Measurement of PEM

1.1. Intra-Year Timing of Earnings Management

Our method is based on the premise that earnings management primarily takes place near the fiscal

year end. With many forces in action, managers have to weigh among alternative motives, calculate a target

earnings level, compare with actual results, and finally decide in what direction and to what degree to

manage earnings. In the early interim periods, there is a great deal of uncertainty concerning both the

management incentives and the actual results. Only later in the year or at the very year-end is the

uncertainty resolved or significantly reduced. Therefore, the closer to the fiscal year end, the less the

uncertainty would be, and the more active earnings management would be. 5

Foster (1986, pp. 225-226) gives a number of examples of such intra-year timing of earnings

management. From an institutional perspective, there are two distinct approaches to interim reporting in

GAAP: the discrete approach views an interim period in the same way as an annual period; the integral

approach views an interim period as a component part of the annual period. APB Opinion 28 generally

favors the integral approach. Under this approach, the fourth quarter becomes a “dumping ground”

(Collins, et al., 1984) in that various adjustments are made in the fourth quarter in order for the interim

results to be consistent with the annual results. Various auditing techniques such as the cutoff test and the

kiting test are designed to deal with the year-end discretion (e.g., Arens and Loebbecke, 1994).

Earnings management may go either direction if not conditional on specific motives. Thus, higher

intensity of earnings management should be reflected in the higher accrual volatility. The increased

incidence of earnings management in the fourth quarter will increase the volatility of fourth quarter

accruals. The other three quarters with relative lower earnings management intensity comprise the base

period for comparison. Formally, we state our working hypothesis as follow:

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Hypothesis: Earnings Management Leads to First-Order Stochastic Dominance of Fourth Quarter Accrual

Volatility over the Base Period.

1.2. Accrual Volatility

The derivation of PEM indices is based on the relative magnitude of fourth quarter accrual

volatility to the base period of the first three quarters. Accrual volatility is measured by the absolute value

of accruals. We apply the Jones’ Model (1991) to control for mechanical adjustments. The controlling

factors include total assets, change in revenues, and gross property plant and equipment.6

TA = α + β

1×ΔRev + β

2×PPE + β

3×1/Ave_A + ε (1)

The residuals from (1), called discretionary accruals (DA) in the literature, provide an estimate of quarterly

accruals purged of mechanical adjustments. We take the absolute value of discretionary accruals (ADA) as

the basis for deriving PEM2.

1.3. KS Distance and PEM Indices

Our PEM indices are based on comparisons of the distributions of accrual volatility between the

base period and the fourth quarter. For PEM1 and PEM2, we use the Kolmogorov-Smirnov (KS) Distance

to measure first order stochastic dominance of the fourth quarter accrual volatility over the other three

quarters. The KS Distance is the maximum vertical distance between the empirical cumulative distribution

functions of the two random variables. Since the KS Distance follows an asymptotic limiting distribution

given in Smirnov (1939), we can construct an index that not only has the convenient feature of being

bounded in [0,1], but also has the valuable feature of having known statistical properties.7 The KS Distance

does not require the accrual volatility to follow a parametric distribution.

We apply KS Distance to total accruals to get PEM1, and to the residuals from the Jones Model to

get PEM2. Conover (1980) points out that the KS Distance is powerful in the center of the distributions,

even when the distributions are not well behaved. But, it is not powerful for measuring first order stochastic

dominance in the tails of the distributions. To measure the behavior at the right tail of the distribution, we

develop PEM3 and PEM4. For PEM3, we define θ as the value at the 95th percentile of absolute total

accruals (ATA) for the base period, and then find the fraction of fourth quarter ATA exceeding θ. We

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subtract 5% from this fraction, as 5% is the expected proportion of absolute accruals exceeding θ under the

null hypothesis of no earnings management. The resulting value is PEM3.8 Hence while PEM1 and PEM2

focus on the patterns of “common” earnings management, PEM3 measures the pervasiveness of large

earnings management. We report the result using measures based on Absolute Total Accruals (ATA), but

extensive additional work yielded qualitatively similar results when Absolute Discretionary Accruals

(ADA) are used instead.

The distance between fourth quarter and based period accrual volatility distributions depends on

the magnitude of earnings management and the percentage of firms involved in earnings management.

Assuming a given magnitude of earnings management, we can estimate the pervasiveness from this

distributional distance. PEM4 is derived from a simulation that randomly adds accruals of a given

magnitude to existing observations in the base period and compares the resulting distribution to the fourth

quarter distribution. The simulation can be summarized in the following four steps:

1. For each quarter i, (i = 1, 2, 3), standard deviations of discretionary accruals are calculated

from quarter-specific Jones Model regressions.

2. A simulated accrual with magnitude of one or two standard deviations is added to or subtracted

from the total accruals of a percentageλ of firms randomly chosen from the COMPUSTAT

sample.

3. The Jones Model is re-estimated and corresponding volatility of discretionary accruals are

calculated.

4. The mean and median of the re-estimated volatility are compared with the fourth-quarter

volatility. The percentageλ is slowly adjusted until the mean (median) of simulated accrual

volatility equals to the observed fourth quarter volatility. PEM4 is the critical value λ *.

PEM4 can be interpreted as the percentage of firms engaged in earnings management of a given magnitude.

We should view all PEM indices as ordinal measures at this early stage of methodological development.

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2. Empirical Results

2.1. Sample Selection

We obtain our sample from the 1997 COMPUSTAT Industrial Files quarterly database, which covers

from the first quarter of 1987 to the third quarter of 1997. The sample consists of all firm/quarters that satisfy

following selection criteria:

1) The necessary firm quarter data have no missing values.

2) The firm is not a financial institution (SIC 6000 to 6999), or unclassified (SIC > 9900).

3) There are at least 24 firm quarter observations per regression where relevant.

Since most firms included in the sample have consecutive quarterly observations in a given year, the third

criterion roughly requires a minimum of six firms per industry per year for sample inclusion. After

discretionary accruals are obtained from the preliminary regressions, we trim our sample by deleting those

firm quarters with discretionary accruals, operating cash flows, or nondiscretionary accruals in the extreme

1% of the entire distribution.

Our final sample comprises 77,574 firm quarters from 4,116 firms in 51 (364) 2-digit (4-digit) SIC

code industries. Table 1 provides the descriptive statistics for the major variables used in the empirical

analysis below. The table is divided into three panels roughly representing the estimation strategy followed in

the analysis. The first panel presents fundamental measures of the sample firms, while the second and third

panels present regression variables used in Tables 2 and 3. Where appropriate, variables are scaled by book

value of assets to facilitate comparison across firms.

Insert Table 1 Here

Overall the firm size distribution based on average assets (Ave_A) for our sample is representative in

that it lies between the distributions for all firms reported by COMPUSTAT and the distribution for NYSE

firms, based on a comparison of the quartile values reported in Table 1 to values extracted from the full

COMPUSTAT universe for the same time period. Similarly, when annualized the distribution of net income

is similar to the distributions for the full COMPUSTAT and NYSE firms over the same time period. Total

accrual (TA) is the difference between net income and operating cash flows (measured by COMPUTSTAT

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quarterly items 8 and 108, respectively)9, and this variable serves as the starting point for our measures of

PEM. In particular, PEM1 is based on the absolute value of total accruals (ATA). PEM2 is based on accruals

purged of mechanical factors, or absolute discretionary accruals (ADA).

The second panel of Table 1 describes regressors used in the Jones Model (assets is presented in the

previous panel). The third panel shows regressors for seasonal accrual volatility, though dummy variable

distributions are not reported. Discussion of these variables and their use in regressions is deferred to Table 3.

It should be noted here that Tax_diff is defined as the difference between the fourth quarter realization of the

effective tax rate and the estimated rate used in the first three quarters. Hence it is normalized to zero for the

first three quarters, and the summary statistics represent only fourth quarter values.

Insert Tables 2 Here

The estimation of Jones Model is based on the cross-sectional regressions for each combination of

two-digit SIC codes and fiscal year, pooling the quarterly observations within the year (see Subramanyam

(1996) for detail). Hence we estimate a total of 436 regressions for the Jones Model. Table 2 presents the

regression results. Both estimates and tests are consistent with the results in the literature. 10 The mean

adjusted R2 is 6.9%. The discretionary accruals (DAs) are measured as the residuals from the regressions.

The absolute value of DA (ADA) is used as the basis for deriving PEM2 and as the dependent variable in

the examination of the association between accrual volatility and earnings management in Table 3.

2.2. Earnings Management and Seasonal Accrual Heteroskedasticity

Our measurement of PEM is based on the premise that earnings management leads to seasonal

accrual heteroskedasticity. The first step for establishing the validity of our measurement is to show

empirical validity of this working hypothesis. Table 3 provides direct evidence by using regression results

from equation (2):

ADA =α′ z + ε (2)

The dependent variable, ADA, is the absolute value of the Jones Model residual, which provides an estimate

of accrual volatility purged of mechanical factors. When we substitute ATA for ADA, the results are similar

to those in Table 3. Control for mechanical factors using Jones Model does not matter much in our analysis

8

of heteroskedasticity. The approach used in equation (2) is similar to Glesjer’s (1969) approach to

modeling determinants of heteroskedasticity.

We specify four groups of explanatory variables z in Table 3. The first is a set of seasonal dummies

that measure the unconditional seasonal pattern in accrual volatility. The second is a set of industry

dummies to control for differences in accrual patterns across industries due to unobserved factors. The third

group includes potential earnings management drivers suggested in previous literature.11 The fourth group

is intended to measure the differential effect of earnings management drivers in the fourth quarter

compared to the first three quarters, the main variables of interest in Table 3. The empirical significance of

the last set of explanatory variables provides validity to our working hypothesis that earnings management

leads to seasonal accrual heteroskedasticity. This working hypothesis allows us to construct indirect indices

based on quarterly accrual volatility for measuring the pervasiveness of earnings management.

Specification 1 in Table 3 shows the pattern of accruals across quarters and industries. It is

immediately apparent that accrual volatility is higher in the fourth quarter. Specification 2 adds the earnings

management drivers, discussed individually below. Specification 3 uses earnings management drivers

without the quarter and industry effects. The difference between specifications 2 and 3 shows that the

earnings management drivers explain most of the variance and are relatively stable estimates with respect

to the inclusion of the dummies. Specification 4 omits insignificant variables in specification 3 and any

further variables that subsequently become insignificant. The remaining set are all statistically significant at

conventional levels, and show that at least some measures associated with earning management, including

the tax rate, leverage, operating cash flow, and annual loss, are related to fourth quarter differential effects

in accrual volatility. We now discuss individual effects in more detail.

Insert Tables 3 Here

The ten explanatory variables in the “Earnings Management Drivers” group are identified in the

literature as possible drivers of earnings management. For all ten drivers, Table 3 shows either estimates

consistent with presence of earnings management, or statistically insignificant estimates under various

levels of control for seasonal and industry factors. The first driver is regulation: a tighter regulatory

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environment reduces the firm’s ability to manage accruals in general and in the fourth quarter specifically.

Table 3 shows that the parameter estimates for regulation are negative and significant in both the crosssection

and for the fourth quarter effect.12

Literature suggests that firm size (Ave_A) and age are both positively associated with quality of

information environment.13 Therefore, these two earnings management drivers should be negatively

associated with seasonal heteroskedasticity. Age is measured as the difference between the observation

year and the first year the company’s data appears in either COMPUSTAT or CRSP, whichever is earlier.

Table 3 shows that age has the predicted sign and is statistically significant. Since we use the inverse of

size (consistent with Jones, as above), the expected sign for the size measure in Table 3 is positive. The

estimated effect is negative but statistically insignificant. Size is also insignificant when seasonal and

industry dummies are omitted in specification 3.

Firms are required to make their best estimate of the effective tax rates expected to be applicable

for the full fiscal year and then to apply these rates to interim income. The farther this rate is from the

actual annual rate, the more fourth-quarter adjustment is needed. Hence, the variable Tax_diff is included

in Panel (D) only. Tax_diff measures the difference between the average estimated rate in the first three

quarters and the realized rate as of the end of the year, and normalizes the first three quarters to zero. This

is an approximation of the surprise in the tax rate to the extent that tax rates estimated from data for the first

three quarters are used to form expectations of annual rates. We expect that the surprise will require

adjustments to taxes payable and deferred taxes, and hence have a positive impact on accrual volatility in

the fourth quarter. Specification 2 shows that the effect of Tax_diff is positive and statistically significant,

as predicted. Tax_diff continues to be significant when quarter and industry dummies are dropped.14 It

should be noted that regulation, size, age, and the fourth quarter tax rate surprise might all be viewed either

as causing mechanical or as limiting discretionary adjustments. In either event they should be included if

significant so that any adjustment effects will not be attributed to other regressors.

Higher audit quality should decrease cross-sectional accrual heteroskedasticity by increasing

constraints on managers. The first three quarterly reports are simply reviewed, whereas annual earnings are

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typically fully audited by CPAs. If the fourth-quarter accrual volatility is mainly due to earnings

management, higher quality auditing should decrease the discretion available to managers and decrease the

variability of fourth-quarter discretionary accruals. We measure audit quality with a dummy variable for

engaging a non-Big-5 audit firm (Auditor). Hence we expect that our proxy should have positive effects in

both cross-section and fourth quarter. The results in Table 3 indicate that audit quality has the predicted

sign in panel (C), but that the marginal impact is negative in the fourth quarter. The negative effect is only

marginally (10%) significant when industry and seasonal dummies are excluded, and drops out entirely in

specification (4).

We expect that looser bond covenant constraints measured in terms of debt/equity ratio will

increase seasonal heteroskedasticity. We include two measures of leverage: Lev1 = total liabilities/total

assets, and Lev2 = long-term debt/total assets. We include two measures because leverage can affect

accrual variance in two different ways. Lev1 is expected to have a positive effect because it measures the

short-term need to manage earnings either up to avoid technical default of debt covenants (Defond and

Jiambalvo, 1994) or down to facilitate renegotiation of debt contracts (DeAngelo, et al., 1994). On the other

hand, Lev2 is expected to have a negative effect because it proxies for restrictions placed by debt contracts

on managers’ choices of accounting procedures (Watts and Zimmerman, 1986, Ch. 9) and creditors’

general monitoring levels. Specification 2 shows that both leverage measures are statistically significant in

the expected directions, both cross-sectionally and in the fourth quarter. Lev1 becomes insignificant in

specification (4).

We include three measures of the effects of cash flows, all with positive expected effects. Our

proxies for this effect include the firm-specific standard deviation of operating cash flow within firm

(SD_OCF); a quarter-specific difference from firm’s median operating cash flow, OCF_m = |current

quarter operating cash flow – firm’s median operating cash flow|; and a quarter-specific difference from

industry median operating cash flow, OCF_indm = |current quarter operating cash flow – industry median

of operating cash flow|. In general, higher variability of operating cash flow will lead to higher crosssectional

and seasonal heteroskedasticity of accruals as managers strive to offset the variability and smooth

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income. Managers have several reasons for smoothing income, including bonus considerations (Healy,

1985). All three cash flow measures are statistically significant in the expected direction in the cross section

in specifications 2 to 4, but the fourth quarter results are mixed. Finally, firms showing a loss for the year

will exhibit seasonal heteroskedasticity. We define Loss = 1 if net income is negative, 0 otherwise, and thus

expect a positive effect. Basu, et al. (1997) suggested that losses contain more transitory elements. Chen

and Lee (1995) find that bonus-related big baths take place in loss years. Our results indicate the loss effect

is strongly positive in the fourth quarter, when year-end adjustments are made.

Although this list of earnings management drivers is likely not exhaustive, we have examined a

fairly large set of drivers found in the literature. The overall results in Table 3 appear to support our

working hypothesis that the difference in accrual volatility between the fourth quarter and the base period is

attributable to earnings management. We provide additional evidence in support of this later, but for the

moment proceed to construct PEM indices based on seasonal heterocedasticity.

2.3. Distributional Properties of Accrual Volatility

Since the construction of PEM indices is based on first-order stochastic dominance of fourth

quarter accrual volatility over the other three quarters, we conduct a preliminary examination on the

distributionsl properties of accrual volatility in Table 4. Moreover, we examine how much the Jones Model

for mechanical factors affects the distributional properties. We report the mean, standard deviation, first

quartile, median, and third quartiles of the distributions. We conduct t-tests to examine the hypothesis that

fourth quarter accrual volatility stochastically dominates the other three quarters. Since accrual volatility is

not normally distributed, parametric t-tests may be biased. In the next subsection, we apply the

nonparametric KS Distance to measure the first order stochastic dominance.

## Measurement of PEM

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