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How pervasive is corporate fraud? [1]

['Dyck', 'Alexander.Dyck Rotman.Utoronto.Ca', 'University Of Toronto', 'Toronto', 'Morse', 'University Of California At Berkeley', 'Berkeley', 'Nber', 'Cambridge', 'Zingales']

Date: 2023-03

The timing of the experiment is as follows. We define a company as having AA as an auditor if AA signed a financial report anytime in the calendar year 2001, irrespective of the firm’s fiscal year. All companies without AA as auditor during this period are non-AA clients. We consider that a fraud was revealed during the detection period if the fraud started before the watershed date of November 30, 2001, and came to light between the watershed date and the end of 2003 (the detection period). Note that our estimates are obtained from the ratio of the fraud caught in AA and non-AA firms. Thus, as long as the amount of fraud committed in AA and non-AA clients responds to cyclical fluctuations in a similar fashion, our estimates are not affected by business cycle fluctuations in the aggregate level of fraud, an important phenomenon documented by Wang et al. (2010).

The count of observations is shown at the bottom of Table 3, Panel A. The natural experiment includes 353 AA clients in the pre-period who survive at least one year in the post-period, and 2,404 non-AA client firms. The number of detected fraud events depends on the fraud measure: 168 restatements, 63 SCACs, 59 AAERs, and 21 auditor-detected fraud.

4.1 Detection likelihood results

Table 3, Panel A reports the main detection likelihood estimates across the four fraud measures – auditor-detected fraud, AAERs, restatements, and SCAC securities fraud. For each of these measures, the estimated coefficient of the Poisson regression we report is the coefficient of a dummy variable equal to one if a company was a former AA client. Thus, if former AA clients have an average frequency of fraud of \({\lambda }_{AA}={e}^{{\theta }_{AA}x}\) and non-AA clients have an average frequency of fraud of \({\lambda }_{N}={e}^{{\theta }_{N}x}\), the estimated coefficient we report is \({\theta }_{AA}-{\theta }_{N}\). Since the detection likelihood ratio is nothing but \(\frac{{\lambda }_{N}}{{\lambda }_{AA}}=\frac{{e}^{{\theta }_{N}}}{{e}^{{\theta }_{AA}}}={e}^{{\theta }_{N}-{\theta }_{AA}}\), we obtain the detection likelihood ratio as \(\frac{1}{{e}^{{\theta }_{AA}-{\theta }_{N}}}\), or the inverse of e raised it to the power of the estimated coefficient. We report both the asymptotic and the exact p-values for the hypothesis that the detection likelihood is equal to 1.

Table 3 Detection likelihood estimates Full size table

As we can see in Panel A of Table 3, the hypothesis that the detection likelihood is bigger or equal to 1 is rejected at least at the 10% level in all four measures and in three out of four cases at the 5% level or better. These findings verify the assumption that after the demise of AA more frauds are caught in AA firms than in non-AA firms (\(Pr\left({\text{caught}}|F|AA\right)>Pr\left({{caught}}|F|\overline{AA }\right)\)).

More specifically, when we look at auditor-detected fraud, the estimated detection likelihood is 0.29, which is different from 1 at the 3% level. For AAERs, the detection likelihood estimate is 0.52, different from 1 at the 7% level. The detection likelihood estimate for accounting violations is 0.34, different from one at the 0.1% level. For the SCAC securities fraud measure, the detection likelihood is 0.47, different from 1 at the 2% level.Footnote 13 In sum, despite the different sources and the different definitions of fraud, there is a clear result: a substantial amount of corporate fraud remains undetected. With detection likelihood between 29 and 52%, there is indeed an iceberg of undetected fraud that ranges between 48 and 71% of total fraud.

If we want to move beyond this simple result and estimate more precisely the amount of undetected fraud, we need to pool together all the possible observations toward the estimation of a single detection likelihood. This is what we do in Table 3, Panel B. The first column reports the estimates obtained by estimating simultaneously the four Poisson regressions, with the restriction that the coefficient should be the same in all four. When we pool the four measures of fraud, the estimated detection likelihood is 0.38, with a 95% confidence interval between 0.30 and 0.49. Thus, we can say with 95% confidence that between 51 and 70% of all fraud is undetected.

These estimates of undetected fraud are downward biased because Assumption 2 (that after the Enron scandal all the fraud in former AA firms was revealed) is unlikely to be satisfied. This is true for all the measures, but particularly so for SCACs and AAERs. The SCAC securities fraud measure includes frauds that are not misrepresentation of accounting information but rather failures to disclose material information. It is unlikely that the additional scrutiny triggered by the AA demise would expose all these failure-to-disclose cases. In such cases, the experiment design implies that 0.47 detection likelihood is only an upper bound (biasing downward the proportion of undetected fraud). Similarly, the detection of an AAER-type of fraud depends on the willingness of the SEC to bring an enforcement action. In any economic analysis of crime and punishment (see Becker 1968), the SEC’s incentives to bring a case against a defunct firm like AA are small. Thus, the 0.52 AAER estimate is also likely an upper bound.

By contrast, Assumption 2 is more likely to hold for misconducts that auditors are more likely to catch, such as accounting restatements and auditor-detected fraud. Thus, in column 2 of Table 3, Panel B, we report the detection likelihood estimate obtained by pooling together only the two fraud measures for which Assumption 2 is more likely to hold. The estimated detection likelihood is 0.33, with a 95% confidence interval of 0.24–0.45. Thus, only one-third of corporate fraud is detected, and the total amount of corporate fraud is three times the corporate fraud that is observed. In the rest of the paper we will treat this as our best point estimate, with a 95% confidence interval that the total amount of fraud is between 2.2 and 4.1 times the fraud observed.

4.2 Detection likelihood robustness

4.2.1 Small firms

Krishnan et al. (2007) document that Big Four auditors were much more likely to issue a going concern qualification in their audits of large former AA clients than in their audits of large non-former AA clients (specifically, 5.6% versus 2.3%). In our experiment, this ratio would imply a detection likelihood of 0.41, quite consistent with our results. Yet, Krishnan et al. (2007) find the opposite for small firms: former AA clients received less than half of the going concern opinions of non-AA clients (6.2% to 14.5%). As the authors recognize, this difference in the results for large and small firms is driven by sample selection. Krishnan et al (2007) restrict their attention to AA firms that are subsequently audited by Big Four auditors. It is likely that Big Four auditors accept all the large former AA clients but only the best of the small ones, leaving the rest to less prestigious auditors. In this paper we can test this conjecture by looking at all former AA clients, not just those subsequently audited by a Big Four auditor. To do so, however, we need to expand the sample to small firms.

Table 4, Panel A reproduces our detection likelihood estimation setup for smaller public corporations – those that were never over $750 million in assets in the pre-period years. We run the experiment in the same setup as Table 3. Since DMZ does not collect auditor-detected data for small firms, the first measure of misconduct is not available for this sample.

Table 4 Detection Likelihood Robustness: Small Corporations & Placebo Full size table

We find, in Panel A, that for all three measures the detection likelihood is less than 1 and that for two out of three measures the detection likelihood is significantly less than 1 at the 1% level. This analysis, suggested by an anonymous referee, provides an out-of-sample validation of our methodology to use the AA-forced turnover to identify misconduct that generally remains undetected.

For the AAER and restatement measures, the detection likelihood estimates obtained using small firms in Table 4 are very similar to the ones obtained using large firms and reported in Table 3: 0.64 versus 0.52 for AAERs and 0.42 versus 0.34 for restatements. By contrast, for securities fraud cases, the detection likelihood falls drastically from 0.47 (large firms) to 0.29 (smaller firms). Most likely, this drop is due to the fact that the probability of a class action suit among small non-AA clients is only 0.5%, versus the 2% observed in large firms. This is hardly surprising. The main reason why DMZ restrict their sample to large companies is that the discovery of a fraud will always lead to a class action suit in large companies, where there is plenty of money to pay the lawyers, but not necessarily in small companies. Thus, the lower detection likelihood reflects a real difference between large and small companies: more fraud goes undetected in small companies.

4.2.2 Placebo

It is possible that AA clients were in businesses intrinsically more prone to corporate fraud or its detection. One way to help to rule out this possibility is to observe these firms in a different time period and check that they are not behaving differently. To this purpose, we reproduce the same experiment comparing former AA and non-AA clients (minus a few firms that do not survive) in the two years after the detection period (i.e., 2004–2006) and measure fraud detection in these years. Since the enhanced scrutiny following the demise of AA cannot last forever, we regard this exercise as a placebo test. This placebo period coincides with the beginning of the implementation of SOX. A large literature has tried to establish what the effects of the introduction of SOX are (see Coates and Srinivasan (2014)). Our test, however, is unaffected by any impact of SOX, since it compares the detection rate in former AA clients and former non-AA clients at the same time.

Table 4, Panel B reports the results. The percentage of firms caught committing fraud is very similar between former AA clients and former non-AA clients (detection likelihood estimates for all three measures are not different from 1), suggesting that there is not a natural proclivity of former AA clients to commit more fraud. In addition, the similarity between the fraud revealed in AA and non-AA clients suggests that the enhanced disclosure of fraud during the treatment period is not just an acceleration of the discovery that would have taken place regardless, but a net increase in discovery.

4.2.3 Industry and geography

In Sect. 3.2, we showed that AA had more clients in Communications & Transport, Refining & Extractive, Services & Healthcare, and Utilities, and fewer clients in Banks & Insurance, Retail & Wholesale, and Computers. If, for unspecified reasons, corporate fraud was more prevalent among sectors in which AA was overrepresented just prior to the detection period and not afterward, then our detection likelihood estimate could be biased. To address this concern, we report the detection likelihood estimates in various subsamples that remove industries where AA was either overrepresented or underrepresented. (Appendix Table A2, Panels B and C report the industry and regional distribution of fraud for all the fraud measures.) As Table 5, Panel A shows, the detection likelihoods remain substantially unchanged.

Table 5 Detection Likelihood Robustness: Industry and Region Subsampling Full size table

The same concern could arise from regional variation in AA clients. For this reason, in Table 5, Panel B, we repeat the same exercise excluding some regions or some large states. Once again, the detection likelihood results appear stable.

4.3 Pervasiveness of corporate fraud results

We now can use the detection likelihood estimates in Eq. (1), \({Pr}\left(F\right)=\) \(\frac{\boldsymbol P\boldsymbol r\mathbf{\left({F,caught}\right)}}{Pr\left(\left.caught\right|F\right)}\), to estimate the overall pervasiveness of corporate fraud. The numerator in Eq. (1) is the observable incidence of fraud that is caught. The denominator in Eq. (1) is the detection likelihood. Table 6 reports observed caught frequencies in Panel A, detection likelihood estimates from Table 3 in Panel B, a baseline estimate of the pervasiveness of fraud across the measures of misconduct and alleged fraud in Panel C, and a best estimate of the pervasiveness of fraud across the measures of misconduct and alleged fraud using the best estimate detection likelihood in Panel D. Since AA firms during the detection period are assumed to have a probability of detection equal to one, we exclude them from Panel A, which computes the frequency of caught frauds under normal circumstances.

Table 6 How Pervasive Is Corporate Fraud? Full size table

Focusing first on Panel A, recall that Fig. 1 showed that observed incidences of misconduct vary widely depending on the definition of corporate fraud and the time period of reference. Since fraud may be cyclical (Wang et al. 2010), we do not want to rely on a specific point in time, instead preferring to estimate pervasiveness over a full cycle of boom and bust years. The start in January 1998 and the end point in December 2005 are each almost exactly halfway through the respective expansion periods; thus the period covers one full business cycle from mid-point to mid-point.Footnote 14

Panel A reports that auditor-detected securities frauds hover around 1%, with a peak of 1.1% in 2000–2001. AAER investigations average 2.6%, with a peak of 3.5% in 2000–2001 and a trough of 2.0% in 1998–99. Accounting violations measured by non-clerical restatements average 13.5% during the entire sample period, with a peak of 18.3% in 2002–2003 and a trough of 7.2% in 1998–1999. The broader SCAC securities fraud averages 3.4%, with a peak of 4.8% in 2000–2001 and a trough of 2.3% in 2004–2005.

Using these observed misconduct averages in Panel A and detection likelihood estimates from Table 3 reproduced in Panel B, Table 6, Panel C reports estimates of the pervasiveness of fraud. A concern with Panel C is that, as we discussed with regard to Table 3, some of the detection likelihood estimates are clearly more biased than others. The biases are always conservative, but they do not help with the precision of our fraud pervasiveness estimates. In particular, our experimental design of using AA’s demise has the most power to identify the whole iceberg of hidden fraud (Assumption 2 holding as an equality) for auditor-detected securities fraud and restatements, as opposed to AAERs and the broader SCAC securities fraud cases, since no matter how rigorous the monitoring of the new auditors is, they will find it difficult to identify cases of price fixing such as Sotheby’s. Thus, the best estimate detection likelihood is based on the pooled detection likelihood of auditor-detected and restatement measures, or 0.33, as highlighted before. We use this detection likelihood to calculate the best estimate of corporate misconduct across all of our fraud measures in Panel D.

Our findings as to the pervasiveness of corporate fraud depend on the measure of misconduct we use. We find that in any year averaged across the business cycle, 2.5% of large corporations are committing severe financial misreporting that auditors can detect. Auditor-detected securities fraud is a subcategory of SCAC alleged securities fraud; thus, it is not surprising that it has a low frequency. Such a measure is interesting for the detection likelihood estimation, given that it maps well to our AA demise design, but of more interest to speak to fraud at large are the SCAC securities frauds.

We find that, during an average year over the business cycle, 10% of large corporations are committing a misrepresentation, an information omission, or another misconduct that can lead to an alleged securities fraud claim settled for at least $3 million (with a 95% confidence interval between 7 and 14%). This result from the SCAC data is our main estimate of the pervasiveness of corporate fraud, since SCAC cases are indeed (alleged) securities fraud. By using the AAER measure, we arrive at similar estimates: 8% of fraud pervasiveness, with a 95% confidence interval range of 6%-11%. This magnitude is similar to the SCAC estimate, even though AAERs have lower observed frequencies because their existence requires the SEC to act. (Recall that the SEC failed to act on Madoff despite six substantive complaints.Footnote 15)

Accounting violations, less severe than alleged securities fraud, are more prevalent, with an average annual pervasiveness of 41% (95% confidence interval between 30 and 55%). We do not want to conclude from this estimate that each year 41% of large corporations commit a severe misreporting. To reach this conclusion we would need some more substantive filters to eliminate inconsequential misreporting. Nevertheless, this estimate does not bode well for the US auditing system. In spite of all the regulation, roughly half of the US financial statements suffer from misreporting more serious than pure clerical errors.

4.3.1 Comparison with pervasiveness estimates in the literature

Taking the estimate of 10% as our main estimate of the pervasiveness of corporate fraud, we now ask how our estimates lines up with the literature. As the summary reported below shows, our estimate is at the low end of the pervasiveness of corporate fraud found in the literature. This is not surprising, since if Assumption 2 is violated, our estimate represents a lower bound.

We begin with evidence concerning the appetite for corporate misdoing for personal gain. Prior to Lie (2005), the existence of the options backdating practice had not been understood, and thus firms wanting to commit fraud in this manner could do so with little detection threat. Bebchuk et al. (2010) look back over the pre-2005 period and identify the percentage of publicly traded firms from 1996 to 2005 in which CEOs or directors were “lucky” in that they received option grants on the day of the month when the stock price was the lowest. By their estimate, 12% of firms had such lucky CEOs, suggesting that the appetite for fraudulent behavior was present in at least 12% of firms.

That at least 12% of firms are committing some fraud is supported also by survey evidence and accounting prediction models. Dichev et al. (2013) survey 169 CFOs of public companies and find that 18% of firms manage earnings to misrepresent performance. Beneish et al. (2013) build a model, based on Beneish (1999), that out of sample was able to predict successfully 71% of the most important accounting violations. They apply this model to estimate the pervasiveness of accounting manipulation and find that 18% of firms are fraudulent each year during the period 1997–2005.

How do the structural approaches to modelling the hidden iceberg of corporate misconduct line up with the evidence reported thus far? Wang et al. (2010) examine financial fraud among the 3,297 IPOs from 1995 to 2005. While their main goal is to show that fraud is procyclical, their bivariate probit model produces predicted probabilities of engaging in fraud of 10%-15%, very much in line with our estimates.Footnote 16 Similarly, in their flexible Bayesian priors approach to partial observability, Hahn et al. (2016) estimate a pervasiveness of SEC-investigated accounting misconduct of 15%. Zakolyukina (2018) uses a structural model to explore detected and undetected GAAP manipulation (more in line with our accounting violation measure) and reports that 73% of CEOs manipulate their financials, with a detection likelihood of only 0.06.

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[1] Url: https://link.springer.com/article/10.1007/s11142-022-09738-5

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