Predicting Accruals based on Problems with Cash Flows

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: September 2014

Abstract We construct empirical proxies for cash-flow timing and matching problems and provide evidence on the ability of this accrual generating factor to explain accruals. Researchers lament our 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 our current knowledge of the role of accruals—not to enter an empirical horse race. We produce three measures of cross-sectional variation in cash-flow problems: (1) negative serial correlation in cash flows (2) the predictive power of current cash flows for future cash flows, and (3) the relative explanatory power of two-year cash flows to one-year cash flows for returns. We find that the Jones-model r-squared increases significantly when cash-flow problems are incorporated and that these increases in explanatory power are larger than those produced by incorporating asymmetrically timely loss recognition into the Jones model (Ball and Shivakumar, 2005). We also show that the explanatory power of the Dechow and Dichev (2002) model increases significantly in subsamples exhibiting strong negative serial correlation in cash flows, suggesting that the explanatory power of this model is tied to its incorporation of cash-flow problems. Our results suggest a way to understand accruals at the firm-year level can be found via improved estimates of the transitory component in current operating cash flows. We thank participants in the Washington University in St. Louis accounting brown bag for comments.

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Predicting Accruals based on Problems with Cash Flows

1. Introduction We investigate the effect of cash-flows problems on accruals. Our goal is to incorporate

our understanding of the economic purpose of accruals into accrual models. We posit that

accruals’ purpose is to combine with cash flows to produce a sum that is a high quality income

measure. Cash-flow “problems” are the deficiencies in the cash-flow measure compared to the

characteristics sought in the sum of cash flow and accruals. We derive these characteristics from

a valuation perspective. They include (1) persistence, (2) association with future cash flows, and

(3) association with returns.1 Our work both contrasts with and follows the method of Ball and

Shivakumar (2006). They, in contrast, follow a stewardship perspective and posit that accruals’

purpose is to enhance the asymmetric timeliness of cash flows. Like Ball and Shivakumar

(2006), we examine whether consideration of accruals’ purpose enhances accrual prediction.2

We show that adding cash-flow changes and industry-specific estimates of cash-flow problems

to accrual models substantially improves explanatory power. This increase in explanatory power

is larger than the improvement gained by incorporating non linearity in gain and loss recognition

to accrual models as in Ball and Shivakumar (2006) and is incremental to Ball and Shivakumar’s

addition. The use of accruals to remediate cash-flow problems can be viewed as self-beneficial

income smoothing by managers—a purpose for accruals difficult to reconcile with efficiency.

Thus, we also examine whether accruals generated by a model incorporating cash-flow problems

1 The characteristics emerge from folk wisdom rather than theory showing them to be an efficient solution to the financial reporting game. See, for example, Penman, 2013, p. 396, Revsine, et al., 2015, p. 329, Dechow and Schrand, 2004, Barth, Cram, and Nelson, 2001, Finger, 1994. 2 Valuation and stewardship considerations need not have mutually exclusive effects on accruals unless we hold that one force overwhelms the other.

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better predict future cash flows and income—an accrual purpose consistent with the valuation

perspective.

Periodic reporting causes cash flows to measure performance with timing problems

because cash flows do not coincide with net benefits to shareholders in a given accounting

period. Researchers have long recognized that one purpose of accrual accounting is to mitigate

the timing and matching problems inherent in cash flows (e.g., Paton and Littleton, 1940,

Dechow, 1994, Dechow, Kothari, and Watts, 1998, Ball and Shivakumar, 2006). Dechow (1994)

shows that the explanatory power of net income relative to cash flows for stock returns increases

as the measurement window declines and working capital increases. She also shows that cash-

flow changes and accruals display negative serial correlation and that the correlation between

cash-flow changes and accruals is negative. These results are consistent with accruals offsetting

temporary components in cash flows. Dechow, Kothari, and Watts (1998) model the source of

negative serial correlation in cash flows and its attenuation by accruals. They show that the

advantage of earnings over cash flows in prediction of future cash flows increases with

operating-cycle length.

We do not add to this theoretical understanding. Instead, we apply it to accrual prediction

and convey a sense of its empirical power. In so doing, we link models of accruals to the purpose

of accruals. The Jones model (Jones, 1991) and its subsequent refinements (e.g., Defond and

Jiambalvo, 1994, Dechow, Sloan, and Sweeney, 1995, Kothari, Leone, and Wasley, 2005,

McNichols, 2002, Owens, Wu, and Zimmerman, 2013) focus on the econometric properties of

the model’s predictions rather than the accounting theory supporting the existence of accruals.

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Notable exceptions include Ball and Shivakumar (2005) and Dechow and Dichev (2002).3 The

former builds the role of asymmetrically timely recognition of loss into the accrual model, while

the latter incorporates the relation between accruals and lead/lag cash flows. Our empirical

approach differs from Dechow and Dichev because we derive accrual properties based on the

deficiencies of cash flows identified by the desired properties of income from the valuation

perspective. 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 inadequate

research designs.4 Our objective is to deflect accrual-model research to a path marked by our

understanding of the purpose of accruals.

We find that cash-flow problems have a substantial effect on working capital accruals in

the cross-section. We estimate three industry-specific cash-flow problem measures using data

from the previous five years, including the negative serial correlation in cash flows, the

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. All three measures are defined so that

a higher value represents a more serious cash-flow problem as a result of the temporary

components contained in cash flows. We find that incorporating any of these measures into a

Jones Model increases explanatory power by approximately 264%. This increase compares to an

increase in explanatory power of approximately 5% when asymmetric recognition of gains and

losses is incorporated into the Jones model. Both negative serial correlation and asymmetric

3 Accruals are an investment in working capital and long term assets (e.g., Fairfield, Whisenant, and Yohn, 2003, Frankel, Levy, and Shalev, 2014). In addition to accounting considerations, factors affecting investment also affect accruals (Arif, Marshall, and Yohn, 2014). 4 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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recognition effects 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 measures. We also find that non-discretionary working-capital accruals estimated from our

proposed accrual model that incorporates cash-flow serial correlation have a better ability to

predict future cash flows and income than that from the standard Jones model or the nonlinear

Jones model.

Although the industry-specific cash-flow serial-correlation measure estimated over the

past five years has significant explanatory power for working capital accruals cross-sectionally,

we find weaker within-industry results for historic firm-specific serial correlation estimated over

the past five years. However, we find contemporaneous firm-specific serial correlation estimated

over year t-2 to year t+2 significantly affects the relation between cash flow change and accruals.

These results suggest that (1) estimating accrual models within industry controls for a large

portion of cross-firm variation in cash-flow serial correlation and (2) culling remaining serial

correlation across firms in an industry requires a finer measure of firm-level serial correlation.

Finally, we estimate the McNichols (2002) model that combines the Jones (1991) model

and the Dechow and Dichev (2002) model within cash-flow serial correlation terciles to confirm

that the increased ability of this model to explain accruals derives from the ability of its lagged

and leading operating cash flow variables to capture the serial correlation in cash flows.

The contribution of our paper relative to Dechow and Dichev (2002) can be viewed as

one of semantics or emphasis. Yet, the distinction is noteworthy because building the accrual

model on the foundation of cash-flow problems suffuses the modelling of accrual characteristics

to their economic use. Absent this consideration accruals prediction devolves to an econometric

problem without accounting content leaving the field open to the unfavorable surmise of

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manipulation when deviations from the model appear. Dechow and Dichev emphasize the

mapping of accruals into lagged, current and lead cash flows. Their objective is to measure

accrual estimation errors rather than to explain why the inter-period allocation via accruals arises

as a solution to a problem.5 We provide this link. We emphasize that (1) reducing negative serial

correlation in current cash flows, (2) increasing the predictive ability of income relative to cash

flow, and (3) increasing the explanatory power of income relative to cash flow for returns, justify

the existence of accruals-based notions of earnings quality arising from the valuation

perspective. In emphasizing the role of accruals in enhancing earnings persistence, we follow the

model developed by Bernard and Stober (1989) and Dechow, Kothari, and Watts (1989).6

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, Finger, 1994) and correlation with

contemporaneous returns (Dechow and Schrand, 2004). At a practical level, incorporating

estimated cash-flow problems into accrual prediction allows the researcher to explain accruals

5 McNichols and Wilson (1988) likewise maps the allowance for doubtful accounts accruals into future write-offs. It, like Dechow and Dichev (2002) as well as many loan loss reserve papers, links current accruals to future outcomes. 6 Dechow, Kothari, and Watts (1998) do not address the issue of efficiency, but they assume the role of accruals is to produce a measure that approximates economic income. In their initial model, economic income is a random walk. Later, they add a mean-reverting component called “fixed costs.” When economic income has a mean-reverting component, they suggest that accounting income will mean revert as well. If so, accounting income need not predict future cash flows or persist. Accounting income can differ from a random walk for a number of overlapping reasons including: verifiability (Patton and Littleton, 1940), white-noise shocks (Dechow, Kothari and Watts, 1989), timely loss recognition (Basu, 1997) and accrual estimation errors (Ball and Watts, 1979, Ramakrishnan and Thomas, 1998). Thus, the time-series properties of the efficient earnings measure depend on the nature of the underlying process that generates economic profitability (e.g., Stigler, 1963 and Fama and French, 2000) and the economic role of GAAP earnings. For example, Dechow and Schrand, 2004, state “Thus, accruals can mitigate volatility and negative serial correlation in cash flows that are irrelevant for valuation. (p. 7)” (emphasis added)—implying that some negative serial correlation is relevant. We leave it to readers to decide whether approximation of economic income is an accrual purpose that arises from the valuation perspective or the stewardship perspective. Our view is that the logical development of these perspectives is not currently at a stage that permits us to deduce an answer. Reichelstein (2000) derives advantages from depreciation-based performance measure over a cash-flow based measure in a principal-agent setting. His results suggest that a better measurement of wealth creation at intermediate dates leads to a more efficient bonus scheme. However, Sloan (1993), Dutta and Reichelstein (2005), Barclay, Gode, and Kothari (2005), and Leone, Wu, and Zimmerman (2006), among a host of others, mark problems with using returns as the basis for management compensation.

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when future cash flow information is not available as in Dechow and Dichev (2002) and Dechow,

Hutton, Kim, and Sloan (2012).

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

The understanding that cash flows do not capture performance in a given period predates

recorded argument. Cash-flow timing and matching problems occasioned the formulation and

use of accrual accounting prior to statements by accounting academics about allocating costs and

recognizing credit sales.7 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, 1969) 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, 1969). The objective of these papers was to understand how earnings

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

than to understand problems with cash flow measures that could be addressed by accruals. This

literature sought to understand the 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.

7 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)

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Dechow (1994) marks a break in the sequence of earnings/returns research.8 Rather than

attempting to understand the short-comings of earnings in explaining returns, she deemed

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

Accountants used accruals to correct timing and matching problems in cash flows. These

problems interfered 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 and valuation

connotations, whereas the latter connotes a valuation perspective.9

Seeking earnings management, researchers developed models to predict accruals (Healy,

1985, DeAngelo, 1986, Jones, 1991, DeFond and Jiambalvo, 1994) and cull ‘normal’ accruals

from manipulated accruals. Refinements were assayed based on whether model residuals could

measure earnings management (Dechow, Sloan, and Sweeney, 1995, Hribar and Collins, 2002,

McNichols, 2002, Kothari, Leone, and Wasley, 2005, Dechow, Hutton, Kim, and Sloan, 2012,

Owens, Wu, and Zimmerman, 2013). Empirical research developed independently, but

simultaneously with theory explaining the source of accruals (e.g., Dechow, Kothari, and Watts,

1998).

Dechow and Dichev (2002) and Ball and Shivakumar (2005) are papers that model

accruals based on their purpose. The former noting accruals allow cash-flow effects to be

recognized on the income statement in periods before or after they are realized. The latter

showing accruals accelerate recognition of losses and delay recognition of gains. As with these

8 She is not the first to investigate the role of accounting earnings (e.g., Paton, 1922, Paton and Littleton, 1940 among many others to be added.) 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). 9 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, 2000).

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papers, we look to 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. We seek the

circumstances provoking this disengagement. Guided by Dechow (1994) and Dechow, Kothari,

and Watts (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-flows changes to be

negatively related to accruals. Therefore, we add cash flow changes to the accrual prediction

model.10 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. 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

10 Dechow (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.

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accrual levels.11 Cash-flow changes should add less explanatory power to the accrual model

when cash-flow properties coincided with the desirable properties of earnings.

Finally, we test a hypothesis to pry the conjecture that earnings smoothing explains

results consistent with hypotheses 1 and 2 from our expectation that accruals fix problems with

cash flows. 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 earnings. In contrast, the accruals-fix-cash-flow-problems story 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 changes 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 average

total assets in year t. ΔREVt controls for changes in the economic environment of the firm and

PPEt controls for the portion of accruals related to depreciation expense. For the dependent

variable, ACCt, we use working capital accruals because our measures of cash-flow problems are

11 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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based on the properties of operating cash flows. Following Dechow and Dichev (2002), working

capital accruals are defined as ΔAccounts Receivable + ΔInventory – ΔAccounts Payable – ΔAR

– 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

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.12

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)

12 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 (1965) Table 1 with Dechow (1994) Table 2.

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

measure of the cash-flow problems resulting from the timing and matching issues of cash flows.

We estimate three industry-specific measures of cash-flow problems.

(a) OCFSCt is industry-specific serial correlation in operating cash flows (OCF),

defined as the average annual serial correlation for each 2-digit SIC industry over the past five

years. The serial correlation for each year is defined as the first-order autocorrelation coefficient

β estimated from (OCFt-OCFt-1) = α + β (OCFt-1-OCFt-2) + ԑ, multiplied by minus one. Cash flow

change for year t is scaled by average total assets in year t. We multiply the first-order

autocorrelation coefficient by minus one so that a higher value indicates more negative serial

correlation (i.e., more severe timing problems) in cash flows.

(b) OCFPREDt is industry-specific cash-flow predictability, defined as the average r-

squared from annual regressions of operating cash flow for the next year (OCFt+1) on operating

cash flow for the current year (OCFt) for each 2-digit SIC industry over the past five years. Cash

flows are scaled by average total assets. We multiply the average r-squared by minus one –

higher OCFPREDt indicates that current cash flow is less able to predict cash flow for the

following year.

(c) OCFVRt is industry-specific relative explanatory power of two-year cash flows to

one-year cash flows for returns, defined as the average difference, over the past five years for

each 2-digit SIC industry, in the r-squared from annual regressions of accumulated two-year

stock returns on two-year cash flows (i.e., year t-1 and year t) and the r-squared from annual

regressions of one-year stock return on one-year cash flow (i.e., year t-1). Stock returns are

adjusted for CRSP equally weighted market returns for the same period. Cash flows are scaled

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by average assets. A higher value for OCFVRt indicates that the one-year cash flow has 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 regressions.13 Under this approach, t-statistics are based

on the time-series distribution of annual coefficients.

Prediction of future cash flows or income

To examine whether non-discretionary working-capital accruals generated by our

proposed model that incorporates cash-flow problems better predict future cash flows and

income (Hypothesis 3), we estimate the various accrual models (i.e., equations (1)-(4)) annually

to get non-discretionary working-capital accruals. We then examine whether the non-

discretionary working-capital income (i.e., non-discretionary working-capital accruals +

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

or net income before extraordinary items in the following year.

Firm-specific serial correlation

Besides industry-specific serial correlation in operating cash flows, we also estimate

firm-specific serial correlation over the past five years. We estimate various accrual models for

each industry-year combination with at least 30 observations with necessary data and at least 5

observations having negative stock returns to examine whether firm-level variation in serial

correlation within a given industry also helps explain accruals.

13 We get qualitatively similar results by using pooled regressions (untabulated).

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Dechow and Dichev (2002) model

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

flows that potentially capture the negative serial correlation in cash flows, we estimate the

Dechow and Dichev (2002) model within each cash-flow serial correlation tercile to examine

whether this model has better ability to explain accruals when there is a more negative serial

correlation in cash flows.

4. Data and empirical results

Sample and data

We obtain data from COMPUSTAT and CRSP for a sample period of 1995-2012. 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

become available after 1988. The sample period starts from 1995 because cash flows for the

previous seven 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 59,394 firm-years.

We present the descriptive statistics of our key variables in Table 1. The mean 0.1966 for

OCFSC suggests that, on average, operating cash flows has a negative first-order autocorrelation

coefficient of -0.1966 over the past five years. Untabulated analysis shows that only 3% of the

sample observations have a non-negative first-order autocorrelation coefficient in cash flows,

suggesting that the timing and matching problem is a common issue for most firms or industries.

The average of -0.4707 for OCFPRED indicates that, on average over the past five years, cash

flow for a year explains 47.07% of the variability of the cash flow for the following year. The

mean 0.0317 for OCFVR suggests that two-year cash flows have a better ability to explain two-

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year stock returns than one-year cash flow for one-year stock return, with an average difference

in r-squared of 3.17%.

[Insert Table 1 here]

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

correlations reported above (below) the diagonal. The Pearson correlation between working

capital accruals (ACC) and cash flow change (ΔOCF) is -0.1044, suggesting that working capital

accruals offset temporary components in cash flows (consistent with Hypothesis 1). The three

industry-specific cash-flow problem measures are positively correlated. For example, the

Pearson correlation between OCFSC and OCFPRED is 0.5577; the Pearson correlation between

OCFSC and OCFVR is 0.1050.

[Insert Table 2 here]

Explaining accruals by considering cash-flow problems

We present the estimation results for equations (1)-(4) using the Fama-MacBeth (1973)

approach in Table 3. The cash-flow problem measures are OCFSC, OCFPRED, and OCFVR in

columns (1), (2), and (3), respectively. For the standard Jones (1991) model in Panel A, the

average r-squared from the 18 annual regressions ranges from 4.96% to 5.17%.14 Once we

consider the asymmetry in gain and loss recognition in Panel B, the r-squared increases slightly

to 5.21% to 5.43%. The percentage increase in r-squared from Panel A to Panel B is about 5%.15

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

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

14 The estimation results in the three columns of Panel A and Panel B differ because, we require non-missing cash-flow problem measures in each corresponding column. 15 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 76%. As a comparison, the percentage increase in r-squared from the standard Jones model to our proposed model that considers cash-flow serial correlation is about 187% if using total accruals.

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coefficient on cash flow change (ΔOCF) is significantly negative (Hypothesis 1). In addition, the

coefficients on the interactions of ΔOCF and each of the cash-flow problem measures are

negative, consistent with Hypothesis 2. Turning to the r-squared, the increase from 4.99% in

Panel A to 18.60% in Panel C in column (1) represents a percentage increase of 272% (similarly,

increases of 265% and 255% 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 asymmetry in gain and loss recognition is considered. In Panel D, when we

consider both asymmetric recognition and cash-flow problems, the r-squared is even higher. For

example, the r-squared increases to 18.95% in column (1), with 18.95% representing a

percentage increase of about 280% from the r-squared of 4.99% for the standard Jones model in

Panel A. We find that the increase in r-squared from Panel A to Panel D (280%) is approximate

the sum of the increases from Panel A to Panel B (5.1%) and from Panel A to Panel C (272.4%),

suggesting that asymmetric recognition and negative serial correlation effects are incremental to

each other. We find similar results in terms of percentage increases in the r-squared for columns

(2) and (3).

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

combines the Jones (1991) model and the Dechow and Dichev (2002) model 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 the previous years, we remove the

cash flow for the following year (i.e., year t+1) from this comparison. We find that in the cross-

section our proposed model does slightly better at explaining accruals. For example, in column

(1), the r-squared of our model in Panel D is 18.95%, while the r-squared of the McNichols

model (without the leading cash flow variable) is 17.51%.

16

[Insert Table 3 here]

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

as reported in Table 4, only the cash-flow serial correlation measure continues to significantly

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

negative coefficient for ΔOCF*OCFSC and the insignificant coefficients for 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 4 here]

Prediction of future cash flows or income

We next examine whether non-discretionary working-capital accruals generated by our

proposed model that incorporates cash-flow problems, particularly cash-flow serial correlation,

better predict future cash flows and income. We first estimate the various accrual models (i.e.,

equations (1)-(4)) annually to get non-discretionary working-capital accruals. We then examine

whether the non-discretionary working-capital income (i.e., non-discretionary working-capital

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

operating cash flow or net income before extraordinary items in the following year (Hypothesis

3). We report the results in Table 5. For prediction of future cash flows in Panel A, we find that

the non-discretionary working-capital income (NDWCI) estimated from the accrual model that

considers cash-flow serial correlation (i.e., Model 4) has a significantly higher explanatory

power for cash flow in the following year than both cash flow in the current year (i.e., Model 1)

and the non-discretionary working-capital income estimated from the standard Jones model (i.e.,

Model 2). We further find that the non-discretionary working-capital income estimated from the

17

accrual model that considers both asymmetric gain/loss recognition and cash-flow serial

correlation (i.e., Model 5) significantly better explains cash flow in year t+1 than both cash flow

in year t (i.e., Model 1) and the non-discretionary working-capital income estimated from the

nonlinear Jones model (i.e., Model 3). In Panel B, we find, similarly, that the non-discretionary

working-capital income estimated from our proposed accrual model that considers cash-flow

serial correlation has significantly better ability to predict net income before extraordinary items

in the following year, no matter whether asymmetric gain/loss recognition is considered.

[Insert Table 5 here]

Firm-specific serial correlation

The results in Table 3 and Table 4 suggest that industry-specific cash-flow serial

correlation has significant explanatory power for accruals across industries. We next estimate

firm-specific serial correlation over the past five years to examine whether cash-flow serial

correlation also helps explain accruals across firms within industry. We estimate various accrual

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

at least 5 observations having negative stock returns and report average results for 186 industry-

year specific regressions during 1995-2012 in Table 6 column (1). To reduce the effect of

extreme values, we form decile ranks of serial correlation for each industry-year. We find that by

adding cash flow change (ΔOCF) and firm-specific historic serial correlation (OCFSC_firm), the

r-squared increases from 8.96% for the standard Jones model in Panel A to 33.37% in Panel C.

The coefficient on the interaction term ΔOCF*OCFSC_firm is significant at 10% level in Panel

C, but become insignificant with a p-value of 0.1237 in Panel D when asymmetric loss

recognition is considered.

18

To examine whether estimation error causes the weaker result for firm-specific serial

correlation in column (1), we also estimate contemporaneous firm-specific serial correlation

(OCFSC_Cfirm). That is, we estimate the serial correlation over year t-2 to year t+2 for each

firm with necessary data. We report the estimation results for the various accrual models using

250 industry-year specific regressions during 1992-2010 in column (2) of Table 6. We find that

the contemporaneous firm-specific serial correlation measure helps explain accruals (with a

significance level lower than 1%), whether or not asymmetric gain/loss recognition is considered.

These results suggest that estimating accrual models within industry controls for a large portion

of cross-firm variation in cash-flow serial correlation. To cull remaining serial correlation across

firms in an industry, we need a finer measure of firm-specific serial correlation by using data

around the current year. Even after we use the contemporaneous data, the explanatory power of

our proposed model within industry is lower than the explanatory power of the McNichols (2002)

model (without the leading cash flow variable) reported in Panel E, suggesting that lagged cash

flow and current cash flow more accurately capture firm-year-specific cash-flow serial

correlation.

[Insert Table 6 here]

Dechow and Dichev (2002) model

To examine whether the lagged and leading operating cash flows used in the Dechow and

Dichev (2002) model capture timing problems related to negative serial correlation in cash flows,

we form terciles for cash-flow serial correlation annually and estimate the McNichols (2002)

model which combines the standard Jones (1991) model and the Dechow and Dichev (2002)

model within each serial correlation tercile to examine whether this model has better ability to

explain accruals when there is a more negative serial correlation in cash flows. The estimation

19

results are reported in Table 7. Indeed, we find that the explanatory power of the model for the

highest tercile (i.e., more negative serial correlation) is at least double of that for the lowest

tercile (e.g., less negative cash-flow serial correlation).

[Insert Table 7 here]

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 our current understanding of the purpose of accruals is useful in

building an empirical model to predict accruals. Many researchers highlight our 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 our

knowledge. Our approach follows that of Ball and Shikumar (2005) 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 problem in

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

provide evidence that the 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 asymmetrically timely recognition in cross-industry estimates. To put

these two accrual drivers in perspective, if asymmetrically timely recognition which results in a

5% increase in Jones-model r-squared is noteworthy, the 270% increase in r-squared resulting

from incorporate cash-flow problems in the Jones model is astonishing. Within industry,

20

consideration of cash-flow effects (r-squared increase of 260%) continues to dominate

consideration of nonlinearity (r-squared increase of 14%), though cross-firm variation in cash-

flow problems is less significantly related to accruals.

Existing refinements to the Jones model, such as McNichols (2002) and Dechow and

Dichev (2002), match and sometimes exceed the gains resulting from incorporating cash-flow

effects into the Jones model. Perhaps, these results undermine the practical importance of our

approach, but, not in our view, the conceptual importance. Given that accruals are central to the

role of financial accounting and researchers have sought methods to isolate earnings

management, we expect more than 20 years of effort to produce a model is tough to beat in an

empirical race. Our goal is to link the empirical properties of accruals to cash-flow problems,

rather than to improve prediction of accruals per se. In particular, we show that the explanatory

power of the Dechow and Dichev model is increasing in serial correlation in cash flows. Its

explanatory power doubles from the weakest cash-flow negative serial correlation tercile (18% r-

squared) to the highest tercile (36% r-squared). Thus, we tie the explanatory power of their

model to its internalizing of a particular cash-flow problem. Our results suggest that estimates of

the negative serial correlation of a given firm-year cash-flow realization produced from past firm

data are noisy. Use of future firm-specific cash-flow realizations reduces the noise in these

estimates. Our results also suggest that the industry average level of negative serial correlation

inherent in cash flows has more explanatory power for accruals than can be gained by

incorporating cross-firm variation in negative serial correlation. Our results suggest a path

toward improving accruals estimates at the firm level lies in improving firm-year estimates of the

transitory component of current operating cash flows.

21

22

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., 1969. 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. Ball, R., and Watts, R., 1979. Some additional evidence on survival biases. Journal of Finance 34, 197-206. Barth, M., Cram, D., and Nelson, K., 2001. Accruals and the prediction of future cash flows, The Accounting Review 76, 27-58. Barclay, M., Gode, D., and Kothari, S. P., 2005, Matching delivered performance, Journal of Contemporary Accounting and Economics 1, 1-25. Basu, S., 1997. The conservatism principle and the asymmetric timeliness of earnings, Journal of Accounting and Economics 24, 3-37. 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. 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. Dutta, S., Reichelstein, S., 2005, Stock price, earnings, and book value in managerial performance measures, The Accounting Review 80, 1069-1110. Fairfield, P., Whisenant, S., and Yohn T., 2003, Accrued earnings and growth: Implications for future profitability and market mispricing, Accounting Review 78, 353-371. Fama, E., 1965, The behavior of stock market prices." Journal of Business 38, 34-105. 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. Frankel, R., Levy, H., and Shalev, R., 2014, What triggers the year-end drop in working capital, New York University working paper. 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 D.W. Collins, 2002. Errors in estimating accruals: Implications for empirical research. Journal of Accounting Research 40, 105–34.

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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. Kothari, S. P., Leone, A., and Wasley, C., 2005. Performance matched discretionary accrual measures, Journal of Accounting and Economics 39, 163-197. Leone, A., Wu., J., and Zimmerman, J., 2006, Asymmetric sensitivity of CEO cash compensation to stock returns, Journal of Accounting and Economics 42, 167-192. 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, Working paper, University of Rochester. 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. Ramakrishnan, R., and Thomas, J., 1998. Valuation of permanent, transitory, and price-irrelevant components of reported earnings, Journal of Accounting, Auditing, and Finance 13, 301-336. Rayburn, J., 1986. The association of operating cash flow and accruals with security returns, Journal of Accounting Research Supplement, 112-133 Reichelstein, S., 2000, Providing managerial incentives: Cash flows versus accrual accounting, Journal of Accounting Research 38, 243-269. Revisine, L., Collins, D., Johnson, B., Mittelstaedt, F., and Soffer, L., 2015, Financial Reporting and Analysis 6th Edition, McGraw Hill Education, New York, NY.

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Sloan, R., 1993, Accounting earnings and top executive compensation, Journal of Accounting and Economics 16, 55-100. 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.

26

Table 1: Descriptive statisticsa Variablesb

N

Mean

Standard Deviation

Min

1st Quartile

Median

3rd Quartile

Max

ACCt 59394 0.0086 0.0793 -1.3133 -0.0201 0.0061 0.0378 0.4876ΔREVt 59394 0.0551 0.2580 -2.0771 -0.0327 0.0460 0.1575 1.5053PPEt 59394 0.5533 0.4071 0.0000 0.2229 0.4538 0.8141 2.5269OCFt 59394 0.0222 0.2200 -3.4726 -0.0093 0.0699 0.1303 0.4657ΔOCFt 59394 0.0086 0.1375 -1.5165 -0.0406 0.0067 0.0549 2.2031ABNRETt 59394 -0.0319 0.6304 -1.3615 -0.4095 -0.1213 0.1904 7.0137DABNRETt 59394 0.6111 0.4875 0.0000 0.0000 1.0000 1.0000 1.0000OCFSCt 58109 0.1966 0.1234 -0.3122 0.1003 0.1777 0.2854 0.5675OCFPREDt 58145 -0.4707 0.1311 -0.8070 -0.5797 -0.4754 -0.3811 -0.0723OCFVRt 57778 0.0317 0.0452 -0.1861 0.0034 0.0246 0.0554 0.2706a This table presents descriptive statistics for the 59,394 sample firm-year observations with necessary data during 1995-2012. b Definition of variables: ACCt working capital accruals for year t, defined as ΔAccounts Receivable + ΔInventory – Δaccounts

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

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

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

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

ΔOCFt change in cash flow from operations from year t-1 to year t, scaled by average 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 industry-specific serial correlation (i.e., first-order autocorrelation coefficient) in OCF, defined as the average annual coefficient for each 2-digit SIC industry over the past five years, multiplied by -1.

OCFPREDt industry-specific cash flow predictability, defined as the average r-squared from annual regressions of OCF for the next year on OCF for the current year for each 2-digit SIC industry over the past five years, multiplied by -1.

OCFVRt industry-specific cash flow value relevance, defined as the average difference, over the past five years for each 2-digit SIC industry, in the r-squared from annual regression of accumulatedmarket-adjusted two-year stock return on accumulated two-year OCF (i.e., year t and year t+1) and the r-squared from annual regression of market-adjusted one-year stock return on one-year OCF (i.e., year t).

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

ACCt 0.2568 -0.0333 -0.1044 -0.2951 0.0497 -0.0357 0.0215 0.0303 -0.0150 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0003)ΔREVt 0.2423 -0.0084 0.1180 0.1420 0.1775 -0.1645 0.0445 0.0609 -0.0003 (<.0001) (0.0413) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.9492)PPEt -0.0359 -0.0028 0.2442 0.0161 0.0219 -0.0350 0.1396 0.0822 0.1103 (<.0001) (0.4977) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001)OCFt -0.2460 0.2041 0.2938 0.2304 0.1316 -0.1472 0.1233 0.1052 0.1241 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001)ΔOCFt -0.3228 0.2102 0.0282 0.4077 0.1129 -0.0868 -0.0040 0.0086 0.0130 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.3338) (0.0375) (0.0017)ABNRETt 0.0427 0.2399 0.0661 0.2676 0.1581 -0.6887 -0.0065 -0.0079 0.0147 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.116) (0.0576) (0.0004)DABNRETt -0.0234 -0.1980 -0.0387 -0.1993 -0.1343 -0.8444 -0.0160 0.0050 -0.0120 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.0001) (0.2293) (0.004) OCFSCt 0.0180 0.0378 0.1837 0.0757 -0.0008 0.0112 -0.0166 0.5577 0.1050 (<.0001) (<.0001) (<.0001) (<.0001) (0.8439) (0.0069) (<.0001) (<.0001) (<.0001)OCFPREDt 0.0179 0.0523 0.0996 0.0574 0.0191 -0.0175 0.0042 0.5420 0.0883 (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (0.3074) (<.0001) (<.0001)OCFVRt -0.0256 -0.0048 0.1233 0.1322 0.0239 0.0096 -0.0122 0.1330 0.1306 (<.0001) (0.2467) (<.0001) (<.0001) (<.0001) (0.0215) (0.0034) (<.0001) (<.0001)

a This table presents Pearson (Spearman) correlations above (below) the diagonal among key variables for the 59,394 sample firm-years during 1995-2012. P-values are reported in parentheses. Variables are defined in Table 1.

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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 0.0065 *** 3.03 0.0063 ** 2.84 0.0065*** 3.02ΔREVt 0.0670 *** 13.77 0.0667 *** 14.12 0.0685*** 13.93PPEt -0.0050 ** -2.84 -0.0047 ** -2.48 -0.0050** -2.79 Adjusted R2 0.0499 0.0496 0.0517 Panel B: nonlinear Jones model (Ball and Shivakumar 2006) Intercept 0.0075 ** 2.75 0.0070 ** 2.51 0.0074** 2.74ΔREVt 0.0671 *** 15.00 0.0668 *** 15.33 0.0685*** 14.94PPEt -0.0059 *** -2.92 -0.0055 ** -2.57 -0.0059** -2.88ABNRETt -0.0034 ** -2.45 -0.0031 ** -2.44 -0.0032** -2.39DABNRETt 0.0038 *** 3.40 0.0040 *** 3.50 0.0041*** 3.57ABNRETt*DABNRETt 0.0122 ** 2.65 0.0119 ** 2.60 0.0127** 2.69 Adjusted R2 0.0525 0.0521 0.0543 Panel C: Jones model, considering cash-flow problem Intercept 0.0056 *** 3.58 0.0100 *** 4.00 0.0069*** 3.96ΔREVt 0.0879 *** 21.52 0.0869 *** 21.91 0.0891*** 20.93PPEt -0.0040 ** -2.62 -0.0036 ** -2.19 -0.0036** -2.51ΔOCFt -0.1112 *** -6.20 -0.3447 *** -8.98 -0.1977*** -13.77OCF SC measuret 0.0050 1.23 0.0078 * 2.02 -0.0062 -0.66ΔOCFt*OCF SC measuret -0.5451 *** -8.57 -0.2992 *** -3.91 -0.4517** -2.29 Adjusted R2 0.1860 0.1811 0.1835 Panel D: nonlinear Jones model, considering cash-flow problem Intercept 0.0073 *** 3.66 0.0109 *** 3.42 0.0081*** 3.40ΔREVt 0.0857 *** 22.79 0.0848 *** 23.20 0.0868*** 21.83PPEt -0.0051 *** -2.91 -0.0047 ** -2.53 -0.0048** -2.87ABNRETt 0.0019 1.24 0.0021 1.49 0.0021 1.42DABNRETt 0.0037 *** 3.20 0.0040 *** 3.32 0.0041*** 3.42ABNRETt*DABNRETt 0.0119 ** 2.33 0.0114 ** 2.20 0.0123** 2.33ΔOCFt -0.1131 *** -6.40 -0.3472 *** -9.01 -0.1998*** -13.73OCF SC measuret 0.0038 1.02 0.0075 ** 2.02 -0.0044 -0.49ΔOCFt*OCF SC measuret -0.5469 *** -8.72 -0.3001 *** -3.94 -0.4635** -2.38 Adjusted R2 0.1895 0.1846 0.1872 Panel E: nonlinear McNichols (2002) model (without OCFt+1) Intercept 0.0072 *** 3.07 0.0067 ** 2.77 0.0075*** 3.27ΔREVt 0.0901 *** 18.72 0.0900 *** 19.49 0.0904*** 18.45PPEt -0.0055 *** -3.60 -0.0052 *** -3.28 -0.0057*** -3.74OCFt-1 0.1856 *** 19.86 0.1851 *** 20.18 0.1864*** 20.02OCFt -0.2014 *** -13.45 -0.2000 *** -13.64 -0.2025*** -13.52ABNRETt 0.0026 1.46 0.0029 1.76 0.0025 1.53

29

DABNRETt 0.0052 *** 4.60 0.0055 *** 4.69 0.0053*** 4.56ABNRETt*DABNRETt 0.0147 ** 2.44 0.0139 ** 2.31 0.0154** 2.50 Adjusted R2 0.1751 0.1743 0.1771

a This table presents the average coefficients estimated using Fama-MacBeth annual regressions for the various accrual models. Adjusted R-square is the average for 18 annual regressions. The sample consists of all firm-year observations with necessary data during 1995-2012. ***, **, and * indicate statistical significance at the 1%, the 5%, and the 10% confidence levels, respectively. Variables are defined in Table 1.

30

Table 4: Fama-MacBeth Estimation of the Accrual Model with All Three Measures of Cash-Flow Problemsa

Variables Coefficient t-statistic Intercept 0.0105 *** 3.53 ΔREVt 0.0864 *** 23.58 PPEt -0.0045 ** -2.50 ABNRETt 0.0024 1.57 DABNRETt 0.0041 *** 3.57 ABNRETt*DABNRETt 0.0115 ** 2.20 ΔOCFt -0.1306 ** -2.23 OCFSCt 0.0008 0.21 ΔOCFt*OCFSCt -0.4701 *** -5.45 OCFPREDt 0.0070 * 1.81 ΔOCFt*OCFPREDt -0.0314 -0.33 OCFVRt -0.0001 -0.01 ΔOCFt*OCFVRt -0.2745 -1.22 Adjusted R2 0.1953

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-square is the average for 18 annual regressions. The sample consists of all firm-year observations with necessary data during 1995-2012. ***, **, and * indicate statistical significance at the 1%, the 5%, and the 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 5: Using Non-discretionary Net Income to Predict Future Operating Cash Flow or Earningsa

Intercept OCF NDNI Adj. R2 Vuong's Z-stat Panel A: Prediction of operating cash flow (OCF) of year t+1 Model 1: OCF

-0.0001 0.874 0.6578 (-0.128) (273.474)

Model 2: NDWCI from the Jones model -0.0064 0.864 0.6558 (-8.673) (272.271)

Model 3: NDWCI from the nonlinear Jones model -0.0064 0.863 0.6555 (-8.676) (272.104)

Model 4: NDWCI from the Jones model, with OCFSC added -0.0072 0.891 0.6697 8.2628 10.2417 (-9.957) (280.847) (vs. Model 1) (vs. Model 2)

Model 5: NDWCI from the nonlinear Jones model, with OCFSC added -0.0071 0.889 0.6693 7.9965 10.1675 (-9.877) (280.606) (vs. Model 1) (vs. Model 3)

Panel B: Prediction of earnings before extraordinary items of year t+1 Model 1: OCF

-0.0824 1.043 0.5535 (-75.286) (219.941)

Model 2: NDWCI from the Jones model -0.0901 1.036 0.5574 (-82.407) (221.653)

Model 3: NDWCI from the nonlinear Jones model -0.0901 1.035 0.5579 (-82.470) (221.867)

Model 4: NDWCI from the Jones model, with OCFSC added -0.0911 1.070 0.5714 7.5046 6.3635 (-84.643) (228.073) (vs. Model 1) (vs. Model 2)

Model 5: NDWCI from the nonlinear Jones model, with OCFSC added -0.0910 1.069 0.5725 7.6109 6.5239 (-84.721) (228.589) (vs. Model 1) (vs. Model 3)

a This table presents the coefficients estimated using OLS regressions for operating cash flow or earnings in year t+1. The sample consists of all firm-year observations with necessary data during 1995-2012. ***, **, and * indicate statistical significance at the 1%, the 5%, and the 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 6: Industry-Year-Specific Estimation of the Accrual Model with Firm-Specific Cash-Flow Serial Correlation Measuresa

OCFSC measure (1) OCFSC_firmt (2) OCFSC_Cfirmt Variables Coefficient t-stat Coefficient t-statPanel A: the standard Jones (1991) model Intercept 0.0075 *** 3.63 0.0075*** 4.43ΔREVt 0.0698 *** 13.66 0.0661*** 13.00PPEt -0.0067 ** -2.33 -0.0076*** -2.99 Adjusted R2 0.0896 0.0919 Panel B: nonlinear Jones model (Ball and Shivakumar 2006) Intercept 0.0065 ** 2.34 0.0082*** 3.88ΔREVt 0.0680 *** 13.13 0.0644*** 12.59PPEt -0.0066 ** -2.06 -0.0102*** -3.82ABNRETt 0.0046 1.07 0.0009 0.23DABNRETt 0.0049 * 1.92 0.0068*** 3.18ABNRETt*DABNRETt 0.0040 0.59 0.0145** 2.56 Adjusted R2 0.1024 0.1090 Panel C: Jones model, considering cash-flow problem Intercept 0.0079 *** 3.86 0.0098*** 5.84ΔREVt 0.1044 *** 21.07 0.0942*** 18.71PPEt -0.0054 ** -2.16 -0.0067** -3.12ΔOCFt -0.2670 *** -13.93 -0.2437*** -13.46OCFSCt 0.0001 0.30 -0.0003 -1.46ΔOCFt*OCFSCt -0.0057 * -1.66 -0.0102*** -3.45 Adjusted R2 0.3234 0.3183 Panel D: nonlinear Jones model, considering cash-flow problem Intercept 0.0077 *** 3.04 0.0112*** 5.63ΔREVt 0.1002 *** 20.20 0.0926*** 18.93PPEt -0.0055 ** -2.10 -0.0088*** -3.73ABNRETt 0.0091 *** 2.62 0.0058* 1.67DABNRETt 0.0057 *** 2.97 0.0046** 2.45ABNRETt*DABNRETt 0.0061 0.98 0.0110** 2.14ΔOCFt -0.2720 *** -14.00 -0.2505*** -13.75OCFSCt 0.0000 -0.14 -0.0003* -1.77ΔOCFt*OCFSCt -0.0053 -1.55 -0.0099*** -3.35 Adjusted R2 0.3337 0.3331 Panel E: nonlinear McNichols (2002) model (without OCFt+1) Intercept 0.0126 *** 5.51 0.0152*** 7.53ΔREVt 0.1039 *** 20.39 0.0917*** 19.33PPEt -0.0011 -0.48 -0.0032 -1.55OCFt-1 0.2399 *** 22.43 0.2309*** 23.64OCFt -0.3567 *** -25.38 -0.3522*** -25.94ABNRETt 0.0078 ** 2.34 0.0033 1.01

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DABNRETt 0.0065 *** 3.56 0.0058*** 3.32ABNRETt*DABNRETt 0.0215 *** 3.32 0.0269*** 5.46 Adjusted R2 0.3568 0.3607

a This table presents the average coefficients estimated using industry-year-specific regressions for the various accrual models. The cash-flow serial correlation measures used in the two columns are decile ranks of firm-specific historic and contemporaneous serial correlation measures, respectively. The firm-specific historic serial correlation measure (OCFSC_firm) is estimated over t-5~t-1 for sample observations in 1995-2012. The firm-specific contemporaneous serial correlation measure (OCFSC_Cfirm) is estimated over t-2~t+2 for sample observations in 1992-2010. Each industry-year combination is required to have at least 30 observations with necessary data and at least 5 observations having negative stock returns (i.e., DABNRET=1). Adjusted R-square is the average for 186 and 250 regressions in columns (1) and (2), respectively. ***, **, and * indicate statistical significance at the 1%, the 5%, and the 10% confidence levels, respectively. Variables are defined in Table 1.

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Table 7: Comparison of the Jones (1991) Model and the McNichols (2002) Model for Each Tercile of the Cash-Flow Serial Correlation Measure (OCFSC)a

(1) Jones Model (2) McNichols Model

Variables Coefficient t-stat Coefficient t-statPanel A: all observations Intercept 0.0065 *** 3.03 0.0082*** 4.84ΔREVt 0.0670 *** 13.77 0.0863*** 16.70PPEt -0.0050 ** -2.84 -0.0072*** -5.34OCFt-1 0.1590*** 18.09OCFt -0.2998*** -21.50OCFt+1 0.1366*** 25.73 Adjusted R2 0.0499 0.2396 Panel B1: lowest tercile Intercept 0.0025 1.10 0.0059*** 3.28ΔREVt 0.0596 *** 10.42 0.0746*** 11.03PPEt 0.0010 0.40 -0.0043* -2.04OCFt-1 0.1407*** 13.85OCFt -0.2402*** -13.58OCFt+1 0.1089*** 11.70 Adjusted R2 0.0350 0.1813 Panel B2: middle tercile Intercept 0.0095 *** 3.51 0.0109*** 4.87ΔREVt 0.0741 *** 11.44 0.1010*** 16.69PPEt -0.0079 *** -3.49 -0.0092*** -4.53OCFt-1 0.1664*** 10.95OCFt -0.3340*** -16.23OCFt+1 0.1508*** 18.48 Adjusted R2 0.0614 0.2841 Panel B3: highest tercile Intercept 0.0101 *** 3.57 0.0126*** 5.70ΔREVt 0.0632 *** 12.54 0.0807*** 14.32PPEt -0.0098 *** -4.74 -0.0058*** -2.97OCFt-1 0.2012*** 19.53OCFt -0.4388*** -18.40OCFt+1 0.1709*** 16.08 Adjusted R2 0.0657 0.3670

a This table presents the average coefficients estimated using Fama-MacBeth annual regressions for the Jones (1991) model and the McNichols (2002) model, for each tercile of the industry-specific cash-flow serial correlation measure. Adjusted R-square is the average for 18 annual regressions. The sample consists of all firm-year observations with necessary data during 1995-2012. ***, **, and * indicate statistical significance at the 1%, the 5%, and the 10% confidence levels, respectively. Variables are defined in Table 1.