Accrual Determinants

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Accrual determinants, sales changes and their impact on empirical accrual models Nicholas Dopuch [email protected] Raj Mashruwala [email protected] Chandra Seethamraju [email protected] Tzachi Zach [email protected] Washington University in St. Louis Olin School of Business Campus Box 1133 Saint Louis, MO, 63130 First draft: September 2005 This draft: September 2005 We thank participants in the workshop at Washington University in St. Louis for helpful comments and suggestions.

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Accrual Determinants

Transcript of Accrual Determinants

Page 1: Accrual Determinants

Accrual determinants, sales changes and their impact on empirical accrual models∗

Nicholas Dopuch [email protected]

Raj Mashruwala

[email protected]

Chandra Seethamraju [email protected]

Tzachi Zach

[email protected]

Washington University in St. Louis Olin School of Business

Campus Box 1133 Saint Louis, MO, 63130

First draft: September 2005 This draft: September 2005

∗ We thank participants in the workshop at Washington University in St. Louis for helpful comments and suggestions.

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Abstract

In this paper we argue that the relationship between working capital accruals and

changes in sales, extensively modeled in the accounting literature by the Jones-type

models, is more complex than portrayed by these models. In addition to sales changes,

accruals are also affected by accrual determinants such as firms’ inventory and credit

policies. In our first set of tests, we document that the coefficient on sales changes in

Jones-type accrual models is related to the accrual determinants. Additionally, we find

that the homogeneity in the accrual-generating process within a given industry, which is

represented by the accrual determinants, affects the significance level of the coefficient

on sales changes. Higher dispersion in accrual determinants is associated with lower

levels of significance. We also identify one source of bias in abnormal accruals -

measurement error in the coefficient of sales changes, which stems from heterogeneity in

the accrual generating process.

Our study has direct implications on studies that use the absolute value of

abnormal accruals as a measure of accrual or earnings quality. Our results indicate that a

high level of heterogeneity in the accrual-generating process within an industry leads to

larger errors in abnormal accruals and thus, larger absolute values of abnormal accruals.

The implication of our results on earnings management studies is more complex and

requires knowledge of the correlation between the partitioning variables in those studies

and industry classification. While our analysis focuses mostly on the more popular cross-

sectional implementation of the Jones-model, the study’s logic and some of the results

also apply to the time-series version of the models.

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1. Introduction

This paper investigates the important relation between accruals and changes in

sales as manifested in common empirical models of accruals. These models have gained

popularity in the accounting literature over the last two decades and have been used

mainly to address questions regarding management’s accounting choices (see Kothari,

2001 and Fields, Lys and Vincent, 2001). More recently, the outputs of these models –

discretionary or abnormal accruals – have also been used as proxies for accrual or

earnings quality (e.g. Frankel, Johnson and Nelson, 2002, Francis, LaFond, Olsson and

Schipper, 2005).

The relation between accruals and sales changes is outlined by the popular accrual

models and is empirically summarized by a regression coefficient that is either firm- or

industry-specific (e.g. Jones, 1991 and modified Jones in Dechow, Sloan and Sweeney,

1995). Depending on the empirical estimation procedure, time-series or cross-sectional,

the assumption underlying the estimation procedure is that a firm either has a stable

accrual-generating process over time, or that a group of firms (typically a 2-digit SIC

code) has a common accrual-generating process.

In this paper, we argue that the relation between accruals and sales changes is

more complex than described by the common empirical models and depends on several

factors that are firm-specific such as credit and inventory policies. Using this intuition,

along with a theoretical model developed by Dechow, Kothari and Watts (1998), we

show that these firm-specific characteristics, labeled “accrual determinants”, exhibit a

large variation across time, and more importantly within an industry-group. Thus, we

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argue that the accrual-generating process is not as homogeneous as implicitly assumed in

empirical applications of a Jones-type model.

The large variation in the accrual-generating process within an industry-group,

over which the cross-sectional version of the accrual models is estimated, has important

implications for the subsequent calculation of abnormal accruals.1 We argue and show

that such large variation causes a measurement error in the Jones coefficients, i.e. a

disparity between the estimated coefficient of the Jones model and the “true” firm

coefficient that ought to be used to compute the residuals of the regression model, i.e. the

abnormal accruals. This measurement error in the coefficients directly translates to

measurement error, and in some instances bias, in the estimated abnormal accruals.

This paper makes several important contributions to the accounting literature.

First, while many papers discuss in length the potential biases that exist in measures of

discretionary accrual, in this paper we investigate a potential source of these biases.

Identifying the source of the bias is necessary if researchers are interested in eliminating

this bias. We believe that knowledge of the causes of measurement errors in the Jones

coefficients is critical in any attempt at reducing such measurement errors and

consequently reducing the bias in abnormal accruals.

Second, this paper furthers our understanding of the relation between sales

changes and accruals. While this relation is very intuitive and is discussed at length in

Dechow et al. (1998), it surprisingly has not as yet been utilized in the empirical

literature. In this paper, we attempt to fill this void. Finally, our results have important

implications for the interpretation of abnormal accrual measures and their use in the

1 Similar arguments could be made for the time-series version of the Jones-type models. We do not explicitly discuss those for brevity.

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extant literature. For example, we suggest caution in interpreting the absolute value of

abnormal accruals as a measure of earnings quality. We show that certain firms,

especially those that belong to industries with high-variation in accrual determinants,

have large measurement errors in their coefficients, leading to large errors in their

abnormal accruals.

Summary of the results. Our first set of results shows that the coefficients on

changes in sales (μ1) estimated from Jones-type models are associated with the four

accrual determinants that we investigate in this study. This implies that the Jones model

does, in fact, capture some of the interaction between sales and accruals. However, as our

next findings suggest, the Jones-type models only partially capture that relation.

When we examine whether the variation in the accrual-generating process within

an industry-group affects the accrual models, we find that the higher the variation in the

determinants related to accounts receivables and inventory, the lower is the likelihood

that the coefficients will be significant.

Finally, we look at the relation between the accrual determinants and abnormal

accruals. Using results in the accounting literature, we generate and test hypotheses about

the relation between the measurement errors of the Jones model’s coefficients and the

bias in abnormal accruals. In one of our tests, we correlate the measurement error in the

coefficients, which is the difference between the actual estimated coefficient and a

theoretical predicted coefficient, with factors associated with bias in abnormal accruals.

We compute the predicted measure using a formula developed in Dechow et al. (1998)

with firm-specific accrual determinants. We find that this measurement error is, in

general, associated with factors that have been associated with bias in abnormal accruals

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such as extreme quartiles of book-to-market ratio. In a second set of tests, we correlate

the absolute value of abnormal accruals, which we argue contain a bias component, with

the measures we find to be associated with measurement error in Jones coefficients,

namely the degree of variation in the accrual-generating process. Again, we find that

higher variation in the accrual-generating process is associated, in most cases, with larger

absolute values of abnormal accruals.

Our study points at one source for the measurement error and bias in abnormal

accruals that arises from measurement error in the Jones coefficients. We acknowledge

that there could be other factors that could affect the measurement of abnormal accruals.

For example, miscalculation of the accrual variable itself (e.g Hribar and Collins, 2000

and Francis and Smith, 2005) could lead to estimation problems and erroneous abnormal

accruals. Another example, which stems from mismeasurement of the coefficients is

violation of the assumptions underlying the classical linear regression model.

The rest of the paper is organized as follows. In section 2 we develop our

hypothesis. In section 3 we describe our data and in section 4 we report the main results.

We discuss the implications of our results in section 5. Finally, we conclude in section 6.

2. Hypotheses development

2.1 The relation between sales changes and accruals

Modeling the accrual process is central to the accounting literature. The need for

aggregate accrual models arose when researchers realized that studies of discrete

accounting choices could only paint a partial picture because managers had a set of

accounting choices at their disposal (Fields, Lys and Vincent, 2001). Over the years, the

literature has evolved from using naïve models as in Healy (1985) to the current industry-

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standard: the Jones (1991) model, the “modified-Jones” model in Dechow et al. (1995)

and other variants (e.g. Dechow, Richardson and Tuna, 2003). The outcome of such

models, often referred to as discretionary or abnormal accruals, are typically used in

examining whether earnings management is present in a particular sample. More

recently, abnormal accruals and their variants, such as the absolute value of abnormal

accruals, have been used as proxies for earnings quality and as surrogate variables in

studying questions other than earnings management.2

The Jones-type models structurally describe the behavior of accruals. The

original version of the Jones (1991) model described in equation (1) below is quite

parsimonious, relying on changes in sales and the level of property, plant and equipment

to explain total accruals:

1 2_i iTA Ch Sales PPEi iα μ μ ε= + ∗ + ∗ + (1)

The Jones-type models rely mainly on the shock to sales to describe the

generation of accruals. However, intuitively, it stands to reason that the creation of

accruals depends on more than just the shock to sales. In fact, there exist certain firm

specific characteristics that along with the shock to sales, determine the levels of

accruals. For example, consider two firms that are identical in all respects except for their

credit policies. Firm A does not grant any credit to its customers while firm B grants

credit. It is evident that for any given shock to sales, firm B will not generate any accruals

related to accounts receivables but firm B will. In addition to credit policies, other firm

2 For example, in the literature that examines the relation between auditor independence and accounting choices, Frankel, Johnson and Nelson (2003) use the absolute value of abnormal accruals as their main measure of earnings quality. Other examples include Klein (2002), Ashbaugh, LaFond and Mayhew (2003), Myers, Myers and Omer (2003), Larcker and Richardson (2004) and Francis, LaFond, Olsson and Schipper (2005).

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characteristics, such as inventory policies and credit terms granted by the firm’s

suppliers, interact with the shock to sales in affecting accruals.

The intuition of the effect of firm characteristics on accruals is modeled explicitly

in Dechow, Kothari and Watts (1998) (hereinafter, DKW). They develop a theoretical

algebraic model that describes the behavior of accruals absent any managerial

intervention. In the DKW model each of the accrual characteristics is summarized by a

parameter in the model. We label these parameters the ‘accrual determinants.’ The DKW

model describes how accruals are generated as a function of sales and the accrual

determinants.

In this paper, we investigate the circumstances under which the lack of explicit

specification in the Jones-type models of the interactions between sales changes, the

accrual determinants and accruals, has an impact on the outcomes of the accrual models.

To measure these accrual determinants we rely on Dechow et al. (1998). They make

several assumptions about the sales process and obtain the following equation describing

working capital accruals:

1 2 1 2[ (1 ) (1 )] (1 )[ (1 )] (1 )t t tWCA 1tα π β π ε γ π β γ β ε βγ γ π ε −= + − − − ∗ − − + − Δ − − Δ (2)

where WCA= working capital accruals; α is the proportion of a firms’ sales that

remain uncollected at the end of the period; β is the proportion of the firms’ purchases

that remain unpaid at the end of the period; Π is the net profit margin on sales; γ1 is target

inventory as a percentage of next period’s forecasted cost of sales; γ2 is a constant that

captures the speed with which a firms adjusts its inventory to the target level.

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Unlike the Jones model’s parsimonious representation of the interaction between

changes in sales and accruals, the DKW model describes a relation that is far more

complex.

Our first objective is to examine whether there is any link between the accrual

determinants such as those suggested by the DKW model and the estimated coefficient

(μ1) in the Jones model. In essence, the impact on accruals of all the accrual determinants,

through their interaction with the shock to sales, is collapsed in the empirical Jones-type

models into a single quantity, μ1, the estimated coefficient on changes in sales. Thus, it is

important to understand what affects the estimation of μ1 because any factors affecting its

estimation will directly influence the outcomes of the model, i.e. the estimates of

abnormal accruals. We argue that if the Jones model’s estimation is meaningful, at a

minimum such a link should be observed.

More formally,

H1: Accrual determinants α, (β), γ1 and π are positively (negatively) associated with the estimated coefficient on sales changes μ1.

2.2 What impacts the Jones’ coefficient on changes in sales?

One important element that affects the estimated coefficient μ1 is the way in

which the Jones accrual model is estimated. Researchers would like to estimate the model

in a sample that is relatively homogeneous with respect to the accrual generating process.

This would increase the probability that the Jones model would adequately capture the

accrual-generating process and ensure that μ1 will be estimated with precision and with

sufficient power. The relation between the accrual determinants and the Jones model

directs us to the kind of homogeneity researchers would like to identify. In particular,

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since μ1 collapses the impact of accrual determinants on the relation between sales

changes and accruals, researchers are interested in homogeneity in the accrual

determinants or, more broadly, homogeneity in the accrual-generating process.

Originally, the Jones-type models were estimated separately for each firm,

utilizing a time-series of observations for that particular firm. Underlying this

implementation is the notion that a particular firm’s accrual-generating process is stable

over time. The disadvantage of this approach is that many firms are dropped from the

sample because they do not have a sufficiently large time-series to warrant a meaningful

estimation (Subramanyam, 1996). As a result, researchers, beginning with DeFond and

Jiambalvo (1994) turned to a cross-sectional version of the model by estimating it

separately for each industry group defined by a common two-digit SIC code. The

assumption underlying this estimation procedure is that each 2-digit SIC code industry

group is homogeneous in its accrual-generating process (see pages 427-428 in Bartov,

Gul and Tsui, 2001).

One limitation of the cross-sectional estimation is that it implicitly assumes a

uniform accrual-generating process within the industry group. That is, the relation

between sales changes and accruals is identical for all firms that comprise a two-digit SIC

code group. If that assumption is violated, then the estimated coefficients could be biased

in unpredictable directions. For example, Bernard and Skinner (1996) note that a single

industry group may contain very different firms. They mention that the makers of heavy

equipment for the oil and gas industry, video games, lawn mowers and personal

computers all belong to the same two-digit SIC code.

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We hypothesize that the degree of precision with which μ1 is estimated depends

on the degree of homogeneity in the accrual-generating process within an industry group.

To operationalize the homogeneity of an industry with respect to the accrual-generating

process, we examine the coefficient of variation of each accrual determinant within the

industry.

H2: The frequency with which μ1 is statistically significant is related to the within-industry variation in the accrual determinants.

2.3 The Bias in Abnormal Accruals

2.3.1 Background

Many studies argue that aggregate accrual models generate abnormal accruals that

are truly normal (e.g. McNichols (2000), Kothari (2001)). That is, these models are

misspecified and lead to erroneous detection of earnings management where in fact no

intentional intervention in the financial accounting process occurred. As such, all

earnings management tests are joint tests of the managerial intervention as well as the

models used to estimate abnormal accruals (Kothari et al., 2005).

The models’ misspecification, it is argued, stems from two correlated (but related)

omitted variables: past firm performance and expected firm performance. Dechow et al.

(1995) find that the Jones-type models “reject the null hypothesis of no earnings

management at rates exceeding the specified levels when applied to samples of firms

with extreme financial performance.” Kasznik (1999) shows that abnormal accruals are

associated with current ROA. In addition, Kothari et al. (2005) argue that if future firm

performance is serially correlated (either exhibits reversal or momentum) then expected

accruals will not be zero and will be related to past firm performance.

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Expected future growth in firm’s operations leads to investments in current

accruals. McNichols (2000) shows that abnormal accruals from the Jones-type models are

associated not only with current and past performance, but also with analysts’ forecasts of

future expected growth.

Kothari et al. (2005) attempt to address the misspecification of the Jones-type

models by employing a control sample and isolating the portion of abnormal accruals that

may in fact be normal. Under the assumption that the models do in fact detect some

earnings management in their normal accruals, the control sample approach detects

abnormal earnings management. McNichols (2000) and Dechow et al. (2003) include a

measure of future sales growth (either forecasted growth by analysts in McNichols (2000)

or actual growth in sales in the following year in Dechow et al. (2003)) in their improved

Jones-type models. Larcker and Richardson (2004) add the book-to-market ratio and cash

flows from operations to the model.

While the studies mentioned above identify variables that may be correlated with

the bias in the models’ outcomes, none of the studies identifies the source of the

mismeasurement in the models that may lead to such bias. Kothari et al. (2005) provide

ample evidence that in random samples drawn from groups of firms with certain

characteristics, the null hypothesis of zero abnormal accruals is rejected too often. For

example, in their Table 3, the null hypothesis is rejected too frequently in favor of the

alternative of negative abnormal accruals in (i) both high and low quartiles of book-to-

market, (ii) the low quartile of sales growth, (iii) the low quartile of earnings-to-price

ratio, (iv) the quartile of smallest firms and (v) the low quartile of operating cash flows.

The null is rejected in favor of the alternative of positive abnormal accruals in (i) the

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quartile of highest sales growth, (ii) high EP ratio, (iii) the quartile of largest firms and

(iv) the quartile of highest operating cash flows.

2.3.2 Measurement error test

Our next set of hypotheses attempts to evaluate the degree and source of bias that

potentially exist in abnormal accruals and that result from estimating the Jones-type

models. We use the results in Kothari et al. (2005) to generate the hypotheses. The goal is

to trace the sources of the documented biases. We argue that one source of the bias is

misestimated coefficients in the Jones model. If the estimation error in the coefficients is

related to the firm characteristics that are associated with abnormal accruals, then we can

conclude that this estimation error in the coefficients is responsible for the bias in

abnormal accruals. This is important, because such a finding will focus researcher’s

efforts on reducing the estimation error in the coefficients potentially leading to reduced

bias in abnormal accruals.

The direction of the bias in abnormal accruals for each firm will depend on the

direction of the estimation error in the coefficients as well as on the sign of the sales

change. This is true holding constant the effect of the intercept and other variables in the

Jones estimated regression model.

Estimation error in the coefficients. When the Jones-type model is estimated, the

resulting coefficient on sales change (μ1) could be biased with respect to the “true”

coefficient because of econometric problems such as the violation of classical

assumptions. In a cross-sectional application of the Jones model the “true” coefficient

could be viewed as an “average” coefficient for the industry. When discussing

mismeasurement of regression coefficients we do not refer to the econometric bias in the

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coefficients, that is, the difference between the estimated industry coefficient and the true

industry coefficient. In other words, we assume that there are no econometric problems in

the estimation that that occur as a result of a violation of the three classical assumptions.

Instead, the mismeasurement of coefficients to which we refer in this paper is the

difference between the “average” estimated industry coefficients and the “true” firm-

specific coefficients. The latter, of course, are not observable by the researcher. However,

these are the coefficients we would like to have when estimating firm-specific abnormal

accruals. As Bartov et al. (2001) state: “…if…sample firms are not much different than

the average firm in their industry, the fact that the cross-sectional version forces the

coefficients to be the same for all firms in the industry should not represent a serious

problem”. In other words, the “average” estimated industry coefficient will be closer to

each of the actual firm coefficients when the industry is more homogeneous with respect

to the accrual-generating process.

If the estimated cross-sectional industry coefficient (μ1EST) is higher than the

firm’s actual predicted coefficient (μ1PRED – discussed below) and the sales change is

positive (negative) then the estimated normal accruals will be too high (low) and the

resulting abnormal accruals will be too low (high). We use this logic to generate

predictions about the direction of the estimation error in the coefficients and their relation

to several firm characteristics that are discussed in Kothari et al. (2005).

To evaluate any potential estimation error in the Jones coefficients, we require

some estimate of what the firm-specific coefficients would be absent any error (μ1PRED).

To do so, we use the term developed in Dechow et al. (1998). In equation (2) the term

preceding the sales change (∆εt) is

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1 2(1 ) (1 ) (1 )[ (1 )]α π β π γ π β γ β+ − − − − − + − (3)

which we label μ1PRED. We calculate this term for each firm-year based on the five-year

averages of the firm-specific accrual determinants.

We summarize our predictions about the relation between the estimation error

(μ1EST-μ1

PRED) and firm characteristics based on the results in Kothari et al. (2005). Such

predictions will help us: (1) corroborate Kothari et. al’s (2005) evidence using a different

methodology, (2) identify the source of the bias in discretionary accruals and (3) validate

a potentially better estimate for the coefficient on sales change which is an outcome of a

theoretical model and does not require a regression estimation.

Book-to-Market ratio. The results in Kothari et al. (2005) suggest that extreme

book-to-market quartiles exhibit high rejection rates of the null hypothesis of zero

discretionary accruals in favor of the alternative of negative discretionary accruals. This

means that in those quartiles estimated discretionary accruals are too low and estimated

normal accruals are too high. Thus, in those sets of firms (i) The absolute value of the

estimation error in the coefficient is expected to be positive, and (ii) the estimation error

in the coefficients (μ1EST-μ1

PRED) is positive (negative) if changes in sales are positive

(negative). This translates into several predictions that we outline below.

P3a: When regressing the absolute value of the measurement error on a continuous measure of the quartile of BM, the estimated coefficient cannot be signed because the potential estimation error exists in both extreme quartiles.

P3b: When regressing the absolute value of the measurement error on an indicator variable for extreme quartile of BM, the estimated coefficient will be positive because in both quartiles we expect some estimation error in the coefficient.

P3c: When regressing the measurement error on a continuous measure of the quartile of BM, the estimated coefficient cannot be signed because the potential estimation error exists in both extreme quartiles.

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P3d: When regressing the measurement error on an indicator variable for extreme quartile of BM, we differentiate between cases when the sales change is positive or negative. If changes in sales are positive, then the relation between the estimation error in the coefficient and the bias in abnormal accruals is positive. Therefore, we expect the estimated coefficient on the indicator variable to be positive. The relation flips when changes in sales are negative. In those cases, we expect the coefficient to be negative.

Size. The results in Kothari et al. (2005) suggest that the quartiles of the smallest

firms exhibit high rejection rates of the null hypothesis of zero discretionary accruals in

favor of the alternative of negative discretionary accruals. This means that in those

quartiles estimated discretionary accruals are too low and estimated normal accruals are

too high. Thus, in those sets of firms the difference μ1EST-μ1

PRED is positive (negative) if

sales changes are positive (negative).

The evidence in Kothari et al. (2005) regarding the quartile of the largest firms

suggests that there is excessive rejection of the null hypothesis in favor of an alternative

of positive discretionary accruals especially in the modified Jones model. Thus, in large

firms, abnormal accruals tend to be too high and normal accruals are too low. In those

sets of firms the measurement error is the difference μ1EST-μ1

PRED and it is negative

(positive) if sales changes are positive (negative). We summarize the above logic in the

following predictions.

P4a: When regressing the absolute value of the measurement error on a continuous measure of the quartile of size, the estimated coefficient cannot be signed because the potential estimation error exists in both extreme quartiles.

P4b: When regressing the absolute value of the measurement error on an indicator variable for extreme quartile of size, the estimated coefficient will be positive because in both quartiles we expect some estimation error in the coefficient.

P4c: When regressing the measurement error on a continuous measure of the quartile of size, the estimated coefficient depends on the sign of sales changes. If

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the sales changes are positive, then that implies a positive error in small firms and negative error in large firms leading to an expected negative coefficient. When sales changes are negative the expected sign flips and turns positive.

P4d: When regressing the measurement error on an indicator variable for extreme quartile of size, we expect positive sign because the estimation error exists in both small and large firms.

Sales Growth. The results in Kothari et al. (2005) suggest that the lowest (highest)

quartile of growth in sales exhibits high rejection rates of the null hypothesis of zero

discretionary accruals in favor of the alternative of negative (positive) discretionary

accruals. This means that in the lowest (highest) quartile estimated discretionary accruals

are too low (high) and estimated normal accruals are too high (low). Thus, in those sets of

firms (i) The absolute value of the estimation error in the coefficient is expected to be

positive and (ii) the estimation error in the coefficients (μ1EST-μ1

PRED) is positive

(negative) if changes in sales are positive (negative). This translates into several

predictions that we outline below.

P4a: When regressing the absolute value of the measurement error on a continuous measure of the quartile of sales change, the estimated coefficient cannot be signed because the potential estimation error exists in both extreme quartiles.

P4b: When regressing the absolute value of the measurement error on an indicator variable for extreme quartile of size, the estimated coefficient will be positive because in both quartiles we expect some estimation error in the coefficient.

P4c: When regressing the measurement error on a continuous measure of the quartile of sales changes, the estimated coefficient is expected to be positive

P4d: When regressing the measurement error on an indicator variable for extreme quartile of sales change, we expect positive sign because the estimation error exists in both extreme quartiles of sales change.

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2.3.3 Abnormal accruals test

To evaluate the sources of bias in abnormal accruals we also employ a second

test. In this test, we regress the absolute value of abnormal accruals on factors associated

with estimation error in the Jones coefficients. These factors are the coefficients of

variation in accrual determinants which capture the degree of homogeneity in the accrual-

generating process in a particular industry. We argue that industries with less

homogeneous accrual-generating processes will have firms with more biased abnormal

accruals.

The absolute value of abnormal accruals will include the true abnormal accruals

and the bias in abnormal accruals. By regressing both components, we hope to capture

the correlation of the bias component with the explanatory variables. This assumes that

the true component of abnormal accruals is not correlated with factors that are associated

with mismeasurement in the Jones coefficients.

Our prediction is that there will be a positive association between the coefficient

of variation of accrual determinants and the absolute value of abnormal accruals.

3. Data

We draw the accounting data necessary for our study from COMPUSTAT’s

primary, secondary and tertiary files. We include all firms with available data to estimate

the accrual models but exclude firms in the financial services industries (SIC codes 6000-

6999).

Accrual determinants. To calculate the accrual determinants we follow the

procedures outlined below. These procedures are similar to those used by Dechow et al.

(1998).

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α : AR= Accounts receivable (ARt + ARt-1)/2*SALESt

β : AP = Accounts payable (APt + APt-1)/2*SALESt (1-π)

γ1 : Target inventory g1/(1-π) ; truncated above at 1 and below at -1

g1 : Regression coefficient

INVt = g1*SALESt + g2*ΔSALESt + εt

π : Profit Margin NIt / SALESt

For each firm, we then define the accrual determinant for year t as the 5-year

average of that determinant including the current year (t) and the previous 4 years. To

obtain industry-level statistics, at the 2-digit SIC code level, we calculate the average,

standard deviation and coefficient of variation based on each individual firm’s 5-year

averages and taking into account all firms belonging to an industry group for a particular

year.

Accrual models estimation. We estimate four versions of accrual models. The first

is the traditional Jones model

1 2_i iTA Ch Sales PPEi iα μ μ ε= + ∗ + ∗ + (4)

Where,

TA = total accruals calculated from the balance sheets as follows:

Δ(Current Assets)- ΔCash- Δ(Current Liabilities) + (current portion of LT debt)-

Depreciation and Amortization

Ch_Sales = the change in sales in year t (SALESt – SALESt-1)/ASSETSt-1

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PPE = Property, Plant and Equipment.

We also estimate the modified-Jones model where we subtract the change in

receivables from the change in sales.

1 2( _ _ )i i iTA Ch Sales Ch REC PPEi iα μ μ ε= + ∗ − + ∗ + (5)

Finally, we estimate a reduced form of the above models, wherein we only

include working capital accruals as the dependent variable, dropping PPE as an

explanatory variable. We do so because the accrual determinants from the Dechow at al.

(1998) model apply to working capital accruals (WCA).

1 _i iWCA Ch Sales iα μ ε= + ∗ + (6),

1 ( _ _ )i iWCA Ch Sales Ch RECi iα μ ε= + ∗ − + (7)

where,

WCA = working capital accruals calculated from the balance sheets as follows:

Δ(Accounts receivables)- Δ(inventories) – Δ(Accounts payable)

We exclude observations with the extreme 1% (from each side) of each variable

in models (4) through (7). In all these models, μ1, the coefficient on sales changes, is

assumed to capture the accrual-generating process.

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4. Results

4.1 Summary statistics

Table 1 Panel A reports some descriptive statistics on the four main accrual

determinants. The summary statistics are calculated over all firm years in our sample and

are reported after eliminating the extreme 0.5% of observations on each side. The mean

(median) α in our sample is 0.245 (0.167) which translates to an accounting receivable

cycle of about 89 (60) days. The mean (median) β is 0.108 (0.078) which is equivalent to

39 (28) days in payables. The target inventory’s mean (median) is 0.129 (0.110) which

translates to an inventory turnover of about 45 days. Finally, the median profit margin is

2.3%. The mean is affected by very extreme negative observations. In general, these

values (especially medians) are in line with those reported in Dechow et. al (1998). It is

worth noting that there is substantial variation in each of the parameters. For example,

α’s inter-quartile range is 0.114 to 0.242. All of the other accrual determinants in Panel A

display similar or greater levels of variation.

Panel B of Table 1 reports some correlations between the accrual determinants.

We note that α and β are positively correlated (0.37) and α and π are slightly negatively

correlated.

In Table 2 we provide additional summary statistics on the various accrual

determinants, broken down into different sub-groups. Note that some of the determinants

vary substantially across different quartiles. For example, γ1’s mean in the lowest book-

to-market quartile is 0.064 and it monotonically increases to 0.149 in the top quartile.

Similar variation appears in the ROA quartiles but not in the size quartiles.

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4.2 The relation between accrual determinants and estimation of the Jones model

In this section we test our first hypothesis which examines the relation between

the empirical estimation of the Jones (1991) model and the accrual determinants. Recall

that μ1, the coefficient on the sales changes in the Jones model, can be viewed as a

parsimonious measure of the underlying accrual-generating process. In effect, the relation

between accruals and sales changes depends on a black box which consists of the

interactions between the accrual determinants and sales changes which, in turn, generate

accruals. In the Jones (1991) model, this black box is summarized by μ1.

To test H1, we regress the μ1 industry-coefficients on the industry means of the

accrual determinants: α, π, γ1 and β. The estimated μ1 is derived from a cross-sectional

implementation of the Jones model within an industry group consisting of all firms

belonging to a common 2-digit SIC code group.3 We average the accrual determinants

within those same industry groups to obtain the independent variables of our regression

model. We employ four regression models as described in section 3.

The results are reported in Table 3. Regardless of the type of model used for the

estimation (Jones or modified Jones, full or reduced), we find very strong evidence that

all four of the accrual determinants are significantly associated with μ1 in the predicted

directions. The receivable policy (represented by α), the profit margin (represented by π)

and the target inventory parameter (γ1) are positively and significantly associated with the

coefficient on sales. On the other hand β, which represents credit policy granted by

suppliers, is significantly negatively associated with μ1, suggesting that the impact of this

determinant is to reduce overall accruals when sales increase.

3 In unreported results, we also regress μ1 coefficients from a time-series version of the Jones model on firm-specific accrual determinants. The conclusions are similar.

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It is worth noting that the reduced-form models, which only involve working

capital accruals, have slightly higher explanatory power. This is expected because the

accrual determinants only pertain to working capital accruals.

In summary, the results in table 3 suggest that the Jones model does, in fact,

capture some of the relation between changes in sales and accruals, as reflected by the

accrual determinants. However, it is evident that this relation may be more complex than

what a simple parsimonious coefficient could capture. This complex interaction can best

be viewed in the more elaborate DKW model.

4.3 The significance of μ1 and variation in accrual determinants within an

industry

In the previous section, we established a link between μ1 and the accrual

determinants. Our second hypothesis argues that the quality of the empirical model

depends on the degree of variation in the accrual determinants within the group in which

the model is estimated. As a proxy for the quality of estimates of μ1 we examine whether

μ1 is statistically significant in a particular industry-year model. The dispersion in accrual

determinants in each industry group is measured by the coefficient of variation of each

accrual determinant.

Our first examination is univariate. We rank into quintiles all industry-years based

on their coefficients of variation of the accrual determinants, separately for each

determinant. Quintile 1 is the quintile with the least degree of variation in the accrual

determinant whereas quintile 5 is the one with the greatest degree of variation in the

accrual determinant. Table 4 reports the frequency with which μ1 is significant in each

quintile of an accrual determinant’s variation.

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Starting with the first accrual determinant, α, we find an almost monotonous

decline in the significance frequency of μ1 from quintile 1 to quintile 5 for the Jones

model. The significance frequency of μ1 is 59.5% in quintile 1, and declines to only

39.1% in quintile 5. The results are similar for the other models as well. For β too, there

is a pattern of decline in significance frequency as we move to higher variation quintiles,

although it is not as strong as in the case of α. Again, the patterns are similar across all

accrual models.

Turning to γ1, the accrual determinant related to inventory, we observe a strong

monotonous decline in significance frequency as we move from low to high variation

quintiles. For example, in the regular Jones model, 68% of the specifications yield a

significant μ1 in the lowest variation quintiles. This proportion drops to 34% in the

highest variation quintile.

In contrast, there is a negative relation between the incidence of statistical

significance of μ1 and the degree of variation in π, the net profit margin. For example, in

the modified Jones specification, the significance frequency increases from 69.3% in the

lowest quintile to 82% in the highest quintile.

The relation between μ1 and the accrual determinants is examined further in a

multivariate logistic regression. The dependent variable is an indicator variable which

equals 1 if μ1 is significant. We use explanatory variables which capture the within-

industry variation in the accrual determinants. Essentially, these are the variables by

which we rank the industry-years in the previous tables. We also include as an

explanatory variable the number of observations used in the cross-sectional accrual

models. Obviously, a larger number of observations will lead to a more accurate

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estimation of μ1. We examine whether our results with respect to the variation in the

accrual determinants are robust to the number of observations included in the accrual

model.

The results presented in Table 5 are largely consistent with those in Table 4. First,

as expected, the number of observations in a regression is positively related to the

significance of μ1. Both alpha and gamma are negatively associated with the likelihood of

μ1 being significant. As for β, the weaker results in the univariate analysis do not show up

in the multivariate logistic model. Thus, the within-industry variation in β does not play

an important role in the estimation of μ1. Recall that the pattern for π in the univariate

analysis was opposite to the pattern on the other accrual determinants. In the multivariate

setting, however, the variation in π is not significant.

In summary, Tables 4 and 5 confirm that the accrual determinants are important in

analyzing the empirical results of the Jones model. We discover that assessing the degree

of homogeneity in the industry-group is important in evaluating the Jones models’

results. While the effect of the degree of variation in an explanatory variable on the

coefficient is very intuitive, we identify the identity of the candidates for high variation.

Thus, in industry groups with low variation in accrual determinants, i.e. a relatively

homogenous accrual-generating process, we expect the Jones models to perform better.

It is important to note that the variation within an industry is with respect to the

accrual-generating process. Currently, the industry measure used in this literature, the 2-

digit SIC code, is weak on two dimensions. First, two firms with very different business

environments could still belong to the same group. For example, Bernard and Skinner

(1996) mention that the makers of heavy equipment for the oil and gas industry, video

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games, lawn mowers and personal computers all belong to the same two-digit SIC code.

Second, it is possible that two firms which operate in the same business environment

have different accrual-generating processes as a result of pursuing different business

strategies.

To illustrate these differences, we plot in figures 1-3, the accrual determinants of

four firms that belong to a common 2-digit SIC code (53): Walmart, Target, Kohl’s and

Neiman Marcus. The variation of the accrual determinants of these firms across time as

well as across the industry is striking. For example, Target’s α has decreased from about

0.15 to about 0.07 over the past 25 years. Such dramatic change is also observed in

Neiman Marcus’ α. More importantly, we observe a large variation of α across the four

firms. Similar patterns emerge in the rest of the accrual determinants.

4.4 The bias in discretionary accruals

We now turn to examining the nature and sources of the bias in the outcomes of

the Jones model, i.e. abnormal accruals. Prior studies document that such bias exists in

specific sets of firms. For example, firms that exhibit high levels of growth and extreme

performance. Prior studies, however, do not point to the sources of such biases. The

purpose of our tests is to ascertain whether some of that bias can be traced to

mismeasurement in the Jones’ coefficients. Such finding will enable researchers to direct

efforts at minimizing the measurement error in the coefficients which will then lead to

reduction in the abnormal accruals’ bias.

Measurement error test. In our first set of predictions we attempt to relate the

estimation error in the μ1 coefficients of the Jones model to the bias in abnormal accruals.

We argue that if the measurement error is in the μ1 coefficients, then the degree of

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measurement error will be systematically associated with firm characteristics that are

related to biases in abnormal accruals.

To assess the degree of measurement error in the μ1 coefficients, we compute a

firm-specific predicted coefficient based on the DKW model. We then regress the

difference between the industry-specific estimated coefficient and the firm-specific

predicted coefficient (μ1EST-μ1

PRED ) on several firm characteristics. The results are

reported in table 6.4

First, we examine the regressions whose dependent variable is the absolute value

of μ1EST-μ1

PRED. The results of these regressions are reported on the right-hand side of

Table 6. We predict that since all extreme quartiles are associated with some bias in

abnormal accruals, based on the results in Kothari et al. (2005), there will be a positive

relation between μ1EST-μ1

PRED and indicator variables for whether a firm belongs to an

extreme quartile of BM, Sales growth and Size (EXT_BM, EXT_SALES, and

EXT_SIZE). The estimation results are consistent with this prediction in the case of

EXT_BM. That is, the coefficient on EXT_BM is positive and statistically significant.

Contrary to our prediction, the coefficient on EXT_SALES is negative and statistically

significant while the EXT_SIZE coefficient is negative but statistically insignificant.

In the models whose independent variable is an ordered rank variable with values

ranging from 1 to 4, we are unable to make definitive predictions because it is unclear

whether the biases are stronger in the lower or higher quartiles. An exception is the

QSALES coefficient. From the results in Kothari et. al. (2005), it is evident based on

higher rejection rates, that the biases are larger for lower quartiles of Sales growth.

4 We report results based on estimation of the full form of the Jones model. The models reported in Table 6 are run separately for each set of independent variables. That is, all the models are univariate.

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Therefore, we make a prediction that the coefficient on QSALES will be negative. The

results indicate that in all variables, there exists a strong negative association between the

absolute value of the bias and the ranks of firm characteristics. This means that the bias is

larger and more likely to occur in the lower quartiles of BM, sales changes and size.

Next, we examine the models whose dependent variable is μ1EST-μ1

PRED. Recall,

that the predictions in these models depended on the signs of sales changes. Therefore,

we also run the models separately for firms that experienced increasing or decreasing

sales. Focusing first on the pooled models, under the heading ‘All’, we find that extreme

book-to-market quartiles tend to have an upward bias in the Jones coefficient (a positive

coefficient of 0.0405) and it seems that this bias is larger in lower quartiles, as evidenced

by the negative coefficients (-0.0403) on QBM. The predictions on these coefficients

were ambiguous. When we estimate the models separately based on the sign of changes

in sales, we can relate directly to P3d. For declining sales, the positive coefficient on

EXT_BM is inconsistent with our prediction. However, the positive coefficient on

EXT_BM when sales are increasing is consistent with P3d. This means that the positive

bias in the Jones coefficients appears in both extreme quartiles of book-to-market.

In the cases of sales and size, the results are similar. Some of the results appear

consistent with our predictions (e.g. the negative coefficient on EXT_SALES) while in

other cases the results are insignificant.

In summary, we find some support for our predictions, although not in all cases.

We conclude that there is some evidence that the bias in abnormal accruals is associated

with measurement error in the coefficient on sales in the Jones model. We emphasize that

the results in table 6 are contingent on a well-specified predicted coefficient. While there

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is a theoretical foundation for the use of the predicted coefficient based on the DKW

model, it is unclear whether that coefficient is the “correct” one. Therefore, our results

depend on the validity of this measure.

Abnormal accruals test. In our second test to evaluate the sources of bias in

discretionary accruals, we regress the absolute value of abnormal accruals directly on

three sets of variables. Recall that in this specification we hope to capture the systematic

variation of the bias in abnormal accruals (which is a component of the dependent

variable) with factors associated with mismeasurement of the Jones coefficients. The first

set of independent variables is similar to that examined in Table 6 and includes indicators

for sets of firms that are known to be associated with biased abnormal accruals. The

second set includes firm-specific values of the accrual determinants. Finally, we include

the variable of interest that is supposed to capture factors associated with measurement

error in the Jones coefficients. This variable is the coefficient of variation of each

determinant in a specific industry-year and it is supposed to track the industry-level

heterogeneity of the accrual generating process.

We report the main results in model I in Table 7. Other models are reported to

help interpret some of the results in model I. In the first model, we find that the

dependent variable, the absolute value of abnormal accruals, is systematically associated

with firm-level accrual determinants. Although we have no expectations for these

coefficients, we find it interesting that the accrual determinants still have strong

association with abnormal accruals. Theoretically, all that variation should have been

captured by the Jones model. We believe that this is additional evidence for the

misspecification of the Jones model with respect to the accrual determinants.

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In the next set of variables, we find that extreme BM and Sales growth quartiles

are more likely to have larger (in absolute value) abnormal accruals. Since the absolute

value of abnormal accruals contains a “true” component and a “bias” and to the extent

that the true component is not associated with these quartiles, we argue that this is

evidence that extreme quartiles are associated with more bias. For BM, these results are

consistent with Table 6. However, with respect to Sales growth these results are in

contrast with those in Table 6. As for Size, we observe that extreme size quartiles are

associated with lower abnormal accruals.

Our main interest, however, lies in our proxies for the degree of homogeneity in

the accrual process. Our prediction suggests that an increased variation in the accrual-

generating process, proxied by the coefficients of variation in each accrual determinant,

will lead to more measurement error in the Jones coefficients and thus to more bias in the

firm-specific abnormal accruals. In model I, we find that larger variation in β and γ1

indeed exhibit a positive and statistically significant association with abnormal accruals.

Interestingly, and contrary to our expectations, we find that greater variation in α is

associated with lower absolute value of abnormal accruals. However, since our prediction

is univariate, we would like to assess whether this negative relation holds when only

CV_α is included in the model. According to results from estimating model IV, it seems

that high variation in α is positively associated with the absolute value of abnormal

accruals. When all industry-specific variables are included in the model, such as in

models I and III, the sign on CV_α flips. It is worth mentioning that conceptually, the

variation in the accrual-generating process that we would like to capture is a combined

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variation of all accrual determinants. However, since we do not have a proxy for this

combination, we use the variation in each individual accrual determinant.

Collectively, the results in Tables 6 suggest that the bias in discretionary accruals

can be traced, in part, to the estimation of the Jones model. In particular, there is evidence

that the estimation error in the coefficients that results from heterogeneity in the accrual-

generating process in a 2-digit SIC group is associated with larger biases in abnormal

accruals.

5. Implications of the results

This paper’s results are important to a large strand of the accounting literature.

Any researcher that uses abnormal accruals would be interested in understanding the

effect of our results on popular abnormal accrual measures. We believe that the

implications of these results are different for two groups of studies: (1) studies that use

the absolute value of abnormal accruals and (2) studies that use the signed values of

abnormal accruals.

Absolute value of abnormal accruals. This paper’s results highlight the relation

between the industry group under which the Jones-type models are estimated and the

outcome of the models. Abnormal accruals that are a result of coefficient

mismeasurement will be present in industry groups that have a large variation in their

accrual-generating process. This bias in abnormal accruals will directly affect any study

that investigates the absolute value of abnormal accruals or uses it to investigate a

separate issue. Thus, to understand whether a particular study is exposed to such bias,

researchers need to ask whether the study draws on firms from industries with high

variation in the accrual-generating process represented by the accrual determinants. The

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inclusion of such firms in samples will tend to bias upward the average measures of

absolute value of abnormal accruals.

Suppose researchers are interested in the relation between X and accrual quality

represented by the absolute value of abnormal accruals. The existence of such a relation

will lead researchers to a conclusion. In light of our evidence, the absolute value of

abnormal accruals is correlated with certain industries. If those industries are related to Y,

a set of characteristic variables, and there is a relation between Y and X, then any

conclusion about the relation between X and accrual quality may be premature.

Signed abnormal accruals. The effect of the bias in abnormal accruals that stems

from the inclusion of firms from high-variation industries in the sample on tests that use

signed abnormal accruals is more subtle. Again, suppose researchers use the correlation

between the average abnormal accruals in the sample and some variable, X. In typical

earnings managements studies this is also referred to as the partitioning variable (e.g.

McNichols and Wilson, 1988). In this study, we show that abnormal accruals are

correlated with industries that have a high variation in the accrual-generating process.

One also needs to show that the partitioning variable, X, is correlated with the firms in

these industries that are likely to have positive (or negative) abnormal accruals. However,

we have yet to outline what factors are associated with such firms, or what factors

determine whether biased abnormal accruals will be positive or negative. We will

investigate these issues in future research.

6. Conclusion

In this paper, we investigate the circumstances under which, the lack of explicit

specification in the Jones-type models of the interactions between sales changes, the

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accrual determinants and accruals, has an impact on the reliability of the accrual models.

This endeavor is especially important, since the residuals from the Jones-type models are

used extensively in the literature to make inferences about earnings management or as

proxies for earnings quality.

We initially explore the relationship between these Jones-type models and various

fundamental accrual determinants related to accounts receivable, accounts payable,

inventory and profit margins. We document that the coefficient on sales changes derived

from the Jones-type models does in fact capture some of the relationship between sales

changes and accrual determinants. The four accrual determinants in our study are

associated with μ1 (the coefficient on sales changes) from the Jones-type models in the

predicted direction. However, we argue that the relationship between sales changes and

accruals is more complex.

Next, we examine the impact of the degree of homogeneity in accrual

determinants in a given industry on the estimation quality of the Jones-type models.

Using univariate and multivariate tests we find that the degree of homogeneity in accrual

determinants and the significance of μ1 in the Jones-type models are related. The within-

industry variation in the accounts receivable parameter and the inventory parameter are

negatively associated with the likelihood that μ1 will be significant. Therefore, we

conclude that assessing the within-industry variation in the accrual determinants is

important when evaluating results from the Jones-type models. We expect that in

industries with low variation in accrual determinants, the Jones-type models will perform

better than in industries with high variation.

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Finally, we attempt to identify the source of the bias in abnormal accruals. We

find the measurement error in the Jones’ coefficient on sales changes is related to various

factors shown in prior literature to be associated with bias in abnormal accruals. We also

find that the absolute value of abnormal accruals, which includes a bias component, is

associated with the degree of within-industry homogeneity in the accrual determinants.

In summary, we conclude that the measurement of abnormal accruals is

significantly affected by measurement error in the coefficient on sales changes in the

Jones model. This measurement error stems from heterogeneity in the accrual-generating

process of firms that are grouped together for the regression estimations. We believe that

to reduce biases in abnormal accruals, researchers should focus on estimating the Jones-

type models in groups that are as homogeneous as possible with respect to their accrual-

generating process. We show that the implied assumption that 2-digit SIC codes represent

such homogeneity may not be descriptive.

We do not comment on other potential sources for bias or measurement errors in

abnormal accruals. These include mis-calculation of the accrual variable itself (e.g Hribar

and Collins, 2000 and Francis and Smith, 2005) or econometric biases that affect the

estimated coefficients and result from violation of the classical assumptions.

Our study has implications for the findings of most studies that use a measure of

abnormal accruals computed using a Jones-type model. While we do not explicitly

recommend an alternate model for eliminating the bias in abnormal accruals, our study

provides a better understanding of the sources of the bias which creates a strong

foundation for building a more appropriate model for estimating abnormal accruals.

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7. References

Ashbaugh, H., LaFond, R., Mayhew, E., 2003, Do nonaudit services compromise auditor independence? Further evidence, The Accounting Review 78(3), 611-639.

Bartov, E., Gul, F., Tsui, J., 2001, Discretionary-accruals models and audit qualifications, Journal of Accounting & Economics 30, 421-452.

Bernard, V., Skinner, D., 1996, What motivates managers’ choice of discretionary accruals?, Journal of Accounting & Economics 22, 313-325.

Dechow, P., Kothari, S.P., Watts, R., 1998, The relation between earnings and cash flows, Journal of Accounting & Economics 25, 133-168.

Dechow, P., Richardson, S., Tuna, I., 2003, Why are earnings kinky? An examination of the earnings management explanations, Review of Accounting Studies, 8, 355-384.

Dechow, P., Sloan, R., Sweeney, A., 1995, Detecting earnings management, The Accounting Review 70, 193-225.

DeFond, M., Jiambalvo, J., 1994, Debt covenant violation and manipulation of accruals: Accounting choice in troubled companies, Journal of Accounting & Economics 17, 145-176.

Fields, T., Lys, T., Vincent, L., 2001, Empirical research on accounting choice, Journal of Accounting & Economics 31, 255-307.

Francis, J., Smith, M., 2005, A reexamination of the persistence of accruals and cash flows, Journal of Accounting Research 45(3), 413-451.

Frankel, R., Johnson, M., Nelson, K., 2002, The relation between auditor’s fees for non-audit services and earnings management, The Accounting Review 77(supplement), 71-105.

Hribar, P., Collins, D., 2002, Errors in estimating accruals: Implications for empirical research, Journal of Accounting Research 40(1), 105-134.

Kothari, S.P., 2001, Capital markets research in accounting, Journal of Accounting & Economics 31, 105-231.

Kothari, S.P., Leone, A., Wasley C., 2005, Performance matched discretionary accruals measures, Journal of Accounting & Economics 39(1), 163-197.

Larcker, D., Richardson, S., 2004, Fees paid to audit firms, accrual choices, and corporate governance, Journal of Accounting Research, 42(3), 625-658.

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Francis, J., LaFond, R., Olsson, P., Schipper, K., 2005, The market pricing of accrual quality, Journal of Accounting & Economics 39, 295-327.

McNichols, M., 2000, Research design issues in earnings management studies, Journal of Accounting and Public Policy 19, 313-345.

McNichols, M., Wilson, G. P., 1988, Evidence of earnings management from the provision for bad debt, Journal of Accounting Research, 26 (Supplement), 1–31.

Myers, J., Myers, L., Omer, T., 2003, Exploring the term of the auditor-client relationship and the quality of earnings: A case of mandatory auditor rotation?, The Accounting Review 78(3), 779-799.

Subramanyam, K.R., 1996, The pricing of discretionary accruals, Journal of Accounting & Economics 22, 249-281.

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Figure 1. Accrual determinants of four firms in the retail industry (SIC code=53). Alpha - Accounts receivables

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Table 1. Summary Statistics and Correlations. This table presents summary statistics of and correlations between the accrual determinants. For each year, we calculate and report the 5-year averages of each determinant. If the firm does not have a 5-year history, we use the maximum number of past years for which there is data as of year t. The variables are calculated as follows. α= (ARt + ARt-1)/2*SALESt

; β=(APt + APt-

1)/2*SALESt (1-π); γ1= g1/(1-π) truncated above at 1 and below at -1; g1 is obtained from the following regression INVt = g1*SALESt + g2*ΔSALESt + εt ; π= NIt / SALESt

Panel A

var mean std max q3 median q1 min

α 0.245 0.439 8.150 0.242 0.167 0.114 0.003

β 0.108 0.125 1.838 0.117 0.078 0.053 0.000

γ1 0.129 0.118 0.828 0.196 0.110 0.028 -0.009

π -0.682 4.383 0.503 0.060 0.023 -0.040 -82.237

Panel B

α β γ1 π

α

β 0.3667***

γ1 -0.0006 -0.0006

π -0.0405*** -0.0003 0.0042*

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Table 2. Summary Statistics. This table presents medians of the accrual determinants calculated separately for quartiles of book-to-market, market capitalization, return on assets, changes in sales and price-to-earnings ratio. For each year, we calculate and report the 5-year averages of each determinant. If the firm does not have a 5-year history, we use the maximum number of past years for which there is data as of year t. The variables are calculated as follows. α= (ARt + ARt-1)/2*SALESt

; β=(APt + APt-

1)/2*SALESt (1-π); δ= ; γ1= g1/(1-π) truncated above at 1 and below at -1; γ2=-g2/g1; g1 and g2 are obtained from the following regression INVt = g1*SALESt + g2*ΔSALESt + εt ; π= NIt / SALESt

1 2 3 4

Panel A: Book-to-Market ratio

α 0.199 0.176 0.163 0.157

β 0.090 0.078 0.075 0.072

γ1 0.064 0.114 0.128 0.149

π -0.052 0.040 0.035 0.020

Panel B: Market Capitalization

α 0.177 0.179 0.173 0.159

β 0.083 0.076 0.073 0.078

γ1 0.118 0.126 0.117 0.109

π -0.014 0.018 0.035 0.054

Panel C: Return on Assets

α 0.212 0.165 0.150 0.158

β 0.095 0.081 0.075 0.066

γ1 0.066 0.115 0.120 0.133

π -0.164 0.018 0.042 0.061

Panel D: Changes in Sales

α 0.180 0.164 0.166 0.159

β 0.083 0.083 0.074 0.076

γ1 0.108 0.078 0.126 0.119

π -0.003 0.039 0.035 0.026

Panel E: Price-to-Earnings ratio

α 0.213 0.148 0.157 0.183

β 0.093 0.073 0.070 0.077

γ1 0.072 0.135 0.133 0.119

π -0.109 0.034 0.050 0.043

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Table 3. The relation between Jones coefficients and accrual determinants. The table reports regression results of the actual coefficient on changes in sales (μ1) estimated using a Jones/Modified Jones models or the reduced form of each of them. Each observation is an industry-year. Industry is a 2-digit SIC code. T-stats are reported in parentheses. α, β, γ1 and π are the accrual determinants described in Dechow et al. (1998). For each industry-year, the independent variables are the average α, β, γ1 and π for that industry-year.

Regular Reduced Form

Jones Modified Jones Jones Modified Jones

Intercept 0.0023 (0.22)

-0.0046 (-0.38)

0.0599*** (6.32)

0.0594*** (5.66)

α 0.4290*** (9.08)

0.3431*** (6.32)

0.6103*** (14.34)

0.4822*** (10.23)

β -0.6941*** (-6.52)

-0.6996*** (-5.72)

-0.8736*** (-9.11)

-0.8631*** (-8.12)

γ1 0.5532*** (15.9)

0.5842*** (14.62)

0.4428*** (14.13)

0.4604*** (13.26)

π 0.0148* (1.73)

0.0114 (1.16)

0.0246*** (3.20)

0.0246*** (2.89)

N 1,434 1,434 1,434 1,434

R2 0.1990 0.1620 0.2305 0.1787

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Table 3. The relation between Jones coefficients and accrual process parameters. Fama-MacBeth estimation by year. (t-stats in parentheses)

Regular Reduced Form

Jones Modified Jones Jones Modified Jones

Intercept 0.0032 (0.27)

-0.0069 (-0.48)

0.0566*** (4.82)

0.0533*** (4.16)

α 0.4231*** (7.92)

0.3486*** (5.77)

0.6390*** (13.11)

0.5252*** (9.70)

β -0.7283*** (-7.13)

-0.7335*** (-6.92)

-0.9152*** (-9.99)

-0.8948*** (-8.45)

γ1 0.5851*** (10.84)

0.6249*** (11.37)

0.4632*** (9.79)

0.4871*** (11.18)

π 0.0208 (1.00)

0.0447 (1.51)

0.0337 (1.27)

0.0698 (1.85)

N 28 28 28 28

R2 0.2831 0.2434 0.3209 0.2616

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Table 4. The table reports the frequencies with which μ1 (the coefficient on change in sales in the Jones-type models) is statistically significant separately for each quintile of dispersion in the accrual parameters. We rank industry-years (where industries are defined as two-digit SIC codes) to quintiles based on the coefficient of variation of each accrual determinant. The accrual determinants are those described in Dechow et al. (1998).

Regular Reduced Form

Jones Modified Jones Jones Modified Jones

Panel A: α

Low 59.5% 81.9% 47.4% 70.1% 1 60.1% 78.7% 49.1% 71.7% 2 55.6% 78.1% 47.1% 69.4% 3 46.8% 73.6% 38.4% 62.3%

High 39.1% 62.1% 33.4% 53.6%

Panel B: β Low 50.9% 75.3% 44.2% 70.1%

1 60.1% 81.8% 49.5% 73.6% 2 51.5% 71.9% 44.5% 63.5% 3 52.4% 75.6% 40.8% 63.6%

High 46.3% 69.8% 36.2% 56.7%

Panel C: γ1 Low 68.2% 85.0% 55.8% 78.3%

1 69.0% 84.2% 61.4% 77.9% 2 55.7% 75.5% 45.6% 67.4% 3 35.0% 63.8% 28.9% 49.8%

High 34.2% 66.4% 22.8% 52.5%

Panel D: π Low 41.1% 69.3% 35.0% 55.4%

1 43.6% 68.8% 32.8% 59.0% 2 48.3% 71.8% 39.0% 59.1% 3 64.3% 82.6% 53.4% 72.2%

High 64.0% 82.0% 49.7% 75.0%

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Table 5. This table reports logit regressions. The dependent variable equals 1 if the coefficient μ1 for that industry-year is significant. The dependent variables are the coefficient of variation of each accrual determinant in the specific industry-year. In addition, the number of observations (Nobs) in each accrual regression model in each industry-year is also included as an independent variable.

Regular Reduced Form

Jones Modified Jones Jones Modified Jones

Intercept 0.4078*** (0.1835)

0.2490 (0.1997)

0.6680*** (0.2136)

0.9612*** (0.2109)

CV_α -0.7101***

(0.1365) -0.4107***

(0.1473) -0.7815***

(0.1435) -0.4826***

(0.1425)

CV_β 0.3428

(0.2520) -0.1422 (0.2849)

-0.3322 (0.2566)

-0.3168 (0.2763)

CV_γ1 -0.6395***

(0.0961) -0.6441***

(0.1089) -0.0216 (0.0355)

-0.5143*** (0.0951)

CV_π -0.0005 (0.0004)

-0.0005 (0.0005)

0.0006 (0.0007)

0.0019 (0.0012)

Nobs 0.0074*** (0.0074)

0.0055*** (0.0006)

0.0224*** (0.0020)

0.0109*** (0.0012)

N 1,662 1,435 1,662 1,435

Pseudo-R2 0.1329 0.1066 0.1808 0.1354

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Table 6. This table reports regressions of the bias in μ1 on ranks of various variables. The dependent variable is the difference between the estimated μ1 from cross-sectional Jones models on an industry level to the predicted firm-level μ1 calculated from the DKW formula as follows: *** GIVE the formula ** The regression models are estimated separately for each year. The reported coefficients are averages of 32 annual coefficients and the t-statistics are based on standard errors calculated from the time-series standard deviation. The independent variables are either (1) Quartiles of BM/Growth in sales or size (0,1,2,3) calculates for each firm separately each year or (2) an indicator variable (EXT_BM) which equals 1 if the firm belongs to an extreme (either high or low) quartile. Dependent variable = μ1

EST-μ1PRED Dependent variable =

ABS(μ1EST-μ1

PRED) All Ch_Sales<0 Ch_Sales>0 All

QBM ? -0.0403*** (-7.39)

? -0.0527*** (-6.65)

? -0.0356*** (-7.53)

? -0.0295*** (-7.33)

EXT_BM ? 0.0405*** (4.24)

- 0.0513*** (5.00)

+ 0.0429*** (4.30)

+ 0.0875*** (9.27)

QSALES + 0.0048 (1.72)

0.2846*** (7.84)

-0.0034 (-0.94)

- -0.0229*** (-9.78)

EXT_SALES - -0.0104* (-1.91)

- -0.2846*** (-7.84)

- 0.0128*** (2.30)

+ -0.0116*** (-2.41)

QSIZE ? -0.0116*** (-2.70)

+ -0.0078 (-1.77)

- -0.0164*** (-3.27)

? -0.0578*** (-10.26)

EXT_SiZE + 0.0036 (0.69)

0.0089 (0.88)

0.0011 (0.17)

+ -0.0137 (-1.75)

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Table 7. This table reports regressions results of models whose dependent variable is the absolute value of abnormal accruals generated using the regular Jones model. The independent variables are firm-sepecific accrual determinants: α, β, γ1 and π; firm-specific indicator variables that equal to 1 if the firm-year observations appears in one of the extreme quartile of the cross-sectional distribution of book-to-market ratio (EXT_BM), market capitalization (EXT_SIZE) and annual changes in sales (EXT_SALES); and industry-level measures of the coefficient of variation of accrual determinants in a particular industry-year – CV_α, CV_β, CV_γ1 and CV_π. T-stats appear in parentheses.

I II III IV V VI VII Intercept -0.003*** 0.059*** 0.040*** 0.076*** 0.036*** 0.072*** 0.080***

(-2.20) (98.61) (32.86) (93.68) (31.77) (144.29) (244.90) α 0.015*** 0.021*** (12.09) (17.24) β 0.090*** 0.093*** (29.03) (29.47) Γ1 0.060*** 0.036*** (20.23) (12.71) π -0.004*** -0.004*** (-38.96) (-38.51)

EXT_BM 0.013*** (20.78)

EXT_SIZE -0.006*** (8.53)

EXT_Sales 0.041*** (65.02)

CV_α -0.007*** -0.008*** 0.004*** (-7.26) (-8.18) (4.65)

CV_β 0.052*** 0.062*** 0.061*** (30.02) (35.20) (39.62)

CV_γ1 0.003*** 0.002*** 0.008*** (8.3) (4.43) (20.20)

CV_π -0.001 -0.001* -0.001*** (1.19) (-1.86) (-2.86)

N 154,313 176,923 176,923 176,923 176,923 176,923 176,923

R2 0.0659 0.0272 0.0106 0.0001 0.0101 0.0026 0.0000