Modelling the accruals process and assessing unexpected accruals*

Modelling the accruals process and assessing unexpected accruals*
Cheng Y. Lai**
Australian School of Business, University of New South Wales, NSW 2052 Australia.
This Version: Feb 2010
Abstract
This paper has two objectives. First, it formalizes the accruals process for both normal and
abnormal accruals under clean surplus accounting in order to better understand their drivers. My
analysis reveals that the factors that drive normal accruals are growth in income and changes in
accrual and deferral policies, while abnormal accruals are driven by growth in income and a
change in accounting policies. Second, this paper assesses the bias in unexpected accruals (the
empirical measure) from existing accruals models in capturing abnormal accruals (the theoretical
construct), and provides determinants and a reason for the bias. For well-specified accrual
models, their unexpected accruals are biased by two factors – income distortion in the
benchmark firms involved in the estimation procedure and deviation in operating policies
between the firm in question and the benchmark firms. A plausible explanation for this bias lies
in the inherent correlation between normal and abnormal accruals. If accrual models are ill-
specified, the omission of relevant variables is likely to further bias their unexpected accruals.
Keywords: Accruals; Accruals process; Abnormal accruals; Normal accruals; Expected
accruals; Unexpected accruals; Earnings management; Accruals management
JEL classification: G12, M41
*This paper forms part of my PhD dissertation.
** Email: cheng.lai@unsw.edu.au. Tel: +61-2-9385-6609. Fax: +61-2-9385-5925
1

1 Introduction
The focus of earnings management research to date has been on the identification, motivation,
and consequences of earnings management (Healy and Wahlen 1999). This paper attempts to
address the identification issue while remaining silent about the other two issues. One common
approach to identifying earnings management is via unexpected accruals where total accruals are
regressed on variables that are proxies for normal accruals and unexpected accruals are the
unexplained components or residual of total accruals (see Healy and Wahlen 1999 for details).
The common accruals models employed in the literature are the Jones model (Jones 1991) and
subsequent modifications, notably the modified Jones model found in Dechow et al. (1995) and
the model in Ball and Shivakumar (2006) that incorporates conditional conservatism.
However, all of these models were developed on an ad-hoc basis and their theoretical validity is
open to question. McNicols (2000) argues that this black-box approach reduces confidence in the
ability of estimates of abnormal accruals capture the exercise of accounting discretion by
management. The paper addresses this concern by focussing on two main objectives. First, this
paper defines accruals, explores the role of normal and abnormal accruals, and models them in a
general setting. This helps us to better understand the drivers of normal and abnormal accruals so
that researchers can adopt a systematic approach (rather than a black-box approach) in
identifying the factors that explain accruals. Second, I assess the bias in unexpected accruals (the
empirical measure) from the aforementioned accruals models in capturing abnormal accruals (the
theoretical construct) and provide determinants and a reason for the bias. To my knowledge, this
is the first paper that has done this to date. This contribution is significant in that it provides new
2

insights into what unexpected accruals actually capture, what determines the direction and the
magnitude of their bias or contamination, and why such a bias or contamination arises.
I begin by adopting the idea in Richardson et al. (2005) to comprehensively measure accruals by
subtracting the income under cash accounting from the income under accrual accounting. In
addition to the balance sheet approach provided in Richardson et al. (2005), I also consider the
income statement approach to calculate accruals under clean surplus accounting. This
reconciliation offers insight into the conclusion in Hribar and Colins (2002) that the accruals
calculated under both methods are different.
With this accruals definition in mind, I first model normal accruals as the accruals resulting from
the neutral accrual process that shifts cash flow recognition in income to a time that unbiasedly
reflects underlying fundamentals. As the sum of accrued and deferred components, normal
accruals are driven by growth in income and changes in accruals and deferrals policies. Second, I
model abnormal accruals as the accruals that distort the neutral accruals process by accelerating
and/or delaying cash flow recognition in income. The two factors that drive abnormal accruals
are a change in accounting policy and forward income growth. Finally, I combine the normal and
abnormal accruals into the final accruals model under clean surplus accounting.
My model is appealing in that it does not impose restrictive assumptions on firms‟ fundamentals.
It merely requires (a) the basic accounting identity to hold, (b) accruals to alter the timing of cash
flow recognition in income over time, and (c) the aggregated income to be equal to the
aggregated cash flow over the life span of firms. These three conditions can hardly be regarded
3

as assumptions as they simply depict how accounting works. This is in contrast to Dechow,
Kothari, and Watts (1998), who model the accruals process based on assumptions about accounts
receivable, accounts payable, sales, purchases, and inventory. 1
More importantly, I decompose accruals into normal and abnormal components and model them
separately, while their model is silent on the effect of accounting distortions. This approach is
crucial to the second objective of this paper for two reasons. First, it enables me to assess the bias
in unexpected accruals in capturing abnormal accruals and the determinants of this bias. Second,
the separate modeling of normal and abnormal accruals allows me to explore the correlation
between the two. This contrasts with previous studies which simply assume that the two
components are independent of each other (such as Jones 1991 and Dechow et al. 1995). It turns
out that this correlation is a crucial factor in explaining why the bias in unexpected accruals
arises in the first place.
Based on this theoretically derived accruals model, I develop an accruals model (referred to as
the „encompassing model‟ from here on) that uses variables in the Jones model. This model is
shown to be theoretically equivalent to the model in Dechow and Dichev (2002) after adjusting
for the drivers of depreciation expense, and to also encompass the Jones model, the modified
Jones model, and the Ball-Shivakumar model. I subsequently investigate whether the unexpected
component of these five models are biased or contaminated in capturing the abnormal accruals
1 First, accounts receivable is assumed to be a constant proportion of sales that follow a random walk process.
Second, they assume an inventory adjustment process in which inventory at a period consists of a target level and a
deviation from that target, and the target inventory is a constant fraction of next period‟s forecasted cost of sales.
Finally, accounts payable is assumed to be a constant proportion of purchases, which in turn is a function of the
sales generating process and the inventory adjusting process.
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attributed to the firm‟s biased accounting policy and provide the determinants of such
contamination.
For well-specified models like the encompassing model and the modified version of the Dechow
and Dichev (2002) model, my analysis reveals that their resulting unexpected accruals capture
deviations in accounting and operating policies between the firm in question and the set of
applicable benchmark firms (benchmark firms are either cross-sectionally comparable firms or
the firm‟s own specific time-series history). Hence, the resulting measure of unexpected accruals
is biased or contaminated by two factors – income distortion by the benchmark firms and
deviation in operating policy between the firm in question and the benchmark firms. Depending
on the relative magnitudes of these two factors, the resulting unexpected accruals will be
exacerbated or attenuated relative to abnormal accruals. Only when these two factors are absent
will unexpected accruals from well-specified models fully capture abnormal accruals; otherwise,
the resulting measure of unexpected accruals will be contaminated.
It may seem puzzling prima facie as to why measures of unexpected accruals estimated from
well-specified models are contaminated. I show that a plausible explanation for this is that there
is an inherent correlation between abnormal and normal accruals, and this correlation is zero
only when the two factors are absent. (Let us illustrate this correlation with a conservative firm
that recognizes revenue when its cash flow is realized rather than when it is earned. The
recognition of credit revenue will initiate positive normal accounts receivables in the period
when the revenue is earned. For this conservative firm to fully delay this recognition so that no
receivables are recognized, it needs to initiate an equal amount of negative abnormal accounts
5

eceivables to offset the positive normal accounts receivables. As normal receivables increase,
more negative abnormal receivables are needed to offset this increase.) This inherent correlation
violates the zero conditional assumption imposed by ordinary least squares (OLS) that the
expected component is orthogonal to the disturbance term. As a result, the regression approach to
extract abnormal accruals as the disturbance term is likely to be problematic.
If accruals models are ill-specified, the omitted relevant variables will be captured by the
disturbance term; and they are likely to further contaminate the resulting unexpected accruals.
This is especially the case for the Jones model, which omits lagged revenue and next period‟s
change in revenue from its explanatory variables that are intended to capture normal accruals. In
addition to normal changes in underlying performance (as discovered in Dechow et al 1995), my
paper shows that two other factors (or determinants) are likely to contaminate Jones-type
measures of unexpected accruals. These are normal changes in accrual policy and normal
deferred accruals. The modified-Jones model suffers from similar problems to the Jones model.
Finally, since conditional conservatism is an accounting distortion, its incorporation into the
Ball-Shivakumar model tends to further contaminate the measure of unexpected accruals by
attributing abnormal accruals from conditional conservatism as expected accruals.
The remainder of the paper continues as follows. Section 2 defines accruals and reconciles direct
and indirect methods to calculate accruals. Section 3 explores the accrual process and models
normal and abnormal accruals. Section 4 assesses determinants of the bias in unexpected in
capturing abnormal accruals. Section 5 demonstrates the correlation between normal and
abnormal accruals, while section 6 concludes.
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2 Direct and indirect method to calculate accruals
2.1 Accounting identity
To calculate comprehensive accruals and their decomposition, I first specify the stock and flows
clean-surplus relations (or accounting identity) for total working capital assets, non-current
operating assets, and financial liabilities. I start by modifying the basic accounting identity
Asset t =Liability t +Equity t to reflect operating and financing activities as (the firm j subscript is
omitted from the modeling process in this paper till section 4)
CASH NOA NFO CSE
t t t
t (1)
where CASH t is cash on hand, NOA is non-cash net operating assets that consists of total
working capital assets (TWC) which arise from day-to-day operating activities and non-current
operating assets (NCO) which arise as a result of capital expenditures, NFO is non-cash net
financial obligations or liabilities, and CSE is common shareholders equity.
The clean surplus relations or identities of these items are summarized in Table 1. These
specifications are similar to those in Feltham and Ohlson (1995) and Penman (2009), who
separate firms‟ activities into operating and financing. However, this paper further separates
operating activities into short-term operating activities that affect day-to-day working capital and
long-term operating activities that affect capital investment decisions.
[Table 1 about here]
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CASH identity: C is cash flow from operations, I is cash flow to investments in operations, (C–I)
is widely known as the free cash flow, F represents the cash outflow for non-equity financing
activities, and D is cash outflow from equity-financing activities (it will be negative if there is a
net contribution from shareholders). This identity asserts that changes in cash on hand are
attributable to free cash flow plus (debt and equity) financing cash flow. It will be reduced to the
cash conservation equation in Penman (2009) if there is no change in cash on hand.
TWC identity: OIB is comprehensive operating income before depreciation and amortization.
TWC includes accounts receivable, inventory, accounts payable, deferred and accrued
components of accruals of other revenue and expenses that stem from day-to-day operations and
are due within and beyond twelve months. This relation asserts that total working capital is
increased by the amounts earned in OIB and reduced by net operating cash flow (C).
NCO identity: DA is depreciation and amortization expenses, which also include realized or
unrealized losses or gains in non-current operating assets. 2 NCO includes both (depreciable and
non-depreciable) tangible and intangible assets that stem from investments on operations. It is
increased by the purchase of new assets net of cash receipt from assets disposal (I) and it is
reduced by depreciation and assets‟ disposal net of asset revaluation (DA).
NOA identity: OI is comprehensive operating income. This identity is simply a combination of
TWC and NCO identities. It asserts that the change in NOA is increased by what is earned in OI
and what is purchased as assets during the period (I). However, they are reduced by the cash
2 Realised or unrealised gains or losses in these assets can be regarded as the reversal or the result of initial
measurement error in depreciation and amortisation expenses.
8

flow associated with income recognised in the past, current or future periods (C). 3 In short, NOA
is increased by OI and reduced by free cash flow.
NFO identity: NFE is comprehensive financing expense (net of financing income). NFO includes
loans, income tax liabilities, preference shares, investments on marketable securities, and
minority interests. It is increased by financing expenses incurred but reduced by actual payment
of financing expenses and principal repayments.
CSE identity: CNI is comprehensive income. This identity can also be obtained if one combines
cash, NOA, and NFO identities. It asserts that owner‟s equity in a firm is increased by income
and reduced by net distributions to shareholders.
2.2 Accrual calculation and the reconciliation between indirect and direct methods
The key difference between accrual and cash basis accounting lies in their timing of recognition
(Statement of Financial Accounting Concepts, No. 6 Paragraph 144). Cash accounting
recognizes a transaction when the associated cash flow is realized rather than expected. As a
result, the change in net operating assets in the NOA identity and the change in net financial
t
obligation in NFO identity Table 1 are both zero under cash accounting (i.e., NOA 0and t
NFO 0 ), where the subscript c denotes cash accounting. 4 This associated with the basic
c
3 According to Dechow and Dichev (2002), Ct consists of
t
t 1 t
t 1
, C , and
t
C t
t
t
. C offsets the cash transactions
t
t 1
recognized in OI. C t 1
reduces NOA
t 1
when earnings recognized in the past are received. C , cash flows received
for earnings to be recognized in future periods, will create operating liability that reduces NOA.
4 This is because C=OIB, I = DA, and F=NFE under cash accounting.
C
t
c
9

accounting identity in expression (1) implies that the change in common equity is simply equal
to the change in cash under cash accounting.
Like Richardson et al. (2005), I measure accruals as the difference between comprehensive
income under accrual accounting and comprehensive income under cash accounting as follows:
TACC CNICNI t t t
c
t t t
OIB Ct DA It FE Ft
TWC NCO NFO
t t t
Given the articulation of income statement to balance sheet, equation (2) demonstrates that the
same total accruals can be calculated indirectly from the balance sheet variables or directly from
the cash flow and income variables. This is signified by the last two lines in equation (2) which
stem from the TWC, NCO, and NFO identities in Table 1. 5
First, total working capital accruals can be indirectly calculated as the change in total working
capital assets or indirectly calculated as comprehensive operating income before depreciation
and amortisation expense minus operating cash flow. Second, non-current operating accruals can
be indirectly calculated as the change in non-current net operating assets, or directly calculated
as capital expenditures minus comprehensive depreciation and amortisation expenses. Third,
operating accruals (the sum of the previous two accruals) can be indirectly calculated as the
change in non-cash net operating assets, or directly calculated as comprehensive operating
income minus free cash flow. Finally, financing accruals can be indirectly calculated as the
5 However, data availability could favour one method over another. For instance, it will be easier to calculate
accruals from cash flows for U.S. data as long term receivables and investments in marketable securities are grouped
into one item #32 in Compustat.
(2)
10

change in net financial obligations, or directly calculated as net financing expenses minus non-
equity financing cash flow.
The reason why direct and indirect methods may result in different measures (in Hribar and
Collins 2002) is because the income used to calculate accruals under the direct method is not
comprehensive. Dirty surplus items are by definition items that increase net assets and bypass the
income statements (Penman 2004). If these items have been accounted for in the calculation of
accruals, the direct and indirect methods will yield the same measure of accruals. For instance,
had the impact of foreign currency translations been accounted for, a classic dirty surplus item, it
would not lead to different measures of accruals under direct and indirect methods.
The compliance of the clean surplus relation is not an assumption, but rather is simply a
depiction of how accounting works. All clean surplus relations in section 2.1 reflect the basic
accounting identity of Asset = Liability + Equity. A violation of the clean surplus accounting
implies a violation of this basic accounting identity and a violation of the fundamental
accounting premise that debits equal credits. For accounting to work, the clean surplus relation or
identity, by definition, has to hold. The empirical evidence that is not in favor of clean surplus
relation does not automatically reject its existence. It can simply be due to the lack of data items
to comprehensively calculate the dirty surplus or non-articulation items. In short, accruals under
the direct and indirect methods should be the same if appropriate adjustments are made to either
method in compliance with clean surplus relations or accounting identities.
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3 The accrual process in detail
3.1 The role of accruals
Accruals are the temporary adjustment between income and cash flow during a period. Income is
the by-product of accrual accounting that records the financial effect of an entity as it occurs
rather than when the cash flow is realized (Statement of Financial Accounting Concepts, No. 6
Paragraph 139). It is defined in Statement of Financial Accounting Concepts, No.1 Paragraph 45
(and similarly in Statement of Financial Accounting Concepts, No. 5 Paragraphs 36 and 38) as
performance measures that relate the benefits from and to the costs of operations and other
transactions, events, and circumstances that affect an enterprise during a period. 6
Essentially, income matches the obligations against the claims of cash flow during a period while
cash flow matches realized cash outlays against actual cash receipts. However, the realization of
cash flow and claims to and obligations of cash flow (i.e., income) need not occur in the same
period. Specifically, the income recognized in a particular period t is attributable to the cash flow
realized at, before, and after this period, while the cash flow realized in the same period are
attributable to the income recognized at, before, and after this period. Accruals, as the difference
between the two, are equal to
6 According to SFAC 5-36, income is a measure of performance during a period that is concerned primarily with the
extent to which asset inflows, associated with substantially completed cash-to-cash cycles, exceed asset outflows,
associated directly or indirectly with the same cycles. Furthermore, SFAC 5-38 says that income focuses on what the
entity has received or reasonably expects to receive for its output (revenues) and what it sacrifices to produce and
distribute that output (expenses). Income also includes results of the entity‟s incidental or peripheral transactions and
some effects of other events and circumstances stemming from the environment (gains and losses).
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t t
TACC CNICFt T
t t t titti CNI tiCNItCNItiCFtCFtCFt
i1
T
t t titi CNI tiCNItiCFtCFt
i1
where CNI is the comprehensive net income, CF is the cash flow from non-equity sources (i.e.,
CFt = ∆CASHt+Dt), and T represents the number of periods it takes accruals to reverse. The
subscript denotes the period where cash flow is realized and the superscript denotes the period
where income is recognized. This identity is first highlighted in Dechow and Dichev (2002). 7
The two components of accruals are the accrued component and the deferred component, in
which their cash flow realization respectively supersedes and precedes the associated income
recognition. While the former includes outstanding expenses and accrued revenue, the latter
includes revenue received in advance, expenses paid in advance, and depreciation and
amortization expenses. Since accruals are temporary adjustments, the initiation of an accrual
item will be reversed in the latter periods. In particular, the accrued component of accruals is
initiated when it is recognized in income and reversed when its associated cash flow is realized.
Alternatively, the deferred component of accruals is initiated when the cash flow is realized and
reversed when they are recognized in income.
The initiated accrued component ( CNI ) and the reversed deferred component ( CNI ) are
t
t i
embedded in recognized income. They are the accruals that shift cash flow realized before and
after period t to income recognition in period t. Alternatively, the reversed accrued component
7 t t
Income recognised and realised in period t equals cash flow realised and recognised in period t, i.e. CNIt CFt
(3)
t
t i
.
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( CF ) and initiated deferred component ( CF ) are embedded in realized cash flow. They are
t i
t
t i
t
accruals that shift cash flow realized in period t out of income recognition in period t. In other
t t
words, accruals include both non-cash-related components in income ( CNI CNI ) and non-
titi titi income-related components in cash ( CF CF ); and this is summarized in Table 2.
t t
[Table 2 about here]
On one hand, the recognition of cash receipts (and payments) realized prior to and subsequent to
the supplies (and consumption) of goods and services in period t is shifted to income in period t.
On the other hand, the cash receipts (and payments) realized in period t for goods and services
supplied (and consumed) prior to and subsequent to period t are shifted out of income in period t.
This reinforces that the main role of accruals is to adjust cash flow to obtain income by shifting
cash flow recognition in income between periods (Statement of Financial Accounting Concept,
No. 1, Paragraph 44, Dechow 1994, and Dechow and Dichev 2002).
3.2 Modelling normal accruals
Normal accruals are the resulting accruals from the neutral accruals process that shifts cash flow
recognition (in and out of income) to the time at which it unbiasedly reflects firms‟ underlying
fundamentals, i.e., they are the „perfect foresight‟ accruals. The role of accruals in shifting cash
flow recognition in income implies that income during a period is made up of cash flows realized
in different periods. Essentially, the cash flow realized in period t and recognized in period t+i
(t–i) is the same as the income realized in period t and recognized in period t+i (t–i). Once the
14

period of income recognition and cash realization is specified, income and cash flow can be
written interchangeably in expression (3).
If CF is replaced with CNI and accruals are assumed to reverse in one period (i.e., T=1) 8 , then
expression (3) becomes
t1 t1t t
u, t u, t u, t u, t 1 u, t 1
TACC CNI CNI CNI CNI
(4)
where the superscript (subscript) denotes the period of income recognition (cash realization) and
the u superscript represents the fact that these accrual items are „unbiased‟ and reflect the
„underlying‟ economic reality. One can rearrange expression (4) as follows
where
11 TACC a CNI CNI a a CNI
u, t t u, t u, t1 t t1 u, t1
t1 t1 t
t u, t1 u, t t1 t u, t1
dtCNICNIdtdtCNI
a CNI CNI
t u, t u, t
t1 t1
a CNI CNI
t1 u, t1 u, t1
t t
d CNI CNI
t u, t u, t
t1 t1
d CNI CNI
t1 u, t1 u, t1
t t
The actual or underlying proportion of the accrued component initiated (reversed) in income is
t t 1
measured by at 1 ( at ). Likewise,
t 1
d t
t
( t 1
(5)
15
d ) measures the underlying proportion of the
deferred component initiated (reversed) in income. These parameters are positive when the
associated revenue is larger than the expenses and vice versa. Since accruals reversal takes place
within one period, the reversed parameter
t 1
at t
( t 1
t t 1
initiated parameters at 1 ( d t
) of the previous period.
d ) of the current period will be the same as the
8 This model can be generalized to the case where accruals take more than 1 period to reverse. See Appendix 1.

If cash flow recognition in income is accelerated and/or delayed, the resulting proportions will
change from their underlying proportions. For instance, if more accrued income (i.e., the
difference between accrued revenue and accrued expenses) is initiated than the underlying
accrued income, the proportion of the initiated accrued component embedded in income will be
t
different from the underlying proportion (if at 1 is not equal to one). Hence, these four
parameters can be seen as indirectly capturing the timing-recognition of accrued and deferred
components.
Expression (5) indicates that normal accruals consist of accrued (in the first line) and deferred
components (in the second line). In particular, the accrued component is shown to be a function
of growth in income and changes in accrual policy. It will be higher if there is more growth in
income, holding the accrual policy constant. Even if there is no growth in income, firms can end
up with more accrued component of accruals if there is a change in accrual policy to grant more
credit sales to debtors or to decrease the proportion of outstanding expenses. 9 If income and the
accrual policy are both constant, the accrued component of accruals will be zero as the reversed
and initiated components will offset one another.
In contrast, the deferred component of accruals is driven by forward income growth and changes
in the deferral policy. Holding deferral policy constant, higher forward income growth will lead
to a higher deferred component of accruals. When income growth is zero, firms can end up with
more deferred component of accruals if there is a change in deferral policy to pre-pay more
9 Provided that the parameter a is positive, i.e. accrued revenue is greater than accrued expenses.
16

expenses or receive less revenue in advance. 10 If there is no growth in underlying income and no
change in deferral policy, the deferred component will be zero, as its reversed component will
offset the initiated component. In short, normal accruals, as the sum of accrued and deferred
components, are driven by growth in income and changes in accrual and deferral policies.
3.3 Modelling abnormal accruals
3.3.1 Definition of abnormal accruals
Abnormal accruals are the reported accruals that deviate from underlying accruals or accruals
under a neutral accounting policy. They are accruals that distort the neutral accrual process, and
they can be attributed to both intentional and/or unintentional measurement errors. Intentional
measurement errors are also referred to as managerial discretion (i.e., managers use their
discretion to intentionally impose errors in their accrual estimates by adopting certain accounting
choices.) Since the intention of management is unobservable (Dechow and Dichev 2002), any
attempts to separate intentional and unintentional measurement errors are likely to be superficial.
As a result, this paper treats all measurement errors as undesirable and attributes them to
earnings management. 11
While some argue that earnings can also be managed through real activities (Roychowdhury
2006), this paper assumes that the accruals attributed to real activities management do not
constitute earnings management as long as they represent underlying fundamentals. Healy and
Whalen (1999) define earnings management as follows:
10 Provided that the parameter d is negative, i.e. deferred revenue is less than deferred expenses.
11 While intentional and unintentional measurement errors have different contracting implications, the separation of
the two is irrelevant when it comes to modeling the behavior of abnormal accruals, see Lai (2009). Also, whether
intentional measurement errors or managerial discretion are efficient or opportunistic (see Watts and Zimmerman
1986) is not the focus of this paper which merely focuses on the identification of earnings management.
17

“Earnings management occurs when managers use judgment in financial reporting and in
structuring transactions to alter financial reports to either mislead some stakeholders about the
underlying economic performance of the company, or to influence contractual outcomes that
depend on reported accounting numbers”
One of the keywords in their definition of earnings management is “alter financial reports to
mislead stakeholders”. Real activities or real earnings management involves the management of
real activities and it clearly does not alter financial reports. Second, Statement of Financial
Accounting Concepts No. 1 indicates that one of the main objectives of financial reporting is to
provide information about enterprise resources, claims to those resources, and changes in them.
If there are changes in real activities, financial reports and accounting figures are supposed to
reflect these changes. Hence, it is the role of financial reporting to reflect firms‟ underlying
fundamentals. The choice of transactions that determine such fundamentals is another issue
entirely.
3.3.2 Modelling earnings management
Since accruals are temporary adjustments, the initiation of an accrual item (normal and abnormal)
must be reversed at some stage. This implies that aggregated accruals over a firm‟s life-span (LP)
are zero and
LP LP
ti CNI CASH tiDti (6)
i0 i0
Aggregated accrued income is the same as aggregated cash income, which is in turn equal to
cash flow from non-equity sources ( titi 18
CASH D ). This relation is consistent with Statement
of Financial Accounting Concepts, No. 1, paragraph 46 and it applies to income reported with

any accounting distortions (conservative, aggressive, or neutral). If CNI u is the underlying
comprehensive income, then it is also true that
LP LP
tiu, ti CNI CNI
(7)
i0 i0
While fundamentally identical firms can report different periodic income due to accounting
distortions, they should have the same aggregate income over their life-span. Hence, with the
given fundamentals, the only way a firm can artificially inflate (deflate) reported income in the
current period is to borrow from (lend to) underlying income in future periods. Earnings
management can be simply regarded as a practice that shifts the recognition of underlying
income between periods.
If the income of a firm is shifted between adjacent periods (i.e., accruals reverse in one period) 12 ,
then it can be represented as
1
CNI CNI m m CNI
(8)
t u, t u, t1
t1, t t, t1
where m t1, t2
is a parameter that represents the proportion of underlying income in period t2
embedded in or shifted to underlying income in period t1. The first and second subscripts denote
the period in which the income is recognized and from which the income is borrowed,
respectively. Zero, negative, and positive mtt , 1 signifies neutral, conservative, and aggressive
accounting distortions in period t respectively. The first line of equation (8) asserts that the
reported income during a period is equal to underlying income minus the current income lent to
the past (i.e., the reversal of past abnormal accruals) plus the income borrowed from the future
12 This model can be generalised to the case where accruals take more than 1 period to reverse. See Appendix 2.
19

(i.e., the initiation of abnormal accruals). The difference between reported and underlying
t u, t
income ( CNI CNI ) is abnormal accruals if there is no distortion in reported cash flow.
The main implication from the abnormal accruals model is that abnormal accruals are driven by
a change in accounting policy and forward income growth. Reported income will be distorted
upward when income growth is positive and when there is accounting aggression and/or an
increase in the aggression level. Similarly, there will be a negative distortion in reported income
when income growth is positive and there is conservatism and/or an increase in the conservatism
level. If one restricts the proportion of future underlying income shifted to the current period to
be the same as the proportion of current underlying income shifted to the past (i.e., mt1, t mt,
t1),
the distortion in reported income is totally driven by the growth in income. Under such a
restriction where the level of accounting distortions are constant or permanent, the model yields
the well documented effect that firms tend to understate income when permanent conservatism is
associated with positive growth, with the opposite being true for permanent aggression. 13
3.4 Combining normal and abnormal accruals models
Total accruals consist of abnormal and normal components as follows
t t
TACC CNICFt u, t u, t t u, t u, t
CNI CF CNI CNI CFt CF
The items in the round brackets are the normal accruals while the items in the square brackets are
the abnormal accruals. Abnormal accruals are simply the difference between reported and
underlying income if there is no distortion in total reported cash flow (as is assumed throughout
13 See Penman (2004) for instance; and for more detailed and comprehensive analyses on the impacts of accounting
distortions on performance measures, please refer to Lai (2009).
(9)
20

this paper). Combining the normal accruals model with the abnormal accruals model (by
substituting expressions (5) and (8) into expression (9)), one yields the following accruals model:
11
t1tt1 1, , 1 1,
TACC a CNI CNI a a CNI
t t u, t u, t1 t t1 u, t1
t t t
t u, t1 u, t t1 t u, t1
d CNI CNI d d CNI
m CNI CNI m m CNI
u, t1 u, t u, t1
t t t t t t
As shown in section 2.2, there are different categories of total accruals. This accruals model can
be generalized to different categories of accruals with their respective clean-surplus flow
components and parameters (see Appendix 1 and 2 for derivation). Table 3 summarizes the
accruals model for total accruals, total working capital accruals, non-current operating accruals,
operating accruals, financing accruals, and short-term accruals used in the Jones model.
[Table 3 about here]
The different accruals models in table 3 look very similar to the one in (10) with several
t
exceptions. Firstly, there is an operating cash flow bias in total working-capital accruals ( TWC )
t
and an associated investing cash flow bias in non-current operating accruals ( NCO ). This is to
reflect the mis-classification of expenses as assets or revenue as liabilities; or vice versa (see
McVay 2006). For instance, firms that aggressively capitalize research and development
expenses will place the cash outflows as I rather than C; this leads to inflated C that is associated
with lower I for the same period. There is no such cash flow bias in total accruals in (10) because
the biases in C and I exactly offset one another. Secondly, there is no accrual component of
t
accruals in non-current operating accruals ( NCO ). This is because the income statement item
in
t
NCO , depreciation expenses, is similar to deferred components of accruals where
(10)
21

ecognition supersedes cash realization (assets are depreciated after they are acquired). Finally,
one obtains the short-term accruals (
22
t t
WC DA ) by excluding non-current working capital
accruals and the cash component of non-current operating accruals from ∆NOA. 14 This is the
accruals model that I will use in the following section in assessing unexpected accruals measures,
given the literature commonly uses short-term accruals to measure accruals (for instance Jones
1991, Hribar and Collins 2002).
The accruals models in (10) and table 3 are developed merely based on the accruals process and
the earnings management process under clean surplus accounting. They are silent on the
distortion or bias imposed by accounting standards, the motivation or consequences of earnings
management, the signaling role of managers, and the fundamentals of firms. 15 While the
omission of these factors can be considered as a shortcoming of my model, it also makes my
model applicable in the general setting. Furthermore, this omission is appropriate given the
empirical accruals models used to identify earnings management are also silent on such issues.
One can certainly incorporate these factors into this model to make a richer and sharper inference.
However, this is not the objective of this paper which is to assess whether the unexpected
accruals extracted from empirical accruals models are able to fully capture abnormal accruals (as
will be seen in the next section).
14
In other words, it is a special case of ∆NOA where (a) I is excluded from non-current operating accruals (i.e.
t t
NCO DA ) 14 t
and (b) working capital accruals take one period to reverse (i.e., T=1 in TWC ), so that only
current operating accruals are included.
15
The ever-changing nature of accounting standards makes it difficult to determine any bias imposed. Given the
FASB‟s recent favouring of „neutrality‟ over „conservatism‟ (Statement of Financial Accounting Concept, No. 2),
bias resulting from accounting standards might approximate zero in the future.

4 Assessing unexpected accruals measures
The identification of earnings management with the unexpected accruals approach critically
depends on the ability of unexpected accruals to capture abnormal accruals. With unexpected
accruals being the empirical estimates of abnormal accruals, the bias in unexpected accruals (i.e.,
the difference between the two) can be determined by three components – measurement error in
variables, heterogeneity in parameters, and omitted variables. Measurement error in variables
arises when accurate measures of accounting variables cannot be obtained. Heterogeneity in
parameters arises when parameters of individual observations differ from the regression
parameters, which reflect the average effect of the parameters of the observations involved in the
regression. Finally, the omission of relevant variables can also cause a difference between
abnormal and unexpected accruals because they will be captured by the regression disturbance
term. Since measurement errors are unavoidable in accounting variables, I only comment on
them whenever appropriate. Much of my analysis will focus on the problems of heterogeneity
and omitted variables.
4.1 Encompassing model
To derive a more general model that encompasses the Jones model, I divide the OIB of short-
term accruals in table 3 by revenue of the same period and divide DA by the lagged non-current
operating assets. Re-arranging yields
WC DA REV REV REV
t t u, t1 u, t u, t1
j j 0, t 1, t j 2, t j 3, t j
where the parameters are represented as
u
C C ,
NCO NCO
u, t1 u, t
4, t j 5, t j t, j
t
a
t
da
u, t1
PM
0, t t t
1, t TWC TWC
(11)
23

and
where
t a t
d
t
m
u, t PM
t m t
dm t d t
dd
u, t1
PM
1 t
m u, t
t m t
dm
t
gm u, t1
,
2, t TWC TWC TWC
3, t TWC TWC TWC TWC
,
4, t NCO
5, t NCO NCO NCO
u, t1 REV u, t REV
3, , 3, 4, , 4, 5, , 5,
t, j 0, t, j 0, t 1, t, j 1, t j 2, t, j 2, t j
REV NCO NCO
u, t 1 u, t 1 u, t
t j t j t j t j t j t j
ut ,
ut ,
PM represents the underlying pre-depreciation profit margin, represents the
economic depreciation rate, and the j subscript represents individual observation. The parameters
without the j subscript ( 0,t to 5,t ) are the regression parameters, while the parameters with the j
subscript ( 0, t, j to 5, t, j
(12)
) are the parameters of the individual observation. If this model is
estimated using time-series observations of the same firm, then the estimated parameters will
reflect the time-series averaged parameters. On the other hand, if this model is estimated using
cross-sectional observations for a given year, then the estimated parameters will reflect the cross-
sectional averaged parameters. 16 The implications of my analysis apply to both types of models,
and I will refer to both of these time-series observations and cross-sectional observations as
„benchmark firms‟.
The encompassing model‟s disturbance term in expression (12) for a particular firm, firm j, is
often referred to as the firm j‟s unexpected accruals. It is entirely attributed to the heterogeneity
in the parameters (i.e., the deviation of firm j parameters from parameters of benchmark firms).
This heterogeneity is shown to be due to deviations in accounting and operating policies between
16 The accruals model in Jones (1991) is originally applied in a time-series fashion. However, the cross-sectional
estimation accruals model seems to be common (in Kothari, Leone, Wasley 2004 for instance). This is probably due
to the superiority of the cross-section model over the time-series model (see Bartov, Gui, and Tsui 2000).
24

firm j and the benchmark firms. These accounting policies include accounting for working
capital accruals ( m and dm ) and accounting for depreciation expense ( m ,
t
NCO
t
TWC
t
TWC
gm ). Alternatively, these operating policies include accrual policy ( a and
ut , 1
policy ( d and dd ), and policies that drive profit margin ( PM ,
t
TWC
t
TWC
ut ,
ut , 1
economic depreciation rate ( and ).
t
TWC
t
NCO
t
dmNCO
25
and
t
da TWC ), deferral
ut ,
PM , and
ut , 1
PM ),
Since the heterogeneity in the parameters of the encompassing model is due to both the normal
accruals parameters and abnormal accruals parameters, one can express the disturbance term as
AbACC AbACC NACC NACC
(13)
t, j j j
where NACC ( AbACC j
) represents the normal (abnormal) accruals based on observation
j
specific parameters and NACC ( AbACC ) represents the normal (abnormal) accruals based on
the regression parameters. For the unexpected accruals to fully capture abnormal accruals (i.e.,
AbACC ), there are two conditions which the encompassing model has to satisfy. The
t, j j
first condition is that the income of the benchmark firm is neutral (i.e., AbACC 0 ) and the
second condition is that there is no deviation in operating policies between firm j and the
benchmark firms (i.e. NACC NACC 0 ). Otherwise, the firm j‟s unexpected accruals
j
extracted from the encompassing model will be biased by one or both of these two factors as
shown in Table 4. 17
17 If one holds the view that earnings management includes real activities or real earnings management
(Roychowdhury 2006), the deviation in underlying operating policies can be seen as capturing real activities
management. Moreover, my analysis shows that one cannot really disentangle the effect of earnings management via
accruals and earnings management via real activities because they are both captured by unexpected accruals in the
encompassing model. However, as argued in section 3.3.1, this paper holds the view that real activities management

[Table 4 about here]
If there is no deviation in operating policies and the benchmark firms are on average neutral (cell
5 of Table 4), unexpected accruals will fully capture the abnormal accruals. The encompassing
model appears to be powerful in detecting earnings management. Specifically, the unexpected
accruals from this model will be zero for firms not engaging in earnings management. They will
be positive for firms engaging in aggressive earnings management and negative for firms
engaging in conservative earnings management. Moreover, the magnitude of these unexpected
accruals will be equivalent to abnormal accruals.
If there is no distortion in the income of the benchmark firms but there is a deviation in operating
policies between firm j and the benchmark firms (in the third column of Table 4), the unexpected
accruals will be contaminated by the amount of this deviation. In particular, the firm j‟s
unexpected accruals will capture the amount of earnings management net of the effect from the
deviation in operating policies. (This deviation can be either between this firm and its past
history or between this firm and its cross-sectional peers.) If this deviation is negative (as in cell
2 of Table 4), unexpected accruals will be biased downward. Alternatively, unexpected accruals
will be biased upward if this deviation is positive (in cell 8 of Table 4). Furthermore, the
magnitude of these downward or upward biases in unexpected accruals will be determined by the
magnitude of the deviation in operating policies ( NACC NACC
j
).
does not constitute earnings management. As a result, the deviation in fundamentals is viewed as a contamination of
unexpected accruals that is supposed to capture abnormal accruals from non-neutral accounting policy in this paper.
26

If there is no deviation in operating policies but the income of the benchmark firms is non-
neutral (as in the third row of Table 4), the unexpected accruals will be contaminated by the
amount of this distortion. In particular, firm j‟s unexpected accruals capture the deviation in firm
j‟s accounting policy from the benchmark firms, rather than the full amount of abnormal accruals
attributed to the firm‟s accounting policy. The classification of firm j as aggressive or
conservative is not relative to an otherwise unbiased accounting policy but it is relative to its
benchmark firms (which can be its own time-series history or cross-sectional peers). If the
income distortion of the benchmark firms is negative (i.e., the benchmark firms are conservative),
unexpected accruals will be biased upward relative to abnormal accruals (as in cell 6). Likewise,
unexpected accruals will be biased downward when the income distortion of the benchmark
firms is positive (as in cell 3). Moreover, the magnitude of these upward or downward biases will
equal the amount of the income distortion of the benchmark firms ( AbACC ).
Finally, if there is a deviation in operating policies for firm j and the income of benchmark firms
is distorted, the bias in firm j‟s unexpected accruals will be a function of these two factors. A
positive distortion in the benchmark firms‟ income associated with a negative deviation in
operating policies between firm j and the benchmark firms will unambiguously bias unexpected
accruals downward (as in the case of cell 1 in Table 4). Likewise, a negative distortion in the
benchmark firms‟ income associated with a positive deviation in operating policies will bias
unexpected accruals upward (as in the case of cell 9 in Table 4). The magnitudes of these biases
in firm j’s unexpected accruals will be equal to the amount of the income distortion of the
benchmark firms plus the amount of the deviation in firm j‟s operating policies.
27

However, there are scenarios in which the direction of the bias in unexpected accruals is
uncertain. This is because the deviation in operating policies and the income distortion of
benchmark firms induces biases in the opposite direction and the net effect depends on the
relative magnitudes of the two biases. This occurs when there is a positive distortion in
benchmark firms‟ income and a positive deviation in operating policies (as in the case of cell 7)
or when there is a negative distortion in benchmark firms‟ income and a negative deviation in
operating policies (as in the case of cell 3).
In short, the determinants of the bias in firm j‟s unexpected accruals are attributable to the
deviation of firm j‟s operating policies from the benchmark firms and the income distortion of
benchmark firms. Whether unexpected accruals will be exacerbated, attenuated, or unaffected
relative to abnormal accruals will depend on the net effect of the two biases. Only in the
restrictive scenario where both biases are zero (cell 5), will firm j‟s unexpected accruals fully
capture its abnormal accruals. In all other cases, the unexpected accruals of firm j will be biased.
The bias in firm j‟s unexpected accruals is negative when the income distortion of the benchmark
firms is positive (cell 4), or the deviation in firm j‟s operating policies is negative (cell 2), or both
(cell 1). However, the bias in firm j‟s unexpected accruals is positive when the income distortion
of the benchmark firms is negative (cell 6), or the deviation in firm j‟s operating policies is
negative (cell 8), or both (cell 9). If the bias in unexpected accruals is extreme, the type I error
for the null of earnings management will be high for firms not engaging in earnings management.
Alternatively, if firms are managing earnings downward (upward) and the bias in unexpected
28

accruals is highly positive (negative), their unexpected accruals will be attenuated. As a result,
the type II error for the null of earnings management for this type of firm will be high.
4.2 Modified version of the Dechow and Dichev (2002) model
In the Dechow and Dichev (2002) model (hereafter DD model), working capital accruals are
regressed on lag, current, and lead cash flow from operations. After some slight modifications, it
can be reconciled with the encompassing model. Specifically, I divide the OIB of
29
t t
WC DA
in Table 3 by C of the same period and divide DA by the lagged non-current operating assets.
Re-arranging yields
t t u u u u, t1 u, t
WC DA C C C NCO NCO
(14)
j j 0, t 1, t t 1, j 2, t t, j 3, t t 1, j 5, t j 5, t j t, j
This modified version of the DD model mirrors the encompassing model. The only difference
between them is that underlying lead, lag, and current cash flow from operations (C) are used in
the former model to capture working capital accruals, while lead, lag, and current underlying
revenue are used in the latter model. This will lead to different parameter estimates (i.e., 1,t , 2,t ,
and 3,t will differ from 1,t , 2,t , and 3,t respectively) but it will not affect the unexpected
accruals which capture the heterogeneity in parameters. Since the interest in identifying earnings
management lies in extracting unexpected accruals and not in estimating the parameters, both
models are equivalent when it comes to detecting earnings management.
Despite this, one may find the modified version of the DD model to be more empirically
desirable because it is more difficult to extrapolate unbiased or underlying revenue relative to
underlying cash flow. While both revenue and cash flow from operations are subject to
management, the latter seems to be subject to relatively less management than the former. As a

esult, unexpected accruals measures from the modified version of the DD model are superior to
those from the encompassing model, and the degree of superiority depends on the extent that to
which measurement errors in revenue are greater than measurement errors in cash flow in
measuring their respective underlying items.
4.3 Jones model
To derive the Jones model, one can first re-parameterize the encompassing model in (11) as
where
WC DA REV REV REV
t t u, t u, t1 u, t1
j j 0, t 1, t j 2, t j 3, t j
NCO NCO
u, t1 u, t
4, t j 5, t j t, j
,
1, t 1, t
,
2, t 1, t 2, t
3, t 1, t 2, t 3, t
This model is econometrically identical to the encompassing model in (11) but with different
combinations of parameters being estimated (Bewley 1979). 18 If one imposes the following
restrictions 2, t 1,
t
where
, 3, 0
t , and 5, t 0
, model (15) will be reduced to
t t u, t u, t1
WC DA REV NCO
j j 0, t 1, t j 4, t j t, j
(15)
(16)
REV NCO
(17)
u, t1 u, t1
t, j 0, t, j 0, t 1, t, j 1, t j 4, t, j 4, t j
This model is commonly referred to as the Jones model, as it was originally employed in Jones
(1991) to extract unexpected accruals to test the extent of downward income management during
import relief investigations. It is simply a version of the encompassing model in (11) with
restrictions 2, t 1,
t
, 3, 0
t , and 5, t 0
.
18 This is only one possible transformation, and there are other possible transformations.
30

These restrictions respectively imply that (a) there is no change in accrual policy and profit
margin of benchmark firms between period t–1 and t, (b) the deferred component of normal
working capital accruals is zero (i.e., deferred expenses and revenue are zero), and there is no
distortion in the working capital accruals of the benchmark firms, and (c) there is no distortion in
the benchmark firms‟ depreciation expenses. Under these restrictions, the Jones model
unexpected accruals for firm j will be totally attributed to firm j‟s heterogeneity in parameters.
All the implications discussed in the encompassing model will apply.
However, if any of the 2, t 1,
t,
3, t 0
, and 5, t 0
31
restrictions do not hold, the Jones model
will be mis-specified and suffer from correlated omitted variable bias. Specifically, one period
ahead revenue growth, one period ahead revenue, and current non-current operating assets are
the relevant variables omitted from the model, and they will be captured by the disturbance term
t, j.
Since revenue is likely to be serially correlated with past revenue, the estimate of 1,t is
likely to be biased. Similarly, 4,t is likely to be biased as non-current operating assets are likely
to be serially correlated. The direction of this omitted variable bias will be determined by the
(positive or negative) signs of 2,t , 3,t , and 5,t and the correlation between the omitted
variables and the included variables (see Greene 2000 for details).
If the omitted variables do not correlate with the included variables, the parameters 1,t and 4,t
will not be biased. However, they will still contaminate the Jones model unexpected accruals,

and this contamination from omitted variables is in addition to the problems of heterogeneity. To
see this, let us re-arrange the Jones disturbance item in (17) as follows
REV NCO
u, t1 u, t1
t, j 0, t, j 0, t 1, t, j 1, t j 4, t, j 4, t j
PM a REV da PM REV
u, t t u, t t u, t1 u, t
TWC j TWC j
t dTWC u, t1 OI
t u, t1
ddTWC OI
TWC TWC NCO NCO NCO
m OI dm OI m dm gm DA
t u, t1 t u, t1 t t t u, t1
Jones model unexpected accruals do capture all portions of abnormal working capital accruals
aside from the reversal of abnormal depreciation expenses from previous period; this is shown in
the fourth line of (18). However, they are also severely contaminated by a significant portion of
normal accruals that are in addition to the heterogeneity problem encountered by the
encompassing model (and these heterogeneity problems are shown in the first line in (18)).
Since the heterogeneity problem is extensively discussed in section 4.1, I will only discuss the
additional problems specific to Jones model unexpected accruals.
Specifically, the normal accruals‟ contamination can be attributed to three sources. The first
source of contamination comes from the change in real profit margin from firm j in period t. This
u, t t u, t
is shown in the second line of (18) as PM a REV and is also equal to the growth in
TWC j
u, t u, t
profit margin ( PM PM ) times the initiated accrued component of working capital
ut ,
accruals ( OIB ). Thus, a 1% growth in profit margin will bias the Jones unexpected accruals
t 1
upward. The amount of this bias will be equivalent to 1% of the accrual component of working
capital accruals which are initiated in that period. The opposite is true if there is a negative
growth in profit margin.
(18)
32

The second source of contamination comes from the change in accrual policy for firm j in period
t. This is shown in the second line of (18) as
t u, t1 u, t
TWC j
33
da PM REV and is also equal to the
changes in accruals policy ( da ) times operating income before depreciation and amortization
t
TWC
(OIB). If the proportion of accrual component of working capital accruals embedded in OIB
increases by 1% (i.e. a relaxation in accrual policy), the Jones unexpected accruals will be biased
upward and the magnitude of this bias will be equal to 1% of OIB. The opposite argument can
be made when there is a restriction in accrual policy.
Finally, the third source of contamination comes from the magnitude of deferred component
accruals which are attributable to deferred revenue and deferred expenses (i.e., the entire third
line in (18)). The Jones model only considers the accrued component of working capital accruals
and totally ignores the deferred component. As a result, a positive deferred component of
accruals will bias Jones model unexpected accruals upward by its amount and vice versa for a
negative deferred component of accruals.
Hence, in addition to the heterogeneity problem, the Jones unexpected accruals are further
contaminated by a significant portion of normal accruals. This contamination can be attributed to
three sources – changes in profit margin, changes in accrual policy, and deferred component of
accruals. If any of these contaminations are extreme, firms that are not engaging in earnings
management will be classified as extreme earnings managers. Ceteris paribus, they will be mis-
classified as extremely aggressive if any or all of these factors is in the positive direction, and
they will be mis-classified as extremely conservative if any or all of these factors are in the
negative direction. The scenario of extreme change in profit margin supports the explanation for

the finding in Dechow et al. (1995) that the null of no earnings management is rejected at rates
exceeding the specified test-levels when applied to firms with extreme performances. However,
this paper also suggests two other scenarios in which the Jones model is likely to be mis-
specified and in which type I error for the null of no earnings management is likely to be high.
For aggressive or conservative firms, unexpected accruals will be attenuated when any or all of
the three sources of contamination is extreme in the opposite direction of the abnormal accruals.
In particular, the positive abnormal accruals of aggressive firms will be attenuated by a decrease
in profit margin, a restriction of accrual policy, and/or a negative deferred component of accruals.
The opposite is true for conservative firms when there is an increase in profit margin, a
relaxation in accrual policy, and/or the positive deferred component of accruals is negative.
These contaminations of normal accruals bias unexpected accruals toward zero, which could be a
plausible explanation for the finding in Dechow et at (1995) that the Jones-type model has
relatively low power to detect earnings managements of economically plausible magnitudes.
4.4 Modified Jones model
The very important assumption in the Jones model is that revenue is non-manipulated (indexed
by the superscript u) in both the estimation and event periods. Since underlying revenue is
unobservable, Dechow et al. (1995) used changes in cash revenue, extrapolated as the difference
between changes in reported revenue and changes in accounts receivable, instead. Hence, they
modified the Jones model to
, 1
WC DA REV REC NCO
(19)
t t m m t t m u t m
j j 0, t 1, t 2, t t, j
34

Even if the use of changes in cash revenue eliminates the problem of measurement errors in
explanatory variables, the modified Jones model still suffers from the same omitted variables
problem as the Jones model. 19 As a result, the modified Jones unexpected accruals will be
contaminated by normal accruals that are in addition to the heterogeneity in parameters problem
present in the encompassing model.
4.5 Ball and Shivakumar (2006) model
Basu (1997) suggests that unrealized losses (gains) tend to be recognized in income when
expected (realized). Ball and Shivakumar (2006) incorporated this asymmetric timeliness into the
modified Jones and modified DD models. The delayed recognition of unrealized gains can also
be regarded as an earnings management practice that shifts the recognition of income from the
current period to future periods. In particular, it will affect
dm OIB and
t
TWC
u, t 1
t t
WC DA in Table 3. These two items can be combined into one item,
t
NCO
u, t 1
35
dm DA in
dm OI , which
t u, t1
OI
captures the distortion in operating income due to changes in the level of distortion. This item
t u, t1 t u, t1
can in turn be modified as
dm OI Var Var D dm OI Var Var to reflect
OI t t ccOI t t
conditional conservatism. After re-parameterization, one yields the following
t t
WC DA 0, , X 3, D 4, VAR 5, D VAR ,
(20)
j j t i t i t t t t t t j
19 The difference between changes in reported revenue and changes in receivables do not equate to cash revenue.
Since changes in revenue (∆REV) consist of changes in deferred revenue (∆DREV), cash revenue (∆CREV), and
accrued revenue (∆AREV) and changes in accounts receivable (∆REC) are equal to accrued revenue (AREV) minus
repayments (REPAY), one can show that: (∆REV t –∆REC t )= ∆CREV t +(∆DREV t +REPAY t –AREV t-1 ). Hence, (∆REV t –
∆REC t )=∆CREV t only in the case where items in the bracket are all zero. Even if this restrictive case holds, the use
of cash revenue to extrapolate underlying revenue need not have eliminated the measurement errors in explanatory
variables problem found in the Jones model. This is because there are at least two ways in which firms can manage
cash revenue. First, managers can manage current cash revenue upward by recognizing the cash inflow associated
with deferred revenue as cash revenue and vice versa for downward management. Second, managers can manage
current cash revenue upward by recognizing the cash flow associated with previous accrued revenue as current cash
revenue and vice versa for downward management.

The main explanatory variables in the model (Xi) vary depending on whether the base model is
the modified Jones or the Dechow and Dichev (2002) model, D is equal to one if there are
unrealized losses (or bad news), and zero otherwise, VAR is the exogenous variable that serves as
a proxy for news, and 4, t j and 4 t, j 5
t, j
are the parameters that capture instances of good and
bad news, respectively. In the absence of a bias in accounting standards, conditional
conservatism is a discretionary distortion and its incorporation into the Ball and Shivakumar
model leads to more abnormal accruals being classified as expected. 20 As a result, unexpected
accruals capture a smaller proportion of abnormal accruals than a model that does not
incorporate asymmetric timeliness.
5 Correlation between normal and abnormal accruals
5.1 Correlation illustration
It may seem puzzling prima facie from the analysis in section 4 as to why the unexpected
accruals from well-specified models (like the encompassing model and the modified version of
the Dechow and Dichev (2002) model) are even contaminated. In this section, I show that such
contamination in unexpected accruals is almost unavoidable as abnormal and normal accruals are
correlated and cannot be explicitly disentangled. To see this correlation, let us make two non-
crucial assumptions – (a) accruals reverse in one period and (b) reported cash flow is unbiased.
With these assumptions, total accruals in expression (10) become
where
* *
t ttt t N D
TACC NACC DACC (21)
NACC a CNI d CNI ,
*
t
u, t u, t1
DACC m CNI ,
* ut , 1
t
20 Recall that the framework of my analysis ignores the role of accounting standard setting, see section 3.4 for details
36

The item
m m CNI
, 1
a a CNI d d CNI ,
N u, t u, t1
t t t
D u t
t t
*
NACC t is the normal accruals in the absence of heterogeneity in the accrual (a) and
deferral (d) parameters, and
*
DACC t is the abnormal accruals in the absence of heterogeneity in
the earnings management parameter (m). The normal accruals ( ) and abnormal accruals ( D
)
due to heterogeneity in parameters are assumed to be independently and identically distributed.
Income is assumed to grow at a constant rate (g) as follows:
1
u, t u, t1
CNI g CNI
(22)
With these assumptions, the correlation between abnormal and normal accruals is shown to be
t t
c orr NACC , DACC
N
t
1 1
1 1
m g a d g
m g a d g
where is the adjustment factor for heterogeneity among observations. 21
and
D N
var t var t
1 1 1
* *
var DACC
t var NACC
t
The correlation between abnormal and normal accruals is equal to positive or negative . The
term serves as an adjustment factor for heterogeneity among observations. It is 1 when the
heterogeneity in parameters is absent (i.e., when there is no deviation in accounting and
operating policies among observations). Furthermore, the direction of the correlation depends on
the direction of earnings management (i.e., m) and the direction of normal accruals (i.e., a–
d(1+g)). For aggressive earnings management, the correlation will be positive if normal accruals
21 See Appendix 3 for derivation.
(23)
37
t

are positive or negative if normal accruals are negative. The converse is true for conservative
earnings management.
In the absence of heterogeneity in parameters (i.e., =1), abnormal accruals and normal
accruals are perfectly correlated either in the same or opposite direction. Let us illustrate this
perfect correlation with accrued revenue for which cash flow is realized one period after income
recognition. In Table 5, this numerical example assumes that accrued revenue is $100 in year 1
and it grows at 20% per year.
[Table 5 about here]
Panel A shows the journal entry for this transaction if it is accounted for unbiasedly and the
resulting accruals (which are the difference between initiated and reversed accounts receivable)
are the normal accruals. Panel B shows the journal entry for this transaction if it is accounted for
conservatively such that no revenue is recognized until the cash flow is realized. Since the
resulting accruals from this conservative treatment are zero, the resulting abnormal accruals are
thus -100% of normal accruals. The correlation between abnormal and normal accruals in this
scenario is thus –1. Finally, Panel C shows the journal entry for this transaction if it is accounted
for aggressively such that 20% of the next period‟s accrued revenue is recognized (prematurely)
in this period. Since the resulting accruals from this aggressive treatment are 24% higher than the
normal accruals, the resulting abnormal accruals are thus 24% of normal accruals. Hence, the
correlation between abnormal and normal accruals in this scenario is 1. 22
22 A similar example can be made for cross-sectional firms
38

Hence, to manage earnings downward (upward), firms can delay (accelerate) the recognition of
positive normal accruals. As a result, total accruals will be lower (higher) than the normal
accruals, and abnormal accruals will be (negative) positive. If the same level of conservatism
(aggression) is to be maintained across time or firms, more negative (positive) abnormal accruals
are needed as normal accruals increase. In such a setting of no heterogeneity in the parameters,
there will be a perfect negative (positive) correlation between abnormal and normal accruals. 23
5.2 Implications
For well-specified models such as the encompassing model and the modified version of the
Dechow and Dichev (2002) model, my analysis reveals their resulting unexpected accruals are
contaminated by two factors – income distortion of the benchmark firms and deviation in
operating policy between this firm and the benchmark firms. One necessary condition for
unexpected accruals to fully capture abnormal accruals is that the benchmark firms‟ income on
average should be neutral (i.e., m=0). It is no coincidence that this is also one of the necessary
conditions that will result in a zero correlation between abnormal and normal accruals among
firms. On the other hand, when the income of benchmark firms is on average biased in one
direction (m≠0), abnormal and normal accruals are correlated. It is also no coincidence that the
resulting unexpected accruals under such a condition fail to capture abnormal accruals in full 24 .
23 The presence of heterogenity is likely to decrease this perfect correlation. In particular, the correlation between
normal and abnormal accruals is an inverse function of the variation in parameters that capture accounting and firm
policies among observations. For instance, if the variation in accounting (firm) policy is as large as the variation in
abnormal (normal) accruals among observations, the absolute correlation will be reduced to 0.5. If the former
variation is lower (larger) than the latter, it will be higher (lower) than the absolute value of 0.5. The matching
procedure proposed by Kothari et al. (2004) is likely to decrease the heterogeneity and increase the correlation.
24 See section 4.1 for details.
39

Hence, the correlation between abnormal and normal accruals could be a plausible explanation as
to why even well-specified accruals models are powerful in detecting abnormal accruals only in
very restrictive circumstances. When abnormal and normal accruals are correlated, the expected
component will unavoidably embed some abnormal accruals. As a result, unexpected accruals
extracted from these models will not capture abnormal accruals in full. Specifically, when there
is no heterogeneity between firms, the r-squared of these models will be close to one and the
model fully explains the variation in accruals which consist of both abnormal and normal
accruals. The resulting unexpected accruals will be close to zero even for serious earnings
managers. Since the high r-squared of a model can be due to its ability in correctly attributing
normal accruals as the expected component or incorrectly attributing abnormal accruals as the
expected component, this raises doubt over whether one should judge a model‟s ability to
correctly extract abnormal accruals by its r-squared.
In short, the correlation between abnormal and normal accruals inevitably leads well-specified
accruals models to incorrectly attribute abnormal accruals as the expected component and less
well-specified accruals models to incorrectly attribute normal accruals as the unexpected
component. The zero conditional assumption imposed by ordinary least squares requires the
disturbance term to be uncorrelated with the explanatory variables. The correlation between
abnormal and normal accruals exactly violates this assumption. As a result, the approach to
identify earnings management via a least square disturbance term of the regression is likely to be
problematic. This echoes the points made in McNicols (2000).
40

6 Conclusion
My analysis reveals that the factors that drive normal accruals are growth in income and changes
in accruals and deferrals policies, while abnormal accruals are driven by growth in income and a
change in accounting policies. Since income growth is the common driver for both accruals, the
two are inherently correlated. This inherent correlation violates the ordinary least squares zero
conditional assumption (that the expected component is orthogonal to the disturbance term). As a
result, even the unexpected accruals from well-specified accrual models are biased by two factors
– income distortion in the benchmark firms involved in the estimation procedure and deviation in
operating policies between the firm in question and the benchmark firms.
Researchers who use unexpected accruals to identify earnings management need to ensure that
the correlation between normal and abnormal accruals is minimized. This can be achieved by
employing the idea of the matching procedure in Kothari et al (2005) with three modifications.
First, instead of utilizing the ill-specified Jones-type models, well-specified models like the
encompassing model or the modified version of the Dechow and Dichev (2002) model should be
used. The latter model could be more empirically desirable if measurement errors are taken into
account as revenue tends to be relatively inferior to cash flow in measuring their respective
underlying items. Second, instead of matching firms on ROA alone, firms need to be matched by
their operating policy. As shown in this paper, the drivers for this operating policy are profit
margin, accrual policy, deferral policy, and economic depreciation rate. Finally, the additional
criteria for the matching firms is that their income distortion should, on average, be zero or
unbiased, i.e., they have no incentives to systematically manage earnings.
41

Alternatively, future research can move away from the unexpected accruals approach and
explore viable alternatives to extract abnormal accruals, such as ratio analysis. Despite the
finding in Beneish (1997) that a combination of changes in accounting ratios is better at
detecting GAAP violations than the Jones model unexpected accruals, his approach lacks
popularity. 25 The first reason could be because his approach yields probability measure rather
than the conventional abnormal accruals, for which interpretation is more intuitive. The second
reason could be because this approach is interested in overall accruals rather than specific
accruals, and it is the overall and not the specific abnormal accruals that determine whether a
firm is aggressive or conservative. Hence, it would be fruitful for future research to overcome
these two issues to develop a ratio analysis-based approach that extracts abnormal accruals from
total accruals.
25 Beneish (1997) examined changes in eight ratios – gross margin, depreciation, SG&A, sales growth, total accruals
to total assets, soft-assets to total assets ratio, inventory turnover, and receivables turnover.
42

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44

Appendix 1: Derivation of Normal Accruals Model
Starting with the expression (3) and rewriting income and cash flow interchangeably (see section
3.1.1 for discussion), one yields the following
where
titit t
T
u, t u, t u, t u, t i u, t i
TACC CNI CNI CF CF
Adding and deducting
i1
T
u, t u, t u, tiu, ti CNI tiCNItiCNItCNIt
i1
T
t t u, t ti u, ti ti u, ti d tiatiCNIat CNI dt CNI
i1
T
t u, t ti u, ti ti u,
ti t u, t
at i CNI at CNI dt CNI
dtiCNI
i1
a CNI CNI , a CNI CNI
t u, t u, t
titi t u, t u, t
titi ti u, ti u, ti t t
d CNI CNI , d CNI CNI
a CNI ,
t u, t1
ti above equations yields the following:
TACC
ut ,
T
i1
tiu, t1
t
ti u, ti u, ti t t
t u, t1
a CNI , d CNI , and
t
ti
u, t
ti t
u, ti t
ti
u, t1
t
ti
u, t1
ti at u, t1 CNI
ti at u, t1
CNI
ti d t
u, ti CNI
t
dt i u, t
CNI t d ti u, t1 CNI
t
dt i
u, t1
CNI
ti d t
u, t1 CNI
ti dt u, t1
CNI
aCNIaCNIaCNIaCNI
Rearranging the equations yields,
TACC
ut ,
T
i1
ti tiu, t1
t
45
d CNI from the
,
, 1
, 1
, 1
,
, 1
,
, 1
,
, 1
t u t u t t t i u t t i u t u t i
atiCNICNIatiatCNIatCNICNI
t u t u t t i t u t t i u t i u t
dtiCNICNIdtdtiCNIdtCNICNI
T T
T
t u, t u, t1 t ti u, t1
ti u, t1 u, ti atiCNICNIatiatCNIatCNICNI
i1 i1
T T T
t u, t1 u, t ti t u, t1 ti u, ti u, t1
d tiCNICNIdtdtiCNIdtCNICNI i1 i1 i1
i1

If one relates
rates
CNI
u, t i
to
CNI
ut , 1
i1
i1
1
k
k
and
1 g
k1
1
g
k1
and relates
CNI
u, t i
to
CNI
ut , 1
respectively, one yields the following:
46
using time-varying growth
T T T i1
1
TACC a CNI CNI a a CNI
a 1
CNI
u, t t u, t u, t1 t ti u, t1 ti u, t1
tititt k
i1 i1 i1 k1
1
g
T T T i1
t u, t1 u, t ti t u, t1 ti k u, t1
dtiCNICNIdtdtiCNIdt1g1CNI
It can be written as
where
a
i1 i1 i1 k1
CNI
T ut ,
t ti ut ,
i1
CNI
da
ga
TACC a CNI CNI da ga CNI
,
d
u, t t u, t u, t1 t t u, t1
d CNI CNI dd gd CNI
T ut ,
t ti ut ,
i1
CNI
t u, t1 u, t t t u, t1
CNI
CNICNI ,
dd
T u, t u, ti t ti t
u, t u, ti i1
CNI CNI
CNI
1
T u, ti i1
t t 1
u, tik i1 CNI k1
1
g
CNICNI ,
T u, ti u, t
t t ti u, ti u, t
i1
CNI CNI
u, ti 1
CNI
1 1
i1 CNI
k1
T i
t t
k
, gd u, t i g
, , 1
k u k u k
g CNI CNI 1
The difference between expression (24) and expression (5) is in the summation signs in the
parameters; they are the direct result of accruals taking more than one period to reverse.
Expression (24) will be reduced to expression (5) if T is restricted to 1. The proportion of
underlying income in period t attributable to the initiated accrued (reversed deferred) component
is
t t
a ( d ). The difference between this proportion and the proportion of the reversed accrued
(initiated deferred) component recognized in underlying income is measured by
steady-state where credit and payable policies are constant,
t
da and
(24)
t t
da ( dd ). In the
t
dd will be zero (i.e., the
proportion of the initiated component of accruals equals the proportion of the reversed
component in the steady-state). Finally,
t t
ga ( gd ) captures the interaction between the reversed

accrued (initiated deferred) proportion of income and the growth in past (forward) income. It can
be seen as an adjustment term for accruals that take more than one period to reverse. They are
zero when (a) there is no growth in past and future income, or (b) no portion of income is
deferred or prepaid in the past and the future, or (c) when T is equal to one, where T is the
number of periods it takes the accruals to reverse.
As in the implications from (5), expression (24) indicates that normal accruals comprise of
accrued and deferred components, with each of them respectively consisting of three parts. The
first part of the accrued (deferred) component of normal accruals captures the interaction
between short-term growth in income and proportions of accrued (deferred) component in
current income. If any of the two factors is zero, then the first part of the accrued (deferred)
component of normal accruals will be zero. The second part is attributed to the relaxation of
credit (payable) policy. With the same level of income, firms can end up with higher magnitudes
of accrued (deferred) components of accruals if a greater proportion of accrued revenue and/or
expenses is recognized. The final part serves as an adjustment term for accruals which take more
than one period to reverse.
Finally, the above expression can be generalized to different categories of accruals. Let AC be a
particular category of accruals, and EC is the income from the associated clean-surplus relation
in Table 1. In our previous derivation AC represents TACC and EC will represent CNI. Likewise,
if AC represents ∆NOA, then EC will represent OI. One can show that for a given AC,
where
a
EC
T ut ,
t ti ut ,
i1
EC
da
ga
,
d
AC a EC EC da ga EC
u, t t u, t u, t1 t t u, t1
T ut ,
t ti ut ,
i1
EC
d EC EC dd gd EC
EC
ECEC ,
dd
T u, t u, ti t ti t
u, t u, ti i1
EC EC
EC
1
T u, ti i1
t t 1
u, tik i1 EC k1 1
gEC
t u, t1 u, t t t u, t1
ECEC ,
T u, ti u, t
t t ti u, ti u, t
i1
EC EC
u, ti 1
EC
1 1
i1 EC
k1
T i
t t
k
, gd u, t i g
EC
, , 1
k u t k u t k
g EC EC
1
EC
(25)
47

Appendix 2: Derivation of Abnormal Accruals Model
If the income of a firm can be shifted between periods, then they can be represented as
t
T
u, t
t, ts
T
u, ts th, t
EC
u, t
s1 h1
CNI CNI m CNI m CNI
where m t1, t2
is a parameter that represents the proportion of underlying income in future periods
embedded in or shifted to period t‟s reported income. The first and second subscripts denote the
period in which the income is recognized and from which the income is borrowed, respectively.
As the maximum that a firm can borrow from the future is what is available to lend, m jt , is
smaller than 1. Zero, negative, and positive mtt , 1 signifies neutral, conservative, and aggressive
accounting distortions in period t respectively.
Adding and deducting the two items
s1 s1
T
T
th , t u, t
t, tsu, t1
m CNI
and m CNI
yields the following:
h1
s1
T T T T
t u, t t, ts u, ts th , t u, t t, ts u, t1 t, ts u, t1
CNI CNI m CNI m CNI mCNImCNI s1 h1 h1 h1
Relating
T T
t, ts u, t1 t, ts u, t1
m CNI m CNI
CNI
u, t i
to
CNI
i1
k
using time-varying growth rates 1 g
ut , 1
equation yields the following
where
T
t u, t th, t u, t1 u, t
CNI CNI m CNI CNI
h1
re-arranging the
T T T s1
t, ts th , t u, t1 t, ts k u, t1
m m CNI m 1 g 1 CNI (26)
k1
h1 h1 s1 k1
CNI m CNI CNI dm CNI gm CNI
u, t t u, t1 u, t t u, t1 t u, t1
T
t t, t h
m m
T T
t t, tsth, t
, dm m m
s1
T s1
t t, ts k
gm m 1g1 s1 k1
s1 h1
48

The portion of underlying income in current periods that is shifted to previous periods is
measured by
t
m . If I aggregate the proportions of underlying income beyond period t shifted to
period t and the proportions of underlying income shifted from period t to periods before t,
measures the deviation between these two aggregated portions which is zero under steady-state
conditions. Finally,
49
t
dm
t
gm captures the interaction between the portion of income shifted to the
current period and future growth in income. It can be seen as an adjustment term for accruals that
take more than one period to reverse. They are zero when (a) there is no growth in future income,
or (b) no portion of income is shifted from future underlying income to the current period, or (c)
when T (the number of periods that it takes for accruals to reverse) is one. The main implication
from the above expression is that the difference between reported and underlying income (i.e.,
the accounting distortion in reported income) is attributed to three parts that respectively capture
short-term growth, temporary accounting distortions, and long-term growth.
The expression (26) can be generalized to operating income and financing income. For a given
earnings component (EC) like CNI, OI, or NFE, the following is true
where
T
t t, t h
EC EC
s1
m m
u, t u, t t u, t1 u, t t u, t1 t u, t1
EC EC m EC EC dm EC gm EC (27)
,
T T
t t, tsth, t
dmEC mEC mEC
s1 h1
11 s1 k1
T s1
t t, ts k
, gmEC mEC gEC
Combining expression (25) and expression (27), one yields the following accruals model:
AC a EC da ga EC
t t u, t t t u, t 1
AC AC AC
d EC dd gd EC
t u, t1 t t u, t1
AC AC AC
t u, t1 t t u, t1 u, t
mACEC dmAC gmAC EC CFCt CFC
where AC is a particular accruals component, and EC and CFC are the income and cash flow
components from the associated clean-surplus relation in Table 1. This accruals model can be
generalised to different categories of accruals with their associated clean-surplus flow
components and parameters as shown in table 3.
(28)

Appendix 3: Correlation between Abnormal and Normal Accruals
If growth is assumed to grow at a constant rate g as follows
This implies the following
1
u, t u, t1
CNI g CNI
(29)
u, t u, t1 u, t1 u, t
CNI CNI g CNI g CNI
u, t1 u, t1
cov g CNI , g 1 g CNI
2 ut , 1
g 1 g var CNI
cov , cov ,
u, t u, t1
CNI g CNI
2 ut , 1
g var CNI
var var
u, t1 CNI g u, t1
g CNI
2 2
ut , 1
g 1 g var CNI
var var 1
As a result, one can show that the correlation between normal and abnormal accruals in the
absence of deviation in accounting policy and fundamentals is as follows:
*, *
corr NDAC DACC
u, t u, t1 u, t1
cov aCNI dCNI , mCNI
u, t u, t1 u, t1
var aCNI dCNI var mCNI
u, t u, t1 u, t1 u, t1
a m cov CNI , CNI d m cov CNI , CNI
2 u, t 2 u, t1 u, t u, t12ut
, 1
avarCNIdvarCNI2adcov CNI , CNI
m var CNI
2 2 2
a m g 1gdmg1g 2 2 2 2 2 2 2 2
2
agdg1g2adg1gmg1g
1 1
2
2
2
2 2
a m g g d m g g
1 2 1 1
2 2 2 4
a d g a d g m g g
1 1
1 1
m g a d g
m g a d
g
50

Hence, the correlation between normal and abnormal accruals in the absence of heterogeneity is
1 1
1 1
m g a d g
m g a d g
In the presence of heterogeneity, one can show that the correlation between normal and abnormal
accruals is as follows:
* N * D
t t, t t
corr NDAC DACC
* N * D * N * D
NDACt t DACCt t NDACt t DACCt t
cov , var var
* * * N *
D
NDACt DACCt NDACt tDACCt t cov , var var var var
* NDAC *
DACC
N
D
cov , var
t t t
var t
11 * * *
*
var NDACt var DACCt var NDACt
var DACCt
N D
var var
* *
t t
corr NDACt, DACCt
1 1
* *
var NDACt var DACCt
1
1
1
1
51

Table 1: Accounting Identity
Item Identity or clean surplus relation
CASH CASH CASH C I F D
CSE
NCO
NFO
t t1 t t t t
t t1 t
CSE CSE CNI Dt
NCO NCO I DA
t t1 t
t
t t1 t
NFO NFO NFE Ft
NOA t t1 t
NOA NOA OI C I
TWC
t t1 t
TWC TWC OIB Ct
t t
Table 1 summarizes the accounting identities for cash (CASH), net operating asset (NOA), total working capital
(TWC), non-current operating asset (NCO), net financing liability (NFO), and common shareholder equity (CSE). C
is the cash flow from operations, I is the cash flow to investments for operations, F represents the cash flow from
non-equity financing activities, D is the cash outflow from equity-financing activities. OI is the comprehensive
operating income. OIB is the comprehensive operating income before depreciation and amortization. DA is the
comprehensive depreciation and amortization expenses. NFE is the comprehensive net financing expenses. CNI is
comprehensive income
52

Table 2: Summary of Accruals Components
Accrued Component
(if t superscript is less
than the t subscript, i.e.,
income recognition
precedes cash flow
realization)
Deferred Component
(if t superscript is more
than the t subscript, i.e.,
income recognition
supersedes cash flow
realization)
Initiation at period t
(if either the t superscript or the t
subscript has a “+” sign, i.e., an
item is initiated in period t and
reversed in period t+i)
t
CNIt i
t i
CFt
Reversal at period t
(if either the t superscript or the t
subscript has a “-” sign, i.e., an
item was initiated in period t-i
and reversed in period t)
t i
CFt
t
CNIt i
Table 2 summarizes the four accruals components depending on whether they are an accrued or deferred component
or whether they are an initiation or reversal component.
53

Table 3: Generalisation of Accruals Model to Different Categories of Accruals
Accrual Drivers
Total
accruals
Total
working
capital
accruals
Noncurrent
operating
accruals
Operating
accruals
Financing
accruals
Shortterm
accruals
TACC a CNI da ga CNI
t t u, t t t u, t1
d CNI dd gd CNI
t u, t1 t t u, t1
t u, t1 t t u, t1
m CNI dm gm CNI
TWC a OIB d OIB
t t u, t t u, t1
TWC TWC
t daTWC t u, t1 gaTWC OIB t ddTWC t u, t1
gdTWC OIB
t
mTWC u, t1 OIB
t dmTWC t u, t1 gmTWC OIB Ct u
Ct
NCO d DA dd gd DA
t t u, t1 t t u, t1
NCO NCO NCO
t u, t1 t t u, t1u mNCODA dmNCO gmNCO DA It I
t
NOA a OI da ga OI
t t u, t t t u, t1
NOA NOA NOA
d OI dd gd OI
t u, t1 t t u, t1
NOA NOA NOA
t u, t1 t t u, t1
mNOAOI dmNOA gmNOA OI
FIN a NFE da ga NFE
t t u, t t t u, t1
FIN FIN FIN
d NFE dd gd NFE
t u, t1 t t u, t1
FIN FIN FIN
t u, t1 t t u, t1
mFINNFE dmFIN gmFE NFE
t u, t t u, t1 t u, t1 t u, t1
aTWCOIB daTWCOIB dTWC OIB ddTWCOIB
t u, t1 t u, t1u mTWC OIB dmTWCOIB Ct Ct
u, t t u, t1 t t u, t1
DA mNCODA dmNCO gmNCO DA
t
WC
t
DA
Table 3 summarizes the accruals model applicable to total working capital accruals (∆TWC), non-current operating
accruals (∆NCO), operating accruals (∆NOA), financing accruals (∆FIN), and short-term accruals (∆WC – DA).
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Table 4: Summary of the Bias in Unexpected Accruals for the Encompassing
Model
NACC NACC0 j
Cell 1:
t, j AbACC j
NACC NACC0 j
Cell 4:
t, j AbACC j
NACC NACC0 j
Cell 7:
Uncertain
AbACC 0 AbACC 0 AbACC 0
Cell 2:
t, j AbACC j
Cell 5:
t, j AbACC j
Cell 8:
, AbACC t j j
Cell 3:
Uncertain
Cell 6:
t, j AbACC j
Cell 9:
, AbACC t j j
Table 4 summarizes the bias in unexpected accruals relative to abnormal accruals for the encompassing model.
WC DA REV REV REV NCO NCO
t t u, t1 u, t u, t1 u, t1 u, t
j j 0, t 1, t j 2, t j 3, t j 4, t j 5, t j t, j
represents the error term extracted from the encompassing model.
t, j
NACC (
j
55
AbACC ) represents the
j
normal (abnormal) accruals based on the observation specific parameter from the encompassing model and
NACC ( AbACC ) represents the normal (abnormal) accruals based on the regression parameter from the
encompassing model.

Table 5: Illustration of the Correlation between Abnormal and Normal Accruals
1 2 3 4 5 6 7 8 9 10 11
Panel A – Unbiased treatment of accrued revenue that will be received one period after
Dr. Receivables 100 120 144 172.8 207.4 248.8 298.6 358.3 430.0 516.0 0.0
Cr. Revenue 100 120 144 172.8 207.4 248.8 298.6 358.3 430.0 516.0 0.0
Dr. Cash 0 100 120 144 172.8 207.4 248.8 298.6 358.3 430.0 516.0
Cr. Receivables 0 100 120 144 172.8 207.4 248.8 298.6 358.3 430.0 516.0
Total accruals 100 20 24 28.8 34.56 41.47 49.77 59.72 71.66 86.00 -515.98
Normal 100 20 24 28.8 34.56 41.47 49.77 59.72 71.66 86.00 -515.98
Abnormal 0 0 0 0 0 0 0 0 0 0 0
Panel B – Conservative treatment of accrued revenue where no revenue is recognised till cash is received
Dr. Receivables 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Cr. Revenue 0 100.0 120.0 144.0 172.8 207.4 248.8 298.6 358.3 430.0 516.0
Dr. Cash 0 100.0 120.0 144.0 172.8 207.4 248.8 298.6 358.3 430.0 516.0
Cr. Receivables 0 0 0 0 0 0 0 0 0 0 0
Total accruals 0 0 0 0 0 0 0 0 0 0 0
Normal 100 20 24 28.8 34.56 41.47 49.77 59.72 71.66 86.00 -515.98
Abnormal -100 -20 -24 -28.8 -34.56 -41.47 -49.77 -59.72 -71.66 -86.00 515.98
Panel C – Aggressive treatment of accrued revenue where 20% of next period‟s revenue is recognised in this period
Dr. Receivables 124 148.8 178.56 214.27 257.13 308.6 370.3 444.3 533.2 639.8 0.0
Cr. Revenue 124 148.8 178.56 214.27 257.13 308.6 370.3 444.3 533.2 639.8 0.0
Dr. Cash 0 124 148.8 178.56 214.27 257.1 308.6 370.3 444.3 533.2 639.8
Cr. Receivables 0 124 148.8 178.56 214.27 257.1 308.6 370.3 444.3 533.2 639.8
Total accruals 124 24.8 29.76 35.71 42.85 51.43 61.71 74.05 88.86 106.64 -639.81
Normal 100 20 24 28.8 34.56 41.47 49.77 59.72 71.66 86.00 -515.98
Abnormal 24 4.8 5.76 6.91 8.29 9.95 11.94 14.33 17.20 20.64 -123.83
This numerical example assumes that accrued revenue is $100 in year 1 and it grows at 20% per year. Panel A shows the journal entry for this transaction if it is
accounted for unbiasedly. Panel B shows the journal entry for this transaction if it is accounted for conservatively such that no revenue is recognized until the
cash flow is realized. Finally, Panel C shows the journal entry for this transaction if it is accounted for aggressively such that 20% of the next period‟s accrued
revenue is recognized (prematurely) in this period.
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