What Have We Learned About Earnings Management? Correcting Disinformation about Discontinuities*

Transcription

1 What Have We Learned About Earnings Management? Correcting Disinformation about Discontinuities* David Burgstahler Julius A. Roller Professor of Accounting University of Washington/Seattle Elizabeth Chuk University of Southern California October 4, 2012 Abstract Earnings distributions commonly exhibit statistically significant discontinuities at prominent performance benchmarks. Discontinuities at zero earnings are widely interpreted as evidence of earnings management to avoid a loss, and discontinuities at zero earnings change or zero earnings surprise as evidence of management to avoid an earnings decrease or negative earnings surprise, respectively. In contrast, two recent papers by Durtschi and Easton (2005, 2009, hereafter DE) assert that discontinuities are instead explained by some combination of prior researchers' choice(s) of sample selection and scaling as well as a systematic relation between the sign of earnings and market prices. Resolution of the conflicting interpretations of discontinuities is important because 1) it affects how investors, regulators, and scholars view earnings management and 2) it demonstrates the importance of a close linkage between theory and research design choices. We evaluate the three alternative explanations proposed by DE. We point out that DE provide no evidence that their explanations create discontinuities, but only evidence showing that their modified research designs eliminate discontinuities. We also demonstrate why the research designs used by DE eliminate evidence of discontinuities when alternative designs using the same data identify highly significant discontinuities. Finally, we outline the key characteristics of the extensive body of evidence documenting discontinuities in earnings distributions that are consistent with the theory that earnings are managed but are generally inconsistent with artifactual theories of discontinuities. JEL classification: G14, M40 Key Words: Earnings management, discontinuities * We appreciate comments and suggestions from Bob Bowen, Ilia Dichev, Weili Ge, Dave Guenther, Frank Hodge, Bjorn Jorgensen, Bill Kinney, Allison Koester, Dave Maber, Rick Mergenthaler, Greg Miller, Shiva Rajgopal, Tatiana Sandino, Terry Shevlin, D. Shores, Bob Trezevant, and workshop participants at the 2010 UBC, Oregon, Washington Accounting Conference, University of Colorado, University of Illinois, University of Michigan, University of Southern California, University of Texas, National University of Singapore, and Singapore Management University.

2 1. Introduction There is pervasive evidence of discontinuities in distributions of reported earnings at prominent earnings benchmarks, where distributions comprise fewer observations immediately left of the benchmark and more observations immediately right of the benchmark than would be expected if the distribution was smooth. 1 For example, Burgstahler and Dichev (1997a, hereafter BD) show that distributions of earnings levels and distributions of earnings changes exhibit discontinuities at zero. In addition, BD document that the strength of discontinuities varies with the costs and benefits of meeting benchmarks. This evidence is widely interpreted as consistent with the theory that managers take actions to ensure that earnings meet benchmarks, e.g., earnings are managed to avoid losses and earnings decreases. 2 This interpretation is further supported by survey evidence in Graham, Harvey, and Rajgopal (2005) indicating that managers are willing to incur real costs in order to meet benchmarks. Two recent papers by Durtschi and Easton (2005, hereafter DE1, and 2009, hereafter DE2) assert that inferences attributing discontinuities to earnings management are "erroneous." These papers observe that discontinuities are eliminated when the research design is changed and assert that discontinuities in earnings distributions are driven by deflation, sample selection, and a difference between the characteristics of profit and loss observations. These assertions have led many to question whether discontinuities represent compelling empirical evidence of earnings management, or instead are due to the artifactual explanations advocated in DE1 and DE2 (hereafter referred to collectively as DE). 1 The smoothness assumption is discussed in more detail in Section 2 and in Burgstahler (2012). 2 While this paper focuses primarily on evidence of discontinuities in distributions of earnings and earnings changes, there is also widespread evidence of similar discontinuities in distributions of earnings surprises, e.g., Degeorge, Patel, and Zeckhauser (1999), Brown (2001), Matsumoto (2002), Brown and Caylor (2005), Burgstahler and Eames (2006). Page 1

3 It is conceivable that discontinuities are eliminated when DE alter the research design used in prior studies because the research design factors that they focus on somehow induce discontinuities. However, an important alternative possibility is that the DE research design choices mechanically obscure discontinuities. The purpose of this paper is to distinguish between these competing interpretations of the effects reported in DE. Research design choices are critical determinants of the power of tests and the interpretation of results. For example, if a significant result is replicated using a design based on a much smaller sample size, the result of the replication may not be statistically significant. However, it is well-understood that an insignificant result from a replication that lacks power due to small sample size does not contradict a significant result from a larger sample, does not confirm the null hypothesis, and does not disprove the alternative hypothesis. The same principle applies in interpreting results of DE research designs that reduce the power of discontinuity tests. First, we show that the absence of discontinuities in unscaled earnings or earnings per share reported in DE is a direct result of the DE research design choices and show how research designs that correct these flaws show significant discontinuities in both unscaled earnings and earnings per share. Thus, the DE results show how lack of scaling combined with inadequate research design can eliminate discontinuities but do not show that scaling creates discontinuities lack of scaling combined with appropriate design yields highly significant discontinuities. Second, we show why the DE speculation that discontinuities in distributions of pricescaled earnings are explained by small negative earnings being pushed away from zero by low price scalers and small positive earnings being drawn toward zero by high price scalers is incorrect. We first note that this argument only applies to price-scaled earnings at the zero benchmark and cannot be applied to much of the discontinuity evidence reported in the literature, including discontinuities for benchmarks other than zero, for other earnings variables such as Page 2

4 earnings changes and earnings surprises, and discontinuities in unscaled earnings and in earnings per share. We then show that discontinuities occur in segments of the population where prices for small negative earnings are not lower than for small positive earnings and that these segments account for almost all of the discontinuity in price-scaled earnings at the zero benchmark. Thus, even for the narrow portion of discontinuity evidence where this explanation could conceivably apply, the relation between price and earnings does not explain discontinuities. Third, we document that firms with missing market prices differ substantially from firms with market prices in a variety of ways that naturally translate into differences between the scaled earnings distributions for firms with and without market prices. The missing price distributions have a high proportion of small loss observations and show little or no evidence of discontinuities, in contrast to distributions for firms with price, which have highly significant discontinuities. These clear differences explain the DE results showing that aggregating the missing price observations together with observations that have price weakens the discontinuity in the aggregated distribution. However, the fact that distributions for firms with missing price are different, and specifically that the missing price distributions lack discontinuities, is not an explanation for discontinuities in the distributions for firms that have prices. In summary, the DE results do not contradict previous evidence of discontinuities nor the common interpretation that discontinuities are due to earnings management to meet benchmarks. Instead, the DE research design choices reduce power and mechanically eliminate the significance of discontinuities because they 1) fail to account for the extremely important effect of size as a covariate, 2) do not fit with the theory that earnings are managed more frequently when the amount of earnings management required to meet the benchmark is smaller, and 3) place inordinate weight on segments of the population where there is little reason to expect evidence of discontinuity given the research design. The DE results show only that these critical research Page 3

5 design flaws can obscure discontinuities there is no evidence showing that any of these research design choices can create discontinuities. The paper is organized as follows. Section 2 provides background and discusses research design for empirical tests of earnings management to meet benchmarks. Section 3 provides empirical evidence showing why the DE research designs predictably lead to non-significant discontinuity evidence and Section 4 explains why artifactual explanations for discontinuities, including the explanations advocated in DE, are generally unable to explain the body of discontinuity that has been reported in the literature. Section 5 concludes. 2. Background Earnings management has been a prominent topic in the accounting literature for many years. Healy and Wahlen (1999) note: "Despite the popular wisdom that earnings management exists, it has been remarkably difficult for researchers to convincingly document it." Earnings management typically cannot be directly observed but must instead be inferred, either by 1) testing whether earnings, or a component of earnings, differs from what would have been expected in the absence of earnings management (for example, tests based on abnormal accruals models), or 2) testing whether the distribution of reported earnings differs from what would have been expected in the absence of earnings management. The second approach adopts an implicit model of the distribution of pre-managed total earnings. Specifically, the model of pre-managed earnings adopted by BD is simply that the distribution of pre-managed earnings should be smooth in the sense that the expected frequency in an interval is approximately equal to the average of the expected frequencies in the two immediately adjacent intervals. 3 As explained below, earnings management to meet benchmarks 3 Other statistical tests for discontinuities rely on more restrictive assumptions about the form of the distribution. Therefore, in these tests a significant test statistic could be due to departures from these assumptions rather than to a Page 4

6 creates discontinuities in the distribution of reported earnings, providing evidence that some firms have taken actions consistent with earnings without specifically identifying which firms have taken these actions. Further, because this approach focuses on reported total earnings, the set of actions included in the definition of earnings management is broad, including all accounting (accrual and disclosure) actions and all "real" operating, investing, and financing actions that affect reported earnings Theory of earnings management to meet benchmarks Economic theory suggests that managers take actions when they believe the benefits exceed the costs. Two assumptions transform this general theory into a specific theory of earnings management to meet benchmarks: 1) The benefit of managing earnings to meet a benchmark is improved terms of transactions with stakeholders. 5 2) The cost of managing earnings is increasing in the amount of earnings management. Let EM j * denote the maximum amount by which earnings for observation j can be managed to meet the benchmark at a cost less than or equal to the discontinuity. For example, the test in Hayn (1995) requires the additional assumption that the distribution of premanaged earnings is normal and a significant test statistic could be due to departures from normality. Other examples include the assumption in Bollen and Pool (2009) that the pre-managed distribution of hedge fund returns is described by a fitted distribution derived from the histogram of reported hedge fund returns and the assumption in Chen et al (2010) of a specific distributional form. 4 McNichols (2000) and Dechow, Richardson, and Tuna (2003) discuss the fact that discontinuity evidence does not reveal which actions have been employed to manage earnings, a limitation that is also recognized in most reviews of earnings management. For example, the review by Healy and Whalen (1999, p. 368) invokes a broad definition of earnings management: "Earnings management occurs when managers use judgment in financial reporting and in structuring transactions to alter financial reports to either mislead some stakeholders about the underlying economic performance of the company or to influence contractual outcomes that depend on reported accounting numbers." Dechow and Skinner (2000) rely on a similarly broad definition that encompasses actions ranging from pure disclosure management to real operating, investing, and financing actions. Schipper (1989, p. 92) focuses on a slightly more narrow definition of "disclosure management" defined as "purposeful intervention in the external financial reporting process, with the intent of obtaining some private gain " but notes that it would be only a minor extension to broaden this definition to encompass "real" earnings management. In contrast, studies that construct models of a specific component of earnings are able to focus on a more narrow definition of earnings management. For example, Dechow, Richardson, and Tuna (2003) focus specifically on the discretionary accruals form of earnings management. 5 As discussed in BD section 4, examples of improvements in terms of transactions when benchmarks are met include lower wage and benefit demands from current and potential employees, better terms from suppliers and creditors, and higher valuation by shareholders. Page 5

7 benefits. When pre-managed earnings are below the benchmark by an amount less than EM j *, earnings are managed upward so that reported (post-managed) earnings are above the benchmark. The values of the EM j * may vary across observations and the values of EM j * are determined by multiple factors, but firm size is an important factor. Because the benefits of meeting the benchmark increase with the number and size of transactions with stakeholders, and because larger firms have more and larger transactions with shareholders, the benefits of earnings management increase with firm size. Consequently, the maximum amount of earnings that can be managed at a cost less than the benefits, EM j *, also increases with firm size. Therefore, in any sample that includes a broad range of sizes, it is essential to account for the effect of size on EM j *. There may be additional factors that affect the benefits or costs of earnings management and therefore also affect the EM j *. As benefits decrease or costs increase due to these other factors, the value of EM j * will move toward zero. Fewer observations will be within EM j * of the benchmark, earnings management will occur for fewer observations, and discontinuities will disappear. Thus, we expect to find less evidence of discontinuities in any segment of the population where firms realize lower benefits or face higher costs of earnings management. 6 For example, firms in financial difficulty are likely to have much lower rates of earnings management. For these firms, the benefits of meeting an earnings target are likely lower (because concerns about financial difficulty reduce any potential improvement in terms of transactions due to meeting the earnings target) and the costs are likely higher (because financial difficulty is associated with decreased flexibility to take actions that could increase reported earnings). 6 For example, BD provide evidence that discontinuities in earnings levels and changes are weaker among firms with a weaker record of recent profitability, consistent with the hypothesis that these firms realize lower benefits or face higher costs of managing to meet benchmarks. Similarly, Beatty et al. (2002) show that the rate of earnings management is lower among private banks than among public banks, consistent with the hypothesis that private banks have lower incentives to manage to meet benchmarks. Page 6

8 2.2 Previous evidence of earnings management to meet benchmarks Numerous anecdotes and conversations with practitioners suggest that earnings are frequently managed upward to meet benchmarks and this theory is also supported by survey evidence. Graham, Harvey and Rajgopal (2005) provide the most well-known and widely-cited survey evidence that shows managers are willing to take actions, and incur significant costs, to meet benchmarks. Thus, there are strong a priori reasons to believe that earnings are managed to meet benchmarks. This theory is further supported by a vast empirical literature documenting discontinuities at a number of alternative benchmarks in a variety of countries and institutional settings. Using U.S. data, studies document discontinuities around various earnings benchmarks, including the profit/loss benchmark, creating a discontinuity in earnings levels at zero (Hayn, 1995; BD, 1997; Degeorge et al., 1999); prior-year earnings, creating a discontinuity in earnings changes at zero (BD, 1997; Degeorge et al., 1999; Beatty et al., 2002; Donelson et al., 2012); and analyst forecasts, creating a discontinuity in earnings surprise at zero (Degeorge et al., 1999; Abarbanell and Lehavy 2003; Burgstahler and Eames, 2006; Donelson et al., 2012). There is also strong evidence using international data (Leuz, Nanda, and Wysocki, 2003; Suda and Shuto, 2005; Haw et al., 2005). Evidence of discontinuities also exists for performance measures other than earnings, such as debt covenant slack ratios (Dichev and Skinner, 2002), current ratios (Dyreng, Mayew, and Schipper, 2012), and professional baseball batting averages and college entrance exam scores (Pope and Simonsohn, 2010). In sum, evidence of discontinuities at prominent benchmarks in distributions of earnings and other performance metrics is found throughout the accounting literature as well as for nonearnings metrics in non-accounting literature. Collectively, the evidence shows that the Page 7

9 discontinuities are not limited to any particular country or setting or benchmark and are robust to a wide variety of research design choices. 3. DE "alternative explanations" for discontinuities DE1 and DE2 assert that "deflation, sample selection, and a difference between the characteristics of profit and loss observations" are "much more likely" explanations for discontinuities than the widely-accepted theory that discontinuities are the result of earnings management to meet benchmarks. Scholars must remain open to alternative theories that might explain discontinuities, such as the DE "very evident" explanations. However, alternative theories should be subjected to a careful evaluation of the theory's consistency with the body of empirical evidence, including empirical evidence from the previous literature and additional empirical evidence presented below. 3.1 Scaling as an alternative explanation In this section, we evaluate the first alternative explanation proposed by DE, scaling, which they summarize as follows: The arguments that net income must be deflated in an attempt to homogenize firms (DPZ, p. 16) or because firms are drawn from a broad range of firm sizes (BD, p. 102) seem reasonable at first glance. But these studies do not provide a priori reasons why heterogeneity or differences in firm size might affect the empirical analyses. More importantly, the implicit assumption is that deflation will not distort the underlying distribution of net income. Our results suggest that it does. Furthermore, since the hypotheses in the extant literature focus on management of earnings to avoid small losses, and since the arguments underlying these hypotheses do not suggest that earnings are managed relative to beginning-of-period price, we question whether it is ever appropriate to examine deflated earnings in an earnings management context. (DE1 p. 559) We begin by considering the research design rationale for scaling. Contrary to the DE1 assertions above, scaling does not rely on "the implicit assumption that deflation will not distort the underlying distribution of net income." Rather, the explicit purpose of scaling is to "distort the underlying distribution" to achieve two goals: 1) to account for size as a covariate that explains Page 8

10 variation in earnings (irrespective of earnings management) and 2) to account for the relation between size j and EM j *, the amount of earnings that can be managed at a cost lower than the benefits. First, effective research design must account for the strong relation between firm size and earnings. Theory and empirical evidence clearly indicate that size explains a great deal of variation in earnings. For example, the mean earnings reported by a $1 billion firm is far larger than the mean earnings reported by a $10 million firm. Similarly, the standard deviation is strongly related to size the probability of an earnings observation $10 million above or below the mean is far larger for a $1 billion firm than for a $10 million firm. We show that by failing to account for the substantial effect of size, the DE design places inordinate weight on observations for the smallest firms and, for reasons explained in the next few paragraphs, also results in low power tests for the smallest firms. Second, effective research design must also account for size-related differences in EM j *. The exact forms of the functions relating benefits and costs to size are unknown, but we assume, as a first approximation, that the ratio of benefits to costs remains constant as firm size increases. For example, we assume that if increasing the size of the firm by a factor of 5 increases the value of improved terms of transactions with stakeholders by a factor of 5, the amount of earnings that can be managed at a cost less than the benefits also increases by a factor of 5. The constant ratio assumption implies that EM j * increases in approximate proportion to size. 7 In terms of dollars, the constant ratio assumption implies the benefits of meeting the benchmark will be about 100 times larger for a $1 billion firm than for a $10 million firm and therefore the maximum amount of 7 Determining the optimal histogram interval width in scaled earnings units is a research design issue, discussed in detail in Section 3. Page 9

11 earnings that can be managed to meet the benchmark at cost less than the benefits will be about 100 times larger for the $1 billion firm. Earnings management to meet a benchmark will transform pre-managed earnings within EM j * of the benchmark into reported earnings above the benchmark, creating a discontinuity in the distribution of reported earnings. The prominence of the discontinuity increases with 1) increases in the product of the number of pre-managed earnings observations in the interval below the benchmark and the rate of earnings management among those observations, creating a trough in the histogram of reported earnings, and 2) increases in the number of observations managed to the interval above the benchmark, creating a peak in the distribution of reported earnings. Conversely, prominence of the trough and the peak dissipate as the numbers of observations managed from the interval immediately below the benchmark and managed to the interval immediately above the benchmark decrease. 8 Thus, the research design must use an interval width that corresponds as closely as possible to the EM j *. In particular, an interval width that does not reflect the effect of size on the EM j * will obscure or eliminate any discontinuity due to earnings management. The following sections show that significant discontinuities exist in distributions of unscaled earnings and earnings per share, contrary to the DE assertion that discontinuities are due to scaling. For both unscaled earnings and earnings per share, the analysis is arranged in three steps: First, an overview figure that shows the strong relation between earnings and size by partitioning the population into quartiles based on size. Second, we examine discontinuities using the same interval width for firms of all sizes for the individual size quartiles and in the aggregate, showing how and why the DE design obscures evidence of discontinuities. Third, we examine 8 See Burgstahler 2012 for analysis of determinants of power of tests for discontinuities. Page 10

12 discontinuities using interval widths that reflects size-related differences in EM j *, showing how this research design leads to highly significant discontinuities Unscaled earnings Figure 1 provides a descriptive overview of the effect of size on earnings distributions. We expect to see a positive relation between size and both the mean and dispersion of earnings distributions because larger firms tend to have larger expected future earnings and there is a positive relation between future earnings and current earnings. We use MVE as the measure of size in the analysis because 1) valuation models provide a direct theoretical link between MVE and expected future earnings, and 2) we expect MVE to be more closely related to differences in the EM j * than alternative measures of firm size, such as total revenues, total assets, and book value of equity. Any of the size measures might be most closely related to benefits of earnings management to meet benchmarks because they all reflect the number and size of transactions with stakeholders (though in slightly different ways). However, costs of earnings management are likely to be most closely related to market value of equity, under the additional assumption that the flexibility to manage current earnings is proportional to the present value of expected future earnings. Therefore, we rely primarily on market value of equity as the measure of size. 9 Figure 1 shows distributions of unscaled earnings for a range that includes earnings of most of the firms on Compustat, $50 to $200 million, and a histogram interval width of $2.5 million. 10 The four panels correspond to the four quartiles of firm size, where size is measured as 9 Most of the results reported below also hold for alternative size measures. Further, results previously reported in the literature show that discontinuities are observed in distributions of earnings scaled by any of these alternative measures of size. See for example, BD p BD found that a large proportion of the small number of exact zero values of unscaled earnings (Compustat item NI) were errors. To avoid incorrectly treating data errors as values that meet the benchmark of zero, all observations with exact zero values of unscaled earnings are deleted throughout the analysis (though values exactly equal to zero are relatively rare so this choice has no effect on our conclusions). Note that this issue arises for unscaled earnings but not for EPS, where exact zero values are relatively common and are not subject to a high rate of errors. Page 11

13 the market value of equity (MVE). 11 Firms from the smallest size quartile have median market value of $7.5 million while firms from the upper three quartiles have median market values of $50.1 million, $235.2 million, and $1,983.1 million, respectively. The range of size across the four quartiles is substantial. In round numbers, median market value increases across each quartile by a multiple of about Figure 1 confirms the expected strong relation between MVE and the location of unscaled earnings and the strong relation between the dispersion and MVE. For the lowest MVE quartile, the distribution of unscaled earnings has a negative median and mean and is highly concentrated in the vicinity of the zero benchmark. For progressively larger MVE quartiles, the medians and means become increasingly positive and the dispersion of the earnings distributions increases. The dotted vertical lines in each panel indicate the range of unscaled earnings examined in the DE research design, unscaled earnings observations between $5 million and $7 million. Figure 1 shows that the preponderance of observations included in the DE design are from the first quartile while only relative few of the observations from the larger MVE quartiles are included, a point we explore in more detail in Figure 2. Figure 2 Panels A-D show distributions of unscaled earnings using an interval width of $100,000, the width used in the DE research design. For reasons explained above, using a constant interval width of $100,000 for firms regardless of size is appropriate only if the maximum amount of earnings that can be managed at a cost lower than the benefits is $100,000 regardless of firm size. When EM j * is much smaller than $100,000, many of the observations in the interval immediately below the benchmark will be too far below the benchmark to be managed and the rate of earnings management will be small, obscuring the discontinuity. When EM j * is much larger 11 Because calculation of MVE requires market price, the results in Figures 2 and 3 are subject to a selection effect that restricts the analysis to firms that have market prices. Selection effects are addressed thoroughly in Section The precise multiple is somewhat greater than 5 moving from Q1 to Q2 (6.7) or Q3 to Q4 (8.4) and slightly smaller than 5 moving from Q2 to Q3 (4.7). Page 12

14 than $100,000, many of the observations in intervals further below the benchmark will be managed, again reducing or eliminating the discontinuity. The results in Panels A-D are consistent with the predicted effects of using a single interval width for firms of all size. Results in Panel B show highly significant evidence of a discontinuity, consistent with what is expected if $100,000 is approximately the value of EM j * for firms in Q2. In contrast, results in Panel A show little evidence of a discontinuity, consistent with expectations if $100,000 is much larger than EM j * for the much smaller firms in Q1. 13 Similarly, results in Panels C and D do not show evidence of significant discontinuities, consistent with expectations if $100,000 is much smaller than EM j * for the much larger firms in Q3 and Q4. Figure 2 Panel E shows explicitly how the combination of the four quartile distributions in Panels A D results in an aggregate unscaled earnings distribution that does not show evidence of a discontinuity. 14 The bottom layer of each histogram bar corresponds to the very small number of observations from Q4 (from Panel D), the next layer corresponds to the slightly larger number of observations from Q3 (Panel C), the next layer to observations from Q2 (Panel B), and the top layer to observations from Q1 (Panel A). The aggregate distribution is dominated by the large number of observations from Q1, where the interval width is much larger than the corresponding EM j *, resulting in insignificant evidence of a discontinuity due to earnings management to meet the benchmark. Evidence of the highly significant discontinuity in Quartile 2, is obscured in the aggregate distribution. 13 The basic problem when the peak falls in the immediate vicinity of the benchmark is that it is often not clear what the pre-managed distribution should have looked like under the null hypothesis of no earnings management. In these cases the distributional evidence is inconclusive the distribution neither confirms nor contradicts the theory that earnings are managed to meet the benchmark. It is incorrect to claim that a reported earnings distribution like the one illustrated in Panel D provides evidence of the existence of earnings management to meet the benchmark, and it is equally incorrect to claim that it provides evidence of the absence of earnings management to meet the benchmark. Jacob and Jorgensen (2007) also discuss the inconclusiveness of tests under this situation. 14 The aggregate distribution here corresponds to distributions in DE1 Figure 3 Panel B and DE2 Figures 1, 6, and 8. Page 13

15 We next consider distributions of unscaled earnings using a research design where interval widths that reflect size-related differences in EM j *. We expect the maximum amount of earnings that can be managed at cost lower than the benefits to be proportional to firm size, so we define EM* relative to size. For example, we expect that earnings would almost never be managed by an amount equal to 100% of market value but we would expect that earnings would almost always be managed by an amount equal to.001% of market value. The exact proportion of market value to use is unclear, but one directly relevant factor is materiality, an amount of financial statement error that is permitted by auditing and reporting standards. Materiality is often discussed as a proportion of earnings, such as 5% of earnings (Newton 1977; Leslie 1985; Nelson 1993; Bernard and Pincus 1996; DeZoort, Hermanson, and Houston 2003; Nelson, Smith, and Palmrose 2005). We can translate this materiality guideline into an approximate proportion of our size measure, MVE. If MVE is typically a multiple of between 10 and 20 times long-run expected earnings, then 5% of expected earnings is between.25% and.5% of MVE. 15 Thus, this range represents an amount of earnings management that could typically be accomplished at reasonably low cost given materiality guidelines. 16 While we want to choose interval widths consistent with the materiality guideline calculation above and consistent with previous research, we also want to facilitate comparisons with results from the DE design. Therefore, we use the DE interval width for the quartile where the DE interval width is closest to.25% of the median quartile MVE. For each of the other 15 These amounts also correspond to the interval widths typically used in the previous literature. For example, BD used interval widths of.5% of market value for distributions of earnings levels and.25% of market value for distributions of earnings changes and subsequent studies have commonly used similar interval widths. 16 To see why the DE interval width of $100,000 is implausibly large for the smallest quartile and implausibly small for the larger quartiles, note that $100,000 represents 1.33% of median market value of $7.5 million (and thus 13.3% to 26.6% of expected future earnings). Thus, for many firms in the first quartile, the cost of managing earnings by $100,000 is likely to be far higher than the benefits from meeting the benchmark. On the other hand, for firms in the third and fourth quartiles where median market values are $235 million and $1.9 billion, respectively, $100,000 represents just.04% and.005% of market value, $100,000 represents an amount of earnings management whose cost is likely to be far below the benefits. Page 14

16 quartiles, we then look at the approximate ratio of MVE for the quartile to the MVE for the quartile where we are using the DE interval width, and adjust the interval widths by that approximate ratio. For example, in Figure 2, the $100,000 DE interval width is about.2% of median MVE for Q2, so Q2 in Panel BB uses a $100,000 interval width. For the other quartiles, we adjust the widths by multiples of 5 because the median market values in successive quartiles increase by factors of approximately 5. For Q1 in Panel AA, the interval width is $20,000 (1/5 of the Q2 width). For Q3 in Panel CC, the interval width is $500,000 (5 times the Q2 width). For Q4 in Panel DD the interval width is $2,500,000 (25 times the Q2 width). 17 Using interval widths that reflect size-related differences in the amount of earnings that can be managed at low cost, the results in Panels AA-DD show highly significant discontinuities at the zero earnings benchmark in all four quartiles. For the upper three quartiles in Panels BB DD, the benchmark is clearly to one side of the peak of the distribution and the interpretation is clearcut. All three upper quartiles show highly significant discontinuities at the zero benchmark. For the first quartile in Panel AA where the benchmark falls near the peak of the distribution, results must be interpreted more cautiously. Nonetheless, the number of observations in the first interval to the right of zero is abnormally large relative to the numbers in the surrounding intervals, and it is highly unlikely that the large number in the first interval above the benchmark could be attributable to random variation Earnings scaled by number of shares (earnings per share) Next, we perform a parallel analysis for earnings per share (EPS) because DE1 "argue that firms do not manage earnings deflated by financial variables; and, although it is possible that firms manage earnings per share, the distribution of earnings per share does not show evidence of 17 These interval widths represent.27% of median market value for quartile 1,.21% for quartile 3, and.13% for quartile 4. Page 15

17 earnings management." 18 Because there is no discontinuity in the distribution of EPS in DE1 Figure 1 Panel B but a distinct discontinuity in the distribution of price-scaled earnings in their Figure 1 Panel A, DE1 erroneously infer that scaling causes the discontinuity. We show below that the lack of discontinuity in their EPS distribution is, in fact, due to substantially the same design flaws that exist in the DE analysis of unscaled earnings, though there are some subtle differences in the interpretation of the results. We again start with an overview of the distributions by quartile, where the quartiles are now defined in terms of the scaler advocated by DE, price per share (PPS). Differences across PPS quartiles do not simply reflect the effects of size, because PPS is a size measure (MVE) scaled by an arbitrary number of shares. The theoretical effect of scaling by arbitrary numbers of shares is indeterminate it is possible for large MVE firms to have small PPS due to a large number of shares and for small MVE firms to have large PPS due to a small number of shares. The empirical effect of scaling by number of shares depends on the relation between number of shares and size, as illustrated by two simplified examples. First, if all firms have the same number of shares outstanding, then PPS is a fraction (1/Number of shares) of MVE, so the distribution of earnings per share would correspond exactly to the distributions of unscaled earnings in Figures 1 and 2 (though scaled by the number of shares). Second, if firms continually adjusted their number of shares to maintain a constant PPS, then the number of shares would reflect differences in market value, and earnings per share would correspond to the distributions in Figures 1 and 2 (but scaled proportional to market value). Empirically, the relation between number of shares and size is more complicated than either of these two examples, so we expect distributions of EPS to differ from distributions of unscaled earnings, but in ways that are impossible to specify ex ante. 18 See the summary of the DE1 arguments in DE2 footnote 19, page Page 16

18 Figure 3 shows distributions of EPS by PPS quartile, and the dotted lines show the range of EPS included in the distributions reported in DE, $1.00 to $1.00. Similar to the results in Figure 1, as PPS increases, the EPS distributions shift to the right and become more dispersed. These effects reflect the effects of size as well as the effect of scaling by number of shares. The empirical result of the effect of size combined with scaling by number of shares is that firms with larger PPS (MVE per share) tend to have more positive EPS (earnings per share), and firms with larger PPS tend to have greater variability of EPS. Figure 4 Panels A-D show the distributions of EPS for each of the four PPS quartiles, using the DE interval width of $.01 and range of $1.00 to $1.00. The $.01 interval width used in the DE design does not allow for differences in the amount of EPS that can be managed at a cost lower than the benefits and provides only limited evidence of discontinuities. 19 Although both the second and third quartiles provide visual evidence of discontinuities, the standardized differences are insignificant or only moderately significant. Figure 4 Panel E shows explicitly why the aggregate distribution of EPS reported in DE does not show evidence of a discontinuity. The aggregate distribution is the sum of the Panel D distribution (the bottom layer of each histogram bar), the Panel C distribution (the second layer), and the Panels B and A distributions (the top two layers). 20 As with unscaled earnings, the preponderance of observations included in the DE EPS distribution are from the smallest size quartile. In the intervals immediately adjacent to the zero benchmark, there are about 10 times as many observations from Q1 as from Q2, and roughly 40 times as many as from Q3, and 80 times as many as from Q4. Because it is dominated by observations from Q1, which does not contain a 19 The DE interval width of $.01 represents 1.33% of median PPS for firms in the first quartile,.18% for firms in the second quartile,.066% for firms in the third quartile, and.03% for firms in the fourth quartile. Therefore, the interval width of $.01 used in DE is too wide for the smallest PPS quartile firms and too narrow for the largest PPS quartile firms. 20 The dashed line at the center of the distribution indicates the EPS=$.00 benchmark. The other dashed lines, indicating EPS benchmarks at multiples of $.10, are discussed in the next paragraph. Page 17

19 discontinuity because the interval width of $.01 is too wide for firms with median PPS of $.75, the aggregate distribution does not contain a clear-cut discontinuity. Before turning to results for the design that adjusts for differences in EM j *, we note another prominent feature of the EPS distribution that is consistent with the theory that earnings are managed to meet benchmarks but inconsistent with the DE alternative explanations for discontinuities. Carslaw (1988), Thomas (1989), Das and Zhang (2003), and Grundfest and Malenko (2009) posit and report evidence of earnings management to achieve rounding in EPS, such as earnings management to increase earnings so that EPS rounds up from positive amounts ending in.x9 to the next highest multiple of 10 cents per share. The dashed vertical lines in Figure 5 Panel E indicate the intervals corresponding to EPS at multiples of 10 cents per share (i.e., $.10, $.20,, $1.00 per share) and discontinuities at the various 10 cent per share benchmarks are significant. 21 Of particular note are the highly significant left and right standardized differences at the $1.00 EPS benchmark, consistent with particularly strong incentives to manage earnings such that earnings per share rounds up to a whole dollar. 22 The significant discontinuities at non-zero benchmarks cannot be explained by the scaling explanation offered by DE and, as discussed further in Section 3.2 below, are also inconsistent with the other DE explanations. 23 Returning to the issue of discontinuities at the zero benchmark, we reexamine the EPS distributions using interval widths that reflect size-related differences in EM j *. Applying the criteria used in defining the interval widths in Figure 2 Panels AA-DD, the interval width for 21 Seven of ten left standardized differences are significantly negative at the.05 level while nine of ten right standardized differences are significantly positive. A more powerful test for the "rounding up" form of earnings management can be constructed based on the average of the standardized differences across the k individual benchmarks and this test yields still more significant results. The standardized average computed from the ten left standardized differences in Figure 5 is and the standardized average for the ten right standardized differences is The discontinuity in the aggregate distribution at EPS= $1.00 is also visually apparent in each of the individual quartile distributions shown in Panels B-D. 23 DE1 footnote 20 acknowledges that discontinuities exist at multiples of 10 cents per share but fails to recognize that these discontinuities cannot be explained by any of the "alternative, much more likely, explanations" proposed in DE. Page 18

20 Quartile 2 is set to the $.01 interval width used in DE. For the other three quartiles, the widths and ranges are, respectively, 1/5, 3, and 7 times the width and range used in Quartile 2, resulting in interval widths of $.002, $.01, $.03, and $.07, roughly equal to.25% of median PPS for the four quartiles of $.75, $5.34, $14.75, and $33.75, respectively. 24 Figure 4 Panels AA-DD show the resulting distributions of EPS. The results for Quartiles 2, 3, and 4 are significant and are discussed first. Then we turn to the results for Quartile 1. For Quartile 2 in Panel BB (which is by construction identical to Panel B except for different vertical scales), there is clear visual evidence of a trough below the $.00 benchmark, and the left standardized difference is significant at the.05 level. However, the results are consistent with the conjecture that there are two benchmarks. The number of observations with EPS equal to $.00 is distinctly larger than the number of observations with EPS equal to $.01 and the number of observations equal to $.01 is also distinctly larger than the number of observations with EPS equal to $.00. This is the pattern expected with dual benchmarks where EPS=$.00 yields benefits from achieving non-negative EPS while EPS=$.01 yields additional benefits from achieving positive EPS. 25 At the benchmark of.00, the left standardized difference of is significant. The right standardized difference of.758 (by definition equal to the left standardized difference 24 The Compustat variable EPSFX, expressed in dollars and cents, is used as EPS for quartiles 2, 3, and 4. However, the bin width of $0.002 for quartile 1 requires EPS measured in fractions of a cent. Therefore, for Panel AA, we compute EPS as Compustat variable IBADJ divided by Compustat variable CSHFD. 25 To illustrate how dual benchmarks affect the standardized difference statistics, consider an example where 1) earnings management to avoid negative EPS leads to a sharply larger number of observations in the $.00 interval than in the $.01 interval, and 2) earnings management to achieve positive EPS also leads to a larger number of observations in the $.01 interval than in the $.00 interval by the same amount. In this example, the left standardized difference at $.00 is negative, because the number of observations with EPS= $.01 is less than the average of the numbers with EPS= $.02 and EPS=$.00. However, because of the assumption that the discontinuities at $.00 and $.01 are the same size, the number of observations with EPS=$.00 is equal to the average of the number of observations with EPS= $.01 and EPS=+$.01. Therefore, the right standardized difference at $.00 is zero (rather than positive). Similarly, the left standardized difference at $.01 (and is by definition equal to the right standardized difference at $.00) is zero. However, the right standardized difference at $.01 is positive because the number of observations with EPS=$.01 is greater than the average of the number of observations with EPS= $.00 and EPS=$.02. Page 19

21 at.01) is insignificant. At the benchmark of.01, the right standardized difference of (not reported in the figure) is significant. For Quartiles 3 and 4, Panels CC and DD show highly significant discontinuities. 26 For Quartile 3, the left and right standardized differences are each significant at the.01 level and for Quartile 4, the standardized differences are each significant at the.05 level. For Quartile 1 in Panel AA, the evidence is inconclusive. The EPS distribution includes many observations of $.00 EPS and, not unexpectedly for a set of firms with median PPS of $.75, a larger proportion of small negative EPS than small positive EPS. 27 Overall, the distribution for firms in Quartile 1 neither confirms nor contradicts the theory that earnings are managed to meet the benchmark. 28 It is also important to recognize that very low PPS also proxies for financial difficulty for institutional reasons. Firms with PPS<$1.00 are generally not allowed to trade on major exchanges, and Table 2 shows that the inability to maintain PPS above this amount is also associated with low revenue, low assets, and negative equity. Thus, firms in the first PPS quartile are more likely to be experiencing financial difficulty, and also likely to have even smaller values of EM j *. Table 2 shows that financial difficulty is especially strongly related to values of PPS<$1.00. In fact, results in Appendix Figure A-3 using interval widths of $.005 show that the 26 Note that the interval widths used in Panels CC and DD group EPS=.00 and EPS=.01 into a single interval, so that the first interval above the benchmark combines all observations meeting either benchmark. 27 Note that in the first quartile, the zero benchmark is somewhat ambiguous. For example, if the zero benchmark is defined by EPS rounded to the nearest whole cent, the zero benchmark is $.005. Thus, observations in the first two intervals below the benchmark, which comprise small negative EPS between.000 and $.002 and between $.002 and $.004, represent $.00 EPS when rounded to the nearest whole cent. This ambiguity will tend to obscure empirical evidence of discontinuities. 28 Beaver et al. (2007) document that the number of shares outstanding is decreasing in earnings around zero. It is possible that the EPS measure used by DE is deflated by a higher number of shares outstanding for loss firms than the lower number of shares outstanding for profit firms. However, this explanation is unlikely to induce discontinuities in EPS because we observe discontinuities at multiples of $0.10 in Figure 5 Panel E, even though there is no evidence in DE or elsewhere in the literature that the number of shares is systematically greater at multiples of $0.09 per share than at the corresponding multiples of $0.10 per share. Page 20