Measuring securities litigation risk
Transcription
Measuring securities litigation risk
Journal of Accounting and Economics 53 (2012) 290–310 Contents lists available at SciVerse ScienceDirect Journal of Accounting and Economics journal homepage: www.elsevier.com/locate/jae Measuring securities litigation risk$ Irene Kim a, Douglas J. Skinner b,n a b George Washington University, School of Business, United States University of Chicago, Booth School of Business, United States a r t i c l e in f o abstract Article history: Received 25 August 2010 Received in revised form 6 September 2011 Accepted 21 September 2011 Available online 6 November 2011 Extant research commonly uses indicator variables for industry membership to proxy for securities litigation risk. We provide evidence on the construct validity of this measure by reporting on the predictive ability of alternative models of litigation risk. While the industry measure alone does a relatively poor job of predicting litigation, supplementing this variable with measures of firm characteristics (such as size, growth, and stock volatility) considerably improves predictive ability. Additional variables such as those that proxy for corporate governance quality and managerial opportunism do not add much to predictive ability and so do not meet the cost–benefit test for inclusion. & 2011 Elsevier B.V. All rights reserved. JEL classification: K22 K41 M41 Keywords: Litigation risk Securities litigation Corporate disclosure 1. Introduction A large body of research in accounting and finance investigates whether litigation risk (the risk of securities class action lawsuits) affects corporate decisions. While much research investigates the effect of litigation risk on managers’ disclosure choices, authors also investigate how litigation affects a large array of managerial decisions.1 Much of this research measures litigation risk using an industry-based proxy, either alone or in conjunction with other variables. A common proxy is based on membership in the biotechnology, computers, electronics, and retail industries. This proxy originates from Francis, Philbrick and Schipper (1994a, 1994b; hereafter FPS), who sample firms drawn from these industries to study the relation between litigation and disclosure because those industries were subject to ‘‘a high incidence of litigation during 1988–1992’’ (1994a, p. 144). These authors do not advocate the use of industry membership generally, or these industries in particular, as a universal proxy for litigation risk. However, the use of this industry proxy (hereafter, the FPS measure) has become pervasive in the literature. $ We appreciate the comments of Bill Mayew, Karen Nelson, Adam Pritchard, Jonathan Rogers, Jerry Zimmerman (editor), Kin Lo (referee), and seminar participants at the University of Chicago, Duke University, Northwestern University, and the DC Area Accounting Symposium. Kim and Skinner appreciate financial support from the George Washington University School of Business and the University of Chicago Booth School of Business, respectively. n Corresponding author. Tel.: þ 1 773 702 7137. E-mail addresses: [email protected] (I. Kim), [email protected] (D.J. Skinner). 1 Papers that investigate the relation between managers’ financial reporting and disclosure decisions and litigation risk include Skinner (1994, 1997), Francis et al. (1994a, 1994b), Johnson et al. (2000, 2001), Baginski et al. (2002), Frankel et al. (2002), Matsumoto (2002), Field et al. (2005), Lennox and Park (2006), Rogers and Van Buskirk (2009), and Donelson et al. (2010), among others. Research also examines how litigation risk affects cash holdings (Arena and Julio, 2010), equity-based compensation (Dai et al., 2008; Jayaraman and Milbourn, 2009), conservatism in debt contracting (Beatty et al., 2008), IPO underpricing (Lowry and Shu, 2002; Weiss Hanley and Hoberg, 2010), institutional monitoring and board discipline (Cheng et al., 2010; Laux, 2010), MD&A disclosures (Brown and Tucker, 2011), audit fees (Seetharaman et al., 2002), and auditors’ resignation decisions (Shu, 2000). 0165-4101/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jacceco.2011.09.005 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 291 It is reasonable to expect that litigation is associated with industry membership. Stock volatility and stock turnover directly affect litigation risk because both are directly related to measures of stockholder damages that drive plaintiff lawyers’ decisions to file lawsuits (e.g., Alexander, 1991; Jones and Weingram, 1996a). Both of these variables are likely to be associated with industry; for example, high technology stocks are by their nature inherently more uncertain with more variable earnings, and hence are more volatile. The use of industry to proxy for litigation risk results from a cost–benefit tradeoff by researchers. While this proxy is simple and readily available, it likely captures industry characteristics that are unrelated to litigation risk but that affect managers’ decisions, creating a potential correlated omitted variables problem. The fact that this proxy is ubiquitous in the literature seems to indicate that it passes the cost–benefit test. However, there is little evidence (of which we are aware) on the construct validity of this proxy or whether other proxies are available that might represent a better cost–benefit tradeoff. Further, beyond reporting pseudo-R squareds, there is little systematic evidence on the ability of extant measures to actually predict litigation. We report on some relatively simple and low cost models that significantly outperform the industry-based proxies in terms of predictive and discriminatory ability. The use of industry membership to capture litigation risk makes it difficult to ensure that industry captures litigation risk as opposed to different underlying factors that affect managers’ disclosure decisions. Consider a study that investigates whether litigation risk affects managers’ disclosure choices and uses industry to proxy for litigation risk. If managers’ disclosure decisions depend on their firms’ information environments (Einhorn and Ziv, 2008) and information environment varies systematically across industry, disclosure will be associated with industry for reasons that have little to do with litigation risk.2 A similar problem arises if firms in high technology industries have higher proprietary costs than firms in more mature industries and proprietary costs systematically affect disclosure. The existence of a well-developed theory of litigation would allow us to identify all of the economic determinants of litigation, in which case the FPS measure would presumably no longer be useful in explaining litigation risk. Although we do not have such a theory (we discuss previous literature in Section 2), one goal of our research is to investigate systematically whether the inclusion of an extensive set of firm-specific characteristics reduces the usefulness of the FPS variable in predicting litigation, as would be expected if these characteristics directly capture litigation risk. We provide two sets of empirical analyses to evaluate how well industry membership proxies for securities litigation risk. We first provide evidence on how litigation rates vary across industries and through time. This evidence shows that while litigation tends to cluster in certain industries, the set of industries varies over time. Nevertheless, the FPS industries generally have consistently higher litigation rates than other industries, although this result is weaker when we focus the analysis on large firms generally subject to higher rates of litigation. Second, we provide evidence on the predictive ability of alternative models of litigation risk. We show that while the relationship between the FPS industry measure and litigation is robust in a statistical sense, using industry membership alone does a relatively poor job of predicting litigation. However, when we supplement this variable with measures of firm characteristics that include size, growth, and stock performance and volatility, predictive ability improves considerably. These variables are readily available to researchers in a broad variety of settings. Further, including additional variables, such as proxies for corporate governance quality, issuance of securities, insider trading, and so forth, adds relatively little to predictive ability. Given the cost of obtaining these variables (which includes possible sample selection biases), more sophisticated models that include these variables are unlikely to be cost beneficial. Conventional measures of goodness of fit (such as pseudo-R-squareds) do not perform well in assessing the fit and predictive ability of these models. We use a number of alternative approaches suggested in the statistics literature (e.g., Hosmer and Lemeshow, 2000; Long and Freese, 2006) to evaluate model fit and predictive ability, most notably the area under the receiver operating characteristic (ROC) curve, or AUC.3 These techniques confirm that models that supplement the FPS measure with a small set of variables that are readily available from CRSP/Compustat provide significant improvements in predictive ability relative to a model that includes the FPS measure alone. By securities litigation risk, we are referring specifically to the risk of securities class action lawsuits, as opposed to the risk of legal action brought by government agencies such as the U.S. Securities and Exchange Commission (SEC), the U.S. Department of Justice, or state attorney generals, which we view as a related but distinct form of litigation risk. SEC Accounting and Auditing Enforcement Releases (AAERs) have been extensively studied in the accounting literature (see Feroz et al., 1991; Beneish, 1999; Dechow et al., 1996, 2011; Schrand and Zechman, 2011, among others).4 As noted in those studies, SEC enforcement actions typically result from cases of serious accounting irregularities, including fraud. While such cases are likely to lead to securities class actions, many securities class actions involve less serious allegations, 2 For example, financial statements are relatively less useful for firms in high technology industries with significant intellectual property and other intangibles (e.g., Lev and Zarowin, 1999; Tasker, 1998) so that managers of firms in these industries have stronger incentives to provide voluntary disclosures as a substitute for mandated disclosure. 3 To this point, these methods have been used infrequently in the accounting literature but, as argued below, are useful for evaluating and comparing the predictive ability of different models. Recent accounting papers that use this measure include Batta and Wongsunwai (2011), Correia et al. (2011), Demers and Joos (2007), Hobson et al. (2011), and Larcker and Zakolyukina (2011). 4 Actions brought by other government agencies, such as the U.S. Department of Justice and state attorney generals usually involve criminal allegations, and are a subset of SEC enforcement actions (i.e., not all SEC enforcement actions relate to allegations serious enough to warrant allegations of criminal wrongdoing). 292 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 such as failure to disclose in a timely manner, and so do not result in SEC enforcement actions. Consistent with this, we provide evidence that less than 10% of securities class actions are associated with SEC enforcement actions. Our goal is to measure ex ante litigation risk. It is well known that certain factors, most notably large and sudden declines in stock price at the time of an information release, increase the risk of litigation considerably ex post (Alexander, 1991; Jones and Weingram, 1996a). Our goal is not to examine whether outcomes such as stock price declines or accounting frauds result in litigation—the evidence confirms that this is the case (e.g., Hennes et al., 2008). Instead, our goal is to capture factors that make firms more vulnerable to litigation before such ‘‘triggering events’’ occur, which is the construct likely to be of most interest to researchers investigating, say, how litigation risk affects firms’ ongoing disclosure practices. Our paper contributes to the literature in several ways. First, we provide comprehensive evidence on the usefulness of the FPS industry variable as a measure and predictor of litigation risk, an important task given the ubiquity of this measure in the literature. Second, we provide evidence that allows us to better understand what makes particular firms and industries vulnerable to litigation. Third, we provide more precise measures of the predictive ability and goodness of fit of models of litigation risk than those typically used in prior literature. Section 2 reviews previous research. Section 3 details the sample and provides evidence on how litigation rates vary over time and across industries and sectors. Section 4 provides evidence on the determinants of litigation risk, comparing the predictive ability of the conventional FPS industry proxy to models that supplement this proxy with additional drivers of litigation risk. Section 5 concludes. 2. Previous research and empirical predictions 2.1. Previous research on litigation risk A considerable body of research in accounting and finance investigates how private securities litigation affects various corporate policies and managerial decisions. Much of this research uses some variant of the FPS industry proxy for litigation risk. For example, many papers use some form of dummy variable for membership in the FPS industries to measure litigation risk (e.g. Matsumoto, 2002; Ajinkya et al., 2005; Beatty et al., 2008; Jayaraman and Milbourn, 2009; Bhojraj et al., 2010; Brown and Tucker, 2011; Donelson et al., 2010; Hribar et al., 2010). Other authors who examine the determinants and effects of litigation risk limit their samples to firms in the FPS industries.5 Ali and Kallapur (2001), Johnson et al. (2000, 2001, 2007), and Choi (2006), examine various hypothesized effects of the Private Securities Litigation Reform Act of 1995 (PSLRA).6 These authors restrict attention to samples of firms drawn from the three high technology industries identified by FPS (Ali and Kallapur show that their results are robust to using a broader sample of firms). Choi (2006) uses a high technology industry dummy as an explanatory variable for litigation pre- and post-PSLRA. Chandra et al. (2004) limit their sample to firms in high technology industries because high litigation risk is hypothesized to explain heightened income conservatism in these industries. A number of papers use predicted probabilities from models of litigation risk to measure litigation risk. These models typically include firm characteristics such as market capitalization, stock volatility, and stock turnover as well as, in some cases, industry dummies based on FPS.7 Johnson et al. (2000) estimate a probit model that explains lawsuit filings as a function of market capitalization, stock beta, cumulative stock return, minimum stock return, return skewness, stock turnover, CEO power, management monitoring, external financings, and insider trading. The market capitalization and stock return variables, including turnover, come from previous research (Alexander, 1991; Jones and Weingram, 1996a; Skinner, 1997) based on the idea that damages in Rule 10b-5 litigation depend on the size of the price decline, the number of shares traded during the period of the alleged fraud, and the stock price.8 (Larger potential damages amounts make firms more attractive to plaintiffs’ attorneys, ceteris paribus, which explains why market capitalization is strongly associated with litigation risk.) The inclusion of the CEO power and monitoring variables is motivated by the fact that CEOs who have more power and/or are less closely monitored are more likely to engage in aggressive financial reporting and other types of 5 Field et al. (2005) also use industry membership to measure litigation risk but develop their own measure by looking at industry litigation rates during the period before the sample test period (1988–1994) and sorting industries according to whether they had litigation rates above or below the median. 6 Choi et al. (2009) use a sample of firms from the high-technology sector because for other sectors ‘‘the incidence of litigation has fluctuated over time for reasons unrelated to the passage of the PSLRA’’ (page 46). They also improve the generalizability of their sample by including other randomlyselected non-financial industries. 7 Jones and Weingram (1996b) use a regression model to explain why technology and financial services firms experienced a high level of securities litigation in the period from 1989 to 1992. They include several stock market explanatory variables in a logit regression, along with a technology and financial services indicator. They find that the technology dummy is statistically insignificant after controlling for stock return variables, but the financial services dummy remains significant. They attribute this finding to an industry effect of the savings and loan crisis. 8 There is little in the way of theory to guide the choice of variable selection in these models. Most research in the law and economics literature discusses the incentives of plaintiffs’ attorneys to file suit (e.g., Alexander, 1991; Coffee, 1985, 1986; Cox and Thomas, 2006; Dunbar et al., 1995; Johnson et al., 2000; Jones and Weingram, 1996a, 1996b; Romano, 1991). These incentives are directly related to potential damages, which explains the inclusion of variables such as firm size, stock volatility, stock turnover, and the likelihood of price drop. This literature is predicated on the idea that most suits are ‘‘nuisance’’ suits that are unrelated to the extent of managerial wrongdoing (e.g., Alexander, 1991; Romano, 1991). I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 293 opportunistic behavior that increases exposure to securities litigation (Dechow et al., 1996). This is supported by evidence that underwriters of D&O liability insurance focus on corporate governance quality to assess liability risk (Baker and Griffith, 2007) and that consulting groups use governance quality to predict litigation risk (The Corporate Library, 2009).9 These studies also commonly include measures of the extent of insider trading which arguably increases the likelihood of stockholder litigation, especially after PSLRA, as well as the extent to which firms have recently issued debt and/or equity. Insider trading activity and external financing provide opportunities for managers to exploit high market valuations; if the valuations are achieved using what can be alleged to be false or misleading information, these activities increase the probability of a lawsuit filing.10 Other papers that model litigation risk include Brown et al. (2005) and Rogers and Stocken (2005), both of which use largely the same set of variables as in Johnson et al. (2000) but supplement them with FPS industry dummy variables. While corporate governance and insider trading variables are plausible measures of managerial opportunism that increase firms’ exposure to litigation, there are two issues when including these types of variables in litigation risk models. First, it is not clear a priori that most securities litigation results from opportunism by managers as opposed to being driven by adverse outcomes. While it is clear that extreme forms of opportunism such as accounting frauds lead to litigation, these suits form a relatively small part of the population of securities class action suits (Section 3). Second, corporate governance and insider trading data are less widely available than data on firm characteristics such as size and volatility, constraining sample sizes and perhaps also biasing sample selection. Although there is some agreement in the literature in terms of the set of covariates usually included in litigation risk models, apart from reporting pseudo-R-squareds, these studies rarely report or discuss in much detail the goodness of fit or predictive ability of these models. Consequently, there is little evidence on the construct validity of the litigation risk measures used in previous research. This is a primary motivation for our research. In the introduction we draw a distinction between the risk of securities class action lawsuits (which we refer to as litigation risk) and the risk of SEC enforcement actions and other types of government legal actions against firms and managers. While securities class actions can allege a range of management improprieties, these are for the most part less serious than those alleged in SEC enforcement actions (AAERs), many of which relate to accounting fraud. Moreover, securities class actions often result from bad outcomes as opposed to malevolent management actions. These differences imply that variables used to predict SEC enforcement actions will be somewhat different to those used to predict securities class actions. Consistent with this, Dechow et al. (2011), who use prior literature to develop a comprehensive prediction model for AAERs, include a number of accruals quality variables (which are likely linked to deliberate earnings overstatements), as well as other variables that capture managerial incentives to overstate earnings. While we include some of these variables in our analysis, the main focus of our prediction model is on variables that make firms and industries vulnerable to lawsuit filings. 2.2. Assessing the validity of the FPS litigation risk proxy The ability of a fixed industry proxy to reliably capture litigation risk is reduced if litigation rates in particular industries vary over time. If economy-wide events cause time-series variation in the fortunes of different industries, litigation risk is not likely to be specific to particular industries or firms. Instead, it is more likely that economic shocks cause losses in value that vary across industries and through time, and that these losses trigger litigation.11 This means that it will be hard to identify particular industries that are always subject to higher litigation risk. FPS identify their four industries based on observed litigation rates during the 1988–1992 period, which includes the recession of the early 1990s. On the other hand, it is possible that there are firm and industry characteristics that make particular firms and industries generally more susceptible to litigation. For example, firms that operate in more volatile operating environments have greater levels of stock volatility, which makes them more susceptible to litigation. This discussion motivates two principal types of empirical tests. First, we provide evidence on the extent to which litigation rates vary across economic sectors and industries over time. Second, we compare the predictive ability of the FPS industry dummy to that of models that also include other firm characteristics likely to drive litigation risk. While including additional variables will usually increase predictive ability, our purpose is to gauge empirically the magnitude of these improvements to provide researchers with information they can use to make the tradeoffs necessary in choosing a proxy for litigation risk. Further, to the extent that underlying firm characteristics (rather than industry membership per se) drive litigation risk, we expect the predictive power of the FPS measure to decline as these more direct measures are included in predictive models. 9 Daines et al. (2010) find that corporate governance and transparency ratings, such as those produced by Risk Metrics/ISS, Governance Metrics International and the Corporate Library, do not have predictive power for identifying lawsuit filings. 10 Johnson et al. (2007) find that abnormal insider selling is more strongly associated with litigation after PSLRA, consistent with their prediction that the Act’s more stringent pleading requirements encourages lawyers to focus on more objective evidence of managerial malfeasance. See also Pritchard and Sale (2005), who discuss the role of insider trading and securities issuances in litigation after PSLRA. 11 Consider two economy-wide events that occur during our sample period—the large shock to prices of technology stocks in 2001 and the financial crisis of 2007–2008. The damage, measured in terms of stockholders’ value losses, of both shocks was concentrated in particular industries. If the effect of shocks varies across firms within a given industry (Albuquerque, 2009), industry will be even less useful in predicting litigation risk. 294 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 We investigate a number of variables in addition to those conventionally employed in the literature to predict litigation risk.12 We add a measure of economic performance (ROA) because as performance deteriorates and scrutiny on managers increases, the risk of aggressive actions that potentially lead to litigation also increases. Similarly, we include Altman’s (1968) Z-score to proxy for the likelihood of financial distress, which should also increase litigation risk. We include several proxies for the nature of the firms’ investment opportunities (working capital, market-to-book, R&D intensity, ratio of PP&E to total assets) because these variables affect corporate policies such as executive compensation, capital structure, and payout policy that could affect litigation risk (Smith and Watts, 1992). We include the ratio of goodwill to assets to measure the extent of the firms’ M&A activity, which likely increases litigation risk. We also include exchange listing (NYSE dummy) to see if listing on the NYSE (as opposed to the NASDAQ) increases the risk of litigation. Finally, we include the percentage of institutional ownership, and debt and equity issuance proceeds. 3. Sample and evidence on the relation between industry and litigation risk We obtain data on filings of securities class action lawsuits from the Stanford Law School Securities Class Action Clearinghouse. These data begin in 1996 and continue through the current time. We include lawsuits filed against public companies (listed on the NYSE, ASE, or NASDAQ) and exclude the IPO allocation, mutual fund, and analyst lawsuits common around 2001.13 The Stanford database also has data on lawsuit outcomes. We restrict attention to lawsuit filings because we believe that managers’ main goal is to avoid filings (and the associated legal, reputational, and time costs).14 Once suits are filed, there are effectively two outcomes—dismissal or settlement. Since 1996, 43.0% of cases were dismissed while 56.7% were settled and 0.3% went to trial (Cornerstone, 2011a, p. 14). Defendants typically wait to see whether their initial motion to dismiss is successful; if it is not, they eventually settle the case.15 Variation in settlements is relatively small: of those cases settled between 1996 and 2010, 57% settled for less than $20 million while 80% settled for less than $25 million (Cornerstone, 2011b, p. 3). We do not take a position on whether ‘‘bad managers’’ get sued; that is, whether managers took some type of opportunistic or unlawful action that resulted in litigation. Instead, we are agnostic about managers’ guilt or innocence and simply address whether, as an empirical matter, certain firm characteristics and/or industry membership increase the likelihood of litigation. Clearly, managers who engage in malfeasance (illegal insider trading, accounting fraud) expose their firms to greater overall litigation risk. However, it is also the case that firms and managers can be sued in situations where there is no obvious wrongdoing. Whether the ‘‘merits matter,’’ in the sense that the legal process correctly identifies and punishes managers who violate the securities laws (as opposed to being unlucky and getting a bad outcome), is the subject of considerable discussion in the law and economics literature (e.g., Alexander, 1991; Romano, 1991). Table 1, Panel A shows the number of lawsuits by year and sector (as defined by Bloomberg); the data are also shown in Fig. 1. There are 2,497 filings from 1996 to 2009, for an average of approximately 178 per year. The number of lawsuits each year varies considerably; for example, there were 220 lawsuits in 2004 but only 112 in 2006. It is not clear what explains this variation. Cornerstone (2011a, p. 4) plots a measure of equity market volatility against filing activities. This variable seems correlated with filings, perhaps because higher volatility increases the likelihood of the sharp declines in firms’ stock prices that can trigger litigation.16 Panel A of Table 1 also reports the fraction of lawsuits that allege a violation of SEC Rule 10b-5 (a misstatement or omission of material information), which are the lawsuits of most interest to researchers interested in financial reporting and disclosure issues. The fraction of 10b-5 cases is high, averaging 89% for the overall period. The most common allegations (untabulated) are material misrepresentations regarding the business, failure to warn, and accounting or internal control problems. Panel B of Table 1 reports the percentage of lawsuits in each sector by year. It is clear that lawsuits cluster by sector. The most lawsuits overall are in the technology (29%), services (21%), healthcare (15%), and financial (15%) sectors, consistent with concentration by industry but somewhat inconsistent with the FPS measure, which is mainly focused on technology firms. At the other end of the spectrum, the basic materials, capital goods, conglomerate, energy, and transportation sectors generally account for a small fraction of litigation (in the 1% to 5% range). The rate of litigation also varies through time for a given sector. For example, the share of litigation attributable to firms in the technology sector is high in 2000 and 2001 (38% and 42%) when stock prices of technology firms fell dramatically but falls to 15% and 11% in 2008 and 2009. Conversely, financial firms had a relatively 12 We acknowledge that this choice of variables, while based on the law and economics literature discussed above, is rather ad hoc. However, part of the motivation for this research is to see whether we can identify new factors that predict litigation risk, and in particular to see whether these factors supplant industry as a predictor of litigation risk. 13 The Stanford database is commonly used as a source of lawsuit filings. To provide some assurance as to the completeness of these data, we search the 10-K filings of all S&P 500 companies from 2007 through the present for references to 10b-5 litigation. Of the 500 companies, 46 had 10-K disclosures indicating involvement in a 10b-5 securities class action. We found all of these cases in the Stanford database, providing assurance that it is reasonably complete. 14 The law and economics literature suggests that the merits of the case do not greatly affect resolutions (e.g. Alexander, 1991; Romano, 1991; Baker and Griffith, 2007; Choi, 2006; Johnson et al., 2007). This reinforces managers’ incentives to avoid litigation. 15 The tendency for both sides of securities class action lawsuits to have strong incentives to settle is well known; see Alexander (1991) and Romano (1991) for further discussion. 16 Alexander (1991) points out that a lawsuit filing following a large stock price decline supports ‘‘an award of attorneys’ fees that would make it worthwhile to bring a case’’ (p. 513). As an empirical matter it is well-established that sharp, significant stock price declines are associated with lawsuit filings (Francis et al., 1994b; Jones and Weingram, 1996a). I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 295 Table 1 Number and percentage of lawsuits by year and sector. In this table, Panels A and B provide the number and percentage of lawsuits by year and sector, respectively. The sector definitions are provided by Bloomberg. The lawsuits in this table are lawsuits filed against publicly-held firms and exclude IPO allocation, mutual fund, and analyst lawsuits. Panel A shows that the number of lawsuits can vary considerably across years. Panel A also shows the percentage of lawsuits alleging a Rule 10b-5 violation (these data are also shown in Fig. 1). The percentages in Panel B are calculated by dividing the number of lawsuits for the sector-year by the total lawsuits for all sectors in the relevant year; in other words, the percentages are the breakdown of sector litigation for the year. Panel A: Number of lawsuits by year and sector Sector Basic materials Capital goods Conglomerates Consumer cyclical Consumer non-cyclical Energy Financial Healthcare Services Technology Transportation Utilities No sector provided 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Total 2 4 0 3 6 2 10 11 20 32 2 0 2 7 4 1 11 4 1 18 17 37 58 3 2 0 4 3 0 11 5 2 22 36 52 81 4 4 1 5 5 3 19 11 4 22 22 51 59 2 0 0 6 4 2 10 8 2 27 19 47 78 3 6 0 6 4 1 10 5 1 13 17 38 76 4 4 0 3 5 3 4 4 6 28 31 52 53 2 21 1 7 5 3 9 7 2 26 38 38 45 1 5 0 5 11 1 8 5 6 34 39 46 55 6 4 0 7 0 1 13 6 2 26 31 31 53 1 1 1 2 4 0 5 4 2 12 19 23 39 2 0 0 2 6 0 6 4 4 40 26 44 33 1 2 0 7 6 2 3 9 6 89 23 19 27 2 3 0 7 3 3 4 3 2 67 22 21 14 0 1 6 70 64 20 116 81 42 434 351 519 703 33 53 11 Total filings by year 94 163 225 203 212 179 213 186 220 173 112 168 196 153 2,497 % of Filings alleging Rule 10b-5 violation 89 90 91 93 91 88 93 96 94 95 90 82 79 75 89 Panel B: Percentage of total lawsuits by year and sector Sector Basic materials Capital goods Conglomerates Consumer cyclical Consumer non-cyclical Energy Financial Healthcare Services Technology Transportation Utilities No sector provided Total 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 All Yrs 2 5 0 4 6 1 11 11 21 35 2 0 2 5 3 1 7 3 1 11 10 19 37 2 1 0 2 1 0 5 2 0 10 17 24 35 2 1 1 2 3 1 9 6 2 11 12 24 29 1 0 0 2 2 1 5 4 1 12 9 21 38 2 3 0 4 2 1 6 3 1 6 8 21 42 3 3 0 2 3 2 2 2 3 12 15 24 24 1 10 0 3 3 2 5 4 1 14 21 19 24 1 3 0 2 5 1 4 2 2 13 18 22 26 3 2 0 4 0 1 7 4 1 14 19 16 31 1 1 1 2 4 0 3 4 2 11 16 22 34 2 0 0 0 4 0 3 3 2 24 19 25 18 1 1 0 4 3 1 2 5 3 40 14 12 15 0 1 0 5 2 3 4 2 1 34 17 16 11 0 1 4 3 3 1 5 3 2 15 15 21 29 1 2 0 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 small share of litigation in 2000 and 2001 (12% and 6%) but a much larger share in 2008 and 2009 (40% and 34%) as a result of the financial crisis. This suggests that industry-based proxies may not be consistently reliable measures of litigation risk. In Section 2.1 we argue that the majority of securities class action filings do not result in SEC enforcement actions (AAERs) because most filings relate to allegations (such as timeliness of disclosure) that are not sufficiently serious to warrant SEC enforcement actions. To provide evidence on this, we examine how many of the 2,497 lawsuit filings (Table 1) involve accounting allegations that could potentially results in enforcement actions. We find that 774 filings (31%) involve accounting allegations. We then obtained data on AAERs, which are available through August of 2006, rather than through the end of our sample period.17 Of the 631 filings that involve an accounting allegation for the period over which the two samples overlap, 171 (27%) are associated with SEC enforcement actions. This implies that less than 10% of all securities filings (0.27 0.31) are associated with SEC enforcement actions. Alternatively, if we take the 1,948 filings for the period over which the samples overlap, 171 filings (9%) are associated with enforcement actions. Thus, it seems clear that the large majority (over 90%) of class action lawsuit filings do not involve the types of allegations that typically result in SEC enforcement actions, consistent with our argument that the two types of risk are related but distinct. Table 2, Panel A reports the number of firms sued in each industry along with industry litigation rates, where industry is measured using two-digit SIC codes.18 To derive this sample we merge the set of lawsuits from Table 1 with Compustat. 17 See Karpoff et al. (2008) for details of the AAER sample. Francis et al. (1994a) sometimes define their high litigation set more finely than two-digit SIC codes. Specifically, they define this group as biotech firms (SIC codes 2833–2836 and 8731–8734), computer firms (3570–3577 and 7370–7374), electronics firms (3600–3674), and retail firms (5200–5961); subsequent research typically follows these definitions. Francis et al. limit their sample to four industries because ‘‘yinvestigations of the information 18 296 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 250 Lawsuit Filings Count 200 150 100 50 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Year Rule 10b-5 Filings Other Class Action Securities Filings Fig. 1. Number of lawsuit filings by year. This figure shows the number of lawsuit filings by year, which is also shown in Table 1, Panel A. This figure shows the fraction of lawsuits that allege a violation of SEC Rule 10b-5 (a misstatement or omission of material information). The unshaded portion of the figure are alleged violations of other class action securities laws, for example violation of Securities Exchange Act of 1933 section 11, 12(a), 15, and Securities Exchange Act section 20(a). To keep the table manageable, we only tabulate FPS industries and industries for which litigation rates exceed 5% in at least one year and eliminate industries with less than ten firms.19 The FPS industries tend to have litigation rates that exceed the overall rate of 1.6%. Chemicals (SIC 28) has a litigation rate of 2.4%, machinery (SIC 35, which includes computers) has a rate of 2.4%, and business services (SIC 73) has a rate of 2.8%, although these numbers are understated by the inclusion of non-FPS industries. On the other hand, some non-FPS industries experience relatively high litigation rates. Litigation rates in financial services (SIC 61–64) are at or above those for the FPS industries, with rates of 2.6% to 5.0%, as are personal services (SIC 72, 4.4%) and health services (SIC 80, 3.2%). Panels B and C of Table 2 report the number and percentage rate of litigation for firms in the FPS industries compared to firms in all non-FPS industries. We report litigation rates for each of the four FPS industry groups, for the FPS industries as a whole, and for the remaining industries as a group. The data in these panels show that, overall, litigation rates in the FPS industries are higher than those of other industries. The litigation rate for the four FPS industries considered together is 2.7% versus 1.2% for all non-FPS industries considered together (w2 ¼13.7, significant at the 1% level). The litigation rate for the FPS industries is higher than for nonFPS industries in all years, with rates that are significantly higher (at the 5% level or better) in eight of 13 years. These results reinforce the validity of the FPS measure. There is evidence that litigation risk increases with firm size (Jones and Weingram, 1996a) and that the effect of industry shocks varies across firm size within a given industry (Albuquerque, 2009). Given this, we examine whether the relation between industry and litigation rates differs for large firms. In Table 3, we reperform the analysis reported in Table 2 for firms in the largest 5% of the size distribution (by year) as measured by assets. Litigation rates are significantly higher for larger firms. The overall litigation rate here is 5.1% (Table 3, Panel B), roughly three times the overall litigation rate of 1.6% shown in Table 2. In addition, the litigation rate for large firms varies more from one year to the next, from lows of around 0.8% in 1996 and 1998 to highs of 12.2% in 2002 and 12.7% in 2008, than does the rate for the overall sample.20 Panel A of Table 3 shows that large firms in some non-FPS industries have relatively high litigation rates. Firms in transportation (SIC 37, rate of 6.5%), instruments (SIC 38, rate of 9.1%), utilities (SIC 49, rate of 5.5%), and financial services (SIC 60–63, rates of 3.0% to 23%) all have litigation rates roughly comparable to or higher than those for the large firms in FPS industries. Panel B of Table 3 shows that litigation rates for large firms in the FPS industries are again higher than for the non-FPS industries but that differences are smaller and less consistent than for the overall sample. The overall litigation rate is 7.8% for the FPS industries compared to 4.8% for the non-FPS industries, a difference that is not significant at the 5% level (w2 ¼ 2.6). Although differences in particular years are sometimes economically significant, the difference is statistically significant in only one of the (footnote continued) mix defense require substantial familiarity with industry-specific information which may temper or offset alleged misleading statements.’’ (Francis et al. 1994a, p. 144). They choose these four industries because they are subject to a ‘‘high incidence’’ of litigation during 1988–1992. 19 These observations are retained in the overall litigation rates reported at the bottom of the table. 20 Size is likely to have counter-veiling effects on the likelihood of litigation. While larger firms have ‘‘deeper pockets’’ and size is likely to increase expected stockholder damages, larger firms are also more diversified, and so less likely to suffer sharp declines in stock price than smaller firms. I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 297 Table 2 Number and percentage of unique companies subject to filings by industry. In this table, Panel A shows the number and percentage of unique companies subject to filings by industry. The lawsuits in this table are lawsuits filed against publicly-held firms (with shares listed on the NYSE, ASE, or NASDAQ) and exclude IPO allocation, mutual fund, and analyst lawsuits listed by 2-digit SIC code. Included in the table are all FPS industries; for non-FPS industries, to make the table wieldier, we only report those industries where litigation rates exceed 5% in at least one year and eliminate industries with less than ten firms. The % sued column is calculated by dividing the number sued column by the number of firms in Compustat for the relevant SIC code Panel A: Number of unique companies subject to filings by industry SIC Industry name Number sued 10 15 16 23 24 26 28a 31 32 35a 36a 37 39 40 42 44 49 51 52a 53a 54a 55a 56a 57a 58a 59a 61 62 63 64 72 73a 78 80 82 87a 99 Metal Mining Building Construction Heavy Construction Apparel Lumber and Wood Products Paper and Allied Products Chemicals and Allied Products Leather Stone, Glass, Clay, Concrete Industrial and Commercial Machinery Electronic and Other Electrical Equipment Transportation Equipment Misc. Manufacturing Inds. Rail Road Transportation Motor Freight Transportation Water Transportation Electric, Gas, Sanitary Services Wholesale Trade, Nondurable Goods Building Materials, Hardware, Garden Supply General Merchandise Stores Food Stores Automotive Dealers Apparel and Accessory Stores Home Furniture, Furnishings, Equip. Eating and Drinking Places Miscellaneous Retail Nondepository Credit Institutions Security and Commodity Brokers Insurance Carriers Insurance Agents, Brokers Personal Services Business Services Motion Pictures Health Services Educational Services Engineering and Management Services Nonclassifiable Establishments Total Filings 8 5 3 11 3 3 123 4 2 76 111 19 8 1 4 3 41 18 1 9 6 1 10 4 9 30 30 36 52 9 8 195 6 29 7 15 8 1,177 a Average industry count % Sued 421 294 188 423 273 500 5,125 182 286 3,167 4,826 1,118 444 167 444 429 2,158 667 71 360 300 250 556 236 818 1,000 600 818 2,000 346 182 6,964 222 906 219 1,154 154 1.9 1.7 1.6 2.6 1.1 0.6 2.4 2.2 0.7 2.4 2.3 1.7 1.8 0.6 0.9 0.7 1.9 2.7 1.4 2.5 2.0 0.4 1.8 1.7 1.1 3.0 5.0 4.4 2.6 2.6 4.4 2.8 2.7 3.2 3.2 1.3 5.2 1.6 Contains FPS industry. In this table, Panels B and C show the number and percentage of unique firms subject to securities lawsuits in the FPS industries. Biotech firms are classified as firms in SIC Codes 2833–2838 and 8731–8734; computer firms are in SIC codes 3570–3577 and 7370–7374; electronics firms are in SIC codes 3600–3674, and retail firms are in SIC Codes 5200–5961. The lawsuits in this table are lawsuits filed against publicly-held firms (with shares listed on the NYSE, ASE, or NASDAQ) and exclude IPO allocation, mutual fund, and analyst lawsuits. The FPS firms and non-FPS firms percentage sued are calculated by dividing the number sued by the number of Compustat firms for the relevant SIC code shown in Panel B. nn and n significant at the 1% and 5% level, respectively. Panel B: Number of unique firms subject to lawsuit filings in FPS classification Biotech Computers Electronics Retail # FPS Firms Sued 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Total 2 286 7 500 2 286 1 333 0 0 18 545 3 300 4 286 7 292 23 547 7 304 3 300 7 292 23 622 3 300 4 286 6 316 26 650 4 333 5 278 9 310 23 511 12 308 5 263 10 313 16 552 11 314 5 263 15 306 12 522 12 308 5 263 18 333 28 509 8 320 9 265 12 333 16 485 11 324 7 259 8 348 9 450 8 320 3 273 15 357 7 438 13 317 6 250 8 333 8 444 7 304 7 241 117 4,189 216 6,750 101 4,040 64 3,556 12 1,333 25 1,471 40 1,429 37 1,480 41 1,577 49 1,400 42 1,448 44 1,419 63 1,432 46 1,394 28 1,400 41 1,367 30 1,304 498 18,444 298 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 Table 2 (continued ) In this table, Panels B and C show the number and percentage of unique firms subject to securities lawsuits in the FPS industries. Biotech firms are classified as firms in SIC Codes 2833–2838 and 8731–8734; computer firms are in SIC codes 3570–3577 and 7370–7374; electronics firms are in SIC codes 3600–3674, and retail firms are in SIC Codes 5200–5961. The lawsuits in this table are lawsuits filed against publicly-held firms (with shares listed on the NYSE, ASE, or NASDAQ) and exclude IPO allocation, mutual fund, and analyst lawsuits. The FPS firms and non-FPS firms percentage sued are calculated by dividing the number sued by the number of Compustat firms for the relevant SIC code shown in Panel B. nn and n significant at the 1% and 5% level, respectively. Panel B: Number of unique firms subject to lawsuit filings in FPS classification # non-FPS Firms Sued 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Total 8 4,000 27 4,500 29 4,143 57 4,071 48 4,000 31 3,875 73 3,842 59 3,933 70 3,889 66 3,883 37 4,111 53 4,077 83 3,952 641 53,417 Panel C: Percentage of unique firms subject to lawsuit filings in FPS classification 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Biotech (%) Computers (%) Electronics (%) Retail (%) 0.7 1.4 0.7 0.3 0.0 3.3 1.0 1.4 2.4 4.2 2.3 1.0 2.4 3.7 1.0 1.4 1.9 4.0 1.2 1.8 2.9 4.5 3.9 1.9 3.2 2.9 3.5 1.9 4.9 2.3 3.9 1.9 5.4 5.5 2.5 3.4 3.6 3.3 3.4 2.7 2.3 2.0 2.5 1.1 4.2 1.6 4.1 2.4 2.4 1.8 2.3 2.9 FPS Firms % Sued Non-FPS Firms % Sued Chi-Squared for diff. 0.9 0.2 3.83 1.7 0.6 3.90n 2.8 0.7 6.35n 2.5 1.4 2.86nn 2.6 1.2 3.77nn 3.5 0.8 7.10nn 2.9 1.9 2.28 3.1 1.5 3.67nn 4.4 1.8 5.41n 3.3 1.7 3.61 2.0 0.9 3.17 3.0 1.3 3.94n 2.3 2.1 0.25 All Yrs 2.8 3.2 2.5 1.8 2.7 1.2 13.68nn 13 years. In seven of the 13 years, the difference is 2% or less or goes in the ‘wrong’ direction. This means that the validity of the FPS proxy for litigation risk, at least in terms of industry litigation rates, is more questionable for larger firms. 4. Predicting litigation risk Our principal goal is to develop and evaluate models that predict litigation risk and to benchmark these models against the FPS measure widely used in the literature. Table 4 reports sample formation for these analyses. We begin with the 2,883 lawsuit filings available from the Securities Class Action Clearinghouse from 1996 to 2008. After eliminating non-Rule 10b-5 cases (120 filings), filings against firms not listed on a major exchange (584 filings), filings related to IPO allocation, mutual fund, and analyst cases (279 cases), and firms without the requisite Compustat and CRSP data, we are left with 720 lawsuit filings. This set of filings translates into 1,562 firm-years which include a lawsuit class period, which when added to our sample of 31,344 nonlawsuit firm-years yields a final sample of 32,906 firm-years.21 As a baseline, we first report the results of an approach under which membership in one of the FPS industries is interpreted as predicting a lawsuit, consistent with how many prior studies operationalize litigation risk. The results of this analysis are shown in Table 5. This approach predicts lawsuits in 26.3% of firm/years, which reflects FPS industry membership. The classification table also reports a number of statistics conventionally used to evaluate model success in predicting lawsuits. In this case the Type I error rate is high, at 93.6%, while the Type II error rate is low, at 4.2%. These rates are expected because predicting that all firms in particular industries will be subject to litigation naturally results in a relatively large number of false positives and a relatively small number of false negatives. We also report model sensitivity, which is 35.3%, and specificity, which is 74.2%.22 If researchers (and managers) are concerned about litigation risk, model sensitivity (or ‘‘hit rate’’) is important because it tells us how often the model correctly forecasts that a firm will be sued. Overall model accuracy (the overall fraction of correctly classified observations) is 72.3%. The advantage of the FPS measure is that it is available in virtually all research settings—other than industry membership, no data are required. Because we are interested in assessing the usefulness of a parsimonious litigation model for researchers in a wide array of settings, we first limit our model to a small set of explanatory variables that we believe will deliver increased predictive ability at relatively modest cost in terms of data requirements. To do this we augment the FPS measure with explanatory variables that are readily available from Compustat and CRSP. We include firm size (log of total assets), sales 21 We require complete data on lawsuit filing (a dummy variable set to one for firm/years for which there is a lawsuit), lagged accounting variables (assets and revenue growth rate), the return variables (prior and contemporaneous skewness of returns, volatility of returns, stock turnover, and year t, t 1, t 2, and t 3 twelve-month cumulative abnormal return), and the FPS industry indicator (a dummy variable that turns on for firm/years in the FPS industries). 22 Sensitivity and specificity are common measures of the performance of prediction models (Hosmer and Lemeshow, 2000, Chapter 5). Sensitivity reports the fraction of true positives correctly predicted. Specificity reports the fraction of true negatives correctly predicted. Similar to Type I and Type II errors, there is usually a tradeoff between sensitivity and specificity; however, it is possible to attain 100% sensitivity and specificity. An analogy can be drawn to metal detectors used in airport security screening. One can set the detector so that sensitivity is high and specificity is low to be sure all true security risks are detected (with the cost that it will incorrectly identify lots of innocent people as security risks). Conversely, if it is relatively costly to pull people aside when they are not true security risks, one can lower sensitivity to increase specificity. I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 299 Table 3 Number and percentage of unique companies subject to filings by year and industry for large firms. In this table, Panel A shows the number and percentage of unique companies subject to securities lawsuits by industry for large firms only. The lawsuits in this table are lawsuits filed against publicly-held firms (with shares listed on the NYSE, ASE, or NASDAQ) above the 95th percentile in size (total assets), and exclude IPO allocation, mutual fund, and analyst lawsuits listed. Included in the table are all FPS industries; for non-FPS industries, to be included in this table, the observation count must be at least 20. Some industries are included in this table but not in Table 2 due to the fact that the minimum % sued in Table 2 criteria is 5% in any year. The % Sued column is calculated by dividing the number sued column by the number of firms in Compustat for the relevant SIC code. Panel A: Number and percentage of companies subject to filings by industry for large firms SIC Industry name 10 20 28a 29 33 35a 36a 37 38 40 48 49 52a 53a 54a 55a 56a 57a 58a 59a 60 61 62 63 73a 87a 99 Metal Mining Food and Kindred Products Chemicals and Allied Products Petroleum Refining and Related Industries Primary Metal Industries Industrial and Commercial Machinery Electronic and Other Electrical Equipment Transportation Equipment Measuring, Analyzing, Controlling Instruments Rail Road Transportation Communications Electric, Gas, Sanitary Services Building Materials, Hardware, Garden Supply General Merchandise Stores Food Stores Automotive Dealers Apparel and Accessory Stores Home Furniture, Furnishings, Equip. Eating and Drinking Places Miscellaneous Retail Depository Institutions Nondepository Credit Institutions Security and Commodity Brokers Insurance Carriers Business Services Engineering and Management Services Nonclassifiable Establishments a Number sued % Sued 42 78 170 172 30 90 112 123 33 43 386 254 8 46 2 1 0 0 11 2 733 119 94 426 41 0 61 0.0 2.6 8.2 1.2 0.0 7.8 4.5 6.5 9.1 2.3 3.4 5.5 12.5 4.3 0.0 0.0 0.0 0.0 9.1 0.0 3.0 11.8 23.4 5.6 7.3 0.0 13.1 Contains FPS industry. In this table, Panel B, shows the percentage of companies subject to securities lawsuits by year for large firms in the FPS industries. Biotech firms are classified as firms in SIC Codes 2833–2838 and 8731–8734; computer firms are firms in SIC codes 3570–3577 and 7370–7374; electronics firms are firms in SIC codes 3600–3674, and retail firms are firms in SIC Codes 5200–5961. The lawsuits in this table are lawsuits filed against publicly-held firms (with shares listed on the NYSE, ASE, or NASDAQ) above the 95th percentile in size, and exclude IPO allocation, mutual fund, and analyst lawsuits listed by year. The FPS firms % large firms sued and non-FPS % large firms sued rows are calculated by dividing the number sued by the number of firms in Compustat for the relevant SIC codes. The bottom of the panel compares the percentage sued of large FPS firms and large non-FPS firms, and a chi-squared for the difference between the two groups. Panel B: Percentage of companies subject to filings by year for large firms in the FPS classification 1996 Biotech (%) Computers (%) Electronics (%) Retail (%) All Large Firms % Sued FPS % Large Firms Sued Non-FPS % Large Firms Sued Chi-squared for difference n 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 All Yrs 0 0 0 0 0 0 0 14 0 13 0 0 0 25 0 0 0 20 0 0 0 11 11 0 30 0 11 20 10 0 0 0 8 14 11 25 10 14 0 0 10 13 0 0 50 0 22 25 9 11 0 0 10 10 4 6 0.8 0.0 0.9 1.9 3.0 1.7 0.8 2.9 0.4 4.9 6.3 4.7 5.4 5.7 5.3 3.3 6.3 2.8 12.2 16.7 11.6 5.8 3.2 6.2 7.8 12.5 7.0 4.1 7.1 3.7 2.1 6.3 1.4 6.6 26.7 3.8 12.7 6.3 13.7 5.1 7.8 4.8 2.58 0.54 1.58 0.37 0.10 1.01 0.79 0.65 1.08 0.87 1.80 4.71n 1.18 2.58 Significant at the 5% level. growth (the change in sales deflated by total assets), as well as a number of stock-return based measures—abnormal returns, return volatility, return skewness, and stock turnover—designed to capture potential stockholder damages. To predict litigation we deliberately avoid variables that directly reflect events that trigger the litigation—as discussed above, we are interested in ex ante litigation risk. In some previous studies, the independent variables are measured in the same period as the litigation. By including abnormal stock returns measured during the period during which the lawsuit is filed, the researcher includes the downward stock price movement that triggers the litigation (as well as any valuation 300 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 Table 4 Sample selection. This table reports sample formation: the progression from securities lawsuit filings from the Securities Class Action Clearinghouse (http://securities. stanford.edu/) from 1996 to 2008 to the ultimate sample used for the regression analysis in Table 7. The sample consists of firm-years in which a lawsuit filing occurred, and firm-years without a lawsuit filing from 1996 to 2008. Lawsuit filings spanning 1996 2008 from Stanford Law School Securities Class Action Clearinghouse 2,883 Less: Less: Less: Less: Less: (120) (584) (279) (818) (362) Non rule 10b-5 violation cases Filings against private companies or filings against firms not listed on the NYSE, ASE, or NASDAQ IPO allocation cases, hedge fund, mutual fund, and analyst cases firm-years for which Compustat or Crsp identifiers are not available no Compustat or Crsp coverage or certain missing data items in the relevant firm-year Total useable lawsuit filings Total useable lawsuit filing firm-years (a class period occurred during the firm-year) 720 1,562 Firm-years for which no lawsuit filing/class period occurred 31,344 Total useable observations 32,906 Table 5 Prediction model under which membership in the FPS industries is interpreted as predicting a lawsuit. This table shows a baseline model under which membership in one of the FPS industries is interpreted as predicting a lawsuit, consistent with how much of the relevant prior literature has operationalized litigation risk. FPS is set to 1 for biotech firms (SIC codes 2833–2836 and 8731–8734), computer firms (3570–3577 and 7370–7374), electronics firms (3600–3674), and retail firms (5200–5961), and 0 otherwise. The table calculates cases where FPS predicts a lawsuit (26%), correctly classified cases (72%), sensitivity (35%), specificity (74%), type I error (94%), and type II error (4%). Lawsuit filing No lawsuit filing FPS¼ 1 FPS¼ 0 551 1,011 1,562 8,098 23,246 31,344 FPS Predicts Lawsuit Correct Classification Sensitivity Specificity Type I Error Type II Error Goodman and Kruskal Gamma Statistic 8,649/32,906 (551þ 23,246)/32,906 551/1,562 23,246/31,344 8,098/8,649 1,011/24,257 8,649 24,257 32,906 26.28% 72.32% 35.28% 74.16% 93.62% 4.17% 0.0021 effects of the litigation). To avoid this, we measure the stock return variables in the fiscal year before the lawsuit filing. To examine the effect of this choice, we present the analyses with the stock return-based variables measured both ways: over the class period (misrepresentation period) and over the prior fiscal year. We report descriptive statistics in Table 6. Panel A reports means and medians for the variables used in the regressions in Table 7 (basic set of variables) and Table 8 (full set of variables). Mean (median) total assets for these firms is $582m ($566m) with annual sales growth of 11.3% (4.6%). As shown in Table 5, 26.3% of these firms are in FPS industries. Mean (median) monthly stock volatility is 3.0% (2.6%). Mean stock returns are lower in year t (which includes the class period) than year t 1, consistent with negative returns in the event period triggering litigation. Similarly, turnover is higher in year t than in year t 1, consistent with high turnover being associated with litigation. Panel B of Table 6 reports Pearson correlations among the variables. The indicator for litigation is positively correlated with the FPS dummy (0.046), size (0.168), sales growth (0.064), and turnover (0.246), and negatively correlated with event year returns ( 0.104). These correlations are all statistically significant at better than 1%. These correlations again suggest that event year returns and turnover drive litigation (the corresponding correlations with lagged returns and turnover are 0.032 and 0.069, respectively). The FPS dummy is negatively associated with size ( 0.226), positively associated with sales growth (0.066), positively associated with return volatility (0.327), and positively associated with lagged turnover (0.322), consistent with the FPS dummy being associated with variables that drive litigation. Size is negatively correlated with return volatility ( 0.548), as expected if larger firms are more diversified. Table 7 reports the results of binomial logistic regressions of the lawsuit dummy variable on the FPS dummy and the other covariates.23 The first model uses only the FPS industry dummy (model 1). The coefficient on this variable is positive 23 We use a binomial logistic regression rather than a hazard model because the traditional Cox proportional hazard model, used for events such as bankruptcy or death, is designed for situations in which (1) there is a single event for each firm (or other observational unit) after which that firm disappears, and (2) the likelihood of that event is likely to systematically change as time elapses for a given firm (or unit). Neither of these conditions is true of class action lawsuits. First, firms are often sued in multiple years. Second, unlike events such as bankruptcy, it is not clear that the likelihood of lawsuits changes as a function of elapsed time. I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 301 Table 6 Descriptive statistics. In this table, Panels A and B present descriptive statistics and correlation coefficients of the variables used in the regressions in Tables 7 and 8, respectively. All variables are winsorized at the 1% and 99% level. Correlation coefficients in Panel B are based on 32,906 observations (from Table 7). Pearson correlation coefficients are shown above the diagonal, and Spearman below the diagonal. Variable definitions are provided in the appendix. Panel A: Descriptive statistics Variable All firm-years (Number of observations: 32,906 (Table 7); 11,597 (Table 8) Mean Table 7 Variables FPSt LNASSETSt 1 SALES GROWTHt 1 RETURNt RETURNt 1 RETURN SKEWNESSt RETURN SKEWNESSt 1 RETURN STD DEVt RETURN STD DEVt 1 TURNOVERt ($million) TURNOVERt 1 ($million) Additional Table 8 variables NYSE t 1 USINCORPt 1 WCt 1 ROAt 1 R&Dt 1 GOODWILLt 1 PP&Et 1 ALTMAN Zt 1 MBt 1 INSTt 1 EQUITY PROCEEDSt 1 DEBT PROCEEDSt 1 INSIDER TRADINGt 1 INSIDER HOLDINGt 1 Std dev Minimum Median Maximum 0.263 6.368 0.113 0.088 0.123 0.310 0.334 0.030 0.031 1.45 1.21 0.440 2.010 0.268 0.441 0.446 1.095 0.982 0.018 0.017 1.52 1.29 0.000 2.170 0.522 1.035 0.951 3.492 3.026 0.009 0.009 0.06 0.05 0.000 6.339 0.046 0.057 0.080 0.274 0.294 0.026 0.026 0.95 0.79 1.000 11.546 1.331 1.570 1.638 4.564 4.049 0.091 0.093 8.44 7.17 0.348 0.991 0.406 0.000 0.095 0.120 0.486 11.255 3.629 0.553 0.078 0.005 0.371 0.020 0.476 0.095 0.350 0.208 0.134 0.165 0.342 16.140 3.934 0.272 0.235 0.026 3.789 0.049 0.000 0.000 0.131 0.923 0.000 0.000 0.035 19.260 4.935 0.010 0.000 0.000 20.065 0.000 0.000 1.000 0.346 0.050 0.048 0.051 0.405 6.748 2.568 0.592 0.000 0.000 0.028 0.003 1.000 1.000 1.924 0.383 0.719 0.817 1.502 92.374 24.416 0.977 1.210 0.170 20.813 0.322 Panel B: Correlations SUEDt SUEDt FPSt LNASSETSt 1 SALES GROWTHt 1 RETURNt RETURNt 1 RETURN SKEWNESSt 1 RETURN STD DEVt 1 TURNOVERt TURNOVERt 1 0.046 o 0.0001 0.123 o 0.0001 0.056 o 0.0001 0.102 o 0.0001 0.033 o 0.0001 0.031 o 0.0001 0.019 0.0005 0.210 o 0.0001 0.092 o 0.0001 FPSt LNASSETSt 1 0.046 0.168 o 0.0001 o0.0001 0.226 o0.0001 0.237 o 0.0001 0.096 0.069 o 0.0001 o0.0001 0.003 0.097 0.5405 o0.0001 0.017 0.070 0.0018 o0.0001 0.078 0.251 o 0.0001 o0.0001 0.351 0.583 o 0.0001 o0.0001 0.320 0.104 o 0.0001 o0.0001 0.337 0.059 o 0.0001 o0.0001 SALES GROWTHt 1 RETURNt RETURNt 1 0.064 o 0.0001 0.066 o 0.0001 0.068 o 0.0001 0.104 o0.0001 0.021 0.0002 0.146 o0.0001 0.056 o0.0001 0.048 o 0.0001 0.144 o 0.0001 0.016 0.0049 0.074 o 0.0001 0.252 o 0.0001 0.201 o 0.0001 0.032 o0.0001 0.037 o0.0001 0.113 o0.0001 0.163 o0.0001 0.015 0.0054 0.047 o0.0001 0.051 0.275 o0.0001 o0.0001 0.169 0.134 o0.0001 o0.0001 0.020 0.020 0.0003 0.0003 0.094 o0.0001 0.5443 RETURN SKEWNESSt 1 0.031 o 0.0001 0.052 o 0.0001 0.217 o 0.0001 0.008 0.1425 0.058 o 0.0001 0.315 o 0.0001 0.241 o 0.0001 0.107 o 0.0001 0.050 o 0.0001 RETURN STD DEVt 1 0.009 0.1102 0.327 o 0.0001 0.548 o 0.0001 0.053 o 0.0001 0.237 o 0.0001 0.220 o 0.0001 0.259 o 0.0001 0.014 0.0110 0.289 o 0.0001 TURNOVERt TURNOVERt 1 0.246 o 0.0001 0.299 o 0.0001 0.022 o 0.0001 0.200 o 0.0001 0.005 0.3347 0.159 o 0.0001 0.023 o 0.0001 0.230 o 0.0001 0.069 o 0.0001 0.322 o 0.0001 0.015 0.005 0.142 o 0.0001 0.096 o 0.0001 0.014 0.0104 0.034 o 0.0001 0.312 o 0.0001 0.731 o 0.0001 0.836 o 0.0001 and highly significant, with a marginal effect of 0.020, indicating that FPS industry membership increases the probability of litigation by 2.0%, roughly consistent with the litigation rates reported in Table 2. Although the coefficient on the FPS variable is significantly associated with litigation in this model, overall goodness of fit and predictive ability are low. The conventional measure of goodness of fit is pseudo-R-squared. We report the McFadden (1973) pseudo-R-squared, perhaps 302 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 Table 7 Models of litigation risk. This table presents the FPS only model in comparison to our multivariate models with contemporaneous and lagged variables. Model (1a) is the logit model with the FPS variable. Model (2) adds lagged assets, lagged sales growth, and contemporaneous stock return variables (market-adjusted return, return skewness, return standard deviation, and turnover) to the FPS variable. Model (3a) is the same specification as model (2), except it uses lagged return variables. Model (4) is the same specification as model (3), except adds two-year and three-year lagged returns. Variable definitions are provided in the appendix. nnn, nn, and n indicate p-values of 1%, 5%, and 10%, respectively. The p-values are based on robust standard errors that control for heteroskedasticity and serial correlation. Marginal effects of the coefficients are reported below the coefficients. SUED ¼ b0 þ b1 ðFPSt Þ þ e ð1aÞ SUED ¼ b0 þ b1 ðFPSt Þ þ b2 ðLNASSESTSt1 Þ þ b3 ðSALES GROWTHt1 Þ þ b4 ðRETURN t Þ þ b5 ðRETURN SKEWNESSt Þ þ b6 ðRETURN STD DEV t Þþ b7 ðTURNOVERt Þþ e ð2Þ SUED ¼ b0 þ b1 ðFPSt Þ þ b2 ðLNASSESTSt1 Þ þ b3 ðSALES GROWTHt1 Þ þ b4 ðRETURN t1 Þ þ b5 ðRETURN SKEWNESSt1 Þ þ b6 ðRETURN STD DEV t1 Þþ b7 ðTURNOVERt1 Þ þ e ð3Þ SUED ¼ b0 þ b1 ðFPSt Þ þ b2 ðLNASSESTSt1 Þ þ b3 ðSALES GROWTHt1 Þ þ b4 ðRETURN t1 Þ þ b5 ðRETURN t2 Þþ b6 ðRETURNt3 Þ þ b7 ðRETURN SKEWNESSt1 Þ þ b8 ðRETURN STD DEV t1 Þþ b9 ðTURNOVERt1 Þ þ e INTERCEPT FPSt ð4Þ Model (1a) Model (2) Model (3) Model (4) 3.135nnn 0.448nnn 0.020 7.718nnn 0.180 0.007 0.463nnn 0.018 0.553nnn 0.021 0.498nnn 0.019 7.883nnn 0.566nnn 0.024 0.518nnn 0.022 0.982nnn 0.044 7.938nnn 0.567nnn 0.024 0.523nnn 0.022 0.896nnn 0.037 0.379nnn 0.016 0.419nnn 0.018 0.201nnn 0.008 0.273nnn 0.011 0.108nnn 0.005 0.101nnn 0.004 25.635nnn 1.076 25.254nnn 1.057 LNASSETSt 1 SALES GROWTHt 1 RETURNt RETURNt 1 RETURNt 2 RETURNt 3 0.359nnn 0.014 RETURN SKEWNESSt RETURN SKEWNESSt 1 14.437nnn 0.550 RETURN STD DEVt RETURN STD DEVt 1 0.0004nnn 0.00002 TURNOVERt 0.00007nn 0.000003 TURNOVERt 1 Pseudo-R2 (McFadden) (%) Pseudo-R2 (Cox-Snell) (%) Area under ROC Curve (AUC) Mean out of sample AUC Hosmer-Lemeshow p-value Observation count 0.01 0.20 0.547 0.558 (0.000) 32,906 25.65 8.14 0.842 0.838 (0.746) 32,906 12.47 4.65 0.756 0.750 (0.747) 32,906 0.00004 0.000002 12.72 4.74 0.759 0.754 (0.165) 32,906 the most common measure, and the Cox and Snell pseudo-R-squared.24 This model has a McFadden pseudo-R-squared of 0.01% and a Cox and Snell pseudo-R-squared of 0.20%, indicative of poor fit. Another way of assessing predictive ability is to use a classification table (as in Table 5). To generate a classification table, the researcher first specifies a cutoff probability (estimated probability above which we predict that an observation will experience a lawsuit). It is common in predicting financial distress to use cutoffs such as 0.5 (Ohlson, 1980) or 0.3 (Altman and Sabato, 2007). However, the predicted probabilities from model 1 are uniformly low, at around 5%, reflecting 24 The McFadden pseudo R2 is based on the ratio of log likelihoods and has the desirable feature of varying between 0 and 1. However, unlike a conventional R square, it cannot be interpreted as the proportion of variation in the dependent variable explained by the regression covariates. See Long (1997, pp. 104–108) for more discussion of different pseudo R-squareds. Because of the non-linear nature of logit models, there is no universally agreed upon pseudo R-squared or, more generally, measure of goodness of fit—there are variety of measures, but each has advantages and disadvantages (e.g., see Hosmer and Lemeshow, 2000, Chapter 5; Long and Freese, 2006). I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 303 both the low unconditional incidence of litigation and the modest effect of the FPS industry variable. Moreover, classification tables cannot be compared for different samples.25 A better way of comparing the predictive ability of different models is to use the Receiver Operating Characteristic, or ROC curve (e.g., Hosmer and Lemeshow, 2000, Chapter 5). This curve ‘‘plots the probability of detecting a true signal (sensitivity) and false signal (1—specificity) for the entire range of possible cutpoints’’ (p. 160, our emphasis). The area under the ROC curve (denoted AUC) provides a measure of the model’s ability to discriminate. A value of 0.5 indicates no ability to discriminate (might as well toss a coin) while a value of 1 indicates perfect ability to discriminate, so the effective range of AUC is from 0.5 to 1.0.26 AUC for model 1, at 0.547, is larger than 0.5 but well below the level normally seen as indicating acceptable discriminatory ability.27 (We also report a corresponding ‘‘out of sample’’ AUC, which is similar, at 0.558.28) This is more clearly seen in Fig. 2, which we use to plot ROC curves for different models. Here we can see that the ROC curve for model 1 is only modestly above (to the north-west) of the 45-degree line that represents no discriminatory ability. For reference, we also plot a single point that represents the discriminatory ability of the approach discussed above (Table 5) of simply using FPS membership to predict litigation risk.29 This point is just above the ROC curve for model 1, also showing relatively low discriminatory ability. Overall, these results suggest that the FPS variable, considered alone, is not a good predictor of litigation risk. We also report the Hosmer-Lemeshow chi-square (Hosmer-Lemeshow, 2000, Chapter 5; Long and Freese, 2006) to measure discriminatory ability. This measure sorts the sample into (usually) ten groups based on predicted probabilities. Within these groups, it then compares the observed frequency of the outcome to the expected frequency of that outcome where the latter is based on the predicted probabilities for the observations within the group. Under the null hypothesis that the model fits well, the observed and expected frequencies are similar within groups. Conversely, rejection of this null indicates that the model fits poorly. The Hosmer-Lemeshow chi-squared statistic for this model is highly significant (p-value of 0.000), which strongly rejects the null that the model fits well, and is again indicative of poor fit. We next report models (denoted 2–4) that include the size, sales growth, and stock market variables along with the FPS industry dummy. The first model (model 2) includes stock market variables measured during the event year. As discussed above, this likely increases predictive ability but is not a realistic approach to measuring litigation risk ex ante. To avoid this problem (and reduce endogeneity concerns), the second model (model 3) measures stock market variables in the year before lawsuit filing. In the third specification (model 4) we add two additional lags of annual stock returns to see whether longer run stock performance helps predict litigation. Size and sales growth are measured in the fiscal year before the lawsuit filing in all models. The general idea behind these variables is that firms tend to get sued after a period of unusually strong growth and/or stock price run up that subsequently reverses (a sharp ‘‘reversal of fortune’’), and that the likelihood of litigation is higher for larger firms and firms with more volatile stock returns. These specifications have significantly higher predictive ability than model 1. For model 2, the McFadden pseudo-Rsquare is 25.7% while the Cox-Snell measure is 8.1%, both substantially larger than for model 1. AUC increases to 0.842, substantially higher than model 1, and indicative of ‘‘excellent’’ discriminatory ability (Hosmer-Lemeshow, 2000, Chapter 5). (The corresponding cross-validation AUC is 0.838.)30 Finally, the Hosmer-Lemeshow chi-squared statistic for model 2 is insignificant (p-value of 0.746), also indicative of good fit. The model 2 coefficients have signs that are largely consistent with expectations. The FPS variable is no longer statistically significant (p-value of 0.12), with a marginal effect of only 0.007, indicating that the inclusion of the other 25 According to Hosmer and Lemeshow (2000, p. 160), ‘‘one cannot compare models on the basis of measures derived from 2 2 classification tables since these measures are completely confounded by the distribution of probabilities in the samples upon which they are based. The same model, evaluated in two populations, could give very different impressions of performancey’’. 26 Intuitively, the area can be thought of as follows. Assume we have n1 firm/years subject to litigation and n2 firm/years that are not. We can thus create n1 n2 pairs. Of the set of all possible pairs, AUC tells us the fraction for which the observation subject to litigation had a higher predicted probability than its pair. Under the null that the model has no discriminatory ability, this fraction is 0.5. 27 Hosmer-Lemeshow (2000, p. 162) indicate that AUC of 0.5 indicates no discrimination, AUC of between 0.7 and 0.8 indicates acceptable discrimination, AUC of between 0.8 and 0.9 indicates excellent discrimination, and AUC greater than 0.9 is considered outstanding discrimination. 28 The first AUC number is based on estimating the model in-sample, using all observations. However, in assessing predictive ability, it is useful to be able to assess how well the model will perform out of sample to avoid an over-fitting problem. One way to do this is to use cross-validation, and in particular we use the ‘‘K-fold’’ cross validation procedure described by Efron and Tibshirani (1993, Chapter 17). The procedure proceeds as follows (using ten folds). First, randomly choose 10% of the full set of observations. This is one fold. Second, take the remaining 90% of observations and randomly choose a second group of equal size (again equal to 10% of the total). This is the second fold. Continue to do this until all observations are classified into ten folds. Third, estimate the model using nine of the ten folds, and apply the model to the fold that was held out of the estimation. This yields an ‘‘out of sample’’ estimate of AUC. Repeat this step using nine different sets of nine folds. This yields ten ‘‘out of sample’’ AUC estimates. We report the average of these ten estimates. 29 This approach plots as a single point because it is not a discriminatory model that generates estimated probabilities. Rather, it is a deterministic rule that simply says that litigation will occur if firms fall in one of the FPS industries and no litigation will occur otherwise. 30 Although AUC has advantages, a disadvantage is that it naturally increases as covariates are added to the model, in a manner somewhat analogous to (unadjusted) R-squares. There is no well-accepted way of adjusting for this problem. However, we note that models (2), (3), and (4) all have the same number of covariates but that model (2) has notably larger AUC which we expect based on our predictions. Conversely, when we estimate a model that includes only a single variable (for comparison to model (1)), either lagged assets or the contemporaneous abnormal return, we obtain AUCs of 0.667 and 0.639, respectively. Thus, it does not seem to be the case that variation in the AUC across the models in Table 7 is simply due to variation in the number of covariates. 304 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 Table 8 Expanded model of litigation risk. This table augments the models in Table 7 with the following additional potential drivers of litigation risk (all lagged): dummy for U.S. incorporation, dummy for NYSE listing, working capital, ROA, R&D intensity, goodwill intensity, PP&E intensity, Altman’s Z, market-to-book, institutional holdings, debt and equity issuances in recent past, and insider trading and holdings. Variable definitions are provided in the appendix. Models 1b and 3b include the same variables as their companion in Table 7, except with the reduced observation count of 11,597. nnn, nn, and n indicate p-values of 1%, 5%, and 10%, respectively. The p-values are based on robust standard errors that control for heteroskedasticity and serial correlation. Marginal effects of the coefficients are reported below the coefficients SUED ¼ b0 þ b1 ðFPSt Þ þ e ð1bÞ SUED ¼ b0 þ b1 ðFPSt Þ þ b2 ðLNASSESTSt1 Þ þ b3 ðSALES GROWTHt1 Þ þ b4 ðRETURN t1 Þ þ b5 ðRETURN SKEWNESSt1 Þ þ b6 ðRETURN STD DEV t1 Þ þ b7 ðTURNOVERt1 Þ þ e ð3bÞ SUED ¼ b0 þ b1 ðFPSt Þ þ b2 ðNYSEt1 Þ þ b3 ðUSINCORP t1 Þ þ b4 ðLNASSESTSt1 Þ þ b5 ðWC t1 Þ þ b6 ðROAt1 Þ þ b7 ðSALES GROWTHt1 Þþ b8 ðR&Dt1 Þ þ b9 ðGOODWILLt1 Þþ b10 ðPP&Et1 Þ þ b11 ðALTMAN Z t1 Þþ b12 ðMBt1 Þ þ b13 ðRETURNt1 Þ þ b14 ðRETURN SKEWNESSt1 Þ þ b15 ðRETURN STD DEV t1 Þ þ b16 ðTURNOVERt1 Þþ b17 ðINST t1 Þþ b18 ðEQ UITY PROCEEDSt1 Þ þ b19 ðDEBT PROCEEDSt1 Þ þ b20 ðINSIDER TRADINGt1 Þ þ b21 ðINSIDER HOLDINGt1 Þ þ e INTERCEPT FPSt Model (1b) Model (3b) Model (5) 3.451nnn 0.692nnn 0.030 6.184nnn 0.599nnn 0.025 5.555nnn 0.473nnn 0.019 0.146 0.006 0.672 0.027 0.257nnn 0.010 0.124 0.005 0.158 0.006 0.835nnn 0.034 0.584 0.024 0.450 0.018 1.017nnn 0.041 0.002 0.000 0.052nnn 0.002 0.264nn 0.011 0.142nnn 0.006 23.730nnn 0.969 0.00000004 0.000 0.742nn 0.030 0.521nn 0.021 2.974n 0.121 0.050nnn 0.002 0.340 0.014 NYSEt 1 USINCORPt 1 0.278nnn 0.012 LNASSETSt 1 WCt 1 ROAt 1 0.850nnn 0.035 SALES GROWTHt 1 R&Dt 1 GOODWILLt 1 PP&Et 1 ALTMAN Zt 1 MBt 1 0.449nnn 0.019 0.177nnn 0.007 22.597nnn 0.942 0.00005 0.000 RETURNt 1 RETURN SKEWNESSt 1 RETURN STD DEV t1 TURNOVERt 1 INSTt 1 EQUITY PROCEEDSt 1 DEBT PROCEEDSt 1 INSIDER TRADINGt 1 INSIDER HOLDINGt 1 Pseudo-R2 (McFadden) (%) Pseudo-R2 (Cox-Snell) (%) Area under ROC Curve Mean out of sample AUC Hosmer-Lemeshow p-value Observation count ð5Þ 1.34 0.49 0.5839 0.5825 (0.000) 11,597 6.35 2.31 0.7053 0.7290 (0.5107) 11,597 9.46 3.41 0.7439 0.7831 (0.4048) 11,597 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 305 100% 90% 45° 80% Sensitivity 70% 60% (0.37, 0.53) 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 - Specificity Model 1, with FPS only Model 2, (AUC=0.842) Model 3 (AUC=0.756) and 4 (0.759) Fig. 2. Receiver operating characteristic (ROC) curve for models in Table 7. This figure shows the ROC curves for regression model 1a, 2, and 3a of Table 7. The area under the ROC curve (denoted AUC) provides a measure of the model’s ability to discriminate. A value of 0.5 (451 line) indicates no ability to discriminate (might as well toss a coin) while a value of 1 indicates perfect ability to discriminate, so the effective range of AUC is from 0.5 to 1.0. For reference, we also plot a single point that represents the discriminatory ability of simply using FPS membership to predict litigation risk (Table 5). This point is just above the ROC curve for model 1, also showing relatively low discriminatory ability. Sensitivity and (1—) specificity are on the y- and x-axis, respectively. Sensitivity and specificity are common measures of the performance of prediction models (Hosmer and Lemeshow, 2000, Chapter 5). Sensitivity reports the fraction of true positives correctly predicted. Specificity reports the fraction of true negatives correctly predicted. variables reduces its role. Coefficients on size and sales growth are positive and strongly significant, with marginal effects of 0.018 and 0.021 respectively. The coefficient on event year abnormal stock returns is negative and highly significant, with a marginal effect of 0.019.31 Because these returns are measured over the class period, this is consistent with the idea that stock price declines cause litigation (and so are associated with litigation ex post). The coefficient on return skewness is negative and highly significant while those on return volatility and turnover are both positive and highly significant, with material marginal effects. Similar to the stock return variable, these variables reflect returns and trading that directly lead to litigation, as opposed to being predictors of litigation. For these reasons, model 2 likely overstates the predictive ability of these variables and for the same reason likely understates the predictive ability of the FPS variable. In model 3 the stock return variables are measured in the period before the filing year. This changes the results in several respects. First, goodness of fit declines, with the McFadden pseudo-R-square falling to 12.5% and the Cox-Snell pseudo-R-square to 4.7%, although these are still substantially higher than for model 1. AUC falls to 0.756, which is indicative of ‘‘acceptable’’ discrimination and still well above that for model 1. (The corresponding cross-validation AUC is 0.750.) The p-value on the Hosmer-Lemeshow chi-squared statistic is 0.747, also consistent with good fit. Second, lagging the stock return variables changes the coefficients on these variables and causes the FPS variable to return to significance. The coefficient on the FPS variable in this specification is 0.566, which is highly significant and larger than for model 1. Its marginal effect is 0.024, also larger than for model 1. The coefficients on size and sales growth remain positive and highly significant, and are larger here than in model 2. To be clearer about economic magnitude, we again report the effect of discrete changes in these variables. Holding other variables at their means, increasing size from $583m (its mean) to $1,000m leads to an increase in the estimated probability from 0.027 to 0.035 when FPS ¼0, and from 0.046 to 0.061 when FPS ¼1. If sales growth increases from its mean of 11.3% to 21.3%, the estimated probability increases from 0.027 to 0.029 when FPS¼0 and from 0.046 to 0.051 when FPS ¼1, a more modest effect. Thus, the effects of size and growth are more pronounced for firms in the FPS industries. The abnormal return variable remains highly significant when lagged but reverses sign, from significantly negative in model 2 (coefficient of 0.498) to significantly positive when lagged in this model (coefficient of 0.379). We interpret this reversal as saying that strong prior period stock performance increases the likelihood of a reversal of fortune, which then triggers litigation. Comparing results for these two specifications implies that including contemporaneous stock returns is what led to the insignificance of the FPS variable. The coefficient on return skewness remains significantly negative but is smaller in magnitude here, consistent with its significance in model 2 being attributable to contemporaneous 31 To give a better sense for economic magnitude, we looked at the change in probability for a discrete change in these covariates with other variables held at their means. If we increase firm size from its mean ($583m) to $1,000m, the estimated probability increases from 2.08% to 2.66% when FPS ¼0 and from 2.49% to 3.17% when FPS ¼1. When sales growth increases from the mean of 0.113 to 0.213 (annual growth rate increases from 11% to 21%), the estimated probability increases from 2.08% to 2.20% when FPS¼ 0 and from 2.49% to 2.62% when FPS ¼ 1. Finally, when the annual stock return decreases from its mean of 8.8% to 20.0% (which might be typical for a firm that is sued), the estimated probability increases from 2.08% to 2.40% for FPS ¼0 and from 2.49% to 2.86% for FPS ¼1. 306 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 Table 7 Model 3 80 70 70 Predicted Litigation Risk (%) Predicted Litigation Risk (%) Table 7 Model 1, with FPS Only 80 60 50 40 30 20 60 50 40 30 20 10 10 0 0 0 10 20 30 40 50 60 Percentile (%) 70 80 90 100 0 10 20 30 40 50 60 Percentile (%) 70 80 90 100 Fig. 3. Predicted litigation risk. This figure compares the distributions of predicted probabilities for Table 7, Models 1a and 3a. For model 1, the distribution is simple, reflecting the fact that the model assigns probabilities according to whether the firm is in an FPS industry. For this model, the predicted probability is 0.064 for firms in an FPS industry and 0.042 for firms that are not. In contrast, model 3 produces a continuous distribution of predicted probabilities, ranging from just over 0 to over 70%. measurement. Stock volatility becomes more significant in this specification, with the marginal effect almost doubling, which is expected because a more volatile stock price makes large stock price declines more likely ex ante.32 The effect of trading volume (turnover) declines in this specification, perhaps because turnover is no longer measured in the event year. Overall, model 3 yields a relatively large improvement in predictive ability over the basic FPS approach (model 1) at relatively low cost. Explanatory power is substantially higher under all measures, with AUC increasing from 0.547 to 0.756. Another way of comparing the usefulness of models 1 and 3 in predicting litigation risk is to compare the distributions of predicted probabilities for these models, as shown in Fig. 3. For model 1, the distribution is simple, reflecting the fact that the model assigns probabilities according to whether the firm is in an FPS industry. For this model, the predicted probability is 0.064 for firms in an FPS industry and 0.042 for firms that are not. In contrast, model 3 produces a continuous distribution of predicted probabilities, ranging from just over 0 to over 70%. Around 10% of observations have predicted probabilities that exceed 0.10, and a small number have substantially higher predicted probabilities. To give a sense for what types of firms have these relatively high predicted probabilities, if we move all variables to one standard deviation above their means, the predicted probability of litigation is 0.151 when FPS¼0 and 0.238 when FPS¼1.33 If we move firm size, sales growth, and return volatility to one standard deviation above their means (holding the other variables at their means), the respective probabilities become 0.136 and 0.218, which indicates that these three variables are relatively more important than the other variables. These results show that the probabilities increase more than proportionately when several variables increase together. In particular, the FPS variable has a larger effect (increasing probability by about 8%) when size, growth, and volatility are all above their means, and vice versa, so the level of all of these variables is important in determining litigation risk. We report a final specification (model 4) that augments model 3 with two additional lags of annual abnormal stock returns. Similar to the single lag of abnormal returns, the coefficients on both variables are positive and significant, with marginal effects of 0.008 and 0.011, respectively. The addition of these variables adds relatively little explanatory power/ predictive ability, with little or no improvement in pseudo-R squared or AUC. The McFadden pseudo-R square is 12.7% while the Cox-Snell pseudo-R square is 4.7%, both very similar to those for model 3. AUC is 0.759 (cross validation AUC of 0.754), also similar to that for model 3. The regressions in Table 7 use a panel of around 33,000 observations. In Table 8, we augment these models with the following additional potential drivers of litigation risk discussed in Section 2 (all lagged): dummy for U.S. incorporation, dummy for NYSE listing, working capital, ROA, R&D intensity, goodwill intensity, asset tangibility (PP&E intensity), Altman’s Z, market-to-book, institutional holdings, recent debt and equity issuances, and insider trading and holdings. Because of the additional data required to compute these variables, sample size is reduced substantially, to around 11,600 observations. We view this as a serious cost for researchers, especially if these data requirements induce survival or other biases in sample composition, so the benefits in terms of improved model predictive ability would have to be substantial to justify the inclusion of these additional variables. 32 If we move stock volatility from its mean of 0.031 to 0.046, the estimated probability of litigation increases from 0.027 to 0.039 when FPS ¼ 0 and from 0.047 to 0.067 when FPS ¼ 1. These are large changes compared to those for the other covariates included in this model. And here again, the effect is larger for firms in the FPS industries. 33 For comparison, if all variables are at their means, the predicted probabilities are 0.027 for FPS¼ 0 and 0.047 for FPS¼ 1. I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 307 The results in Table 8 show this not to be the case. We again compare a simple model containing only the FPS dummy to a model that includes the full set of covariates; we refer to these as models 1 and 5, respectively (model 3 from Table 7 is also reported for comparison). Similar to the result in Table 7, in model 1 the FPS variable is highly significant, with a material marginal effect (0.030) but relatively low predictive ability. The McFadden and Cox-Snell pseudo-R squareds are 1.34% and 0.49%, respectively, and AUC is 0.584. The inclusion of the full set of covariates increases predictive ability, as expected, over model 1, but this model does not dominate models 3 and 4 in Table 7. The McFadden and Cox-Snell pseudo-R squareds are 9.5% and 3.4%, respectively, for this model, compared to 12.5% and 4.7%, respectively, for model 3 in Table 7. AUC is 0.744, slightly below the corresponding numbers for models 3 and 4 in Table 7.34 Overall, given the large cost in terms of data requirements, the payoff to including these additional explanatory variables is relatively small, which reinforces our conclusion that models along the lines of model 3 in Table 7 are probably the most cost effective solution for researchers interested in measuring litigation risk. It is clear from the results in Tables 7 and 8 that the FPS variable generally remains significant (economically and statistically) even when a large set of firm characteristics are included in the regressions.35 Further, the effects of size, growth, and volatility are all larger for firms in the FPS industries. This implies that there is something about industry membership that is important in explaining litigation that is not captured by the set of other variables (i.e., that is not explained by size, volatility, growth, asset tangibility, etc.) and that, in fact, complements those variables. One possibility is that this has something to do with how the information environment and managerial disclosure vary by industry. Another possibility is that plaintiffs’ attorneys specialize by industry, perhaps because there are economies of scale in bringing suit in particular sectors. Whatever the explanation, it seems important to continue to include the FPS variable in models of litigation risk, although it is also clear that using this variable alone does a poor job of capturing litigation risk. 5. Conclusion We provide evidence on the validity of the industry-based litigation risk proxy commonly used in previous research. We define litigation risk as the risk of private securities class action lawsuits, as opposed to more serious legal actions such as SEC enforcement actions. We provide two principal empirical findings. First, we show that although litigation rates vary significantly across sectors and industries over time, litigation rates in the four FPS industries (biotechnology, computers, electronics, and retail) are generally consistently higher than those in other industries. While the overall litigation rate across all firm/years in our sample is 1.6%, the rate for firms in the FPS industries is 2.7%, a difference that is statistically significant. Differences in litigation rates between the FPS industries as a group and other industries are statistically significant in 8 of 13 sample years. For the largest firms in the economy (those in the top 5% of the size distribution), the litigation rate is 5.1% across all firm/years, with the rate for firms in the FPS industries at 7.8% (this rate is not significantly higher than that for non-FPS industries). Second, we estimate and compare a number of models of litigation risk. While the FPS industry measure is simple, readily available, and associated with higher litigation rates, it is nevertheless unclear how well this variable performs as a predictor of litigation risk. We evaluate predictive ability using a number of measures in addition to the pseudo-R squareds usually reported in extant research. While the FPS variable is clearly associated with litigation risk—the coefficients on this variable are both economically and statistically significant—the ability of this variable to predict litigation is modest. Pseudo-R squareds from models that only include the FPS variable are around 1%. This conclusion is supported by alternative measures of predictive ability, such as AUC and the Hosmer-Lemeshow chi-squared, which the statistical literature suggests as better measures of predictive ability. When the FPS variable is augmented with measures of firm size, sales growth, and return characteristics, predictive ability increases markedly, suggesting that the inclusion of a few widely available variables can result in significant improvements in model performance. AUC is around 0.55 for models that include the FPS variable alone, only marginally higher than 0.5, the benchmark for no predictive ability. When we augment the FPS variable with size, growth, and return volatility, AUC increases substantially, to 0.76, which indicates good predictive ability. This improvement in predictive ability is achieved at relatively low cost because these additional variables are readily available to researchers. Interestingly, the FPS variable complements these other variables, which have larger effects on estimated litigation risk for FPS firms than for non-FPS firms. Augmenting the model with additional covariates, such as those that measure the quality of firms’ corporate governance, insider trades, the extent to which firms are raising capital, etc., does little to further increase predictive ability, and so fails the cost–benefit tradeoff given the costs usually associated with obtaining these variables. Our suggested model of litigation risk generates predicted probabilities that have desirable properties. This model generates a relatively continuous distribution of predicted probabilities, ranging from close to zero to over 70%. While most observations have predicted probabilities of less than 10%, some firm/years have probabilities well in excess of this 34 When we estimate model 3 using the smaller sample in Table 8, the numbers for this model drop somewhat, with pseudo-R squareds of 6.4% and 2.3%, respectively, which are not as high as those for model 5. AUC for model 3 in Table 8 is 0.705, slightly below that for model 5 and also below that for model 3 in Table 7. 35 This continues to be true for various sample subperiods. 308 I. Kim, D.J. Skinner / Journal of Accounting and Economics 53 (2012) 290–310 level. We show that firms in FPS industries that are relatively large, with high volatility and sales growth, have litigation rates that can be substantially higher than 10%, and that the joint distribution of these variables is important in determining litigation risk (firms that are both relatively large and volatile face substantially higher litigation rates than firms that are relatively large or volatile). Appendix A See Table A1. Table A1 Variable definitions. This table provides definitions of the variables used in the tables in alphabetical order. For all non-stock return and turnover variables, the year t represents the filing year for sued firms, and the firm-year for non sued firms. Accumulation period for stock return and turnover variables is provided in the data definition. Variable Definition ALTMAN Zt 1 DEBT PROCEEDSt 1 Altman (1968) Z score at the end of year t 1 Dollar amount of public debt proceeds issued by the firm during year t 1 and year t 2 scaled by beginning of year t 1 total assets Dollar amount of equity proceeds issued by the firm during year t 1 and year t 2 scaled by beginning of year t 1 total assets Equals 1 if the firm is in the biotech (SIC codes 2833–2836 and 8731–8734), computer (3570–3577 and 7370–7374), electronics (3600–3674), or retail (5200–5961) industry, and 0 otherwise End of year t 1 goodwill scaled by beginning of year t 1 total assets Average of all insider shares held in year t 1 scaled by beginning of year t 1 total shares outstanding Average of year t 1 and t 2 insider sales net of acquisitions scaled by year t 1 revenue Percentage of market value held by institutional investors at the end of year t 1 Natural log of total assets at the end of year t 1 Market value of equity scaled by book value of equity at the end of year t 1 Equals 1 if the firm is listed on the New York Stock Exchange, and 0 otherwise Property, plant and equipment at the end of year t 1 scaled by beginning of year t 1 total assets Research and development expenses in year t 1 scaled by beginning of year t 1 total assets Market-adjusted 12-month stock return. For sued firms, the accumulation period ends with the lawsuit class period end month. For non sued firms, the accumulation period ends with the fiscal year-end month Market-adjusted 12-month stock return. For sued firms, the accumulation period ends with the fiscal year-end before the filing year. For non sued firms, the accumulation period ends with year t 1 fiscal year-end month For sued firms, the market-adjusted 12-month stock return for year t 2 before the filing year. For non sued firms, the market-adjusted 12-month stock return for year t 2 For sued firms, the market-adjusted 12-month stock return for year t 3 before the filing year. For non sued firms, the market-adjusted 12-month stock return for year t 3 Skewness of the firm’s 12-month return Skewness of the firm’s 12-month return for year t 1 Standard deviation of the firm’s 12-month returns Standard deviation of the firm’s 12-month returns for year t 1 Return on assets, defined as year t 1 net income scaled by beginning of year t 1 total assets Year t 1 sales less year t 2 sales scaled by beginning of year t 1 total assets Equals 1 if a class period of a lawsuit filing occurred during the year, and 0 otherwise Trading volume accumulated over the 12-month period ending with the lawsuit class period end month (for sued firms), and the fiscal year-end month (for nonsued firms) scaled by beginning of the year shares outstanding. Note that the coefficient on TURNOVER is multiplied by 1000 for expositional convenience Trading volume accumulated over the 12-month period ending with the fiscal year-end before lawsuit filing (for sued firms), and year t 1 fiscal year-end month (for non sued firms) scaled by beginning of year t 1 shares outstanding. Note that the coefficient on TURNOVERt 1 is multiplied by 1000 for expositional convenience Equals 1 if the firm is incorporated in the United States, and 0 otherwise Working capital accruals (current assets current liabilities) at the end of year t 1 scaled by beginning of year t 1 total assets EQUITY PROCEEDSt 1 FPSt GOODWILLt 1 INSIDER HOLDINGt 1 INSIDER TRADINGt 1 INSTt 1 LNASSETSt 1 MBt 1 NYSEt 1 PP&Et 1 R&Dt 1 RETURNt RETURNt 1 RETURNt 2 RETURNt 3 RETURN SKEWNESSt RETURN SKEWNESSt 1 RETURN STD DEVt RETURN STD DEVt 1 ROAt 1 SALES GROWTHt 1 SUEDt TURNOVERt TURNOVERt 1 USINCORPt 1 WCt 1 References Ajinkya, B., Bhojraj, S., Sengupta., P., 2005. 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