In 1992 the world's six largest accounting firms asserted that the accounting profession faced a liability crisis characterized by "unwarranted litigation and coerced settlements" (Arthur Andersen et al. 1992, 1). Of particular concern to Arthur Andersen et al. were securities class-action lawsuits, which they cited as the source of 30 percent of all lawsuits against auditors (1992, 6) and which account for more than one-half of accounting firms' settlement payments (Mednick and Peck 1994, 896). In 1994 the Advisory Panel on Auditor Independence asserted that litigation against auditors "has had a damaging and costly impact on the profession--and on the public it serves" (1994, 29). Such concerns prompted leaders of the accounting profession to campaign for legislative reform to curb "abusive" securities fraud lawsuits (O'Malley 1993; Simonetti and Andrews 1994). The culmination of this campaign was the passage of The Private Securities Litigation Reform Act of 1995 (PSLRA), designed to "reduce the number of frivolous class-action securities lawsuits" (Journal of Accountancy 1996, 13). However, a study recently released by PricewaterhouseCoopers reports that the number of securities class-action lawsuits filed each year has remained virtually unchanged since the passage of the PSLRA, and that the number of complaints alleging accounting irregularities has almost doubled since 1995 (Dooley 2001).
In response to recent calls for academic research on issues related to accountant's liability (Elliott 1993; Kinney 1994; Palmrose 1997; Cloyd et al. 1998), this paper analyzes a game-theoretic model of securities litigation and settlement under present institutional arrangements in the United States. This analysis addresses two questions. First, what factors explain the outcomes of securities lawsuits against independent auditors in the U.S.? These outcomes include protracted and costly pretrial litigation, a high proportion of cases that are settled before trial, and settlement amounts that are often a relatively small proportion of the claimed damages. Second, what (if any) strategies exist that accounting firms might employ to deter unwarranted securities litigation, coerced settlements, and other outcomes as cited above that are objectionable to them?
Recent papers in the accounting literature utilize game-theoretic models to examine the effects on audit quality or effort of differences in legal regimes, such as joint and several vs. proportionate liability (Narayanan 1994; Chan and Pae 1998; Hillegeist 1999), strict vs. "vague" negligence (Schwartz 1997; Radhakrishnan 1999; Zhang and Thoman 1999), and the U.S. and British systems of allocating legal costs (Boritz and Zhang 1997; Smith and Tidrick 1997). This paper differs from these prior papers in that our objective is to understand the factors that influence the outcomes of securities litigation against independent auditors under the legal regime that currently prevails in the U.S. We believe that such an understanding provides a stronger foundation for research that examines the effects of differences in legal regimes on auditor behavior. For example, our model demonstrates that the incentives of the plaintiffs' attorney have a major influence on the outcome of securities litigation against independent auditors. Yet, none of the eight papers cited earlier in this paragraph properly specify the incentives faced by plaintiff's attorneys; in fact, all of these papers except Narayanan (1994) incorrectly assume that the plaintiff (usually the investor) is the primary decision maker on the plaintiff's side of a securities lawsuit.
In addition, the models examined by Narayanan (1994), Schwartz (1997), Chan and Pae (1998), Radhakrishnan (1999), and Hillegeist (1999) all assume that audit litigation cases are tried, despite pervasive evidence that most securities class-actions in the U.S. are settled and very few actually go to trial. (1) Numerous papers in the law and economics literature utilize models where settlements are a possible outcome, (2) as do Boritz and Zhang (1997), Smith and Tidrick (1997), Zhang and Thoman (1999), and Holloway et al. (1999) in the accounting literature. This paper draws on that literature where possible. But the latter four papers (and most of the papers in the law and economics literature) model the incentives and behavior of the plaintiff, so it is unclear whether their conclusions apply to securities class-action litigation where the plaintiffs' attorney is the dominant player and the plaintiff plays a limited role. In summary, the unique contribution of this paper to the accounting literature is the development of a model of securities litigation that analyzes the behavior of the plaintiffs' attorney and incorporates settlement as one possible litigation outcome.
THE LEGAL REGIME
Since our objective is to understand the outcomes of securities litigation against auditors in the U.S., we construct a model that has the predominant elements of the existing legal regime in the U.S. Among these are (1) private enforcement of securities laws through class-action lawsuits, (2) a "vague negligence" liability rule as described by Schwartz (1997, 390), (3) proportionate liability as set forth in the PSLRA, and (4) the American system of allocating legal costs, under which each party pays their own costs.
One of the most salient features of this legal regime is that plaintiffs' attorneys in securities class-action litigation are the primary (often the exclusive) decision maker on the plaintiffs' side of the case. In her classic study of securities class-action cases, Alexander (1991,534) notes that "the class representatives in securities class-actions involving publicly traded companies in fact have no meaningful role in key litigation decisions," because they have only a nominal stake in the litigation, and thus are "not motivated to sustain the information costs or expend the energy and attention required to keep abreast of the progress of the litigation and make informed decisions" (Alexander 1991, 535). Moreover, Coffee (1986, 682) suggests that plaintiffs' attorneys in securities class-action cases generally find their clients, rather than vice versa. In response to widespread concern about the plaintiffs' attorneys' dominant role, a key provision of the PSLRA was intended to encourage investors to exercise primary control over securities class-actions. In particular, the Act encourages courts to appoint the investor with the largest damage claim (usually an institution) as class representative. However, this provision has not been effective, as evidenced by the SEC's (1997, 2) recent conclusion that "securities class-actions generally continue to be controlled by plaintiffs' law firms." (3) Based on this understanding of the realities of securities litigation, the model developed in this paper assumes that the plaintiffs' attorney (hereafter PA) makes all strategic decisions for the plaintiffs.
This situation implies that proper specification of the incentives of PAs is crucial to modeling of securities lawsuits against accounting firms. In the accounting literature it is commonly assumed that attorneys' fees in investor lawsuits against auditors are determined as a percentage of the amount recovered (DeJong 1985; Narayanan 1994; Trueman 1997; Radhakrishnan 1999). In securities class-action cases, however, this assumption is at odds with reality. Under the currently prevailing method of determining the PA's fee in securities class-action cases, known as the lodestar method, the PA's fee is established by the court based on (1) the number of compensable hours reported by the PA, multiplied by a reasonable noncontingent hourly rate, followed by (2) possible adjustment of this "lodestar" figure using a multiplier. The multiplier is often greater than 1.0, reflecting the delay incurred by the PA in receiving payment, the difficulty of the case, and related factors. (4) However, since the PA's fee must come out of the settlement fund or judgment amount, a multiplier less than 1.0 might be used if the judge believes that the lodestar figure would consume too high a percentage of the class's recovery. In addition, the court must approve reimbursement of the PA for out-of-pocket expenses, and this also comes out of the settlement fund or judgment amount. So the contingent fee percentage operates as an upper bound on the PA's compensation and expense reimbursement in securities class-action cases, but in all other respects the PA is compensated on an hourly basis. In short, the PA's compensation function increases linearly in hours worked (at the PA's billing rate) until it reaches a cap determined by the size of the settlement fund; beyond this point, increases in PA compensation are constrained by the cap. In addition, if they do not achieve a recovery for the class, PAs receive neither compensation nor reimbursement for out-of-pocket expenses (Alexander 1991, 537-540; see also Mosely 1978). (5)
One other feature of our legal regime deserves further comment. This is the concept of "fair share" proportionate liability incorporated into the PSLRA. As pointed out by King and Schwartz (1997, 96, specified in their Figure 1), the Act provides that defendants may be liable for joint and several liability under certain conditions. One of these conditions, the existence of an uncollectible share of damages, often holds in securities litigation against auditors due to the bankruptcy of the corporation. A second condition, a determination by the court that the auditor knowingly violated securities laws, is much less likely to occur. Crucially, however, these provisions do not come into play unless a trial judgment is rendered in favor of the plaintiffs. As noted earlier, most securities litigation cases are settled; very few result in a trial judgment. Hence the prospect that joint and several liability will be imposed on the auditor in a particular securities litigation case is relatively remote. At most, this prospect provides the PA with some "threat value" in settlement negotiations, but this would only be true in cases where the auditor clearly committed a known violation of securities laws.
We model the case of a PA who elects to file a securities litigation lawsuit against an accounting firm (hereafter AF) under the legal regime outlined in the previous section. Both the PA and AF are assumed to be risk-neutral. The assumption of risk neutrality is realistic for the PA, who may be viewed as having a portfolio of securities class-action cases and are involved in many individual lawsuits (plays of the game). Regarding the AF, this assumption has no effect on the results and is made to simplify the model. Assuming that the AF is risk-averse would merely strengthen the AF's incentives to behave as predicted by the model. It is also assumed that the lawsuit meets some minimum threshold of merit, such that it will not be dismissed by the court before it is settled or tried, and the PA has a positive expected payoff from filing it. The amount of damages claimed in the lawsuit, denoted W, is exogenously determined, but presumably is based on the total decrease in the market value of the securities of the corporation named in the suit. To simplify the analysis, it is assumed that W would also be the amount of a judgment if the plaintiff prevailed in a trial.
The lawsuit may consist of either one or two phases, labeled the pre-trial phase, and the trial phase. The trial phase only occurs if no settlement is reached in the pre-trial phase. Throughout the pre-trial phase, both the PA and AF are faced with several decisions, including (1) the number of attorney hours to be invested in pre-trial activities, labeled [h.sub.p] and [h.sub.a] respectively; (2) whether to make a settlement offer, and if so, when to make the offer and at what amount; and (3) whether to accept a settlement offer made by the other party. These decisions are interrelated. For example, the timing of a settlement in the model is represented by the value of the vector ([h.sub.p], [h.sub.a]) at the point when both players agree to settle. In addition, both parties' choice of attorney hours may be affected by whether they anticipate that the suit will be settled or tried.
To simplify the analysis in this section, it is assumed that both parties anticipate that the lawsuit will be settled before trial. This assumption has empirical support based on extensive evidence, cited in footnote 1, that the vast majority of securities class-actions are settled before trial. The assumption also has theoretical support based on the analysis of Cooter and Rubinfeld (1989, 1074-1079), who demonstrate that, unless one of them has a mistaken expectation about the outcome of a trial, both the plaintiff and defendant in any legal dispute anticipate a higher expected payoff from a settlement. This is due to several factors, most importantly the incremental legal costs of a trial. In the context of this paper, Cooter and Rubinfeld's (1989) conclusion applies to the AF, but not necessarily to the PA, who may expect to be compensated for attorney hours expended at trial.
Notwithstanding our assumption in this section that both the PA and AF anticipate a settlement, a complete answer to the research questions posed at the outset of this paper demands that our analysis be expanded to incorporate the possibility of a trial. The main reason for this is that the threat of a trial may influence the expected payoffs of the parties, especially when there is the possibility of repeated plays of the litigation game. So the following section of the paper extends our analysis of the litigation game to incorporate the possibility of a trial. This analysis also derives the conditions under which PAs in securities litigation prefer settlements to trials.