The Economics of Setting Auditing Standards

Transcription

1 The Eonomis of Setting Auditing Standards Minlei Ye University of Toronto Dan A. Simuni University of British Columbia Ralph Winter University of British Columbia April 2010 ABSTRACT: This paper develops a theory of the negotiating positions, or preferenes over auditing standards, of the interest groups that may set suh standards or negotiate hanges in standards. We represent auditing standards by two properties: toughness and vagueness (or lak of preision). Our model predits that auditors and investors would onsider both toughness and vagueness to influene or set auditing standards (e.g., preferene over vagueness depends on the level of toughness.) Sine the market is omposed with auditors with different wealth and different investment projets, the optimal level of standards would be different for these parties. Therefore, in general, auditing standards with a ertain level of vagueness is preferred. By analyzing eonomi inentives in the proess of setting auditing standards, we help explain how the standards have developed into their urrent form. We greatly appreiate the advie from Kin Lo, Hugh Neary, and Sandra Chamberlain. An earlier version of the paper benefited from omments by Florin Saba and Paul Fisher. We also wish to thank Paul Newman, Bill Kinney, Volker Laux, Gordon Rihardson, Ping Zhang, Gilles Hilary, Jeroen Suijs, Robert Knehel, the anonymous referee for CAPANA onferene, and seminar partiipants at the University of British Columbia, University of Toronto, University of Texas at Austin, HEC Paris, Tilburg University, and City University of Hong Kong. 1

2 1. Introdution Auditing standards evolve as an outome of regulations among affeted interest groups, as well as hanges in the relative influene of these groups. This paper is based on the premise that a theory of different groups preferenes over auditing standards an shed light on the setting and evolution of the standards. Prior to 2002, the Amerian Institute of Certified Publi Aountants (AICPA) set Generally Aepted Auditing Standards (GAAS) as the standards for audits onduted for both publi and private ompanies in the United States (U.S.). The AICPA is the national professional organization for Certified Publi Aountants (CPAs), so this meant that the auditing profession was able to set its own auditing standards. The Sarbanes-Oxley At of 2002 (SOX), however, reated the Publi Company Aounting Oversight Board (PCAOB) to oversee the auditors of publi ompanies, and authorized the PCAOB to establish auditing and related professional pratie standards for publily held ompanies. At the time, an artile in BusinessWeek proposed that the PCAOB take over audit standards and write tougher rules that protet the publi investors, not CPAs. 1 SEC ommissioner Paul S. Atkins laimed that, The PCAOB was reated beause of deep failings in the U.S. aounting profession s ability to regulate itself. 2 However, the U.S. situation is not unique as auditing standards in most ountries are set by professional organizations of auditors. Moreover, in reent years, auditing standard-setting boards around the world have been trying to improve the larity of auditing standards by, for example, adding objetives for eah standard and making strutural hanges to improve the readability of the standards. 3 1 Mike MNamee, Aounting Wathdog-or lapdog? Here s how you ll know. BusinessWeek, Nov. 11, Speeh by SEC Commissioner: The Sarbanes-Oxley At of 2002: Goals, Content, and Status of Implementation, February 5, The goals of these larity projets inlude addressing onerns over length and omplexity of standards, and making standards easier to read, understand and implement. Interestingly, these projets ause auditing standards to be more priniple-based or less detailed, whih implies that the resulting standards are vaguer, as defined in this paper. 2

3 These fats raise interesting questions. From an eonomi point of view, was it appropriate to transfer the authority for establishing auditing standards for publily held ompanies from the AICPA to the PCAOB in the U.S., and why are different auditing standard boards implementing larity projets? This paper analyzes different parties (namely investors and audit firms of varying sizes) preferenes onerning the properties of auditing standards to provide impliations for the standard setting. Among other things, we find that investors generally have the same preferene for auditing standards as auditors, whih implies that investors will not neessarily be better off if they an set the standards diretly. Moreover, auditing standards do not have to be perfetly preise in order to be effiient. Vagueness (whih may be haraterized as adopting priniples-based standards) an add value to the effiieny of auditing standards and an be preferred by standard-setters, in some irumstanes. In the design of auditing standards, as in the design of any law, regulation or rule, two dimensions must be onsidered. The stringeny or toughness of the requirements imposed by the standard on auditors is of ourse entral. But the degree of generality or vagueness in the language speifying the standard is also ritial. No standard will be written so preisely that the language eliminates all disretion in auditing ativities and on the other hand a standard that is expressed in language that is too broad has less meaning and an generate unertainty in the auditing setting. Therefore, this study fouses on two properties of auditing standards: toughness and vagueness (or lak of preision). We interpret the average level of audit work required by the standards as the toughness or stringeny of auditing standards. In ontrast, the magnitude of judgment variation onerning possible audit effort levels that ould be onsidered as in ompliane with the auditing standards represents the vagueness or impreision of auditing standards. Thus, standards with less ambiguity onerning a due diligent audit effort level are defined as being more preise. Also, as noted earlier, rules-based standards are likely to be more preise than priniples-based standards. We analyze how the properties of auditing standards affet auditors behavior and om- 3

4 pare different parties preferenes for the toughness and vagueness of auditing standards. Based on Dye [1993], we present a model of the audit market relating auditors legal liability to auditing standards and in whih the pereived audit quality is linked to an auditor s wealth. Our innovation is the introdution of unertainty or vagueness in auditing standards. The vagueness of auditing standards affets the pereived probability of ompliane, thereby influening the auditor s expeted legal liability, whih in turn influenes audit effort. This approah allows us to analyze the impat of vagueness on auditor s effort, as well as the auditor s and investors attitudes towards vagueness. To our knowledge, this is the first study that represents auditing standards in terms of their two essential properties: toughness and vagueness. 4 Turning to results, when auditing standards an be made preise, we find, small (less wealthy) auditors who have less to lose from litigation prefer less tough rules than large (wealthy) auditors, when auditor wealth is observable. Investors have the same preferenes as auditors that they will hire. This is true beause a group of investors who are interested in undertaking an investment projet will hire an auditor with wealth greater than a ertain utoff point, whih is a funtion of the amount of investment. Hene a unique set of auditing standards an be optimal for both the investor and the auditor, while the variation in investments allows for the existene of small auditors. Regarding the preferene for vagueness, an auditor prefers preise auditing standards if the toughness an be set at the optimal (wealth-maximizing) level. If the toughness an not be set optimally, then the auditor prefers vague auditing standards - whether the toughness is too high or too low. When the standards are too tough (e.g., higher than optimal level), vagueness allows the auditor to exert a lower level of effort without faing penalties with ertainty. That is, the auditor an exploit the vagueness of standards and exerise professional judgment to avoid performing unneessary proedures. When the standards are too weak, a level of unertainty in the standards an help the auditor ommit to a higher 4 To make the model more realisti, we also onsider not perfetly preditable auditor responses to vagueness. This variation as shown in the last subsetion does not affet our impliations. 4

5 level of effort beause his wealth is at risk. Investors have the same preferenes regarding vagueness as the auditor in the weak-standards senario, sine vagueness indues the auditor to undertake the desired level of audit effort, from the investors point of view. Investors also have the same preferenes regarding vagueness as the auditor in the ase of exessively tough standards sine vagueness redues the expeted osts of the audit. In the real world, an auditor has lients with projets requiring different amount of investments, so there is not one unique level of effort that is optimal for all the lients, whih implies the toughness an not be set optimally. Therefore, auditing standards with a ertain level of vagueness is preferred. Additionally, different auditors have heterogeneous wealth, the optimal level of standards would be different for eah party. Our theory predits that vague standards are preferred. This is onsistent with the fat that the standards have been vague. Some of the osts and benefits of vagueness have been reognized in general. For example, a greater level of preision allows greater preditability in the standard on the part of both auditors and investors - and greater preditability on the part of purhasers of the professional servies as to the level and quality of servie that will be supplied. On the other hand, as a matter of positive rather than normative theory, an exessively preise theory may be diffiult to enat when various parties who are affeted, and who influene the setting of the standard, have sharply different preferenes. A proposed vague standard may be entral to gathering enough politial support to beome an adopted standard while preise standards may never garner enough support to beome adopted. In ontrast, our paper proposes another interesting and perhaps equally important theory regarding the preferenes. As stated above, a perfetly preditable standard has zero variane and would be preferred by both parties, providing that toughness is at the level that generates maximum ombined expeted wealth for the parties. Surprisingly, however, both parties prefer vague standards onditional upon a suboptimal level of toughness. To summarize, this paper ontributes to the literature by investigating standard setters eonomi inentives to develop auditing standards with ertain properties and to negotiate 5

6 hanges in auditing standards. We believe the researh is timely given the reent transfer of authority over auditing standards for publi ompanies from the AICPA to the PCAOB in the U.S., and the world-wide trend of improving the larity of auditing standards. Our researh thereby helps to explain why the standards have developed into their urrent form. Setion 2 positions the paper in the ontext of the existing literature. Setion 3 provides the definition and mathematial representation of toughness and vagueness of auditing standards. Setion 4 presents the model, and Setion 5 demonstrates the players objetives. Setion 6 and 7 present the model s preditions. Setions 8 onludes. 2. Prior Researh While several papers have examined auditors reations to variations in either toughness or vagueness of auditing standards, to our knowledge, no researh has onsidered the question of how the properties of auditing standards - namely both toughness and vagueness - would be hosen by standard-setters (i.e., auditors and investors). Studies in the law and eonomis literature analyze the impat of unertain liability rules on parties behavior. Calfee and Craswell [1984] find that unertainty about the appliation of legal standards an give parties eonomi inentives to overomply or to underomply, that is, to modify their behavior to a greater or lesser extent than a legal rule requires. Kolstad et al. [1990] show that where there is unertainty, there are ineffiienies assoiated with the exlusive use of negligene liability and that ex ante regulation an orret the ineffiienies. Most studies in the urrent audit literature assume liability rules are preise or ertain, as expressed in Zhang [2007], Narayanan [1994], Dye [1993], Melumad and Thoman [1990], Nelson et al. [1988], and others. Dye [1993] and Zhang [2007] are losely related to our paper. Dye [1993] analyzes auditors attitudes toward and responses to the level (toughness) of auditing standards. He shows that the average quality of audits may deline as auditing standards are raised. Moreover, auditors who intend to omply with the standards typially 6

7 prefer higher standards than those who do not omply, when auditors wealth levels are observable to outsiders; when auditors wealth levels are not publily observable, the reverse is true. Dye [1993] does not onsider the interation between legal liability regimes and auditing standards, nor the fat that auditing standards are inherently vague. The level of auditing standards is perfetly preise in Dye s model. Zhang [2007] finds that the publi s expetations an indue an auditor to exert a higher level of effort. This result is similar to our finding that when the standards are too weak, vagueness an help an auditor ommit to a higher level of effort sine his wealth is at risk. While we onstrut the likelihood of an auditor being found liable based on the ourts interpretation of auditing standards, the probability of being found liable in Zhang [2007] is influened by whether ourts will use publi expetations to make a deision. Willekens et al. [1996] and Shwartz [1998] analyze the impat of unertainty about auditor due are (negligene) on audit effort or quality, and the role of professional auditing standards in a setting of an unertain legal environment. Willekens et al. [1996] argue that audit standards only affet auditor behavior if legal standards of are are unlear, and the audit standards help to larify the legal standards. Shwartz [1998] finds that the ommitment to perform aording to auditing standards is not redible if the auditor legal liability regime is strit liability or negligene-based liability with a lear legal due are standard. She shows that under a negligene-based liability regime with vague due are, the ommitment to perform aording to auditing standards an improve audit effort. The auditing standards themselves, however, are always assumed to be perfetly preise in Willekens et al. and in Shwartz s theory. The vagueness (or lak of preision) of auditing standards an vary aross ountries and through time. Vagueness affets auditors legal liability sine it influenes ourts judgment as to the auditors due diligene. However, little existing researh analyzes how the vagueness of auditing standards affets auditors effort, and how the vagueness of auditing standards is determined by standard-setters. Willekens and Simuni [2007] and Ewert [1999] are the 7

8 exeptions. Willekens and Simuni [2007] model the impat on audit effort of hanges in the vagueness of auditing standards and onlude that dereasing the preision of the standards initially indues an auditor to produe higher audit quality by exerting more effort, but beyond a ertain ritial value, dereasing preision leads to dereasing effort and auditors gambling that they may or may not be deemed to have violated the standards. When vagueness exeeds a seond ritial value, auditors exert no effort at all. The auditing standards are exogenously determined in Willekens and Simuni [2007]. That is, the authors do not model the standard setting proess, and they do not onsider the interation of the toughness and vagueness of auditing standards. In this paper, we analyze the optimal standards for different standard setters (auditors vs. investors). Sine the level of toughness of auditing standards affets the auditors and investors preferenes towards the vagueness of auditing standards, we onsider the interation of toughness and vagueness when standard setters hoose the properties of auditing standards. We find that heterogeneity in auditor wealth is essential in our theory, while Willekens and Simuni assume homogeneous auditor wealth. Ewert [1999] argues that vague auditing standards an outperform preise standards by induing higher audit quality, higher quality of finanial statements, lower expeted legal osts, and lower diret as well as total audit osts than preise standards. However, reasonable extensions of his model seem to lead to the possibility of (non-degenerate) equilibria with pure auditor strategies, whih do not support his main argument (Breuer [1999]). We haraterize the equilibria with auditor pure strategies, and onsider the probability that the ourt judges auditing level a as a sub-standard when the standards are vague. Ewert s finding is onsistent with one part of our results in that, for some levels of toughness and vagueness, vaguer standards indue higher audit effort and lower osts than preise ones. We further find that under other onditions, audit effort is lower when the standards are vaguer. Our analysis shows that auditors preferene over vagueness depends on the level of toughness. When toughness is optimal for auditors, they weakly prefer preise standards. When toughness is non-optimal, the auditors prefer vaguer standards. 8

9 Finally, Patterson and Smith [2003] analyze the effet of materiality unertainty on the auditor s evaluation of audit evidene and a manager s hoie of earnings overstatement. They find that when the expeted ost of aepting finanial statements that are materially misstated is relatively large, an inrease in unertainty over materiality results in a more onservative auditor evaluation of the audit evidene and a derease in the amount of intentional overstatement. Otherwise, the reverse is true. Our representation of unertainty is similar to their onstrut of unertainty (mean-variane approah). But our fous is on the unertainty of audit effort required by auditing standards while their fous is on unertainty of materiality. Our fous allows us to analyze the impat of auditing standards on auditors and identify the eonomi fores driving the evolution of auditing standards. We find that the mean of the distribution affets the impat of variane on auditors and their preferene over variane, while Patterson and Smith s model provides evidene on the impat of unertainty on auditors and managers judgments, onditional on the trade-off between ost of audit failure and ost of further audit proedures. 5 To summarize, while existing researh has onsidered ertain aspets of how auditors, investors, and managers may behave given a set of auditing standards, this paper explores the proess of setting suh standards by different interest groups. Moreover, we jointly onsider the two basi properties of auditing standards - their toughness and vagueness, with an objetive of synthesizing some ritial ideas within the urrent literature and advaning our understanding of the eonomi fores underlying the standard setting proess. 5 Moreover, Patterson and Smith assume the materiality follows a normal distribution instead of a uniform distribution. Use of the uniform distribution allows us to find losed-form solutions, while the normal distribution does not, and later analysis will show our results are not sensitive to this assumption. 9

10 3. Definitions and Mathematial Representations 3.1 DEFINITIONS The first property of auditing standards under onsideration is toughness or stringeny. This onept is important in analyzing auditing standards beause auditing standards determine the amount of work auditors must undertake. We define the toughness of auditing standards as: Definition D1: The toughness of auditing standards is the average level of audit effort required by the standards. The seond property of auditing standards analyzed is vagueness. With perhaps the exeption of ertain mathematial onepts and ategories, virtually all onepts or ategories used in everyday life are vague, and therefore it would follow that auditing standards are haraterized by vagueness as well. We analyze vagueness onerning the level of audit effort that an be onsidered as in ompliane with auditing standards. Vagueness is simply the unertainty of this audit effort. The probability of non-ompliane an be redued by inreasing audit effort, whih is ostly to auditors. Audit effort in pratie may inlude olleting and evaluating audit evidene, and the auditor onferring with the manager when the two parties disagree with eah other. We assoiate a higher level of audit effort with higher audit quality. 6 Formally, we define the vagueness of auditing standards as the following: Definition D2: The vagueness of auditing standards is the unertainty of audit effort levels that ould be onsidered by different parties as in ompliane with the auditing standards. 6 It is important to note that our fous is on the vagueness of auditing standards rather than the vagueness of aounting standards. The vagueness of aounting standards is related to the representational faithfulness of different transations (Caplan and Kirshenheiter [2004], Shipper [2003], Vinent et al. [2003], Nelson [2003], Dye and Sridhar [2008]). We do not onsider the impat of aounting vagueness on auditors. Rather, we analyze vagueness in relation to the level of audit effort that an be onsidered as in ompliane with auditing standards. 10

11 3.2 MATHEMATICAL REPRESENTATIONS We use the mean-variane approah to represent the properties of auditing standards. This approah assumes that the level of audit effort required by expressed standards is a random variable s, whih has density g(s) (or distribution G(s)) with mean m and variane δ 2. A tougher standard is an inrease in the mean of the distribution. A vaguer standard is an inrease in the unertainty in G, i.e., in the sense of seond-order stohasti (SS) dominane. In other words, if standard No. 1 (s1) SS-dominates standard No. 2 (s2) at the same mean, then s1 islessvaguethans2. Under the mean-variane approah, the variane of the distribution represents the vagueness of auditing standards and the mean represents the toughness of auditing standards. Note that when the standards are perfetly preise, the level of audit effort required by expressed standards, s, equals the toughness m. To illustrate the impats of the properties of auditing standards on auditors, we analyze the simplest and most intuitive distribution: the standard s is distributed uniformly. Suppose s is distributed uniformly within the support of lower bound s l and upper bound s h,then the mean m = s l+s h and the variane δ 2 = (s h s l ) 2. The lower bound an be denoted by 2 12 m 3δ, and the upper bound is m+ 3δ. The toughness of the standards is represented by m. Thus, the vagueness of the standards is represented by the variane δ 2 (or the standard deviation δ). The mean-variane approah is reasonable sine real-world auditing standards are unertain. For example, paragraph 6 of PCAOB Auditing Standard No. 3 (A.S.3), Audit Doumentation, states that the auditor must doument the proedures performed, evidene obtained, and onlusions reahed with respet to relevant finanial statement assertions. Audit doumentation must learly demonstrate that the work was in fat performed.... This standard requires auditors to doument the proedures, evidene, and onlusions, but the extent of the doumentation required is unertain. A.S.3 paragraph 7 states that, In determining the nature and extent of the doumentation for a finanial statement assertion, 11

12 the auditor should onsider the following fators: (1)...(5). Appliation of these fators determines whether the nature and extent of audit doumentation is adequate. This paragraph redues the unertainty assoiated with the doumentation proedures. The toughness is the number of fators and vagueness is the range of possible fators an auditor should onsider. Overall, the advantage of the mean-variane approah is that we an analyze how vagueness affets audit effort while holding the toughness onstant, and how standard setters would hoose the vagueness given the toughness. We will employ this approah to analyze how different parties will set or influene auditing standards. 4. The Model This is a single-period model with two sets of risk neutral players (prospetive investors in a firm and an auditor). 7 A firm seeks to raise apital in the form of equity to start a projet. 8 With probability β this projet is a good projet and generates a ash flow of B (whih belongs to the prospetive investors), whereas with probability 1 β it is a bad projet and yields zero return in the future. This projet needs $I upfront investment from potential investors. 9 The above information is known to the investors, but they do not know the true type of the projet when they make the investment deision. Assume that β(b I) +(1 β)(0 I) > 0, so that the investors would invest in the projet without knowing the projet s type, but would not make the investment if they know that the projet is bad. 10 The firm manager issues a report, whih we interpret to be in the form of finanial 7 Risk aversion would not signifiantly affet our results. 8 Our analysis is not restrited to new issuers. As is ommon in the aounting, finane, and entrepreneurial literature, it is standard to representa firm as a projet. Changing the model desriptionto one generation of investors is selling its firms to another generation of investors for life yle reasons as Dye [1993], Dye [1995], Dye [2002] will not affet the analysis. 9 We will show the impat of variation of the investment amount I in a later analysis. 10 This assumption is to ensure that the investors will invest when the auditor reports a good signal even if ex ante they know there is possibly a Type-II error, and that they will not invest when the auditor reports a bad signal. 12

13 statements, whih dislose his estimate of the projet. 11 The investors an hire an auditor (there is only one auditor in the market) to issue an audit report with respet to the finanial statements in order to obtain an independent assessment of the projet. 12 The auditor exerts effort a [0, 1] in the audit proess and obtains a binary signal about the projet s type (i.e., signal {good, bad}). The level of audit effort is not publily observable when the auditor s report is issued: it beomes observable when the auditor is sued. The auditor might not be able to detet material misstatements due to audit tehnology limitations or inadequate audit effort. As is ommon in the literature, the relation between the audit report and the true type of projet is as follows: Pr(g good, a) =1andPr(b bad, a) =a, where g denotes the auditor s signal that the projet is good, and b denotes the bad signal (finanial statements have material misstatements). We use a to denote the level of effort as well as the probability of deteting the bad projet onditional on a bad projet and effort a. This assumption indiates that the auditor will make no mistakes when there is no misstatement in the finanial reports (i.e., there is no Type-I error), and that he may fail to detet misstatements depending on his audit effort (i.e., there may be a Type-II error). 13 We assume the auditor is independent and reports the observed signal truthfully. Audit failure is the situation in whih the projet is bad but the auditor issues a good report; in other words, he does not detet material misstatements in the finanial statements. The investors will make an inappropriate investment deision in this ase and inur a loss of 11 To keep the model simple, we do not onsider the manager s dislosure inentives, his deision onerning internal ontrol, or litigation against the manager. It is assumed that the manager would always laim that the projet type is good. The auditor may be viewed as obtaining information about the veraity of the manager s assertions about the projet type. The auditor would provide either a qualified or unqualified opinion. This assumption is similar to the one in Laux and Newman [2009]. A strategi manager assumption will affet the level of optimal effort, but not our finding on the auditor and investors preferenes towards the standards. 12 We will first assume there is only one auditor/audit firm in the market, whih an be regarded as an aggregation of many auditors with the same wealth, and then analyze how the results will hange if there are many audit firms with different wealth. 13 We assume no Type-I error sine we onsider only auditor liability resulting from the failure to detet misstatements. Relaxing this assumption inreases audit effort, but will not affet the key results. 13

14 $I. The probability of audit failure onditional on the projet being bad is given by 1 a. 14 The investors will sue the auditor if an audit failure ours and the probability of the auditor being found liable is positive. One the auditor is found liable, he is required to pay the entire loss I or his wealth, whihever is smaller. 15 The innovative element in our model is an assumption that in addition to the above events, there is one more event that ours in the first stage of the game: the standardsetting board (either an organization representing investors interests or the professional organization for auditors) sets the auditing standards. The auditing standards affet the auditor s pereived liability and thereby his effort hoie. To analyze the relation between auditing standards and auditors behavior, we need to disuss the link between auditing standards and auditors legal liability, sine the impat of auditing standards on auditors is affeted by the types of legal regimes. Shwartz [1998] suggests that the interation between auditing standards and auditors liability ours only when legal due are for auditors is not learly defined, sine this ambiguity indues ourts to resort to auditing standards for guidane on due are. Under a hypothetial strit liability regime, the auditor is liable for losses resulting from investor reliane on materially misstated finanial reports, independent of the amount of audit effort exerted. Thus, the probability of being held liable equals one at all effort levels if the auditor fails to detet material misstatements. Auditing standards will inrease audit effort beause greater effort implies a higher probability of deteting misstatements, but will not help to redue the probability of being found liable by ourts one audit failure (i.e. a failure to detet a material misstatement) ours. Under a negligene-based liability regime, the auditor is liable for the losses inurred by investors only if he failed to exerise due are. Due are is the minimum effort level that the auditor is required to exerise in order to avoid liability. When due are is not speified in 14 Assuming the probability of audit failure to be exp( a) as in Newman et al. [2005] will not hange the analyses. 15 Changing the liability payment from I to any amount less than I will not affet the analyses. 14

15 the law (i.e., when legal due are is vague), the ourts resort to auditing standards in order to determine the due are level and auditor negligene. Currently in the U.S. and elsewhere, the legal liability regime for auditors is negligene-based and the due are level expeted from an auditor is not defined by law. Hene, the professional auditing standards affet auditors liability, and therefore affet auditors behavior under a negligene-based liability regime with vague due are. We assume auditors liability is under a negligene-based liability regime with due are defined by auditing standards to simplify the analysis. 16 Reall that we assume a single audit firm ( the auditor ) in the main analysis. If the auditor an ontrol the setting of auditing standards, then in equilibrium he will hoose the properties of auditing standards strategially to maximize his expeted profit. Moreover, sine the auditor s inentive to work is limited by his wealth and in the atual audit market auditors have heterogeneous wealth levels, we will analyze how the auditor s wealth affets his preferenes towards the properties of auditing standards. In reality, people an judge whether the auditor is relatively wealthy, although they may not know his exat wealth. Here, we simply assume the auditor s wealth to be observable. This ompletes the desription of the basi model and the key assumptions. 5. The Players Objetives The investors and auditor s objetives and the sequene of events after onsidering the effet of legal liability regimes and auditing standards are summarized in Figure 1. Investors objetives are derived as follows. When an audit is onduted, the auditor an detet a bad projet with probability a. The investors will not invest if they know it is a bad projet, thus saving $I. The probability of the projet being bad is 1 β. Hene, the gross benefit the investors an obtain by hiring an auditor is $(1 β)ai. Moreover, these potential investors may reover some money if there is an audit failure and they sue the auditor. They also need to pay an audit fee to hire the auditor. Therefore, the net benefit or value of hiring an 16 Further analysis shows our results hold for a large lass of liability rules. 15

16 auditor inludes three omponents: (1) gross benefit $(1 β)ai; (2) the expeted liability payment investors an obtain from the auditor; and (3) the audit fee. The sum of the first two omponents (i.e., (1 β)ai +EL(a)) is the benefit of the audit. The audit fee is the ost of hiring an auditor. Note that we do not onsider the ase when investors need to inur a litigation ost in this model, sine the litigation ost affets investors suing deisions, and it will result in the auditor hoosing sub-standard effort in equilibrium, whih is not the fous of our paper. The formal analysis inorporating investors suing deisions is available from the authors upon request. Formally, the net benefit that investors obtain through an audit is alulated as follows: V (a) =(1 β)ai + EL(a) F. (5..1) The expeted liability the investors an obtain from the auditor who exerts effort a is given by: EL(a) =(1 β)(1 a)(1 P (a)) min[w, I], (5..2) where 1 β is the probability of the projet being bad; the probability of audit failure is 1 a; P (a) is the probability of ompliane (i.e., the probability that given an effort a the auditor will be found in ompliane, or Prob(s a)); 1 P (a) is the probability of being found liable, I represents the investment losses, and W is the auditor s wealth. limited liability, the auditor s liability will be either W if W I or I if I<W. 17 Due to Under a negligene-based liability regime with due are defined by auditing standards, P (a) is determined by the auditing standards. Therefore, the investors objetive is to indue the auditor to exert the level of effort that maximizes the value of the audit, as indiated by equation The auditor s objetive is to hoose an effort level to maximize his profit, whih is the audit fee, denoted by F, minus the total expeted ost, whih is the sum of the osts of the effort expended on the audit plus the auditor s expeted liability payments to the investors. 17 The audit fee is only a small part of the auditor s final wealth. 16

17 Formally, the auditor s objetive is: a =argmax [0,1] F (a) EL(a), (5..3) where (a) is the auditor s resoure ost of produing an audit effort level a. Itisonvexand inreasing in a (i.e., (a) > 0and (a) > 0). To derive a losed-form solution, we assume (a) = 1 2 a2,where (a) =a > 0and (a) =>0. 18 The expeted liability EL(a) isas defined in Equation FIRST-BEST SOLUTION The first-best ontrat an be struk if the level of audit effort is observable and ontratible. We will solve for the first-best optimal level of effort and the audit fee in this setion. This first-best result serves as a benhmark for the later analyses when the level of effort is not observable. The investors problem is: max F,a (1 β)ai F s.t. F (a) 0, where (a) = 1 2 a2. Solving the above problem, we obtain the first-best level of effort (a) = (1 β)i (marginal ost equals marginal benefit). Under the funtional form assumption (a) = 1 2 a2, the first-best level of effort equals a =(1 β)i/. Note that a also represents the probability of deteting the bad projet. To ensure an interior solution, we assume (1 β)i/ 0, that is, (1 β)i. 18 Assuming this quadrati form simplifies the exposition and is ommonly used in the auditing literature. The results presented in the remainder of this paper are robust to other speifiations of (positively sloped) onvex ost funtions. 17

18 5.2 AUDIT EFFORT IS UNOBSERVABLE In reality, the level of audit effort is not observable to investors. The auditor s hoie of effort is subjet to an inentive onstraint. As ommonly employed in the reent theoretial literature on problems of auditor liability, we assume ontingent audit fees are prohibited. This is onsistent with the odes of professional ethis of most ountries, inluding the U.S.. In equilibrium, the auditor will hoose a level of effort that minimizes the total audit osts. The investors antiipate the auditor s strategy and set the audit fee equal to the auditor s reservation payoff so that he is indifferent to aepting or delining the audit engagement. Note that a monopoly auditor an set the audit fee and earn eonomi rents, but the equilibrium level of effort is the same whoever an earn rents. One might argue that the auditor an maximize his profit by (a) exerting NO effort and (b) always reporting that the projet is bad, sine the auditor will neither inur liability nor effort osts. This senario is avoided, sine we assume that the auditor will be punished severely if he reports bad and the signal is revealed later to be good. This assumption is reasonable beause the auditor is able to observe good projets with ertainty given effort a (i.e., Pr(g good, a) =1). As disussed in Setion 4., the model is derived under a negligene-based liability regime with due are defined by auditing standards. To analyze how the vagueness of auditing standards affets the auditor s effort hoie, we first demonstrate the auditor s behavior assuming the auditing standards are perfetly preise. Perfetly Preise Auditing Standards As a benhmark, we onsider first the ase where auditing standards an be perfetly preise, and analyze the impat of toughness in auditing standards on auditor effort. When perfetly preise auditing standards define due are, the auditor an redue the probability of being held liable to zero if his effort is greater than or equal to the level speified in the standards. 18

19 In this ase, his total ost will be limited to the resoure ost. If he does not omply with the auditing standards, then he will definitely be found liable if audit failure ours, and his total ost will be the sum of resoure ost and expeted liability payment (i.e., TC(a s )= 1 2 a2 s +(1 β)(1 a s ) min[w, I] wherea s = (1 β)min[w,i] ). Thus, there is a range of s within whih the auditor will omply. Reall that when the standards are perfetly preise, the level of audit effort required by expressed standards, s, equals the toughness m. Let s be the highest standard with whih the auditor will omply. As illustrated in Figure 2, if the standard equals s, then the auditor s ost of omplying is (s )whihis less than TC(a s ). Moreover, if the standard equals s, then the auditor s ost of omplying (s ) is greater than TC(a s ). Therefore, the highest standard with whih the audit will omply is suh that the auditor is indifferent between ompliane and nonompliane (i.e., (s) =TC(a s )). Therefore, the seond-best results under the assumption of preise standards are a = s if s s and a 2 = a s if s>s, wheres = (1 β) min[w, I] (1 β)2 (min[w,i]) 2 and a 2 s = (1 β)min[w,i]. The auditor will omply with the auditing standards as long as the toughness of auditing standards is less than the ritial value s. Otherwise, the auditor will not omply with the auditing standards. Note that s varies with auditor wealth. These results are onsistent with Shwartz [1998] s finding that auditing standards in a vague negligene regime help auditors ommit to a higher level of effort than under a strit liability regime. The differene between our findings is that we further develop the onditions under whih an auditor will omply with the standards. Moreover, representing standards in toughness and vagueness allows us to distinguish the impat of these two fators on auditors. In the following setion, we will show the impat of vagueness on auditors. Vague Auditing Standards In this setion, we analyze the impat of vagueness in auditing standards on the auditor s effort hoie. This analysis has important impliations for standard setters. It is also the 19

20 foundation of the analysis onerning standard setters eonomi inentives to hoose the vagueness of auditing standards. Again, the auditor hooses a level of effort a to minimize total audit osts, whih equals the audit fee. The key here is the probability of ompliane P (a). In this ase, the P (a)equals one if audit effort a is greater than or equal to the upper bound of the distribution m + 3δ, equals zero if a<m sδ, and equals a m+ 3δ 2 if m sδ a<m+ 3δ. Correspondingly, 3δ the auditor s effort hoie inludes m + 3δ, a s,anda v,wherea s = (1 β)min[w,i] and a v = (1 β) min[w, I](1 + 3δ + m) 2, 3δ +2(1 β) min[w, I] dereasing in δ (i.e., av < 0). The detailed proof an be found in the Appendix equation 5. δ Figure 3 illustrates the auditor s effort hoie (i.e., m + 3δ, ora v,ora s ) as a funtion of m and δ. Reall m is the mean and δ is the variane of the distribution. The grey (dash dot dotted) line is the indifferene urve where m+ 3δ is equal to a v. The red line (dash dotted) provides the values of m and δ for whih the auditor is indifferent in hoosing m+ 3δ or a s. At the blue (dashed) line, the auditor is indifferent between a s and a v. The line indiated by 1 3δ is the boundary for m, sinem + 3δ should be less than or equal to one. The feasible region, whih is below 1 3δ, is partitioned into three sets by the grey, red, and blue lines. When m and δ fall into region A, the auditor hooses his effort equal to m + 3δ. When the toughness and vagueness are in region B, the auditor will hoose a v to be his effort level. When m and δ is in the upper orner, region C, the auditor will hoose a s. To illustrate the auditor s effort reation towards inreased vagueness at a given value of m, we hoose a partiular m and draw a figure illustrating the auditor s effort hoie as a funtion of δ. Suppose m is quite high, for example, m =0.81 as indiated by the dotted line. We an see that as δ inreases, an auditor first hooses effort equal to m + 3δ; then a v ;thena s ;andthena v one again. Figure 4 illustrates this ase. The auditor s effort will inrease with the vagueness of auditing standards when the equilibrium level of effort is m + 3δ, and will derease with the vagueness if the equilibrium level of effort is a v. If a = a s, then the vagueness of auditing standards will not affet the auditor s effort. 20

21 When m is fixed at values other than 0.81 in the above example, auditor s effort hoie as a funtion of δ will hange aordingly. If m is fixed at a very high value (m (s = 2as a 2 s, 1]), the auditor will not omply with the standards and hoose a s whatever δ is. If m is fixed at a moderately high value (m (s (1 β)min(w,i)(1 s), s]), the auditor will 2s hoose effort equal to m + 3δ and then a s. Define m as the minimum value of m suh that the auditor will hoose effort equal to a s.ifmis between m and s (1 β)min(w,i)(1 s), then the auditor first hooses effort equal 2s to m + 3δ; thena v ;thena s ;andthena v one again as illustrated in Figure 4. For the vast majority of values of m (e.g., m<m ), the auditor s effort will be m + 3δ and then a v as vagueness inreases, suggesting that the auditor will initially inrease and then derease his effort. Thus, varying the vagueness of auditing standards an hange the level of audit effort in unexpeted ways. An inrease in the vagueness of auditing standards an derease or inrease audit effort. When the toughness is below the utoff point m and the vagueness is very low, the auditor will attempt to omply with the upper bound to avoid liability. As the vagueness inreases, however, his effort inreases. But after the vagueness passes a ritial point, the auditor will hoose an effort level between the two bounds, and the level of effort dereases as vagueness inreases. Lemma 1 summarizes the findings formally. The proof an be found in Appendix. Lemma 1. Givenastandardwithtoughnessm less than m, the auditor s effort initially inreases with inreasing vagueness, but after the vagueness passes a ritial point, the auditor s effort dereases with vagueness. Note that m is quite large, so it is generally true that auditor s effort inreases and then dereases as the vagueness inreases. To this point, we have shown how the auditor s effort varies with the toughness and vagueness of the auditing standards. The next question is how the different standard setters would hoose these properties of auditing standards to maximize their payoffs in the 21

22 equilibrium. We analyze this question in the following setions. 6. Toughness Preferene Given Perfetly Preise Auditing Standards This setion analyzes how different parties hoose the toughness when the auditing standards are perfetly preise. This is a benhmark for studying the hoie of vagueness of auditing standards. We investigate the levels of toughness the auditor and investors would hoose under a negligene-based liability regime with due are defined by perfetly preise auditing standards. In order to get an understanding of the negotiations and interest group pressures to hange auditing rules, we investigate the optimal standards preferred by eah group. The ourts determine auditors liability based on the liability rules and auditing standards. 6.1 AUDITOR S PREFERENCE In this setion, we analyze how the auditor will set the toughness of auditing standards if the standards an be set with perfet preision. This is the ase of self-regulation. The auditor s objetive for given standards would be to minimize his total ost if audit effort were his only hoie. However, when he an hoose the toughness of auditing standards, his objetive beomes maximizing his total profit sine the audit fee generally inreases with the toughness of auditing standards beause audit effort inreases with the toughness as long as the toughness is below a ritial value. The auditor an use the auditing standards as a devie to ommit to a level of effort. Sine audit effort is unobservable, the auditor with low wealth an not redibly ommit to the optimal level of effort that he would like to hoose. He has an inentive not to omply beause the ost of nonompliane will be lower than that of ompliane. Therefore, in equilibrium the auditor hooses the auditing standards in view of the audit fee and the audit effort to whih he would like to ommit. The entral idea behind the auditor s hoie of auditing standards is to onvey a level of redibility in relation to the 22

23 quality of servie that he will provide. The investors will hire the auditor if their expeted payoff is greater than the reservation payoff. Assuming that auditor wealth is observable to investors, we find that an auditor with high wealth will set the toughness equal to the first-best level of effort (i.e., (1 β)i/) and an auditor with less wealth will set the toughness equal to the highest possible auditing standards to whih his wealth allows him to ommit (i.e., (1 β)w/ + ɛ), whih is less than (1 β)i/ but higher than the nonompliane effort (i.e., (1 β)w/). Proposition 1 summarizes the argument. The proof an be found in Appendix. Proposition 1. Given other parameter of the model, there exists a wealth level W suh that an auditor with wealth greater than W will set the level of toughness equal to the first-best level of effort (i.e., (1 β)i/); An auditor with wealth less than W will hoose a lower toughness, but this toughness is inreasing in auditor wealth. 19 This proposition is onsistent with Dye [1993] s finding that auditors who intend to omply with the standards typially prefer higher standards than those who do not omply, when auditors wealth levels are observable to outsiders. We further find the onditions under whih an auditor will omply with higher standards. 6.2 INVESTORS PREFERENCE Given the assumption that there is one auditor with any wealth in the market, the auditor and investors have the same preferenes related to the toughness, sine they prefer the same optimal level of effort. An auditor with wealth greater than or equal to W an ommit to a standard requiring the first-best level of effort, sine if he doesn t exert the first-best effort, his wealth will be used to pay off the liability owed to the investors. An auditor with small wealth an not ommit to the first-best level of effort, sine his wealth is not large enough to pay all the damages, and hene it is less ostly for him to exert sub-standard effort (lower 19 The wealth utoff point W is equal to 1 1 (1 β) 2 I 2 / 2 (1 β)/. 23

24 than first-best). He is better off when the standard is at a level that he an ommit to, rather than a high standard with whih he an not omply. The investors an onjeture the auditor s behavior after observing his wealth, and set the standard to be the first-best if the auditor has large wealth, or the highest standard to whih the auditor an ommit if he has smaller wealth. As disussed in the previous sub-setion, an auditor with large wealth will set the toughness equal to the first-best level of effort, and an auditor with small wealth will set the toughness equal to the highest possible auditing standards to whih his wealth allows him to ommit, whih is less than the first-best. Therefore, ontrary to the onventional wisdom that investors prefer tougher standards than auditors, we find that the investors have the same preferene for toughness as the auditor. Formally, Proposition 2 summarizes the findings, and is based on the assumption that the standards are preise and there is one auditor in the market or many auditors with the same wealth. The proof an be found in the Appendix. Proposition 2. The investors have the same preferene for toughness as the auditor when the standards are preise and there is one auditor (or many auditors with the same amount of wealth) in the market. 6.3 MULTIPLE AUDITORS WITH HETEROGENEOUS WEALTH AND MUL- TIPLE PROJECTS WITH DIFFERENT INVESTMENTS In this subsetion we analyze whether Proposition 2 is sensitive to the assumption of one auditor and one group of investors in the market, and disuss the impat of multiple auditors with heterogeneous wealth and multiple projets with different investments on our results. First, if the market has many auditors with different wealth levels and only one projet (or many projets with the same level of investment), then the investors will hire a large auditor and have the same preferene over toughness as the auditor. 20 Seond, if there are 20 If there is a positive exogenous probability that the investors would hoose a small auditor, the average auditing standards preferred by auditors as a group might be lower than the ones preferred by the investors. 24