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Inference of economic truth from financial statements for detecting earnings management: inventory costing methods from an information economics perspective
Hemantha S.B. Herath | Xiaoting Lu
Department of Accounting, Goodman School
of Business, Brock University, St. Catharines,
Ontario, Canada
Correspondence
Hemantha S. B. Herath, Department of
Accounting, Goodman School of Business,
Brock University, Taro Hall 240, 500 Glenridge
Avenue, St. Catharines, Ontario L2S 3A1,
Canada.
Email: [email protected]; hemantha.
Funding information
Social Sciences and Humanities Research
Council (SSHRC), Grant/Award Number: 410‐ 2009‐1398
We introduce uncertainty in the classic inventory costing choice problem to investigate the
underlying partitions imposed by two accounting inquiries (processes of generating information):
variable costing and absorption costing. In a contemporaneous reporting environment, we show
that absorption costing provides a finer partition of the state space compared to variable costing
when a firm arbitrarily increases the production level (opportunistic overproduction), and the
predetermined fixed overhead rate is adjusted. Grounded in an information economics perspec-
tive, the intent of the article is to propose an approach to detect real earnings management by
extracting information from financial statements. The resulting managerial biases arising from
earnings management are also discussed.
1 | INTRODUCTION
How accounting as an information system can convey information is the
focus of accounting research in information economics. More specifi-
cally, attempts to understand how much and what information is con-
veyed are the prime objective. In this regard, ranking of information
systems is an important topic within information economics. The design
of accounting information systems is a complex task. Nevertheless, in
this article, we consider a specific subproblem, the classic inventory
costing choice problem of absorption costing verses variable costing
to understand how the choice of an accounting method changes the
characteristic of the accounting system. The overarching theme of the
article is to raise awareness that accounting is an information science.
Fellingham (2015) adopts the view that accounting is an informa-
tion science, and he uses carefully crafted information theorems to
show that double entry systems are distinct and a valuable contribu-
tion to information science. He refers to the mutual information theo-
rem as the fundamental theorem of accounting and shows that it
establishes the operational equivalence of accounting and information
science. Consequently, as Fellingham (2015) illustrates, accounting
appears on the dollar side of the theorem's equality, and probabilities
and information science appear on the other side. Within an informa-
tion science paradigm, Arya, Fellingham, Glover, and Sivaramakrishnan
(2000) explore the connection between information system design and
the level of managerial slack during capital project implementation.
More specifically, in line with Fellingham (2015) and Arya et al.
(2000), the objective of this article is the inference of economic truth
of economic transactions from financial statements. Hence, we pro-
pose the following research question. Is there a way to detect real
earnings management by extracting information from financial state-
ments? More specifically, if one is able to compare two accounting
inquiries (the process of generating information) such as variable cost-
ing (VC) and absorption costing (AC) from an information economics
perspective, which accounting inquiry would reveal a manager engag-
ing in opportunistic production to boost earnings?
Much of the literature that investigates the choice of alternate
inventory costing methods does not incorporate uncertainty or an
information science approach in the analysis (see Black & Gray,
1995; Winsen & Stefano, 1979). If there is no uncertainty, then there
is no demand for information. As Fellingham (2015) and Christensen
and Demski (2003) emphasize, probabilities are the building blocks of
information. From an information economics perspective, when uncer-
tainty is introduced, accounting provides a mapping and an illustration
of the economics of the firm. Thus, an important function of financial
statements as an information source is that they allow users to invert
the mapping that produces the information so that the user can learn
the primitive underlying state, realization, or event (set of events; Antle
& Demski, 1989; Demski & Sappington, 1990).
In the accounting literature, compared to financial accounting
choices for earnings management (see surveys by Benson, Clarkson,
Received: 31 March 2017 Revised: 29 September 2017 Accepted: 4 December 2017
DOI: 10.1002/mde.2912
Manage Decis Econ. 2018;39:389–402. Copyright © 2017 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/mde 389
Smith, & Tuttici, 2015; Brown, Beekes, & Verhoeven, 2011; Gonedes,
1972, among others), relatively sparse attention has been given to
empirical and analytical examination of cost accounting choices that
would allow manipulation of reported earnings (Sun, Lan, & Liu,
2014; Winsen & Stefano, 1979). The reason is the difficulty in
obtaining information on actual cost accounting practices compared
with financial accounting choices that are disclosed or can be extracted
from financial statements (Winsen & Stefano, 1979). Financial
accounting choices consist of accrual earnings management, which
has no direct impact on cash flows such as using loan loss provisions,
claim loss reserves, deferred tax allowances, bad‐debt provisions, and
asset write‐offs (Healy & Wahlen, 1999; Roychowdhury, 2006).
Dichev and Li (2013) investigate for a positive relation between
growth and the aggressiveness of accounting choices, which are purely
financial accounting.
Using a nonstochastic mathematical setup, Winsen and Stefano
(1979) show that in an absorption costing system, manipulation of
budgeted fixed manufacturing cost and normal volume1 can be used
for earnings management. If overhead allocation rates could be
adjusted frequently with production changes, managers could manipu-
late the cost of goods sold and balance sheet inventory numbers
(Horngren, Foster, Datar, & Teall, 2004). The costing method used
for external reporting (i.e., absorption costing) creates opportunities
for managers to manipulate fixed overhead allocations and manage
earnings (Black & Gray, 1995; Gupta, Pevzner, & Seethamraju, 2010;
Horngren et al., 2004; Winsen & Stefano, 1979). This is referred to
as “real earnings management” in Gupta et al. (2010). Cost accounting
choices consist of real earnings management that often impacts cash
flows. Real earnings management consists of choices such as overpro-
duction, reduction in research and development expenditures, product
price reductions to increase sales, and reduction in discretionary
expenditures, and it entails allocation of resources (Gupta et al.,
2010; Healy & Wahlen, 1999; Roychowdhury, 2006).
In this article, following Christensen and Demski (2003), we intro-
duce uncertainty in the classic inventory costing choice problem
discussed in management accounting textbooks to investigate the
underlying partitions imposed by two inventory costing choices or
accounting inquiries: VC and AC. The costing choices relate to the
costs that are recorded as inventory assets. Assuming a contempora-
neous reporting setting, we show that absorption costing provides a
finer partition of the state space compared with variable costing when
a firm increases the production level in each period and adjusts the
predetermined fixed overhead rate (opportunistic overproduction). If
the production is increased arbitrarily, then production volume vari-
ance is random. In all other instances, absorption costing and variable
costing provide the same underlying partition of the state space. Our
results indicate that absorption costing provides better information
than variable costing from an information economics perspective, as
it provides a finer partition. This allows users to learn what the under-
lying primitive state is.
The analysis of the inventory choice problem under uncertainty is
a contribution to the accounting literature two ways. First, the article
proposes a methodology to detect earnings management by extracting
information from financial statements. More specifically, it enhances
our understanding of accounting as an information science that is
emphasized in Fellingham (2015). Second, in a recent article focusing
on real earnings management, Gupta et al. (2010) investigate the mar-
ket valuation implications of absorption costing and production deci-
sions by firms. Consequently, our paper contributes to the earnings
management literature by presenting an approach for detecting inven-
tory overproduction aimed at decreasing the cost of goods sold. More
specifically, we provide an alternate approach to investigate whether
managers are manipulating earnings through opportunistic inventory
management by comparing absorption costing and variable costing
methods from an information economics perspective.
2 | MOTIVATION
An important issue pertaining to accounting research is the choice of an
information system. In a seminal paper, Feltham (1968) introduced a
theoretical framework based on information economics for measuring
the value of a change in information systems. In addition, he discussed
the basic accounting concepts of relevance, timeliness, and accuracy
in light of this theoretical framework. There are two main streams of
research pertaining to the evaluation of information systems. One
stream relates to the decision theoretic structure (Blackwell, 1951),
whereas the other relates to the game structure of agency models (Arya,
Glover, & Sivaramakrishnan, 1997; Gjesdal, 1981; Grossman & Hart,
1983; Hölmstrom, 1979; Kim & Suh, 1991, among others).
Our article deals with the evaluation of accounting information
systems due to alternate inventory costing methods from a manage-
ment control perspective using the decision theoretic structure.
Feltham (1968) called for both theoretical and practical decision
models for extending ideas in information economics that are applica-
ble to accounting. More recently, an intriguing textbook by Fellingham
(2015) proposes enhancing our understanding of accounting as an
information science vis‐à‐vis scientific understanding of accounting
information. Prior research, however, focused primarily on theoretical
models. In order to fill this gap, we focus on developing a practical
management accounting decision and control model with an informa-
tion economics flavor, which is sparse in the literature.
Despite the lack of empirical support, it is widely claimed in man-
agement accounting texts that firms with high levels of manufacturing
overhead have incentives to overproduce in order to delay expensing
overhead to earnings by capitalizing it into inventory (Gupta et al.,
2010). Gupta et al. (2010) refer to such overproduction as “opportunis-
tic” overproduction as stated in Horngren et al. (2004, p. 327), such
opportunistic overproduction is possible because both the Canadian
and American generally accepted accounting principles (GAAP) man-
date the use of absorption costing, that is, the full allocation of
manufacturing overhead into units produced. As a result, manufactur-
ing overhead that is allocated to units that remain unsold at the end of
the period is not expensed; it remains on the balance sheet as part of
inventory. Consequently, the reported income for the period is higher
due to the reduction in cost of goods sold. On the other hand, had
there been no overproduction and inventory buildup, a lower income
number would have been reported. In an empirical earnings manage-
ment study, Roychowdhury (2006) provides evidence of firms over
producing to lower the cost of goods sold that supports the motivation
390 HERATH AND LU
for the proposed research. Controlling for cross‐sectional variation in a
fixed cost structure, Gupta et al. (2010) extend Roychowdhury's (2006)
findings through a well‐designed empirical investigation of absorption
costing effects on firms' earnings.
The inventory costing choice is a classic problem in management
accounting and is important to firms with high manufacturing over-
head. Kim and Suh (1991) mention it as an example along with the
choice between cash and accrual accounting in their analysis of the
stewardship role of accounting from an information economics‐based
agency framework. Kim and Suh (1991) develop a ranking criterion
based on the variance of the likelihood ratio but do not model the
specifics of the inventory costing choice problem. Our article differs
from Kim and Suh (1991), as we specifically model the unique fea-
tures of the inventory costing choice problem from an information
economics angle. More specifically, we use a decision theoretic
structure to gain insight into how information resulting from cost
accounting procedures can be used in practice for management con-
trol. Our objective is to propose an approach to detect earnings
management by extracting information from financial statements
with a view to gain insight into real earnings management actions
by high fixed‐cost firms.
3 | LITERATURE REVIEW
The applicable literature consists of information economics, account-
ing as an information science, and real earnings management, which
are discussed below.
3.1 | Information economics
The subject of economics deals with production and allocation of
resources, whereas the discipline of accounting aims to measure them
(Demski, 2008). In a broad sense, information economics deals with
how information and information systems affect economic decisions of
production and resource allocation because information plays an impor-
tant role in many economic problems. More generally, economic agents
optimize their behavior based on available information, and because all
agents do not have access to the same information set, information
asymmetries arise (Akerlof, 1970; Fudenberg & Triole, 1991, among
others). The origins of information economics can be attributed to the
general equilibrium view with perfect information, which was later
replacedbytheviewthatinformationwasimperfectandcostlytoobtain,
and information asymmetries play a fundamental role (see Frieden &
Hawkins, 2010; Stiglitz, 2000 for a detailed review). Information eco-
nomicsresearchisquitelargeandspansanumberofdisciplinesincluding
economics, accounting, and management science (Repo, 1989).
In this article, we focus primarily on the information school of
accounting research. In this school of thought, accounting is not simply
viewed as measures of resources but as information about these
resources. More specifically, this article focuses on economics of
uncertainty, and accounting forms a mapping from underlying acts
and events into real numbers (Demski, 2008). Contributors to the
accounting information school of thought include Butterworth (1972)
and Feltham (1968), among others. More broadly, opportunistic
overproduction is a resource allocation decision and is modeled in
terms of states, acts, and outcomes following Savage (1954) in the
information school setting. The acts are the choices, an outcome is
the consequence of an act, and because there is uncertainty in the out-
comes, a set of states is defined where the ambiguity (uncertainty) is
described by probabilities (or the likelihood of the states). Information
revises the probabilities and provides insight into the uncertainty, and
an information source is modeled as a partition of the set of possible
states. The states and probabilities are the foundation for modeling
uncertainty in this setup.
According to Ward, Miles, and Winterfeldt (2007), Bell, Raiffa, and
Tversky (1988) distinguish three different perspectives in the study of
decision making, namely, the normative perspective based on rational
choice as in Savage (1954), which uses probability theory and Bayesian
statistics; the descriptive perspective as in Kahneman, Slovic, and
Tversky (1982), which focuses on real people making judgments and
decisions (i.e., the prospect theory model) and captures how individ-
uals deviate from the normative model; and the prescriptive perspec-
tive that combines the normative perspective and limitations of
human judgment to ensure decisions are not affected by biases and
errors known from the descriptive approach. In the prescriptive
approach, training, tools, and debiasing techniques are used to avoid
errors and biases (Ward et al., 2007).
In information economics and other disciplines, there are situations
where uncertainty may be measured differently. In addition to using
probability as a measure of uncertainty, often variance may be used as
a measure of uncertainty. For example, if the prior or posterior probabil-
ity distribution of states describes what a decision maker knows, then
his or her uncertainty is measured using the unconditional and condi-
tional variance (Lawrence, 1999). We use both the probability assigned
to the states and the associated variances (Christensen, 2010a, 2010b)
as measures of uncertainty in this article. We use the perspective of
Christensen (2010a, 2010b), because it relates to the information
school of accounting. Another useful measure of uncertainty, though
it is not used in this article, is entropy (Lawrence, 1999). Although this
article uses probability as a measure of uncertainty, it is used from a nor-
mative perspective and assumed as a comprehensive description of
ambiguity, unlike the descriptive perspective of Hubbard (2007).
The applied decision economics approach of Hubbard (2007)
broadly defines uncertainty as the lack of certainty, limited knowledge
that makes it impossible to describe the existing state, and a future
outcome or multiple outcomes. Uncertainty is estimated using cali-
brated probability assessments as subjective assessments of probabili-
ties or confidence intervals given by individuals trained to minimize
overconfident biases (Hubbard, 2007; Kahneman et al., 1982; Slovic
& Lichtenstein, 1971). According to Hubbard (2007), calibrated individ-
uals are the most subjectively Bayesian. In order to capture uncertainty
rather than using simple averages, Hubbard (2007) recommends using
a range of values, calibrated probabilities, and Monte Carlo simulation
techniques, which are quite different from the approach used in this
article. Quantitatively analyzing uncertainty using random sampling
as in Monte Carlo simulation is also suggested in Myerson (2005).
In a series of recent articles, Christensen (2010a, 2010b) provides
an elegant conceptual foundation for accounting from an information
economics perspective. Christensen (2010a) argues that accounting
HERATH AND LU 391
should be viewed as an information system and that errors are the car-
riers of information according to Bayes' Theorem. As Christensen
(2010a, p. 1828) states: “Most of these errors originate from the dis-
crepancy between the accounting model and the underlying econom-
ics of the firm.” Consequently, accounting should pay more attention
to errors because errors are essential for updating beliefs. He empha-
sizes that accountants need to look beyond the mean (value) and also
focus on the variance of accounting numbers, because both are equally
important. Christensen (2010a) also discusses how both the financial
accounting system and the cost/managerial accounting system contain
endogenous errors. Because the information is embedded in the
errors, a natural question he brings into focus is how to extract infor-
mation from these endogenous errors.
It is well‐known in decision theory that Bayes' Theorem provides
the basis for updating prior information with new information. Sup-
pose there is an event of interest, and new information (signal) can
be obtained. The initial beliefs of the decision maker are encoded in
the prior probability distribution. The updated probabilities via Bayes'
formula (or the conditional probability) reflect the likelihood of the
event of interest conditional on the new information. Christensen
(2010a) uses Bayesian revision for the normal conjugate family to rein-
force the insight that both the mean and variance are important in the
accounting context. If the new information has very little variance
(information is reliable), then the updated conditional mean value (pos-
terior mean) is equal to the mean value of the signal. When the signal is
of lower quality (variance is larger), the updating adjusts accordingly, as
the magnitude of the updating is a decreasing function of the variance
of the signal. Christensen (2010a) illustrates its implication for
accounting using an example from Christensen and Demski (2003) to
show that accounting valuation seldom coincides with market
valuation.
Consider a set of events Ω = {θ1, θ2, θ3, …} that defines a
probabilizable partition on the state space S. The prior beliefs about
θ1, θ2, θ3, …, are represented by P(θi), and the likelihood of the event
y given θi is the conditional probability P(y|θi). Then, using Bayes'
Theorem, we can calculate the posterior beliefs about the events of
interest given the signal y (or posterior probability) as P(θi|y). Compar-
ing the prior probability P(θi) with the posterior probability, P(θi|y)
allows one to detect how an information signal y exerts influence on
a decision maker's beliefs. If P(θi|y) ≠ P(θi), then the decision maker's
posterior belief about the events is different from his prior belief,
which means the information signal y has economic value. Conversely,
if P(θi|y) = P(θi), we conclude that the information signal y has no impact
on revising a decision maker's belief from an information economics
perspective.
In this paper, we let η represent an information system and Y = {y}
represent the set of possible signals that might be generated by η. As
previously described, the information system η defines a partition of
the state space as the set of subsets of states that result in a particular
signal for each subset. This partition is an equivalent representation of
the information system. Therefore, one approach for evaluating two
information systems is to compare their respective partitions of the
state space. If they generate the same partition, we can conclude that
they are informationally equivalent.2 In this article, we use the
approach of comparing the partition of a state space.
3.2 | Accounting as an information science
According to Borko (1968), “information science is the discipline which
investigates the properties and behavior of information, the forces
governing the flow of information, and the means of processing infor-
mation for optimal accessibility and usability” (p. 3). It consists of both
a pure science component and an applied science component that
develops products and services. Furthermore, it is an interdisciplinary
science derived from and/or related to mathematics, computer tech-
nology, operations research, library science, communications, and
other fields (Borko, 1968). Proponents of information science and the
public regard it as essentially a practical activity involving computers,
the microchip, and telecommunication technology (Brookes, 1980). A
Critical Delphi study conducted in 2003–2005 involving 57 leading
scholars from 16 countries representing all the subfields by Zins
(2007a, 2007b) indicates that there is no uniform concept of informa-
tion science. The information science field may follow different
approaches and traditions, an objective approach versus cognitive
approaches, a library versus documentation tradition, and the compu-
tation tradition (Zins, 2007a).
The definition of information science as the study of all aspects of
management of information broadly pertains to the field of informa-
tion technology/systems (IT/S). Under this definition, the concepts of
data, information, and knowledge form the fundamental building block
of the field of information science. It is based on the model called the
knowledge pyramid (Rowley, 2007; Song & Zhu, 2016; Zins, 2007b). In
a detailed literature review of 152 scholarly articles, books, and reports
over the last 15 years, Shaikh and Karjaluoto (2015) find the need to
better understand how society and human beings have been affected
by IT/S. More specifically, their study focuses on the understanding
of IT/S and strengthening information technology and systems' contin-
uous usage as a field of study. Our article, which focuses on under-
standing accounting information as an information science, relates to
an alternate definition of information science as articulated in Zins
(2007a), namely, information science as a mathematical discipline that
studies technological ways of conveying information.
Fellingham (2015) discusses that information issues arise naturally
when accounting is studied rigorously and calls for the scientific under-
standing of accounting information as an information science. Funda-
mental information theories of entropy, mutual information, and
linear algebra is used to establish the operational equivalence of
accounting as an information science. The notion of stock values
(beginning balance) and flows (economic transactions) in T‐accounts
is used in a Bayesian setting with probabilities holding the structure
together. More specifically, the prior probabilities of the state of the
worlds are the stocks, the evidence or transactions are flows, and pos-
terior probabilities from the Bayesian revision are the updated stock
(Fellingham, 2015). Using a stylized example, with an appropriate
amortization rate and performing cash and amortization entries as in
double entry accounting, is shown to give the updated probabilities.
Viewing accounting as an information science, Arya et al. (2000)
explore the connection between information systems design and
incentives for capital investment appraisal and implementation. The
costs and benefits of managerial slack generated during project imple-
mentation are explored in an agency framework to incorporate
392 HERATH AND LU
information such as coarse information, late information, and a mix of
monitoring and self‐reporting information to maximize information
system design. Fellingham (2015) and Arya et al. (2000) treat informa-
tion science as extensions of the normative perspective that integrates
the mathematical theory of communication (see Gray, 2011) into the
accounting discipline. Brookes (1980), however, cautions that it may
be difficult to observe information in isolation with the detachment
that scientific inquiry traditionally demands because information per-
vades all human activity. In this context, the suggestion by Shaikh
and Karjaluoto (2015) to focus on collaborative systems where infor-
mation sharing between different departments within an organization
ensure better planning and decision making is quite relevant to the
study of accounting as an information science.
3.3 | Real earnings management
Benson, Faff, and Smith (2014) describe earnings management as
accounting, investing, and reporting choices by firms to opportunisti-
cally manage earnings or signal future benefits to shareholders
(Herbohn & Ragunathan, 2008) by manipulation of accruals (Bowman
& Navissi, 2003; Bradbury, Mak, & Tan, 2006; Capalbo, Frino, Mollica,
& Palumbo, 2014) or real earnings management (Bennett & Bradbury,
2010); that is, they broadly classify earnings management into two cat-
egories: accruals management and real activity manipulation. Dechow
and Skinner (2000) defined accruals management as accounting choices
under GAAP that try to obscure true economic performance that does
not have any direct cash flow consequences. Earnings management
has also been documented based on type of the firm (distressed or
healthy) (Charitou, Lambertides, & Trigeorgis, 2011), subject to price
control regulation (Bowman & Navissi, 2003), change of CEO and
CEO/CFO characteristics (Amir, Kallunki, & Nilsson, 2014; Choi, Kwak,
& Choe, 2014; Godfrey, Mather, & Ramsay, 2003; Hossain & Monroe,
2015), and overvalued equity (Coulton, Saune, & Taylor, 2015). The lit-
erature on earnings management/earnings quality is vast (see Benson
et al., 2014; Benson et al., 2015), and it also encompasses corporate
governance (see Brown et al., 2011 for a detailed survey; Hassan,
2008 for role of AC vs. VC on corporate governance reform); hence,
the focus in this article is primarily on real earnings management.
Real earnings management occurs when managers intentionally
change the timing or structuring of an operation, investment, or financ-
ing transaction to influence the output of the accounting system
(Gunny, 2010; Roychowdhury, 2006). In real earnings management,
firms take actions that deviate from normal business practices, which
affect cash flow and, eventually, earnings. There are mainly four types
of real earnings management situations discussed in the literature.
They are (a) decreasing discretionary research and development
expenses, (b) decreasing discretionary advertising expenses, (c) timing
the sale of fixed assets to report gains, and (d) overproduction
reflecting an intention to decrease the cost of goods sold.
Although much of the recent research has focused on detecting
abnormal accruals, research on manipulating earnings through real
earnings management is relatively sparse attention. Only a few articles
have examined real activity manipulation by managers as compared to
accrual earnings management (Sun et al., 2014). These include research
and development investment expenditure manipulations (Chen, Rees,
& Sivaramakrishnan, 2010; Zang, 2012); real earnings manipulation
through overproduction and timing of fixed asset sales (Gunny, 2010;
Gupta et al., 2010; Roychowdhury, 2006); and real economic action
through increased sales resulting in reduced inventories and increased
cash‐flow from sales (Bennett & Bradbury, 2010; Ibrahim, Xu, &
Rogers, 2011).
Ewert and Wagenhofer (2015) investigate the economic relation-
ship among earnings quality and indicate that, including productive
effort (real earnings management) in their analytical model can provide
insights to real earnings management that decreases firm value (see
Ewert & Wagenhofer, 2005). Sun et al. (2014) investigate the effec-
tiveness of independent audit committees to minimize real earnings
management. Enomoto, Kimura, and Yamaguchi (2015) compare
accrual‐based earning management versus real earnings management
across countries 38 countries and find a substitution effect, that is,
countries with stronger investor protection engage in real earnings
management.
Empirical evidence suggests that inventory accruals are suscepti-
ble to managerial manipulation through opportunistic overproduction
(Abarbanell & Bushee, 1997; Gunny, 2010; Gupta et al., 2010; Lev &
Thiagarajan, 1993; Roychowdhury, 2006). Gupta's et al. (2010) findings
are not driven by negative demand shocks to sales that managers can-
not incorporate in a timely manner into inventory production decisions
but rather by real earnings management involving inventory manipula-
tion. Textbooks and the extant literature argue that variable costing,
which involves less unfavorable managerial action, is better for internal
control purposes than absorption costing (Horngren et al., 2004). The
premise is that earnings under variable costing will not change accord-
ing to actual production volumes controllable by managers, because
they relate to actual sales, which are determined by the uncertain eco-
nomic environment. As such, less real earnings management is
expected under variable costing. The structural nature of absorption
costing, which is the recommended method under GAAP for external
reporting (CICA Handbook IAS 2), however, allows deferring a portion
of the fixed manufacturing overhead in inventory.
4 | RECONCILING THE DIFFERENCE BETWEEN VARIABLE AND ABSORPTION COSTING
In this section, as exposition to aid in the development of the stochas-
tic model, we first illustrate and reconcile the difference between
variable and absorption costing without introducing uncertainty. The
salient points are the following:
• Under variable (also referred to as direct) costing, only variable
manufacturing costs are included as inventory costs, but fixed
manufacturing costs are treated as a period cost. Consequently,
the cost of goods sold or the cost of a product in inventory does
not include any fixed manufacturing costs.
• Absorption costing (or conventional costing) treats all variable and
fixed manufacturing cost as product costs. Consequently, inven-
tory absorbs the total manufacturing costs, and this is frequently
referred to as full costing.
HERATH AND LU 393
• The difference in operating income under absorption costing and
variable costing is equal to the change in units of inventory on
hand multiplied by the fixed manufacturing overhead rate.
• Alternatively, the difference in operating income under absorption
costing and variable costing is equal to the difference in fixed
manufacturing overhead charged as an expense under the two
inventory costing methods and computed as the sum of the por-
tion of fixed manufacturing overhead in cost of goods sold and
production volume variance.
The difference between variable and absorption costing is really a
difference of timing (Horngren & Sorter, 1961). Proponents of absorp-
tion costing argue that income is greater when production exceeds
sales than when production equals sales because fixed facilities are
better utilized and render benefits in the form of inventory that will
bring future revenues. Conversely, proponents of variable costs main-
tain that fixed factory overhead relates to capacity to produce and
whether the capacity is used to the full extent or not is irrelevant. That
is, production in advance of sales does not avoid any fixed manufactur-
ing overhead costs in future periods.
Consider a single‐product manufacturing firm with high fixed
manufacturing overhead over a 3‐year horizon (t = 1, 2, 3). In order
to develop the model, we define the following variables:
• Dt: sales demand in period t
• St: quantity sold in period t
• pt: unit selling price in period t
• mt: direct material cost per unit in period t
• lt: direct labor cost per unit in period t
• vt: variable manufacturing overhead rate in period t
• ft: fixed manufacturing overhead rate in period t
• Ft: budgeted total fixed manufacturing overhead in period t
• qBt : budgeted normal production level in period t
• uACt : unit production cost under absorption costing in period t
• uVCt : unit production cost under variable costing in period t
• Qt: level of production in period t
• It: level of inventory on hand in period t
The budgeted fixed manufacturing overhead rate is given by
ft ¼ Ft q Bt
. If qBt is assumed to be constant each year, then ft ¼ Ft q B
for
each period. The unit production cost under variable costing and
absorption costing can be computed as u VCt ¼ mt þ lt þ vt and u ACt ¼ mt þ lt þ vt þ ft, respectively. Let the beginning inventory level be denoted by It − 1, and the ending inventory level be denoted by It.
Then assuming that St = Dt, the expression for the quantity sold can
be written as Dt = It − 1 + Qt − It. Because the total demand is not
known in advance, the quantity sold will be the minimum of sales
demand and the quantity available for sale, given by St = Min [Dt,
It − 1 + Qt]. We assume that work‐in‐progress is minimal and that
there are no marketing costs. Further, in order to highlight the differ-
ence in AC and VC income, we assume that there are no price,
efficiency, or spending variances pertaining to cost items over the
2‐year period.
The income statement prepared under variable costing and
absorption costing produces different net income numbers. These dif-
ferences can be quite large, and hence, it is important to explain and
reconcile the reasons for the difference in income. Illustrating the pro-
duction volume variance irrelevance proposition, Black and Gray
(1995) demonstrate the real reason for the difference between AC
and VC income as change in fixed cost component of beginning and
ending inventories in AC. This is formalized in Lemma 1.
Lemma 1. Difference in operating income from absorp-
tion costing and variable costing is due to the moving of
fixed manufacturing costs into inventories.
Formally, the difference in operating income from absorption cost-
ing and variable costing can be computed by
AC incomeð Þ‐ VC incomeð Þ ¼ Itft−It−1ft−1ð Þ: (1)
Proof Consider the left‐hand side of the formula for
any period t
AC incomeð Þ‐ VC incomeð Þ ¼ ¼ Dtpt− It−1uACt−1 þ QtuVCt þ fqBt −ItuACt
� �h i
− Dtpt− It−1u VC t−1 þ QtuVCt −ItuVCt
� � −fqBt
h i
¼ It uACt −uVCt � �
−It−1 u AC t−1−u
VC t−1
� � :
Because u VCt ¼ mt þ lt þ vt and u ACt ¼ mt þ lt þ vt þ ft, we obtain u ACt −u
VC t ¼ ft and thus (AC income) ‐ (VC income) = Itft − It − 1ft − 1.
Lemma 2. Net income in each period under variable
costing and absorption costing is identical if there is no
ending inventory.
Proof From Lemma 1, (AC income) ‐ (VC income) =
Itft − It − 1ft − 1. If there is no ending inventory such as
just‐in‐time (JIT), then (i.e., It = It − 1 = 0) we obtain
the required proof.
From Lemma 1, it can be seen that when inventory increases
It > It − 1, then a part of the fixed manufacturing cost in the current
period does not appear in the income statement as cost of goods sold
but is deferred to the next period's balance sheet as part of the inven-
tory cost. The deferring of costs is termed as fixed manufacturing over-
head deferred in inventory. Thus, the difference in operating income
under absorption costing and variable costing can be reconciled by
multiplying the change in units of inventory on hand by the fixed
manufacturing overhead rate.
The above difference is also equal to the difference in fixed
manufacturing overhead charged as expenses under the two inventory
costing methods. Notice that under the absorption costing format, the
fixed manufacturing overhead appears in two places: (a) in the cost of
goods sold and (b) as “production volume variance” that occurs when-
ever actual production deviates from the expected (budgeted) volume
394 HERATH AND LU
of production used in computing the fixed overhead rate (Horngren
et al., 2004). Under variable costing, the fixed manufacturing overhead
charged is what is incurred in year t given by ftq B t (fixed manufacturing
overhead is assumed to be incurred as budgeted). Notice that this is
the amount that is expensed as a period cost under variable costing.
Under absorption costing, as shown in Table 1, Panel B, a portion
of the fixed manufacturing overheard appears in the cost of goods
sold. Notice that there is an amount of fixed manufacturing overhead
accounted in the beginning inventory that was deferred from the prior
period equal to the beginning inventory times the fixed manufacturing
overhead rate (It − 1ft − 1). An amount of Qtft was added due to produc-
tion, and an amount of Itft remained as ending inventory, which is
deferred to the next period. Thus, the amount of fixed manufacturing
overhead that appears in the cost of goods sold is (It − 1ft − 1 + Qtft − Itft).
The other part of the fixed manufacturing overhead appears as pro-
duction volume variance, which can be written as
actual volumeð Þ‐ expected volumeð Þ½ �×ft ¼ Qt−qBt � �
ft. If Qt>q B t , then
the production volume variance is favorable, and conversely, if
Qt<q B t , then the production volume variance is unfavorable. The favor-
able variance will reduce the cost of goods sold; thus, the total fixed
manufacturing overhead under absorption costing is
It−1ft−1 þ Qtft−Itftð Þ− Qt−qBt � �
ft ¼ It−1ft−1−Itft þ qBt ft. Therefore, the dif- ference in the fixed manufacturing overhead between variable costing
and absorption costing is qBt ft− It−1ft−1−Itft þ qBt ft � �
¼ Itft−It−1ft−1.
5 | AN INFORMATION MODEL OF ABSORPTION AND VARIABLE COSTING FOR PLANNING AND CONTROL
In order to investigate the information economics perspective of the
two inventory costing choices, we introduce uncertainty to the tradi-
tional setting as follows. Suppose the sales demand in the first year is
D1 ± d1, in the second year is D2, and in the third year is D3 ± d3. The
two‐period stochastic setup (Years 1 and 3) implies that there are four
possible demand states: first up and third up, first up and third down,
first down and third up, and first down and third down. The four demand
states are denoted by Ω = {θ1, θ2, θ3, θ4} ∈ Θ. In each case, assume that
the increase/decrease in demand in Years 1 and 3 (i.e., ±d1 and ±d3) is
independent and equally likely events (i.e., P(θi) = 0.25) for i = 1, 2,
3, 4. In order to keep the model general, we consider that in any period,
the sales quantity is not exactly equal to the demand.
The decision maker is considering minimizing opportunistic over-
production. From a control dimension, an accounting information sys-
tem (an accounting procedure VC or AC) provides information to help
determine if there is opportunistic production or simply negative
demand shock that a manager is not able to incorporate in a timely
manner. It is assumed that compensation is positively correlated with
the level of income that is announced. The association between cash
compensation and earnings is well documented in the prior literature
(Biddle & Choi, 2006). Lambert and Larcker (1987) provide empirical
support of the association between changes in cash compensation
and earnings. Sigler (2011) indicates a positive relationship between
chief executive compensation and company performance measured
by return on equity. Gaver and Gaver (1998) find that cash compensa-
tion is positively related to earnings as long as the earnings are posi-
tive, which supports our assumption.
We define the following additional notation for the stochastic
model:
• θj: j th state of nature
• Dθjt: demand pertaining to state θj at time t. Notice that in the
nonstochastic case, Dθjt ¼ Dt • Sθjt: sales quantity pertaining to state θj at time t
• uVCt−1−u VC t ¼ uVCt−1;t: decrease in unit variable cost from period t − 1 to
period t
• u ACt−1−u AC t ¼ u ACt−1;t: decrease in total unit cost from period t − 1 to
period t
• Qt−q B t
� � ft ¼ ψt: production volume variance in period t
In order to provide an intuitive discussion regarding the difference
in net income, we present two separate income statements over a 3‐
year period: one using absorption costing and the other using variable
TABLE 1 Summary of variable costing and absorption costing operating income according to states for periods t = 1, 2, 3
Panel A: Variable costing
State NOIVC1 NOI VC 2 NOI
VC 3
θ1 Sθ11 p1−u VC 1
� � −I0u
VC 0;1−q
B 1f1 Sθ12 p2−u
VC 2
� � − I0 þ Q1−Sθ11½ �uVC1;2−qB2f2 Sθ13 p3−uVC3
� � − I0 þ Q1 þ Q2−Sθ11−Sθ12½ �uVC2;3−qB3f3
θ2 Sθ21 p1−u VC 1
� � −I0u
VC 0;1−q
B 1f1 Sθ22 p2−u
VC 2
� � − I0 þ Q1−Sθ21½ �uVC1;2−qB2f2 Sθ23 p3−uVC3
� � − I0 þ Q1 þ Q2−Sθ21−Sθ22½ �uVC2;3−qB3f3
θ3 Sθ31 p1−u VC 1
� � −I0u
VC 0;1−q
B 1f1 Sθ32 p2−u
VC 2
� � − I0 þ Q1−Sθ31½ �uVC1;2−qB2f2 Sθ33 p3−uVC3
� � − I0 þ Q1 þ Q2−Sθ31−Sθ32½ �uVC2;3−qB3f3
θ4 Sθ41 p1−u VC 1
� � −I0u
VC 0;1−q
B 1f1 Sθ42 p2−u
VC 2
� � − I0 þ Q1−Sθ41½ �uVC1;2−qB2f2 Sθ43 p3−uVC3
� � − I0 þ Q1 þ Q2−Sθ41−Sθ42½ �uVC2;3−qB3f3
Panel B: Absorption costing
State NOIAC1 NOI AC 2 NOI
AC 3
θ1 Sθ11 p1−u AC 1
� � −I0u
AC 0;1 þ ψ1 Sθ12 p2−uAC2
� � − I0 þ Q1−Sθ11½ �uAC1;2 þ ψ2 Sθ13 p3−uAC3
� � − I0 þ Q1 þ Q2−Sθ11−Sθ12½ �uAC2;3 þ ψ3
θ2 Sθ21 p1−u AC 1
� � −I0u
AC 0;1 þ ψ1 Sθ22 p2−uAC2
� � − I0 þ Q1−Sθ21½ �uAC1;2 þ ψ2 Sθ23 p3−uAC3
� � − I0 þ Q1 þ Q2−Sθ21−Sθ22½ �uAC2;3 þ ψ3
θ3 Sθ31 p1−u AC 1
� � −I0u
AC 0;1 þ ψ1 Sθ32 p2−uAC2
� � − I0 þ Q1−Sθ31½ �uAC1;2 þ ψ2 Sθ33 p3−uAC3
� � − I0 þ Q1 þ Q2−Sθ31−Sθ32½ �uAC2;3 þ ψ3
θ4 Sθ41 p1−u AC 1
� � −I0u
AC 0;1 þ ψ1 Sθ42 p2−uAC2
� � − I0 þ Q1−Sθ41½ �uAC1;2 þ ψ2 Sθ43 p3−uAC3
� � − I0 þ Q1 þ Q2−Sθ41−Sθ42½ �uAC2;3 þ ψ3
Note. Demand outcome for each probability state θj is as follows: θ1 ≡ [D1 + d1, D2, D3 + d3], θ2 ≡ [D1 + d1, D2, D3 − d3], θ3 ≡ [D1 − d1, D2, D3 + d3], and θ4 ≡ [D1 − d1, D2, D3 − d3]. The sales in each state are given by Sθ11 ¼ Sθ21 ¼ Min D1 þ d1; I0 þ Q1½ �, Sθ31 ¼ Sθ41 ¼ Min D1−d1; I0 þ Q1½ �, Sθ12 ¼ Sθ22 ¼ Sθ32 ¼ Sθ42 ¼ Min D2; I1 þ Q2½ �, Sθ13 ¼ Sθ33 ¼ Min D3 þ d3; I2 þ Q3½ �, and Sθ23 ¼ Sθ43 ¼ Min D3−d3; I2 þ Q3½ �.
HERATH AND LU 395
costing as in Table 1, Panels A and B. In general, the net operating
income for state θj in period t ≥ 0 under variable costing and absorp-
tion costing can be expressed as follows:
NOI VCt ¼ Sθjt pt−uVCt � �
− I0 þ ∑ t−1
i¼1 Qi−Sθii � ��
uVCt−1−u VC t
� � −qBt ft; (2)
NOIACt ¼ Sθjt pt−u ACt � �
− I0 þ ∑ t−1
i¼1 Qi−Sθii � ��
u ACt−1−u AC t
� � þ Qt−qBt � �
ft; (3)
where
Sθjt ¼ Min Dθjt; It−1 þ Qt � �
and It−1 ¼ I0 þ ∑ t−1
i¼1 Qi−Sθii � �
.
The change in net operating income is given by the following:
NOI ACt −NOI VC t ¼ ΔNOI
¼ −Sθjtft þ Qtft− I0 þ ∑ t−1
i¼1 Qi−Sθii � ��
ft−1−ftð Þ: (4)
Theorem 3. Accounting system choice is irrelevant if
and only if Dθjt>Qt for all ∀θj and t ≥ 0, as then
Sθjt ¼ Qt∀θj and zero inventories hold.
Proof Because Sθjt ¼ Min Dθjt; It−1 þ Qt � �
, when
Dθjt>Qt, then actual sales are equal to the actual pro-
duction, that is, Sθjt ¼ Qt.
ΔNOI ¼ −Sθjtft þ Qtft− I0 þ ∑ t−1
i¼1 Qi−Sθii � ��
ft−1−ftð Þ
¼ −Qtft þ Qtft− 0 þ ∑ t−1
i¼1 Qi−Qið Þ
� ft−1−ftð Þ ¼ 0:
Thus, NOI ACt ¼ NOI VCt and It − 1 = It = 0.
5.1 | Costing system choices and resulting partitions
We consider the following set of situations to illustrate the state parti-
tions imposed by variable costing and absorption costing. In order to
compare the partitions in each period imposed by the two accounting
choices, a contemporaneous reporting setting is assumed where
accounting history is ignored. Contemporaneous reporting setting
has been used previously in accounting research. For example, associ-
ation studies measure the contemporaneous relationship between
financial statement variables and stock returns (Ball, Robin, & Sadka,
2008). More specifically, Dechow (1994) hypothesizes a stronger con-
temporaneous association between stock returns and earnings com-
pared with stock returns and cash flows over short measurement
intervals. The contemporary reporting setting assumption allows ease
of modeling; however, it is a strong limiting assumption, because busi-
nesses operate as going concerns.
Expenses such as the variable and fixed selling and administrative
expenses are not considered, as they do not affect product cost. Also,
the unit selling price, unit variable manufacturing cost, budgeted fixed
manufacturing costs, and increase/decrease in demand are assumed to
be constant over the planning horizon (i.e., pt = s, u VC t ¼ v, dt = d, and
Ft = F for t = 0, 1, …, τ), resulting in uVCt−1;t ¼ 0. Often, deterministic inventory models including the economic order quantity model assume
the demand rate to be constant and steady over an infinite horizon
(see Ardalan, 1991; Dave & Patel, 1981, among others). Again, this
strict assumption provides modeling ease, but the consequence of
such an assumption is that it assumes away practical reality.
In order to illustrate the partitions imposed by the two information
systems, we consider the following set of scenarios:
• Case A: JIT production (the firm holds no inventories of finished
goods): Predetermined fixed overhead rate is constant. The JIT
case serves as the proper benchmark because, as we have shown
in Lemma 2, both absorption costing and variable costing provide
the same net income; hence, no earnings management due to
overproduction is possible.
• Case A (i) Actual production equals budgeted production:
Qt ¼ qBt ¼ Q, ft ¼ F
qBt ¼ f, It = 0, D1 + d = Q, D2 < Q, then
Min[D1 + d, Q] = D1 + d, Min[D1 − d, Q] = D1 − d, and Min[D2,
Q] = D2. Because the predetermined fixed overhead rate is con-
stant, uACt ¼ w and uACt−1;t ¼ 0. Furthermore, the contribution per unit and gross profit per unit are constant (i.e., pt−u
MC t ¼ c and
pt−u AC t ¼ g). Equations 2 and 3 now simplify to NOIVCt ¼ Sθjtc− F
and NOIACt ¼ Sθjtg þ Qt−qBt � �
ft where Sθjt ¼ Min Dθjt; It−1 þ Qt � �
.
The net operating income for the four uncertain states during the
3‐year period is given in Table 2, Panels A and B. Accordingly, we
observe the following state partitions under variable costing: Year 1
→ [θ1, θ2][ θ3, θ4], Year 2 → [θ1, θ2, θ3, θ4], and Year 3 → [θ1, θ3]
[ θ2, θ4]. The observed state partition when absorption costing is used
is Year 1 → [θ1, θ2][ θ3, θ4], Year 2 → [θ1, θ2, θ3, θ4], and Year 3 →
[θ1, θ3][ θ2, θ4], which is identical to the state partition observed under
variable costing.
• Case A (ii) Actual production not equal to budgeted production:
Qt = Q, q B t ¼ q, but Q ≠ q, ft ¼
F
qBt ¼ f, It = 0, D1 + d = Q, D2 < Q,
then Min[D1 + d, Q] = D1 + d, Min[D1 − d, Q] = D1 − d, and
Min[D2, Q] = D2. Notice that this case is similar to Case A (i) except
now there is a production volume variance given by
ψt ¼ Qt−q Bt � �
ft ¼ Q−qð Þf ¼ ψ under absorption costing. It is easy to verify that the resulting state partitions under the two costing
systems are Year 1 → [θ1, θ2][ θ3, θ4], Year 2 → [θ1, θ2, θ3, θ4],
and Year 3 → [θ1, θ3][ θ2, θ4], which is identical to Case A (i).
TABLE 2 Case A (i) just‐in‐time production summary of variable costing and absorption costing operating income
Panel A: Variable costing
θ1 θ2 θ3 θ4
NOIVC1 (D1 + d)c − F (D1 + d)c − F (D1 − d)c − F (D1 − d)c − F
NOIVC2 D2c − F D2c − F D2c − F D2c − F
NOIVC3 (D3 + d)c − F (D3 − d)c − F (D3 + d)c − F (D3 − d)c − F
Panel B: Absorption costing
θ1 θ2 θ3 θ4
NOIAC1 (D1 + d)g (D1 + d)g (D1 − d)g (D1 − d)g
NOIAC2 D2g D2g D2g D2g
NOIAC3 (D3 + d)g (D3 − d)g (D3 + d)g (D3 − d)g
396 HERATH AND LU
• Case B: Real Earnings Management (the firm increases the produc-
tion level in each period and adjusts the predetermined fixed over-
head rate).
The actual production is not equal to the budgeted production:
Because the unit variable costs are constant, (pt−u MC t ¼ c), uVCt−1;t ¼ 0.
However, because q Bt is not constant (i.e., q B 1≠q
B 2≠q
B 3), ft ¼
F
qBt ,
pt−u AC t ¼ gt, and uACt−1;t≠0. Without a loss of generality, we assumed that
I0 = 0, D1 + d = Q, D2 < Qf0 = f1,Q1 ¼ Q ¼ qB1, Q2 = Q + d, and Q3 = Q + 2d, but because f0 = f1, u
AC 0;1 ¼ 0. Notice that there is production volume
variance given by ψt ¼ Qt−qBt � �
ft under absorption costing.
The net operating income for the four uncertain states during
the 3‐year horizon is given in Table 3, Panels A and B. We now
observe the following state partitions under variable costing: Year 1
→ [θ1, θ2][ θ3, θ4], Year 2 → [θ1, θ2, θ3, θ4], and Year 3 → [θ1, θ3]
[ θ2, θ4]. The observed state partition when absorption costing is
used is now different and given by Year 1 → [θ1, θ2][ θ3, θ4], Year
2 →[θ1, θ2][ θ3, θ4], and Year 3 → [θ1 ][θ3][θ2][θ4]. When a firm
revises the budgeted production, then the underlying state partitions
imposed by variable costing and absorption costing are different. This
arises because of the variation in the production volume variance and
inventory value. Notice that unlike variable costing in the above
situation, absorption costing provides perfect information. That is, if
absorption costing is used, by looking at the accounting numbers
one is able to invert the mapping that produces the information so
that the user learns exactly which demand state occurs. Thus,
absorption costing provides more information than variable costing
from an information economics perspective. The underlying state
partitions pertaining to the JIT inventory and real earnings manage-
ment strategies are shown in Figure 1.
Suppose a manager takes some unobservable inventory produc-
tion strategy (or act) a ∈ A ⊂ R, which together with a random state
of nature (demand) θ ∈ Ω generates a signal y that is commonly
observed (reported). The signal y = η(a, θ) ∈ R, generated by the infor-
mation system η, is received after the manager chooses a. Kim and
Suh (1991) indicate that the monetary outcome could also be an infor-
mation signal whenever it is commonly observed. For the purpose of
this article, we consider the monetary outcome (manager compensa-
tion) x as a function of the information signal x = v(y). The technologies
(information systems) that generate information signals are the two
inventory costing procedures (VC vs. AC). An information system η
can be described by the probability distribution function g(y|a),
parameterized by the manager's act. The probability distribution func-
tion g(y|a) ∈ Γ can be interpreted as an information system that gener-
ates a signal y informative about a, where Γ denotes the set of
information systems (Kim & Suh, 1991).
TABLE 3 Real earnings management summary of variable costing and absorption costing operating income
Panel A: Variable costing
θ1 θ2 θ3 θ4
NOIVC1 (D1 + d)c − F (D1 + d)c − F (D1 − d)c − F (D1 − d)c − F
NOIVC2 D2c − F D2c − F D2c − F D2c − F
NOIVC3 (D3 + d)c − F (D3 − d)c − F (D3 + d)c − F (D3 − d)c − F
Panel B: Absorption costing
θ1 θ2 θ3 θ4
NOIAC1 (D1 + d)c − F (D1 + d)c − F (D1 − d)g1 (D1 − d)g1
NOIAC2 D2g2 + ψ2 D2g2 + ψ2 D2g2− Q2−D1½ �uAC12 þ ψ2 D2g2− Q2−D1½ �uAC12 þ ψ2 NOIAC3 D3 þ dð Þg3− Q2−D2½ �uAC23 þ ψ3 D3−dð Þg3− Q2−D2½ �uAC23 þ ψ3 D3 þ dð Þg3− 2Q2−D1−D2½ �uAC23 þ ψ3 D3−dð Þg3− 2Q2−D1−D2½ �uAC23 þ ψ3
FIGURE 1 Information‐induced partitions under variable and absorption costing (AC) at time t = 3. VC = variable costing
HERATH AND LU 397
We consider the following two unobservable production strate-
gies: act a1 ∈ A, a JIT production strategy with zero inventories on
hand, and act a2 ∈ A, an opportunistic overproduction strategy in line
with the earnings management hypothesis tested in empirical research.
For each of these acts, we apply the two inventory costing choices VC
and AC. These two inventory costing procedures are in fact two infor-
mation systems that are labeled ηMC and ηAC and which pertain to each
act.3 The manager's compensation is a function of the commonly
observed signal y, which is the level of income announced. As the level
of income or signal y = η(a, θ) depends on a and θ, we can compute the
net operating income pertaining to each act a or state θ under a given
inventory costing procedure as πηa;θ. Because manager compensation is
based on the level of income that is announced, it is given by
xηa;θ ¼ v π η a;θ
� � .
Consider an information system ηk (where k = 1 for VC and k = 2
for AC) which partitions the state space Ω into {{θ1, θ3}, {θ2, θ4}} then
η1∈ y 1 1; y
2 1
� . The superscripts (1 and 2) label the partition. That is, there
are two possible levels of net income or information signals
y11: π 1 a1θ1
¼ π1a1θ3 � �
and y21: π 1 a1θ2
¼ π1a1θ4 � �
. With y = η(θ), the probability
of a signal conditional on the information system can be computed as
P yjηð Þ ¼ ∑ θ∈Ω such that y¼η θð Þ
P θð Þ. More specifically, P y11 ��η1� � ¼ P θ1ð Þ þ P θ3ð Þ
and P y21 ��η1� � ¼ P θ2ð Þ þ P θ4ð Þ. Having received a signal y, the condi-
tional probability (or the posterior probability) is given by the Bayes
formula as
P θjy; ηð Þ ¼ P θð Þ P yjηð Þ if y ¼ η θð Þ:
0 Otherwise;
8< :
more specifically, P θ1jy11; η1 � �
¼ P θ1ð Þ P y11
��η1� �. One can repeat these com- putations for the information system η2.
Once the posterior probabilities are obtained for each signal y, the
conditional expected utility with act a can be obtained using
E uja; y; ηð Þ ¼ ∑ θ∈Ω
xηa;θP θjy; ηð Þ. The optimal expected utility to the deci-
sion maker is obtained using E ujy; ηð Þ ¼ min a∈A
E uja; y; ηð Þ. The expected utility associated with an information system η can be obtained using
E ujηð Þ ¼ ∑ y∈η
P yjηð ÞE ujy; ηð Þ. The well‐known simple ranking criterion
based on the expected payoff to a decision maker indicates that sys-
tem η1 is at least as good as system η2 if and only if E(u|η1) ≤ E(u|η2),
as the objective is to minimize the expected costs.
The inquiry or the process of generating the information signals
relates to the inventory costing choices. The messages or signals pre-
dict the state with some degree of accuracy. The probability measure
of the messages, conditional on each state, is the likelihood of the mes-
sage space and is denoted by P y; ηjθð Þ ¼ P θ; yð Þ P θð Þ . For the fixed θ,
P(y, η|θ) is a proper probability distribution on Y. When y is fixed and
if one views P(y, η|θ) as a function of θ, it defines the likelihood func-
tion, which is not a proper distribution function. A message yi is a pre-
diction that the state θi will occur. If P(yi, η|θi) = P(yj, η|θj) for i ≠ j, then
the process of generating the information provides perfect informa-
tion; otherwise, the information is imperfect.
Theorem 4. Absorption costing inquiry provides perfect
information when a firm increases the production level
in each period and adjusts the predetermined fixed over-
head rate.
Proof Consider the NOI of time period t = 3 under a
JIT strategy and an earnings management strategy as
shown in Table 4.
Using the prior probability P(θ) and likelihood function
P y; ηjθð Þ ¼ P θ; yð Þ P θð Þ , we can compute the joint probabilities, likelihood,
and posterior probabilities for the JIT strategy and earnings manage-
ment strategy as seen in Table 5.
The likelihood function P y; ηjθð Þ ¼
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 BBB@
1 CCCA becomes an
identity matrix when the budgeted production is not equal to the
actual production and the production level is arbitrarily increased. That
is, in this case, the likelihood is a proper probability function (i.e.,
TABLE 4 Partitions y = η(a, θ) at t = 3 under absorption costing
State JIT strategy Earnings management strategy
θ1 (D3 + d)c − F D3 þ dð Þg3− Q2−D2½ �uAC23 þ ψ3 θ2 (D3 − d)c − F D3−dð Þg3− Q2−D2½ �uAC23 þ ψ3 θ3 (D3 + d)c − F D3 þ dð Þg3− 2Q2−D1−D2½ �uAC23 þ ψ3 θ4 (D3 − d)c − F D3−dð Þg3− 2Q2−D1−D2½ �uAC23 þ ψ3 Partitions [θ1, θ3][ θ2, θ4] [θ1 ][θ3][θ2][θ4]
Note. JIT = just‐in‐time.
TABLE 5 Priors, likelihood function, and posterior probabilities for JIT and earnings management strategies
θ1 θ2 θ3 θ4
Prior: P(θ) 0.25 0.25 0.25 0.25
JIT strategy
Likelihood: P y11 ��θ� � 1 0 1 0
P y21 ��θ� � 0 1 0 1
Posterior: P θjy11 � �
0.50 0 0.50 0
P θjy21 � �
0 0.50 0 0.50
Earnings management strategy
Likelihood: P y12 ��θ� � 1 0 0 0
P y22 ��θ� � 0 1 0 0
P y32 ��θ� � 0 0 1 0
P y42 ��θ� � 0 0 0 1
Posterior: P θjy12 � �
1 0 0 0
P θjy22 � �
0 1 0 0
P θjy32 � �
0 0 1 0
P θjy42 � �
0 0 0 1
Note. JIT = just‐in‐time.
398 HERATH AND LU
P y12 ��θ� � = P y22
��θ� � = P y32 ��θ� � = P y42
��θ� � = 1), and absorption costing provides perfect information.
5.2 | Managerial control
From a managerial control angle, however, further analysis may be
required. More specifically, we are interested in the Bayesian revision
of information arising from the inventory costing choices (Amershi,
Demski, & Fellingham, 1985; Bailey & Jensen, 1979; Birnberg, 1964;
Mattessich, 2006). Bayesian revision pertains to the normative per-
spective, and the analysis in this article is in the spirit of Bayesian ratio-
nality (Ward et al., 2007), which is the optimal revision of prior
probability assessments (Uecker, 1978). This contrasts with conserva-
tism in studies of human probabilistic information processing (see
Slovic & Lichtenstein, 1971; Uecker, 1978), where it has been found
that on average individuals are conservative in their belief revisions
compared with the Bayesian model. The Bayesian model is useful as
a standard against actual judgments of decision makers (Slovic &
Lichtenstein, 1971; Uecker, 1978, among others). The probability P(θ)
is the unconditional distribution of the state, and P(θ|y, η) is the poste-
rior distribution of the state conditional upon receipt of a signal or spe-
cific forecast. In this regard, the expected utility associated with an
information system η is the posterior mean value of the compensation
paid to the manager, that is, μ″ ¼ E ujηð Þ ¼ ∑ y∈η
P yjηð ÞE ujy; ηð Þ. The pos-
terior standard deviation of the compensation can be computed using
the formulaσ″ ¼ ∑ y∈η
E ujy; ηð Þ−E ujyð Þð Þ2P yjηð Þ �1
2
. The prior belief is that
all four of the uncertain demand states are equally likely. Thus, the
decision maker could compute the prior mean and the variance of
the compensation to be paid as μ′a ¼ ∑ θ∈Ω
xηa;θP θð Þ and
σ′a ¼ ∑ θ∈Ω
xηa;θ−μ ′ a
� �2 P θð Þ
�1 2
.
We select the following setup, which allows an investigation of
real earnings management actions by a manager from a management
control dimension. In order to analyze the managerial biases, we con-
sider the following cases resulting from action choice and randomiza-
tion‐related information partitions. First, as in Case A (i), we consider
a JIT strategy with zero inventories, and a budgeted production equal
to the actual production is assumed as the benchmark scenario. Case
A (i) is labeled as a*B¼A1 , and as shown in Proposition 1, both accounting
inquiries (AC and VC) provide the same information partitions, because
there are no ending inventories and the production volume variance is
zero. The second is again a JIT strategy with zero inventories, and the
budgeted production is not equal to the actual production as in Case A
(ii), which is denoted by aB≠A1 . Finally, as in Case B, we consider the set-
ting where a manager arbitrarily increases production regardless of the
forecast demand (real earnings management) with the budgeted pro-
duction not equal to the actual production, which is labeled as aB≠A2 .
In Cases A (i) and (ii), the underlying partitions imposed by the two
inquiries are identical by construction, as there are no inventories. In
the third scenario, however, the underlying information partitions
imposed by the two inquiries are different, because the inventories
are carried forward and randomization occurs as the budgeted
production is not equal to the actual production. In all three scenarios,
for reporting purposes, the inquiry that is relevant is absorption cost-
ing, as it is required by GAAP. However, from a management control
point of view, Case A becomes the basis for comparison, as variable
costing and absorption costing provide identical partitions, and coinci-
dentally, for external reporting purposes, either method can be used.
Therefore, in analyzing the biases, we consider the information parti-
tion resulting from using absorption costing as the process of
generating information.
We define the following three resulting biases. Notice that in our
analysis, the biases are expressed in dollar amount of manager com-
pensation, but they can be expressed as dollar amount of net income
using the same approach once we define the outcome function to be
the income signal. The “forecast bias” (FB) is the difference in prior
means of JIT strategy (with budgeted production not equal to actual
production), and JIT strategy (with budgeted production equal to
actual production) is given by FB ¼ μ′aB≠A 1
−μ′ aB¼A 1
. The “total bias” (TB) is
the difference in prior means of earnings management strategy (arbi-
trary increase in production with budgeted production not equal to
actual production) and JIT strategy (with budgeted production equal
to actual production) given by TB ¼ μ′aB≠A 2
−μ′ aB¼A 1
. The “earnings manage-
ment bias” is the difference in prior means of earnings management
strategy (an arbitrary increase in production with the budgeted pro-
duction not equal to the actual production) and JIT strategy (with the
budgeted production not equal to the actual production) given by
TB ¼ μ′aB≠A 2
−μ′ aB≠A 1
. Notice that we cannot use the posterior means,
because the optimal action choices under each signal for the two inqui-
ries may change from a1 to a2 and vice versa.
6 | CONCLUSION, LIMITATIONS, AND FUTURE RESEARCH
In this article, we introduce uncertainty to the classical variable costing
and absorption costing problem to investigate the choice between the
two inventory costing methods from an information economics per-
spective. We apply the conceptual notion of information as a partition
in some of the underlying sets of states to find out whether both
absorption costing and variable costing systems generate the same
partition or not for a stylized set of scenarios. Our findings indicate
that although real earnings management through opportunistic over-
production in high fixed manufacturing‐cost firms can be somewhat
mitigated by using the normal production capacity to compute the
fixed overhead rate, when overhead rates are adjusted frequently with
production changes (randomization), absorption costing provides a
finer partition of the underlying state than variable costing.
Taking an information science approach to accounting, we have
shown that absorption costing disentangles the exogenous uncertainty
and endogenous earnings management. Although the GAAP require-
ment is the motivation for absorption costing that allows earnings
management, we have illustrated that it is also absorption costing that
provides the finer partition that detects endogenous earnings manage-
ment. Although variable costing does not provide the finer partition, it
provides identical net income in a JIT environment and thus serves as
HERATH AND LU 399
the benchmark. Managerial accounting for decision making and control
purposes does not need to comply with GAAP. Thus, by combining var-
iable costing with absorption costing, the principal has a control tool.
There are several limitations of the proposed approach, which pro-
vide opportunities for future research. We used two knife‐edge sce-
narios, which serve as a benchmark analysis towards understanding
accounting as an information science by exploring the structure of
accounting data and choice problem that governs the production of
accounting data. The general case of a firm manager tailoring produc-
tion decisions to changes in market demand and whether one inven-
tory costing method would be more informative would be of interest.
Earnings are aggregate accounting signals, and hence, it may be worth-
while to explore the possibility of using revenues as flow measure and
inventory as stock measure. Fellingham (2015) demonstrates that not
all underlying information can be inferred from financial statements,
and hence, it would be worthwhile to investigate when information
loss would occur in the choice of costing methods.
Another limitation of the proposed approach is the strict assump-
tions of contemporaneous reporting and constant increase or decrease
in demand over a planning horizon. Such assumptions are useful to
reduce model complexity, but they are farfetched from real world sit-
uations. Thus, future research may perhaps investigate relaxing the
contemporaneous reporting and constant increase or decrease
demand assumptions. Finally, one approach to mitigate real earnings
management is to determine the accounting error by comparing the
expected mean net income with the production adjustment for antici-
pated external demand shock and the expected mean net income with
the arbitrary increase in production level regardless of external
demand shock. Such comparison is only able to tease out the extent
of real earnings management.
In summary, this article raises and brings awareness in understand-
ing accounting as an information science and contributes to the man-
agement accounting literature. In addition to filling a gap between
information economics theory and its application, our paper has a ped-
agogical contribution, because it provides a nice example for teaching
information economics.
ACKNOWLEDGEMENTS
The primary author acknowledges research funding from the Social
Sciences and Humanities Research Council (SSHRC) of Canada (Grant
410‐2009‐1398). The authors thank the participants at the Research
Forum of the Management Accounting Section (MAS) Research and
Case Conference, Houston, Texas, 2012, 3rd Global Accounting and
Organizational Change Conference (GOAC), Malaysia, 2012, ASAC
2011 for their valuable input. The authors wish to thank Anil Arya,
Ohio State University, for his valuable suggestions for improving the
article. The usual disclaimers apply.
ENDNOTES 1 Real earnings management can be somewhat mitigated using the normal production capacity (Horngren, Foster, Datar, & Teall, 2004) in calculat- ing the fixed overhead rate. But the normal volume may be manipulated (see Winsen & Stefano, 1979).
2 Comparing informativeness on the basis of likelihood functions is another way to evaluate information systems (Christensen & Feltham, 2003). Under this method, we refer to information system ηi in terms
of the |Θ| × |Yi| Markov matrix ηi, whose element in row θ and column yi is the likelihood P(yi|θ).Then, by definition, an information system η2
is at least as Θ‐informative as η1 if, and only if, there exists a |Y2| × |Y1| Markov matrix B with elements b(y1|y2) ≥ 0 such thatη1 = η2B. Yet the third approach is to relate informativeness to value, which is Blackwell's key result. An information system that is at least as Θ‐informative as another is at least as valuable for all decision settings in which Θ is an outcome‐relevant partition of S.
3 The information systems may be identical in the JIT situation, because the net operating income is equivalent under both variable costing and absorption costing (i.e., the induced partition of the state space based on the income signal is identical).
ORCID
Hemantha S.B. Herath http://orcid.org/0000-0002-3150-6974
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How to cite this article: Herath HSB, Lu X. Inference of eco-
nomic truth from financial statements for detecting earnings
management: inventory costing methods from an information
economics perspective. Manage Decis Econ. 2018;39:389–402.
https://doi.org/10.1002/mde.2912
402 HERATH AND LU
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