kothari et al - 2005 - performance matched discretionary accrual measures

The resultssuggest that performance-matched discretionary accrual measures enhance the reliability ofinferences from earnings management research when the hypothesis being tested does no

Journal of Accounting and Economics 39 (2005) 163–197

Performance matched discretionary

a Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02142, USA

b William E Simon Graduate School of Business Administration, University of Rochester, Rochester,

NY 14627, USA Received 18 April 2001; received in revised form 22 September 2004; accepted 17 November 2004

Available online 23 January 2005

Abstract

We examine the specification and power of tests based on performance-matcheddiscretionary accruals, and make comparisons with tests using traditional discretionaryaccrual measures (e.g., Jones and modified-Jones models) Performance matching on return onassets controls for the effect of performance on measured discretionary accruals The resultssuggest that performance-matched discretionary accrual measures enhance the reliability ofinferences from earnings management research when the hypothesis being tested does notimply that earnings management will vary with performance, or where the control firms arenot expected to have engaged in earnings management

r 2004 Elsevier B.V All rights reserved

!Corresponding author Tel.: +1 617 253 0994; fax: +1 617 253 0603.

E-mail address: kothari@mith.edu (S.P Kothari).

1 Introduction

Use of discretionary accruals in tests of earnings management and market

managers act as if they believe users of financial reporting data can be misled intointerpreting reported accounting earnings as equivalent to economic profitability’’(Fields et al., 2001, p 279) Naturally, earnings management research is of interestnot only to academics, but also to practitioners and regulators

Inferences drawn from tests of hypotheses related to incentives for earningsmanagement hinge critically on the researcher’s ability to accurately estimatediscretionary accruals That is, all tests are joint tests of the researcher’s model of

research on the modeling of discretionary accruals and the empirical specification ofthe models However, accurate estimation of discretionary accruals does not appear

‘‘The only convincing conclusion appears to be that relying on existing accrualsmodels to solve the problem of multiple method choices may result in seriousinference problems,’’ where multiple method choices refers to earnings managementusing accruals

Our objective in this paper is to test whether a performance-matcheddiscretionary-accrual approach (a type of control sample approach) is both wellspecified and powerful at estimating discretionary accruals Use of such an accrualmeasure, subject to important caveats about type of hypotheses being tested, mayenhance the reliability of inferences from earnings management studies with respect

to discretionary accruals We discuss below the kinds of hypothesis tests wherematching may be beneficial

Previous research examines the specification and power of various

hypothesis of no earnings management at rates exceeding the specified test levelswhen applied to samples of firms with extreme financial performance.’’ These resultsillustrate the importance of a careful consideration of the hypotheses being tested,because firms with extreme performance are also likely to engage in earningsmanagement Under that hypothesis, discretionary accrual models may, in fact,

discretionary accrual models might be misspecified when applied to samples of firmswith extreme performance in part because performance and estimated discretionaryaccruals exhibit a mechanical relation (as discussed below) To the extent the concern

is model misspecification, and because earnings management research typicallyexamines non-random samples (e.g., samples that firms self-select into by, forexample, changing auditors), earnings management studies must employ some

1 In the context of testing market’s efficiency with respect to earnings management, the tests are joint tests of discretionary accrual models and market efficiency.

means of mitigating the misspecification to reduce the likelihood of incorrectinferences In this vein, use of a control sample to address specification issues iscommon in the literature By relying on a control sample to calibrate earningsmanagement, the earnings management identified by our approach must beinterpreted as ‘abnormal’ earnings management In other words, adjusting forperformance, firms identified as having managed earnings are in fact managingearnings at a rate higher than the comparison sample.

We examine properties of discretionary accruals adjusted for a matched firm’s discretionary accrual, where matching is on the basis of a firm’sreturn on assets and industry membership Our motivation to use ROA as thematching variable as opposed to other candidates (e.g., size, earnings growth,

model of accruals discussed in Section 2 suggests ROA controls for the effect ofperformance on measured discretionary accruals Second, matching on ROA follows

(Barber and Lyon do not focus on accruals) using a matched-firm research design.They find that matching on an operating performance measure similar to the ROAtends to be better than matching on other variables

Performance matching cannot and does not solve all the problems arising frombad discretionary accrual models or from a researcher’s failure to recognize theaccrual management incentives that are unique to the research question beingaddressed Rather, our approach provides additional controls for what is considered

‘normal’ earnings management In other words, firms classified as havingabnormally high or low levels of earnings management are those that manage morethan would be expected given their level of performance Researchers shouldconsider using either the fitted values of our model (normal level of earningsmanagement) or the residuals from the model (abnormal level of earningsmanagement), depending on the specific hypotheses being tested (see Section 2.3for further elaboration) Notwithstanding this caveat, the importance of controllingfor the effect of performance in tests of earnings management is not surprising and

to this literature as the first study to thoroughly examine and document thespecification and power of performance-based discretionary accrual measures across

a wide variety of settings representative of those encountered in accounting research.Conceptually, our motivation for controlling for performance stems from the

model shows that working capital accruals increase in forecasted sales growth andearnings because of a firm’s investment in working capital to support the growth insales Therefore, if performance exhibits momentum or mean reversion (i.e.,performance deviates from a random walk), then expected accruals would be non-zero Firms with high growth opportunities often exhibit persistent growth patterns(i.e., earnings momentum) Similarly, accounting conservatism can produce earningspersistence (i.e., momentum) in the presence of good news and mean reversion in the

As a result, accruals of firms that have experienced unusual performance areexpected to be systematically non-zero A correlation between performance andaccruals is problematic in tests of earnings management because commonly used

mis-specified when applied to samples experiencing extreme performance (see

Dechow et al., 1995).2

While we control for the impact of performance on estimated discretionaryaccruals using a performance-matched firm’s discretionary accrual, an alternative is

discussion of this issue) However, doing so requires imposing a specific functionalform linking accruals to past performance in the cross-section Because of the lack of

a theory, we control for performance using a performance-matched firm’sdiscretionary accrual Using a performance-matched firm’s discretionary accrualdoes not impose a particular functional form linking accruals to performance in across-section of firms Instead, the assumption underlying performance matching is,

at the portfolio level, the impact of performance on accruals is identical for the testand matched control samples For comparative purposes we also conduct tests thatcontrol for performance on discretionary accruals using a linear regression (i.e.,ROA is added to the Jones and modified-Jones models as an additional regressor).The comparison reveals that tests of discretionary accruals using a performance-matched approach are better specified than those using a linear regression-basedapproach This result is due in part to the non-linear relation between accruals andperformance

While adjustment of discretionary accruals for those of performance-matchedsamples is common in the literature, researchers choose from a wide range of firmcharacteristics on which to match without systematic evidence to guide their choice.Lack of such guidance hinders inter-study comparability of results For example,

a ‘‘control firm’’ as the median performance of the subset of firms in the same

return on assets We provide a systematic treatment of the specification and power ofthe test using performance-based discretionary accruals This analysis should aid inthe design of future earnings management and market efficiency studies

Summary of results: The main result from our simulation analysis is thatdiscretionary accruals estimated using the Jones or the modified-Jones model, andadjusted for a performance-matched firm’s discretionary accrual, tend to be the bestspecified measures of discretionary accruals across a wide variety of simulated eventconditions We report results using performance matching on the basis of industry

2 Recent research attempts to develop accrual models as a function of performance (see Kang and Sivaramakrishnan, 1995 ; Healy, 1996 ; Dechow et al., 1998 ; Peasnell et al., 2000 ; Barth et al., 2001 ).

Matching based on ROAtperforms better than matching on ROAt!1 We believe

error in estimating the discretionary accrual of a treatment firms affects the

impact of performance-related accrual on the properties of subsequent period’sestimated discretionary accrual of the treatment firm is better controlled for when

compared to other measures of discretionary accruals parallels the result in thecontext of operating performance measures and long-horizon stock returns (see

Barber and Lyon, 1996, 1997;Lyon et al., 1999;Ikenberry et al., 1995)

Performance-matched discretionary accruals exhibit only a modest degree of specification when firms are randomly selected from an extreme quartile of stocksranked on the basis of firm characteristics such as the book-to-market ratio, firmsize, sales growth, and earnings yield (i.e., performance) However, in the samesamples, comparative results based on traditional discretionary accrual measuresexhibit a far greater degree of mis-specification

mis-A caveat related to our analysis is that firms in stratified-random samples might beengaging in earnings management for contracting, political or capital marketreasons Thus, the well-specified rejection rate of the performance-matched approach

al., 1996) In this context, our result that performance-matched measures are wellspecified is applicable only insofar as a researcher desires to calibrate the degree ofearnings management (i.e., discretionary accruals) by the treatment sample relative

to a matched sample that has not experienced a contracting, political, or capitalmarket-related treatment event (also see Section 2), but is otherwise identical to thetreatment sample in all other economic respects Obviously, the success of thematched-firm approach hinges on the researcher’s ability to identify an appropriatecontrol sample This, in turn, depends on the specific earnings managementhypothesis being tested

Section 2 provides the motivation for using a performance-matched approach tomeasure discretionary accruals and Section 3 describes the simulation procedure.Section 4 summarizes the results on the specification of the test and Section 5 reportsresults for the power of the test Section 6 reports the results of a wide range ofsensitivity analyses and Section 7 summarizes and discusses recommendations forfuture research

2 Motivation for performance matching

Economic intuition, extant models of accruals, earnings, and cash flows, andempirical evidence all suggest that accruals are correlated with a firm’s

1996;Dechow et al., 1998, 1995;Barth et al., 2001) While the Jones and Jones models attempt to control for contemporaneous performance, empirical

modified-assessments of these models suggest that estimated discretionary accruals aresignificantly influenced by a firm’s contemporaneous and past performance (e.g.,

performance and accruals This framework provides the motivation for developing acontrol for firm performance when estimating discretionary accruals and whencomparing discretionary accruals between samples of firms

2.1 Properties of earnings, cash flows and accruals

To formalize a relation between firm performance and accruals, we begin with a

et al (1998) Ignoring the depreciation accrual and assuming: (i) sales, St, follow a

changes are not zero (i.e., sales depart from a random walk) or when profit margins

or other parameters affecting accruals change, then forecasted earnings changes aswell as accruals are non-zero The direction of forecasted sales and earnings changesdepend on whether performance is expected to mean revert or to exhibit momentum.Extreme one-time increases or decreases in performance are likely to produce meanreversion, whereas growth stocks might exhibit momentum for a period of time.Mean reversion or momentum in sales and earnings performance is quite likely forfirms exhibiting unusual past performance This predictability in future performancegenerates predictable future accruals Unless the discretionary accrual modelsadequately filter out this performance-related predictable component of accruals,there is a danger of spurious indication of discretionary accruals Previous research

3 This conclusion also holds for models that capture the complexity of accounts payables and fixed costs (see Dechow et al., 1998 ) However, the result cannot be demonstrated as cleanly as for the simple model

we present.

(e.g., Dechow et al., 1995;Guay et al., 1996) suggests the likelihood of a spuriousindication of discretionary accruals is extremely high in samples experiencing

2.2 Controlling for the effect of performance on accruals

Theoretically, the need to control for the effect of current or past year’s return onassets on estimated discretionary accruals is guided by the modeling of earnings, cashflows and accruals summarized above In particular, Eq (4) for the prediction ofaccruals suggests that when sales changes are predictable, earnings changes will also

not random with respect to prior firm performance, earnings changes are predictableand accruals are also expected to be non-zero

One means of controlling for the influence of prior firm performance on estimateddiscretionary accruals is to expand the set of independent variables used intraditional regression models of discretionary accruals (e.g., the Jones model) In thisspirit, we augment the Jones and modified-Jones models to include current or pastyear’s return on assets Our motivation to use return on assets as a performancemeasure is two-fold First, by definition, earnings deflated by assets equals return onassets, which in turn measures performance Second, prior research analyzing long-run abnormal stock return performance and abnormal operating performance findsmatching on ROA results in better specified and more powerful tests compared to

al., 1999;Ikenberry et al., 1995)

An alternative to the regression-based approach to control for the effect ofperformance on estimated discretionary accruals is to adjust a firm’s estimateddiscretionary accrual by that of a performance-matched firm Such an approachwould also mitigate the likelihood that the estimated discretionary accruals aresystematically non-zero (i.e., lead to invalid inferences about accrual behavior).Specifically, the performance-matched discretionary accrual measure adjusts a firm’sestimated discretionary accrual by subtracting the corresponding discretionary accrual

of a firm matched on the basis of industry and current or prior year’s return on assets.The relative efficacy of the matched-firm approach versus including a performancevariable in the discretionary accrual regression model is an empirical issue Theregression approach imposes stationarity of the relation through time or in the cross-section, and perhaps more importantly, imposes linearity on the relation between themagnitude of performance and accruals For statistical as well as economic reasons,

we expect the mapping of current performance into future performance, or the

4 In the presence of mean reversion, momentum, and/or other departures from a random walk property

of sales, the inclusion of sales change as an explanatory variable in a discretionary accrual regression model is not sufficient to forecast all of the firm’s non-discretionary accruals related to sales.

5 As the simple model suggests, an alternative to return on assets would be to match on past sales growth However, matching on return on assets serves to incorporate other factors contributing to the firm’s accrual generating process, which our simple model does not capture, but which are likely to affect the magnitude of nondiscretionary accruals.

mapping of performance into returns, to be non-linear (e.g., Brooks andBuckmaster, 1976;Beaver et al., 1979;Freeman and Tse, 1992;Basu, 1997;Watts,

average performance is quite persistent, which implies a non-linear relation betweencurrent and future performance across the entire cross-section

Economic reasons for the non-linearity are rooted in accounting conservatism and

anticipated For example, asset write-offs, goodwill impairment, and restructuringcharges all entail reporting the capitalized amounts of losses In contrast, gains fromasset revaluations and capitalized amounts of expected benefits from research anddevelopment and/or patents are not included in earnings until realized in futureperiods Therefore, reported earnings include capitalized amounts of losses, whereaspredominantly the gains included in earnings are flow amounts Capitalized amountsare far less persistent compared to gains, which imparts a non-linearity in therelation between current and future earnings A similar non-linearity is predicted as aresult of management’s tendency to take a ‘‘big bath’’ in bad economic times.Unless a discretionary accrual model, like the Jones or modified-Jones model, isimprovised to address non-linearities, we do not expect the regression approach to beeffective at controlling for non-zero estimated discretionary accruals in stratified-random samples We do not entertain non-linear regression approaches to controlfor the effect of performance on accruals in part because theory to guide the non-linear modeling is currently unavailable This means experimentation with a range ofnon-linear specifications might be warranted Such an exercise is beyond the scope ofour study and potentially suffers from over-fitting of the data

In contrast to the regression approach, the matched-firm approach does notimpose any particular functional form on the relation between performance andaccruals It simply assumes that, on average, the treatment and control firms havethe same estimated non-event discretionary accruals Ultimately, the success of thematched-firm approach hinges on the precision with which matching can be doneand the homogeneity in the relation between performance and accruals for thematched and the sample firm As a result, we examine both the linear regression andthe matched-firm approach as a means to control for the effect of performance onestimated discretionary accruals

2.3 Does controlling for performance over-correct for performance-related accruals?

An important question related to our approach is will the use of industry andperformance-matched control firms remove, in part, discretionary accruals resultingfrom treatment firms’ earnings management activities? This would make it moredifficult to reject the null hypothesis when it is false (i.e., the power of test usingperformance-based discretionary accruals would be reduced) This concern ofpotentially ‘‘throwing the baby out with the bath water’’ arises because matched(control) firms in the industry might have similar incentives to manage earningswhen compared to the treatment firms

While, on the surface, such a concern seems reasonable, controlling forperformance-related accruals is nevertheless warranted In an earnings managementstudy, researchers are typically interested in testing whether an event (e.g., aseasoned equity offer) influences reported earnings performance in the pre- and post-event years If the treatment firms’ earnings performance in the post-event period isindistinguishable from that of the control firms, then the conclusion would be thatthe firms experiencing the event do not manage earnings any more or less than thematched firms that do not experience the event Of course, it is possible that bothtreatment and control firms manage earnings, but this is not what the researcher isinterested in testing More precisely, central to the researcher’s study is thehypothesis that the event itself contributes to earnings management for reasonsbeyond other known or observable factors like performance This point can be mademore transparent by considering the three components of estimated discretionaryaccruals: (i) discretionary accruals related to the ‘‘treatment’’ event (e.g., a seasonedequity offer), which is zero for the control firm; (ii) discretionary accruals arisingfrom other incentives (e.g., bonus contract, meeting analysts’ forecasts), whichinfluence both treatment and control firms; and (iii) an accrual correlated withperformance The success of the performance-matched approach is predicated on theassumption that estimated discretionary accruals arising from (ii) and (iii) are, onaverage, the same for the treatment and control firms This, of course, is the essence

of and rationale for the typical matched-firm research design (see, for example,

estimated discretionary accruals of the treatment and control firms are differenced,only the discretionary accrual related to the event of interest remains To the extentthe non-event accrual items (ii) and (iii) are systematically different between thetreatment and control firms, the performance-matched discretionary accrualapproach would not be as effective in isolating the discretionary accrual of interest(i.e., item (i)) The key point here is that the power of test using performance-baseddiscretionary accrual measures is not sacrificed so long as the researcher seeks toestimate the earnings management impact of the treatment event itself (i.e., item (i))

To summarize, performance matching can and will remove earnings ment that is motivated by (poor or superior) performance because both treatmentand matched control firms by design experience similar performance Thus,performance-matched discretionary accruals represent ‘‘abnormal’’ earnings man-agement, not total earnings management Since it’s designed to capture the earningsmanagement effect that is beyond that attributable to performance, the use ofperformance-matched discretionary accruals is appropriate in controlling for thewell-known misspecification of the discretionary-accrual models associated withperformance

manage-3 The simulation procedure

This section describes the simulation procedure used to assess the specification andpower of the test using alternative measures of discretionary accruals We discuss

sample selection (Section 3.1), discretionary accrual measures (Section 3.2),performance matching (Section 3.3), and the test statistics (Section 3.4) Section3.5 presents descriptive statistics and Section 3.6 reports serial correlation propertiesfor all discretionary accrual measures The descriptive statistics provide preliminaryevidence of potential biases inherent to traditional measures of discretionaryaccruals Such biases contribute to test statistic misspecification in actual empiricalstudies.

3.1 Sample selection

We begin with all firm-year observations from the COMPUSTAT IndustrialAnnual, and Research files from 1962 through 1999 Consistent with priordiscretionary accrual research, we exclude firm-year observations that do not havesufficient data to compute total accruals (described in Section 3.2) or the variablesneeded to estimate the Jones model We also exclude all firm-year observationswhere there are fewer than ten observations in any two-digit SIC code in any givenyear This is designed to exclude observations for which the regression-model-baseddiscretionary accrual estimates are likely to be imprecise Collectively, these filtersyield a sample of roughly 210,000 observations Since we match firms on the basis ofperformance (described below) and analyze stratified sub-samples based onperformance (e.g., book-to-market, market capitalization, earnings/price ratio, salesgrowth and operating cash flow), the sample size is reduced to about 123,000 afterexcluding observations that cannot be performance matched or that do not have

We report simulation results for 250 samples of 100 firms each We draw sampleswithout replacement from the full sample or from stratified subsets The subsets arethe lowest and highest quartiles of firms ranked on book-to-market, past salesgrowth, earnings-to-price, size (market value of equity, referred to as large and smallfirms) and operating cash flow To construct the subsets, each year we rank all firm-year observations on the basis of each partitioning characteristic (e.g., book-to-market or size, measured at the beginning of the year) Each year we only retain theupper and lower quartiles of the sample For each partitioning variable, we then poolobservations across all years to form two sub-samples, one based on pooling all datafrom the annual upper quartiles and another based on pooling all data from theannual lower quartiles

6

An issue that arises is how different are the firm-years excluded from our analysis as a result of the performance matching-requirement (roughly 80,000) from the firm-years included in our analysis (roughly 123,000) While the included and excluded firms have significantly different (based on t-tests and two sample Wilcoxon tests) E–P ratios, book-to-market ratios, market values of equity, total accruals and operating cash flow to total asset ratios, economically the mean and median differences are quite small For example, excluded firms have mean (median) E–P ratios of !0.05 (0.06) compared to –0.06 (0.05) for included firms Corresponding values for excluded (included) firms book-to-market ratios are mean ¼ 0.81 and median ¼ 0.64 (mean ¼ 0.86 and median ¼ 0.67), total accruals are mean ¼ !0.01 and med- ian ¼ !0.03 (mean ¼ !0.03 and median ¼ !0.03) and market values of equity are mean ¼ $454.5M and median ¼ $51.9M (mean ¼ $570.8M and median ¼ $50.5M).

3.2 Discretionary accrual measures

that the Jones and the modified-Jones models (i.e., the modification by Dechow etal.) perform the best The main difference between the two models is that themodified-Jones model attributes the entire change in receivables to earningsmanagement (see details below) We begin our analysis with the Jones andmodified-Jones models We estimate the performance-matched Jones modeldiscretionary accrual as the difference between the Jones model discretionaryaccrual and the corresponding discretionary accrual for a performance-matchedfirm We similarly estimate the performance-matched modified-Jones modeldiscretionary accrual To compare the effectiveness of performance matching,versus a regression-based approach, we estimate an additional discretionary accrualmeasure where we include return on assets (ROA) in the models For both theregression-based approach and the performance-matched firm approach we presentresults based on current or last year’s ROA as a means to control for firmperformance

To estimate the discretionary accrual models, we define total accruals (TA) as thechange in non-cash current assets minus the change in current liabilities excludingthe current portion of long-term debt, minus depreciation and amortization, scaled

by lagged total assets With reference to COMPUSTAT, total accruals ¼ ðDData4 !DData1 ! DData5 þ DData34 ! Data14Þ=lagged Data6: The Jones model discre-tionary accrual is estimated cross-sectionally each year using all firm-yearobservations in the same two-digit SIC code

statistics for the annual, cross-sectional, industry models show that deflationreduces, but does not eliminate heteroskedasticity

While prior research typically does not include a constant in the above model, weinclude a constant in the estimation for several reasons First, it provides anadditional control for heteroskedasticity not alleviated by using assets as thedeflator Second, it mitigates problems stemming from an omitted size (scale)

based on models without a constant term are less symmetric, making power of thetest comparisons less clear-cut Thus, model estimations including a constant termallow us to better address the power of the test issues that are central to our analysis.Where appropriate, we comment on the differences between results based on modelsincluding versus excluding a constant

We use residuals from the annual cross-sectional industry regression model in (6)

as the Jones model discretionary accruals To obtain modified-Jones modeldiscretionary accruals we follow prior studies that estimate the modified-Jones

DSALESit prior to estimating model (6) See DeFond and Park (1997),

Our approach to estimate the modified Jones model (i.e., cross-sectionally) differs

sales are not managed in the estimation period, but that the entire change inaccounts receivable in the event year represents earnings management Therefore,Dechow et al use the parameters from the Jones model estimated in the pre-eventperiod for each firm in their sample, and apply those to a modified sales change

event period This approach is likely to generate a large estimated discretionaryaccrual whenever a firm experiences extreme growth in the test period compared to

‘‘pre-event’’ period where we can assume that changes in accounts receivable areunmanaged, we estimate the model as if all changes in accounts receivable arise fromearnings management That is, we cross-sectionally estimate the modified-Jonesmodel using sales changes net of the change in accounts receivables [i.e., we use

As noted above, we also estimate a model that is similar to the Jones and

This approach is designed to provide a comparison of the effectiveness ofperformance matching versus including a performance measure in the accrualsregression The model is

TAit ¼ d0þ d1ð1=ASSETSit!1Þ þ d2DSALESit

þ d3PPEitþ d4ROAitðor it!1Þþ uit: ð7Þ

3.3 Performance matching

We match each firm-year observation with another from the same two-digit SIC

when we present descriptive statistics for estimated discretionary accruals (see

7

As an example of a treatment sample experiencing high growth, consider Teoh et al (1998b, p 68)

description of their IPO firms: ‘‘The mean and median sales growth scaled by assets, an explanatory variable in the Jones (1991) model for accruals, are 54% and 28% Loughran and Ritter (1995) also report high sales growth for new issuers.’’ Although Teoh et al (1998a, b) tabulate results using the modified- Jones model, they report that their results are robust to using the Jones model.

8 In calculating ROA, we use net income rather than net income plus net-of-tax interest expense (the traditional measure used to calculate ROA) to avoid potential problems associated with estimating a tax rate However, using net income imparts error in our matching procedure if leverage varies substantially within an industry While we do not believe the error to be severe in the simulations we perform in the study, researchers should consider the trade off between potential errors in estimating the appropriate tax rate with the potential benefits of more precise matching as it relates to their particular setting, when deciding between net income and net income plus net-of-tax interest expense.

Table 1) We define the Jones-model performance-matched discretionary accrual forfirm i in year t as the Jones-model discretionary accrual in year t minus the matchedfirm’s Jones-model discretionary accrual for year t: Performance-matched modified-Jones model discretionary accrual is defined analogously.

3.4 Test statistics

For each of the 250 randomly selected samples (per event condition), we assess thesignificance of the mean discretionary accrual using a t-test The t-test is defined asthe equal-weighted sample mean discretionary accrual divided by an estimate of itsstandard error and assumes cross-sectional independence in the estimated discre-tionary accruals of the sample firms This assumption seems justified given that weconstruct samples by selecting firms without regard to time period or industrymembership (i.e., our samples are not clustered by industry and/or calendar time).The test statistic is

alternative discretionary accrual models described above), DA is the meandiscretionary accrual for the sample, s(DA) is the estimated standard deviation of

DA and N is sample size (i.e., 100)

3.5 Descriptive statistics for discretionary accrual measures under the null hypothesis

Table 1reports descriptive statistics for total accruals and discretionary accrualsbased on the Jones and Modified Jones models with and without performancematching Panel A contains results for the full sample while Panel B contains resultsfor various stratified-random samples (all values in the table are reported as apercent of total assets) From Panel A, the ratio of total accruals to beginning totalassets is !3.03% The negative value is due largely to depreciation The inter-quartilerange of !8.4% to 1.87% of total assets, coupled with a standard deviation of11.62% of total assets indicates that the distribution of total accruals to total assets isleptokurtic relative to a standard normal distribution Across the discretionaryaccrual measures in Panel A, average values are positive (negative) in three (eight) ofthe 11 total cases Since these are regression residuals, they are expected to average to

The samples in Panel B are from the lower and upper quartiles of the firms ranked on each partitioning variable at the end of the year t The

performance-matched discretionary accrual measures are constructed by matching each treatment firm with a control firm based on return on assets in period t or t!1.

Firm-year accrual observations are from the COMPUSTAT Industrial Annual and Research files from 1963 through 1999 We exclude observations if they do

not have sufficient data to construct the accrual measures or if the absolute value of total accruals scaled by total assets exceeds one We eliminate observations

where there are fewer than ten observations in a two-digit industry code for a given year and where a performance-matched firm cannot be obtained The

underlying accrual models (Jones and modified-Jones) include a constant term All discretionary accrual measures are reported as a percent of total assets and

all variables are winsorized at the 1st and 99th percentiles The final sample size is 122,798

Panel A Descriptive Statistics for Discretionary Accrual Measures: a

Description Mean Standard Deviation Lower Quartile Median Upper Quartile

Modified Jones model with ROAt!1 !0.04 9.94 !4.55 0.00 4.42

Modified Jones model with ROA t !0.03 10.98 !5.01 !0.15 4.52

Performance-matched Jones model ROAt!1 0.08 14.38 !6.88 0.04 7.07

Performance-matched Jones model ROA t !0.02 15.50 !7.29 0.00 7.28

Performance-matched modified-Jones model ROAt!1 0.09 14.83 !7.03 0.04 7.26

Performance-matched modified-Jones model ROA t !0.02 15.93 !7.45 0.00 7.43

Panel B Means (Medians) of Discretionary Accrual Measures for Stratified-Random Sub-Samples:a

Book/Market Sales Growth E/P Ratio Size Operating Cash Flow

Description High Low High Low High Low Large Small High Low

(0.01) (!0.41) (0.38) (!0.21) (!0.08) (!0.97) (!0.11) (!0.75) (!0.74) (!0.39) Modified-Jones model with ROAt!1 !0.14 !0.63 1.74 !1.69 0.28 !2.67 0.00 !1.12 0.12 !1.89

(0.02) (!0.38) (1.16) (!0.89) (0.12) (!1.82) (!0.02) (!0.62) (!0.21) (!1.44) Modified-Jones model with ROA t !0.35 !0.31 1.90 !1.65 !0.15 !1.73 !0.20 !1.35 !0.48 !0.57

(!0.15) (!0.43) (1.06) (!0.98) (!0.17) (!1.24) (!0.19) (!1.03) (!0.79) (!0.65) Performance-matched Jones model ROAt!1 0.45 !0.69 0.72 !0.45 0.14 !1.58 !0.28 !0.36 !0.80 !0.77

(0.27) (!0.47) (0.44) (!0.07) (0.03) (!1.25) (!0.11) (!0.19) (!0.48) (!0.74) Performance-matched Jones model ROA t !0.16 !0.18 0.53 0.06 !0.30 !0.17 !0.87 !0.14 !1.20 0.99

(0.0) (!0.11) (0.21) (0.2) (!0.02) (!0.15) (!0.32) (0.0) (!0.7) (0.7) Performance-matched modified-Jones model ROAt!1 0.30 !0.57 1.81 !1.35 0.20 !1.92 !0.22 !0.60 !0.50 !1.04

(0.21) (!0.36) (1.31) (!0.81) (0.06) (!1.53) (!0.07) (!0.37) (!0.29) (!0.99) Performance-matched modified-Jones model ROA t !0.27 !0.07 1.51 !0.75 !0.40 !0.21 !0.91 !0.30 !1.28 1.04

(0.0) (!0.05) (1.04) (!0.36) (!0.06) (!0.17) (!0.32) (!0.12) (!0.74) (0.67)

a Total Accruals (TAit) is defined as the change in non-cash current assets minus the change in current liabilities excluding the current portion of long-term debt

minus depreciation and amortization [with reference to COMPUSTAT data items, TA ¼ ðDData4 ! DData1 ! DData5 þ DData34 ! Data14Þ=lagged

Data6': Discretionary accruals from the Jones model are estimated for each industry and year as follows: TA i;t ¼ a 0 þ a 1 =ASSETS i ;t!1 þ a 2 DSALES i;t

þa 3 PPEi;tþ ! it ; where DSALES i;t is change in sales scaled by lagged total assets and PPE i,t is net property, plant and equipment scaled by lagged assets.

Discretionary accruals from the modified-Jones model are estimated for each industry and year as for the Jones model except that the change in accounts

receivable is subtracted from the change in sales Discretionary accruals from the Jones Model (Modified-Jones model) with ROA are similar to the Jones

Model (Modified-Jones model) except for the inclusion of current or lagged year’s ROA as an additional explanatory variable For performance matched

discretionary accruals, we match firms on ROA in period t or t!1 To obtain a performance-matched Jones model discretionary accrual for firm i we subtract

the Jones model discretionary accrual of the firm with the closest ROA that is in the same industry as firm i A similar approach is used for the modified Jones

zero However, some deviation from zero arises because we winsorize extremeobservations by setting the values in the bottom and top one percent to the values of

Results in panel A show that performance matching on current ROA yieldsdiscretionary accrual estimates that have both mean ( ¼ !0.02%) and median( ¼ 0%) close to zero for both Jones- and modified-Jones models We also find that

performance improvement Specifically, while the average discretionary accruals areclose to zero for both models, the medians differ between the Jones or the modified-

Performance matching increases the standard deviation of the Jones modeldiscretionary accruals from about 10% of total assets to about 14–16% of totalassets for the performance-matched Jones model discretionary accrual The 40–50%increase in variability is approximately the increase one would expect if the estimateddiscretionary accrual of the sample firm were uncorrelated with that of the matchedfirm Assuming independence, the variance of the difference between two randomvariables with identical variances is twice the variance of the individual randomvariables Therefore, the standard deviation would be the square root of two or 1.41times the standard deviation of the individual random variable

Consistent with claims in previous research, descriptive statistics in panel Bdocument the inability of discretionary accrual models to generate mean-zeroestimates when applied to stratified-random samples Bold numbers in Panel Bcorrespond to the mean and median value closest to zero in each column of the table.The bias (non-zero values) in the discretionary accrual measures in Panel B is ofconcern because the greater the bias the more likely it is that the null hypothesis ofzero discretionary accruals will be spuriously rejected

model produces the lowest mean and median values (in absolute magnitude) Thisapproach produces the lowest mean value in three of the ten cases and lowest median

in five of the ten cases The next best performing accrual measure is the Modified

median value two times each) In summary, the performance matching approach

performance-related sub-samples that are closest to zero more often than the othermeasures

A final observation on the results in Panel B is that the mean and medianperformance-matched discretionary accruals for the operating cash flow sub-sample

performance-matched discretionary accrual Holding ROA constant, high operatingcash flow stocks must necessarily have low accruals compared to the matched ROAfirm Thus, we expect a negative average for the current year’s performance-matched

9 Whether winsorization imparts any bias that leads to erroneous inferences depends on the research context (see Kothari et al., 2005 ).

discretionary accrual for high operating cash flow stocks and a positive value for thelow operating cash flow stocks This is precisely what is observed in panel B This

3.6 Serial correlations

Under the null hypothesis of no earnings management, the typical discretionaryaccrual or earnings management study implicitly assumes estimated discretionaryaccruals to have zero mean and exhibit no serial correlation For example, a study ofearnings management around IPOs would hypothesize that the accruals managedaround the IPO reverse in subsequent years The null hypothesis is that discretionaryaccruals in the IPO and subsequent years are zero and that the (serial) correlationbetween the IPO-year discretionary accruals with the subsequent years’ discretionaryaccruals is zero That is, under the null hypothesis, a zero coefficient in a regression

of subsequent years’ discretionary accruals on the IPO-year discretionary accruals ispredicted Thus, from a statistical perspective, discretionary-accrual estimates (i.e.,error terms from the models) that are serially uncorrelated satisfy one of thedistributional properties of the test statistic under the null hypothesis

In non-random samples, total accruals themselves are likely to be correlated,which can lead to serially correlated estimates of discretionary accruals The serialcorrelation in total accruals arises due to economic/operating reasons (e.g., actions

by management such as expanding receivables or inventories in periods of growth)

A major objective of the discretionary accrual models like the Jones model is to filterout non-discretionary accruals from total accruals to obtain estimates ofdiscretionary accruals that have a zero mean and are serially uncorrelated asexpected under the null hypothesis of no earnings management We expect well-specified discretionary accrual models to be successful in filtering out non-discretionary accruals that are serially correlated

We report estimates of the serial correlation in various discretionary accrualmeasures Serial correlations are slope coefficients from the following cross-sectionalregression model estimated annually from t ¼ 1962 to 1999:

where Xitis the current value of the variable of interest (e.g., return on assets, totalaccruals, Jones- or modified-Jones model discretionary accrual) The serialcorrelation estimate from the cross-sectional regression in (11) assumes it is identical

unlikely to be true, the regression estimate is unbiased and thus it is an estimate ofthe cross-sectional average serial correlation We attempt to mitigate the variation inserial correlation across firms by estimating the model for sub-samples that are, apriori, likely to be homogeneous A distinct advantage of using (11) compared to afirm-specific time-series regression is that sample attrition and survival biasstemming from requiring a long time series of data for each firm are avoided

estimates for each variable and sub-sample Significance tests for a zero mean are