Measurement of PEM

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


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