working paper series...positive earnings, and 6.5 percent of firms try to beat the earnings from...

College of Business Administration

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2005/2006 No. 6

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Office of the DeanCollege of Business AdministrationBallentine Hall7 Lippitt RoadKingston, RI 02881401-874-2337www.cba.uri.edu

William A. Orme

Shaw Chen, Bing-Xuan Lin, Yaping Wang, Liansheng Wu

A Parametric Model and Empirical Analysis

Detecting the Frequency and Magnitude of Earnings Management

Detecting the Frequency and Magnitude of Earnings Management


Shaw Chen*, Bing-Xuan Lin*, Yaping Wang**, Liansheng Wu**

* College of Business Administration, University of Rhode Island, Kingston , RI 02881

** Guanghua School of Management, Peking University, Beijing 100871, China

August 2005

Abstract

We apply a parametric model to estimate both the magnitude and frequency of

earnings management across all firms in the economy. Specifically, we model the

distribution of earnings as a mix-normal distribution and obtain parameter estimators that

measure the frequency and magnitude of earnings management under three different

thresholds. We show that the incentive to meet or beat analysts’ forecasted earnings is the

greatest (over 9% of our sample firms). On the other hand the magnitude is the greatest

when firms manage earnings to avoid earnings decreases (over $585 billion between

1976 and 2004). We also find evidence that firms actively manage earnings to avoid

losses. Our paper overcomes many of the deficiencies in previous studies and is the first

attempt to discover both the extent and scope of earnings management in U.S. market.

JEL classification: M41; G10; G30; C89

Keywords: Earnings management; earnings distribution; analysts’ forecasted earnings

1

Detecting the Frequency and Magnitude of Earnings Management:


The practice of earnings management (EM) by corporate management has long

been recognized in academic literatures (See DeAngelo 1988; Jones 1991). Prior

researches have examined various incentives and approaches of earnings management

and shown that the pervasiveness of earnings management has reached to a level that

significantly compromises the integrity of financial reporting (See Healy and Wahlen

1999). In his 1998 remark concerning earnings management, Chairman of SEC, Arthur

Levitt, commented “…I fear we are witnessing erosion in the quality of earnings, and

therefore the quality of financial reporting.” Since equity returns as well as

management’s compensation are highly related to the firm’s cumulative earnings (Easton,

Harris and Ohlson (1992); Gaver, Gaver and Austin (1995)), managers have very strong

incentives to use judgment in financial reporting and in structuring transactions to alter

financial reports.

Studies on detecting EM are largely based on (1) aggregate accruals, (2) specific

accruals, or (3) distribution of earnings after management (McNichols 2000); however

we still do not have sufficient understanding regarding the extent and the scope of

earnings management (See Healy and Wahlen 1999). For the obvious reason that the true

earnings are often unobservable, it is not an easy task to infer how often and/or how large

earnings are managed. In this paper, we assume that the distribution of earnings follows a

2

mixed normal distribution1 and use a parametric model to estimate the frequency and

magnitude of earnings management when firms try to avoid reporting (1) negative

earnings, (2) earnings below those of prior year, and (3) earnings below analysts’

forecasted earnings.

We make several contributions to the extant literature. First of all, our model fills

the gap in the existing research and provides a theoretical model and a simple framework

to estimate the frequency and magnitude of earnings management at different thresholds.

Unlike previous studies (Tech, Wong and Rao (1998), Sweeney (1994)), our studies are

not conditioned on a specific corporate event and therefore are more applicable to the

study of the overall economy. To our knowledge, it is the first model that simultaneously

estimates the frequency and magnitude of EM in one unified framework. Secondly, we

provide a model that overcomes many of the limitations in some popular models such as

Degeorge, Patei and Zeckhauser (1999) and Burgstahler and Dichev (1997). Our model

belongs to the group where EM are detected based on the overall earnings distribution,

however we do not rely on the choices of interval width, nor do we apply the assumption

of symmetry as in Burgstahler and Dichev (1997). In addition, our model has the least

amount of information attrition when compared to extant models that examine earnings

distribution. We find that less than 2 percent of firms engage in earnings to announce

positive earnings, and 6.5 percent of firms try to beat the earnings from prior year, and

9.33 percent of firms aim to meet or beat analyst forecasted earnings. The magnitude of

EM is around $30 billion for loss aversion, over 585 billion for avoiding earnings

decreases, and around $15 billion for meeting or beating analyst forecasted earnings. The

1 Previous studies have shown both the earnings and the analyst forecasts are skewed (Frecka and Hopwood (1983), Gu and Wu (2003)); therefore tests based on the normal distribution are not well specified and the use of mixed normal distribution is more appropriate.

3

frequency of EM is the highest for firms trying to meet or beat analysts’ forecasted

earning, while the magnitude is the largest for firms that try to avoid earnings decreases.

The remainder of the paper proceeds as follows. In section II, we review the

relevant literature on earnings management and discuss our contribution with respect to

other papers. Section III discusses the parametric model of earnings management. Section

IV applies the model and computes the frequency and magnitude of EM in U.S. market.

Section V offers concluding remarks.

II. Literature Review

A large body of literature examines reasons firms may manage their earnings. For

example, Teoh, Wong and Rao (1998) show that firms engaging equity offerings are

more likely to inflate reported earnings prior to the offering; Healy and Palepu (1990)

examine if firms manage earnings when they are close to their dividend constraint;

Dechow and Sloan (1991) propose that CEOs manage reported earnings in their final

years in office to maximize their compensation contracts. Healy and Wahlen (1999)

review the earnings management literature and categorize these incentives into three

large groups: (1) capital market motivation, (2) contracting motivation, and (3) regulatory

motivation. For each category of earnings management incentives, researchers are able to

document occurrence of earnings management and in some cases the size and/or the

extent of earnings management. For example, Teoh, Wong and Rao (1998) show that

12% of IPO firms manage their earnings and the extent of earnings management

measured by median unexpected accrual is 4-5% of assets. However, knowing the

percentage of IPO firms that employ earnings management sheds little light on how

4

pervasive earnings management is for other firms that do not participate in the same

corporate activity. Similarly, knowing that banking and insurance companies use specific

accruals (loan loss reserve for the bank and claim loss reserves for insurers) to manage

earnings (Liu, Ryan and Wahlen (1997), Beaver and McNichols (1998)) offers little help

to understand the magnitude and size of earnings management for companies in other

industries.

Accrual-based models by Healy (1985), DeAngelo (1988), Jones (1991) and

Dechow, Sloan and Sweeney (1995) have been widely used to detect earnings

management. One of the major weaknesses of such models is their heavy reliance on the

measure and the assumption of accruals. For example, DeAngelo Model assumes that

nondiscretionary accruals are constant and Jones Model implicitly assumes that revenues

are nondiscretionary. Dechow, Sloan and Sweeney (1995) evaluate alternative accrual-

based models and show that these models all generate tests of low power for earnings

management of economically plausible magnitudes. The other disadvantage of accrual

based model is its inability to capture EM through cash flows such as different treatments

of R&D and advertising expenditure (Healy and Wahlen (1999)).

Another strand of literature focuses on a set of pre-determined threshold earnings

and examine if the distribution of the reported earnings is more concentrated around these

threshold points. The seminal work by Burgstahler and Dichev (1997) shows that there

exist low frequencies of small decrease in earnings (and small losses) and unusually high

frequencies of small increases in earnings (and small positive income). Their finding is

consistent with the hypotheses that managers try to manage the earnings to exceed

specific thresholds such as (1) prior earnings or (2) zero. Other studies have used other

5

thresholds such as analyst forecasted earnings and argue the discontinuity at zero in the

distribution of analysts’ forecasts errors is that earnings are managed to meet or beat

analysts’ forecasts (Degeorge, Patel and Zeckharser (1999)). The approach of identifying

the discontinuity in earnings distribution has been widely adopted in the literature. Using

the method described in Burgstahler and Dichev (1997) and Degeorge, Patel and

Zeckharser (1999), Xue (2004) studies the information content of earnings management.

Leuz, Nanda and Wysocki (2003) look at earnings management and investor protection

across 31 countries. Shen and Chih (2005) compare EM within the banking industry

internationally. Shuto (2003), Suda and Shuto (2002) examine the practice of earnings

management in Japan. The extensive application of this approach to measure EM has

produced many insightful researches.

Existing studies have made significant progress estimating the frequency of

earnings management around various thresholds; however they do not provide any

insights into the magnitude of earnings management. Furthermore, extant studies using

pooled, cross-sectional distribution of reported earnings to proxy earnings management

suffer some severe drawbacks. Holland (2004) points out that the result is very sensitive

to the choice of interval width; the symmetric assumption used to test the frequency of

EM might not be justified and the approach may not provide statistically reliable and

robust results if the peak of the distribution is adjacent to a threshold. Along with this line,

Durtschi and Easton (2005), Dechow, Richardson and Tuna (2003) and Beaver,

McNichols and Nelson (2003) mention that discontinuity in earnings distribution may be

driven by other factors, such as exchange listing requirement, systematic bias in the

denominator used to scale earnings and different tax treatment of profits and losses. They

6

caution researchers to be careful when interpreting the discontinuity in earnings

distribution.

Our model has significant advantages over extant approaches in Burgstahler and

Dichev (1997), Degeorge, Patel and Zeckharser (1999) and Xue (2004). It overcomes all

of the weaknesses pointed out in Holland (2004) since we make no assumption of

distribution interval width nor do we assume a symmetric distribution. Although we are

unable to exhaust alternative explanations regarding the presence of discontinuity in the

earnings distribution, we follow Xue (2004) and conduct a series of tests to ensure the

robustness of our results. For example, to remedy the concern that different tax treatment

of profits and losses may cause discontinuity in earnings distribution, we substitute net

income with pre-tax earnings and rerun our analysis. To mitigate the noise created by

biased denominator used to scale earnings, we use both market value of equity and book

value of equity for our analyses. Alternative explanations may exist to explain why

earnings are kinky, nevertheless we can’t rule out the main reason being earnings

management. Studies that apply this approach to study EM might be overstating the size

or scope of EM, nevertheless it provides the upper bound of EM. Moreover, we can also

gain useful knowledge regarding the change in the pattern of EM around various

thresholds and time periods. Assuming biases are consistent for earnings close to

respective threshold, comparisons between the frequency and magnitude of EM under

different incentives and cross various time periods are still viable.

III. Model

7

To find out the frequency and the magnitude of earnings management across all

firms, we need to first estimate the true earnings so that we can compare the difference

between the observable reported earnings and the unobservable true earnings.

We assume that there are two types of firms in the economy. Earning is a normal

random variable with mean 1μ and variance for the first type and with mean 21σ 2μ and

variance for the second type. The probability for a firm to be type one or two will be 22σ

ρ or 1 ρ− . Thus the true earnings follow a mixed normal distribution2

1( ) ( ) (1 ) ( )2x x xϕ ρϕ ρ ϕ= + − (1)

where ρ is a real number between 0 and 1， ( 1,2i i )ϕ = is the density function for a

normal distribution with mean equal to iμ , and variance equal to 2iσ .

(i.e.2

2( )

21( )2

i

i

x

ii

x eμσϕ

πσ

−−

= ). Clearly when 0ρ = or 1ρ = , )(xϕ becomes a normal

distribution.

We assume the threshold value for EM is α ，a firm’s true earning is x , and its

reported earning is y . When x α< , the firm may engage in EM and the reported earning

y α≥ . Since the cost of EM is higher the further away x is fromα , we can safely assume

the likelihood of EM is smaller when x is much lower than the threshold valueα , and it

will decrease exponentially. The likelihood for EM can be measured by:

(2) 1 ( )0 0( ) (0 1, 0)xP x e κ ακ κ− −= ≤ ≤ 1κ >

2 The mixed normal distribution assumes that sample firms might have different properties. This is a more robust assumption since it does not rule out the likelihood that sample firms might have similar properties (when ρ equals to 0 or 1). Since we do not observe the real earnings distribution, any parametric model is likely to be incorrect. To solve such problem, researchers usually apply non-parametric approaches to approximate the distribution and then convert it to a parametric model (Titteringtom, Smith and Makov 1985). Our model presented here falls in this category.

8

In equation (2), we can interpret 0κ as the probability for a firm to do EM if its true

earning is just below α and 1κ as the disincentive for a firm to manage earning as its

earning falls too far below the threshold value.

If a firm decides to manage its earning, the reported earning y will be greater than

the threshold valueα . In addition, the probability of EM is lower the further away

earning is from the threshold valueα , because the cost of EM is higher. If y follows an

exponential distribution, the reported earning can be distributed as：

( )

( )0

ye yf y EM

y

λ αλ αα

− −⎧ ≥= ⎨

<⎩ (3)

whereλ characterizes the distribution of the reported earnings for firms that employ EM.

Combining equation (1) to (3), the distribution function of the reported earnings

for the whole sample (firms with and without EM) becomes

( ) ( ) ( )f y f y x xϕ+∞

−∞

= ∫ dx

[ ]( ) ( ) ( )(1 ( )) ( ) ( ) ( )f y EM P x y P x x dx y x dxα

α

δ ϕ δ ϕ+∞

−∞

= ⋅ + − +∫ ∫ (4)

where ( )yδ is the Dirac function. The first part of equation (4) shows that if x α< , the

probability for a firm to engage in EM is equal to and the reported earning y will

follow a distribution

( )P x

( )f y EM . Subsequently, the probability for a firm to report its true

earnings will be 1 and the reported earnings will equal to the true earnings ((P x− ) y x= ).

The second term of equation (4) shows that if α≥x then there is no need to do EM and

y x= . Therefore we can convert equation (4) to equation (5):

9

(1 ( )) ( )( )

( ) ( ) ( ) ( )

P y y yf y

f y EM x P x dx y yα

ϕ α

ϕ ϕ α−∞

− <⎧⎪= ⎨ + ≥⎪⎩

∫ (5)

Using equation (1) and (5), we can obtain the true earnings distribution for the

firms that engage in EM.

( )r x

( ) ( ) ( ) / ( ) ( )r x P x x x P x dx xα

ϕ ϕ−∞

= <∫ α (6)

The frequency and magnitude of EM can therefore be computed using the following

equations:

a) Percentage of firms in the whole sample that use EM

( ) ( )x P x dxα

ϕ−∞∫

(7)

b) Firms that use EM divided by Firms that have true earnings less than the

threshold value

( ) ( ) ( )x P x dx x dxα α

ϕ−∞ −∞∫ ∫ ϕ (8)

The frequency of EM within other intervals of earnings can be computed likewise.

c) Difference between the true earnings and the threshold value for firms that

employ EM

( ) ( ) ( ) ( )x x P x dx x P x dxα α

ϕ ϕ−∞ −∞∫ ∫ (9)

d) Difference between the reported earnings and the threshold value for firms that

employ EM

10

1( )yf y EM dyα

λ

∞

=∫ (10)

Obviously, the total magnitude of EM is the sum of equation (9) and (10).

In the above equations,

2 21 1 1 1 1

0 11

( ) ( ) ( )exp ( )2

ax P x dx aα 2

1μ σ κ σ κϕ ρκ μ κσ−∞

⎡ ⎤− −= Φ − +⎢ ⎥

⎣ ⎦∫

2 22 2 1 2 1

0 22

(1 ) ( ) exp ( )2

a a2

1μ σ κ σ κρ κ μ κσ

⎡ ⎤− −+ − Φ − +⎢ ⎥

⎣ ⎦

1 2

1 2

( ) ( ) (1 ) ( )a ax dxα μ μϕ ρ ρ

σ σ−∞

− −= Φ + − Φ∫

( ) ( )x x P x dxα

ϕ−∞

=∫

( )222 2 21 1 121 1 1 1 1 1

0 1 1 1 1 1 21 1

exp ( ) { ( )( ) exp }2 22

aaaμ σ κσ κ μ σ κ σρκ μ κ μ σ κ

σ σπ

⎡ ⎤− −⎡ ⎤ − − ⎢ ⎥− + Φ + − −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

( )222 2 22 2 122 1 2 2 1 2

0 2 1 2 2 1 22 2

(1 ) exp ( ) { ( )( ) exp }2 22

aaaμ σ κσ κ μ σ κ σρ κ μ κ μ σ κ

σ σπ

⎡ ⎤− −⎡ ⎤ − − ⎢ ⎥+ − − + Φ + − −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦（where Φ ⋅ is the standard normal distribution function） ( )

Given the reported earnings y, we can apply the maximum likelihood estimate to

obtain the parameters 1 1 2 2, , , ,p μ σ μ σ for the distribution of the true earnings.

Furthermore, we can also estimate the parameters 0 1, ,κ κ λ for EM. Subsequently,

applying the parameter estimates, we can compute the frequency and magnitude of EM

using equation (7) to (10).

11

Our model has several advantages over the existing models that examine the

distribution of reported earnings. Holland (2004) conducts a methodological review of

the distribution of reported earnings approach and points out that (1) the choice of

interval width is a critical consideration and we may render different result for different

choice of interval width, (2) the assumption of symmetry used by Burgstahler and Dichev

(1997) may not be applicable if the distribution is skewed, (3) tests for the discontinuity

in the distribution are questionable, if the peak of the distribution is adjacent to the

threshold. In our model, we overcome all of the above concerns and provide a uniform

framework to consider the frequency and magnitude of EM simultaneously.

IV. Empirical Tests

Following Burgstahler and Dichev (1997) and Degeorge et al. (1999), we apply

three thresholds to examine the frequency and magnitude of EM. The first threshold is to

report positive earning; the second is to report earning higher than that of previous year,

and the third is to report earning that meet or beat the analyst forecasted earning.

Degeorge et al. (1999) detail various justifications of using such thresholds to examine

EM.

1) Report earnings to avoid losses

We obtain the sample between 1976 and 2004 using annual industrial and

research Compustat databases. To make our results more comparable with those in

Burgstahler and Dichev (1997), we follow their data selection criteria. Specifically, we

remove banks, financial institutions, and firms in regulated industries (e.g., utilities). Our

measure of earnings is net income scaled by beginning-of-the-year market value of

12

common equity. Furthermore, we sub-divide our sample into pre-1994 (including 1994)

period and post-1994 period for easy comparison with the results in Burgstahler and

Dichev (1997). In total, our sample includes 126,976 firm-year observations with 73,513

observations from 1976 to 1994 and 53,463 observations from 1995 to 2004 (See Panel A

of Table 1). In line with the approach suggested in Degeorge et al. (1999), we focus on

the interval between –0.15 and 0.3 for the earnings3. Accordingly, the distribution density

function specified in the model is adjusted to match the interval. This allows us to have a

better goodness-of-fit for the data and it represents 77.13% of the total sample and

79.42%/73.98% for the pre/psot-1994 sub-sample. We also apply other intervals such as

(-0.25, 0.40), (-0.35, 0.50) … (-0.65, 0.80) and the estimations are quite stable and the

results are materially similar.

Insert Table 1 Here

In Panel B of Table 1, we report the values of parameter estimation and the

associated standard deviations. The ratio of value to the standard deviation is

approximately t-distributed, which can be used to test the parameter significant. First of

all, we see that the parameter ρ is significantly different from zero or one for the full

sample and two sub-samples, suggesting that the distribution of true earnings is indeed

non-normal. This provides statistical support for using mix-normal distribution to model

earnings. The means and standard deviations for the mix-normal distribution are

estimated through 11,σμ and 22 ,σμ . More importantly, for the full sample, we see that

3 The choice of this interval represents the skewness of earnings distribution.

13

the t-ratio for 0κ is 11.1 (0.2840/0.0255), which means that 0κ is significantly different

from zero. Hence we cannot reject the hypothesis that EM exists in the sample. 1κ is

significantly positive demonstrating that the probability for a firm to manage earning

decreases as its earning falls further below the threshold value. As stated in equation (3),

λ characterizes the distribution of reported earnings for firms doing EM. Asλ increases

the proportion of firms doing EM is likely to be smaller. In Panel B of Table 1, the value

of λ is quite large meaning managed earnings are quite close to the threshold value.

These parameter estimation characteristics are also true for both the pre-1994 sub-period

and post-1994 sub-period.

In Panel C of table 1 we report the goodness-of-fit of the model. For the reported

distribution and our fitted distribution, we examine the differences in means, standard

deviations and percentage of observations with negative earnings to measure the

goodness-of-fit. The reported distribution has mean 0.0556 and standard deviation of

0.0875, while the fitted distribution has mean 0.0556 and standard deviation of 0.0874. In

the sample of reported earnings there are 22.52% observations report negative earnings,

and our fitted model predicts 22.59%. From these measurements, we can see that our

model fits the data very well. The goodness-of-fits are also very high for both sub-

samples. Figure 1A through 1C demonstrate the goodness-of-fit for the whole sample and

two sub-samples. In these figures, earnings density functions generated by our model (the

solid lines) are plotted against the reported earnings (the histogram bars). We can see that

they match very closely to each other.

Insert Figure 1-A through 1-C Here

14

Panel D of Table 1 reports the frequency of EM. We find that 1.58% of our full

sample 4 manage earnings to avoid losses. This translates into 6.55% of firms with

negative earnings5. The percentage increases to 23.41% as we narrow the interval to (-

0.01, 0.00). We also find that 13.38% of firms with negative earnings engage in EM in

the pre-1994 period; however it drops to 2.88% in the post-1994 period. This is consistent

with recent papers that suggest the loss-aversion incentive in EM has dropped compared

to other incentives (Dechow, Richardson and Tuan (2003)). For comparison with the

results in Burgstahler and Dichev (1997), we calculate the frequency of firms doing EM

when the true earnings are in the interval of (-0.03, 0.00), (-0.02, 0.00), (-0.01, 0.00) for

the pre-1994 sample. They are 31%, 36% and 42% while Burgstahler and Dichev

(1997)’s results are 30%, 35% and 44% respectively.

Panel E of Table 1 reports the magnitude of EM. For those firms performed EM

in the full sample, the mean estimate of true earnings is -0.0187 and the mean actual

reported earnings is 0.0132. Therefore the total amount of EM is 0.0319: the difference

between true earnings and reported earnings. In another words, earnings as measured by

net income scaled by beginning-of-the-year market value of common equity is managed

upward by 3.19 percentage points to avoid reporting losses. We also find that the

magnitude of EM drops from 0.08 during the pre-1994 period to only 0.01 during the

post-1994 period.

A more detail description of the frequency and magnitude of EM can be found in

Table 2. Panel A of Table 2 reports the number of observations in each interval. For

4 See the true earnings in (-0.15, 0.30) in Panel D, Table 1. 5 Since our initial interval for earnings is (-0.15, 0.30), the negative earnings interval here will be (-0.15, 0.00).

15

97,933 firms with earnings within the interval (-0.15, 0.30), the estimated true earnings

for the full sample are negative for 23,675 observations (24% of all firms within the

interval). If we divide the sample into the following intervals (-0.10, 0.00), (-0.03, 0.00),

(-0.02, 0.00) and (-0.01, 0.00), the numbers of firms are 18711, 7107, 4955, and 2612 in

each respective interval.

Insert Table 2 Here

Panel B of Table 2 shows the exact number and percentage of firms that manage

earnings to avoid reporting losses. For our full sample observations with earnings interval

between -0.15 and 0.00, there are 1,551 cases of EM. It is about 1.6% of our sample, and

6.6% of firms with negative true earnings. Number of EM within various intervals and

the percentage of firms doing EM are also shown in this table. Interestingly, we see a

significant drop in the frequency of EM in the post-1994 period. For the pre-1994 period

over 13% of firms with negative earnings engage in EM, while it is only 2.9% in the

post-1994 period.

To obtain an estimation of the overall size of EM in dollar terms, we turn our

attention to Panel C of Table 2. The average equity value of firms with negative earnings

in our full sample is $606.89 million. Given the average magnitude of EM is 0.0319 and

the total number of firms that employ EM is 1551, we can approximate the total dollar

amount of EM for our whole sample is over $30 billion. For the pre-1994 period, the

amount is $27.1 billion and for the post-94 period, the amount is $3.7 billion. It seems

16

that both the frequency and magnitude of applying EM to avoid losses have decreased in

recent years.

The frequency and magnitude of EM are also shown in Figure 1A through Figure

1C. In these figures, the histogram bars represent reported earnings, the solid curves are

the fitted earnings distribution density functions using maximum likelihood estimate, and

the dotted curves are the estimated true earnings distribution density functions assuming

true earnings follow mix normal distributions. We can see that our fitted earnings

distribution density functions trace very well with the actual reported earnings. This

suggests very high degrees of goodness-of fits. The areas between two curves to the left

of the threshold value represent the estimated true earnings for firms that perform EM.

The areas between these two curves to the right of the threshold value represent the

reported earnings by firms that manage earnings.

2) Report earnings to avoid earnings decreases

To study if companies report earnings to avoid earnings decreases, we require

sample firms to have earnings information for two consecutive years. Using annual

industrial and research Compustat database, we clean up the data using prior filters, and

retain observations for which changes in earnings can be computed between two

consecutive years. Changes in earnings between year t-1 and t are scaled by beginning-

of-the-year market value of equity from year t-1. The sample for this group contains

112,555 firm-year observations (see Panel A in Table 3).

Insert Table 3 Here

17

We then apply various intervals and attempt to use the largest interval available

with a high level of goodness-of-fit. As reported in Panel A of Table 3, using the interval

(-0.3, 0.3) we cover over 84% of the overall sample. Our results are robust using other

intervals as well.6

Similar to Panel B in Table 1, we see that parameter estimate for 0κ is

significantly different from zero in Panel B of Table 3. This shows that firms actively

manage earnings to avoid earnings decreases. Interestingly, the parameter estimate for

1κ is zero, suggesting that the probability for a firm to manage earning does not change as

its earning falls further below the threshold value. This result indicates that the incentive

for a firm to avoid reporting earning decrease is very high and we shall expect to see

more firms engage in this type of EM in our sample. The interpretations for other

parameters listed in Panel B of Table 3 are similar to those in Panel B of Table 1.

Panel C in Table 3 reports the goodness-of-fit for our fitted distributions. In all

samples, both means and standard deviations of our fitted values are very close to the

sample mean and standard deviation. In the sample there are 42.42% observations report

earnings decreases, and our model predicts 42.28%. From these measurements, we can

see that our model fits both the full sample and two sub-samples very well. Figure 2A

though Figure 2C plots the goodness-of-fit for full sample and for two sub-samples.

Insert Figure 2A through 2C Here

6 We also apply other intervals such as (-0.4, 0.4), (-0.5, 0.5) … (-0.8, 0.8) and the results are all similar to those reported using interval (-0.3, 0.3).

18

Panel D of Table 3 shows the frequency of EM for the full sample and pre/post

1994 sub-samples. We find 6.5% of the observations in the full sample managing

earnings to avoid earnings decreases, and this equals to 13.33% of the sample with true

earnings decreases from year t-1 to t.7 The percentage is slightly higher for pre-1994

(15.43%) period than for post-1994 period (11.26%). As discussed in the prior section,

when the parameter for is zero, the probability that a firm will employ EM to avoid

earning decrease does not depends on its true earning. This is also true for two sub-

samples. Interestingly, except for the smallest interval (-0.01, 0.00), we notice that the

frequency to do EM to avoid earnings decrease is much higher for firms in the post-1994

than to avoid losses as reported in Table 1. Overall, it suggests that for the overall sample

the incentive to avoid earnings decreases (6.50%) is greater than the incentive to avoid

losses (1.58%). However, the percentage of firms that employ EM to avoid earnings

decreases is not sensitive to the choice of earnings interval, while the percentage of firms

that conduct EM to avoid losses is much greater for firms with true earnings closer to

zero.

1κ

The magnitude of EM is shown in Panel E of Table 3. For the full sample of firms

whose true earnings decrease from year t-1 to t, the mean difference in true earnings

between year t and t-1 is -0.0742 and the mean reported increase in earnings from year t-

1 to year t is 0.0147, resulting in a total magnitude of EM of 0.0889. The EM magnitude

reported here is more than twice the size of that reported in Table 1. This finding is

highly consistent with the results shown in Panel C of Table 3 where the frequency of

EM is also higher, and the results in Panel B where the parameter estimation for 1κ is zero.

7 See the true earnings in (-0.3, 0.0) in Panel D, Table 3.

19

In the case of avoiding losses, firms may consider the cost (the magnitude) of EM and

choose appropriate strategies. However, firms are more committed to managing earnings

so that earnings show evidence of improvement. Our finding suggests that a behavioral

bias is likely to drive such phenomenon. Doing better than last year is more important

than just showing a positive earning for corporate management. Therefore, the likelihood

of EM is less sensitive to the true earnings even though EM is costly and large in size.

In Panel A of Table 4, we report the number and percentage of firms that have

true earnings decreases from year t-1 to year t. Our full sample includes 95,022 firms that

have differences in earnings between (-0.3, 0.3). Within this sample, there are 46,351

firms that have earnings decrease and this represents 48.78% of our sample. The

percentages of earnings decreasing firms are 48.72％ and 49.24% in pre/post 1994 sub-

samples. We also report the numbers of earnings-decreasing firms in other intervals. For

example, there are 3,128 firms that decrease their earnings by less than 0.005 and

earnings decline by less than 0.1 for 33,349 firms. Panel B of Table 4 presents the

number and percentage of companies that employ EM to avoid earnings decreases. For

the overall sample, 6,177 firms manage earnings and it represents 6.5% of the whole

sample, and 13.33% of firms that have true earnings decreases. Panel C of Table 4 reports

the magnitude of EM in the case of avoiding earnings decreases. For our sample firms

whose earnings differences between year t-1 and t fall in the interval of (-0.3, 0.3), the

mean equity value is 1,065.95 million dollars. Since average magnitude of EM is 0.0889

and the total number of firms that do EM is 6,177, we can calculate the total amount of

EM for our sample firms is more than $585 billion. Between 1976 and 1994, the total

20

amount of EM is around $189 billion, while the amount increases to over $338 billion in

the period of 1995 to 2004.

Insert Table 4 Here

Figure 2A through 2C depict the frequency and magnitude of EM to avoid

earnings decreases. In addition, they also show the goodness-of-fit between our fitted

values (the solid lines) and the actual reported values (the histogram bars). We can see

that our estimated earnings distributions fit very well with the reported earnings

distributions. Similar to earlier discussions, the areas to the left of zero between the

dotted lines and the solid lines represent the estimated true earnings differences for firms

that perform EM. The areas between these two curves to the right of the threshold value

represent the actual earnings differences reported by firms that manage earnings.

3) Report earnings greater than those forecasted by analysts

I/B/E/S database contains both analysts’ forecasts of earnings as well as the actual

reported earnings. We obtain annual EPS data from 1976 to 2004. Analysts’ forecasted

earnings are the means of the analysts’ forecasts and the actual earnings have been

adjusted to be consistent with the assumptions used in forecasted earnings. The

percentage forecast errors are found by subtracting forecasted earnings from actual

earnings then divided by actual earnings. In total we obtain 80,210 firm year observations

for the full sample where 42,411 observations are classified into pre-1994 sub-sample

and 37,799 observations are in the post-1994 sample (see Panel A in Table 5).

21

Insert Table 5 Here

The interval reported in table 5 is (-0.3, 0.3). This interval includes 75.22% of the

observations for the full sample, 73.11% for the pre-1994 sub-sample, and 77.59% for the

post-1994 sub-sample. We also applied other intervals to ensure the robustness of our

results and find very similar results as those reported in Table 5.

The parameter estimates are reported in Panel B of Table 5. We show that firms

engage in EM to meet or beat analysts’ forecast earnings since 0κ is significantly

different from zero. 1κ is significantly positive demonstrating that the probability for a

firm to manage earning decreases as its earning falls further below the threshold value.

The parameter estimation for λ is very large meaning that when doing EM firms are

likely to report earnings very close to the threshold value, in this case earnings forecasted

by analysts.

Panel C of Table 5 shows the means and standard deviations for the sample

reported values and for our estimated fitted values. We can see that the signs are identical

and the coefficients are very close to each other. In the sample there are 39.18%

observations reporting earnings below the forecasted earnings, and our model predicts

39.27%. These comparisons indicate a fine goodness-of-fit. Figure 3A through Figure 3C

plot the observed distributions, fitted distributions and the estimated true distributions for

the percentage analyst forecast errors. These figures demonstrate the goodness-of-fit

between the observed distributions and our fitted distributions.

22

Insert Figure 3A through 3C Here

Panel D of Table 5 reports the frequency of EM. Using analysts forecasted

earnings as threshold, we find 9.33% of the whole sample8 engages in EM to meet or

beat forecasted earnings. This corresponds to over 19% of the firms that fall short of

forecasted earnings9. For the same interval of (-0.3, 0.0), in the pre-1994 sample, around

14% of the observations employ EM and the percentage increases significantly to 25% in

the post-1994 sample. It is worth noticing that for the post-1994 sample, the percentage

of EM is the highest when earnings are benchmarked against analysts’ forecasted

earnings. This finding is in line with greater attention and emphasis given to analysts’

forecasted earnings by investors and corporate management. If we only examine firms

with true earnings within 10% below the forecasted earnings10, we see the frequency of

EM goes up to 24.88% for the whole sample and 29.43% for the post-1994 sub-sample.

We also find that as the interval narrows, the incentive to manager earnings increases. For

firms that are only 1% below the forecasted earnings11, the frequency of EM within the

whole sample is close to 35%. The frequency goes up to 51% in the post-1994 sub-

sample. Our findings are consistent with those in Dechow, Richardson and Tuna (2003).

They look at the changing patterns in earnings discontinuity and find that the ratio of

firms meeting or just beating analyst forecasts has considerably strengthened in recent

years.

8 See percentage forecast errors in (-0.30, 0.30) in Panel D, Table 5. 9 See percentage forecast errors in (-0.3, 0.0) in Panel D, Table 5. 10 See percentage forecast errors in (-0.1, 0.0) in Panel D, Table 5. 11 See percentage forecast errors in (-0.01, 0.00) in Panel D, Table 5.

23

Panel E of Table 5 illustrates the average magnitude of EM. For the full sample of

firms whose true percentage forecast errors are negative, the mean percentage forecast

errors between true earnings and forecasted earnings is –3.52%. The mean forecast

errors computed using reported earnings and forecasted earnings is zero. Therefore the

total magnitude of EM is 3.52%. The small magnitude of EM (the large value of

λ estimation) suggests that firms in this sample are more likely to meet rather than to

beat the benchmark. This phenomenon appears also in two sub-samples. The average

magnitude of EM for the pre-1994 sub-sample is 8.28% and 2.56% for the post-1994 sub-

sample. Therefore, the average size of EM decreases and the number of EM increases

after 1994.

Table 6 gives the number and dollar amount of EM for both the full sample and

two sub-samples. Our sample includes 60,332 firm-year observations with percentage

forecast errors between -0.3 and 0.3. Panel A gives the number and percentage of

observations with percentage forecast errors in various intervals. For example, 34.99%

(21,110 observations) fall short of analysts forecasted earnings by less than 10%12 and

6.6% (3,979 observations) are less than 1% short of forecasted earnings13. In Panel B of

Table 6, we detail the number and percentage of observations that engage in the practice

of EM. For observations with percentage forecast errors within interval (-0.30, 0.00),

there are 5,627 observations commit EM. It is 9.33% (5,627/60,332) of the whole sample

and 19.19% (5,627/29,319) of the observations with negative percentage forecast errors.

Moving down in Panel B, we see that for observations with percentage forecast errors

between -0.10 and 0.00, 8.70% (5,252/60,332) of the whole sample engage in EM. This

12 See # and % of obs. with percentage forecast errors in the interval (-0.10, 0.00) in Panel A, Table 6. 13 See # and % of obs. with percentage forecast errors in the interval (-0.01, 0.00) in Panel A, Table 6.

24

translates into 17.91% (5,252/29,319) of the observations with negative percentage

forecast error and 24.88% (5,252/21,110) of the observations within the interval of (-0.10,

0.00). Clearly, the closer actual earnings are to forecasted earnings, the greater the

frequency of EM is. The analysis on the two sub-samples also reveals some interesting

results. The percentage of observations doing EM increases greatly from 7.57% in the

pre-1994 sample to 11.18% in the post-1994 sample14. This is true for all intervals. For

example the percentage goes from 14.42% to 51.17% for observations with percentage

forecast error between (-0.01, 0.00). This pattern holds for all intervals and we can

conclude that more EM takes place in the post-1994 sample to meet analysts’ forecasted

earnings.

Insert Table 6 Here

Interestingly, the magnitude of EM is relatively small when compared to previous

two EM incentives (See Panel C in Table 6). Between 1976 and 2004, the total amount of

EM approximates $14.92 billion. The amount is roughly $7 billion for the pre-1994

period and $8.79 billion for the post-1994 period. Overall, our results suggest that there

are a large number of firms with their actual earnings residing close to the forecasted

earnings. The cost of EM is relatively small, and many of these firms do choose to do EM

to meet forecasted earnings.

14 See percentage forecast errors in (-0.30, 0.00) in Panel B of Table 6.

25

V. Conclusions

We use a parametric estimate approach to approximate the frequency and

magnitude of earnings management in the economy. Overcoming the deficiencies of

previous methodologies that use earnings distribution to infer EM, we provide both a

theoretical framework and an empirical analysis to compute the number and percentage

of firms that engage in EM and the average magnitude of EM. We show that the

incentive to meet or beat analysts’ forecasted earnings is the greatest (over 9% of our

sample firms). In contrast, the magnitude is the greatest when firms manage earnings to

avoid earnings decreases (over $585 billion between 1976 and 2004). We also find

evidence that firms actively manage earnings to avoid losses. We infer our results by

estimating the overall sample parameters without relying on knowing specific EM

approaches. In addition, our analysis does not hinge on specific corporate events such as

IPO or SEO, therefore our findings are more general and more applicable to the macro-

analysis of EM within the economy. To our knowledge, this is the first paper that

simultaneously examines the frequency and magnitude of the EM in one model using

large sample. Our study addresses the concern raised by Healy and Wahlen (1999) where

they emphasize the importance to understand the extent and the scope of earnings

management.

Future researches may look into difference across various industries and

determine the extent and the scope of earnings management in each industry. This will

enable regulators to better monitor the integrity of company reporting, and help investors

to better anticipate future firm performance. In addition, researchers can apply the model

prescribed in this paper and examine EM in different countries and markets.

26

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27

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28

The data is from 1976 to 2004. Our measure of earnings is net income scaled by beginning-of-the-year market value of common equity. We truncate the data and keep earnings between -0.15 and 0.30. Number of observations is the total number of firms with annual earnings information available. Number of observations within interval (-0.15, 0.30) is the total number of observations with earnings between -0.15 and 0.30. Percentage of observations used is defined as number of observations within the interval divided by total number of observations. Parameters in Panel B are defined in equation (1) through (10). In Panel C the means and standard deviations are the parameters that define the mixed-normal distributions. In Panel D, frequency of EM is defined as # of obs. doing EM divided by # of obs. within each respective interval. In Panel E, means of true earnings are the average estimated true earnings for firms that engage in EM, means of reported earnings are the average observable reported earnings for firms that engage in EM. Magnitude of EM is defined as the difference between mean of reported earnings and mean of true earnings.

Full Sample Pre-1994 Post-1994Panel A: Sample Description

# of obs. 126976 73513 53463

# of obs. within interval (-0.15, 0.30) 97933 58383 39550

% of obs. used 77.13 79.42 73.98Panel B: Parameter Estimation

Value Std Value Std Value Stdρ 0.7076 0.0042 0.7608 0.0053 0.6240 0.0069

1μ 0.0397 0.0008 0.0590 0.0011 -0.0014 0.0029

1σ 0.1252 0.0019 0.1214 0.0008 0.1250 0.0016

2μ 0.0648 0.0005 0.0735 0.0007 0.0556 0.0005

2σ 0.0333 0.0091 0.0344 0.0005 0.0333 0.0004

0κ 0.2840 0.0255 0.5037 0.0273 0.1786 0.0448

1κ 41.2670 7.9650 36.2670 4.4961 61.2670 25.5271

λ 75.5500 13.3770 15.9030 4.3302 125.5500 48.2084Panel C: Goodness-of-Fit

Reported Fitted Reported Fitted Reported Fitted

Mean 0.0556 0.0556 0.0685 0.0685 0.0366 0.0367

Standard deviaton 0.0875 0.0874 0.0896 0.0895 0.0806 0.0804

% of obs. with negative earnings 22.52 22.59 19.04 19.16 27.64 27.33Panel D: Frequency of EM

Value Value Value

True earnings in (-0.15, 0.30) 1.58 2.96 0.81

True earnings in (-0.15, 0.00) 6.55 13.38 2.88

True earnings in (-0.10, 0.00) 8.23 16.37 3.77

True earnings in (-0.03, 0.00) 16.81 31.43 8.76

True earnings in (-0.02, 0.00) 19.66 36.25 10.69

True earnings in (-0.01, 0.00) 23.41 42.41 13.45Panel E: Magnitude of EM

Mean of true earnings -0.0187 -0.0215 -0.0034

Mean of reported earnings 0.0132 0.0603 0.008

Magnitude of EM 0.0319 0.0818 0.0114 Table 2: Frequency and Magnitude of EM: the Case of Avoiding Losses The data is from 1976 to 2004. Our measure of earnings is net income scaled by beginning-of-the-year market value of common equity. We truncate the data and keep earnings between -0.15 and 0.30. Number of obs. that do EM is

29

computed using equation (7) through (10), and the % of obs. that do EM are computed against the whole sample, the obs. with true earnings less than 0 and the obs. within the respective interval. Magnitude of EM in dollar amount is proxied by multiplying average market value of common equity in the sample with the average magnitude of EM and with the number of firms that do EM.

Full sample Pre-1994 Post-1994 Panel A: Sample Description # of obs. with true earnings in (-0.15, 0.30) 97933 58383 39550 # of obs. with true earnings in (-0.15, 0.00) 23675 12913 11131 % of obs.with true earnings in (-0.15, 0.00) 24.18 22.12 28.14 # of obs. with true earnings in (-0.10, 0.00) 18711 10454 8511 % of obs. with true earnings in (-0.10, 0.00) 19.11 17.91 21.52 # of obs. with true earnings in (-0.03, 0.00) 7107 4044 3224 % of obs. with true earnings in (-0.03, 0.00) 7.26 6.93 8.15 # of obs. with true earnings in (-0.02,0.00) 4955 2805 2281 % of obs. with true earnings in (-0.02,0.00) 5.06 4.80 5.77 # of obs. with true earnings in (-0.01, 0.00) 2612 1465 1225 % of obs. with true earnings in (-0.01, 0.00) 2.67 2.51 3.10 Panel B: Number and Percentage of Obs. that Manage Earnings for Different Intervals of True Earnings

# of obs. that do EM 1551 1728 321 % of the whole sample 1.58 2.96 0.81

True earnings in (-0.15, 0.00)

% of obs. with true earnings < 0 6.55 13.38 2.88

# of obs. that do EM 1540 1711 321 % of the whole sample 1.57 2.93 0.81 % of obs. with true earnings < 0 6.50 13.25 2.88


% of obs. in the interval 8.23 16.37 3.77 # of obs. that do EM 1195 1271 282 % of the whole sample 1.22 2.18 0.71 % of obs. with true earnings < 0 5.05 9.84 2.53






% of obs. in the interval 23.41 42.41 13.45 Panel C: Magnitude of EM in Dollar Amount Average equity value of the firms with negative earnings($ million) 606.89 191.53 1029.24 Average magnitude of EM 0.0319 0.0818 0.0114 # of obs. that do EM 1551 1728 321 Magnitude of EM( $ billion) 30.03 27.07 3.77

30

Table 3: Manage Earnings to Avoid Earnings Decreases The data is from 1976 to 2004. Our measure of earnings is difference in earnings between year t-1 and t scaled by beginning-of-the-year market value of equity from year t - 1. We truncate the data and keep earnings between -0.3 and 0.3. Number of observations within interval (-0.3, 0.3) is the total number of observations with differences in annual earnings between -0.3 and 0.3. Percentage of observation used is defined as number of observations within the interval divided by total number of observations. Parameters in Panel B are defined in equation (1) through (10). In Panel C the means and standard deviations are the parameters that define the mixed-normal distributions. In Panel D, frequency of EM is defined as # of obs. doing EM divided by # of obs. within each respective interval. In Panel E, means of true earnings differences are the average estimated true earnings differences for firms that engage in EM. Means of reported earnings differences are the average observable reported earnings differences for firms that engage in EM. Magnitude of EM is defined as the difference between mean of reported earnings difference and mean of true earnings difference.

Full sample Pre-1994 Post-1994Panel A: Sample Description

# of obs. 112555 64180 48375


% of obs. used 84.42 84.84 83.86

Panel B: Parameter Estimation


1μ -0.0033 0.0051 -0.0041 0.0079 -0.0031 0.0067

1σ 0.1510 0.0028 0.1532 0.0043 0.1478 0.0038

2μ 0.0032 0.0005 0.0038 0.0008 0.0021 0.0006

2σ 0.0350 0.0003 0.0369 0.0004 0.0324 0.0004

0κ 0.1333 0.0285 0.1543 0.0405 0.1126 0.0405

1κ 0.0000 3.8640 0.0000 4.8699 0.0000 6.5122

λ 68.0000 6.9404 56.7340 8.3530 81.5040 12.5918Panel C: Goodness-of-Fit


Mean 0.0059 0.0058 0.0070 0.0070 0.0043 0.0043

Standard deviaton 0.0974 0.0974 0.0983 0.0982 0.0962 0.0962

% of obs. with negative earnings 42.42 42.28 41.27 41.21 43.96 43.70

Panel D: EM Frequency

True earnings differences in (-0.300, 0.300) 6.50 7.52 5.55






Panel E: EM Magnitude

Mean of true earnings differences -0.0742 -0.0761 -0.0718

Mean of reported earnings differences 0.0147 0.0176 0.0123

Average magnitude of EM 0.0889 0.0937 0.0841

31

Table 4: Frequency and Magnitude of EM: the Case of Avoiding Earnings Decreases The data is from 1976 to 2004. Our measure of earnings is difference in earnings between year t-1 and t scaled by beginning-of-the-year market value of equity from year t-1. We truncate the data and keep earnings between -0.3 and 0.3. Number of obs. that do EM is computed using equation (7) through (10), and the % of obs that do EM are computed against the whole sample, the obs. with true earnings less than 0 and the obs. within the respective interval. Magnitude of EM in dollar amount is proxied by multiplying average market value of common equity in the sample with the average magnitude of EM and with the number of firms that do EM.

Full sample Pre-1994 Post-1994 Panel A: Sample Description # of obs. with true earnings differences in (-0.300, 0.300) 95022 54453 40569 # of obs. with true earnings differences in (-0.300, 0.000) 46351 26531 19978 % of obs. with true earnings differences in (-0.300, 0.000) 48.78 48.72 49.24 # of obs. with true earnings differences in (-0.100, 0.000) 33349 18874 14561 % of obs. with true earnings differences in (-0.100, 0.000) 35.10 34.66 35.89 # of obs. with true earnings differences in (-0.015, 0.000) 9102 4970 4172 % of obs. with true earnings differences in (-0.015, 0.000) 9.58 9.14 10.29 # of obs. with true earnings differences in (-0.010, 0.000) 6176 3368 2835 % of obs. with true earnings differences in (-0.010, 0.000) 6.50 6.19 6.99 # of obs. with true earnings differences in (-0.005, 0.000) 3128 1705 1436 % of obs. with true earnings differences in (-0.005, 0.000) 3.29 3.13 3.54 Panel B: Number and Percentage of Obs. that Manage Earnings


True earnings differences in (-0.300, 0.000)

% of obs. with true earnings < 0 13.33 15.43 11.26 # of obs. that do EM 4445 2912 1640 % of the whole sample 4.68 5.35 4.04 % of obs. with true earnings < 0 9.59 10.98 8.21








% of obs. in the interval 13.33 15.43 11.26 Panel C: Magnitude of EM in Dollar Amount Average equity value of the firms with decreased earnings($ million) 1065.95 492.34 1788.78 Average magnitude of EM 0.0889 0.0937 0.0841 # of obs. that do EM 6177 4093 2250 Magnitude of EM($ billion) 585.35 188.82 338.48

32

Table 5 Manage Earnings to Meet or Beat Analyst’s Forecast The data is from 1976 to 2004. Our measure of earnings is the percentage forecast error of analysts’ forecasted earnings. It is found by subtracting forecasted earnings from the actual earnings then divided by actual earnings. We truncate the data and keep earnings between -0.3 and 0.3. Number of observations is the total number of firms with earnings available. Number of observations within interval (-0.3, 0.3) is the total number of observations that have earnings in interval (-0.3, 0.3). Percentage of observations used is defined as number of observations within interval divided by total number of observations. Parameters in Panel B are defined in equation (1) through (7). In Panel C the means and standard deviations are the parameters that define the mixed-normal distributions. In Panel D, frequency of EM is defined as # of obs. doing EM divided by # of obs. within each respective interval. In Panel E, means of true earnings are the average true earnings for firms that do EM, means of reported earnings is the average observable earnings for firms that do EM. Average of magnitude of EM is defined as the difference between mean of reported earnings and mean of true earnings.

Full Sample Pre-1994 Post-1994

Panel A: Sample Description

# of obs. 80210 42411 37799


% of obs. used 75.22 73.11 77.59

Panel B: Parameter Estimation


1μ -0.0121 0.0013 -0.0296 0.0048 -0.0011 0.0017

1σ 0.1624 0.0017 0.1674 0.0032 0.1595 0.0023

2μ 0.0049 0.0004 0.0015 0.0008 0.0089 0.0005

2σ 0.0367 0.0002 0.0401 0.0004 0.0328 0.0003

0κ 0.3716 0.0154 0.1442 0.0257 0.5621 0.0199

1κ 13.0000 1.4454 0.0000 2.2866 19.4710 1.9863

λ 600000 109122 700000 61275 700000 32627

Panel C: Goodness-of-Fit


Mean 0.0015 0.0015 -0.0039 -0.0038 0.0072 0.0072

Standard deviaton 0.0987 0.0986 0.1011 -0.1010 0.0957 0.0957

% of obs. with negative earnings 0.3918 0.3927 0.4501 0.4494 0.3302 0.3331

Panel D: EM Frequency

Percentage forecast errors in (-0.30, 0.30) 9.33 7.57 11.18






Panel E: EM Magnitude

Mean of true percentage forecast errors -0.0352 -0.0828 -0.0256

Mean of reported percentage forecast errors 0.0000 0.0000 0.0000

Magnitude of EM 0.0352 0.0828 0.0256

33

Table 6: Frequency and Magnitude of EM: the Case of Meeting/Beating Analysts’ Forecasted Earnings The data is from 1976 to 2004. Our measure of earnings is the percentage forecast error of analysts’ forecasted earnings. It is found by subtracting forecasted earnings from the actual earnings then divided by actual earnings. We truncate the data and keep earnings between -0.3 and 0.3. Number of obs. that do EM is computed using equation (7) through (10), and the % of obs that do EM are computed against the whole sample, the obs. with true earnings less than 0 and the obs. within the respective interval. Magnitude of EM in dollar amount is proxied by multiplying average market value of common equity in the sample with the average magnitude of EM and with the number of firms that do EM. Full sample Pre-1994 Post-1994 Panel A: Sample Description # of obs. with percentage forecast errors in (-0.30, 0.30) 60332 31005 29327 # of obs. with percentage forecast errors in (-0.30, 0.00) 29319 16283 13045 % of obs. with percentage forecast errors in (-0.30, 0.00) 48.60 52.52 44.48 # of obs. with percentage forecast errors in (-0.10, 0.00) 21110 11112 9537 % of obs. with percentage forecast errors in (-0.10, 0.00) 34.99 35.84 32.52 # of obs. with percentage forecast errors in (-0.03, 0.00) 10791 5169 5352 % of obs. with percentage forecast errors in (-0.03, 0.00) 17.89 16.67 18.25 # of obs. with percentage forecast errors in (-0.02, 0.00) 7627 3587 3886 % of obs. with percentage forecast errors in (-0.02, 0.00) 12.64 11.57 13.25 # of obs. with percentage forecast errors in (-0.01, 0.00) 3979 1841 2080 % of obs. with percentage forecast errors in (-0.01, 0.00) 6.60 5.94 7.09 Panel B: Number and Percent of Observations that Manage Earnings


Percentage forecast errors in (-0.30, 0.00) % of obs. with true earnings < 0 19.19 14.42 25.12


Percentage forecast errors in (-0.10, 0.00) % of obs. in the interval 24.88 14.42 29.43






Percentage forecast errors in (-0.01, 0.00) % of obs. in the interval 34.86 14.42 51.17 Panel C: Magnitude of EM in Dollar Amount # of shares of the firms with negative forecast error ( million) 75.31 36.00 104.79 Average magnitude of EM 0.0352 0.0828 0.0256 # of obs. that do EM 5627 2348 3277 Magnitude of EM($ billion) 14.92 7.00 8.79

34

Figure 1: Manage Earnings to Avoid Losses Earnings are measured as net income scaled by beginning-of-the-year market value of common equity. The histogram bars are the true reported earnings. The dotted lines are the distributions of true earnings and the solid lines are the fitted distributions. The nearness between the histogram bars and the solid lines measures the goodness-of-fit. The areas between the dotted lines and the solid lines capture firms that employ EM. The areas to the left of zero between the dotted lines and the solid lines represent the differences between true earnings and the threshold value. The areas between these two curves to the right of zero are the differences between the reported earnings and the threshold value.

-0.2 -0.1 0.0 0.1 0.2 0.3

earnings

0

2

4

6

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 1-A 1976-2004

-0.2 -0.1 0.0 0.1 0.2 0.3

earnings

0 1 2 3 4 5 6

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 1-B 1976-1994

-0.2 -0.1 0.0 0.1 0.2 0.3 earnings

0

2

4

6

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 1-C 1995-2004

35

Figure 2: Manage Earnings to Avoid Earnings Decreases Earnings are measured by difference in earnings between year t-1 and t scaled by beginning-of-the-year market value of equity from year t-1. The histogram bars are the differences in firms’ true reported earnings between year t-1 and t. The dotted lines are the distributions of the differences in true earnings. The solid lines are the fitted distributions. The nearness between the histogram bars and the solid lines measures the goodness-of-fit for our estimated distributions. The areas between the dotted lines and the solid lines capture firms that employ EM. The areas to the left of zero between the dotted lines and the solid lines represent the differences between true earnings and the threshold value. The areas between these two curves to the right of zero are the differences between the reported earnings and the threshold value.

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

earnings

0

2

4

6

8

10

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 2-A 1976-2004

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

earnings

0

2

4

6

8

10

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 2-B 1976-1994

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

earnings

0

2

4

6

8

10

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 2-C 1995-2004

36

Figure 3: Manage Earnings to Meet or Beat Analysts’ Forecasts Earnings are measured by the percentage forecast error of analysts’ forecasted earnings. It is found by subtracting forecasted earnings from the actual earnings then divided by actual earnings. The histogram bars are the actual percentage forecast errors. The dotted lines are the estimated true distributions of the forecast errors. The solid lines are the fitted distributions of the percentage forecast errors. The nearness between the histogram bars and the solid lines measures the goodness-of-fit. The areas between the dotted lines and the solid lines capture firms that employ EM. The areas to the left of zero between the dotted lines and the solid lines represent the differences between true earnings and the threshold value. The areas between these two curves to the right of zero are the differences between the reported earnings and the threshold value.

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3earnings

0 5

10 15 20 25

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 3-A 1976-2004

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3earnings

0

5 10 15 20 25

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 3-B 1976-2004

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3earnings

0

10

20

30

prob (%)

Reported earnings

Fitted earnings

True earnings

Figure 3-C 1976-2004

37

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