Predicting earnings management a nonlinear approach

Because firms with extreme performance are more likely to engage in earnings management Guay, Kothari, & Watts, 1996, the conventional linear accrual models that do not consider the asym

Ruei-Shian Wu

DOI: doi: 10.1016/j.iref.2013.11.001

To appear in: International Review of Economics and Finance

Received date: 3 March 2011

Revised date: 6 November 2013

Accepted date: 10 November 2013

Please cite this article as: Wu, R.-S., Predicting Earnings Management: A

Nonlinear Approach, International Review of Economics and Finance (2013), doi:

10.1016/j.iref.2013.11.001

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Predicting Earnings Management: A Nonlinear Approach

Ruei-Shian Wu

Yuan Ze University College of Management

135 Yuan-Tung Road Chung-Li 32003, Taiwan Phone: +886-3-463-8800 ext.2195 Fax: +886-3-463-3824 E-mail: rswu@saturn.yzu.edu.tw

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1 Introduction

Accrual accounting, with all its strength and weaknesses, occupies the dominant position in

external financial reporting and is, therefore, the primary means by which the capital market

measures firm value To reflect positively on economic activity during a given period,

accrual accounting temporally disconnects the recognition of revenues and expenses from

their associated cash flows The result is earnings and balance sheet measures with prime

roles in performance measurement, valuation, and contracting However, the judgments

required within accrual accounting offer managers opportunities to mislead stakeholders

and alter contractual results to their benefit Previous research has examined earnings

management via consideration of specific accruals, total accruals, and the decomposition of

total accruals to their abnormal and discretionary components Normal accruals relate to

changes in economic circumstances, such as changes in sales and fixed assets Accruals

other than normal accruals are perceived as discretionary That is, discretionary accruals are

considered those accruals that are prone to manipulation (Healy, 1985) The literature has

widely investigated the association between discretionary accruals and earnings

management

Researchers have commonly employed the Jones (1991) model and the modified Jones

model (Dechow, Sloan, & Sweeney, 1995) to estimate the discretionary component of

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accruals Using simulation studies, Dechow et al and Kothari, Leone, and Wasley (2005)

show that these models often provide reasonable estimates for detecting earnings

management However, they point out that the models present problems for firms

experiencing extreme levels of performance Such problems may reflect measurement

errors Thus, to improve the estimation quality, accrual models must consider the context to

which earnings management is hypothesized

In addition to the measurement error inherent in discretionary accruals models (e.g.,

McNichols & Wilson, 1998), coefficient bias can also stem from using balance sheet data

rather than cash flow statement data (Hribar & Collins, 2002) Thus, possible improvements

to the Jones model and the modified Jones model include adding cash from operations,

earnings, and return on assets (DeAngelo, DeAngelo, & Skinner, 1994; Jeter & Shivakumar,

1999; Kothari et al., 2005; Rees, Gill & Gore, 1996), controlling for firm performance

(Holthausen et al., 1995; Kothari et al., 2005), and using cash flow statement data to check

the robustness (Hribar & Collins, 2002)

In addition, researchers have recently begun to question the assumption that the

accrual-generating process in the existing empirical cross-sectional accrual models is

inherently homogeneous That is, cross-sectional accrual models such as the Jones model

and the modified Jones model implicitly assume that firms within the same industry in a

given year have a homogeneous accrual-generating process Dopuch, Seethamraju,

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Mashruwala, and Zach (2007) argue that the assumption of a uniform accrual-generating

process is violated in industries Because the accrual-generating process affects the

measurement of the accrual models’ coefficients, whether a substantial variation exists in

the estimated coefficients of each explanatory variable across the different levels in accrual

models is important

Because firms with extreme performance are more likely to engage in earnings

management (Guay, Kothari, & Watts, 1996), the conventional linear accrual models that do

not consider the asymmetric influences of performance variables may lead to biased

inferences Previous studies (Ball & Shivakumar, 2006; Kothari et al., 2005) have attempted

to solve the nonlinear relation between accruals and performance proxies Kothari et al.’s

performance-matched accrual model, which uses return on assets (ROA) as a proxy for

performance, does not assume a linear relation between accruals and performance Although

Kothari et al.’s nonlinear model is less misspecified than the Jones model and the modified

Jones model, the model still suffers overrejection or underrejection when adopting

earnings-to-price ratio, firm size, and operating cash flow as the performance proxy

Moreover, by matching each firm-year observation with another firm in the same industry

and year and then calculating the differences for the Jones and modified Jones discretionary

accruals with the closest ROA, the model assumes that firms in the same industry with

similar ROA have comparable discretionary accruals Therefore, if either firm numbers in

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an industry are small or the variation in ROA in an industry is large, a measurement error is

generated In addition, if the hypothesis of earnings management is applied to a firm with an

extreme earnings-to-price ratio, firm size, or operating cash flow, Kothari et al.’s

ROA-matched discretionary accrual model leads to misspecified tests

Although Ball and Shivakumar (2006) adopted a piecewise linear regression model to

address the impact of losses on accruals, their study does not focus on the coefficient bias

resulting from the nonlinear relation between accruals and performance proxies other than

economic losses I examine the variation of coefficients across performance quartiles and

the effect of the nonlinear relation between accruals and performance Because the

performance-matched accrual model exhibits these limitations, I adopt a three-breakpoint

piecewise linear regression to accommodate the possibility of a nonlinear relation between

accruals and performance proxies

A number of studies show that the Jones model suffers an omitted variable problem

(DeAngelo et al., 1994; Dechow et al., 1995; Jeter & Shivakumar, 1999; Kothari et al., 2005;

Rees et al., 1996) However, commonly used accrual models do not include cost- or

expense-related variables According to a U.S Government Accountability Office (GAO;

2007) report, revenue recognition issues account for approximately 38 percent of

restatements between January 1997 and June 2002 and are the main reason for restatements

during this period Nevertheless, cost- or expense-related issues account for more than

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one-third of the restatements from July 2002 through September 2005 and surpass revenue

recognition as the most frequently identified cause of restatements in the period after the

passage of the Sarbanes–Oxley Act (SOX) Therefore, I further take cost- and

expense-related variables into account

To compare the ability of conventional linear accrual models and my nonlinear

expense-related accrual model to discriminate between firms engaging in earnings

management and firms not engaging in earnings management, I use GAO (2002, 2006,

2007) reports to identify firms with a financial restatement to proxy for firms with earnings

management The control group is composed of firms in the same industries but not in the

GAO reports and without a financial restatement record in Compustat

The results suggest that the relation between accruals and performance proxies is

nonlinear The findings show that the nonlinear expense-related accrual model is

well-specified and enhances the reliability of inferences in earnings management issues My

objective is not to develop a cure-all accruals model, in terms of either accounting theory or

empirical fit with accruals data Rather, I demonstrate a specification improvement in

nonlinear accrual models by incorporating the asymmetric influence of performance levels

associated with specific earnings management issues (i.e., event-specific studies of earnings

management) In addition, I show the robust results after the passage of SOX

The remainder of the paper is organized as follows Section 2 presents the variation of

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coefficients across performance partitions Section 3 develops the models with

consideration for the nonlinear relation between accruals and performance proxies Section

4 describes the data selection procedure, and Section 5 outlines the results Section 6

presents my conclusions

2 Coefficient bias

Prior studies estimate the accrual models using time-series (e.g., Dechow et al., 1995; Jones,

1991), cross-sectional (e.g., Cheng, Davidson, & Leung, 2011; Kothari et al., 2005; Shu &

Chiang, 2013), and panel (e.g., Ball & Shivakumar, 2006) regressions Using samples to

estimate coefficients in conventional linear accrual models assumes the slope coefficients

are constant within the sample, that is, observations in the sample have a uniform

accrual-generating process (Bartov et al., 2000) If an accrual model estimates the

coefficient within the same industry, it assumes that firms in the same industry have similar

accrual-generating processes However, the uniform accrual-generating process assumption

may not be proper for firms with extreme performance within the industry, leading to biased

discretionary accrual estimates In the following discussion, I review the properties of

coefficients in linear regressions and then inspect whether the coefficients are equal across

firms in different performance quartiles

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2.1 Properties of coefficient in linear accrual models

In conventional linear accrual models the coefficients are estimated under the uniform

accrual-generating process This study relaxes this assumption for firms within the same

industry category in a given year but with different levels of performance To assess

coefficient bias in relation to performance, I consider coefficients for subsamples based on

performance Let B be the pooled sample coefficient matrix, x be the independent variable

vector, and y be the dependent variable matrix I divide the pooled sample into m

subsamples; therefore, the subsample’s independent and dependent matrices are



] [

]

][

[ ]

 

m

m y y x

x x x

)

( ]

 

m

m y x x x y

x x

x     

   1

1 1 1

] [

] [

m

m y x x x y

x x

x       

   1

1 1 1

] [

] [

m m m m m

m x x x x y x

x x y

x x x x x x

x         

1 1 1 1 1 1 1 1

] ][

[ ] [

] ][

[ ] [

 ,   [1 m] i 1 , ,m is

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a matrix of the ratios of the sum of subsample values squared to the sum of full sample values squared, and   [1 m]  i 1 , ,m is the coefficient matrix of subsample is For equation (1), the pooled sample coefficient is calculated by subsample coefficients

with the weights of a function of subsample independent variables The linear accrual

models directly estimate the coefficient of B and do not take into account the corresponding coefficient matrix of subsamples, which are identified by performance levels If 1through mare not statistically different from B, that is, if the accrual-generating processes for the subsamples are identical, the conventional linear accrual model will not misestimate

discretionary accruals for subsamples formed based on performance Otherwise, the

uniform accrual-generating assumption that restricts the vector β equals B and may result

in biased discretionary accruals and false inferences of earnings management I discuss the

likely biases separately for the upward and downward earnings management

 Case 1: Upward earnings management (discretionary accruals > 0) If the estimated coefficients overestimate the true coefficients, the discretionary accruals will be

undervalued Such misspecification results in a rejection rate that is too low and

biased in favor of the null hypothesis However, if the coefficient matrix

underestimates the true values, the discretionary accruals will be too large This

misspecification leads to a higher rejection rate

 Case 2: Downward earnings management (discretionary accruals < 0) If the

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coefficient matrix overestimates the true coefficients, discretionary accruals will be

undervalued Large negative discretionary accruals produce a high rejection rate and

are associated with overrejection Nevertheless, the undervaluation of the coefficient

matrix causes the discretionary accrual to be overvalued and to approach zero from

left; the closer to zero the discretionary accrual is, the harder it is to reject the null

hypothesis Therefore, if the coefficient matrix is overvalued (undervalued), the null

hypothesis is overrejected (underrejected)

2.2 Relations between accruals and performance

In the conventional linear accrual model, explanatory variables are obtained from financial

statements Because a number of studies confirm a negative relation between size and

performance (Fama & French, 1992; Lakonishok, Shleifer, & Vishny, 1994, among others),

I recognize size as a performance proxy Here I consider the relations between accruals and

various performance proxies If the relations are linear, prior earnings management studies

regarding performance are still reliable (Bartov et al., 2000) Otherwise, the coefficient bias

may lead to misspecified tests and either overrejection or underrejection

To capture intuitively the relation between accruals and performance proxies, in Figure

1 I plot mean values of accruals scaled by total assets at the beginning of the year across

performance deciles Specifically, Figures 1.1 to 1.8 plot, respectively, mean accruals across

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deciles of (a) change in sales; (b) change in sales less change in accounts receivable; (c)

property, plant, and equipment; (d) the inverse of beginning total assets for the period; (e)

lagged total accruals; (f) return on assets; (g) change in cost of goods sold less change in

inventory; and (h) change in operating cash flow The average accruals positively correlate

to change in sales, change in sales adjusted by accounts receivable, lagged total accruals,

and return on assets Not surprisingly, operating cash flow has negative correlation with

average accruals The relations between average accruals and performance are nonlinear,

except for lagged total accrual

[FIGURE 1 ABOUT HERE]

3 Discretionary accrual measurement

I replicate the results of prior research by using conventional linear accrual models and

pooled data as the comparison benchmark I then apply a piecewise linear regression

approach to create the nonlinear Jones model and nonlinear modified Jones model These

nonlinear models use the same independent variables as the conventional Jones model and

modified Jones model but relax the linearity assumption to allow the effect of each predictor

variable to vary across different predictor quartiles By comparing the conventional Jones

model with the nonlinear Jones model and the modified Jones model with the nonlinear

modified Jones model, we can observe the influence of nonlinearity in the accrual models

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Next, I consider the nonlinear influence of performance, which is commonly related to

earnings management scenarios of interest I reproduce Kothari et al.’s (2005)

performance-matched discretionary accruals Because researchers commonly use the

accruals model to detect earnings management, it can be used as a comparison benchmark

Finally, I construct my nonlinear accrual model by further considering cost- or

expense-related earnings management, which is omitted in previous accrual models In my

nonlinear accrual model, I also employ a piecewise linear regression approach to estimate

discretionary accruals

3.1 Linear accrual models

I employ Kothari et al.’s (2005) adaptation of the Jones and modified Jones accruals models

Like Kothari et al., I include an intercept term as an additional control for heteroskedasticity

that is not alleviated by using assets as the deflator and to mitigate problems stemming from

an omitted size variable The resulting Jones and modified Jones models are, respectively,

as follows:

t t t

)

1

1 1

t t t

t t

)

1

1 1

where Act is accruals in year t, Sales t is change in sales, PPEt is gross property, plant,

and equipment, and AR t is change in accounts receivable, all scaled by beginning of the

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period total assets (TAt–1)

3.2 Nonlinear Jones and nonlinear modified Jones models

To address the nonlinearity issue, I first relax the linear assumption in the Jones and

modified Jones models I employ a three-breakpoint piecewise linear regression to consider

the nonlinear relation among total accruals, change in sales, change in sales adjusted by

change in accounts receivable and property, plant, and equipment The nonlinear Jones

model is

t Q

Q i

i t t i

t t

i t i t i

t t

t t

PPE DP Sales

DS DP

DS

PPE Sales

TA Ac

1

, ,

, ,

1

])()

(1[

)()(

)

1(

The nonlinear modified Jones model is

t Q

Q

i

i t t i

t t

t i t i t i

t t

t t

PPE DP AR

Sales DS

DP DS

PPE Sales

TA Ac

1

, ,

, ,

1

])()

(2[

)()(

)

1(

where DS1i,t, DS2i,t and DPi,t are dummy variables that equal 1 if change in sales, change in

sales adjusted by accounts receivable and gross property, plant, and equipment are located

respectively in the quartile i groups (Qi) in year t, and zero otherwise, and  is the error term

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3.3 Performance-matched accrual model

The performance-matched accrual model proposed by Kothari et al (2005) is based on the

Jones or modified Jones model with one more step: matching firms on current or annually

lagged return on assets For the performance-matched discretionary accrual measure for

Firm A, I subtract Firm A’s model-derived discretionary accrual estimate from the estimate

for the firm in the same industry with most closely matched ROA or lagged ROA Previous

studies also adopt ROA or lagged ROA as an additional independent variable in accrual

models and yield results similar to those found using the previously mentioned

sample-matched approach To enhance the comparability among various accrual models, I

report the empirical results of the performance-matched model by adopting ROA or lagged

ROA as an additional variable in the regression model The performance-matched Jones

model on ROA is

t t t

t t

TA



)()()(

)

1

1 1

the performance-matched Jones model on lagged ROA is

t t t

t t

TA



)(

)()(

)

1

1 1

the performance-matched modified Jones model on ROA is

t t t

t t

)

1

1 1

the performance-matched modified Jones model on lagged ROA is

t t t

t t

)()(

)

1

1 1

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where ROAt and ROA t-1 are return on assets in year t and year t–1, respectively

3.4 Nonlinear expense-related accrual model

I further consider the nonlinear relation between accruals and performance by employing

piecewise linear regression to allow the coefficients to vary with performance In terms of

performance, I include cost- and expense-related variables A number of studies show that

the Jones model suffers an omitted variable problem (e.g., DeAngelo et al., 1994; Dechow

et al., 1995; Jeter & Shivakumar, 1999; Kothari et al., 2005; Rees, Gill & Gore, 1996)

Therefore, I amend the basic model to include additional explanatory variables I include

the explanatory variables of the Jones model with an adjustment to the change in sales

Dechow et al (2003) suggested change in accounts receivables should not be fully deducted

They suggested using ((11)Sales t AR t)as an explanatory variable, where

 1

 is the coefficient estimate of Sales t, instead of (Sales t AR t) They estimated the following

equation:

t t

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Because previous studies show that prior accruals have predictive power for current

accruals (Beneish, 1997; Chambers, 1999; Dechow, 2003), I add lagged total accruals as an

explanatory variable Then, I add ROA and change in operating cash flow to control for

performance (Ball & Shivakumar, 2006; Kothari et al., 2005; McNichols, 2000) I add

change in cost of goods sold adjusted by change in inventory to consider the role of expense

management The Jones model does not specifically address the role of expenses According

to a GAO (2007) report, revenue recognition issues accounted for almost 38 percent of

restatements from January 1997 through June 2002, but cost- or expense-related issues

account for more than one-third of the restatements from July 2002 through September

2005, surpassing revenue recognition as the most frequently identified cause of restatements

in this subsequent period Therefore, I construct a nonlinear model that considers cost- or

expense-related earnings management as

t Q

Q i

t t i t i t

 3

1

, ,

Di,t is a dummy variable matrix, where the element equals 1 if the explanatory variable is

located in the quartile i group (Qi) in year t, and zero otherwise B t, Γt, and Λt, are corresponding coefficient matrices of independent variables

3.5 Logit model analysis

To compare the discriminatory power in identifying presumably managing firms from the

presumably nonmanaging firms, I adopt a logit model to analyze the explanatory power

among discretionary estimates among various accrual models:

{)(Y1 

i

where Y1is a dummy variable equals 1 when the firm is in GAO group, P(Y1) is the

probability of firms falling into the GAO group, DA i , i = 1,…,11 is a matrix of discretionary

accrual estimates including



1

DA the discretionary accrual estimate based on the cross-sectional Jones model for

each two-digit SIC code in any given year,

DA the discretionary accrual estimate based on the performance-matched Jones

model on lagged ROA,



7

Jones model on ROA,



8

DA the discretionary accrual estimate based on the performance-matched modified

Jones model on lagged ROA,

DA the discretionary accrual estimate based on the nonlinear modified Jones

expense-related accrual model, and



11

DA the discretionary accrual estimate based on the nonlinear expense-related

accrual model

Industry control dummies, SICj, represent the jth industry classified by two-digit SIC codes

Ψ and Φ are coefficient matrices of the corresponding variables

I adopt each discretionary accrual estimate and industry control variables in the logit

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model to confirm the model’s ability to detect the GAO group Then I adopt each

discretionary accrual estimate and the difference of discretionary accruals estimated

between the nonlinear expense-related accrual model and the other accrual models to

compare the discriminatory power among various discretionary accrual measures

{)(Y1 

i i

i

where DA 11 –DA i is the additional effect generated by the nonlinear expense-related accrual model and λ is the corresponding coefficients If the conventional linear accrual models,

performance-matched accrual models, and the nonlinear Jones or nonlinear modified Jones

model do not serve as good tools to detect presumably managing firms, the estimated

coefficients of these models would not be significant At the same time, the marginal

contribution of the nonlinear expense-related model would be significant

4 Sample selection

My sample firms with financial restatements during the period from 1997 to 2005 are

obtained from GAO (2002, 2006, 2007) Specifically, the GAO used the LexisNexis online

information service to search for press releases and other media coverage on restatements

for publicly listed companies trading on the New York, NASDAQ, and Amex exchanges

GAO excluded announcements involving stock splits, changes in accounting principles, and

other financial restatements not made to correct errors in the application of accounting

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standards The GAO (2002) report includes a list of 845 restatement announcements from

January 1997 to June 2002, GAO (2006) report includes a list of 1,390 restatements from

July 2002 to September 2005, and GAO (2007) report includes a list of 396 restatements

from October 2005 to June 2006 These 2,631 firms (hereafter, GAO firms), identified by

the GAO as restating due to financial reporting fraud or accounting errors, represent my

sample of firms that I presume to have managed earnings Because GAO merely provides

company names and restatement announcement years, I further hand-collect the restated

reporting years from the LexisNexis database by matching company names to the released

restatement presses

I obtain financial statement data from the Compustat Industrial Annual files To

eliminate measurement error stemming from the use of balance sheet data (Collins & Hribar,

2002), I use cash flow statement data to calculate accruals by subtracting total cash flows

from operations (Compustat #308) from the reported net income (Compustat #172) I

estimate coefficients in accrual models by using presumably nonmanaging samples that are

not included in the GAO samples and that do not have restatement data in Compustat

Discretionary accruals are measured by residuals of the Jones, modified Jones,

performance-matched, and my expanded nonlinear accrual models

To generate the final samples, I exclude financial services firms (one-digit SIC code = 6)

and observations with missing data I restrict my samples with ROAs or the absolute value

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of total accrual scaled by beginning total assets of less than 1 and truncate 1% extreme

values of the other independent variables in each tail Following Kothari et al (2005), I

eliminate firm-year observations with fewer than 10 observations in any two-digit SIC code

in each sample year To mitigate the possible heteroskedasticity in residuals, I scale

independent and dependent variables by total assets (Compustat #6) at the beginning of year

t I include constants in the estimation and estimate discretionary accruals both for

cross-sectional and time-series

5 Results

5.1 Summary statistics

Panels A, B, and C of Table 1 present summary statistics and correlations between the

accrual model variables for observations without restatements for the entire sample, GAO

firms, and nonrestated firms, respectively In Panel A, negative mean and median total

accruals are consistent with prior studies The mean, median, and standard deviation for

change in sales are greater than for change in sales adjusted by change in accounts

receivable Not surprisingly, the interquartile range is broader for change in sales than for

change in sales adjusted by change in accounts receivable In my model’s settings, I

consider the proper level of change in accounts receivable to generate an adjusted change in

sales The upper quartile of adjusted change in sales is higher than the upper quartile of

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change in sales for the modified Jones model but the lower quartile of adjusted change in

sales is smaller than the lower quartile of change in sales for the modified Jones model The

untabulated extreme value of change in sales for the Jones model is higher (lower) than the

extreme value of adjusted change in sales in the right (left) tail

[TABLE 1 ABOUT HERE]

Panel B of Table 1 shows a more negative mean value of –0.1012 for total accruals for

GAO firms relative to the mean value of –0.0752 (–0.0717) for the pooled sample

(nonrestated firms) in Panel A (Panel C) The range between first and third quartiles of total

accruals for GAO firms is wider than the range for the pooled sample (nonrestated firms) in

Panel A (Panel C) The mean value of cost of goods sold adjusted by change in inventory is

approximately 5 percent of total assets for the pooled sample, GAO firms, and nonrestated

firms The mean value of ROA is –0.0576 for GAO firms, which underperforms the pooled

sample (nonrestated firms) mean value of –0.0217 (–0.0169), as reported in Panel A (Panel

C) I observe similar results for the median values of ROA

Table 2 presents the Pearson and Spearman correlations for my variables Echoing the

relations observed in Figures 1.1 to 1.8, I find positive correlations between accruals and the

following variables: change in sales, change in sales adjusted by change in accounts

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receivable, lagged accruals, return on assets, and adjusted change in sales The remaining

variables are generally negatively correlated with accruals, except the reciprocal of

beginning total assets The graph of the relation between accruals and the reciprocal of

beginning total assets is flat before the eighth decile and drops sharply thereafter

[TABLE 2 ABOUT HERE]

5.2 Jones (modified Jones) versus the nonlinear Jones (modified Jones) models

I initially obtain discretionary accrual estimates by the conventional linear Jones and

modified Jones models and the nonlinear Jones and nonlinear Jones models In terms of the

nonlinear Jones model, I allow four different slopes for each explanatory variable

Specifically, the coefficients of explanatory variables are independently estimated for each

quartile of the explanatory variables For the nonlinear modified Jones model, the

estimation procedure is the same as that of the nonlinear Jones model, except that the

change in sales is replaced by change in sales adjusted by change in accounts receivable I

partition change in sales, change in sales adjusted by change in accounts receivable, and

PPE by quartiles within each year-industry combination Panel A of Table 3 provides

descriptive statistics for the explanatory variables within quartiles The mean value for PPE

in the fourth quartile is approximately twice as large as PPE in the third quartile In addition,

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the mean value of change in sales and change in sales adjusted by change in accounts

receivable for the first quartile are negative, and the value in the other quartiles are positive

The quartile statistics suggest that the mean and median values of explanatory variables in

the Jones and modified Jones models are fairly distinct and may generate different

accrual-generating processes

[TABLE 3 ABOUT HERE]

Panel B of Table 3 reports coefficient estimates for the cross-sectional and time-series

Jones models and the cross-sectional and time-series modified Jones models The adjusted

R-squares for the four linear accrual models show that cross-sectional accrual models

perform better than the time-series accrual models do Panel C reports the coefficient

estimates for the performance-matched accrual models The adjusted R-squares show that

current ROA is clearly a better proxy for performance than lagged ROA The result is

consistent with Kothari et al (2005) In addition, the four performance-matched accrual

models perform better than the Jones and modified Jones models regardless of whether they

are cross-sectional or time-series

Panel D of Table 3 reports coefficient estimates computed by the nonlinear accrual

models, including the nonlinear Jones, the nonlinear modified Jones, and the nonlinear

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expense-related models I first compute the estimated coefficients among quartiles in the

nonlinear model and compare to the coefficients in the linear model in Panel B Take change

in sales as an example: The coefficients for the first to the fourth quartile of change in sales

in the nonlinear Jones model are –1.3889 (–0.5050 – 0.8839), –1.8958 (–0.5050 –

0.3908), –0.8589 (–0.5050 – 0.3539), and –0.5050, respectively The coefficient estimate of

change in sales in the cross-sectional (time-series) Jones models is 0.0509, which is larger

than the estimates in the nonlinear Jones model Take PPE as another example: The

coefficients for the first to the forth quartile of PPE in the nonlinear modified Jones model

are –2.2687 (–1.5646 – 0.7041), –1.6641 (–1.5646 –0.0995), –2.7902 (–1.5646 –1.2256),

and –1.56463, respectively In terms of the nonlinear expense-related accrual model, the

coefficient estimates of PPE for the first to the fourth quartiles are –6.4177 (–1.8336 –

4.5841), –3.6614 (–1.8336 – 1.8278), –6.1096 (–1.8336 – 4.2760), and –1.8336,

respectively The coefficient estimates computed by the nonlinear modified Jones and

nonlinear expense-related models both change across PPE quartiles However, the

coefficient estimate in the cross-sectional (time-series) modified Jones model is –0.0419

(–0.0387), which is flatter than the coefficient estimates in the nonlinear modified Jones

model The results of Table 3 suggest that the accrual-generating process may not be

homogeneous Therefore, relaxing the linearity assumption may lead to better specified

accrual models

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Next, I separately consider instances of positive and negative discretionary accruals and

compare the discretionary accruals for the GAO and the nonrestated groups for both upward

earnings management (DA>0) and downward earnings management (DA<0) Table 4

reports the summary statistics of discretionary accrual estimates for GAO firms and

nonrestated firms for the case of positive DA by employing the linear, performance-matched,

and nonlinear accrual models in Panels A, B, and C, respectively I assume that the GAO

sample observations encompass earnings management and that discretionary accruals

reflect this management; therefore, these accruals should differ for these groups Otherwise,

discretionary accruals fail as a proxy for earnings management For positive discretionary

accruals, the differences in discretionary accruals between GAO firms and nonrestated firms

are significant in the cross-sectional Jones, the performance-matched, and the nonlinear

accrual models To compare the specification between linear models and nonlinear models,

I take the cross-sectional Jones and the nonlinear Jones models as an example The

difference in the mean (median) discretionary accruals between GAO and nonrestated firms

in the Jones model is 0.0092 (0.0118) as DA is positive In contrast, the difference in the

mean (median) discretionary accruals between GAO and nonrestated firms in the nonlinear

Jones model is 0.1457 (0.0767), which is approximately fifteen times that of the Jones

model In terms of the nonlinear expense-related accrual model, the difference reaches

1.4972, which is also significant

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[TABLE 4 ABOUT HERE]

Furthermore, I observe a broader distribution, as manifest by both a greater standard

deviation and broader interquartile range, for the nonlinear as opposed to the usual Jones

model in Table 4 When estimating discretionary accruals by the Jones model, the range of

estimates between first and third quartiles for GAO firms overlaps a large part of the range

for nonrestated firms That is (0.0229, 0.0910) for GAO firms and (0.0186, 0.0833) for

nonrestated firms However, generating discretionary accruals by the nonlinear Jones or the

nonlinear expense-related models mitigates this phenomenon When using the nonlinear

Jones model to estimate discretionary accruals, the ranges of discretionary accruals are

(0.0495, 0.2432) for GAO firms and (0.0173, 0.1162) for nonrestated firms When using the

nonlinear expense-related model to estimate discretionary accruals, the ranges are (0.1248,

2.5433) for GAO firms and (0.0019, 0.3219) for nonrestated firms Estimating discretionary

accruals by the Jones model when investigating upward earnings management may be

subject to underrejection Namely, the nonlinear Jones and nonlinear expense-related

models are more capable of discriminating firms with earnings management

Table 5 reports the summary statistics of discretionary accrual estimates for GAO firms

and nonrestated firms when DA is negative Panels A, B, and C report the results measured

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by the linear, performance-matched, and nonlinear accrual models For negative

discretionary accruals the mean (median) discretionary accruals calculated by the

cross-sectional Jones model, the nonlinear Jones model, and the nonlinear expense-related

model for GAO firms are –0.1102 (–0.0762), –0.3702 (–0.1798), and –0.1.6938 (–0.9517),

respectively Performance-matched accrual models generate relatively small values for

discretionary accruals when DA is negative Again, the standard deviation of discretionary

accruals and the interquartile range are substantially greater for the nonlinear Jones and the

nonlinear expense-related accrual models than for the Jones model The significance of the

differences in discretionary accruals between GAO firms and nonrestated firms is similar

However, the difference as measured by the nonlinear model has the greatest magnitude

whereas the difference as measured by the Jones model generates the smallest magnitude

Collectively, these results suggest that the estimates from the nonlinear accrual models

provide greater discriminatory power in identifying both upward and downward earnings

management

[TABLE 5 ABOUT HERE]

5.3 Accrual model comparison

I also adopt a logit model to compare the explanatory power among various accrual models,

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including the Jones, modified Jones, performance-matched Jones on ROA,

performance-matched modified Jones on ROA, performance-matched Jones on lagged ROA,

performance-matched modified Jones on lagged ROA, and nonlinear expense-related

models To reduce the effect of omitted variables, I consider industry fixed effect in the logit

model Panel A of Table 6 shows the significance of each discretionary accrual on the

likelihood of identifying restated firms for the pooled sample The nonlinear

expense-related model is the only model in which the estimated coefficient is significantly

different from zero, suggesting that the nonlinear expense-related accrual models have the

power to detect the GAO group for the pooled sample Next, I include a variable to proxy

for the marginal effect from the nonlinear expense-related model in the logit model with

each discretionary accrual also estimated by the other accrual models as explanatory

variables and control industry variables Panel B shows that the marginal effect from the

nonlinear expense-related model significantly explains the likelihood of identifying restated

firms

[TABLE 6 ABOUT HERE]

Table 7 reports the discriminatory power in identifying restated firms among the linear,

performance-matched, and nonlinear accrual models Panels A and B report the case for

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firms engaging in upward earnings management (DA>0), and Panels C and D report the

case for firms engaging in downward earnings management (DA<0) Panel A shows that the

performance-matched (Models 5–8) and nonlinear (Models 8–11) models have the power to

detect the GAO group However, among the linear accrual models, only the cross-sectional

Jones and modified Jones models present significant discriminatory power in detecting

restated firms Panel B shows that for the performance-matched Jones model and the

nonlinear modified Jones model, the nonlinear expense-related model is marginally

effective in detecting restated firms Panel C shows that only the nonlinear Jones, nonlinear

modified Jones, and nonlinear expense-related models (Models 9, 10, and 11, respectively)

present significant discriminatory power in detecting restated firms In addition, the results

in Panel D show that the nonlinear expense-related model provides marginal explanatory

power in detecting the probability of engaging in downward earnings management

Collectively, the findings suggest that the nonlinear expense-related model is better able to

discriminate presumably managing firms from the presumably nonmanaging firms than the

other models, especially when whether firms are conducting upward or downward earnings

management is unknown

[TABLE 7 ABOUT HERE]

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5.4 Robustness test

Since the report issued by the GAO (2007) specifies that cost- or expense-related issues are

the noteworthy reason for restatements from July 2002 following the passage of the SOX,

this study investigates whether the empirical results are robust or even more significant in

the subperiod of 2003 to 2005 Table 8 reports the differences in discretionary accruals

measured by the linear, performance-matched, and nonlinear accrual modes when firms

engage in upward earnings management from 2003 to 2005 Panels A and B show that the

average differences in discretionary accruals between GAO and nonrestated firms are not

statistically significant when using the linear and performance-matched accrual models

However, the differences in discretionary accruals measured by the nonlinear Jones,

nonlinear modified Jones, and nonlinear expense-related models are 0.3676, 0.5126, and

2.4246, respectively, which are significant

[TABLE 8 ABOUT HERE]

Table 9 reports the differences in discretionary accruals measured by the linear,

performance-matched, and nonlinear accrual modes when firms engage in downward

earnings management from 2003 to 2005 Panels A and B show that the average differences

in discretionary accruals are not statistically significant when using the linear and

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performance-matched accrual models In addition, in Panel C only the nonlinear

expense-related model has the power to detect restated firms, suggesting that

expense-related variables are worth taking into account when estimating discretionary

accruals after 2003

[TABLE 9 ABOUT HERE]

Table 10 reports the comparison of the discriminatory power in detecting restated firms

among various accrual models during 2003 to 2005 Panels A and B report the results for

upward earnings management, and Panel C reports the results for downward earnings

management Panel A shows that the average differences in discretionary accruals are

statistically significant only when using the nonlinear accrual models In Panel B, the

nonlinear expense-related model has greater power to identify GAO firms in Models 1, 5, 6,

8, and 9 Panel C shows that most of the accrual models are capable of identifying restated

firms with negative discretionary accruals Therefore, Panel D shows less additional

detecting power from the discretionary accruals measured by the nonlinear expense-related

model

[TABLE 10 ABOUT HERE]

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To compare the discriminatory power among these accrual models before and after

SOX, Table 11 reports the results in detecting restated firms for the period from 1997 to

2002 The results of Panel A show that nonlinear accrual models present better

discriminatory power in detecting restated firms Panel B indicates that the nonlinear

expense-related model has superior power to recognize restated firms Panel C shows that

most accrual models are good at recognizing restated firms with negative discretionary

accruals Panel D shows that nonlinear expense-related model has better detecting power

than the other accrual models Collectively, the findings suggest that expense-related

variables are worth taking into account In addition, the nonlinear expense-related model is

better able to discriminate presumably managing firms from the presumably nonmanaging

firms than the other models, especially when whether firms are conducting upward or

downward earnings management is unknown

[TABLE 11 ABOUT HERE]

6 Conclusion

This paper investigates measurement errors in conventional linear accrual models when

applied to firms experiencing different performance levels I report that coefficients on the

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independent variable in linear accrual models vary across performance quartiles The

difference in estimated coefficients among performance quartiles leads to asymmetric

influences on accruals If researchers use linear accrual models to consider the performance

variable, they will generate a smoother estimated coefficient than in nonlinear models This

measurement error, obtained by ignoring the nonlinear relation between accruals and the

performance variable, leads to biased discretionary accrual estimates

I use GAO (2002, 2005, 2007) reports to identify firms with financial restatements to

proxy for firms with earnings management The control group is composed of firms not in

the GAO reports and without a financial restatement record in Compustat I compare the

conventional linear accrual models and nonlinear models, including the nonlinear Jones,

nonlinear modified Jones, performance-matched, and nonlinear expense-related models, to

evaluate their ability to discriminate among firms with and without earnings management

The findings suggest that the estimates using nonlinear accrual models provide greater

discriminatory power in identifying both upward and downward earnings management The

regression results also show that the nonlinear expense-related accrual model outperforms

the nonlinear Jones and modified Jones models for the pooled sample and for the case in

which firms engage in downward earnings management Because upward or downward

earnings management is unforeseeable, the nonlinear expense-related accrual model is the

best-specified model and enhances the reliability of inferences in earnings management

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issues The results are robust after the passage of SOX

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Acknowledgment

The author gratefully acknowledges the financial support of National Science Council

(96-2416-H-155-024) and Yuan Ze University I have benefited from the helpful comments

and suggestions made by the Editor (Carl Chen), anonymous referees, Jia-Chi Cheng, Kevin

Chen, Michael Eames, Yueh-hsiang Lin, Huai-Chun Lo and seminar participants at

National Taiwan University, Yuan-Ze University, and seminar participants at the 2008

Financial Management Association annual meeting All remaining errors are my own

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