Predicting Accruals based on Cash-Flow Properties

Richard Frankel* and Yan Sun**

*Olin Business School

Washington University in St. Louis Campus Box 1133

One Brookings Drive St. Louis, MO 63130-4899

**John Cook School of Business

Saint Louis University 3674 Lindell Blvd.

St. Louis, MO 63108

First draft: August 2014 Revised: June 2015

Abstract Accruals sum with cash flows to produce an income measure with fewer timing and matching problems. We construct proxies for cash-flow timing and matching problems and provide evidence on the ability of these factors to explain accruals. Researchers lament the meager understanding of the process that spawns accruals (Owens et al., 2013; Ball, 2013; McNichols, 2000). Our aim is to map the explanatory-power boundaries demarcated by current knowledge. Our findings are as follows. (1) The R-squared of accrual models increases significantly when negative serial correlation in cash-flow changes is incorporated, and this increase in explanatory power is larger than that produced by incorporating asymmetrically timely loss recognition (Ball and Shivakumar, 2006). (2) The explanatory power of cash-flow change for accruals derives from cash-flow serial correlation. (3) Nondiscretionary accruals estimated from a model that incorporates cash-flow serial correlation better predict future cash flows and income. (4) The explanatory power of the Dechow and Dichev (2002) and the Jones (1991) models increases significantly in the subsample exhibiting strong cash-flow serial correlation, suggesting that a significant portion of the explanatory power of these models stems from their indirect incorporation of cash-flow serial correlation. (5) Serial-correlation-matched discretionary accruals are better specified and more powerful in detecting earnings management than performance-matched discretionary accruals. We thank conference and workshop participants at the Columbia University Burton Conference, Washington University in St. Louis accounting brown bag, Rice University, and Rutgers University for comments and Tim Gray for editing.

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Predicting Accruals based on Cash-Flow Properties

1. Introduction One can precisely model accruals using changes in current balance sheet accounts, but

the output of this model would say nothing about whether accruals reported by a firm are

consistent with their raison d’être. The mitigation of timing and matching problems in cash flows

is said to be a reason for the existence of accruals (Dechow, 1994; Dechow, Kothari, Watts, 1998;

Ball and Shivakumar, 2006). Our goal is to understand the extent to which cash-flow timing and

matching problems explain accruals. We posit that negative serial correlation in cash-flow

changes captures these problems. By adding proxies for negative serial correlation to established

accrual models (Jones, 1991; Ball and Shivakumar, 2006), we investigate whether a proposed

economic role for accruals explains observed accruals. Moreover, we examine whether the

explanatory power of the Jones (1991) and Dechow and Dichev (2002) models stems from their

ability to capture variation in cash-flow persistence. Finally, we check the specification and

power of discretionary accruals computed by matching on cash-flow serial correlation, compared

to the Jones model and the performance-matched approach (Kothari et al. 2005).

We relate accruals to a user-oriented purpose (i.e., cash-flow predictability) and distill the

concept of cash-flow timing and matching problems to the underlying issue of negative serial

correlation in cash-flow changes. Owens et al. (2013) argue, “As a profession, we have very

limited theory of the accrual generating process….” Similarly, Ball (2013) argues that “limited

knowledge of the determinants of accruals in the absence of manipulation” fosters of culture of

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inadequate research design.1 We use the ideas of Dechow (1994) to predict accruals rather than

explain returns. Our objective is to redirect accrual-model research to a path marked by a deeper

understanding of the purpose of accruals. Our findings demonstrate that this approach offers

specification and power advantages.

Guided by Dechow (1994) and Dechow et al. (1998), we expect cash-flow changes to be

negatively related to accruals as accruals offset the transitory components of cash-flow changes.

We also predict that the negative correlation between accruals and cash-flow changes will grow

as cash-flow problems intensify because accruals will increasingly counteract cash-flow changes

as a firm’s cash flows increasingly stray from these desired properties. We estimate three

measures of cash-flow timing and matching problems using data from the previous five years,

including the negative serial correlation in cash-flow changes, the lack of predictive power of

current cash flows for future cash flows, and the relative explanatory power of two-year cash

flows to one-year cash flows for returns. The negative serial correlation in cash-flow changes is

measured using two economic characteristics, operating cycle and profit margin, as suggested by

Dechow et al. (1998). All three measures are defined so that a higher value represents a more

serious cash-flow problem. Our findings are as follows.

First, using the Fama-MacBeth (1973) approach, we find a negative relation between

cash-flow change and accruals, suggesting that accruals offset the transitory components of cash

flows. More importantly, we find that incorporating cash-flow change and any of these cash-flow

problem measures into the Jones model increases its explanatory power by approximately 226%

on average. This increase compares to an increase in explanatory power of approximately 3%

when asymmetric recognition of gains and losses is incorporated. In addition, we find that the

1 See also McNichols (2000): “Given the limited theory we have of how accruals behave in the absence of discretion, the task of identifying and controlling for potentially correlated omitted variables is daunting indeed” (p. 314).

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effects of the cash-flow problem and asymmetric recognition are incremental to each other.

When we consider all three cash-flow problem measures in the same regression, we find that the

serial-correlation measure subsumes the other two. Using industry-year specific regressions, we

find a similar increase in the R-squared from the inclusion of the cash-flow change and cash-

flow serial correlation, suggesting that the cash-flow serial correlation measure is not merely

capturing common industry characteristics.

Second, when we estimate the Jones model with cash-flow change added, within

subsamples formed for each value of expected cash-flow negative serial correlation, we find that

both model R-squared and the magnitude of the negative coefficient on cash-flow change

increase monotonically as expected cash-flow serial correlation becomes more negative. Ball and

Shivakumar (2006) suggest that cash-flow changes capture the effect of gains and losses on

accruals. However, our results indicate that the explanatory power of cash-flow changes for

accruals stems primarily from its relation to negative serial correlation in cash-flow changes.

Third, we find that nondiscretionary accruals estimated from our proposed model better

predict future cash flows and income than those from the Jones model or the nonlinear Jones.

This result is consistent with our hypothesis that accruals fix problems in cash flows, instead of

being used to smooth earnings.

Fourth, we estimate the Dechow and Dichev (2002) and the Jones (1991) models within

subsamples formed for each cash-flow serial correlation value to examine whether the

explanatory power of these models varies with cash-flow serial correlation. We find that the R-

squared of both models increases significantly in a subsample exhibiting stronger expected

negative serial correlation in cash-flow changes. This result suggests that the explanatory power

of the Dechow and Dichev (2002) model relates to the ability of its lagged and leading operating-

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cash-flow variables to capture negative serial correlation in cash-flow changes, and that the Jones

(1991) model inadvertently captures cash-flow serial correlation.

Finally, instead of using cash-flow change and cash-flow serial correlation as additional

explanatory variables for accruals, we estimate serial-correlation-matched discretionary accruals

in a way similar to the computation of performance-matched discretionary accruals by Kothari et

al. (2005). The matching based on cash-flow serial correlation is consistent with the economic

role of accruals and is less likely to be correlated with earnings management incentives than the

matching based on performance. We find that the serial-correlation-matched approach has better

specification and power than the performance-matched approach.

Our work both contrasts with and extends the approach of Ball and Shivakumar (2006).

They follow a stewardship perspective and explore whether accruals enhance the asymmetric

timeliness of cash flows.2 Like Ball and Shivakumar (2006), we examine whether consideration

of accruals’ purpose enhances accrual prediction. However, we focus on how accruals’ role in

mitigating the timing and matching problems of cash flows aids accrual prediction.

Aside from our new empirical results, our contribution relative to Dechow and Dichev

(2002) is one of emphasis. Dechow and Dichev emphasize the mapping of accruals into lagged,

current and leading cash flows. Their objective is to measure accrual estimation errors rather

than to explain why the inter-period allocation via accruals arises.3 We provide this link.

We emphasize that negative serial correlation in cash-flow changes leads to accruals-

based-on-earnings-quality notions arising from the valuation perspective. In emphasizing the role

2 Valuation and stewardship considerations need not have mutually exclusive predictions on the properties of accruals. Desirable properties derived from these perspectives can coincide. Moreover, even where they conflict, unless we hold that one force overwhelms the other, reporting outcomes reflect a compromise. 3 McNichols and Wilson (1988) likewise map the allowance for doubtful accounts accruals into future write-offs. Their work, like that of Dechow and Dichev (2002), as well as many loan loss reserve papers, links current accruals to future outcomes.

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of accruals in enhancing earnings persistence, we follow the model developed by Bernard and

Stober (1989) and Dechow et al. (1998). Earnings persistence is a commonly proposed measure

of earnings quality (e.g., Penman, 2013, p. 396; Revsine et al., 2015, p. 329; Dechow and

Schrand, 2004), as are prediction of future cash flows (e.g., Barth, Cram, and Nelson, 2001;

Barth, Clinch, and Israeli, 2015; Finger, 1994) and correlation with contemporaneous returns

(Dechow and Schrand, 2004). At a practical level, incorporating estimated cash-flow-measure

deficiencies into accrual prediction allows the researcher to explain accruals when future cash

flow information is not available, as in the work of Dechow and Dichev (2002) and Dechow,

Hutton, Kim, and Sloan (2012). Finally, we provide an explanation for the explanatory power of

existing accrual models. We find that the R-squared of both the Dechow and Dichev (2002)

model and the Jones (1991) model is significantly higher when there is a stronger negative serial

correlation in cash-flow changes. This result suggests that these two models capture the cross-

sectional variation in cash-flow serial correlation and derive their ability to explain accruals

primarily from cases where negative serial correlation in cash-flow changes is more likely. This

result also suggests that cash-flow serial correlation should be considered when estimating the

accrual models.

The remainder of the paper is organized as follows. We develop the hypotheses in

Section 2, describe the research design in Section 3, report the empirical results in Section 4, and

conclude in Section 5.

2. Literature and hypothesis development

Cash-flow timing and matching problems occasioned the formulation and use of accrual

accounting long before statements by accounting academics about allocating costs and

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recognizing credit sales.4 Yet groundbreaking empirical work relating earnings to security prices

treated accounting income as proportionate to dividends (e.g., Kormendi and Lipe, 1987; Collins

and Kothari, 1989), a noisy (Beaver, Lambert, and Morse, 1980; Beaver, Lambert, and Ryan,

1987; Ball and Brown, 1968) or a lagging measure of change in value (Freeman, 1987; Collins,

Kothari, Shanken, and Sloan, 1994). Other studies explored whether accruals provide

incremental explanatory power to cash flows (Bernard and Stober, 1989; Wilson, 1987; Rayburn,

1986; Ball and Brown, 1968). The objective of these scholars was to understand how earnings

mapped into prices and whether earnings added explanatory power beyond cash flows, rather

than to understand deficiencies of cash-flow measures remediated by accruals. This literature

sought properties of earnings that enfeeble its relation to value and therefore securities prices. In

this respect, one could substitute the “dividends” for “earnings” and run similar tests.

Dechow (1994) marks a break in the sequence of earnings/returns research.5 Rather than

attempting to understand the shortcomings of earnings in explaining returns, she deems earnings

an attempt to improve the explanatory power for returns beyond that of cash flows. Accountants

use accruals to correct timing and matching problems in cash flows. These problems interfere

with the mapping between cash flows and returns. Dechow (1994) straddles the valuation and

stewardship perspectives when justifying this role for accruals—substituting the word

“performance” for “returns.” The former word has stewardship connotations, whereas the latter

connotes valuation.6

4 According to Paton (1922), “Conventional accounting income is not exclusively cash income. In a particular case cash collections may be very slow and the cash condition quite unsatisfactory; yet the showing of income may be highly favorable. Evidently a part of income in such a case has not been realized in cash” (p. 452). 5 She is not the first to investigate the role of accounting earnings (e.g., Paton, 1922; Paton and Littleton, 1940; among many others). However, hers is the notable paper, because it marks an attempt to contrast the empirical properties of earnings to cash flows based on an economic role for accruals Anno Ball and Brown). 6 Her paper’s introduction uses the stewardship perspective to link her tests to efficiency. Yet she uses value relevance as a proxy for usefulness, a practice dating back to Ball and Brown (1968) that was adopted by papers recognized as adopting the valuation perspective later disdained (e.g., Holthausen and Watts, 2001).

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Seeking to measure earnings management, researchers developed models to predict

accruals (Healy, 1985; DeAngelo, 1986; Jones, 1991; DeFond and Jiambalvo, 1994) and separate

normal accruals from manipulated ones. Refinements were assayed based on whether model

residuals could measure earnings management (Dechow et al., 1995; Hribar and Collins, 2002;

McNichols, 2002; Kothari, Leone, and Wasley, 2005; Dechow et al., 2012; Owens et al., 2013).

Empirical research developed independently, but simultaneously, with theory explaining the

source of accruals (e.g., Dechow et al., 1998).

Dechow and Dichev (2002) and Ball and Shivakumar (2006) model accruals based on

their purpose. Dechow and Dichev note that accruals allow cash-flow effects to be recognized on

the income statement in periods before or after they are realized. Ball and Shivakumar show

accruals accelerate recognition of losses and delay recognition of gains. As with these papers, we

examine the function of accruals to guide refinement of accrual models. Our research can be

viewed as enriching the idea used by Dechow and Dichev that accruals break the correspondence

between cash-flow realization and income-statement recognition. However, our approach differs

theirs in that, instead of using leading/current/lagged cash flows that reflect firm-year

characteristics, we derive measures of cash-flow timing and matching problems based on

persistent firm characteristics. These measures help to identify the circumstances provoking the

disengagement between cash flows and income-statement recognition. Guided by Dechow

(1994) and Dechow et al. (1998), we hypothesize that accruals will alter the timing of the

recognition of cash-flow realizations when the cash-flow series has problems. Because cash-flow

changes exhibit negative serial correlation (i.e., a transitory component), we expect cash-flow

changes to be negatively related to accruals. Therefore we add cash-flow change to the accrual

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prediction model.7 Cash-flow problems become more intense as the properties of the cash-flow

series further diverge from the desired properties of the earnings series. Earnings properties that

enhance its usefulness for valuation include (i) persistence, (ii) association with future cash

flows, and (iii) association with current returns (Dechow and Schrand, 2004). We predict that the

negative correlation between accruals and cash-flow changes will grow as cash-flow problems

intensify because accruals will increasingly counteract cash-flow changes as a firm’s cash flows

increasingly stray from these desired properties. Our first two hypotheses are as follows.

H1: Accrual levels will be negatively correlated with cash-flow changes.

H2: The negative correlation between accrual levels and cash-flow changes will grow as cash-flow problems intensify.

An alternative formulation of H2 is that the explanatory power of cash-flow changes for

accrual levels will increase as cash-flow problems intensify, because the transitory component of

cash-flow changes is one source of the negative correlation between cash-flow changes and

accrual levels.8 Cash-flow changes should add less explanatory power to the accrual model when

cash-flow properties coincide with the desirable properties of earnings.

Given that reducing transitory cash flows can be viewed as self-serving income

smoothing by managers—a purpose for accruals counter to efficiency—we test a hypothesis to

pry the conjecture that earnings smoothing explains results consistent with hypotheses 1 and 2.

We examine the relation between the incremental portion of accruals explained by cash-flow

change and cash-flow problems with future cash flows or earnings. If earnings smoothing begets

the incremental portion explained, it should have less explanatory power for future cash flows or 7 Dechow’s (1994) table 2 shows that cash-flow changes exhibit negative serial correlation and that working capital accruals are negatively related to cash-flow changes. More recently, Bushman, Lerman, and Zhang (2014) explore the negative relation between accruals and cash-flow levels, noting accruals “smooth temporary timing fluctuations” in operating cash flows and examining reasons why the relation between accruals and cash-flow levels has declined overtime. 8 Another source of the negative correlation between cash-flow changes and accruals is substitution between cash realizations and accruals—for example, a customer pays cash instead of purchasing on credit.

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earnings. In contrast, the notion that accruals fix cash-flow problems suggests that the

incremental portion of accruals explained should increase the explanatory power of predicted

accruals for future earnings and cash flows. Thus our third hypothesis is as follows.

H3: The incremental portion of accruals explained by cash-flow change and cash-flow problems increases the explanatory power of predicted accruals for future earnings and cash flows.

3. Research design

Explaining accruals using different models

The standard Jones (1991) model deems accruals to be a linear function of changes in

revenue and gross property, plant, and equipment:

ACCt = α0 + α1ΔREVt + α2PPEt + ԑt (1)

where ACCt is accruals in year t, ΔREVt is change in net revenue from year t−1 to year t, and

PPEt is gross property, plant, and equipment at the end of year t. Variables are scaled by

beginning total assets in year t. For the dependent variable, ACCt, we use working capital

accruals because our measures of cash-flow problems are based on the properties of operating

cash flows. Following Dechow and Dichev (2002), we define working capital accruals as

ΔAccounts Receivable + ΔInventory – ΔAccounts Payable – ΔTaxes Payable + ΔOther Assets

(net).

To incorporate the asymmetry in the recognition of gains and losses by accruals, Ball and

Shivakumar (2006) propose the following nonlinear accrual model:

ACCt = α0 + α1ΔREVt + α2PPEt

+ α3ABNRETt + α4DABNRETt + α5ABNRETt * DABNRETt + ԑt, (2)

where ABNRETt is abnormal stock return in year t, relative to CRSP equally weighted market

return in the same year, and DABNRETt is an indicator variable that takes a value of one if

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ABNRETt is negative and zero otherwise. Because losses are recognized by accruals in a more

timely manner than gains, the coefficient on DABNRETt*ABNRETt is expected to be positive.9

To incorporate the role of accruals in mitigating the timing and matching problems

inherent in cash flows into the accrual models, we propose to modify the standard Jones model

and the nonlinear accrual model as follows:

ACCt = α0 + α1ΔREVt + α2PPEt

+ α6ΔOCFt + α7OCFProblemt + α8ΔOCFt * OCFProblemt + ԑt. (3)

ACCt = α0 + α1ΔREVt + α2PPEt

+ α3ABNRETt + α4DABNRETt + α5ABNRETt * DABNRETt

+ α6ΔOCFt + α7OCFProblemt + α8ΔOCFt * OCFProblemt + ԑt, (4)

where ΔOCFt is change in operating cash flows from year t−1 to year t, and OCFProlemt is a

measure of cash-flow problems related to timing and matching.

Guided by desired properties of income from the valuation perspective, we estimate three

measures of cash-flow problems: persistence, association with future cash flows, and association

with stock returns (Dechow and Schrand, 2004).

(a) OCFSC, serial correlation in operating-cash-flow changes, is defined using the

two economic drivers suggested by Dechow et al. (1998). Because of credit sales and purchases

and inventory holdings, cash flows for a particular period differ from earnings. The timing and

9 Ball and Shivakumar (2006) use four proxies for gains and losses, including level of cash flows, change in cash flows, industry-adjusted cash flows, and market-adjusted abnormal stock returns. We regard market-adjusted abnormal stock returns as a relatively cleaner proxy for news because cash-flow-based proxies measure news with error. For example, the level of cash flows suffers from the timing and matching problems; the change in cash flows reflects negative serial correlation of cash flows. News, by definition, should not be serially correlated, and returns have lower serial correlation than cash flows. For example, compare Fama’s (1965) Table 1 with Dechow’s (1994) Table 2. In unreported analysis, we add level of cash flows, change in cash flows, and industry-adjusted cash flows, instead of the stock returns, to the Jones model. We find that the coefficients on all three cash-flow based measures are significantly negative. This result is consistent with the results reported by Ball and Shivakumar (2006) in Table 3 (p. 219) and Table 5 (p. 224). However, this result is inconsistent with the interpretation that the cash-flow based measures capture news (i.e., gains and losses). We conduct additional tests on this issue in the empirical section.

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matching problems related to cash outflows and inflows imply that the cash flow increase in one

period is likely associated with a cash flow decrease in the previous or the following period,

leading to a negative serial correlation in cash-flow changes. In Dechow et al.’s (1998) model,

working-capital accruals offset the negative serial correlation in operating-cash-flow changes and

earnings better predicts future cash flows. In their model (equation (11) on page 139), the serial

correlation in operating-cash-flow changes, ρ∆OCF , ∆OCF , is a function of net profit margin

(π) and operating cash cycle (δ).

ρ∆CF , ∆CF δ π δ

π 2δ 2δπ.

The partial derivative of ρ∆OCF , ∆OCF with respect to operating cash cycle (δ) is:

22 2

.

This partial derivative is negative for most firms, given that Dechow et al. (1998) show

that π δ is the case for the overwhelming majority of firms. That is, holding net profit margin

(π) constant, a longer operating cash cycle (δ) implies a more negative serial correlation in cash-

flow changes.

The partial derivative of ρ∆OCF , ∆OCF with respect to net margin (π) is:

22 2

.

This partial derivative is positive when π is positive but negative when π is negative,

suggesting a V-shape relation between net margin (π) and the serial correlation in cash-flow

changes. In particular, as the magnitude of net margin (π) decreases, the serial correlation in

cash-flow changes becomes more negative.

We define net profit margin as earnings before extraordinary items and discontinued

operations divided by net revenue (Dechow et al., 1998) and operating cash cycle as net revenue

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divided by average accounts receivables plus cost of goods sold divided by average inventory

minus purchases divided by average accounts payables. We compute average net profit margin

and average operating cash cycle over the past three years for each firm-year observation. We

classify a firm-year as having a long (short) cash cycle if the firm’s three-year average cash cycle

is higher (lower) than the median for all observations with necessary data over the same period.

A firm-year is classified as having high (low) positive profit margin if the firm’s past average

profit margin is higher (lower) than the median for all positive-profit-margin observations over

the same period. Similarly, a firm-year is classified as having a high (low) negative profit margin

if the magnitude of the firm’s past average profit margin is higher (lower) than the median for all

negative-profit-margin observations over the same period. We define OCFSC as −1 if a firm-

year has short cash cycle but high positive or high negative profit margin, 1 if a firm-year has

long cash cycle but low positive or low negative profit margin, and 0 otherwise, as illustrated in

the figure below. With this definition, a higher value of OCFSC indicates greater negative serial

correlation in cash-flow changes, suggesting more severe timing problems in cash flows and less

persistent cash flows.

Profit Margin High negative Low negative Low positive High positive

Short Cash Cycle -1 0 0 -1 Long Cash Cycle 0 1 1 0

(b) OCFPRED, cash-flow predictability, is defined as the R-squared from the

regression of operating cash flow for the next year on operating cash flow for the current year

estimated over the past five years for each firm with necessary data. Cash flows are scaled by

beginning total assets. We multiply the R-squared by −1 so that a higher OCFPRED indicates

that current cash flow is less able to predict cash flow for the following year.

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(c) OCFVR, value relevance of two-year cash flows versus one-year cash flows, is

defined as the difference in the R-squared from the regression of accumulated two-year stock

returns on two-year cash flows (i.e., year t and year t+1) and the R-squared from the regression

of one-year stock return on one-year cash flow (i.e., year t). Regressions are estimated over the

past five years for each firm with necessary data. Stock returns are adjusted for CRSP equally

weighted market returns for the same period. Cash flows are scaled by beginning assets. A

higher value for OCFVRt indicates that current-year cash flows have a relatively lower

explanatory power for stock returns.

All three measures suggest that current-period cash flows contain temporary components.

Because accruals aim to offset the temporary components in cash flows, we expect negative

coefficients on both ΔOCFt and ΔOCFt * OCFProblemt, as stated in Hypotheses 1 and 2. To test

Hypotheses 1 and 2, we estimate annual Fama-MacBeth (1973) regressions of equations (1)–(4)

and compare explanatory power across different accrual models. 10 Under this approach, t-

statistics are based on the time-series distribution of annual coefficients.

Fama-MacBeth (1973) regressions help examine whether serial correlation in cash-flow

changes has explanatory power for accruals across industries. To examine whether cash-flow

serial correlation helps to explain accruals across firms within industries defined using two-digit

SIC codes, we estimate various accrual models for each industry-year combination with at least

30 observations with necessary data and at least five observations having negative stock returns.

Prediction of future cash flows or income

To examine whether nondiscretionary working-capital accruals generated by our

proposed model better predict future operating cash flows and earnings (Hypothesis 3), we

estimate various accrual models (i.e., equations (1)–(4)) annually to get nondiscretionary 10 We get qualitatively similar results using pooled regressions (untabulated).

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working-capital accruals. We then examine whether the nondiscretionary working-capital

income (i.e., nondiscretionary working-capital accruals + operating cash flows) estimated from

our model has a greater association with operating cash flow or earnings before extraordinary

items in the following year.

Dechow and Dichev (2002) model and Jones (1991) model

Since Dechow and Dichev’s (2002) model includes lagged and leading operating cash

flows that may capture the negative serial correlation in cash-flow changes, we estimate their

model within subsamples formed for each value of cash-flow serial correlation. We do this to

examine whether this model better explains accruals when there is a more negative serial

correlation in cash-flow changes. We also estimate the Jones (1991) model for each cash-flow

serial correlation value to examine whether this model’s explanatory power for accruals

increases with cash-flow serial correlation. This analysis will illuminate the source of the

explanatory power for accruals for both models.

Specification and power of serial-correlation-matched discretionary accruals

In equation (3), we directly add cash-flow change and cash-flow serial correlation as

additional explanatory variables for accruals to the Jones model. Discretionary accruals for a

firm-year are the residual from the equation estimation. An alternative approach to control for

the effect of cash-flow serial correlation on accruals is to identify a matched control firm from

the same industry-year and with the same cash-flow serial correlation and closest cash-flow

change. The difference between the discretionary accruals estimated from the Jones model for

the firm under examination and those of the matched control firm will be the serial-correlation-

matched discretionary accruals. This second approach resembles the computation of

performance-matched discretionary accruals by Kothari et al. (2005).

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The serial-correlation-matched approach has two advantages over the performance-

matched approach. First, it directly considers the economic circumstances that generate accruals

(Dechow et al., 1998). Second, cash-flow serial correlation is less likely to be correlated with the

earnings-management incentives under investigation than performance (i.e., ROA). Kothari et al.

(2005) show that the performance-matched approach is better specified but less powerful than

the Jones model. To provide a practical implication of the serial-correlation-matched approach,

we check its specification (Type I error) and power (Type II error), compared with the Jones

model and the performance-matched approach.

4. Data and empirical results

Sample and data

We obtain data from Compustat and CRSP for a sample period of 1993–2012. To avoid

problems of accrual computation using balance sheet data (Hribar and Collins 2002), working

capital accruals and cash flows are based on data from statement of cash flows that became

available after 1988. The sample period starts from 1993 because cash flows for the previous five

years are needed to compute the cash-flow problem measures. We remove financial institutions

and firm-years with acquisitions. To reduce the influence of outliers and data errors, we truncate

the 1% extreme observations in each tail of each continuous variable for each year. The final

sample contains 50,552 firm-years.

We present the descriptive statistics of our key variables in Table 1 Panel A. The average

of −0.2468 for cash-flow predictability (OCFPRED) indicates that, on average over the past five

years, cash flows for a year explain 24.68% of the variability of cash flows for the following year.

The mean 0.0796 for cash-flow value relevance (OCFVR) suggests that two-year cash flows

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better explain two-year stock returns than one-year cash flows for one-year stock returns, with an

average difference in R-squared of 7.96%.

The mean −0.0790 for serial correlation in cash-flow changes (OCFSC) suggests that the

number of sample observations with a value of −1 for OCFSC is greater than the number of

observations with a value of 1. As discussed earlier, our definition for OCFSC is based on net

profit margin and operating cash cycle as suggested by Dechow et al. (1998). To check the

validity of this definition, we compute average serial correlation of cash-flow changes for each

profit margin/cash cycle subgroup of firms and report the results in Table 1 Panel B. We find that

firms with low cash cycle but high positive or high negative profit margin have less negative

serial correlation and that firms with high cash cycle but low positive or low negative profit

margin have more negative serial correlation, consistent with the model of Dechow et al. (1998)

and our definition of serial correlation of cash-flow changes (OSFSC).

[Insert Table 1 here]

Table 2 presents the correlations between our key variables, with Pearson (Spearman)

correlations reported above (below) the diagonal. Consistent with literature, working-capital

accruals (ACC) are positively associated with revenue change (ΔREV) but positively associated

with property, plant, and equipment (PPE). The Pearson correlation between working-capital

accruals (ACC) and cash-flow change (ΔOCF) is −0.1548, suggesting that these accruals offset

temporary components in cash flows (consistent with Hypothesis 1). The three cash-flow

problem measures are significantly positively correlated. For example, the Pearson correlation

between cash-flow serial correlation (OCFSC) and cash-flow predictability (OCFPRED) is

0.0999; the Pearson correlation between cash-flow serial correlation (OCFSC) and cash-flow

value relevance (OCFVR) is 0.0161. However, the low magnitude of the correlations between

17

the three cash-flow problem measures suggests that these three measures capture different

properties of cash flows.

[Insert Table 2 here]

Explaining accruals by considering cash-flow problems

We present the estimation results for the different accrual models (i.e., equations (1)–(4))

using the Fama-MacBeth (1973) approach in Table 3. The cash-flow problem measures are cash-

flow serial correlation (OCFSC), cash-flow predictability (OCFPRED), and cash-flow value

relevance (OCFVR) in columns (1), (2), and (3), respectively. For the standard Jones (1991)

model in Panel A, the average R-squared from the 20 annual regressions ranges from 7.12% in

column (3) to 7.89% in column (1).11 Once we consider the asymmetric gain/loss recognition in

Panel B, the R-squared increases slightly to 7.39% to 8.14%. The average percentage increase in

R-squared from Panel A to Panel B across the three columns is about 3%.12

[Insert Table 3 here]

In Panel C, we report results for our modified Jones model by adding cash-flow change

(ΔOCF) and estimated cash-flow problem measures. As we expect, the coefficient on cash-flow

change (ΔOCF) is significantly negative, suggesting that cash flows contain transitory

components that are offset by accruals (Hypothesis 1). The negative coefficient on cash-flow

change (ΔOCF) is inconsistent with the conjecture of Ball and Shivakumar (2006) that cash-flow

change is a proxy for news or economic gains. In addition, the coefficients on the interaction of

ΔOCF and cash-flow serial correlation (OCFSC) in column (1) and the interaction of ΔOCF and

11 The estimation results in the three columns of Panel A and Panel B differ because we require a nonmissing value for the cash-flow problem measure in each corresponding column. 12 We aim to explain working capital accruals in the paper. In untabulated analysis using total accruals, we get a significantly greater percentage increase in the R-squared from the standard Jones model to the nonlinear Jones model at about 34%. As a comparison, the percentage increase in the R-squared from the standard Jones model to our proposed model that considers cash-flow change and cash-flow serial correlation is about 170% if using total accruals.

18

cash-flow predictability (OCFPRED) in column (2) are significantly negative, consistent with

Hypothesis 2 that the negative relation between accruals and cash-flow change increases as cash-

flow problems intensify. The interaction of ΔOCF and cash-flow value relevance (OCFVR) in

column (3) is negative but insignificant, suggesting that value relevance does not have significant

implication for the relation between accruals and cash-flow change.

Turning to the R-squared, the increase from 7.89% in Panel A to 23.46% in Panel C in

column (1) represents a percentage increase of 197%. (Similarly, there are increases of 224% and

257% in columns (2) and (3), respectively.) This percentage increase in explanatory power from

Panel A to Panel C is much greater than the increase from Panel A to Panel B when asymmetric

gain/loss recognition is considered. Although the majority of the increase in R-squared from

Panel A to Panel C is due to the inclusion of cash-flow change (ΔOCF), 13 the negative

coefficient on cash-flow change (ΔOCF) suggests that this increase in R-squared is derived from

the ability of cash-flow change to capture transitory components in cash flows and thus negative

serial correlation in cash-flow changes. To see this directly, we estimate the regression in Panel

C within subsamples formed for each cash-flow serial correlation value and report the results in

Table 4. We find that the explanatory power of the Jones model with cash-flow change added

increases from 13.28% for the subsample with weak negative serial correlation (i.e., OCFSC=−1)

to 40.69% for the subsample with strong negative serial correlation (i.e., OCFSC=1). In addition,

the coefficient on cash-flow change (ΔOCF) decreases from −0.1598 to −0.3844. These results

suggest that adding cash-flow change (ΔOCF) increases the explanatory power of the accrual

model significantly more when there is stronger negative serial correlation in cash-flow changes

13 Adding cash-flow change (ΔOCF) to the Jones (1991) model leads to an increase in the R-squared from 7.89% in Panel A to 21.73%.

19

because cash-flow change (ΔOCF) captures the transitory components in cash flows that lead to

cash-flow negative serial correlation.

[Insert Table 4 here]

In Table 3 Panel D, when we consider both asymmetric gain/loss recognition and cash-

flow problems, the R-squared is even higher. For example, the R-squared increases to 23.83% in

column (1), with 23.83% representing a percentage increase of about 202% from the R-squared

of 7.89% for the standard Jones model in Panel A. We find similar results in terms of percentage

increases in the R-squared for columns (2) and (3). In addition, we find that the average increase

in the R-squared across all three columns from Panel A to Panel D (231%) is approximately the

sum of the percentage increases from Panel A to Panel B (3%) and from Panel A to Panel C

(226%), suggesting that asymmetric gain/loss recognition and cash-flow problems are

incremental to each other.14

In Panel E, we estimate a nonlinear version of the McNichols (2002) model, which

combines the Jones (1991) model, the Dechow and Dichev (2002) model, and asymmetric

gain/loss recognition, to compare the ability of this model to explain accruals with that of our

proposed model. Given all variables in our proposed model are based on data from the current

year or previous years, we remove cash flows for the following year from this comparison. We

find that, in the cross-section, our proposed model better explains accruals in all three columns.

For example, in column (1), the R-squared of our model in Panel D is 23.83%, while the R-

squared of the McNichols model (without the leading cash-flow variable) is 17.16%.

14 In untabulated analysis, we also include stock-return volatility as an additional independent variable for the various accrual models, as Arif et al. (2014) show that firms with greater uncertainty hold less working-capital accruals. Consistently, we find a negative coefficient on stock return volatility. The inclusion of this variable leads to an average absolute increase in R-squared for the accrual models of about 0.1% and does not change our results for cash-flow change or cash-flow-problem measures.

20

When we put all three cash-flow-problem measures into the same regression, we find that,

as reported in Table 5, only the cash-flow serial-correlation measure (OCFSC) continues to

significantly affect the relation between cash-flow change and working-capital accruals. The

significantly negative coefficient on ΔOCF*OCFSC and the insignificant coefficients on

ΔOCF*OCFPRED and ΔOCF*OCFVR suggest that the cash-flow serial-correlation measure

subsumes the other two cash-flow-problem measures. And thus we focus on the serial-

correlation measure in later analysis.

[Insert Table 5 here]

Prediction of future cash flows or income

We next examine whether nondiscretionary working-capital accruals generated by our

model better predict future cash flows and earnings. We first estimate the various accrual models

annually to get nondiscretionary working-capital accruals. We then examine whether the

nondiscretionary working-capital income (i.e., nondiscretionary working-capital accruals +

operating cash flow) estimated from our model has a stronger association with operating cash

flows or earnings before extraordinary items in the following year (Hypothesis 3).

We report the results in Table 6. For the prediction of future cash flows in Panel A, we

find that the nondiscretionary working-capital income (NDWCI) estimated from the accrual

model that considers cash-flow change and cash-flow serial correlation (i.e., Model 6) has a

significantly higher explanatory power for cash flows in the following year than both cash flows

in the current year (i.e., Model 1) and NDWCI estimated from the standard Jones model (i.e.,

Model 2) or from the McNichols model without leading cash flows (i.e., Model 4). We further

find that NDWCI estimated from the accrual model that considers both asymmetric gain/loss

recognition and cash-flow serial correlation (i.e., Model 7) significantly better explains cash

21

flows in year t+1 than both cash flows in year t (i.e., Model 1) and NDWCI estimated from the

nonlinear Jones model (i.e., Model 3) or from the nonlinear McNichols model without the

leading cash flow (i.e., Model 5). In Panel B, we find, similarly, that NDWCI estimated from our

proposed accrual model that considers cash-flow serial correlation has significantly better ability

to predict earnings before extraordinary items in the following year, no matter whether

asymmetric gain/loss recognition is considered.

[Insert Table 6 here]

Industry-year-specific estimation

The results in Table 3 suggest that cash-flow serial correlation has significant explanatory

power for accruals across industries. We next examine whether cash-flow serial correlation also

helps to explain accruals across firms within two-digit SIC industries. We estimate various

accrual models for each industry-year combination with at least 30 observations with necessary

data and at least five observations having negative stock returns and report average results for

431 industry-year specific regressions during 1993–2012 in Table 7. We find that the

incorporation of asymmetric gain/loss recognition into the Jones model increases the R-squared

from 10.49% in Panel A to 12.74% in Panel B, an increase of about 21%. We further find that by

adding cash-flow change (ΔOCF) and cash-flow serial correlation (OCFSC), the R-squared

increases from 10.49% for the standard Jones model in Panel A to 34.07% in Panel C, an

increase of 225%. In addition, the coefficient on the interaction term ΔOCF*OCFSC is

significant at 1% level in Panels C and D, suggesting that the negative relation between accruals

and cash-flow change grows as cash-flow problems intensify, consistent with Hypothesis 2.

The explanatory power of our proposed model within industries in Panel D is only

slightly greater than the explanatory power of the nonlinear version of McNichols (2002) model

22

(without the leading cash-flow variable) reported in Panel E (35.9% versus 35.6%), suggesting

that lagged cash flows and current cash flows do a good job in capturing the variation in cash-

flow serial correlation across firms within industries.

[Insert Table 7 here]

Dechow and Dichev (2002) model and Jones (1991) model

To examine whether the Dechow and Dichev (2002) and Jones (1991) models capture

timing problems related to negative serial correlation in cash-flow changes, we estimate both

models within subsamples formed for each cash-flow serial correlation value to examine whether

these two models have better ability to explain accruals when there is a stronger negative serial

correlation in cash-flow changes. The estimation results are reported in Table 8. For the Dechow

and Dichev (2002) model reported in Panel A, we find that the R-squared is as low as 8.95% for

the group of sample observations with less negative cash-flow serial correlation (i.e.,

OCFSC=−1), and as high as 31.41% for the group with more negative cash-flow serial

correlation (i.e., OCFSC=+1). For the Jones (1991) model reported in Panel B, the R-squared

increases from 4.24% to 15.71%. These results suggest that variables in these two widely used

accrual models inadvertently capture cross-sectional variation in cash-flow serial correlation.

Our results provide a new explanation for the source of the explanatory power of existing accrual

models.

[Insert Table 8 here]

Specification and power of serial-correlation-matched discretionary accruals

Following prior studies (e.g., Dechow et al., 1995; Kothari et al., 2005), we use random

samples to check the specification and power of the serial-correlation-matched model, compared

to the Jones model and the performance-matched model. Both tests are based on 37,187

23

observations for which each industry-year combination has at least 30 observations. For

specification, we compute Type I errors for 10 random samples of 1,000 firm-years from the full

sample, or from the upper and lower quartiles of book-to-market ratio, sales growth, earnings-to-

price ratio, market value of common equity, and operating cash flow.15 The random samples are

formed sequentially without replacement. We report in Table 9 the average rejection rates for the

10 random samples that the null hypothesis of nonnegative (Panel A) or nonpositive earnings

management (Panel B) is rejected at the 5% significance level. The test is misspecified if the

rejection rate is higher than 8% or lower than 2%. We find that all three models are well

specified if the random samples are drawn from the full sample. However, when the samples are

drawn from firms with certain characteristics, the serial-correlation-matched discretionary

accrual measure is better specified than the discretionary accruals estimated from the Jones

model or from the performance-matched approach because that measure is misspecified for only

four out of 10 cases in Panel A and two out of 10 cases in Panel B.

[Insert Table 9 here]

For the power (Type II errors) comparison, we compute the average rejection rates for the

above random samples by adding plus or minus 1%, 2%, 4%, or 10% of the firm’s beginning

total assets to accruals before estimating discretionary accruals and report the test results in Table

10. Following Kothari et al. (2005), we assume 50% of the seeded earnings management is

related to credit sales manipulation. We find that the performance-matched and the serial-

correlation-matched discretionary accrual measures both have lower power in detecting earnings

management than the discretionary accrual measure from the Jones model. However, the serial-

correlation-matched discretionary accrual measure generates higher rejection rates (i.e., better

power) than the performance-matched discretionary accrual measure not only for the full sample, 15 The same five firm characteristics are used in the tests by Kothari et al. (2005).

24

but also for nine out of 10 cases in Panel A and six out of 10 cases in Panel B when the random

samples are drawn from firms with certain characteristics.

[Insert Table 10 here]

The results on Table 9 and Table 10 suggest that the serial-correlation-matched approach

that directly considers the economic role of accruals is not only better specified but also more

powerful in detecting earnings management than the performance-matched approach.

5. Conclusion

We argue and show that consideration of cash-flow problems substantially improves the

explanatory power of the Jones accrual model in predicting working capital accruals. Our

purpose is to explore whether current understanding of the purpose of accruals is useful in

building an empirical model to predict accruals. Many researchers highlight the inadequate

understanding of the process that generates accruals (Owens et al., 2013; Ball, 2013; McNichols,

2000). Our aim is to produce a rough map of the empirical boundaries circumscribed by current

knowledge. Our approach follows that of Ball and Shivakumar (2006), who note that accruals

enhance the asymmetric timeliness of earnings beyond that of cash flows and show that adding

variables to account for nonlinearity of gain and loss recognition to the Jones model increases its

explanatory power.

Dechow (1994) shows that accruals offset timing and matching problems in cash flows.

We construct empirical proxies for cash-flow timing and matching problems and provide

evidence that consideration of this accrual generating factor improves explanatory power of the

Jones model. The improvement in explanatory power far exceeds that resulting from

consideration of asymmetric recognition of gains and losses in cross-industry estimation. To put

these two accrual drivers in perspective, if asymmetrical gain/loss recognition, which results in a

25

3% increase in Jones-model R-squared is noteworthy, the 226% increase in R-squared resulting

from incorporating cash-flow problems in the Jones model is astonishing. Within industries,

consideration of cash-flow effects (an R-squared increase of 225%) continues to dominate

consideration of asymmetric gain/loss recognition (an R-squared increase of 21%).

We show that the magnitude of the negative relation between accruals and cash-flow

change increases with cash-flow serial correlation, suggesting that the explanatory power of

cash-flow change for accruals is derived from its relation with cash-flow serial correlation. This

result contrasts with that of Ball and Shivakumar (2006), who interpret cash-flow change as a

proxy for news. We also find that the nondiscretionary working-capital accruals estimated from

our proposed model incorporating cash-flow change and cash-flow serial correlation better

explains cash flows and income in the following year than those estimated from the Jones (1991)

and McNichols (2002) models (without leading cash flows). This result suggests that the

negative relation between accruals and cash-flow change arises because accruals fix the

transitory components in cash-flow changes as opposed to smooth earnings. Moreover, we find

that the explanatory power of the Dechow and Dichev (2002) and Jones (1991) models for firms

with more negative serial correlation is about 3.5 times and 3.7 times of that for firms with less

negative cash-flow serial correlation, respectively. This result suggests that these two models

have inadvertently captured the negative serial correlation in cash-flow changes. Finally, we find

that the serial-correlation-matched discretionary accrual measure is better specified and more

powerful in detecting earnings management than the performance-matched discretionary accrual

measure, suggesting that the serial-correlation-matched approach that considers the economic

role of accruals has practical advantage over the performance-matched approach.

26

Given that accruals are central to the role of financial accounting and researchers have

sought methods to isolate earnings management, we believe that our study is important as we

model accruals by considering their economic use. In particular, we link the empirical properties

of accruals to cash-flow problems. Our study provides a new explanation for the source of the

explanatory power of existing accrual models, such as those of Dechow and Dichev (2002) and

Jones (1991). At a practical level, our study highlights the importance of incorporating cash-flow

change and estimated cash-flow serial correlation into accrual prediction, especially when future

cash flow information is not available.

27

6. References Arif, S., Marshall, N., and Yohn, T., 2014, The investment perspective of accruals: Do theories of investment under uncertainty provide insight into factors that shape a firm’s level of accruals?, Kelly School of Business, Indiana University working paper. Ball, R., and Brown, P., 1968, An empirical evaluation of accounting numbers, Journal of Accounting Research 6, 159-178. Ball, R., and L. Shivakumar, 2006, The role of accruals in asymmetrically timely gain and loss recognition, Journal of Accounting Research 44 (2), 207-242. Ball, R., 2013, Accounting informs investors and earnings management is rife: Two questionable beliefs, forthcoming Accounting Horizons. Barth, M., Clinch, G., and Israeli, D., 2015, What do accruals tell us about future cash flows? Stanford University working paper. Barth, M., Cram, D., and Nelson, K., 2001, Accruals and the prediction of future cash flows, The Accounting Review 76, 27-58. Beaver, W., Lambert, R., and Morse, D., 1980, The information content of security prices, Journal of Accounting and Economics 2, 3-28. Beaver, W., Lamber, R., and Ryan, S., 1987, The information content of security prices: A second look, Journal of Accounting and Economics 9, 139-157. Bernard, V., and Stober, T., 1989, The nature and amount of information in cash flows and accruals, The Accounting Review 45, 624-652. Bushman, R., Lerman, A., and Zhang X.F., 2014, The changing landscape of accrual accounting, University of North Carolina working paper. Collins, D., and Kothari, S. P., 1989, An analysis of intertemporal and cross-sectional determinants of earnings response coefficients, Journal of Accounting and Economics 11, 143-181. Collins, D., Kothari, S., Shanken, J., and Sloan, R., 1994, Lack of timeliness versus noise as explanations for low contemporaneous return-earnings association, Journal of Accounting & Economics 18, 289-324. DeAngelo, L., 1986, Accounting numbers as market valuation substitutes: A study of management buyouts of public stockholders, Accounting Review 61, 400-420.

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Dechow, P., 1994, Accounting earnings and cash flows as measures of firm performance: The role of accounting accruals, Journal of Accounting Economics 18 (1), 3-42. Dechow, P. and Dichev, I., 2002, The quality of accruals and earnings: The role of accrual estimation errors, The Accounting Review 77, 35-59. Dechow, P., S.P. Kothari, R. Watts, 1998, The relation between earnings and cash flows, Journal of Accounting and Economics 25, 133-168. Dechow, P., and Schrand, C., 2004, Earnings Quality, Research Foundation of CFA Institute. Dechow, P., Sloan, R., and Sweeney, A., 1995, Detecting earnings management, The Accounting Review 70, 195-225. Dechow, P., Hutton, A., and Kim J., and Sloan, R., 2012, Detecting earnings management: A new approach, Journal of Accounting Research 50, 275-334. DeFond, M., and Jiambalvo, J., 1994, Debt covenant violation and manipulation of accruals, Journal of Accounting and Economics 17, 145-176. Fama, E., and MacBeth, J., 1973, Risk, return and equilibrium – empirical tests, Journal of Political Economy 81, 607-641. Finger, C., 1994, The ability of earnings to predict future earnings and cash flow, Journal of Accounting Research 32, 210-223. Freeman, R., 1987, The association between accounting earnings and security returns for large and small firms, Journal of Accounting and Economics 9, 195-228. Healy, P., 1985, The effect of bonus schemes on accounting decisions, Journal of Accounting and Economics 7, 85-107. Hribar, P., and Collins, D., 2002, Errors in estimating accruals: Implications for empirical research, Journal of Accounting Research 40, 105–34. Holthausen, R., and Watts, R., 2001, The relevance of the value-relevance literature for financial accounting standard setting, Journal of Accounting and Economics 31, 3-75. Jones, J., 1991, Earnings management during import relief investigations, Journal of Accounting Research 29, 193–228. Kormendi, R., and Lipe, B., 1987, Earnings innovations, earnings persistence, and stock returns, Journal of Business 60, 323-345.

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Kothari, S. P., Leone, A., and Wasley, C., 2005, Performance matched discretionary accrual measures, Journal of Accounting and Economics 39, 163-197. McNichols, M., 2000, Research design issues in earnings management studies, Journal of Accounting and Public Policy 19, 313-345. McNichols, M., 2002, Discussion of The quality of accruals and earnings: the role of accrual estimation errors, The Accounting Review 77, 61-69. McNichols, M., and Wilson, P., 1988, Evidence of earnings management from the provision of bad debts, Journal of Accounting Research 26, 1-31. Owens, E., J. Wu, and J. Zimmerman, 2013, Business model shocks and abnormal accrual models, University of Rochester working paper. Paton, W., 1922, Accounting Theory with Special Reference to the Corporate Enterprise, The Ronald Press Company, New York. Paton, W., and Littleton, A. C., 1940, An introduction to corporate accounting standards, American Accounting Association Monograph No. 3. Penman, S., 2013, Financial Statement Analysis and Security Valuation 5th Edition, McGraw-Hill Irwin, New York, NY. Rayburn, J., 1986, The association of operating cash flow and accruals with security returns, Journal of Accounting Research Supplement, 112-133. Revsine, L., Collins, D., Johnson, B., Mittelstaedt, F., and Soffer, L., 2015, Financial Reporting and Analysis, 6th Edition, McGraw Hill Education, New York, NY. Wilson, G. P., 1987. The incremental information content of the accrual and funds components of earnings after controlling for earnings, The Accounting Review 42, 293-321.

30

Table 1: Descriptive statistics Panel A: Descriptive statistics for the variablesa Variablesb

N

Mean

Standard Deviation

Min

1st Quartile

Median

3rd Quartile

Max

ACCt 50552 0.0123 0.0901 -1.7468 -0.0202 0.0068 0.0410 0.9573ΔREVt 50552 0.0715 0.2819 -1.6199 -0.0363 0.0460 0.1657 3.4890PPEt 50552 0.6149 0.4511 0.0000 0.2563 0.5112 0.8963 3.8922OCFt 50552 0.0324 0.2264 -4.9641 -0.0075 0.0741 0.1401 0.6659ΔOCFt 50552 0.0100 0.1421 -2.0186 -0.0424 0.0067 0.0578 2.5081ABNRETt 50552 -0.0198 0.6221 -1.3615 -0.3893 -0.1075 0.1962 7.0137DABNRETt 50552 0.6023 0.4894 0.0000 0.0000 1.0000 1.0000 1.0000OCFSCt 50552 -0.0790 0.7408 -1.0000 -1.0000 0.0000 0.0000 1.0000OCFPREDt 24746 -0.2468 0.2525 -0.9763 -0.3954 -0.1537 -0.0372 0.0000OCFVRt 20032 0.0796 0.3746 -0.8816 -0.1583 0.0576 0.3447 0.9106a This table presents descriptive statistics for the 50,552 sample firm-year observations with necessary data during 1993–2012. b Definition of variables: ACCt working capital accruals for year t, defined as ΔAccounts Receivable + ΔInventory – ΔAccounts

Payable – ΔTaxes Payable + ΔOther Assets (net), scaled by beginning total assets.

ΔREVt change in net revenue from year t−1 to year t, scaled by beginning total assets.

PPEt gross property, plant, and equipment at the end of year t, scaled by beginning total assets.

OCFt cash flows from operations for year t, scaled by beginning total assets.

ΔOCFt change in cash flow from operations from year t−1 to year t, scaled by beginning total assets.

ABNRETt abnormal stock return in year t, relative to CRSP equally weighted market return in the same year.

DABNRETt an indicator variable that takes a value of one if abnormal market return in year t is negative andzero otherwise.

OCFSCt serial correlation in cash-flow changes, defined as −1 if a firm-year has short cash cycle but high positive or high negative profit margin, 1 if a firm-year has long cash cycle but low positive or low negative profit margin, and 0 otherwise. We classify a firm-year as having long (short) cash cycle if its average operating cash cycle over the past three years is higher (lower) than the median for all observations over the same period. We classify a firm-year as having high (low) positive profit margin if its average profit margin in the past three years is higher (lower) than the median for all positive-profit margin observations over the same period. Similarly, we classify a firm-year as having high (low) negative profit margin if the magnitude of its past average profitmargin is higher (lower) than the median for all negative-profit margin observations over the same period. Profit margin is earnings before extraordinary items and discontinued operations divided by net revenue. Operating cash cycle is net revenue divided by average receivables pluscost of goods sold divided by average inventory minus purchases divided by average payables.

OCFPREDt cash flow predictability, defined as the average R-squared from the regression of OCF for the next year on OCF for the current year for each firm with necessary data over the past five years, multiplied by −1.

OCFVRt cash flow value relevance, defined as the difference in the R-squared from the regression of accumulated market-adjusted two-year stock return on accumulated two-year OCF (i.e., year t and year t+1) and the R-squared from the regression of market-adjusted one-year stock return on one-year OCF (i.e., year t), estimates over the past five years for each firm with necessary data.

31

Panel B: Computed cash-flow serial correlation for each cell in OCFSC definitionb Profit Margin High negative Low negative Low positive High positive Cash cycle

Short -0.143 -0.354 -0.397 -0.220255 222 387 388

Long -0.187 -0.380 -0.433 -0.374162 192 307 300

b This table shows the average coefficient estimated from annual regressions of ∆ ∆ for sample observations in each cell of the definition of serial correlation in cash-flow changes (OCFSC). The average number of observations for each cell across the 20 years during 1993–2012 is reported in italics.

32

Table 2: Correlation matrixa ACCt ΔREVt PPEt OCFt ΔOCFt ABNRETt DABNRETt OCFSCt OCFPREDt OCFVRt

ACCt 0.3017 -0.0365 -0.1548 -0.3194 0.0579 -0.0425 0.0252 0.0237 -0.0123 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0002) (0.0816)ΔREVt 0.2604 0.0286 0.1053 0.1471 0.2019 -0.1790 -0.0091 -0.0080 0.0155 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0402) (0.2063) (0.028) PPEt -0.0298 0.0565 0.2367 0.0212 0.0439 -0.0521 -0.1428 0.0169 -0.0060 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0078) (0.3947)OCFt -0.2407 0.2317 0.3121 0.3111 0.1161 -0.1371 0.0876 0.0981 0.0127 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0718)ΔOCFt -0.3352 0.2159 0.0374 0.4227 0.1213 -0.0943 -0.0264 -0.0097 0.0152 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.1255) (0.032) ABNRETt 0.0525 0.2637 0.0893 0.2654 0.1587 -0.6837 0.0250 -0.0018 0.0077 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.7811) (0.2738)DABNRETt -0.0319 -0.2164 -0.0561 -0.2006 -0.1356 -0.8477 -0.0240 -0.0112 -0.0047 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0792) (0.5082)OCFSCt 0.0308 0.0048 -0.0890 -0.0290 -0.0205 0.0345 -0.0240 0.0999 0.0161 (<.0001) (0.2842) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0225)OCFPREDt 0.0223 -0.0116 0.0165 0.0046 -0.0176 0.0107 -0.0103 0.0835 -0.0042 (0.0004) (0.0672) (0.0095) (0.4725) (0.0057) (0.093) (0.1049) (<.0001) (0.5593)OCFVRt -0.0086 0.0148 -0.0093 0.0195 0.0153 0.0095 -0.0051 0.0154 -0.0033 (0.223) (0.0364) (0.1866) (0.0057) (0.0307) (0.1807) (0.4674) (0.0296) (0.6434)

a This table presents Pearson (Spearman) correlations above (below) the diagonal among key variables for the 50,552 sample firm-years during 1993–2012. P-values are reported in parentheses. Variables are defined in Table 1.

33

Table 3: Fama-MacBeth Estimation of the Accrual Modelsa

OCF Serial Correlation (SC) Measure (1) OCFSCt (2) OCFPREDt (3) OCFVRt Variables Coefficient t-statistic Coefficient t-statistic Coefficient t-statisticPanel A: the standard Jones (1991) model Intercept 0.0106 *** 4.75 0.0096 *** 3.59 0.0097*** 3.70ΔREVt 0.0842 *** 12.85 0.0826 *** 14.17 0.0807*** 13.99PPEt -0.0087 *** -4.58 -0.0073 *** -3.43 -0.0072*** -3.63 Adjusted R2 0.0789 0.0740 0.0712 Average N 2528 1268 1022 Panel B: nonlinear Jones model (Ball and Shivakumar 2006) Intercept 0.0106 *** 3.69 0.0101 *** 3.29 0.0093*** 3.05ΔREVt 0.0846 *** 13.74 0.0829 *** 15.13 0.0803*** 14.94PPEt -0.0095 *** -4.42 -0.0079 *** -3.62 -0.0079*** -3.96ABNRETt -0.0015 -1.05 -0.0033 * -1.96 -0.0004 -0.19DABNRETt 0.0049 *** 4.09 0.0043 *** 3.41 0.0050*** 3.08ABNRETt*DABNRETt 0.0112 ** 2.12 0.0143 *** 3.09 0.0127** 2.32 Adjusted R2 0.0814 0.0759 0.0739 Average N 2528 1268 1022 Panel C: Jones model, considering cash-flow problem Intercept 0.0104 *** 5.84 0.0112 *** 5.06 0.0089*** 4.64ΔREVt 0.1059 *** 18.63 0.1074 *** 20.28 0.1079*** 21.22PPEt -0.0070 *** -4.46 -0.0058 *** -3.43 -0.0054*** -3.64ΔOCFt -0.2667 *** -20.47 -0.2957 *** -14.61 -0.2800*** -15.95OCF SC measuret 0.0025 ** 2.22 0.0092 *** 4.80 -0.0018 -1.31ΔOCFt*OCF SC measuret -0.1000 *** -11.62 -0.1235 *** -4.33 -0.0177 -0.78 Adjusted R2 0.2346 0.2395 0.2543 Average N 2528 1268 1022 Panel D: nonlinear Jones model, considering cash-flow problem Intercept 0.0113 *** 4.61 0.0117 *** 4.57 0.0090*** 3.84ΔREVt 0.1035 *** 19.34 0.1044 *** 21.38 0.1042*** 21.73PPEt -0.0082 *** -4.67 -0.0066 *** -3.83 -0.0062*** -4.11ABNRETt 0.0046 ** 2.60 0.0042 ** 2.28 0.0070*** 3.25DABNRETt 0.0041 *** 3.41 0.0043 *** 3.86 0.0041*** 3.34ABNRETt*DABNRETt 0.0101 * 1.93 0.0119 ** 2.38 0.0101 1.61ΔOCFt -0.2692 *** -20.48 -0.2979 *** -14.51 -0.2837*** -15.86OCF SC measuret 0.0021 * 1.86 0.0091 *** 4.97 -0.0017 -1.24ΔOCFt*OCF SC measuret -0.1002 *** -11.55 -0.1228 *** -4.29 -0.0179 -0.80 Adjusted R2 0.2383 0.2423 0.2596 Average N 2528 1268 1022 Panel E: nonlinear McNichols (2002) model (without OCFt+1) Intercept 0.0123 *** 4.42 0.0104 *** 3.68 0.0099*** 3.60ΔREVt 0.0975 *** 16.68 0.0975 *** 18.20 0.0961*** 16.80

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PPEt -0.0052 *** -3.02 -0.0048 ** -2.56 -0.0047** -2.79OCFt-1 0.1046 *** 13.64 0.1663 *** 11.40 0.1833*** 10.25OCFt -0.1671 *** -11.24 -0.2123 *** -9.68 -0.2319*** -9.35ABNRETt -0.0005 -0.28 0.0009 0.45 0.0049* 1.84DABNRETt 0.0052 *** 4.64 0.0056 *** 4.99 0.0058*** 4.31ABNRETt*DABNRETt 0.0222 *** 4.06 0.0233 *** 5.33 0.0196*** 3.19 Adjusted R2 0.1716 0.2001 0.2191 Average N 2528 1268 1022

a This table presents the average coefficients estimated using Fama-MacBeth annual regressions for the various accrual models. Adjusted R-squared is the average for 20 annual regressions. The sample consists of all firm-year observations with necessary data during 1993–2012. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 4: Estimation of the Jones Model with Cash-Flow Change Added for Each Value of the Cash-Flow Serial Correlation Measure (OCFSC)a

Dependent Variable = ACCt Variables Coefficient t-statistic Coefficient t-statistic Coefficient t-statistic

OCFSC=-1 OCFSC=0 OCFSC=+1 Intercept 0.0060 *** 3.09 0.0152 *** 6.28 0.0087*** 3.91ΔREVt 0.0797 *** 7.50 0.0973 *** 17.27 0.1516*** 26.13PPEt -0.0035 * -1.84 -0.0113 *** -4.73 -0.0055** -2.40ΔOCFt -0.1598 *** -9.36 -0.2641 *** -15.50 -0.3844*** -35.24 Adjusted R2 0.1328 0.2345 0.4069 Average N 801 1125 602

a This table presents the average coefficients estimated using the Jones Model with cash-flow change (ΔOCF) added, for each value of the cash-flow serial-correlation measure (OCFSC). Adjusted R-squared is the average for 20 annual regressions. The sample consists of all firm-year observations with necessary data during 1993–2012. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 5: Fama-MacBeth Estimation of the Accrual Model with All Three Measures of Cash-Flow Problemsa

Variables Coefficient t-statistic Intercept 0.0099 *** 4.53 ΔREVt 0.1048 *** 23.28 PPEt -0.0062 *** -4.98 ABNRETt 0.0072 *** 3.27 DABNRETt 0.0041 *** 3.28 ABNRETt*DABNRETt 0.0100 1.63 ΔOCFt -0.3102 *** -17.31 OCFSCt 0.0030 ** 2.36 ΔOCFt*OCFSCt -0.0837 *** -5.02 OCFPREDt 0.0044 ** 2.51 ΔOCFt*OCFPREDt -0.0562 -1.51 OCFVRt -0.0019 -1.35 ΔOCFt*OCFVRt -0.0006 -0.03 Adjusted R2 0.2881 Average N 983

a This table presents the average coefficients estimated using Fama-MacBeth annual regressions for the accrual model that considers all four measures of cash-flow problems. Adjusted R-squared is the average for 20 annual regressions. The sample consists of all firm-year observations with necessary data during 1993–2012. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 6: Using Nondiscretionary Net Income to Predict Future Operating Cash Flow or Earnings

Panel A: Prediction of operating cash flow (OCF) of year t+1a

Intercept OCF NDWCI Adj. R2 Vuong's Z-stat Model 1: OCF

0.0125 0.8759 0.6301 (5.95) (45.83)

Model 2: NDWCI from the Jones model 0.0030 0.8635 0.6278 (1.12) (44.62)

Model 3: NDWCI from the nonlinear Jones model 0.0031 0.8622 0.6272 (1.14) (43.77)

Model 4: NDWCI from the McNichols model (without OCFt+1) -0.0002 0.9335 0.6370 (-0.08) (46.57)

Model 5: NDWCI from nonlinear McNichols model (without OCFt+1) -0.0002 0.9317 0.6353 (-0.05) (46.18)

Model 6: NDWCI from the Jones model, with OCFSC added 0.0010 0.9080 0.6479 7.2336*** 9.6685*** 5.7820*** (0.34) (47.75) (vs. Model 1) (vs. Model 2) (vs. Model 4)

Model 7: NDWCI from the nonlinear Jones model, with OCFSC added 0.0011 0.9051 0.6467 6.5860*** 9.302*** 5.8833*** (0.38) (46.67) (vs. Model 1) (vs. Model 3) (vs. Model 5)

a This table presents the average coefficients estimated from annual regressions for operating cash flow in year t+1. The sample consists of all firm-year observations with necessary data during 1993–2012. A constant sample is used to estimate all accrual models. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. NDWCI is nondiscretionary working-capital income, computed as the sum of nondiscretionary working-capital accruals estimated from each accrual model and operating cash flow (OCF).

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Panel B: Prediction of earning before extraordinary items of year t+1a

Intercept OCF NDWCI Adj. R2 Vuong's Z-stat Model 1: OCF

-0.0642 0.9883 0.5458 (-14.66) (35.13)

Model 2: NDWCI from the Jones model -0.0750 0.9799 0.5497 (-18.14) (35.53)

Model 3: NDWCI from the nonlinear Jones model -0.0750 0.9793 0.5501 (-18.12) (35.26)

Model 4: NDWCI from the McNichols model (without OCFt+1) -0.0786 1.0573 0.5559 (-19.88) (37.85)

Model 5: NDWCI from nonlinear McNichols model (without OCFt+1) -0.0786 1.0574 0.5566 (-19.91) (37.95)

Model 6: NDWCI from the Jones model, with OCFSC added -0.0773 1.0297 0.5666 8.5264 8.1025 4.3958 (-18.92) (38.16) (vs. Model 1) (vs. Model 2) (vs. Model 4)

Model 7: NDWCI from the nonlinear Jones model, with OCFSC added -0.0772 1.0280 0.5672 8.5646 8.1543 4.3369 (-18.87) (37.74) (vs. Model 1) (vs. Model 3) (vs. Model 5)

a This table presents the average coefficients estimated from annual regressions for earnings before extraordinary items in year t+1. The sample consists of all firm-year observations with necessary data during 1993–2012. A constant sample is used to estimate all accrual models. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. NDWCI is nondiscretionary working-capital income, computed as the sum of nondiscretionary working-capital accruals estimated from each accrual model and operating cash flow (OCF).

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Table7: Industry-Year-Specific Estimation of the Accrual Modelsa

Variables Coefficient t-stat Panel A: the standard Jones (1991) model Intercept 0.0098 *** 7.26 ΔREVt 0.0787 *** 19.31 PPEt -0.0061 *** -3.02 Adjusted R2 0.1049 Average N 95 Panel B: nonlinear Jones model (Ball and Shivakumar 2006) Intercept 0.0120 *** 6.69 ΔREVt 0.0767 *** 18.32 PPEt -0.0077 *** -3.62 ABNRETt -0.0010 -0.32 DABNRETt 0.0030 1.57 ABNRETt*DABNRETt 0.0119 *** 2.53 Adjusted R2 0.1274 Average N 95 Panel C: Jones model, considering cash-flow problem Intercept 0.0107 *** 9.01 ΔREVt 0.1036 *** 25.37 PPEt -0.0070 *** -4.04 ΔOCFt -0.3137 *** -36.99 OCFSCt 0.0010 1.14 ΔOCFt*OCFSCt -0.0608 *** -5.27 Adjusted R2 0.3407 Panel D: nonlinear Jones model, considering cash-flow problem Intercept 0.0141 *** 8.78 ΔREVt 0.0991 *** 24.81 PPEt -0.0087 *** -4.65 ABNRETt 0.0023 0.88 DABNRETt 0.0016 0.98 ABNRETt*DABNRETt 0.0137 *** 3.25 ΔOCFt -0.3183 *** -37.73 OCFSCt 0.0009 1.04 ΔOCFt*OCFSCt -0.0634 *** -5.43 Adjusted R2 0.3590 Average N 95 Panel E: nonlinear McNichols (2002) model (without OCFt+1) Intercept 0.0197 *** 11.69 ΔREVt 0.0921 *** 24.73 PPEt 0.0005 0.30 OCFt-1 0.1832 *** 25.43 OCFt -0.3361 *** -32.08

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ABNRETt 0.0006 0.22 DABNRETt 0.0034 ** 2.34 ABNRETt*DABNRETt 0.0325 *** 7.34 Adjusted R2 0.3560 Average N 95

a This table presents the average coefficients estimated using industry-year-specific regressions for the various accrual models during 1993–2012. The cash-flow serial correlation measures used is OCFSC. Each industry-year combination must have at least 30 observations with necessary data and at least five observations having negative stock returns (i.e., DABNRET=1). Adjusted R-squared is the average for 431 regressions. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 8: Estimation of the Dechow and Dichev (2002) Model and the Jones (1991) Model for Each Value of the Cash-Flow Serial Correlation Measure (OCFSC)a

Dependent Variable = ACCt Variables Coefficient t-statistic Coefficient t-statistic Coefficient t-statisticPanel A: Estimation of the Dechow and Dichev (2002) model

OCFSC=-1 OCFSC=0 OCFSC=+1 Intercept 0.0069 *** 4.93 0.0164 *** 6.04 0.0213 *** 5.79OCFt-1 0.0382 *** 6.01 0.0742 *** 8.81 0.1621 *** 14.60OCFt -0.1448 *** -12.06 -0.2390 *** -12.14 -0.5277 *** -30.06OCFt+1 0.0987 *** 9.64 0.1362 *** 10.86 0.1996 *** 12.18 Adjusted R2 0.0895 0.1320 0.3141 Average N 641 919 495 Panel B: Estimation of the Jones (1991) model

OCFSC=-1 OCFSC=0 OCFSC=+1 Intercept 0.0066 ** 3.18 0.0153 *** 5.44 0.0068 *** 2.38ΔREVt 0.0543 *** 5.06 0.0770 *** 11.91 0.1285 *** 18.79PPEt -0.0051 ** -2.54 -0.0127 *** -4.77 -0.0040 * -1.49 Adjusted R2 0.0424 0.0814 0.1571 Average N 801 1125 602

a This table presents the average coefficients estimated using Fama-MacBeth annual regressions for the Dechow and Dichev (2002) model and the Jones (1991) model, for each value of the cash-flow serial correlation measure (OCFSC). Adjusted R-squared is the average for 20 annual regressions. The sample consists of all firm-year observations with necessary data during 1993–2012. The average number of observations is smaller for the Dechow and Dichev (2002) model because of the requirement of leading cash flow data. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 9: Comparison of Specification (Type I Error) of Various Accrual Modelsa

All firms

BTM Sales growth EP MVE OCF High Low High Low High Low High Low High Low

Panel A: HA: Discretionary accruals<0 Jones 5.2% 4.5% 9.7% 8.0% 6.8% 3.1% 11.7% 1.8% 9.8% 9.4% 6.7%Performance-matched 5.2% 4.4% 8.5% 8.0% 5.8% 3.8% 8.3% 3.0% 7.2% 8.5% 6.0%Serial-correlation-matched 5.1% 4.5% 9.7% 7.0% 7.8% 2.7% 11.5% 2.2% 8.9% 5.7% 8.9%Panel B: HA: Discretionary accruals>0 Jones 5.6% 4.3% 7.8% 8.8% 6.6% 5.6% 5.1% 2.0% 7.6% 1.1% 16.3%Performance-matched 5.0% 3.9% 8.3% 7.7% 6.3% 4.0% 8.2% 1.8% 7.5% 1.3% 14.5%Serial-correlation-matched 5.2% 4.0% 7.8% 8.2% 5.3% 5.0% 5.6% 2.1% 6.8% 2.5% 11.7%

a This table presents the average rejection rates based on 10 random samples of 1,000 firm-years that the null hypothesis of nonnegative (Panel A) or nonpositive earnings management (Panel B) is rejected at the 5% significance level. Rejection rates that are higher than 8% or lower than 2% are reported with bold numbers. For each column, the random samples are drawn from the full sample or from the upper and lower quartiles of book-to-market (BTM) ratio, sales-growth rate, earnings-to-price (EP) ratio, market value of common equity (MVE) and operating cash flow (OCF). The analysis is based on 37,187 firm-year observations during 1993–2012, for which each industry-year combination has at least 30 observations. Performance-matched discretionary accruals are computed as the difference between discretionary accruals estimated from the Jones mode and those of a matched control firm from the same industry-year and with the closest ROA. Serial-correlation-matched discretionary accruals are computed as the difference between discretionary accruals estimated from the Jones mode and those of a matched control firm from the same industry-year and with the same cash-flow serial correlation and the closest cash-flow change.

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Table 10: Comparison of Power (Type II Error) of Various Accrual Modelsa

All firms

BTM Sales growth EP MVE OCF High Low High Low High Low High Low High Low

Panel A: HA: Discretionary accruals<0 Rejection rates for the Jones model 0 5.2% 4.5% 9.7% 8.0% 6.8% 3.1% 11.7% 1.8% 9.8% 9.4% 6.7%-1 88.3% 89.0% 82.8% 84.2% 84.5% 90.9% 82.6% 99.9% 66.4% 95.0% 72.2%-2 94.0% 95.2% 90.0% 91.4% 92.1% 95.7% 90.9% 100.0% 82.8% 98.1% 83.7%-4 97.7% 98.6% 95.6% 96.4% 96.9% 98.9% 96.3% 100.0% 93.0% 99.4% 92.8%-10 99.6% 99.8% 98.9% 99.3% 99.4% 99.9% 99.3% 100.0% 98.7% 99.9% 98.2%Rejection rates for the performance-matched Jones model 0 5.2% 4.4% 8.5% 8.0% 5.8% 3.8% 8.3% 3.0% 7.2% 8.5% 6.0%-1 83.3% 83.9% 76.3% 78.6% 77.6% 88.2% 73.1% 99.8% 54.7% 91.6% 63.3%-2 91.0% 91.9% 85.3% 87.4% 87.4% 94.0% 85.0% 100.0% 73.2% 96.5% 77.5%-4 96.0% 96.9% 92.5% 94.0% 94.1% 97.8% 92.4% 100.0% 87.8% 99.0% 87.6%-10 99.2% 99.5% 98.0% 98.5% 98.6% 99.8% 98.0% 100.0% 97.1% 99.8% 96.7%Rejection rates for the serial-correlation-matched Jones model 0 5.1% 4.5% 9.7% 7.0% 7.8% 2.7% 11.5% 2.2% 8.9% 5.7% 8.9%-1 85.0% 85.5% 79.2% 80.1% 81.9% 88.6% 78.9% 99.9% 59.4% 91.1% 68.9%-2 92.3% 93.3% 87.6% 88.5% 90.8% 94.2% 88.3% 100.0% 77.2% 96.0% 81.8%-4 96.6% 97.6% 94.0% 94.7% 96.0% 98.2% 94.4% 100.0% 89.9% 98.7% 91.3%-10 99.3% 99.6% 98.5% 98.9% 99.1% 99.7% 98.8% 100.0% 97.9% 99.7% 97.8%Panel B: HA: Discretionary accruals>0 Rejection rates for the Jones model 0 5.6% 4.3% 7.8% 8.8% 6.6% 5.6% 5.1% 2.0% 7.6% 1.1% 16.3%-1 88.0% 87.9% 81.2% 84.2% 83.7% 92.7% 76.7% 100.0% 64.9% 88.0% 79.1%-2 94.0% 94.7% 88.8% 90.9% 91.8% 96.9% 87.2% 100.0% 81.5% 94.2% 88.6%-4 97.8% 98.1% 94.7% 96.2% 96.9% 98.9% 94.1% 100.0% 92.5% 97.5% 94.6%-10 99.6% 99.6% 98.6% 99.1% 99.2% 99.9% 98.6% 100.0% 98.4% 99.6% 98.7%Rejection rates for the performance-matched Jones model 0 5.0% 3.9% 8.3% 7.7% 6.3% 4.0% 8.2% 1.8% 7.5% 1.3% 14.5%-1 83.9% 82.9% 77.0% 79.7% 79.0% 88.5% 72.7% 99.9% 55.1% 84.5% 73.2%-2 91.5% 91.9% 85.7% 88.0% 89.1% 95.0% 84.3% 100.0% 74.5% 91.7% 84.4%-4 96.4% 97.0% 92.9% 94.6% 95.2% 98.2% 92.2% 100.0% 88.7% 96.4% 92.4%-10 99.2% 99.4% 97.9% 98.5% 98.9% 99.7% 98.0% 100.0% 97.3% 99.2% 98.1%Rejection rates for the serial-correlation-matched Jones model 0 5.2% 4.0% 7.8% 8.2% 5.3% 5.0% 5.6% 2.1% 6.8% 2.5% 11.7%-1 85.1% 84.5% 77.6% 81.8% 78.8% 90.4% 71.7% 99.7% 57.3% 87.7% 72.0%-2 92.4% 92.9% 86.4% 89.5% 88.4% 96.0% 83.5% 99.8% 76.4% 93.8% 83.7%-4 96.7% 97.1% 92.8% 95.0% 94.7% 98.7% 91.6% 99.8% 89.1% 97.5% 91.4%-10 99.2% 99.2% 98.0% 98.7% 98.7% 99.7% 97.7% 99.8% 97.7% 99.5% 97.8%

a This table presents the average rejection rates that the null hypothesis of nonnegative (Panel A) or nonpositive earnings management (Panel B) is rejected at the 5% significance level. The analysis is based on the random samples in Table 9 by adding plus or minus 1%, 2%, 4%, or 10% of the firm’s beginning total assets to accruals before estimating discretionary accruals. We assume 50% of the seeded earnings management is related to credit sales manipulation. Performance-matched discretionary accruals and serial-correlation-matched discretionary accruals are defined in Table 9.