Detecting Target‐Driven Earnings Management Based on the Distribution of Digits

• Published date: 01 January 2017
• Date: 01 January 2017
• DOI: http://doi.org/10.1111/jbfa.12223

Journal of Business Finance & Accounting

Journal of Business Finance & Accounting, 44(1) & (2), 63–93, January/February 2017, 0306-686X

doi: 10.1111/jbfa.12223

Detecting Target-Driven Earnings

Management Based on the Distribution

of Digits

Robert Ullmann∗and Christoph Watrin

Abstract: We present a novel research design to detect target-driven earnings management

in accounting data. As a particular concern in this line of research, information about the

exact earnings target value of a given firm is often not available. We therefore develop an

empirical strategy that does not require such information. To this end, we rely on the concept

of the distribution of digits rather than the distribution of the earnings metric itself. We

then theoretically derive that the mean of the distribution of digits, in particular, exhibits a

specific pattern around the earnings target that can be exploited to investigate target-driven

earnings management. This pattern arises regardless of the distribution of digits that obtains

in unmanaged data. We extensively test our theoretical predictions using both simulated and

archival data.

Keywords: distribution of digits, target-driven earnings management, Benford’s Law

1. INTRODUCTION

The measurement of cross-sectional differences in earnings management continues

to be one of the most relevant issues in accounting research (Jorgensen et al.,

2014). Within this subject area, one important line of research focuses on earnings

management activity intended to meet (or exceed) a given earnings target. Target-

beating is a specific dimension of earnings quality and, consequently, requires its

own proxies (Dechow et al., 2010). Previous research in this area largely focuses on

three distinct earnings targets, namely (i) zero earnings, (ii) previous-period earnings,

and (iii) analysts’ forecasts (Dechow et al., 2010). However, numerous alternative (yet

unobservable) earnings targets exist.

We develop a research design that allows the investigation of target-driven earnings

management in accounting data when information concerning relevant earnings

target values is not available. To this end, we rely on a concept that is well established

∗The first author is from the Institute for Taxation, Cluster Finance & Information, University of Augsburg,

Universit¨

atsstr. 16, 86159 Augsburg, Germany.The second author is from the Institute for Accounting and

Taxation,Westf¨

alische Wilhelms-University, Universit¨

atsstr.14-16, 48143 M ¨

unster,Germany. (Paper received

December 2013, revised revision accepted September 2016).

Address for correspondence: Robert Ullmann, Faculty of Business and Economics, University of Augsburg,

Universit¨

atsstr. 16, 86159 Augsburg, Germany.

e-mail: Robert.Ullmann@wiwi.uni-augsburg.de

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2016 The Authors Journal of Business Finance & Accounting Published by John Wiley & Sons Ltd 63

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which

permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not

used for commercial purposes.

64 ULLMANN AND WATRIN

in previous research on target-driven earnings management – although not among

the most common measures – namely, the distribution of digits (e.g., Bhattacharya et al.,

2010). The distribution of digits draws inferences not from the total value of a certain

metric but instead from its numerical structure, i.e., the frequency of occurrence and the

exact sequence of the digits ‘0’ to ‘9’ in the mantissa.

As a more technical aspect, previous research has relied on, as a benchmark, a

certain set of theoretically derived distributions of digits that might be expected to

obtain in accounting data in the absence of any earnings management (most notably,

Benford’s Law) – even though empirical evidence on the validity of such an approach

is limited (e.g., Watrin et al., 2008). To the contrary, our empirical strategy does not

rely on any theoretically derived distribution of digits. This advancement is made

possible through the identification of a pattern in the mean of the distribution of

digits in managed earnings that obtains regardless of the underlying distribution

of digits in unmanaged earnings. This then enables reliance on relative comparisons

of the distributions of digits between two or more groups of firms. We recognize that

the advantage of not relying on a theoretically derived distribution of digits trades off

against the requirement that data on at least two groups of firms must be available to

the researcher. We argue that such a data requirement does not limit the applicability

of our research design in practice, as most earnings management studies are already

based on relative comparisons, with group allocations based on, for instance, listing

status (e.g., Dechow et al., 2010), country of residence (e.g., Burgstahler et al., 2006)

or periods of time (e.g., before and after the US 1986 Tax Reform Act, Shackelford

and Shevlin, 2001).

We contribute in three ways. First, testing of target-driven earnings management

is facilitated in settings that are not accessible with current methods. Specifically, our

research design is applicable when information on earnings targets cannot be obtained

and, moreover, even when the above-mentioned theoretically derived distributions of

digits are suspected to be invalid in unmanaged data. It can even be applied when

all groups under investigation manage earnings to a different degree. Second, our

research design has low data requirements and thus low implicit costs of inference

testing. Notably, it is applicable in simple cross-sectional analyses, whereas most other

earnings management measures require panel data. Along the same lines, we require

availability of only the earnings metric directly affected by target-driven earnings

management. Building on these features, researchers can pool more firms into their

samples with our research design than with designs that have more rigorous data

requirements. Finally, we report superior statistical characteristics. To this end, we

first note that the research design can be easily implemented and interpreted –

once developed and well understood – as programming and inferential analysis are

nearly trivial. More importantly, we report that our research design has higher power

in small samples relative to the most closely related method developed in Carslaw

(1988).

The paper proceeds as follows: Section 2 summarizes the relevant research in

target-driven earnings management. We distinguish between research on observable

earnings targets (i.e., zero earnings, previous-year earnings, analysts’ forecasts) and

research on non-observable earnings targets, where the latter relates to previous

work on the distribution of digits. Section 3 combines these two research streams

to develop our novel empirical strategy from a theoretical perspective. In this

regard, we also elaborate on the general concept of the distribution of digits. In

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2016 The Authors Journal of Business Finance & Accounting Published by John Wiley & Sons Ltd