1. Reporting Bias with an Audit Committee1 Judson Caskey UCLA Los Angeles, CA 90095judson.caskey@anderson.ucla.eduVenky NagarUniversity of MichiganAnn Arbor, MI 48109 venky@umich.edu Paolo Petacchi Ohio State University Columbus, OH 43210petacchi.2@osu.edu November 20081We are particularly grateful to the editor, two anonymous referees, Madhav Rajan, and Robert Verrecchia. We also thank Adam Gileski, Clement Har, and seminar participants at Ohio State University, UCLA, and University of Michigan for their comments.

2. Reporting Bias with an Audit CommitteeAbstract This study models a manager who privately reports earnings to an independent audit committee that, after due diligence, publicly reports to rational investors who then price the report. The audit committee alters the reporting and pricing dynamics by attempting to remove the managers reporting manipulations, but then presenting the information it has collected with the committees own bias. The price informativeness still improves, but several reporting conflicts emerge. For example, increasing a partys misreporting penalties reduce its reporting bias, but spurs the other partys reporting bias, sometimes to the point where both the aggregate bias and price informativeness increase. Our simultaneous consideration of the manager, the audit committee, and investors provides a new framework on the reporting and valuation process and sheds new light on the interpretation of empirical earnings quality research that has largely studied the management effects and the auditor effects in two separate research streams. 3. Reporting Bias with an Audit Committee I. Introduction Audit committees of publicly traded companies have the task of ensuring the integrity of thefinancial reporting process.1 The audit committee executes this role by overseeing financial reportingand internal audit functions. While audit committees have played a role in the financial reportingprocess for many years, they have received increased attention as the Sarbanes-Oxley Act of 2002(hereafter SOX) highlighted and increased the regulatory treatment of audit committees, e,g., byrequiring the audit committee and the external auditor it hires to be independent of the management.2The more recent subprime and financial crisis only served to highlight the interaction betweenmanagement and audit committees. Despite the SOX requirement that only independent directorsserve on the audit committee, Duhigg (2008), Morgenson (2008) and Plevin and Efrati (2008) reporthow the dynamics between the management and audit committee led to the willful misreporting atkey financial firms such as Fannie Mae, AIG, and Merrill Lynch. Such misreporting has given pauseto previous calls for rolling back SOX provisions by blue ribbon panels such as the Committee onCapital Markets Regulation (www.capsmktreg.org). This study analyzes the reporting and thevaluation process in a model in which an audit committee oversees a companys reporting functionand the management and the audit committee are not fully goal congruent. We use the Fischer and Verrecchia (2000) (henceforth FV) model as the building block ofour setting.3 The manager in FV has an objective function with respect to the firms price that, due to 1See the SEC rules at http://www.sec.gov/rules/final/33-8220.htm. According to KMPGs Audit Committee Institutes (http://www.kpmg.com/aci) top10 to-do list for 2008, audit committees should catalyze risk management, monitor the management disclosure committee, be informed on key financial reporting issues, enable the CFO, ensure a shared vision for internal audit, improve audit communication channels, be prepared for a crisis, and apprise the full board of its activities. 2See www.sec.gov/spotlight/sarbanes-oxley.htm for details. 3 We are grateful to Robert E. Verrecchia for suggesting this approach. 1 4. contracting incompleteness, is not entirely known to investors.4 This uncertainty about themanagers objective function, combined with a finite penalty for misreporting, leads him to issue abiased earnings report. Rational investors then price this report. This framework allows for a simpleunified treatment of misreporting penalties, misreporting incentives, and rational investor pricing. We extend FVs basic framework to a setting where the manager does not directly report toinvestors but instead makes his earnings report privately to an audit committee that, after its own duediligence and information gathering (e.g., by hiring an auditor), modifies the report for public releaseto investors, who then rationally price the report.5 This committee, following Section 301 in SOX andthe SEC rule 10A-3, is independent of the management. However, as with the managementsobjective function, there is also some uncertainty about the audit committees direct and indirectinterest in the firms stock performance. In addition, as with the management, the audit committeealso faces misreporting costs.6 We show that our extension of FV still yields a unique equilibrium. Consistent with theirinstitutional mandate, the audit committees due diligence activities improve overall informationquality. The key reporting dynamic that emerges is that from the audit committees perspective, themanagers reporting bias is a source of noise. The audit committee therefore makes the sameadjustment to the managers report that investors would make given the same information. However,the audit committee then presents the information it collects from its activities with its own bias.This reporting dynamic, which is reflected in investor pricing, changes the comparative statics on 4The manager may be contemplating a secret management buyout of the firm, or may be anticipating option grants unknown to investors. These secret side-objectives will influence the managers interest in the price. 5In this study, we view all the audit committee members and all the people under their purview (e.g., all the relevant employees of the audit firm) as a single actor called the audit committee. 6 Section II motivates these assumptions institutionally.2 5. misreporting penalties, information gathering, and uncertainty about objective functions relative to adirect managerial reporting setting.7 A simple way to control reporting bias that has received much legislative attention is toincrease misreporting penalties. Not surprisingly, we find that increased misreporting penaltiesagainst the audit committee make the committee more reluctant to bias its report. This causesinvestors to rely more on the audit committees report so that prices react more strongly to it. Such investor behavior, our model shows, has an important side effect. It increases themanagers benefit from biasing his report while leaving his misreporting penalties unaltered. Themanager biases his report more aggressively. This source of noise dampens the investors pricereaction to the audit committees report relative what it would have been absent the managersstrategic behavior. A similar countervailing effect obtains when the managers penalty increases. In fact, incertain situations, our model predicts a backward bending pricing effect where an increase in themanagers misreporting penalty can increase the audit committees aggressiveness to such an extentthat there is an increase in the combined effect of the two parties private biases on the report to theinvestors. At the same time the price responsiveness to earnings also increases because theinformation content of the report increases by more than the amount of earnings management. Suchcountervailing effects do not arise in the standard FV model which only has one reporting party. Thecountervailing pricing effects of adding a second party, we later argue, can explain why someempirical studies on audit penalties that ignore the management effect have generated mixedfindings. 7 Note that the audit committee may be relatively more bullish than the management with respect to the price (e.g., the management is secretly planning a management buyout), or relatively more bearish than the management (e.g., the management has career concerns or is secretly planning a seasoned equity offering). In propagating its own views, the committee can thus adjust the management report either up or down. 3 6. If the audit committee introduces its own bias, why have this committee in the first place?We show that, despite its bias, the audit committee improves price informativeness as long as itcollects due-diligence information. We then endogenize the audits committees incentives to collectsuch information in the first place. We show that if the audit committees stakes are too high, or ifthe audit committees misreporting penalties are too low, the audit does not wish to collectinformation. While initially surprising, the source of this behavior lies in the committees interactionwith rational investors. Rational investors will not trust a reporting party that they know has highstakes, access to high quality information, and the ability to misreport. In such settings, the auditcommittee will voluntarily restrict its information acquisition activities.8 Audit committeeparameters thus affect not just the ex post reporting process, but also the ex ante informationcollection process. In particular, an audit committee that is less tied to short-term price movementsand more on the long-run value of the firm can actually serve to be a better information source. Finally, we explore reporting within a hierarchical organization. We show that the reportingbias increases with the level of organizational hierarchy, with maximum bias occurring at thetopmost rung. Note that this result is not due to some size or scale effect of business segments: it is apure reporting hierarchy effect. Our model thus makes the novel prediction that otherwise similarfirms with differing internal reporting hierarchies should have differences in reporting quality. Inparticular, our model supplements experimental studies that argue that judgmental and psychologicalfactors drive reporting biases in hierarchical reporting settings (e.g., Messier, Owhoso, and Rakovski2008). Our paper contributes both to empirical and analytical studies on reporting. The vastempirical literature on earnings reporting quality can be fairly clearly separated into those thatexamine the audit effect (e.g., Frankel, Johnson and Nelson, 2002; Ashbaugh, LaFond and Mayhew, 8 Although in a different setting and under different modeling assumptions, Rajan and Saouma (2006) obtain a somewhat similar result that a principal may prefer an uninformed manager. 4 7. 2003; Weber, Willenborg and Zhang 2008) and those that examine the management effect (e.g.,Bartov and Mohanram 2004; Cheng and Warfield 2005). The main empirical implication of ourresult that management and the audit committee have countervailing effects on earnings managementis that empirical studies that consider only the management or the audit committee incentives canhave significant biases in their estimates. For example, in the audit literature substream, Frankel,Johnson and Nelson (2002), Ashbaugh, LaFond and Mayhew (2003), and Larcker and Richardson(2004) reach different conclusions on the link between reported earnings quality and auditindependence, which they attribute to the econometric issue of measurement errors and regressionspecification techniques. Other audit studies lay the blame for mixed results on the misidentificationof auditor misreporting penalties (e.g., Weber, Willenborg and Zhang 2008). Likewise, Bartov andMohanram (2004) argue that the mixed results in management incentive studies arise from a lack ofstatistical power, and recommend examining reporting quality around extreme changes inmanagement incentives. Our study, by contrast, suggests that any empirical specification thatfocuses either exclusively on audit parties or management misses the full picture.Our simultaneous treatment of management, audit committee, and investors also contributesto the analytical literature on auditing. While large, this literature can be framed in terms of theimportance different papers give to different aspects of the relations among auditor parties, managers,and investors. Some papers, for example, focus more on the auditor-manager relationships (e.g.,Magee and Tseng 1990). Other papers, like ours, include all three parties. Hillegeist (1999) and Paeand Yoo (2001) have a manager reporting to an auditor who reports to investors. However, theauthors of those papers are more interested in damage rules and not in pricing; the audit report inthose models is not an earnings report but a going concern qualification that is binary in nature:invest or do not invest in the firm. Newman, Patterson and Smith (2005) model the auditors roleafter investors have invested their cash. Once again, the audit report is not an earnings report but a5 8. binary qualification report: the manager has either expropriated investors cash or he has not. Theaudit committees earnings report in our model, by contrast, is a continuous real number that feedsinto an explicit pricing process. As a result, our earnings report is amenable to standard earningsresponse coefficient analyses, which is the key association of interest in the empirical reporting andvaluation literature.The remainder of the paper is organized as follows. Section II describes the model andconstructs the equilibrium. Section III conducts comparative statics, and Section IV exploresalternative versions of the basic model including one with an explicit treatment of the principal-agentformulation. Section V extends the model from two parties to a reporting in a hierarchy. Section VIconcludes. All proofs are included in the Appendix unless otherwise noted.II.ModelThe context of our model is a single-firm, single-period reporting game. The firms terminalvalue v is normally distributed with mean zero and precision v . The reporting process consists of a manager who privately reports rm to an audit committee that after its own due diligence publiclyreports f to investors. Investors price the firm as p = E[v | f ] based on their conjectures of themanagers and audit committees reporting strategies. Both the manager and the audit committeehave discretion in the number they report. Figure 1 illustrates the models timeline.The manager in the course of his responsibilities receives a signal sm = v + em of firm value where em is a normally distributed noise term with mean zero and an exogenous precision m that is independent of v . The manager reports rm to the audit committee. This report is private reflectingthe fact that audit adjustments and other audit committee-management negotiations are private and6 9. investors do not receive the unadjusted management reports (Rittenberg, Schwieger and Johnstone2008, Ch. 5; Hatfield, Agoglia, and Sanchez 2008).1 The audit committee bases its report to investors on both the information reported by themanager and information generated specifically for the audit committee. The audit committeegenerates the latter information by monitoring the companys risk management practices andevaluating accounting judgments and estimates and internal controls (KPMG 2008).2 The auditcommittees signal sd = v + ed where ed is a normally distributed noise term with mean zero and precision d that is independent of v but possibly correlated with the managers noise em . Positivecorrelation between the noise terms reflects the possibility that the manager and audit committeeobtain information from overlapping sources. We restrict attention to cases in which corr(em , e d ) md < m / d .3 The audit committee determines its signals precision d (which we assume is commonknowledge) prior to observing the managers report. This timing reflects current audit committeepractice of overseeing not just the managements accounting report, but also the integrity of overallcontrols. Such auditing emphasis on business risk (the Business Risk Auditing model) calls forexpanded evidential bases, more comprehensive risk assessment, and the deployment ofprofessionals who possess the knowledge and the competence to direct audit resources accordingly(Bell, Doogar and Solomon 2008, p. 730). These procedures take considerable planning, and are1The management may have directly made earnings forecasts. We can fold those forecasts in the prior distribution of v. 2 In this task, it is assisted by parties such as an independent auditor. We label all these parties the audit committee (see footnote 5). 3 If the condition md < m / d fails to hold, then the audit committee primarily uses the managers report to filter noise from its own signal sd ; the coefficient on the managers signal sm in E[v | sd , sm ] is then negative. In such cases, high values in the managers report tend to lower the audit committees posterior expectation of firm value v even under truthful reporting. We believe that such cases are not descriptive.7 10. typically designed far in advance rather than waiting till the year-end for the managements report(Rittenberg, Schwieger and Johnstone 2008, Ch. 4-7). KPMG (2008) notes that audit committeesmet on average for 6.4 times in 2007, and 40 percent of audit committee chairs devoted more than100 hours to the role. These activities suggest that the audit committee is active throughout the year,not just after year-end.4 We assume that both managers and the audit committee have incentives to bias theircommunications. FV provide a parsimonious means to incorporate the incentive to bias. Due toincomplete contracting, the level of the managers interest in the price is not fully known toinvestors, and is therefore a stochastic variable from the investor perspective. In addition, themanager faces a quadratic penalty for misreporting. The quadratic penalty represents the expected expost penalties and/or the ex ante effort spent to manipulate reports.We assume that the audit committee also has an interest in the firms stock performance.This interest can arise directly through contractual arrangements such as ownership, or indirectlythrough reputational effects of being associated with a successful firm and through committeemembers business and personal relationships with people having some performance interest in thecompany (e.g., customers, competitors suppliers, bankers, etc.).5 As a result, investors are also 4 Audit committees may also engage in contingent additional year-end information gathering if, for example, the management report deviates substantially from the audit committees own due diligence. We leave this scenario outside of our model and focus on the committees ex ante information precision choices. In private conversations, audit partners suggested that such year-end ad hoc information gathering procedures triggered by the managements report become much more crucial if it appears that the audit is headed towards some exceptional outcome such as a qualified audit. In the normal course of business risk auditing, the audit sampling procedures are more a function of the ex ante business risk than the eventual number put out in the management report. Additionally, from a modeling viewpoint, any contingent ad hoc information precision choices by the audit committee would affect both the managers reporting strategy and the investors pricing strategy. The pricing effect can become particularly difficult to solve if the optimal ad hoc information precision strategy is a non-linear function of the management report. Studies such as Baiman and Demski (1980) model non-linear contingent ex post investigation, but they, unlike us, do not have to subsequently fold their procedure into a rational expectations pricing model and incorporate expectations of this pricing model back into the reporting partys objectives. 5 The external auditor, for instance, is barred from taking a direct ownership interest, but the indirect performance interest effect can still exist. 8 11. somewhat unsure of the audit committee members level of interest in the firms price. 6 Allinvestors know is the expected degree to which the audit committee prefers high share prices andthat, following Section 301 in SOX and the SEC rule 10A-3, the committee is independent of themanagement. We represent the managers and audit committees interests in the firms price throughrandom parameters x and y , respectively. The two parameters are privately known to the managerand audit committee, respectively. Others uncertainty about x and y is modeled as these variables being jointly normally distributed with strictly positive means x and y and precisions x and y .The strictly positive means imply that the management and the audit committee have positivefiduciary duty with respect to the stock price. We model the independence requirement of Section301 of the Sarbanes Oxley Act by assuming that x and y are uncorrelated with each other (inaddition to being uncorrelated with v, em , and ed ). Why would an audit committee be unaware of x, the managers objective with respect to theprice? Note that x arises not just from stock compensation, but from indirect effects such asmanagement career concerns or managements secret planning of a management buyout(Merganthaler et al. 2008; Hafzalla 2009). The audit committee may not be privy to suchinformation (KPMG 2008, p.15). In its information acquisition activities, the audit committee couldtry to obtain information about x to better interpret the managers private report, but in context of ourlinear model, the audit committees signal about v, the firm value, effectively accomplishes the same. 6 Our extension to FV has a strong institutional basis. FVs innovation in their modeling of the managers objective is what the legal literature has noted: although the law holds managers to the highest standards of fiduciary duty (de jure), the reality (de facto) is that there is still some play in their motives. Our paper simply extends this uncertainty in motives to a party with no higher a standard of fiduciary duty: the audit committee. For an empirical illustration, see Larcker, Richardson, Seary and Tuna (2006) who document the complex web of director relations and affiliations. Also see McBride and Berman (2006) for a recent anecdotal example.9 12. As with FV, there is a cost of misreporting. The parameters cm and cd determine themagnitude of the managers and the audit committees expected costs of misreporting, respectively. Given a conjectured price function p , the objectives are then:71 Manager: x E[ p | sm ] cm E[(v rm ) 2 | sm ] 2 1 Audit committee: y p cd E[(v f ) 2 | sd , rm ] (1b) 2 An equilibrium in the reporting stage is a situation where the conjectures and the actions ofall the three parties managers, audit committee, and investors are self-fulfilling. The followingproposition establishes the existence of a unique linear reporting and pricing equilibrium: Proposition 1: Assume that the audit committee has already chosen the precision d . Forevery choice of d , there exists a unique linear equilibrium in which the manager reportsrm = E[v | sm ] + rx x to the audit committee ( rx > 0 ); the audit committee reports f = E[v | sd , rm ] + y p f / cd to investors; and the investors set the firms price as p = p f f p 2 y / cd ( p f [0,1] ). The endogenous coefficients p f and rx are the unique fpositive real roots to the equations g d () and g m () defined as:7Misreporting penalties could be proportional to (rm E[v | sm ])2 and ( f E[v | sd , rm ])2 rather thanE[(v rm ) 2 | sm ] and E[(v f ) 2 | sd , rm ] . Both penalty functions yield identical reporting strategies; however, they affect the audit committees incentives to gather information, a feature that we will study later in the paper. In particular, if the audit committees penalty function is proportional to ( f E[v | sd , rm ]) 2 , the audit committees ex ante expected utility depends on its choice of precision d primarily via its impact on price. By contrast, the penalty function in (1b) directly penalizes the posterior uncertainty var(v | sd , rm ) in the audit committees ex ante utility. This direct penalty reflects the audit committees institutional mandate to conduct high-quality due diligence for reasons broader than the committee members self-interest in the price.10 13. g d p 3 + cd y var(E[v | sd , rm ]) p f cd y var(E[v | sd , rm ]) = 0f 2 2 pfg m rx3 + x var(E[v | sm ] | sd )rx x cov(v, E[v | sm ] | sd ) = 0 cmThe equilibrium described by Proposition 1 generalizes the equilibrium of the two-persongame in FV to allow for an independent information-collecting intermediary between the managerand investors.8 While FV obtain a unique equilibrium in their two-person game, the uniqueness ofthe Nash equilibrium is by no means guaranteed as the number of players expands. This is becausethe third player affects the conjectures and the actions of both the existing players. Proposition 1shows that, despite this added complexity, the game has sufficient structure to yield uniqueness. The form of the audit committees report to investors f = E[v | sd , rm ] + f y y is key tounderstanding the model. The audit committee attempts to undo the managers bias, but thenpresents its report with the committees own bias.9 Because the managers report rm is a noisy version of the information contained in the managers signal sm , we can write the first term in the audit committees report as:E[v | sd , rm ] = E [ E[v | sd , sm ] | sd , rm ] This is the audit committees best estimate of the total information E[v | sd , sm ] available toboth the manager and the audit committee. As a result, investors only have to contend with the auditcommittees bias because the audit committees report already removes the managers bias to theextent possible.8If there is no uncertainty about the audit committees objective and the audit committee collects no information ( y , d = 0 ), the equilibrium is identical to that in FV. We follow FV in using linear rational price conjectures. Grossman (1976, p.577) describes the market micro-structure underlying the formation and the validation of these conjectures. 9 Note that the committee may be relatively more bullish than the management with respect to the price (e.g., the management is secretly planning a management buyout), or relatively more bearish than the management (e.g., the management has career concerns or is secretly planning a seasoned equity offering). In propagating its own views, the committee can thus adjust the management report either up or down.11 14. The coefficients f y and rx in the audit committees and managers reports, respectively, maybe interpreted as their sensitivities to preference shocks. The overall impact of the audit committeebias on its report can be seen by decomposing the overall variance of f into the portion due to theaudit committee information and the portion due to its bias:var( f ) = var(E[v | sd , rm ]) + f y2 y 1 1442443 {Audit Auditcommittee committeeinformation biasManagerial bias thus affects the report via the audit committees information var(E[v | sd , rm ]) .Finally, Proposition 1 takes d , the precision of the auditor committees information system, asgiven. The next section, in addition to comparative statics, also expands Proposition 1 to include theaudit committees choice of precision d based on its expected benefits in the reporting stage versus an information collection cost c ( d ) to the audit committee. III.Comparative StaticsThis section first explores the ex post comparative statics on the reporting and valuationdynamics. We divide the comparative statics into three categories: a) the effects of changingmisreporting penalties, b) the uncertainty about the objectives of the management and auditcommittee, and c) the precision of the information collected by the management and the auditcommittee. We then consider the audit committees ex ante choice to acquire information, and showhow this information acquisition choice adds value.The common feature across all the comparative statics is that the change in each exogenousparameter changes the conjectures and therefore the behaviors of all the three parties, which in turnwill have feedback effects on their conjectures. We will use the feed-forward and the feedbackframework to describe the underlying mathematics. 12 15. 3.1 Ex post Reporting and Valuation Comparative StaticsComparative Statics on Penalties Corollary 1: Higher expected penalties on the audit committee (higher cd ) yield lower auditcommittee bias f y but higher managerial bias rx . Higher expected penalties on managers(higher cm ) yield lower managerial bias rx but higher audit committee bias f y . Increasingeither penalty increases the earnings response coefficient, p f , in the price function as well as the price informativeness, var(E[v | p]) .1 An increase in the audit committees penalty cost affects the behavior of all three parties: thecommittee, the manager, and the investors. The audit committee reduces its reporting bias, as expected. This reduction increases p f , the pricing multiple, which has the feedback effect ofincreasing the audit committees benefit from biasing. However, this feedback benefit in equilibriumis unable to overcome the increased penalty costs of biasing. The above result is what FV find as well. Our contribution is to show that increasing auditor penalties has the opposite effect on the managers internal reporting. Specifically, the increase in p falso increases the managers biasing benefits. However, his misreporting costs have not changed.The manager therefore adopts a more aggressive reporting schedule (i.e., higher rx ).2var(E[v | p ]) = v var(v | p ) and attains its maximum v when p is fully revealing (p=v) and its minimum of 1 11zero when p is pure noise. 2 Pae and Yoo (2001) and Newman, Patterson and Smith (2005) obtain similar results in auditor-manager interaction, albeit in a non-valuation context. Our finding obtains in the context of a rational asset market, as a result of which we can study the implication of this interaction on the pricing of the earnings report.13 16. The managers reporting manipulations temper the effect of penalties on the investors price response p f to the earnings report. Formally, the derivative of p f with respect to cd would equalg dg d the positive term if the effect on the manager were ignored. The following cd p f computation shows that the consideration of the managers response to the change in p f dampensthe investor response:d pf g cd1 = dd cdg p f g r g m p f14d 3 1 d x24Effect g d p f g m rx > 0 ignoring 14442444443manager's (0,1) responseThe second term in , which is the attenuation effect, is between zero and one because g m p f < 0 while the other partial derivatives of g d and g m are positive.We can further interpret the product of partial derivatives in the denominator of the secondterm in as:g d rx g m p f g pg rx 1 d24f4 3 1m 3 424Investor responseManagerial responseto managerial bias (0)In sum, therefore, the above discussion illustrates the how the channels through which anypenalty operates involve the beliefs and the actions of all three parties the manager, the auditcommittee, and the investors.Thus far we showed how the presence of the manager tempers the investor response toincreases in auditor penalty. We next show how the presence of the manager affects the linkage 14 17. between an increase in the audit committee penalty and the audit committees reporting bias. The elasticity of the audit committees bias f y with respect to the audit committee penalty cd is:d f y cd d p f cd=1 < 0 d cd f y d cd p f The proof of Corollary 1 derives inequality . From , the managers response to changes inp f reduces d p f d cd and therefore makes the elasticity of f y with respect to cd more negative. The intuition for this result is that the audit committee determines its reporting bias bycomparing its penalty costs against the benefit of misreporting. Recall that the concurrent increase in the managers reporting bias tempers the investor price response p f , thus reducing the auditcommittees valuation benefits. This decrease in the valuation benefit makes the audit committeemore sensitive to the increased penalty costs of biasing its reports, as a result of which it improves itsreporting quality. Overall therefore, the managers strategic behavior attenuates improvements in thepricing process, but improves the audit committees reporting process. Symmetrically, when the managers penalties are increased, the presence of the auditcommittee attenuates the improvements in the investors pricing response, but improves the managers private reporting process. However, the latter effect obtains only when p f > 1 / 2 (i.e., the derivative d rx d cm is more negative than it would be without the audit committees strategic response only when p f > 1 / 2 ).3 3 The condition p f > 1 / 2 is the point at which p f is more responsive to changes in audit committee bias f y2 y 1 than it is to changes in the audit committees information var(E[v | sd , rm ]) . To see this, note that p f = var(E[v | sd , rm ]) var(E[v | sd , rm ]) + f y2 y 1 , which is greater than 1/ 2 when var(E[v | sd , rm ]) > f y2 y 1 . The 2 1 magnitude of the partial derivative of p f with respect to var(E[v | sd , rm ]) is greater than with respect to f y y when var(E[v | sd , rm ]) > f y y or, equivalently, p f > 1/ 2 .2 1 15 18. We further explore the manner in which increases in management penalties increase the auditcommittees reporting aggressiveness. We find that, in some cases, the net effect of an increase inmanager penalties is an increase in the overall bias included in the audit committees report. Thefollowing corollary formally states this result: Corollary 2: Denote the overall impact of bias on f by the amount of variation in f due to the bias parameters x and y , which is var(E[ f | x, y ]) . The overall bias var(E[ f | x, y ]) isincreasing in manager penalties cm for small levels of cm . That is, d var(E[ f | x, y ])limc 0> 0 .4m d cm While an increase in manager penalties may increase the level of earnings management in theaudit committee's report, it also induces more truthful reporting by the manager, which improves theaudit committee's information. The increase in information is relatively greater than the increase inmanipulation so that the price response to the audit committee's report increases as stated inCorollary 1. Such backward bending effects are unlikely to obtain in a single reporting partysetting. Figure 2 illustrates the overall bias var(E[ f | x, y ]) as a function of the manager penalty cm . Implications A clear implication of Corollary 1 and 2 that the managers behavior can temper thevaluation effect of audit committees behavior and vice versa. This leads to clear omitted correlatedvariable bias if empirical studies that focus on audit issues ignore management incentive issues. Thispoint is an important one in the audit earnings quality literature, which has largely ignoredmanagement issues. Instead, much of the debate over the mixed evidence of audit parameters on4The sensitivities of the managers and the audit committees reports to their private objectives are rx and fy respectively. Because these two variables are moving in opposite directions, we use var(E[f | x, y]) as an aggregate measure of the bias that incorporates both parties private objectives. 16 19. earnings quality and valuation is viewed as an econometric problem of measurement issues (correctaccrual and audit committee independence measures) and regression specification techniques (OLSversus latent class models).5 Other studies view the mixed evidence as resulting from improperidentification of auditor misreporting penalties (Weber, Willenborg and Zhang 2008; Venkatarman,Weber, and Willenborg 2008). These studies then use specific smaller settings (e.g., KPMGGermanys audit of Comroad AG, the setting of initial public offerings, etc.) to better identify thesevarious auditor costs. Our model suggests that managerial behavior plays a key confounding role onboth both reporting and valuation patterns when the audit committee costs change.Weber, Willenborg and Zhang (2008) note that researchers can exploit institutionalvariations in auditor misreporting penalties provide to test reporting quality. Recent legislation suchas SOX has changed not just the audit committee penalties, but also the management penalties. Ourmodel can tell us when which penalty will have the greatest impact on the price response to earnings.Direct computation shows that:d pfd pf 2cm var(E[v | sd , rm ])c 2 + 2 x var(rm | sd ) dd cd d cm pf var(E[v | sd , rm ]) var(E[v | sd ]) cm 14444444444 244444444443 2The sign of equation can switch with the parameters. When the audit committee penalty is smallrelative to management penalty, investor response to earnings is more sensitive to audit committeepenalties, otherwise investors are more sensitive to management penalties. Figure 3 shows this switch graphically: using reasonable parameter values, the derivative d p f d cm exceeds d p f d cdonly when the audit committee penalty is over 10 times as large as the managers penalty.Otherwise, investors are more sensitive to audit committee penalties.5See the spirited debates in Ashbaugh, LaFond and Mayhew (2003) and Larcker and Richardson (2004).17 20. Equation provides a conceptual framework to think about when each penalty is moreeffective at increasing price response to earnings. It suggests that empirical studies can increase theirpower by considering settings where the penalty of interest has more impact on the valuation process.For example, our model suggests that studying the effects of legislated increases in managementpenalties is unlikely to yield a significant valuation impact if the researcher examines a country or asetting where the audit industry is protected under an implicit too big to fail regulatory approach. Investor Uncertainty about Management and Audit Committee ObjectivesRecall from Figure 1 that investors are uncertain about managements and audit committeesobjectives with respect to price. Comparative statics on this uncertainty yields the followingcorollary:Corollary 3: An increase in uncertainty y about the audit committees objective function 1 reduces both managerial bias parameter rx and the audit committee bias parameter f y . It also reduces the investors price response p f and the price informativeness var(E[v | p ]) . Similarly, an increase in uncertainty x about the managers objective function reduces rx , f y 1 , p f and var(E[v | p ]) . Increases in uncertainty reduce investors sensitivity to the audit committees report. There isa feedback effect in that this reduction in sensitivity causes the managers and the audit committee toreduce their reporting bias, but these feedback bias reductions do not fully compensate for theincrease in uncertainty. In this dimension, our model parallels FV who show that increases inmanagement uncertainty reduce both the price responsiveness and the reporting bias.18 21. As with FV, the empirical implication of Corollary 3 is that studies of audit quality and auditinformativeness need to incorporate measures of uncertainty about management compensation. Alarge body of empirical accounting literature examines how investors react when information aboutthe details of executive compensation are disclosed (Lo 2003; Aboody, Barth and Kasznik 2004).This literature heretofore is unconnected with the empirical audit literature. What our modelsuggests is that better disclosure of executive compensation (especially their exposure to stock price)can be an important mediating factor in audit quality and earnings quality. For examples, disclosuresof planned executive equity transactions that clarify executive objectives may improve the reportingprocess (e.g., Cheng, Nagar, and Rajan 2007).3.2 Ex ante Information Acquisition Comparative StaticsIf the audit committee introduces its own bias, why have this committee in the first place?We show that the committee improves price informativeness as long as it collects due-diligenceinformation. Corollary 3 implies:Corollary 4: The audit committee with an uncertain objective only improves the price informativeness var(E[v | p ]) to the extent that it collects information ( d > 0 ) .The point again here is that without any information gains from the audit process, just addinganother party with an uncertain objective only serves to reduce the quality of the report. When theaudit committee collects its own information, it adds information to system despite its reporting bias.The following corollary describes more specifically the effect of the precision of the auditcommittees signal.Corollary 5: Assume that the noise in the managers and the audit committees signals are uncorrelated ( md = 0 ). The price response p f and the price informativeness var(E[v | p ])19 22. are increasing in the precision d of the audit committees signal. The managers bias parameter rx is increasing in d if and only if the elasticity of p f with respect to d exceeds the absolute value of the elasticity of the coefficient m cov(v, rm | sd ) / var(rm | sd ) with respect to d .FV also find that increasing the quality of the reporters private signal improves investorsprice response. The interesting aspect of our case is the managers response to an increase in the precision of the audit committees signal depends on two opposing forces. The increase in p fincreases the managers biasing benefits. However, the audit committee relies less on the managersreport as the committees own information becomes more precise. Given the existing level of hismisreporting penalties, the managers net benefits to biasing his private report are reduced. The condition on the elasticities of p f and the coefficient cov(v, E[v | sm ] | sd ) / var(rm | sd ) correspondsto which of the two forces dominates. Figure 4 illustrates two examples where each force dominates.This result has implication for empirical studies such as Cohen, Dey, and Lys (2008) whoexamine changes in earnings management pre- and post SOX, based on the premise that SOXincreased managerial misreporting penalties. Overall, they find evidence that SOX reduces accrual-based earnings management. However, their tests on the role of management stock-price incentivesin this reporting process yield several insignificant results, which they label unintuitive (p. 779).Our model provides a way of structuring these stock compensation-related findings. In ourmodel, stock compensation affects the managers incentives to bias the report to the audit committee.However, SOX also led to improvements in the quality of information available to the auditcommittee by mandating that the audit committee have authority to engage outside advisors and that 20 23. the internal audit function report directly to the audit committee.6 Corollary 4 suggests that suchincreases in the quality of the audit committees information can temper the effect of increasedmanager incentives to internally bias the report. As a result, the net effect of compensation can behard to detect in the data pre- and post-SOX, leading precisely to the insignificance Cohen, Dey, andLys (2008) find. Corollary 5 suggests that partitioning the data on the information asymmetrybetween the management and the audit committee might yield more powerful tests on the linkagesbetween management compensation and reporting quality. For example, many firms may have beenin compliance with SOXs audit committee requirements well before the effective date of SOX. Audit Committee Choice of InformationWe show that despite its bias, the audit committee creates value through the due-diligenceinformation it provides investors. However, we have taken the precision d of the audit committeesdue diligence signal to be exogenous. Acquiring such signals can entail significant costs (Larkin2008). We endogenize this choice by assuming that the audit committee incurs a cost of c( d ) to obtain a signal with precision d . For computational simplification, we assume that the correlation md between the managers and audit committees signal errors is zero. Following the timeline inFigure 1, we also assume that the audit committee selects the precision prior to learning itspreference parameter y . For example, one can imagine the objectives of the audit committeeevolving stochastically as unexpected business events arise. The committee anticipates theequilibrium of Proposition 1 and selects the precision to maximize its expected payoff. c p 2 1f cE y p d ( f v ) 2 c ( d ) =( y y ) d var(v | sd , rm ) c( d ) 2 2 2cd 26See http://www.sec.gov/rules/final/33-8220.htm and http://www.sec.gov/rules/pcaob/34-49544.htm . 21 24. The first term in equation mirrors the benefits of bias in FVs corollary 5, with the value of bias being positive if and only if y < y . The second term in reflects the audit committees incentives 2 1 to provide information to investors.7 The first derivative of with respect to the precision d is the following: pfd pf cd var(v | sd , rm ) var(v | sd , rm ) d rx ( y 1 y ) c ( d ) 2 +cdd d2 drx d d Using the definitions of d p f d d and d rx d d , can be rewritten as: p f 1 c var(E[v | sd , rm ]) d p f( y y ) + d2 c ( d ) cd2 p f d d where the term var(E[v | sd , rm ]) p f > 0 is defined by differentiating the equilibrium relation between var(E[v | sd , rm ]) and p f with respect to p f .8 The following proposition followsimmediately from : Proposition 2: Sufficient conditions for the audit committee to collect information ( d > 0 )are y y and c (0) = 0 .12Proof: Because var(E[v | sd , rm ]) p f > 0 and d p f d d > 0 , the conditions stated in theproposition imply that the audit committees ex ante objective function is increasing in d atd = 0. Why would an audit committee not want to collect information? The solid line in Figure 5 provides a numerical example where the audit committees y is sufficiently larger than y that its2 17 The term involving var(v | sd , rm ) arises because the audit committees penalty is based on the difference between firm value and the disclosure rather than the audit committees intentional bias f E[v | sd , rm ] . See footnote 7. 8 See in the Appendix. 22 25. ex ante expected utility is decreasing in the precision of its signal. The intuition is as follows.Consider a reporting party with very high stakes, access to very precise information, and the abilityto misreport. Investors would be hesitant to believe this partys report because they know that thisparty is very interested in the price, and that the party knows the truth. This is a classic pre-commitment problem, and the reporting party is better off either reducing its stake, or reducing itsinformation quality, or reducing its opportunities to misreport (see footnote 8). The last option iseasily accomplished by increasing the misreporting penalty cd as shown in the dashed line in Figure5. More important, by the first option, reducing the audit committees interest in the short term pricecan actually benefit the reporting process.In sum, therefore, the audit committees incentives and its misreporting penalty thereforeplay two roles: a) they affect the ex post misreporting bias, and b) they affect the ex ante collection ofinformation through high-quality due diligence procedures. IV. Extensions Manager Observes the Audit Committee ReportThe model can be easily extended to the situation where the manager observes the auditcommittees signal prior to giving his report. This extension obtains because we allow forcorrelation between the managers signal and the audit committees signal. The managers reportingfunction in a linear equilibrium takes the form rm = E[v | sd , sm ] + rx x while the audit committees strategy remains f = E[v | sd , rm ] + f y y . Because the manager compresses his two-dimensional information set ( sd , sm ) into the single report rm , this setting is equivalent to one in which the23 26. manager observes a single signal sm 2 such that E[v | sm 2 ] = E[v | sd , sm ] . In particular, the signal sm 2 may be defined as follows:cov(v, sd | sm )cov(v, sm | sd )ed +em E[v | sd , sm ]var( sd | sm ) var( sm | sd ) sm 2 =v+cov(v, sd | sm ) cov(v, sm | sd )cov(v, sd | sm ) cov(v, sm | sd ) + + var( sd | sm ) var( sm | sd )var( sd | sm ) var( sm | sd ) 144444424444443 em 2The signal sm 2 satisfies E[v | sm 2 ] = E[v | sd , sm ] and satisfies the correlation restriction corr(em 2 , ed ) 2 < var(ed ) / var(em 2 ) if and only if the original signals satisfy the correlation restriction md < m / d from Section II.Because we have allowed for a correlation between the error terms of the managers andaudit committees signals, the use of the signal definition allows us to apply all the previoussections results (except Corollary 5 and Proposition 2) when the manager observes the auditcommittees signal. The analysis of this setting simply requires an appropriate choice of themanagers signal variance and correlation with the audit committees signal. Executive compensationWe now embed the reporting problem in an explicit principal-agent problem. We do this fortwo reasons. First, one of the main explicit reasons for the managers interest in the stock pricearises from stock price-based compensation. Second, an explicit formulation will account for the factthat payments to the manager have a negative income effect on the shareholders who are the residualclaimants of the firms cash flows. This income effect, we show below, changes the reportingbehavior.24 27. Specifically, we assume that the firm offers the manager a compensation contract of the forms0 + x p where s0 and x are constants determined by shareholders. The manager chooses anaction a that impacts the mean of the stochastic firm value through some formulation E[v; a] . Thisaction a, for example, could be a major investment project that is implemented over some horizon.By contrast, the managers stochastic objective evolves continuously as unexpected business events(such as upcoming option grants) arise. As the result, the manager takes the action a prior to learning his preference shock ex , where ex has zero mean and variance x . As before, investors are not 1 privy to shocks in the managers equity objectives (e.g., Cheng, Nagar, and Rajan 2007). The sum x + ex is identical to the preference x in the preceding analysis.1 The investors payoff, net of compensation, is: v s0 x pIn this setting, the equilibrium is nearly identical to that in Section II and is given in the followingproposition. Proposition 3: Assume that the manager receives compensation s0 + x p and selects hisaction a prior to learning his preference shock ex . Also assume that the audit committee hasalready chosen the precision d . For every choice of d and x , there exists a unique linearequilibrium in which the manager reports rm = E[v | sm ] + rx x to the audit committee ( rx > 0); the audit committee reports f = E[v | sd , rm ] + y p f / cd to the investors; and investors set the firms price as: 1 One could explicitly derive the value of x in a linear-contract, principal-setting where a risk-averse agent with exponential utility takes an action that impacts the expected firm value. See, for example, the centralized regime setting in Bushman, Indjejikian and Penno (2000). An example derivation is available from the authors upon request. We omit these details because the determination of the contract is not the focus of this study. 25 28. p= ( 1 (1 + ) p ) E[v; a] s xf0 p2fy + pff 1 + xcd1 + x ( p f [0,1 / (1 + x )] ). The endogenous coefficients p f and rx are the unique positive realroots to the equations g d () and g m () defined as:g d p 3 + cd y var(E[v | sd , rm ]) p f cd y var(E[v | sd , rm ]) (1 + x ) = 0f 2 2pfg m rx3 + x var(E[v | sm ] | sd )rx x cov(v, E[v | sm ] | sd ) = 0 cmThe following corollary describes how the managers incentives affect the reporting-stageequilibrium: Corollary 6: The price response to earnings p f is decreasing in the level of the managersincentives x . Both the audit committees reporting bias parameter f y and managersreporting bias parameter rx are decreasing in x .FV show that, absent an audit committee, increases in x increase the managers reporting bias to investors. In the standard version of our model, changes in x have no effect on bias becausethe audit committee removes expected managerial bias from its report. This effect changes inCorollary 6. The reason is Equation , the income equation. Investors are the residual claimants andthus care only about what they receive after the manager has been paid. As the managers stock priceinterest increases, investors realize that any share price appreciation will lead to more payments tothe manager. Investors thus tend to discount the earnings report more than if this income effect didnot exist.2 This reduction in the price response, coupled with unchanged penalties, diminishes boththe managers and the audit committees incentive to misreport earnings.2This is also evident in pf which has a smaller range relative to Proposition 1.26 29. Corollary 6 has an important empirical implication. A main result in Cheng and Warfield(2005) is that managers with more equity report fewer positive income increasing abnormal accruals.Cheng and Warfield (2005) suggest that these managers tend to save such income increasingmanipulation for later periods. This, we believe is a somewhat incomplete explanation, for a datasetcovering as many periods as Cheng and Warfields should eventually show these earnings surprises.Bartov and Mohanram (2004) argue that such mixed results are a power issue, and recommendexamining reporting quality in settings with very large changes in management equity positions. Our model suggests two reasons for these empirical results. First, our results in Section IIindicate that empirical studies on the effect of managerial compensation on the reporting processwould benefit by introducing the audit committee effect. Second, the income effect can also play arole in mediating the reporting process. Cheng and Warfields (2005) results occur naturally in thecontext of our Corollary 6.V. Hierarchical Reporting Thus far, we have only had a single layer of management. The linear structure of our modelis easily scalable to a hierarchy of managers, although analyzing equilibrium effects becomes morechallenging as the structure expands. The following proposition summarizes the equilibrium inwhich N managers report in a hierarchical fashion, with manager n reporting to manager n 1 andmanager 1 reporting to the audit committee. In this case, we assume that each manager n has anobjective function of the form: cmn xn E[ p | sn , rn +1 ] E[(v rn ) 2 | sn , rn +1 ] 2where xn is normally distributed with mean xn and precision xn . For tractability, we assume that the shocks xn to the objective functions are uncorrelated, although this assumption is more tenuous27 30. than in the case of the audit committee. Note, however, that this does not preclude correlation in theaverage sensitivity to price xn . For example, firms that heavily use equity compensation may have managers with high levels of xn , but shocks from that mean are uncorrelated. Proposition 4: Assume that the firm has N managers who report sequentially with manager n reporting to manager n 1 and manager 1 reporting to the audit committee. There exists a unique linear equilibrium in which the audit committee issues a report of the formf = E[v | sd , r1 ] + y p f / cd to investors, who then determine the firms price as p = p f f p 2 y / cd ( p f [0,1]) . The endogenous coefficients p f , r1 ,K , rxN are fdetermined by the solutions to the following equations: g d p 3 + cd y var(E[v | sd , r1 ]) p f cd y var(E[v | sd , r1 ]) = 0f 2 2 pfg m1 rx31 + x1 var(E[v | s1 , r2 ] | sd )rx1 x1 cov(v, E[v | s1 , r2 ] | sd ) = 0 cm1g mn , n {2,K , N } rxn + xn var(E[v | sn , rn +1 ] | sn 1 )rxn3 p f cov(v, r1 | sd ) n 2 cov(v, rk +1 | sk ) cov(v, E[v | sn , rn +1 ] | sn 1 ) = 0 cmn var(r1 | sd ) k =1 var(rk +1 | sk ) Proposition 4 implies that the following ratio of bias coefficients:n 1 n 1rxnc cov(v, r | sk ) c var(E[v | sk +1 , rk + 2 ] | sk ) c= n ii var(r k +1| s ) = cni var(E[v | s< n i k +1 , rk + 2 ] | sk ) + rx , k +1 x , k +121 rx ,n i cn k =n k +1 kn k = n i cnwhich immediately implies the following corollary because each term in the product in is less thanone. Corollary 7: If managers report sequentially and the managers misreporting penalties are equal, cm1 = c m 2 = L = cmN , then higher-level managers (lower n ) incorporate more bias intheir reports than lower-level managers (higher n ). That is, rx1 > rx 2 > L > rxN .28 31. Corollary 7 suggests that earnings management primarily occurs at higher levels in theorganization so long as the earnings penalties are not too large at higher levels relative to lowerlevels. The intuition is that the further down the chain a manager is, the more his report getsdistorted along the chain (recall that each manager imperfectly removes prior bias and then adds hisown bias). The lower reporting contribution of the lower-level manager, combined with similarmisreporting penalties causes the lower-level manager to bias his report less. Note that this is not scale or scope effect of a decentralized firm: this effect is purely areporting hierarchy effect. While this result lends support to the standard empirical focus on topexecutive incentives in studies of earnings management, its novel implication is that the reportinghierarchy itself is an important determinant of the reporting bias.1In particular, the model applies to the reporting process in the audit firm itself, where seniorsreport to audit managers who report to partners. Experimental studies such as Messier, Owhoso, andRokovski (2008) argue that reporting biases in an audit firm arise from cognitive and psychologicaljudgment differences across the layers of management hierarchy; our models provides an additionalincentive-based reason for such reporting biases.VI. ConclusionEmpirical research on reporting quality largely splits into two streams. One stream examinesthe audit effect (e.g., Frankel, Johnson and Nelson 2002; Ashbaugh, LaFond, and Mayhew 2003).Another stream examines the management effect (e.g., Bartov and Mohanram 2004; Cheng andWarfield 2005). Given the mixed evidence in these two literature streams, more recent studies such 1Numerical estimations showed that reducing the manager Ns information precision to zero (effectively an N-1 level organization) reduced the final reporting bias. The intuition arises from the standard consequence of our model: the overall information available to the remaining N-1 managers in the organization is now lower, thus reducing valuation benefits, while penalties remain unchanged. We also compared the levels of reporting bias across two firms that were identical except for that one firm reported sequentially and the other had all N managers reporting directly to the audit committee. While we could not definitively prove any analytical results, our numerical estimates suggest that direct reporting typically yields a greater price response to the earnings report. Flatter reporting structures therefore appear to perform better.29 32. as Larcker and Richardson (2004) and Dey (2008) incorporate both management and audit measures.However, these authors resort to exploratory statistical analyses to uncover empirical patterns. Whatis thus needed (and not appears to have been fully developed in current analytical literature) is aunified analytical treatment of management, audit, and rational pricing issues. In this study, weprovide such a framework. We show that this framework has the power to resolve many empiricalpuzzles and the power to suggest new empirically testable predictions. The main result of our model is that the reporting objectives of the manager and auditcommittee conflict. The audit committee attempts to strip away any of the managers reportingmanipulations, but then presents its own bias when communicating to investors.1 This interactionimpacts the effectiveness of misreporting penalties because a reduction in one partys bias may havethe effect of facilitating bias by the other party. As a result, greater misreporting penalties maysometimes even increase the overall amount of earnings management. In addition to misreporting penalties, we conduct a rich set of comparative statics to illustratethe importance of factors such the managers and the audit committees information precision in thereporting and the pricing process. In particular, we explicitly model the managers interest in theprice as arising from a stock price-based compensation contract. The compensation payout is anexpense to investors. We show that this income effect itself can alter the reporting and the valuationprocess. We highlight the relevance of these comparative statics to the current empirical research onreporting and valuation. Why should a firm have an audit committee? We show that, despite its bias, the value of theaudit committee arises from the additional information it provides investors through it due diligenceactivities. We then endogenize the audit committees ex ante incentives to engage in due diligence. 1 Note that the audit committee may be relatively more bullish than the management with respect to the price (e.g., the management is secretly planning a management buyout), or relatively more bearish than the management (e.g., the management has career concerns or is secretly planning a seasoned equity offering). In propagating its own views, the committee can thus adjust the management report either up or down.30 33. We show that if audit committees stakes are too high, or if the audit committees misreportingpenalties are too low, the committee does not wish to collect information. An audit committee with asmaller interest in the current price therefore benefits the reporting process. Our model also extends to reporting in a hierarchical organization, and shows that thereporting hierarchy itself is a variable affecting the reporting bias. Our model thus suggests novelways in which organizational design parameters are tied to the reporting process.In conclusion, there are many ways to model communication among multiple parties usingnon-cooperative game theory: one could use bargaining models, signaling models, repeated gamemodels, etc. (Kreps 1990, Ch. 11 Ch. 18). The main technical difficulty arises when we fold thesecommunication games into a rational expectations pricing process. The technical elegance of the FV(Fischer and Verrecchia 2000) model is that communication and rational pricing problems can besolved in a relatively tractable manner. As this paper shows, the model can also be extended toinclude more than one reporting party. 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The manager and investors both assume that the audit committee reports: f = E[v | sd , rm ] + f 0 + f s sd + f r rm + f y yFinally, the audit committee and the manager both assume that investors set the price as: p = p0 + p f fGiven the audit committees conjectures of rm and p , its objective function is: 1max f y ( p0 + p f f ) cd E[(v f ) 2 | sd , rm ]2The second order condition is always satisfied for cd > 0 so that the first order condition yields theaudit committees best response: pff = E[v | sd , rm ] +ycd{fy35 38. Given the managers conjectures of f , p and E d [v | sd , rm ] where E d [] denotes theexpectation given the managers conjecture that the audit committee assumes , his objective functionis:(( max rm x p0 + p f E E d [ v | sd , rm ] | rm + f 0 + f s sd + f r rm + f y y ))1 cm (rm E[v | sm ]) 22The conjecture that E d [v | sd , rm ] is linear in rm implies that the second order condition is satisfied for cm > 0 so that the first order condition yields the managers best response: p f cov d (v, rm | sd ) rm = E[v | sm ] + + fr x cm vard (r | s ) 14444 m d 24444 3 rxLastly, the investors conjectures that the manager and audit committee follow linearstrategies imply that the public report f is a linear function of sm and sd so that f is jointlynormally distributed with v . This implies that p = E[v | f ] is a linear function of f : cov(v, f )p= var( f ) ( f0 + f r ( r0 + rx x ) + f y y ) + cov(v,f f) ) f var(1444444 24444444 1 24 4 3 4 3p0 pfThe manager, the audit committee and investors all find that linear strategies are a bestresponse to their conjectures that other parties follow linear strategies. What remains is to show thatthere are solutions to the coefficients in through given by the conditions, and . The auditcommittees condition implies that f 0 = f s = f r = 0 . The managers condition implies that r0 = rs = 0 . These imply that p0 = p f f y y = p 2 y / cd . What remains is to solve for rx and fpf .36 39. Condition implies: cov(v, f )var(E[v | sd , rm ]) pf ==2 var( f ) p f 1 var(E[v | sd , rm ]) + y cd where var(E[v | sd , rm ]) is a function of the endogenous parameter rx via var(rm | sd ) : cov(v, rm | sd ) 2 var(E[v | sd , rm ]) = var(E[v | sd ]) +var(rm | sd )cov(v, E[v | sm ] | sd ) 2 = var(E[v | sd ]) +var(E[v | sm ] | sd ) + rx2 x 1 The managers reporting strategy then implies that:p f cov(v, rm | sd ) p f cov(v, E[v | sm ] | sd )rx = = cm var(rm | sd )cm var(rm | sd ) Equations and can be rearranged as follows:g d p 3 + cd y var(E[v | sd , rm ]) p f cd y var(E[v | sd , rm ]) = 0 f2 2 pf g m rx3 + x var(E[v | sm ] | sd )rx x cov(v, E[v | sm ] | sd ) = 0 cm Both of the cubic polynomials in and are of the form x 3 + p x + q where p f plays the role of x in and rx plays the role of x in . Both polynomials are such that 4 p 3 + 27q 2 > 0 , which implies thateach has exactly one real root and two complex roots. The real root must be positive because both approach positive infinity as their arguments ( p f and rx , respectively) approach positive infinity andboth are negative when their arguments equal zero.1 The solution to and therefore determines the unique equilibrium, which is such that p f > 0 and rx > 0 .1Recall that we restrict md < m / d .37 40. The restriction that p f 1 in the proposition follows because setting x = q / p in the cubic x 3 + p x + q yields a value of q 3 / p 3 , which is positive when p > 0 and q < 0 as they are in and . This implies that p f < 1 and:p f cov(v, E[v | sm ] | sd )rx < cm var(E[v | sm ] | sd )where the latter inequality for rx is not stated in the proposition but is used in later proofs.Some of the comparative statics require applications of the implicit function theorem to and .The following lemma states the Jacobian matrix used in these applications. The proof follows from direct computations, the condition md < m / d and the results in Proposition 1 that p f [0,1] and rx > 0 .Lemma A1: Define the polynomial in as g d and the polynomial in as g m . The Jacobianmatrix is: g / p f g d / rx D g ( p f , rx ) = d g m / p f g m / rx with the following elements:g d= 3 p 2 + cd y var(E[v | sd , rm ]) > 0f 2p f g d 2 y cov(v, E[v | sm ] | sd ) 2= 2cd(1 p f )rx > 0 rx ( x var(E[v | s ] | s ) + r 2 1) 2 m d x xg m 1= x cov(v, E[v | sm ] | sd ) < 0 p fcm g m= 3rx2 + x var(E[v | sm ] | sd ) > 0 rxand determinant D g ( p f , rx ) > 0 .38 41. The proof of Lemma A1 is by direct computation.d pf d rx Lemma A2: The sign of the derivatives and , where z denotes an arbitrarydzdzexogenous variable, are: d pf g d g m g m g d sign = sign dz rx z rx z dr g g g g m sign x = sign m d d dz p f z p f z In equilibrium:p4f var(E[v | p ]) = var(E[v | f ]) = p f var(E[v | sd , rm ]) = cd y (1 p f )2 The derivative of var(E[v | p ]) is as follows, where the term that multiplies p f / z is positive because p f < 1 in equilibrium: d var(E[v | p ]) p4 d 1 f (4 3 p f ) p 3 d p f f = 2 + 2dz 1 p f d z cd y cd y (1 p f ) 2 d z The proof follows from the implicit function theorem because D g ( p f , rx ) > 0 . follows from . Proof of Corollary 1 Manager penaltyThe partial derivative g d / cm = 0 while:g m pf= 2 x cov(v, E[v | sm ] | sd ) > 0 cm cmwhere the inequality follows from Proposition 1. Applying Lemma A2, this gives the followingwhere the inequalities follow from and Lemma A1:39 42. d pf g d g m dr g d g m sign = sign >0sign x = sign p f cm 0 and: d cm cd d cm 2 d var(E[v | p ]) 3 2 p f pf d pf = 2 >0d cmcd y 1 pf d cm Audit committee penalty Direct computations give:g dg m= 2cd y var ( E[v | sd , rm ]) (1 p f ) < 0=0 cd cdApplying Lemma A2, this gives the following where the inequalities follow from and Lemma A1: d pf g m g d sign = sign >0 d cd rx cd dr g g sign x = sign m d > 0 p f cd d cd d fy p f d p f cd The derivative= 1 and is negative if and only if the elasticity of p f withd cd cd d cd p f2 respect to cd is less than one. The following computations show that this is indeed the case:d p f cd 2 cd y var ( E[v | sd , rm ]) (1 p f )k12 = d cd p f (f 2)p f 3 p 2 + cd y var ( E[v | sd , rm ]) k1 + k2 2 cd y var ( E[v | sd , rm ]) (1 p f )2

0 rx g d g m 1 p f cov(v, E[v | sm ] | sd )3k2 = 2cd y 2 rx > 0 rx p fcmvar(rm | sd ) 2Now substitute in the numerator using to obtain: 2 cd y var ( E[v | sd , rm ]) (1 p f )2 d p f cd2 p2f0 Taking limits, rx as cm 0 and var(E[v | sd , rm ]) var(E[v | sd ]) as cm 0 , whichgives: var(E[v | sm ] | sd ) rx2 x 1 var(E[v | sm ] | sd )rx2 x 1 = 1var( rm | sd )var(E[v | sm ] | sd )rx2 + x 1 while g d p f is positive so that the term in parentheses is positive as cm 0 and d var(E[ f | x, y ]) d cm is positive for small cm .42 45. Proof of Corollary 3 Manager preferences Direct computations give: cov ( v, E[v | sm ] | sd ) 2 2 g d = cd x2 rx (1 p f ) > 0 x1 var(rm | sd ) 2 g m 2 pf = x var ( E[v | sm ] | sd ) rx cov ( v, E[v | sm ] | sd ) > 0 x1cmwhere the inequality in follows from Proposition 1 and the inequality in follows from . From Lemma A2: d rx g g d g dg m sign 1 = sign m 0>0 Direct computations show that: d pf2 g m g 2 pf rx m x cov(v, E[v | sm ] | sd ) rx3 + x var(E[v | sm ] | sd ) rxd x 1 x x1 rx3 cm1 pf = x cov(v, E[v | sm ] | sd ) < 03 cmwhere the last inequality uses the equilibrium condition . The other derivatives ared fy 1 d pf=< 0 and: d x 1cd d x 1 2 d var(E[v | p ]) 3 2 p f pf d pf = 2 0 2 =0 y 1 y 1 Applying Lemma A2, this gives the following where the inequalities follow from and Lemma A1: d pf g g d sign 1 = sign m 0>0 0 d dcd y (1 p f ) 2 d d2If y = 0 then the equilibrium is identical to one with no audit committee. Otherwise, prices differ by a constant y cd . 45 48. For the second part, define m as the coefficient on the managers report rm in E[v | sd , rm ] , which equals cov(v, rm | sd ) / var(rm | sd ) = cov(v, E[v | sm ] | sd ) / var(rm | sd ) . Direct computations, including a substitution for rx using , give: mx1 cm g m =0 m d d>0d dp f d p f dg d g m g m Multiplying through by g m rx , subtractingfrom both sides and rearranging shows rx p f dthat holds if and only if: g m d p f x d pf d m d d d d cmd d p f d mwhich completes the proof. Proof of Proposition 3The proof is similar to the proof of Proposition 1 and we only outline the steps. We assumethe following conjectures for the managers reporting strategy rm , the audit committees reportingstrategy f and the pricing function p are the same as in Proposition 1. This implies that the reportf is jointly normally distributed with v so that p solves: cov(v, f ; a ) p = E[v s0 x p | f ; a] = E[v; a ] +( f E[ f ; a ]) s0 x p var( f ; a )Substituting from the conjectures and solving for p gives: 46 49. cov(v, f ; a )E[v; a ] E[ f ; a] s0var( f ; a) cov(v, f ; a )p= +f 1 + x(1 + x ) var( f ; a) 144444 2444444 144244343p0 pf The audit committee and manager strategies are essentially the same as in Proposition 1.Despite the assumption of managerial risk aversion, the managers first-order condition is the sameas in Proposition 1. Solving gives condition g d in the proposition and the solving for rx in the managers reporting strategy as in the proof of Proposition 1 gives condition g m . Proof of Corollary 6 The Jacobian determinant as in Lemma A1 is positive. The partial derivative g m x = 0so that:d pfg m g d 0 >0 d rxgg d m 0 , implying that each has exactly one real root and two complex roots. Thus, the system of N + 1 equations can be solved to yield the solutions to p f , rx1 ,K , rxN . 48 51. Figure 1: Timeline Firm valueManagerAudit Investors Audit v isManager privatelyprice thecommittees committee realizedreceivesreports rm report faudit selects the and isprivateleading to to the generates audit planunknown signal of va price of auditsignal precision ofto allcommitteeThe p its signal of partiescommittee firm value v publiclyreleasesreport f49 52. Figure 2: Overall bias as a function of manager penalties E ff y 0 .6 20 .6 1 v a r E f x , y v a r f 0 .6 00 .5 90 .5 80 .5 70 .5 60 .0 0 .2 0 .40 .6 0 .8 1 .0cm Figure 2 plots the proportion of the variance of the mangers forecast f that is due to bias. This graph uses the parameters v = x = y = d = 1, m = 3, = 0 and cd = 0.5 . These parameter values imply that the managers and audit committees combined information explains 80% of the variation in firm value and that the manager has three times more information than the audit committee. 50 53. Figure 3: Investor response to earnings as a function of the managerial penalty and the audit committee penalty0 .0 1 5 d p f d cd0 .0 1 0d p f0 .0 0 5d cm0 .0 0 0 6 8101214 cdCoefficient p f is the investor response to earnings; the manager penalty is cm ; and the audit committee penalty cd . This graph uses the parameters v = x = y = d = 1, m = 3, = 0 andcm = 0.5 . These parameter values imply that the managers and the audit committees combined information explains 80% of the variation in firm value and that the manager has three times more information than the audit committee. The audit committee penalty cd ranges from 10 to 30 times that of the penalty cm to the manager.51 54. Figure 4: Impact of the audit committees due diligence precision on the audit committees0 .4a report and the audit committees response to the managers reportP a n e l a a m m 0 .1d dm dd 0 .3ddd dm 0 .2 d p f dd ddd p f 0 .1 0 .0 0 .1 0 .2 0 .3 0 .40 .50 .6 0d 0 .1 0 .4b P anel b bm m 3 0 .3 0 .2 d dm dd ddd dm0 .1d p f dd ddd p f 0 .0 0 .1 0 .2 0 .3 0 .40 .50 .6 0d 0 .1 Figure 4 illustrates the elasticities of the price response p f to earnings and the coefficient m cov(v, rm | sd ) / var( rm | sd ) with respect to the audit committees due diligence precision d . The managers bias rx is increasing in d when the elasticity of p f with respect to d is greater than that of m . In panel a, where the precision m of the managers signal is 0.1, rx is increasing in d for d < 0.24 . In panel b, where m = 3 , there is no region in which rx is increasing in d . This graph uses the parameters v = x = y = 1, = 0 and cd = cm = 0.5 . 52 55. Figure 5: Audit committees ex ante payoff as a function of the committees due diligence information choice and penalty0 .8 604d12 3 4 1c d d 0 .5 2 3 cd d 5 4 5 Figure 5 illustrates the audit committees expected utility as a function of its signal precision d .The solid line depicts the function when the audit committees cost parameter cd = 0.5 and thedashed line depicts the function when cd = 5 . When cd = 0.5 , the audit committee will notcollect any information ( d = 0 ), but an increase in expected penalties induces the collection ofinformation. In this example, penalties slightly larger than cd = 1 induce the collection ofinformation and a penalty of cd = 5 induces the selection of precision d = 0.86 . This graph usesthe parameters v = x = y = 1, cm = 0.5, md = 0, m = 3, y = 2 and c( d ) = 0.25 d .2 53