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The Detection of Earnings Manipulation Messod D. Beneish Indiana University (formerly at Duke University)

November, 1994

The Detection of Earnings Manipulation

Messod D. Beneish*

First Draft: December 1993 Current Version: November 1994

Comments Welcome

* Associate Professor, Duke University, Fuqua School of Business. I have benefitted from the comments of Andy Alford, Jack Ciesielski, Linda DeAngelo, Martin Fridson, Cam Harvey, David Hsieh, Charles Lee, Mike Moore, Laureen Maines, Bob Nau, Vic Pastena, Eric Press, Katherine Schipper, Bob Whaley, Mark Zmijewski, an anonymous reviewer,workshop participants at Duke, Temple, Université Laval, Université du Québec à Montréal and participants at the 1994 AAA Conference. I am especially indebted to David Hsieh for his generous econometric advice and the use of his estimation subroutines, and to Jack Hughes for many insightful discussions. I thank Julie Azoulay, Pablo Cisilino and Melissa McFadden for expert assistance. This research is supported by the Center for Accounting Research at the Fuqua School of Business.

1.

Introduction This paper presents a model to distinguish manipulated from non-manipulated reporting. I

define earnings manipulation as an instance where management violates GAAP in order to beneficially represent their firms' financial performance. I use financial statement data to construct variables that capture either the effects of manipulation or preconditions which may prompt firms to engage in such activity. Since manipulation typically consists of an artificial inflation of revenues or deflation of expenses, I find that variables that take into account the simultaneous bloating in asset accounts have predictive content. I also find that sales growth has discriminatory power as the primary characteristic of firms involved in earnings manipulation is that they have high sales growth prior to periods during which manipulation is in force. Since instances of manipulation are infrequent and the relative costs of classification errors are not amenable to measurement, my analysis assesses what levels of relative error costs are necessary to justify departing from a naive strategy that classifies all firms as non-manipulators. My research design identifies earnings manipulators that violate GAAP rather than earnings managers that operate within the bounds of GAAP (Schipper (1989)). 1 find that sample manipulators typically overstate earnings by recording fictitious, unearned, or uncertain revenue, recording fictitious inventory, or improperly capitalizing costs. The context of earnings manipulation is an annual report or a 10-K for about two-thirds of the sample and a security offering prospectus (initial, secondary, debt offering) for the remaining third. Sample manipulators are relatively young, high growth firms, suggesting that they manipulate in an effort to allay the perception of growth deceleration. Manipulation has significant financial statement and stock market impacts. On average, restatements reduce previously reported retained earnings by about 45%, total assets by about 10%, and shareholder wealth losses range from -24.9% to 30.0% in the three days and two weeks surrounding manipulation disclosure.

I conduct tests using a sample of 74 firms that manipulate earnings and all COMPUSTAT firms matched by two-digit SIC for which data are available in the period 1982-1992. 1 estimate a model for detecting earnings manipulation using sample manipulators and their controls in the period 1982-1988 and evaluate the model's performance on a holdout sample in the period 19891992. The model distinguishes manipulators from non-manipulators, and has pseudo-R2s of 30.6% and 37.1% for two different estimation methods.1 The evidence indicates that the probability of manipulation increases with: (i) increasing days sales in receivables, (ii) deteriorating gross margins, (iii) decreasing asset quality (as defined later), (iv) sales growth, and (v) increasing accruals. I show that the model discriminates manipulators from non-manipulators in the holdout sample. I also show that the expected costs of misclassification of the model compare favorably to those of a naive strategy that classifies all firms as non-manipulators. The results are robust to different estimates of the prior probability of earnings manipulation, several specifications of the model and various transformations of the explanatory variables. The results are also insensitive to the choice of estimation and holdout samples. The evidence needs to be interpreted in light of possible sample selection biases. The estimation addresses the bias arising from oversampling manipulators, but it is based on a sample of discovered manipulators. It is possible that there are successful, unidentified manipulators. My conjecture is that asset and earnings inflation cannot be sustained over an extended period of time, and that the sample of manipulators represents a substantial portion of the manipulators in the population. Given this caveat, the evidence of a systematic relation between the likelihood of manipulation and financial statement variables suggests that accounting data are useful in detecting manipulation and assessing the reliability of accounting earnings.

1

I estimate the probability of manipulation using weighted exogenous sample maximum likelihood probit (WESML), in addition to unweighted probit, because manipulators are oversampled relative to their true proportion in the population.

The paper proceeds as follows. Section 2 presents the sample, analyzes the characteristics of manipulators, and presents evidence of the effects of manipulation. Section 3, discusses the estimation method and choice of explanatory variables. Section 4 presents the empirical results and section 5 concludes.

2. Data 2.1

Sample Selection I obtain a sample of manipulators from two sources: (i) firms subject to accounting

enforcement actions by the SEC and (ii) a news media search. These sources are complementary since according to Feroz, Park, and Pastena (1991), over a third of the SEC enforcement actions are initiated from scanning the financial press and there is a lag of three to four years between the occurrence of manipulation and the SEC enforcement action. I identified firms subject to accounting enforcement actions by the SEC using Accounting and Auditing Enforcement Releases (AAERS) numbers 132 to 502 issued from 1987 to 1993. Of 363 AAERs examined (#372 to #379 were not assigned by the SEC), I eliminated 80 AAERs relating to financial institutions, 13 relating to auditing actions against independent CPAs, nine relating to 10-Q violations that were resolved in annual filings, and 157 relating to firms for which no financial statement data are available on either COMPUSTAT, S&P Corporate Text or 10-K microfiche. As described in Table I Panel A, the final sample of 102 AAERs relates to 48 firms that violate GAAP.2 These manipulators’ reporting violations originate in fraud, gross negligence, and reckless disclosure. 2

The SEC focusses on actions that have a high chance of success and does not pursue "earnings managers." For example, consider a firm involved in front-loading. If the firm offers customers or distributors credit or even return incentives, and the latter make large purchases towards year end, is this earnings management or manipulation? One could argue it either way but I find no instance where the SEC equates front-loading alone to manipulation. Sample firms that front-load also are involved in recording unearned or fictitious revenue. For example, ASK Group also keeps the books open past the end of the accounting period, and Software Toolworks also records sales pursuant to a fictitious licensing agreement.

I also conducted an extensive news media search on LEXIS/NEXIS in the period January 1987 to April 1993. Specifically, the search encompassed the following data bases in LEXIS/NEXIS: Barron's, Business Week, Business Wire, Corporate Cash Flow, Disclosure Online, Forbes, Fortune, Institutional Investor, Investor Daily, Money, The Courier Journal, The New York Times, The Wall Street Journal, The Washington Post, and The Reuter Business Report. I used the following keywords: "earnings management;" "earnings manipulation; "cooking the books;" "financial statements or reports" with adjectives such as deceptive, false, fraudulent, misleading, illusive, inappropriate, misstated, and spurious; and "inflated or overstated" with either profits, earnings, or income. The search identified 80 firms mentioned in articles discussing earnings manipulation. In addition to seven firms that are identified by the SEC search, I eliminate ten firms for which no financial statement data are available on either COMPUSTAT, S&P Corporate Text or 10-K microfiche, five financial institutions, and 17 firms mentionned in articles with no discussion of an accounting or disclosure problem.3 I require ex post evidence of manipulation for the remaining 41 firms. That is, I require that firms restate earnings to comply with GAAP at the request of auditors or following the conclusion of an internal investigation. This requirement makes sample entry consistent with the SEC search in the sense that a restatement is usually the outcome of successful SEC investigations (in addition to a permanent injunction from future violations of security laws). This criterion eliminates fifteen firms and is imposed to eliminate firms that manage earnings within GAAP and to ascertain that the articles are not based on self-serving rumors by short sellers. That is, some firms such as Battle Mountain Gold, Blockbuster, and Community Psychiatric Centers voluntarily change their accounting choices or estimates as a result of pressure from the investment community. Since their choices were initially within GAAP they are not manipulators. 3

For example, Flynn and Zellner (1992), in an article on the manipulation of earnings at Chambers Development, discuss other firms in the waste management industry such as Sanifill Inc., and Waste Management, without referring to any accounting measurement or disclosure problem.

Additionally, there are firms that do not restate. For example, articles by Hector (1989), and Khalaf (1992), discuss changes in useful lives at General Motors, unusual charges at General Electric and short sellers’ interest in Advanta Corp. Neither firm is subsequently required to reverse the effects of its accounting decisions and thus, the firms are excluded from the sample. The 26 additional manipulators identified by the news media search have similar size, leverage, liquidity, profitability and growth characteristics than the 48 SEC manipulators suggesting that manipulators in both searches are not drawn from different populations. The final sample consists of 74 firms that manipulated earnings and 2332 COMPUSTAT non-manipulators matched by 2-digit SIC industry and year for which financial statement data used in the model (see section 3) are available.4 There are 63 different four-digit SIC codes represented, with four firms in SIC 7372 (Software), and three firms in both SIC 3571 (Computers), and SIC 5731 (Audio-visual retail stores). Table 1, Panel B reports the distribution of manipulators by two-digit SIC groups. Manufacturing (SIC 30-39) and Personal and Business Services industry groups (SIC 70 to 79) represents 45% of the sample.

2.2

First Disclosure of Manipulation I identify the first disclosure of manipulation to assess the stock market impact of earnings

manipulation discovery and gain insights about the parties that first disclose the manipulation. The analysis is based on 53 firms because there are no news media announcements for 21 of the 48 firms identified by the SEC search. The event date (day 0) is the date of the first article discussing actual or alleged manipulation of earnings. The source of the event dates is the Wall Street Journal (49 times), wire services (three times) and Barron's (once). The 53 disclosures consist of announcements of (i) SEC investigations, including charges by the SEC or joint 4

I treat firms in the same industry for which my searches do not identify an instance of manipulation as nonmanipulators. Since successful manipulators would not be identified by the searches, it is possible that the control sample of 2332 contains manipulators. This biases against discriminating manipulators from non-manipulators, making the tests more conservative.

criminal investigations (19 times), (ii) internal investigations, including suspensions or firing of officers for wrongdoing or embezzlement, CEO resignations, directors or new CEOs questioning accounting practices, withdrawals of fmancial statements, and indications that material adjustments are required (18 times), (iii) filings of lawsuits by one or several claimholders for fmancial statement fraud or misrepresentation (eight times), (iv) auditors resigning, withdrawing previous years opinions, disagreeing with management, and requiring restatements (eight times). This suggests various sources of manipulation discovery and is consistent with how the SEC initiates enforcement actions.5 The public discovers the manipulation through the actions of the SEC for 40 out of 74 firms or 54% (including the 21 firms in the SEC search without a news media announcement), and through the actions of auditors and investors for 16 firms (22 %). Interestingly, for the remaining quarter of the sample, the public first becomes aware of the manipulation from disclosures by the firm itself. Such disclosures are likely made at the request of a subset of directors or officers fearing the consequences of lawsuits. It is possible that several interested parties discover manipulation simultaneously, but only one source is identified in news-media articles.

2.3

Characteristics of Sample Firms In Table 2, 1 compare manipulators’ financial characteristics to those of industry-matched

controls. I find that in the fiscal year prior to the year containing the public disclosure of earnings manipulation, manipulators are smaller (when size is measured in terms total assets and sales), less profitable, and more levered. Manipulators also differ from controls in that they experience higher growth. The median sales growth of manipulators (34.4%) is significantly larger than that of controls (9.4%). This raises the question of whether growth is exogenous or results from 5

Feroz, Park and Pastena (1991) report that in the opinion of a former SEC Chief Accountant, the SEC obtains 50% of the leads from reviews of financial statements and security offerings; a third from scanning the financial press, and the rest result from tips.

manipulation. In the year prior to the fiscal year of manipulation, I find that manipulators also have significantly higher growth that non-manipulators (medians are 29.4% v. 10.6%) suggesting that growth originates exogenously. This profile of manipulators as firms with high growth prospects could explain why I find that manipulators and controls have similar size when size is measured as the market value of equity.

2.4

Type and Effect of Earnings Manipulation Table 3, Panel A reports the frequency of various types of earnings manipulation. There

are 107 instances of revenue and expense manipulation identified for 74 firms. The most frequent type of manipulation is an overstatement of revenues that is achieved by recording fictitious, unearned or uncertain revenue (40 cases). Examples of revenue manipulation include creating false invoices, keeping the books open past the end of the accounting period, and recognizing revenues before products are completed, shipped or contracts signed. Earnings are also manipulated by understating expenses. Typically, this is achieved by recording fictitious inventory, capitalizing expenses, or underproviding reserves. Examples of expense manipulation include the bloating of inventory via double counting, treating non-existent inventory as in transit, and capitalizing expenses such as executive salaries, travel expenses, legal costs, advertising costs, and R&D costs. There are also a few instances where one-time items are lumped with operations, and two instances where manipulation is by disclosure omission.6 In Table 3 Panel B, I report the financial statement effect of reversing earnings manipulation. The amount of earnings overstatement is estimated from information in SEC's 6

Caterpillar failed to warn readers in its Management Discussion and Analysis that its 1989 results were significantly affected by the consolidation of its Brazilian subsidiary. Not only had this subsidiary benefitted from one-time tax breaks and export subsidies, it was incorporated in the US financial statements at an artificially high rate of exchange that was unlikely to prevail in the future given that Brazil was experiencing four-digit inflation. Poloron Products failed to warn readers that, in a significant contract, the firm had failed to conform to the specifications of the Department of Defense in the production of grenade bodies.

Accounting and Auditing Enforcement Releases, the income statement, footnotes, and the management discussion and analysis in 10-K reports. For 57 out of 74 firms with available subsequent financial statements, I measure the amount of earnings overstatement as the difference between retained earnings as initially reported and the corresponding restated retained earnings. I find that the mean (median) effect of earnings manipulation is an overstatement of 44.9% (46.7%) of retained earnings and an overstatement of 10.6% (5.5%) of total assets. In Table 3 Panel C, I present evidence of the stock market impact of earnings manipulation disclosures (see Table 3 for a description of prediction error estimation). Cumulative average prediction errors (CAPE) for periods ranging from three days to two weeks surrounding the event date indicate significant shareholder wealth losses ranging from -24.9% to 30.0%. The median CAPEs are -18.5% and -20.4% and only six and eight firms have positive CAPEs, thus rejecting the null that the proportion of positive and negative CAPEs are equal. This is consistent with evidence in Feroz, Park and Pastena (1991), who report a -13% shareholder wealth loss among firms subject to SEC accounting enforcement actions.

3. Method This section discusses the estimation of the earnings manipulation detection model and the selection of the model’s variables. The model is written as follows: ~ M i = β' X i + ∈ i

(1)

where M is a dichotomous variable coded 1 for manipulators and 0 otherwise, X is the matrix of ~ is a vector of mean zero independent and identically normally explanatory variables, and ∈ distributed residuals. 3.1

Estimation Earnings manipulators are oversampled relative to their true proportion in the population.

The sample is state-based, as in previous research by Zmijewski (1984), Palepu (1986) and

Dopuch, Holthausen and Leftwich (1987). The econometric justification for a state-based sample is that a random sample would likely generate a smaller number of manipulators, thus making the identification of an earnings manipulation classification model difficult. However, estimation of a dichotomous state model that ignores the state-based sample procedures yields asymptotically biased coefficient estimates (Hsieh, Mansky, and McFadden (1985)). Thus, following Zmijewski (1984), and Dopuch, Holthausen and Leftwich (1987), 1 use weighted exogenous sample maximum likelihood probit (WESML). WESML accounts for state-based sampling by weighing the likelihood function according to the proportion of earnings manipulators in the sample and in the population. The model is estimated by maximizing the following weighted log-likelihood function:

(

)

[(

L WEMSL = α p α S ∑ M i ln [Φ(β' X i )] + 1 − α p N

i =1

) (1 − α S )]∑ N

i =1

(1 − M i ) ln [1 − Φ(β' X i )]

(2)

where Φ is the cumulative distribution function for a unit normal, and αS, αp are the proportions of firms which manipulate earnings in the sample and in the population. The estimation sample spans the period 1982-1988 and consists of 50 manipulators and 1708 controls. Using WESML requires an estimate of the proportion of firms in the population that manipulate earnings. Assuming that the population from which the firms are sampled is the population of COMPUSTAT firms, one estimate of the proportion of manipulators in the population (αp) equals .0069 (50/7231). Because I have no way of assessing the validity of this assumption, I evaluate the sensitivity of the model to the different specifications of the prior probability of manipulation.7 I find that the results are similar when that probability is specified as either .0059, .0079, .0089, and .0099. Further, I estimate the model with unweighted probit, given evidence in Dopuch, Holthausen and Leftwich (1986) that for prediction, but not parameter inference, unweighted probit performs as well as WESML. Using unweighted probit assumes that 7

For example, one problem is that the sample only contains discovered manipulators. If there are successful manipulators and they are not identified, it is impossible to determine the true proportion of manipulators in the population.

the prior probability of earnings manipulation is .02844 (50/1758), thus providing further evidence on the model's sensitivity to the specification of the prior probability of manipulation. Having discussed estimation issues, I now turn to the composition of the X matrix.

3.2

Explanatory Variables Can accounting data be used to detect earnings manipulation? If the manipulation

encompasses not only earnings but also the signals that investors and analysts presumably rely on to avoid raising red flags, then the discriminatory power of accounting data is diminished. This would bias the results against rejection of a null hypothesis on the variables’ coefficients, and limit the usefulness of using accounting information for detecting earnings manipulation. There is some casual evidence suggesting that accounting signals are not usually manipulated. For example, discussing the fraud at MiniScribe Corporation, where accounting signals were also manipulated, Kellogg and Kellogg (1991, p. 16-33) state:

"We have never seen such an understanding of the relationships between inflating sales and profits and the effects of inventory. In all our experiences [emphasis added], the inflation of sales and earnings results in a continuous rise in inventories so that sooner or later the inventories are so bloated that the fraud is apparent." This statement by the publishers of one of three newsletters with an accounting focus suggests that manipulators cannot inflate revenues or deflate expenses without simultaneously bloating an asset account.8 In the absence of a theory of manipulation, I rely on four sources to choose explanatory variables based on financial statement data. First, I consider variables used in financial statement 8

To my knowledge, there are three active advisory newsletters with an accounting focus: The Analyst’s Accounting Observer (Jack Ciesielski), Behind the Numbers (David Tice) and Financial Statement Alert (Kellogg and Associates). These newsletters command a subscription price that is 20 to 30 times that of over 100 analysts’ newsletters whose reports appear in the Investor’s Digest. If this is because they cater to institutional rather than individual investors, it suggests that sophisticated investors demand their services.

analysis such as measures of liquidity, leverage, profitability, size, and growth. Second, I draw variables that analysts consider as signposts for the future from Lev and Thiagarajan (1993) and consider additional signals about future performance that appear in the professional literature (O'Glove (1987), Fridson (1991), Kellogg and Kellogg (1991), and Siegel (1991)). The presumption is that earnings manipulation is more likely when firms’ future prospects are poor. Third, I consider variables based on cash flows and accruals.9 Fourth, I consider variables drawn from positive theory research that hypothesizes contract-based incentives for earnings management. The model includes up to nine variables.10 The variables are measured using data from the fiscal year of the first reporting violation, e.g., the first year for which the firm is subsequently required to restate. I designate seven of the nine variables as indices as they are intended to capture distortions arising from manipulation by comparing financial statement measures in the year of the first reporting violation to the year prior. The variables are thus not measured contemporaneously with manipulation discovery since, in line with Feroz, Park, and Pastena (1991), manipulation becomes public on average 19 months after the end of the fiscal year of the first reporting violation. The nine variables, constructed so as to expect each variable to positively affect the likelihood of manipulation, are as follows. Days sales in receivables and days sales in inventory Index (DSRI and DSINV) gauge whether receivables, inventories and revenues are out-of9

Recent research has provided evidence of the incremental information content of cash flows and accruals and used accrual measures to provide evidence consistent with earnings management. See for example Wilson (1986), DeAngelo (1988), McNichols and Wilson (1988) and Jones (1991). 10

I also considered but did not include in the model four other types of variables to examine whether the model could be improved: (i) variables isolating the income effect of non-recurring items, (ii) variables capturing the rate and changes in the rate of intangible amortization as well as variables identifying the funding status of pension funds, (iii) cash flow based variables such as the cash flow adequacy ratio and the cash flow coverage of debt service, and (iv) signals of earnings quality documented by Lev and Thiagarajan (1993), such as changes in the receivable provision, changes in capital expenditures. None of these variables improved the model performance hence are not reported.

balance. A large increase in days sales in receivables or inventory raises the likelihood that receivables and inventory, and thus earnings and sales are inflated. The asset quality index (AQI) evaluates changes in the proportion of total assets for which future benefits are potentially less certain and is an aggregate measure of the change in the asset realization risk analysis suggested by Siegel (1991). An increase in asset realization risk indicates an increased propensity to capitalize and thus defer costs.11 Sales Growth Index (SGI), is included under the assumption that growth firms have greater incentives to manipulate earnings because, while they are rewarded for their performance, the first indication of a slowdown has a large adverse effect on stock prices.12 The Gross Margin Index (GMI) assesses whether gross margins have deteriorated, a negative signal about firms’ prospects (Lev and Thiagarajan (1993)). The assumption is that firms with poorer prospects are more likely to engage in earnings manipulation. The same rationale applies to the Sales General and Administrative Expenses Index (SGAI) which assesses changes in SGA to sales and to Depreciation Index (DEPI) which measures changes in the rate of depreciation. Leverage Index (LVGI) measures the change in leverage (total debt to total assets) and is included to capture debt covenant incentives for earnings manipulation. Working Capital Accruals to Total Assets (WCATA), calculated as in Jones (1991), is included to capture how much of accounting earnings are cash based. In table 4, 1 describe how each of these variable is calculated using COMPUSTAT codes, and compare its distribution for manipulators and non-manipulators in the estimation sample. The results indicate that on average, manipulators have significantly larger increases in days sales in receivables, greater deterioration of gross margins and asset quality, higher growth, and a greater involvement in accruals. 11

The variable is computed as the change in the proportion of non-current assets other than PPE to total assets. Recognizing that part of the change can be attributed to acquisitions involving Goodwill, I also calculate this variable using the ratio of non-current assets other than PPE and Goodwill to total assets and obtain similar results. 12

To this end, Fridson (1993, pp. 7-8) states: "Almost invariably, companies try to dispel the impression that their growth is decelerating, since that perception can be so costly to them."

4.

Empirical Results I discuss the empirical findings in two parts. First, I present the estimation of the model

with WESML and unweighted probit, and assess the model’s performance on a holdout sample. Second, I compare the model’s expected costs of misclassification to those of a benchmark naive strategy that classifies all firms as non-manipulators.

4.1

Model Estimation and Holdout Sample Tests Table 5, Panel A reports the results of the WESML probit and unweighted probit

estimations of the model. The likelihood ratio test indicates that for both estimations the model has significant power, with χ2 statistics (p-values) of 34.5 (.000) and 129.2 (.000). The model has descriptive validity with pseudo-R2s of 30.6% and 37.1%. Since coefficient estimates have similar magnitudes and significance across estimations, I discuss the results of the WESML estimation.13 The variable days sales in receivables index has a positive coefficient, .821, and is significant at the 5% level with an asymptotic t-statistic of 6.40. This is consistent with disproportionate increases in receivables raising the likelihood that a firm has inflated revenues. The variable gross margin index has a positive coefficient of .459 that is over three standard deviations from zero. This is consistent with firms facing poor prospects having greater incentives for earnings manipulation. The asset quality index also has a significant positive coefficient (.306, t-statistic 2.82), consistent with the likelihood of earnings manipulation increasing when firms’ change their involvement in cost deferral. The sales growth index has a positive coefficient that is over three standard deviations from zero, consistent with growth firms facing growth deceleration having more incentives to manipulate earnings. The accruals to total 13

The results reported in Table 5 do not contain the days sales in inventory variable (DSINV). This is because about 20% of sample firms have no inventory. When the model is estimated with DSINV, the variable does not attain significance and I obtain similar results for the remaining variables.

assets has a significant positive coefficient consistent with there being less cash behind accounting income for manipulators. The coefficients on the leverage, depreciation and SGA variables are not significant. It is possible that these variables are associated with earnings management, not manipulation. For example, a change from accelerated depreciation to straight line or a revision that lengthens useful lives, would result in higher values of the depreciation index. However, this is an instance of earnings management and the firm would not be included in the sample. Similarly, for the leverage variable, incentives to comply with debt covenants may be insufficient to induce earnings manipulation because the costs of non-compliance are small (Beneish and Press (1993) estimate these costs to range between 1 and 2% of market value of equity).14 In table 5, Panel B I report the estimated probabilities of earnings manipulation for both the estimation and holdout samples. For the estimation sample, the model estimated using WESML predicts higher average (median) probability of earnings manipulation .107 (.024) for manipulators than for non-manipulators .006 (.003). Similarly, the model estimated using unweighted probit predicts higher average (median) probabilities for manipulators .237 (.099) than for non-manipulators .022 (.011). Wilcoxon and median tests reject the null hypothesis that estimated probabilities for manipulators and non-manipulators are drawn from the same distribution. Results for the holdout sample of 24 SEC manipulators and 624 controls are similar to the estimation sample findings. The model predicts that manipulators are, on average, about 10 times more likely to manipulate earnings. The distributions of estimated probabilities for manipulators and non-manipulators based on unweighted probit illustrate these differences in Figures 1 and 2. For the estimation sample, Figure 1 indicates that nearly all the non-manipulators (93.4%) have an estimated probability less than .05 compared to 38.0% of the manipulators. The same pattern appears for the corresponding distributions for the holdout sample in Figure 2. For 14

I also consider three alternative definitions of leverage: total debt to market value of equity, total debt to book value of equity, and long-term debt to total assets as well as using leverage level variables instead of changes. None of the alternative leverage measures attains significance.

example, 56.1% of the non-manipulators have an estimated probability less than .01, compared to 20.8% of the manipulators. I assess the robustness of the results in three ways. First, even though collinearity is not likely to be a problem (none of the 36 Pearson correlation coefficients is greater than .25), 1 drop up to four variables from the model to assess the stability of the coefficient estimates. Dropping the depreciation, leverage, SGA, and accrual variables one at a time and in combination yields similar results for the remaining variables. Second, I assess the sensitivity of the WESML estimation results to the specification of the prior probability of manipulation. In addition the estimations based on prior probabilities of .0069 and .02844 (implicit in unweighted probit), I estimate the model with four alternative prior probabilities of earnings manipulation, namely .0059, .0079, .0089, .0099. The four new estimations yield similar results with χ2 statistics ranging between 29.61 and 48.65 and pseudo-R2s ranging from 29.81 % and 32.65 %. Moreover, the coefficients estimates are similar in size and significance across the four new specifications of the prior probability of manipulation (results available on request). Third, while the holdout sample is chosen to be independent from the estimation sample, I assess the sensitivity of the results to the choice of estimation and holdout samples. To do so, I generate 100 random samples of 50 manipulators and 1500 controls with the RANUNI function in SAS and use these to estimate the model 100 times. I report descriptive statistics on the 100 estimations using unweighted probit in Table 6, Panel A. All 100 estimations are significant with χ2 statistics ranging from 51.90 to 142.69 and pseudo-R2s ranging from 12.4% and 44.4%. The magnitude and significance of the estimated coefficients generally parallels that reported in Table 5. That is, the coefficients on the receivables, asset quality, sales growth and accrual variables are significant at the 5% level at least 95 times out of 100, while the coefficients on the depreciation, SGA and leverage variables rarely attain significance. A difference with the results in Table 5 occurs for the gross margin index as its coefficient is only significant at the 5% level 84 times out

of 100. While I previously argued that a deterioration of the gross margin increases the likelihood of manipulation, it is possible that increasing gross margins (e.g., as an artifact of inventory inflation), can also increase the likelihood of manipulation. I obtain 100 random holdout samples by treating the complement of 24 manipulators and 832 controls to each random estimation sample as a holdout sample and reproduce the tests on estimated probabilities in Table 6, Panel B. As in Table 5, I find that manipulators are predicted to be significantly more likely to manipulate than controls. The evidence thus suggests that the results are not sensitive to the choice of estimation/holdout samples. Overall, the estimation results provide evidence of a systematic relation between the likelihood of manipulation and financial statement data. Since the model distinguishes manipulators from non-manipulators, I investigate its performance relative to a benchmark naive strategy that classifies all firms as non-manipulators.

4.2

Comparing the model to a Naive Strategy I assess the usefulness of the model as a classification tool by comparing its expected costs

of misclassification to that of a naive strategy that classifies all firms as non manipulators under various error cost assumptions.15 The cost of Type I errors (classifying a firm as a nonmanipulator when it manipulates) and Type II errors ( classifying a firm as a manipulator when it does not manipulate) are not measured. Following prior research, I consider relative costs ranging from 1:1 to 100:1 and compute the expected costs of misclassification (ECM) as follows: ECM = P(M) PI C1 + (1-P(M)) PII CII

15

(3)

An alternative naive strategy that classifies all firms as manipulators is also considered when it has lower expected costs of misclassification. This occurs when the ratio of relative costs is greater than the inverse of the prior probability of manipulation. The switch occurs at costs of 40:1 for unweighted probit (> 1/.02844). I believe that the naive strategy is a reasonable benchmark because discovered manipulation is an infrequent event. In addition, though one may question the appropriateness of the naive strategy as the relative cost of errors rises, there is, to my knowledge, no easily implementable alternative benchmark.

where P(M) is the prior probability of encountering earnings manipulators (.0069 for WESML and .02844 for unweighted probit), PI and PII are the conditional probabilities of a Type I and Type II errors and C1 and CII are the costs of Type I and Type II errors.16 In Table 7, I compare the model's expected costs of misclassification to those of a naive strategy of classifying all firms as non-manipulators. The naive strategy makes no Type 11 errors (PII=O) and the conditional probability of a Type I error (PI) is one. Thus, ECM(naive)=P(M) C1 or .0069 CI for the WESML comparison and .02844 CI for the unweighted probit comparison. Panel A describes the results for the WESML estimation. In the estimation sample, the results 17

indicate that the model has lower expected misclassification costs than a naive strategy when the

cost of a type I error is greater than that of a type II error. As the relative cost increases, the frequency of Type I errors is smaller, and the model's misclassification costs decrease relative to those of a naive strategy. The point estimates of misclassification costs are similar in the holdout sample and the model's costs compare favorably to those of a naive strategy when Type I to Type II error costs are greater that 1:1. In Panel B, I report similar results for the model estimated using unweighted probit. That is, when the ratio of Type I to Type II error costs is equal to 1, the model and the naive strategy make the same errors and have the same expected cost of misclassification. However, for costs ratios of say, 10:1 and 20:1, the model's estimated cost of misclassification is 25.8% and 38.0% lower than that of a naive strategy. In Table 8, I analyze whether the probability of a type I error varies depending on the type of manipulation. I distinguish four sources of manipulation depending on whether the manipulation originates primarily in revenues, expenses, disclosure omission or has multiple 16

The conditional probabilities are calculated for each possible cut-off probability by dividing the number of Type I and Type II errors by the number of manipulators and non-manipulators in the sample. For each level of relative costs j, I select the cut-off probability (CUTOFFij) that minimizes the expected costs of misclassification using estimated probabilities by evaluating equation (3) for each observation in the estimation sample: CUTOFFij = P(Mi) such that ECMij = Min{ECM1j, ECM2j,. . . , ECM1708j}

sources. I find that the model makes less type one errors when the manipulation originates from multiple sources and that the model never detects manipulation by disclosure omission. The preceding evidence suggests that the model outperforms the naive strategy when the cost of a Type I error is greater than that of a Type II error. Assessing whether the model captures economic agents’ judgements about the likelihood of manipulation requires determining their relative error costs. While relative errors costs cannot be measured, frequent discoverers of manipulation (the SEC, auditors, and investors) are likely to have high Type I error costs. For example, regulators (the SEC) seeking to protect public interests or auditors seeking to avert losses from lawsuits are likely to have relatively high Type I error costs. Investors are also likely to have relatively high Type I error costs if the stock price loss at discovery is an indication of a Type I error penalty, whereas their Type II error cost would be low given the availability of substitutes. Thus, the model likely captures assessments of the likelihood of manipulation made by the SEC, auditors, and investors.18

5.

Conclusion The evidence in this paper should be interpreted in light of two assumptions. First, the

model's validity depends on the sample identified representing a substantial proportion of the manipulators in the population. Second, the holdout sample results are based on a comparison to a naive strategy that classifies all firms as non-manipulators and the assumption that costs of Type I errors are greater than the corresponding cost of Type II errors. Given these warnings, the evidence indicates that earnings manipulation—with its dramatic effects on both financial statements and stock prices—can be detected using financial statement variables.

18

Since for several proxies of earnings manipulation, I rely on notions of earnings and assets quality that are commonly used by analysts, it raises the question of why analysts are not more frequently the source of manipulation discovery. There is anecdotal evidence that analysts acting of their suspicions were barred from access to firms’ information, became the subject of an investigation, or got fired leading Galant (1993, p. 174) to suggest that analysts are "better off being wrong with the crowd and writing a lot of tickets." That analysts are careful when issuing negative recommendations is likely an indication that their cost of making a Type II error-incorrectly considering a firm as manipulator is large.

Evidence of a systematic association between earnings manipulation and financial statement data is of interest to both accounting researchers and professionals because it suggests that accounting data not only meet the test of providing useful information but also enable an assessment of reliability. Accounting researchers can use the model as a proxy for the reliability of information in earnings announcements. For example, research on the earnings-returns relation suggests that the usefulness of earnings signals is limited. The model can improve the association between earnings and returns by allowing researchers to discount earnings surprises depending on the likelihood that the surprises originate from earnings manipulation. The explicit classification model only requires two years of data (one annual report) to evaluate the likelihood of manipulation and can be inexpensively applied by the SEC, auditors, and investors to screen a large number of firms and identify potential manipulators for further investigation. The screening use of the model may also be appropriate in research investigating financial reporting behavior in the context of security offerings and litigation. Since earnings manipulation occurs frequently in the context of a security offering and manipulators are often subject to lawsuits, it may be useful to determine whether the behavior being studied is earnings management or earnings manipulation.

References Beneish, M. D. and E. Press. "Costs of Technical Violation of Accounting-Based Debt Covenants." 7he Accounting Review (April 1993): 233-57. DeAngelo, L. E. "Accounting Numbers as Market Valuation Substitutes: A Study of Management Buyouts of Public Stockholders." The Accounting Review (July 1986): 400-20. Dopuch, N.; R. W. Holthausen; and R. W. Leftwich. "Abnormal Stock Returns Associated with Media Disclosures of ‘Subject to’ Qualified Audit Opinions." Journal of Accounting and Economics (June 1986): 93-118. _______ "Predicting Audit Qualifications with Financial and Market Variables." The Accounting Review (July 1987): 431-54. Feroz, E. H.; K. Park; and V. S. Pastena. "The Financial and Market Effects of the SEC’s Accounting and Auditing Enforcement Releases." Journal of Accounting Research (Supplement 1991): 107-48. Financial Accounting Standards Board. Accounting Standards: Original Pronouncements. 1987/88 Edition, Homewood, IL:Irwin, 1988. Flynn, J. and W. Zellner. "Buying Trash in Big Holes--On the Balance Sheet." Business Week (May 11, 1992): 88-9. Fridson, M. S. Financial Statement Analysis: A Practitioner’s Guide. New York: John Wiley 1991. Galant, D. "Financial Misstatements." Institutional Investor (July 1993): 171-74. Hector, G. "Cute Tricks on the Bottom Line."Fortune (April 24, 1989): 193-200. Hsieh, D.A.; C. F. Mansky; and D. McFadden. "Estimation of Response Probabilities from Augmented Retrospective Observations." Journal of the American Statistical Association (September 1985): 651-62. Jones, J. J. "Earnings Management During Import Relief Investigations." Journal of Accounting Research (Autumn 1991): 193-228. Kellogg, I. and L. B. Kellogg. Fraud, Window Dressing, and Negligence in Financial Statements. New York: McGraw-Hill, 1991. Khalaf, R. "Fuzzy Accounting." Forbes (June 22, 1992): 96. Lev, B. and S. R. Thiagarajan. "Fundamental Information Analysis." Journal of Accounting Research (Autumn 1993): 190-215.

Maddala, G. S. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press, 1983. McNichols, M. and G. P. Wilson. "Evidence of Earnings Management from the Provision for Bad Debts." Journal of Accounting Research (Supplement 1988): 1-31. O’Glove, T. L. Quality of Earnings. New York: The Free Press, 1987. Palepu, K. G. "Predicting Takeover Targets: A Methodological and Empirical Analysis." Journal of Accounting and Economics (March 1986): 3-36. Schipper, K. "Earnings Management." Accounting Horizons (December 1989): 91-102. Siegel, J. G. How to Analyze Businesses, Financial Statements, and the Quality of Earnings. 2nd Edition, New Jersey: Prentice Hall, 1991. Zmijewski, M. E. "Methodological Issues Related to the Estimation of Financial Distress Prediction Models." Journal of Accounting Research (Supplement 1984): 59-82.

Table I Selection Criteria for a Sample of Earnings Manipulators in the Period 1987 to 1993, and Distribution of Sample firms by 2-digit SIC. Panel A: Sample Selection Identification of Firms Subject to Accounting Enforcements by the SECa 363b

Accounting and Auditing Enforcement ReLeases (AAER) #132 to #502 Minus: AAERs relating to financial institutions AAERs relating to auditing actions against independent CPAs AAERs relating to 10-Q violations AAERs relating to firms without data on COMPUSTAT, S&P Corporate Text or 10-K microfiche Remaining AAERs Number of Firms relating to the 102 AAERs

80 15 9 157 102 48

Identification of Firms Using a news media search on Lexis/Nexis Firms mentioned in articles Minus:

80

Firms mentioned in articles with no discussion of accounting or disclosure problem Firms for which there is no ex-post evidence of manipulation Firms for which 10-Ks or annual reports are not available on either microfiche or the S&P Corporate Text data base Firm identified by SEC Search Firm is a financial institution (SIC 6000-6350)

17 15 10 7 5

Firms identified by the news media search Sample Manipulators

26 74

Panel B: Distribution by 2-digit SIC 2-digit SIC

Industry description

10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89

Mining and Construction Commodity production Manufacturing Transportation and Utilities WholesaLe and Retail Financial Services (excl. 60-63) Personal and Business services HeaLth and Other Services

Number of Firms 4 12 18 6 13 1 16 4 74

% 5.40% 16.22% 24.32% 8.11% 17.57% 1.35% 21.63% 5.40% 100.00%

a Following Feroz, Park, and Pastena (1991), I examine Accounting and Auditing Enforcement Releases #132 to #502 from 1987 to 1993 to identify firms subject to accounting enforcement by the SEC. b

The number of AAERs examined is 363 instead of 371 because AAER numbers 372 to 379 were not used (see Federal Securities Law reporter (1993)). c The news media search on Lexis/Nexis encompassed the following databases (from January 1987 to April 1993): Barron's, Business Week, Business Wire, Corporate Cash Flow, Disclosure Online, Fortune, Institutional Investor, Investor Daily, Money, The Courier Journal, The New York Times, The Wall Street Journal, The Washington Post, and The Reuter Business Report. The seach was conducted using the following keywords and their variants: "earnings management;" "earnings manipulation;" "cooking the books;" "financial statements or reports," with adjectives such as deceptive, false, fraudulent, misleading, illusive, inappropriate, misstated, and spurious; "inflated or overstated" with either profits, earnings or income.

Table 2 Corrparing Characteristics of 74 Sample Firms vs. 2332 Firms Matched by 2-digit SIC Industry in the Year Prior and the Year After the Fiscal Year Containing the Public Disclosure of Manipulation Earningsa

Characteristic

Sample Firms Median Mean

Other Firms in Industry Mean Median

Wilcoxon -Z b P-Value

Median χ2 P-value

Size Total assets Sales Market Value

467.33 469.87 323.72

43.20 53.56 74.90

1140.38 1295.22 813.35

95.84 122.54 64.59

.003 .001 .884

.004 .007 .701

.264 2.544

.279 1.833

.298 2.545

.312 2.110

.472 .103

.345 .473

.583

.583

.514

.520

.027

.098

-.007 .580

.031 .344

.027 .132

.046 .094

.063 .000

.078 .001

Liquidity/Leverage Working capital to total assets Current ratio Total debt to total assets Profitabitity/Growth Return on assets Sales growth

a

The COMPUSTAT firms in the same 2-digit SIC code for which financial statement data are available comprise the comparison sample. b The Witcoxon Rank-Sum Test and the median test are used to evaluate the null hypothesis that the size, liquidity, profitability, and growth characteristics of manipulators and non-manipulators are drawn from the same population.

Table 3 Type and Effect of Earnings Manipulation in the SampLe of 74 Manipulators Panel A: Type of Earnings Manipulation Revenue manipulationa Recording fictitous unearned or uncertain revenue Reporting one-time gains as ordinary income Failing to book sales returns Recording franchise fees as current period income when future services are still due Improperly using the percentage of completion method

Number of Firms 40 5 4 2 2

Expense manioulationa Recording fictitous inventory Capitalization of marketing, pre-opening and R&D costs Underproviding reserves for closing landfills, warranties, and doubtful accounts Understating liabilities

53

18 11

Othera Pooling with subsequent gains on sale of acquired assets. Overstating the value of Marketable Securities Misleading representations about company's prospects Reporting non-existing assets Misleading reporting of intercompany transactions Misleading representation in MDA Improper provision for contingent liabilities No disclosure of Technical Default

9 4

42

3 2 2 2 1 1 1 1

12

Total

107

Panel B: Financial Statement Effect of Earnings Manipuation Mean

Std. Deviation

Max

Median

Min.

Amount of earnings overstatementb ($ millions)

11.869

38.693

285.320

2.259

.000

As a percentage of retained earningsc

.449

.467

2.740

.280

.000

As a percentage of total assetsc

.106

.159

.795

.055

.000

Panel C: Stock Market Effect of Earnings Manipulationd Days Relative to d Event Day -300, -61 -60, -2 -1, +1 +2, +60 -5, -5 -5, +0 -3, +3

Percentage Cumulative Average Prediction Errors # of Days in Cumulation Mean t-statistice Median 240 59 3 59 11 6 7

.162 -.229 -.249 -.156 -.300 -.299 -.267

.98 - 2.80 -13.51 - 1.90 - 8.50 -11.45 - 9.47

.038 -.200 -.185 -.090 -.204 -.218 -.203

# Positive 27 17 6g 23 8g g 5 g 6

a

The type of manipulation is determined by reference to two sources: (i) the SEC's Accounting and Audint gEnforcement Releases, and (ii) 10-K or annual reports in the fiscal year of and the fiscal year after disclosure of manipulation. b

I measure the amount of earnings overstatement as the difference between beginning retained earnings as perviously reported and the corresponding restated retained earnings when these data are available in the sources listed in footnote a. the reported statistics are based on the 57 firms for which such data are available. c

Retained earnings and total assets are measured at the end of the fiscal year prior to the year in which public disclosure of manipulation occurs. d

The event date (day 0) is the first announcement of a firm's manipulation or alleged manipulation. The analysis is based on 53 firms because there are no news media announcements for 21 days of the 48 firms identified with the SEC searhc. The selection of event dates and their source is described in the Appendix.

(

)

Market model prediction errors PEit are calculated as PE it = R it − αˆ 1 + βˆ 1R mt , where R it and R mt are the continuously compounded rates of return on the common stock of firm i and the equally-weighted NYSE and ASE index on event day t. Market model parameters are estimated over 200 trading days from day +61 to

e

k

N

+261 relative to the day of announcement of manipulation; CAPE k = ∑ APE t where APE t = 1 N ∑ PE k .

(

t =1 1/ 2

)

i =1

T-statistics are calculated as follows: t(CAPEk) = CAPE k ks (APE t ) , where s (APE t ) is the estimated variance of average prediction errors over days +61 to +261 relative to Day 0 and k is the number of days in the cumulation period. The statistics are distributed approximately t with 199 degrees of freedom. Similar results are obtained using a pre-estimation period from days –261 to –61. 2

2

f

I also assess the statistical significance of the observed abnormal performance using a standardized test statistic (see Depuch et al. (1986)) and obtain similar results. For example, the standardized test statistics equal .65 for CAPE (-300, -61), -3.10 for CAPE (-60, -2), -19.71 for CAPE (-1, +1), and -1.68 for CAPE (+2, +60). g

The hypothesis that the proportion of firms with positive CAPEs is eqal to .5 is rejected at the 5%.

Table 4 Potential Predictive Variables: Descriptive Statistics for the Estimation Sample of 50 pre-1989 Manipulators and their 1708 Industry-Matched Non-Manipulators Witcoxon -Zc P-Vatue

Median-χ2 P-Value

2.847

.000

.000

.078

4.105

.006

.007

1.000

.335

7.398

.096

.246

1.134

1.106

.509

5.204

.000

.000

4.278

1.001

.974

.147

7.652

.307

.774

.388

2.140

1.054

1.010

.033 14.696

.271

.389

1.030

.228

2.802

1.037

1.000

.123

3. 772

.394

.077

.061

.034

-.109

.399

.018

.013

-.704

.425

.000

.002

1.309

1.087

.136

9.590

1.048

.990

.024 26.912

.207

.360

Characteristica

Sample Firms (N=50) Mean Median Min. Max.

Mean

Controls (N=1708) Median Min. Max.

Days in Receivables Index

1.465

1.281

.392

3.617

1.031

.996

.047

Gross Margin Index

1.193

1.036

.224

4.192

1.014

1.001

Asset Quality Index

1.254

1.000

.034

4.282

1.039

Sales Growth Index

1.607

1.411

.612

4.644

Depreciation Index

1.077

.966

.153

SGA Index

1.041

.960

Leverage Index

1.111

Accruals to total assets Days in Inventory Index'

For each variable, I provide a definition, and the COMPUSTAT data item number. Year t refers the first year in which earnings manipulation occurs: Days Sales in Receivables Index = (Receivablest[2]/Salest[12]/(Receivablest-1/Sales t-1)  Sales t -1 [12] − Costs of Goods Sold t -1 [41]   Gross Margin Index =   Sales t −1 [12]  

 Sales t − Cost of Goods Sold t   Sales t 

   

 Current Assets t -1 + PPE t −1   1 −   Total Assets t -1  

 Current Assets t [4] + PPE t [8]   Asset Quality Index = 1 −  Totals Assets t [6]   Sales Growth Index = Sales t [12] / Sales t −1  Depreciation t -1 [14 min us 65]   Depreciation Index =    Depreciation t −1 + PPE t −1 [8]   SGA expense t [189]   SGA Index =   Sales t [ 2]  

 Depreciation t   Depreciation + PPE t t 

   

 SGA expense t -1      Sales t −1  

 LTD t [93 + Current Liabilities t [5]   Leverage Index =   Total Assets t [6]  

 LTD t −1 + Current Liabilities t -1      Total Assets t -1  

Accruals to Total Assets = [(∆Current Assets t [4] − ∆Cash t [1]) − (∆Current Liabilities) - ∆Current Maturities of LTD t [44] − ∆Income Tax Payablet [71]) − Depreciation and Amortization [14])/TA t [6] b

c

Only 44 manipulators and 1642 matched firms have inventory data.

The Wilcoxon Rank-Sum orwl the Median tests compare the distribution of sample firms' characteristics to the corresponding distribution for non-manipulators. The reported P-vatues indicate the smallest probability of incorrectly rejecting the null hypothesis of no difference.

Table 5 WESML and Unweighted Probit Estimation Results Based on an Estimation Sample of 50 Manipulators and 1708 Non-maniputators (Panel A). Estimated Probabilities of Manipulation for the Estimation Sample and for a Holdout Sample of 24 Manipulators and 624 Non-manipulators (Panel B)a Panel A: Estimation Results

Constant Predicted Sign

Days in Receivables Indexb

Gross Margin Index

Asset Quality Index

Sales Growth Index

Depreciation lndex

SGA Index

Accruals to total Assets

Leverage Index

(+)

(+)

(+)

(+)

(+)

(+)

(+)

(+)

Pseudo R2c

χ 2statistic p-valuec

WESML

-4.954 (-11.80)

.789 (6.40)

.459 (3.02)

.306 (2.82)

.701 (3.43)

.033 (.15)

-.006 (- .04)

3.937 (3.07)

-.264 -(.83)

.306

34.50 ( .00)

Unweighted Probit

-4.840 (-11.01)

.920 (6.02)

.528 (2.20)

.404 (3.20)

.892 (5.39)

.115 (.70)

-.172 (- .71)

4.679 (3.73)

-.327 (-1.22)

.371

129.20 (.00)

Panel B: Estimated Probabilities of Manipulation WESML Estimation Sample Manipulators Non-Maniptitators Mean St. Dev. MaximLxn Median Minimum Witcoxon-Z' (p-vatue) Median test-X' (p-vatue)

.107 .175 .851 .024 .001

.006 .021 .615 .003 .001

8.049 (.000) 23.785 (.000)

Holdout Sample Manipulators Non-Maniptilators .097 .223 .999 .009 .001

.007 .044 .999 .002 .001

Unweighted Probit Estimation Sample Holdout Sample Manipulators Non-maniputators Manipulators Non-Maniptitators .237 .275 .980 .099 .001

.022 .051 .960 .011 .001

.181 .288 .999 .037 .004

4.721 (.000)

8.314 (.000)

4.630 (.000)

13.995 (.003)

26.667 (.000)

11.056 (.001)

a

The estimation sanpte consists of the pre-1989 manipulators and their controls and the holdout sample of the post-1988 manipulators and their controls.

b

See Table 4 for variable definitions.

.019 .063 .999 .009 .001

Table 6 Sensitivity Analysis to the Choice of Estimation and Holdout Samples. Descriptive Statistics for Estimation Based on 100 Random Samples of 50 Manipulators and 1500 Non-Manipulators [Panel A], and Descriptive Statistics on the Estimated Probabilities of 100 Holdout Samples of 24 Manipulators and 832 Non-Manipulators (Panel B]a Panel A: Descriptive statistics on 100 Estimation Samples Mean

Standard Deviation

-4.223

Days in Receivables Index

Percent Positive

Percentage Significent at 10%b

Percentage Significant at 5%b

Percentage Significant at 2.5%

Max

Median

Min

.549

-3.404

-4.040

-5.853

0.0

100.0

100.0

100.0

.857

.097

1.065

.864

.588

100.0

100.0

100.0

100.0

Gross Margin Index

.488

.115

.871

.487

.222

100.0

95.0

84.0

66.0

Asset Quality Index

.453

.113

.789

.438

.223

100.0

100.0

98.0

96.0

Sates Growth Index

.374

.365

1.232

.152

.103

100.0

100.0

100.0

100.0

Depreciation Index

.059

.183

.437

.097

-.782

81.0

37.0

18.0

10.0

SGA Index

-.144

.180

.333

-.156

-.559

25.0

30.0

12.0

4.0

Accruals to Total Assets

4.370

.965

7.219

4.464

2.090

100.0

99.0

95.0

93.0

Leverage Index

1.0

Constant b

-.110

.165

.278

-.114

-.544

25.0

8.0

2.0

2

Pseudo-R

.242

.068

.444

.220

.124

--

--

--

χ -statistic

89.79

19.59

142.69

84.49

51.90

--

100.0

100.0

2

Panel B: Descriptive Statistics on Estimated Probabilities on 100 Holdout Samples

Manipulators Non-Manipulators

Mean

Standard Deviation

Max

Median

.178 .028

.049 .002

.316 .033

.164 .028

Min .091 .024

a

Witcoxon- ?? P-vatued 12.212 ( .000)

Median χ2 P-valued 199.09 (.000)

Random samples are generated using the RANUNI function in SAS. RAPUNI is used 100 times to generate 100 samples of 50 manipulators out of 74 and 1500 controls out of 2 Each time, the complement of 24 manipulators and 832 non-manipulators is considered as a holdout sample. b c d

Significance based on one-talted test. Variables and statistics are defined In Tables 4 and 5. Tests that the estimated probabilities for manipulators and non-manipulators are drawn from the same distribution.

c

(

)(

)

The pseudo-R2 is equal to L2Ω/ n − L2ω/ n 1 − L2ω/ n where LΩ is the log likelihood for the WESML probit model (unconstrained), Lω is the log likelihood with only the constant tem In the model (constrained) and n the number of observations (See Maddala (1983, p. 40)). The log likelihood ratio test statistic is equal to -2 times the difference In the log likelihood of the unconstrained and constrained models is asymptotically distributedχ2, with degrees of freedom equal to the difference In the number of parameters of the two models.

d

Weighted exogenous maximum likelihood probit Is estimated assuming that prior probability of manipulation is .0069. Sensitivity analysis on the prior probability of manipulation yields coefficients estimates of similar magnitude ard significance. When the prior probability of manipulation is specified as .0059, .0079 and .0089 and .0099 the estimation yields χ2 statistics of 29.60, 39.22, 43.95 and 48.65, significant at the 1% level or lower. Unweighted probit implicitly assumes that the prior probability of manipulatlon is .02844 (50/1758). e

Tests that the estimated probabilities for manipulators and non-manipulators are drawn from the same distribution.

Table 7 Cut-off probabilities Costs of Misclassification, and Probability of Type I and Type II Errors for Various Levels of Relative Costs in the Estimation Sample (50 manipulators, 1708 non-manipulators) and in the Holdout Sample (24 manipulators, 624 non-manipulators)a Panel A: WESML Estimation Sample Relative Costs of Type I and Type II errors 1:1 10:1 20:1 30:1 40:1 60:1 100:1

Cut-off Probabilityb 1.0000 .2905 .0512 .0512 .0223 .0092 .0087

Probability of Classification Errors Type I Type II 1.0000 .9000 .5600 .5600 .4600 .2800 .2600

.0000 .0004 .0409 .0409 .0632 .1329 .1417

Holdout Sample Cost of Model Errors Relative To Naive Strategyc 1.000 .991 .855 .757 .688 .597 .464

Probability of Classification Errors Type I Type II 1.0000 .9166 .7500 .7500 .6667 .5000 .5000

.0000 .0048 .0112 .0112 .0240 .0689 .0753

Cost of Model Errors Relative to Naive Strategy 1.000 .986 .830 .804 .753 .665 .608

Panel B: Unweighted Probit Estimation Sample Relative Costs of Type I and Type II errors 1:1 10:1 20:1 30:1 40:1 60:1 100:1 a

Cut-off Probability 1.0000 .0685 .0376 .0376 .0294 .0294 .0294

Probability of Classification Errors Type I Type II 1.0000 .4200 .2600 .2600 .2400 .2400 .2400

.0000 .0761 .1382 .1382 .1747 .1747 .1747

Holdout Sample Cost of Model Errors Relative To Naive Strategy 1.000 .680 .496 .417 .433d d .562' .819 d

Probability of Classification Errors Type I Type II 1.0000 .6250 .5000 .5000 .4583 .4583 .4583

Cost of Model Errors Relative to Naive Strategy

.0000 .0353 .0721 .0721 .0913 .0913 .0913

A Type I error Is defined as classifying an observation as a non-manipulator when it manipulates. A Type II error Is defined as classifying an observation as a manipulator when it is a nonmanipulator. b Cut-off probabilities are chosen for each level of relative costs to minimize the expected costs of misclassification as defined In equation (3). c A naive strategy classifies all firms as non-manipulators. As such, the naive strategy's expected cost of misciassification is .0069 C1 for the WESML model and .02844 C1 for the unweighted probit. d In these computations, the naive strategy classifies all firms as manipulators. The switch in naive strategies minimizes the expected costs of misclassification because the ratio of relative costs Is greater than ??? is the proportion of manipulators. The switch occurs at 40:1 for unweighted probit (> I/.02844).

1.000 .746 .623 .582 .628 d d .896 1.535 d

Table 8 Probability of Type I Errors ord Type of Manipulationa Panel A: WESML Estimation Sample Relative Costs of Type I and Type II errors 1:1 10:1 20:1 30:1 40:1 60:1 100:1

Holdout Sample

Total (N=50)

Revenues manipulation (N=28)

Expense manipulation (N=8)

Disclosure Manipulation (N=1)

Multiple (N=13)

Total (N=24)

Revenue manipulation (N=6)

Expense Manipulation (N=6)

1.000 .900 .560 .560 .460 .280 .260

1.000 .893 .536 .536 .464 .250 .214

1.000 1.000 .625 .625 .500 .375 .375

1.000 1.000 1.000 1.000 1.000 1.000 1.000

1.000 .846 .538 .538 .385 .231 .231

1 .916 .750 .750 .666 .500 .500

1.000 1.000 1.000 .667 .667 .500 .500

000 1.000 .833 .833 .833 .500 .500

Disclosure Manipulation Multiple (N=1) (N=11) 1.000 1:000 1.000 1.000 1.000 1.000 1.000

1.000 .828 .556 .556 .556 .456 .456

Panel 8: Unweighted Probit Estimation Sample Relative Costs of Type I and Type II errors 1:1 10:1 20:1 30:1 40:1 60:1 100:1

a

Holdout Sample

Total (N=50)

Revenues manipulation (N=28)

Expense manipulation (N=8)

Disclosure Manipulation (N=1)

Multiple (N=13)

Total (N=24)

Revenue manipulation (N=6)

Expense Manipulation (N=6)

1.000 .420 .260 .260 .240 .240 .240

1.000 .393 .250 .250 .215 .215 .215

1.000 .500 .375 .375 .375 .375 .375

1.000 1.000 1.000 1.000 1.000 1.000 1.000

1.000 .385 .154 .154 .077 .077 .077

1.000 .625 .500 .500 .458 .458 .458

1.000 .667 .500 .500 .500 .500 .500

1.000 .667 .500 .500 .500 .500 .500

Disclosure Manipulation Multiple (N=1) (N=11) 1.000 1.000 1.000 1.000 1.000 1.000 1.000

A Type I error is defined as classifying an observation as a non-manipulator when it manipulates. I distinguish four types of manipulation depending on whether the manipulation originates primarily In revenues, expenses, disclosure (MDA, footnotes) or has multiple sources.

1.000 .556 .456 .456 .364 .364 .364