characteristics where earnings management appeared possible because the earnings distributions were
inconsistent with Benford’s Law, including companies with low capitalization (below forty-five billion dollars),
companies with higher levels of inside trading (three percent and higher), and three companies that have been publicly
traded for less than twenty-five years. Hsieh and Lin (2013) analyzed the second digit of quarterly net income reported by
8,817 firms in the U.S. marine industry between the first quarter of 1980 and the first quarter of 2009. Finding
significantly more zeros in the second digit than would be expected in a Benford distribution, they conclude that managers
in the industry engage in managing earnings through rounding earnings numbers to achieve key reference points.
Several researchers have used Benford’s Law to scrutinize government entities. Michalski and Stoltz (2013) analyzed
data from 1989 through 2007, and they concluded that some countries strategically provide manipulated financial data to
economic agents. They observed non-Benford distributions for the first digits of data issued by groups of countries that
are more vulnerable to high capital outflows, have fixed exchange rate regimes, have the highest levels of net
indebtedness, and those that were running current account deficits. In addition, they report rejection of the Benford
distribution for the first digits of the balance of payments statistics for euro-adopting countries after these countries joined
the euro zone.
Johnson and Weggenmann (2013) subjected the first digits in a small set of American state government data to Benford’s
Law. The accounts for each of the fifty states examined were: 1) total general revenues of the primary government; 2)
total fund balance of the general fund; and 3) total fund balance of governmental funds; all of which are often used as
benchmarks in financial analysis. Most authorities (e.g., Durtschi, et al., [2004]) agree that Benford’s Law is most
effective when applied to large data sets, but in the Johnson and Weggenmann study, only three (unidentified) years of
data were collected, yielding 150 data points for each state/balance. The authors report distributions in conformity with
Benford’s Law for the first two accounts, but nonconformity for the total fund balance of governmental funds.
de Freitas Costa, et al., (2012) analyzed 134,281 contracts issued by twenty management units in two Brazilian states and
discovered significant deviations in the distribution of the first and second digits from the distribution predicted by
Benford’s Law. The first digit of the contract data contained an excess amount of the numbers seven and eight, while nine
and six were rare occurrences, which the authors assert denoted a tendency to avoid conducting the bidding process.
Analysis of the second digit revealed a significant excess of the numbers zero and five, which is indicative of rounding
being used in determining the value of contracts.
Given recent events, it is interesting to note that Müller (2011) used Benford’s Law to conclude that the macroeconomic
data the Greek government reported to the European Union before entering the Eurozone was probably fraudulent, albeit
years after the country joined.

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REIT Earnings Management
REITs provide an interesting venue for the study of earnings management. Like firms in other industries, REITs can
manage earnings through accruals earnings management and/or by real activities earnings management. Accruals
earnings management is accomplished by choosing different accounting methods (e.g., depreciation), which do not alter
the REITs’ economic activities nor have any direct cash flow consequences, to disguise true profitability. Real activities
earnings management occurs when REITs depart from normal operational practices with the intent to mislead at least
some stakeholders into believing certain financial goals have been met in the normal course of operations. Manipulation
of real activities normally has direct cash flow consequences (e.g., cutting discretionary expenditures such as maintenance
or selling real properties).
After analyzing data for over 8,000 nonfinancial firms in the Compustat annual industrial and research files for the period
1987–2005, Cohen et al., (2008) observed that accruals earnings management increased from 1987 until the Sarbanes-
Oxley (SOX) legislation was enacted in 2002. Since then, they note that a decline in accrual earnings management that
appears to have been accompanied by an increase in (harder to detect) real activities manipulation. This finding is
consistent with the results presented by Zang (2011) who concludes that when a firm is subject to more regulatory
scrutiny and/or its’ financial reporting policies are more transparent, managers tend to substitute real activities
management for accruals management.
Previous studies report that REITs have engaged in earnings management. One possible motivation for manipulating
earnings is the desire to reduce the cost of obtaining external financing. If security issuers can increase reported earnings,
they can improve the terms on which securities are sold to the public. A higher security price benefits the firm because,
for a given issue size, the issuer receives more money, or for a given amount of new equity funding there will be less
ownership dilution. Zhu et al., (2010) used regression analysis to analyze quarterly data including discretionary accruals
and Funds from Operations (FFO) from 140 REITs over the period 2001 through 2006. They found that manipulation of
both accruals and FFO occurred in their sample, with FFO being manipulated more, and up to three quarters prior to the
financing. The authors also concluded that REITs with deteriorating cash flow and frequent SEO have more FFO
manipulation. In addition, they report that REITs with lower external auditor quality and institutional holdings are more
likely to engage in earnings management. Interestingly, they found FFO manipulation decreased over the study period as
both the regulatory environment and corporate governance inside REITs strengthened. In contrast, no clear trend was
discovered for management of discretionary accruals, and the effect of the SOX Act on earnings management was not
obvious when only equity-issuing REITs were considered.
Other recent studies report additional evidence of REIT earnings management. Ben-Shahar et al., (2011) analyzed
financial data from ninety-six REITs for the years 2001–2008. They conclude that FFO has superior information content
because, unlike net income, FFO excludes depreciation, which their analysis indicated was subject to manipulation.
Anglin, et al., (2013) analyzed data from sixty-eight equity REITs over the years 2004 through 2008. They found that
corporate governance quality is unrelated to accruals earnings management and manipulation of FFO, but report
significant, less visible, real activities manipulation for earnings management purposes.
Inflated earnings management is the more common issue investigated by researchers, but some REITs may be motivated
to manipulate taxable income downward. REITs face strong binding constraints regarding the use of internal funds as the
tax code specifies that to avoid Federal income tax, a REIT must pay out at least ninety percent of (what would be)
taxable income as dividends. This constraint forces REITs to access external sources to fund capital investments, but a
REIT can increase its retained earnings and lower its need for external funds by lowering taxable income. Empirical
evidence of this practice is presented by Ambrose and Bian (2010) who employed regression analysis to investigate both
accruals and real activities management using data from 104 REITs for the years 1999 through 2006. They concluded
that REITs employ both types of earning-reducing manipulations to lower taxable income and the amount of dividends
that must be paid to meet the regulatory requirement. Another motivation for REITs to manage earnings would be to
smooth income during burgeoning real estate markets; although this motivation is untested to date.
Despite the relatively transparent reporting requirements faced by REITs, the studies described above indicate that
earnings management has occurred with some regularity in the REIT industry. And this practice has continued since
passage of the 2002 SOX Act. Note that all but one of the REIT studies mentioned above examined data that straddled
passage of the SOX and one was limited to post SOX data. However, it seems plausible that detecting REIT industry-

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wide earnings management with a Benford test may be problematic if some REITs are managing earnings downward
while others are managing them upward.
Data and Methodology
REITs listed on either the New York Stock Exchange (NYSE) or NASDAQ were identified by examining the REIT
Directory at NAREIT.com.4 Data for each REIT was obtained from their unaudited quarterly Statements of
Comprehensive Income contained in their 10-Q filings with the Securities and Exchange Commission for the years 2009
through 2014. The 183 REITs in our sample consist of 141 equity REITS and twenty-six mortgage REITs listed on the
NYSE, as well as fourteen equity REITs and two mortgage REITs listed on NASDAQ.
Several measures of REIT operating performance might serve as the variable of interest in a Benford test. Because
authorities (e.g., Phatarfod, 2013) have pointed out that goodness of fit tests tend to become insignificant with small
samples, an important consideration in selecting a performance measure was that it would preserve observations. FFO is
the industry standard in determining REIT profitability, but its value in this case is limited because it is not defined by
generally accepted accounting principles (GAAP), and is not included in 10-Q filings.5 Net operating income from
continuing operations, and net income attributable to common shareholders are two other widely used REIT profitability
measures.6 Two problems with the former are: 1) that it is not defined by GAAP; and 2) its use here would preclude the
inclusion of almost all mortgage REITs because they (and some equity REITs) do not report net operating income from
continuing operations. Net income attributable to common shareholders is defined by GAAP, but its use would eliminate
a substantial number of observations as many REITs do not report this measure in their quarterly reports. To overcome
these difficulties, net income, which all REITs report, is used as our variable of interest.7
The 183 REITs in our sample present a potential 3,294 observations for study, but 360 observations were lost because
some of the REITs were not in operation for the full study period. In addition, because accounting authorities (e.g.,
Nigrini, 2011) suggest that tests of Benford’s Law should be conducted on either positive numbers or negative numbers,
but not both in the same analysis, we elect to focus on positive valued observations, and, therefore, 686 observations with
negative values were eliminated from the database. This reduced the number of observations in the final sample to 2,248.
Following the precedent of previous researchers, we limit our investigation to the first and second digits of the variable of
interest and strip the numbers in each of these places from each observation.
Using the entire sample, the proportion of all observations accounted for by each number in the first digit of net income
was calculated and the distribution of these proportions was tested for goodness of fit to the Benford’s distribution by
calculating the sample distributions mean absolute deviation (MAD). The same methodology was then followed for the
second digit. Drake and Nigrini (2000) assert that MAD provides for a more precise analysis than simply examining the
individual differences in the sample distribution with Benford’s distribution. MAD is defined by Equation (4) as:
= 
 

 || (4)
where N is the total possible numbers that may occur as the digit of interest (i.e., nine for the first digit and ten for the
second and all subsequent digits), xi is the proportion of the sample accounted for by each number (i) in N, and x
̄ is
proportion of the sample that i should represent according to Benford’s Law. The critical values in Table II were
developed by Drake and Nigrini (2000) to assess how well a sample distribution fits the Benford distribution for first and
second digits using MAD.
Finally, to observe the effect of reduced sample size on the level of conformity with a Benford’s distribution, the above
described methodology is applied to subsamples of the data. For this purpose, the data was arbitrarily grouped based
upon: 1) where the REIT shares are traded; and 2) whether the REIT is classified as an equity or mortgage REIT.
Table II: Mean Absolute Deviation Critical Values for First and Second Digits
Goodness of Fit First Digit Second Digit
Close Conformity 0.000 – 0.004 0.000 – 0.008
Acceptable Conformity 0.004 – 0.008 0.008 – 0.012
Marginally Acceptable Conformity 0.008 – 0.012 0.012 – 0.016
Nonconformity > 0.012 > 0.016
Source: Drake and Nigrini (2000)

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Results
Comparison of the Mean Absolute Deviations for the full sample, shown on the last line of Table III, with the critical
MAD values presented in Table II indicates that the distribution of the first digit of REIT quarterly net income is in
marginally acceptable conformity with Benford’s Law, while the second digit is in close conformity.
Table III: Mean Absolute Deviation: Full Sample
Comparison of the MAD values shown in the upper panels of Table IV and V with the critical values shown in Table II
will reveal similar results were discovered for REITS traded on the NYSE and those classified as an equity REIT (i.e.,
marginally acceptable conformity for the first digit and close conformity for the second digit). Comparison of the MAD
values shown in the lower panel of Table IV with the critical values shown in Table II indicates that while the distribution
of the second digit of net income for REITs traded on the NASDAQ system are in close conformity with Benford’s Law,
the first digit is in nonconformity. Finally, comparison of the MAD values shown in the lower panel of Table V with the
critical values shown in Table II indicates that the distribution of the second digit of net income for mortgage REITs are in
marginally acceptable conformity with Benford’s Law, but the distribution of the first digit for these REITs is in
nonconformity.
Table IV: Mean Absolute Deviation by Exchange Listing
NYSE REITs
1st
Digit
2nd
Digit
Number # of Obs. % of Obs.
Predicted
Proportion Absolute
Difference # of Obs. % of Obs.
Predicted
Proportion
Absolute
Difference
0
249
0.11835
0.11968
0.00133
1
605
0.28755
0.30103
0.01348
254
0.12072
0.11389
0.00683
2
404
0.19202
0.17609
0.01593
215
0.10219
0.10882
0.00663
3
272
0.12928
0.12494
0.00434
234
0.11122
0.10433
0.00689
4
224
0.10646
0.09691
0.00955
215
0.10219
0.10031
0.00188
5
190
0.0903
0.07918
0.01112
208
0.09886
0.09668
0.00218
1st
Digit
2nd
Digit
Number # of Obs. % of Obs.
Predicted
Proportion Absolute
Difference # of Obs. % of Obs. Predicted
Proportion
Absolute
Difference
0
270
0.12011
0.11968
0.00043
1
660
0.29359
0.30103
0.00744
266
0.11833
0.11389
0.00444
2
429
0.19084
0.17609
0.01475
235
0.10454
0.10882
0.00428
3
289
0.12856
0.12494
0.00362
248
0.11032
0.10433
0.00599
4
245
0.10899
0.09691
0.01208
229
0.10187
0.10031
0.00156
5
197
0.08763
0.07918
0.00845
224
0.09964
0.09668
0.00296
6
123
0.05472
0.06695
0.01223
212
0.09431
0.09337
0.00094
7
113
0.05027
0.05799
0.00772
205
0.09119
0.09035
0.00084
8
113
0.05027
0.05115
0.00088
174
0.0774
0.08757
0.01017
9
79
0.03514
0.04576
0.01062
185
0.0823
0.08500
0.00270
Total
2248
1.00000
1.00000
0.07779
2248
1.0000
1.0000
0.03431
MAD
0.00864
0.00343

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6
117
0.05561
0.06695
0.01134
202
0.09601
0.09337
0.00264
7
109
0.05181
0.05799
0.00618
190
0.09030
0.09035
0.00005
8
107
0.05086
0.05115
0.00029
162
0.07700
0.08757
0.01057
9
76
0.03612
0.04576
0.00964
175
0.08317
0.08500
0.00183
Total
2104
1.00000
1.00000
0.08188
2104
1.00000
1.00000
0.04082
MAD
0.00910
0.00408
NASDAQ REITs
1st
Digit
2nd
Digit
Number # of Obs. % of Obs.
Predicted
Proportion Absolute
Difference # of Obs. % of Obs.
Predicted
Proportion
Absolute
Difference
0
21
0.14583
0.11968
0.02615
1
55
0.38194
0.30103
0.08091
12
0.08333
0.11389
0.03056
2
25
0.17361
0.17609
0.00248
20
0.13889
0.10882
0.03007
3
17
0.11806
0.12494
0.00688
14
0.09722
0.10433
0.00711
4
21
0.14583
0.09691
0.04892
14
0.09722
0.10031
0.00309
5
7
0.04861
0.07918
0.03057
16
0.11111
0.09668
0.01443
6
6
0.04167
0.06695
0.02528
10
0.06944
0.09337
0.02393
7
4
0.02778
0.05799
0.03021
15
0.10417
0.09035
0.01382
8
6
0.04167
0.05115
0.00948
12
0.08333
0.08757
0.00424
9
3
0.02083
0.04576
0.02493
10
0.06944
0.08500
0.01556
Total
144
1.00000
1.00000
0.25968
144
1.00000
1.00000
0.16894
MAD
0.02885
0.00169
Table V: Mean Absolute Deviation by REIT Classification
Equity REITs
1st
Digit
2nd
Digit
Number # of Obs. % of Obs. Predicted
Proportion Absolute
Difference # of Obs. % of Obs. Predicted
Proportion
Absolute
Difference
0
229
0.11921
0.11968
0.00047
1
563
0.29308
0.30103
0.00795
238
0.12389
0.11389
0.01000
2
381
0.19833
0.17609
0.02224
191
0.09943
0.10882
0.00939
3
249
0.12962
0.12494
0.00468
206
0.10724
0.10433
0.00291
4
216
0.11244
0.09691
0.01553
190
0.09891
0.10031
0.00140
5
169
0.08798
0.07918
0.00880
201
0.10463
0.09668
0.00795
6
99
0.05154
0.06695
0.01541
186
0.09682
0.09337
0.00345
7
86
0.04477
0.05799
0.01322
176
0.09162
0.09035
-0.00127
8
88
0.04581
0.05115
0.00534
146
0.076
0.08757
0.01157

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9
70
0.03644
0.04576
0.00932
158
0.08225
0.08500
0.00275
Total
1921
1.00000
1.00000
0.10250
1921
1.00000
1.00000
0.04863
MAD
0.01139
0.00486
Mortgage REITs
1st
Digit
2nd
Digit
Number # of Obs. % of Obs. Predicted
Proportion Absolute
Difference # of Obs. % of Obs.
Predicted
Proportion
Absolute
Difference
0
41
0.12538
0.11968
0.00570
1
97
0.29664
0.30103
0.00439
28
0.08563
0.11389
0.02826
2
48
0.14679
0.17609
0.02930
44
0.13456
0.10882
0.02574
3
40
0.12232
0.12494
0.00262
42
0.12844
0.10433
0.02411
4
29
0.08869
0.09691
0.00822
39
0.11927
0.10031
0.01896
5
28
0.08563
0.07918
0.00645
23
0.07034
0.09668
0.02634
6
24
0.07339
0.06695
0.00644
26
0.07951
0.09337
0.01386
7
27
0.08257
0.05799
0.02458
29
0.08869
0.09035
0.00166
8
25
0.07645
0.05115
0.02530
28
0.08563
0.08757
0.00194
9
9
0.02752
0.04576
0.01824
27
0.08257
0.08500
0.00243
Total
327
1.00000
1.00000
0.12555
327
1.00000
1.00000
0.14901
MAD
0.01395
0.01490
Summary and Conclusions
Benford’s Law holds that naturally occurring numbers tend to follow a logarithmic distribution such that numbers
beginning with smaller digits appear more frequently than those beginning with larger ones. Manipulated data, on the
other hand, does not usually conform to a Benford distribution. Thus, Benford’s Law has been used to identify suspicious
data in a variety of settings. One researcher, for example, that analyzed the first digit of net income and earnings per share
from a group of randomly selected American companies reported several characteristics that may be associated with
earnings management. Another researcher analyzed the second digit of quarterly net income reported by firms in the U.S.
marine industry and concluded that managers in the industry manage earnings through rounding earnings numbers to
achieve key reference points. Neither of these issues is discovered for the full sample examined here even though
previous studies indicate that earnings management has been commonplace within the REIT industry. Using a sample of
2,248 observations of unaudited quarterly net income collected from 183 REITs over the six-year period 2009 through
2014, it is discovered that the distribution of the first digit is in marginally acceptable conformity to the distribution
predicted by Benford’s Law, while the distribution of the second digit closely conforms.
The above results are consistent with the possibility that REITs did not engage in earnings management during our study
period, or that they reduced it to a level that was undetectable by a Benford test. The ability of REIT managers to practice
earnings management may have been limited by additional scrutiny due to SOX, and a lack of balance sheet bloat as
suggested by Copeland (1968). In addition, Strobl (2013) suggests that managers have lower incentives to engage in
upward earnings manipulation during times when their performance cannot be explained by general market trends, which
suggests that REITs may have limited earnings management during the sample period.
The above results are also consistent with the assertion of some critics that Benford’s Law lacks power as a diagnostic
tool. Possibly, during the study period REITs employed a less detectable form of earnings management. This theory
seems a real possibility if REITs continued the earlier trend noted by Cohen et al., (2008) of substituting real activities
earnings management for accrual earnings management. Similarly, the observation of Zang (2011) that firms subject to

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more regulatory scrutiny tend to substitute real activities management for accruals management seems applicable in the
post SOX era. Another factor that may cause the Benford test to result in a false negative is the possibility that the
earnings management activities of some REITs offset the earnings management activities of others (i.e., while some
REITS manage earnings upward to achieve certain financial objectives, others are managing earnings downward to
conserve retained earnings or to smooth income.
Grouping the data based on the exchange on which the REIT’s shares were traded provided results similar to those
obtained for the full sample for the 2,104 observations from the NYSE, but for the 144 observations that occurred on the
NASDAQ the distribution of the first digit did not conform to a Benford’s distribution. Interestingly, the second digit was
found to be in close conformity despite the fact that both zero’s and five’s were overrepresented (which previous studies
have suggested is a sign that rounding may have occurred). When the data was grouped based upon REIT classification,
the results for the 1,921 equity REITs were like those for the full sample, but for the 327 mortgage REITs, the distribution
of the second digit conformed only marginally acceptable and the first digit did not conform to a Benford distribution.
Whether the poor first-digit conformity for mortgage REITs and those traded on the NASDAQ is a true indication of
suspicious data is debatable, however, because of the relatively small number of observations for both groups. Even
supporters of Benford’s Law acknowledge that the level of conformity to a Benford’s distribution and sample size are
positively related. Diekmann and Jann (2010), however, question this type of result and refer to it as a circularity
problem; how can a sample that conforms to a Benford’s distribution consist of subsamples that do not?
When employing Benford testing, financial auditors recommend focusing on an accounting measure that is subject to
Generally Accepted Accounting Principles (GAAP) because they are concerned with discovering GAAP violations. Net
income, which was the focus of our study, is subject to GAAP, but the industry standard of profitability in the REIT
industry, FFO, is not. We believe that an interesting extension of this initial research would be to investigate whether tests
of Benford’s Law detect earnings management behavior by REIT managers on FFO.
Endnotes
1. Earnings management is the manipulation of accounting numbers within the scope of GAAP. Jackson and Pitman
(2001) provide three definitions of earnings management: 1) the purposeful intervention in the external financial
reporting process with the intent of obtaining some private gain; 2) an intentional structuring of reporting or
production/investment decisions around the bottom line impact; and 3) the use of judgment in financial reporting
and in structuring transactions to alter financial reports to either mislead some stakeholders about the underlying
economic performance of the firm, or to influence contractual outcomes.
2. Nigrini (1996) results provide evidence that conformity with a Benford distribution does not guarantee problem-
free data. He reported that aggregate data submitted on income tax returns to the United States Internal Revenue
Service closely conformed to a Benford distribution, yet cases of tax evasion are a regular occurrence.
3. Financial auditors use computer aided audit techniques such as the Audit Command Language and CaseWare
IDEA to assist in evaluating large data sets for unusual amounts, relationships, and frequencies. Embedded in
these data extraction software is a profile of digit placement probabilities based on Benford’s Law. Company
data which falls outside the Benford profile can offer helpful information to auditors in their preliminary
assessment of the financial statements.
4. https://www.reit.com/investing/investing-tools/reit-directory/searchable-directory
5. FFO equals net income plus depreciation and amortization of expenses less gains (or plus losses) on the
disposition of property. Authorities on Benford’s Law suggest that it is best to use an accounting measure that is
subject GAAP when employing Benford testing, but we believe an interesting extension of this research thread
could focus on FFO.
6. The following definitions are provided in the SECs interactive 10-Q. Net operating income from continuing
operations is the amount of income (loss) from continuing operations attributable to the parent. Net operating
income from continuing operations is also defined as revenue less expenses and taxes from ongoing operations
before extraordinary items, but after deduction of those portions of income or loss from continuing operations that
are allocable to noncontrolling interests. Net income attributable to common shareholders is the amount after tax
of other comprehensive income (loss) attributable to the parent entity.

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7. Net income is defined on the SECs interactive 10-Q as the portion of profit or loss for the period, net of income
taxes, which is attributable to the parent. Some REITs refer to this as consolidated net income.

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References
Alali, F. and S. Romero. (2013). Characteristics of failed U.S. commercial banks: An exploratory study. Accounting &
Finance, 53:4, 1149–1174.
Ambrose, B. W. and X. Bian. (2010). Stock market information and REIT earnings management. Journal of Real Estate
Research, 32:1, 101–137.
Anglin, P., R. Edelstein, Y. Gao, and D. Tsang. (2013). What is the relationship between REIT governance and earnings
management? Journal of Real Estate Finance & Economics, 47:3, 538–563.
Ben-Shahar, D., E. Sulganik, and D. Tsang. (2011). Funds from operations versus net income: examining the dividend
relevance of REIT performance measures. Journal of Real Estate Research, 33:3, 415–441.
Benford, F. (1938). The law of anomalous numbers. Proceedings of the American Philosophy Society, 78, 551–572.
Cohen, D. A., A. Dey, and T. Z. Lys. (2008). Real and accrual-based earnings management in the pre- and post-SOX
periods. The Accounting Review, 83:3, 757–787.
Copeland, R.M. (1968). Income smoothing, Journal of Accounting Research, 6:3, 101–116.
de Freitas Costa, J. I., J. dos Santos, and S. K. de Melo Travassos. (2012). An analysis of federal entities' compliance with
public spending: Applying the Newcomb-Benford law to the first and second digits of spending in two Brazilian
states. Revista Contabilidade & Finanças - USP, 23:60, 187–198.
Diekmann, A. and B. Jann. (2010). Benford's Law and fraud detection: Facts and legends. German Economic Review,
11:3, 397–401.
Drake, P. D. and M. J. Nigrini. (2000). Computer assisted analytical procedures using Benford’s law. Journal of
Accounting Education, 18:2, 127–146.
Durtschi, C. W. Hillison, and C. Pacini. (2004). The effective use of Benford’s law to assist in detecting fraud in
accounting data. Journal of Forensic Accounting, V, 17–34.
Gava, A. M. and L. Vitiello. (2014). Inflation, quarterly balance sheets and the possibility of fraud: Benford's law and the
Brazilian case. Journal of Accounting, Business and Management, 21:1, 43–52.
Giles, D. A. E. (2007). Benford's law and naturally occurring prices in certain eBay auctions. Applied Economics Letters,
14:3, 157–161.
Hsieh, C. H. and F. Lin. (2013). Applying digital analysis to detect fraud: An empirical analysis of U.S. marine industry.
Applied Economics, 45:1, 135–140.
Jackson, S. B. and M. K. Pitman. (2001). Auditors and earnings management. CPA Journal, 71:7, 39–44.
Johnson, G. (2009). Using Benford's law to determine if selected company characteristics are red flags for earnings
management. Journal of Forensic Studies in Accounting & Business, 1:2, 39–65.
Johnson, G. and J. Weggenmann. (2013). Exploratory research applying Benford's law to selected balances in the
financial statements of state governments. Academy of Accounting and Financial Studies Journal, 17:3, 31–44.
Kumar, K. and S. Bhattacharya. (2007). Detecting the dubious digits: Benford’s law in forensic accounting. Significance,
4:2, 81–83.
Ley, E. (1996). On the peculiar distribution of the U.S. stock indexes’ digits. The American Statistician, 50:4, 311–313.
McGinty, J. C. (2014). Accountants increasingly use data analysis to catch fraud: Auditors wield mathematical weapons
to detect cheating. WSJ.com. Retrieved on 1/6/2015 from http://www.wsj.com/articles/accountants-increasingly-
use-data-analysis-to-catch-fraud-1417804886
McGinty, J. C. (2014a). When using math to catch crooks, you can’t jump to conclusions. WSJ.com. Retrieved on
1/6/2015 from http://blogs.wsj.com/numbers/when-using-math-to-catch-crooks-you-cant-jump-to-conclusions-
1870/

Journal of Forensic & Investigative Accounting
Volume 9: Issue 2, July–December, 2017
790
Michalski, T. and G. Stoltz. (2013). Do countries falsify economic data strategically? Some Evidence That They Might.
The Review of Economics and Statistics, 95:2, 591–616.
Mir, T., M. Ausloos and R. Cerqueti. (2014). Benford's law predicted digit distribution of aggregated income taxes: the
surprising conformity of Italian cities and regions. European Physical Journal B -- Condensed Matter, 87:11, 1–8.
Müller, H. C. (2011). Greece was lying about its budget numbers. Forbes, September 12, 2011.
Newcomb, S. (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of
Mathematics, 4, 39–40.
Nigrini, M. J. (1996). Taxpayer compliance application of Benford’s law. Journal of the American Taxation Association,
18:1, 72–92.
Nigrini, M. J. (2011). Forensic analytics: Methods and techniques for forensic accounting investigations. John Wiley &
Sons, Hoboken, New Jersey.
Özer, G. and B. Babacan. (2013). Benford's law and digital analysis: Application on Turkish banking sector. Business and
Economics Research Journal, 4:1, 29–41.
Phatarfod, R. (2013). Some aspects of the Benford law of leading significant digits, Mathematical Scientist, 38:2, 73–85.
Strobl, G. (2013). Earnings manipulation and the cost of capital, Journal of Accounting Research. 51:2, 449–473.
Varian, H. (1972). Benford's law. The American Statistician, 23, 65–66.
Zang, A. (2012). Evidence on the tradeoff between real activities manipulation and accrual-based earnings management.
The Accounting Review, 87:2, 675–703.
Zhu, Y., S. Ong and W. Yeo. (2010). Do REITs manipulate their financial results around seasoned equity offerings?
Evidence from US equity REITs, Journal of Real Estate Finance & Economics, 40:4, 412–445.