Auditing, Reporting Bias and Market Valuation

Transcription

1 Auditing, Reporting Bias and Market Valuation D. Paul Newman McCombs School of Business University of Texas Evelyn R. Patterson Kelley School of Business Indiana University J. Reed Smith Kelley School of Business Indiana University April 015 Preliminary: Please do not quote.

2 Auditing, Reporting Bias and Market Valuation Abstract The fundamental qualitative aspects of useful financial information are relevance and faithful representation. Because management oversees many aspects of financial reporting such as revenue recognition and estimation, they have the ability to bias financial reports, which can reduce the usefulness of those reports. We consider a game that includes the market, a manager, and an auditor where the manager can engage in costly misreporting in order to increase the market value of the firm. However, the auditor has the ability to detect and deter such behavior, which also affects market valuation. As part of our analysis, we provide empirical implications related to the market s weighting on reported earnings, the auditor s report-contingent audit strategy, expected bias and the auditor s expected probability of detecting bias.

3 Auditing, Reporting Bias and Market Valuation 1. Introduction According to the Statement of Financial Accounting Concepts No. 8 (010) (SFAC8), the fundamental qualitative aspects of useful financial information are relevance and faithful representation. SFAC8 supersedes previous concept statements and is intended to provide a better framework for addressing the usefulness of accounting information. Because management oversees many aspects of financial reporting such as revenue recognition and estimation, they have the ability to bias financial reports. 1 Reporting bias can affect the faithful representation aspect of financial reports and in turn, their usefulness. Auditors, in determining which audit procedures to apply, are particularly sensitive to these characteristics of financial reporting and to the manager s incentives for biasing the report. The usefulness of financial reporting information not only depends on the inherent characteristics of the financial reporting framework but also on reporting bias and how the auditor might detect or deter such behavior. The purpose of this paper is to examine the linkage among auditing, reporting bias and the usefulness of financial reports as reflected by the market valuation of reported earnings. Fischer and Verrecchia (FV) (000), provide insight into the usefulness of the earnings report where a manager has the incentive to bias the report. They model the 1 Dechow, Ge and Shrand (010) (DGS) note that The second noteworthy feature of our definition of reported earnings is that reported earnings does not equal X (actual earnings) because an accounting system that measures an unobservable construct (X) inherently involves estimations and judgment, and thus has the potential for intentional bias. AU-C 00 Overall Objectives of the Independent Auditor and the Conduct of an Audit in Accordance With Generally Accepted Auditing Standards specifically notes that auditors should consider the effect of estimates, the business environment, complex transactions and management override in assessing the risk of material misstatement and the extent of audit procedures. Moreover, AU-C 40 Consideration of Fraud in a Financial Statement Audit states that the auditor should consider the manager s incentives in assessing the risk of intentional misstatement. 1

4 impact of financial reporting on market valuation where a manager has private information about his incentives to bias the earnings report as well as private information about earnings. FV illustrate how information about underlying earnings characteristics, coupled with the costs and benefits to the manager of biasing the earnings report, affects market valuation. Included in these incentives are costs associated with the discovery of management bias. However, in FV, the detection of bias is assumed to be exogenous. In this environment, the inclusion of a strategic auditor potentially plays a crucial role in determining the detection probability of bias and in the market valuation of the firm. As in FV, we examine a model in which the firm s market price is a linear function of reported earnings and where uncertainty exists about both earnings and the manager s incentives to misreport. The market s weighting of reported earnings measures the degree of association between the earnings report and the market value of the firm. An increase in the weighting indicates a stronger association and an increase in the usefulness of reported earnings. We examine the effects of adding a self-interested auditor to this setting. In our model, the auditor determines the extent of costly audit testing to perform after observing the manager s report. If the auditor detects reporting bias, the manager must restate the earnings report to its correct value. Overall, report-contingent auditing reduces the variability in the manager s report and increases the market s weighting on reported earnings. More specifically, we find that the market s weighting on reported earnings increases as the auditor s expected liability for a failed audit increases, strengthening the association between the market value of the firm and the earnings report. On the other hand, the market s weighting on reported earnings decreases as the cost of audit testing increases. Further, the market s

5 weighting on reported earnings increases as more becomes known about the manager s incentive to misreport because the market is better able to back out reporting bias. These results seem reasonably intuitive. By contrast, we also find that the market s weighting on reported earnings increases as the manager s benefit from bias increases and decreases as the manager s cost of biasing increases. Further, in some cases, expected bias may decrease while the weight on the earnings report also decreases. These less intuitive effects are due to a corresponding change in reporting variability and emphasize that the usefulness of reported earnings is not simply a function of a single reported number but also depends on other related information. 3 Moreover, our analysis examines the auditor s response to the manager s report. We find that as the auditor s expected liability for undetected bias increases, the auditor relies more on the earnings report in determining the amount of audit testing, while the opposite is true for an increase in the cost of auditing. Both the expected liability for undetected bias and the cost of auditing directly affect the extent of auditing, which in turn influences the manager s choice of reporting bias and the market s reaction to the earnings report. Thus, the auditor s reliance on the earnings report as well as the market s response to the earnings report increase in the auditor s expected liability and decrease in the cost of auditing. On the other hand, other changes in information related to the choices of reporting bias and market valuation have indirect effects on the auditor s choice of report-contingent auditing. For example, the auditor relies less on the earnings report as more becomes known about the manager s incentive to misreport. In this case, 3 See DGS for a discussion about how various aspects of the accounting system affect the usefulness of financial reporting. 3

6 the earnings report is not as informative about bias because just as the market is better able to back out bias, so is the auditor. Caskey, Nagar, and Petacchi (010) (CNP) also extend the FV model with an auditing component that is defined as the firm s audit committee. CNP assume a sequential process that produces the firm s report. First, the firm manager (as in FV) observes a noisy but unbiased signal of firm value. The manager produces a report that is an assertion of that value. Then, the audit committee combines the manager s report with an independent signal of firm value to produce a firm report. Both the manager and the audit committee benefit from a higher price for the firm and both incur costs of misstating their reports relative to the true, but unknown, firm value. Hence CNP assume that both the manager and the audit committee have incentives for bias and that the overall bias in the report results from the difference between the audit committee s report and the true firm value. However, the extent of auditing in CNP is independent of the manager s report. The audit function in the CNP model does not include an external auditor that can strategically detect and correct bias as we do. As a result, CNP is necessarily silent regarding the equilibrium effect of the manager s report on the extent of auditing. Our model focuses on the linkages among reporting, bias, and how much investigative work the auditor performs. Unlike previous studies, this focus allows us to suggest predictions about audit effort and audit costs in different reporting environments. In another related study, Dye and Sridhar (004) (DS) derive a linear pricing equilibrium, but in a setting where the owner in the first period sells the firm to an investor in the second period. In their model, DS consider two sources of information 4

7 that an accountant can aggregate to produce a financial statement report. One source is management s possibly biased assertion about the expected discounted cash flows of the firm. The other source is a noisy, but unbiased, representation of the discounted cash flows. The DS model retains many of the fundamental model features that are in FV. As with FV, the model in DS is characterized by a linear, rational expectations pricing function. In addition, both papers assume costly bias in the manager s payoff, though the form of this cost differs in the two papers. In FV, the effect of market price on the manager s payoff is private information but the manager incurs a known cost for bias in the report. On the other hand, in DS, the manager s misreporting cost is uncertain, but his benefit from overstatement is common knowledge. We adopt the DS assumptions regarding the manager s benefit from overstatement and misreporting cost. Our model also incorporates several important features found in the strategic auditing literature. Similar to Newman, Rhoades, and Smith (1996), Newman, Patterson, and Smith (001), and Patterson and Noel (003), the auditor in our model conditions his audit strategy on the manager s report, and the manager, in turn, chooses his report with this fact in mind. 4 Several additional papers, including Chan and Pae (1998), Newman, Patterson, and Smith (005), and Beyer and Sridhar (006), study the impact of the audit on the market valuation of the client firm. But because they do not consider an earnings report by management, they provide no basis for evaluating the importance of the earnings report in market valuation. We combine both of these features in our model to determine how auditing impacts both the manager s incentives to misreport and the market reaction 4 Other models, such as Newman and Noel (1989), Shibano (1990), Newman, Park, and Smith (1998), Hillegeist (1999), and Laux and Newman (010) either avoid the reporting issue altogether or assume a binary report. 5

8 to the manager s report. Hence, we can provide predictions about how the report impacts auditing and how auditing affects the market pricing of the firm. Empirical accounting research has examined many aspects of auditing and financial reporting quality where one quality measure used in these studies is the impact that the earnings report has on market valuation (see for example, Teoh and Wong 1993 and Liu and Thomas 000). They presume that as earnings quality increases the market s weighting on reported earnings increases. In addition, studies about audit quality assert that audit quality and the market s weighting on reported earnings are positively correlated. However, these studies provide no explanation about how and why these measures are related. Defond and Zhang (DZ) (014) suggest that financial reporting quality and audit quality are inextricably entwined and state that research would benefit from more conceptual guidance in disentangling the complex relation between audit quality and financial reporting quality. In this paper, we attempt to provide conceptual guidance about the drivers of the market s weighting of reported earnings in valuing the firm, which in turn is often used as an indicator of financial and audit quality in empirical studies. The remainder of this paper is organized as follows. In section, we describe the model. We derive our equilibrium results in section 3, provide a comparative analysis in section 4, and discuss the empirical implications of our analysis in section 5. Finally, in section 5, we provide concluding remarks.. Model We begin by assuming that the firm realizes earnings π that are normally distributed with mean µ π and variance σ π. Subsequent to privately observing π, management issues an earning report ˆr. We follow FV by conjecturing that the market 6

9 price of equity P is a linear function of management s reported earnings ˆr and then showing that the linear conjecture is satisfied in equilibrium. The market values the firm at the expected value of earnings π given ˆr or P( ˆr ) = E( π ˆr ) = β ˆr + α (1) where β measures the degree of association between market price and the earnings report. In the presence of an audit, we assume that if the auditor detects bias in the report, the report is restated to the correct earnings π and the market prices the firm at π. 5 If the auditor does not detect bias, then the bias is included in the final report and the market prices the firm according to (1). Next we describe the payoffs and strategies of the manager and auditor. The manager obtains a benefit proportionate to the market price of equity τ P where the scaling parameter τ is common knowledge. τ depends on the manager s equity holdings in the firm or compensation arrangements such as stock options, stock appreciation rights, restricted stock and stock award plans. Because the market price is E( π ˆr ) if no bias is detected and π if bias is detected, the manager s total expected benefit from reported earnings is τ ( 1 δ )E π ˆr probability of detecting bias. ( + δπ ) where δ is the auditor s The manager also incurs a reporting cost of q ( ˆr π ε ) where ε represents the manager s type, is privately known to the manager, and is distributed normally with 5 We assume that if the audit detects bias, earnings are restated and this restatement is publicly observable. 7

10 mean µ ε and variance σ ε. 6 The manager s type ε serves to influence bias ( ˆr π ) by mitigating the cost of bias for higher values of ε. 7 The parameter q measures the costs associated with overriding internal control, legal penalties and loss of reputation while ε represents the unknown sensitivity to those costs. The manager observes true earnings π, his private information ε and then issues a report ˆr. As a result, the manager s expected payoff is 8 ( + δπ ) q ˆr π ε M = τ ( 1 δ )E π ˆr. () We conjecture that the manager s reporting strategy is linear in true earnings π and his type ε. ˆr = b m π + c m ε + a m (3) We assume that the auditor earns a fixed, pre-determined fee. Hence, we are concerned only with the auditor s expected costs. The auditor observes the report ˆr and chooses the probability of detecting bias δ. We focus on overstatements so that the auditor s expected penalty is L( ˆr E( π ˆr )) whenever bias goes undetected where the legal liability parameter L reflects the auditor s litigation or regulatory environment. In addition, the auditor incurs a cost of k δ for choosing detection probability δ where the 6 There are many ways that the manager s private information and reporting cost might be modeled. FV model the manager s private information as the multiplier on market price, but assume that the cost of bias is known. In the model with auditing, no linear pricing equilibrium exists with the FV structure. Our model of misreporting cost is consistent with DS, who also model the manager s cost of biasing the report as uncertain. 7 We assume, for simplicity, that µ ε > 0, which implies that the manager is more inclined to overstate. 8 We model the manager s expected payoff without the manager s cost of reporting bias being dependent on auditor detection. This allows us to consider only linear equilibria, but does not eliminate the strategic tension between the auditor and the manager. ( 1 δ )E( π ˆr ) + δπ provides the strategic tension in our model, which is consistent with previous strategic audit studies such as Hillegeist (1999) and Newman, Rhoades and Smith (1996). 8

11 cost parameter k represents the costliness of the audit environment. For example, a larger k could be due to a more complex client firm environment, a smaller audit firm, or less familiarity with the client s industry. As a result, the auditor s total expected costs are A = ( 1 δ )L ˆr E π ˆr ( ) + k δ (4) where the auditor chooses δ to minimize these expected costs. We also conjecture that the auditor chooses a linear strategy in the report or δ ( ˆr ) = b A ˆr + a A. (5) The equilibrium is therefore defined by the vector ( α,β,a m,b m,c m,a A,b A ) such that: the market condition (1) is satisfied as an equality, the manager s choices of ( a m,b m,c m ) in (3) maximize his payoff in () with respect to ˆr and the auditor s choices of ( a A,b A ) in (5) minimize his costs in (4) with respect to δ. Because the manager chooses his report prior to the auditor s detection strategy and because the market price is determined after the audit, backward induction conditions must be satisfied, as well. 3. Equilibrium Analysis Because the reporting, audit and pricing decisions are sequential, we first solve for market price because that is the final choice of the game. This is followed by the auditor s choice of detection probability and then the manager s reporting decision. In the event that the auditor detects and eliminates bias, the market knows that the restated report ˆr = π is correct and values the stock accordingly. In the event that the auditor has not detected bias, the market adjusts for the expected bias in determining the market price. Of course, even though some bias remains in the report, auditing acts as a 9

12 deterrent. The market price, in this case, is the expected value of earnings given the report. Cov π, ˆr P( ˆr ) = E( π ˆr ) = E( π ) + ( ˆr E( ˆr )) (6) Var( ˆr ) This expression represents the Bayesian updated expectation of earnings given the manager s report. Using conditions (3) and (6), we obtain the following expression for the market price as a function of the manager s choice parameters. P( ˆr ) = b m σ π b m σ π + c m σ ˆr + µ π ε b m σ π b m σ π + c m σ ε b m µ π + c m µ ε + a m (7) Expression (7) can be rewritten in the form required by equation (1), P( ˆr ) = β ˆr + α where β = b m σ π b m σ π + c m σ ε, (8) b α = µ π m σ π b m σ π + c m σ ε b m µ π + c m µ ε + a m (9) and the values of b m, c m and a m are determined in equilibrium. Given the manager s choices of b m, c m and a m, the auditor chooses δ to minimize the cost in expression (4). The auditor s first order condition for δ is equal to L( ˆr E( π ˆr )) + kδ = 0, (10) which implies that δ = L k ( ˆr E ( π ˆr )). (11) Recall that E( π ˆr ) = P( ˆr ) = β ˆr + α, where β and α are given by (8) and (9) respectively. As a result, (11) can be expressed as 10

13 δ ( ˆr ) = b A ˆr + a A (1) where b A = L k 1 b m σ π b m σ π + c m σ ε and (13) a A = L k µ b π + m σ π b m σ π + c m σ ε b m µ π + c m µ ε + a m. (14) Finally we derive the manager s choices of b m, c m and a m. The manager s payoff in () is maximized by his choice of ˆr given the equilibrium reactions of the auditor and the market. The manager s first order condition for ˆr is equal to ˆr ( q + b A βτ ) + q + b A τ From (15), π + qε + (( 1 a A )β b A α )τ = 0. (15) ( ˆr = q + b Aτ )π + qε + (( 1 a A )β b A α )τ q + b A βτ (16) Rewriting expression (16) we have ˆr = b m π + c m ε + a m (17) where b m = c m = q + b Aτ q + b A βτ, (18) q q + b A βτ and (19) (( a m = 1 a A )β b A α )τ q + b A βτ (0) 11

14 Combining (1), (8), (9), (1), (13), (14), (17), (18), (19) and (0), we obtain the equilibrium described in Proposition 1. For simplicity, we substitute γ = σ π σ π + σ ε where γ measures the relative uncertainty of earnings π to the manager s private information ε. 9 Proposition 1: The equilibrium strategies for the manager, the auditor and the market are as follows; Manager: ˆr = b m π + c m ε + a m Auditor: Market: δ ( ˆr ) = b A ˆr + a A P( ˆr ) = β ˆr + α if no detection occurs and π if detection occurs. where b m = (All proofs are in the appendix) q + b A τ q + b A βτ, c m = q ( q + b A βτ, a = a 1 β A + β )τ, m q + b A βτ b A = L k 1 qγ q + b Aτ q b A γτ, a A = L k ( 1 β )µ π + β k qµ ε + βτ kq + Lβτ, β = qγ ( q + b Aτ ) and α = 1 β q b A γτ µ β k qµ + βτ ε. π kq + Lβτ Note that if b A is unique, then β is unique and each strategy is also uniquely defined. Corollary 1 proves that while b A = L k 1 qγ q + b Aτ q b A γτ is a cubic function of b, only A one of three solutions results in b A > 0 and β > 0, which we require. Further, similar to 9 This also measures the uncertainty of earnings relative to the total uncertainty of earnings plus the manager s payoff-type, but we describe this measure more intuitively as the relative uncertainty of earnings π to the manager s private information ε. 1

15 FV, we assume that the mean of µ ε is sufficiently large and that the variances σ π and σ ε are such to maintain positive bias and audit effort in equilibrium with high probability. Finally, we require k > Lµ ε +υ where υ is a constant such that that δ < 1 with high probability. 10 We first discuss some of the characteristics of the equilibrium values for b A, b m, β and c m. These four values relate to the equilibrium weightings of ˆr, π and ε in the manager s strategy, the auditor s strategy and the market pricing function. We present these results as a corollary to Proposition 1. Corollary 1: Given the equilibrium described in Proposition 1, we have the following: 1. The market s multiplier β on reported earnings ˆr lies between 0 and 1, approaches 1 as γ = σ π σ π + σ ε approaches 1 and approaches 0 as γ approaches 0.. The auditor s multiplier b A on reported earnings ˆr lies between 0 and L k, approaches 0 as γ approaches 1 and approaches L k as γ approaches The manager s multiplier b m on observed earnings π is strictly positive and convex in γ, approaches 1 as γ approaches 1 and 10 These expressions could be stated in closed form, but their complexity would add more confusion than intuition. Thus for simplicity we express the equilibrium implicitly. 13

16 approaches 1+ Lτ kq as γ approaches 0 4. The manager s multiplier c m on his payoff-type ε is strictly positive and convex in γ, approaches 1 as γ approaches 1 and approaches 1 as γ approaches 0. Corollary 1 highlights the reasonableness of the equilibrium results and helps to demonstrate the role of auditing on the market s weighting ( β ) of reported earnings for extreme values of γ. Note that γ approaches zero when the variance of earnings σ π is very small relative to variance of the manager s misreporting type σ ε. In this case, the market puts little weight on the manager s report while the auditor puts maximum weight on the manager s report in choosing the probability of detection. The auditor emphasizes the use of the report in choosing audit procedures when relatively little is known about the manager s incentives. The manager also maximally weights observed earnings and his payoff-type in choosing the amount of overstatement. In the opposite situation in which γ approaches 1, σ ε is small compared to σ π. As a result, the market knows a great deal about the manager s incentive for misreporting, anticipates the amount of reporting bias and prices shares correctly by backing out the manager s bias. Auditing adds little information about firm value and the auditor finds the report less useful in determining the amount of auditing. In this case the auditor uses a fixed amount of auditing equal to expected bias times L/k. The market does not need restated earnings to know true earnings but the auditor requires evidence to propose an audit adjustment to the manager. 14

17 4. Comparative Analysis To better understand how the addition of a strategic auditor affects our comparative analyses, we first consider a benchmark case in which the level of auditing is fixed (or, equivalently, a setting in which the auditor selects the level of auditing without considering the manager's report). 4.1 Benchmark comparative analysis equal to In the case where the audtor fixes audit effort at level δ, the manager s report is τγ 1 δ ˆr = π + ε + q q τγ 1 δ EB = µ ε +. where β = γ and expected bias is equal to When δ is fixed and b A is necessarily equal to zero, Proposition presents a comparative analysis of the primary equilibrium values. Proposition : When audit effort is fixed exogenously the following holds. 1. The market s weighting on reported earnings β a. increases as relatively more is known about the manager s payoff-type (σ π increases or σ ε decreases), b. is unaffected by all other parameter changes.. The manager s expected bias EB a. increases in the manager s expected payoff-type µ ε, b. increases in the manager s benefit multiplier τ, c. increases as relatively more is known about the manager s payoff-type 15

18 (σ π increases or σ ε decreases), d. decreases as audit effort δ increases, and e. decreases in q. These results are fairly intuitive. When the variance of the manager s payoff-type decreases, the market relies more on reported earnings than µ π in assessing firm value and the market s weighting on reported earnings increases. At the same time expected bias EB increases because the manager knows that market valuation is more sensitive to ˆr. When the manager s benefit multiplier τ and expected payoff-type µ ε increase, the manager s incentive to increase bias increases and thus, EB increases. Likewise when the cost of biasing q increases, bias becomes more costly and EB decreases. Finally, if audit effort δ increases, the manager anticipates a higher detection rate and EB decreases. Thus, EB increases in the auditor s probability of non-detection ( 1 δ ). The above results also hold when we allow the auditor to behave strategically without the benefit of relying on the report to determine his audit effort. 11 In this case, audit effort increases in the liability multiplier L and decreases in the cost multiplier for audit effort k. As expected, these results, in turn affect EB, where EB increases in k and decreases in L. Moreover, audit effort decreases in q and increases in τ, while also increasing as relatively more becomes known about the manager s payoff-type. The important feature of our benchmark setting is that β is only affected by the market s uncertainty about the manager s incentives to misreport relative to uncertainty 11 In this case, EB = k( qµ + γτ ) ε kq + Lγτ and δ = L qµ + γτ ε. kq + Lγτ 16

19 about the underlying earnings. None of the auditor s or manager s incentive parameters affect the market s weighting on reported earnings. As we show in the next section, introducing a strategic auditor who responds to the manager s report yields quite different results. 4. Preliminaries Next we consider how changes in the underlying parameters affect the primary equilibrium values in our model. These include: (1) the weighting on reported earnings β, () the expected equilibrium bias, (3) the auditor s report-contingent effort choice b A, and (4) the expected probability of the auditor detecting bias. For ease of exposition, we also refer to the expected probability of detecting bias as expected audit effort. As expected audit effort increases, the expected probability of detecting bias also increases. In our analysis we consider how our model parameters affect these equilibrium values. While bias and audit effort depend upon realizations of π and ε, we can compute the ex ante expected amount of bias and audit effort, in equilibrium, for a given set of parameters. Expected equilibrium bias, denoted EB, is equal to EB = E( ˆr ) µ π = ( b m 1)µ π + c m µ ε + a m. (1) Substituting for the equilibrium values of b m, c m and a m from Proposition 1 and simplifying, we obtain the following equilibrium expression for expected bias. 1 EB = k ( qµ ε + βτ ) kq + Lβτ () To compute expected audit effort, we observe from Proposition 1 and expression () that 1 A detailed derivation of EB is shown in the appendix as part of the proof to Proposition 1. 17

20 E( δ ) = L k (( 1 β )E( ˆr ) ( 1 β )µ π + β EB) (3) From (1) we get EB + µ π = E( ˆr ) to obtain = L k EB = L ( qµ ε + βτ ) E δ kq + Lβτ (4) earnings, β. We begin our comparative analysis with the market s weighting on reported 4.3 The market s weighting on reported earnings, β. Empiricists often regress stock price on reported earnings to infer its strength of association with market value where the degree of assoication is measured by the slope coefficient β. Our model offers predictions concerning empirical estimates of β based on changes in the underlying parameters when auditing is explicitly considered in market valuation. When the market knows the manager s type (σ ε = 0 ), β is constant and equal to one. In this case the market knows the amount of reporting bias is equal to EB = k ( qµ + τ ε ) = α and adjusts price P by backing out the bias. Reported earnings kq + Lτ allows the market to perfectly infer true earnings π. However, as in FV, we assume that there is uncertainty regarding the manager's reporting objective or σ ε > 0. As a result the earnings report becomes a noisy signal of true earnings and the slope coefficient varies with respect to various model parameters. These variations are presented in Proposition 3. 18

21 Proposition 3: The market s weighting on reported earnings, β 1. is unaffected by changes in expected earnings µ π,. is unaffected by changes in the manager s expected payoff-type µ ε, 3. increases as relatively more is known about the manager s payoff-type (σ π increases or σ ε decreases), 4. increases in the manager s benefit multiplier on price τ, 5. decreases in the manager s cost multiplier on bias q, 6. increases in the auditor s liability multiplier L, and 7. decreases in the auditor s cost multiplier on effort k. First, note that by contrast to our benchmark case, b A (see Proposition 5) is affected by incentive parameters of both the manager and the auditor when the auditor adjusts his strategy in response to the manager s report. Further, given uncertainty about the manager s incentives ( γ < 1), β = γ when there is no report-contingent auditing or b A = 0 and β > γ, when we add an auditor with report-contingent auditing or b A > 0. This result is intuitive but non-trivial. With auditing, the manager s report is more meaningful because auditing effectively reduces some of the uncertainty associated with the manager s private information about his payoff-type. As a result, the market s weighting on reported earnings increases when we add an auditor who uses a reportcontingent strategy and by contrast to Proposition, β is now affected by more than just a change in γ. The market price P is based on an updated expectation of earnings conditional on the earnings report. This conditional expectation is a linear combination of the earnings 19

22 expectation µ π and the report ˆr. The β coefficient associates the variation in market price relative to reported earnings and thus, β is independent of µ π and µ ε. Variances σ π and σ ε represent the degree of uncertainty that exists about earnings and the manager s payoff-type. In our model, all that matters is the relative degree of uncertainty, which is measured by γ = σ π σ π + σ. As γ increases, either σ π ε increases or σ ε decreases and relatively more becomes known about the manager s payoff-type than true earnings. As relatively more is known about the manager s payofftype, the market s weight on reported earnings increases because the market can better anticipate and take into account the amount of bias in estimating the amount of earnings. As τ increases, the manager s expected benefit from biasing the report increases while the dominant effect is that the variability in reported earnings decreases. Increases in τ dampen the effects of increases in q. As the manager s cost multiplier on bias q increases, the dominant effect is again an increase in the variability of the manager s report and β decreases. Overall, reportcontingent auditing ( b A > 0) decreases the noise in reported earnings associated with the manager s payoff-type. However, increasing the manager s cost-multiplier for bias increases the noise in the report and dominates any incremental reductions associated with b A. The change in β relative to q can be expressed as dβ dq = β db A b A dq + β q. As q increases, it directly decreases β by β < 0 and indirectly increases β by q 0

23 β db A β > 0 where > 0 and db A b A dq b A dq > As q becomes very large, β approaches its minimum value γ because β q dominates the overall change in β (see Figure 1). Consequently, government regulations, such as SOX, that impose severe penalties on managers for biasing reports have the potential effect of undoing beneficial gains from auditing. The relation between q and β is different from that found in FV. They find that if the cost multiplier on the manager s penalty for bias increases, then the market s weighting on reported earnings or β increases. The difference is due to our modeling assumptions. FV assume that there is no auditing and that the manager s payoff-type is defined by a multiplier on price P. We assume, as in DS, that the manager s payoff-type affects his penalty from bias. When there is no report-contingent auditing (or the audit level is determined and fixed ex ante) in our model, a change in q has no effect on the manager s earnings-contingent reporting strategy and thus has no effect on β. When we add report-contingent auditing (b A > 0), an increase in the penalty cost multiplier q decreases the market s weighting on reported earnings. Overall, the market s weighting on reported earnings increases when the auditor chooses effort based on the report, which concurrently results in β being sensitive to changes in q. As the cost of biasing increases, the manager s expected payoff decreases for a given report and the manager is less inclined to bias on average. However, the incentive to bias depends not only on q but also on the random outcome of the manager s 13 See Proposition 5, where we show that b A increases in q. 1

24 payoff-type ε. Thus, increasing q decreases the incentive to bias but also increases the variability of the report because it is included in the multiplier on payoff-type, and the market has a harder time in predicting the amount of reporting bias. As a result β decreases in q. An increase in the auditor s legal liability cost multiplier L results in an increase in β. As the auditor is penalized more heavily for non-detection of reporting misstatements, the auditor s incentive to increase his detection probability increases, which is reflected in greater market confidence for reported earnings. The increase in L decreases the noise associated with the uncertainty of the manager s payoff-type. 14 dβ dl = β db A b A dl > 0 Note that L affects β indirectly by increasing the report-contingent auditing multiplier b A. A change in the auditor s cost multiplier k has the opposite effect. This is contrary to case of fixed auditing (Proposition ) where a change in L has no effect on β. Reportcontingent auditing results in increasing the market s weighting on reported earnings through an increase in b A based on an increase in L. 4.4 The manager s expected bias Next we consider how the manager s expected bias EB is affected by various parameter changes. These are included in Proposition Proposition 4: The managers expected bias EB: 1. is unaffected by changes in expected earnings µ π, 14 See Proposition 4 where we show that b A increases in L. 15 While γ > 1/ is a sufficient condition for our proofs of deb/dl < 0 and deb/dk > 0, we can find no numerical examples where deb/dl > 0 or deb/dk < 0.

25 . increases in the manager s expected payoff-type µ ε, 3. Increases as relatively more is known about the manager s payoff type (σ π increases or σ ε decreases), 4. increases in the manager s benefit multiplier on price τ, 5. decreases in the manager s cost multiplier on bias q, 6. decreases in the auditor s liability cost multiplier L when γ > 1/, and 7. increases in the auditor s cost multiplier k when γ > 1/. Expected bias EB is a function of the difference between expected reported earnings and expected earnings. Thus, it depends on the manager s expected payoff-type µ ε and not expected earnings µ π. Expected bias increases in µ ε because as µ ε increases, the manager has a greater incentive to bias the report. Expected bias also increases when relatively more is known about the manager s payoff-type. The market can better anticipate bias and the manager increases EB to compensate for potentially negative changes in market price. When τ increases the manager s benefits from an increase in bias and expected bias increases. Expected bias also decreases in the manager s cost multiplier q because biasing becomes more costly. An increase in the auditor s liability multiplier L decreases expected bias while an increase in the auditor s effort cost k decreases expected bias. The change in expected bias is the manager s reaction to a change in audit effort where audit effort increases in L but decreases in k (see Proposition 6). Expected bias EB and β change in the same direction when auditing is fixed (Proposition ). Only when we add a report-contingent auditor (Propositions 3 and 4), 3

26 do we have instances of β increasing while expected bias EB decreases. As the auditor s expected liability L increases or k decreases, the market s weighting on reported earnings increases and expected bias EB decreases. 4.5 The auditors choice of report-contingent audit effort and expected audit effort To get a better understanding of how the auditor s choice of report-contingent effort b A and expected audit effort E( δ ) affect the auditor s overall effort choice, we begin by reviewing his effort function δ ( ˆr ). From Proposition 1, we know that audit effort is a linear function of the manager s report ˆr or δ ( ˆr ) = b A ˆr + a A. We also know from Proposition 1 that audit effort can be written as δ ( ˆr ) = L k (( 1 β )( ˆr µ π ) + β EB) = b A ( ˆr µ π ) + β E( δ ). (5) Without benefit of having seen the client s reported numbers, the auditor can make a preliminary choice of audit effort represented by β E( δ ). This amount of audit effort is based on factors such as the prior year audit and the current year assessments of internal control, both of which provide information about the expected amount of bias. Once the manager has a report for the auditor to observe, the auditor adjusts his audit effort based on the report. For example, the auditor would interpret higher reported earnings compared to his expectation of earnings (or( ˆr µ π )) as indicative of a higher risk of an earnings overstatement, resulting in an increase in audit effort based on the report. On the other hand, higher values of β for fixed L and k also imply that the report 4

27 is a better indicator of earnings, thereby lessening the possibility of overstatement associated with a higher report and reducing audit effort. For fixed L and k, as the market s weighting on reported earnings increases, the less relevant the earnings report is in determining audit effort. In such cases, the auditor relies more on expected bias in determining audit effort. In the limit, when β = 1, the auditor employs a non-report-contingent audit strategy and when β = 0, the auditor uses the difference between reported earnings and µ π times L/k in determining his audit strategy. 16 Based on expression (5), we see the relative importance of the auditor s reportcontingent strategy b A and expected audit effort E( δ ) in determining the auditor s effort choice. Proposition 5 focuses on changes in b A with respect to changes in our game parameters and Proposition 6 examines changes in E( δ ). Proposition 5: The auditor s choice of report-contingent audit effort, b A 1. is unaffected by changes in expected earnings µ π,. is unaffected by changes in the manager s expected payoff-type µ ε, 3. decreases as relatively more is known about the manager s payoff (σ π increases or σ ε decreases), 4. decreases in the manager s benefit multiplier on price τ, 5. increases in the manager s cost multiplier on bias q, 6. increases in the auditor liability multiplier L, and 16 In equilibrium, β is never equal to 0 or 1. 5

28 7. decreases in the auditor s cost multiplier on audit effort, k. Changes in b A due to changes in µ π,µ ε,q,τ,σ π and σ ε follow directly from Proposition 3, because we know that b A = L ( k 1 β ). Any parameter change not involving L or k has opposite effects on b A versus β. As the market s weighting on reported earnings increases, it is less influential on audit effort because an increase in ˆr is associated less with changes in bias. Thus, as relatively more is known about the manager s payoff-type, the auditor relies less on reported earnings in choosing his audit effort. Similarly, as the manager s benefit multiplier τ increases (or, equivalently, the cost multiplier q decreases), the auditor relies less on the report (as expected bias (Proposition 4) and expected audit effort decreases (Proposition 6)). L and k are the only parameter changes resulting in the same directional changes for both β and b A. Below we demonstrate how b A increases in L. db A dl = b A L + b A dβ β dl = 1 ( k 1 β ) L dβ k dl > 0 where the positive direct effect of an increase in L dominates the indirect negative effect of an increase in β due to an increase in L. There is an increase in report-contingent auditing but the increase is lessened by the increase in the market s weighting on reported earnings. In a similar fashion, as auditor efficiency decreases ( k increases), the amount of report-contingent auditing decreases. Proposition 6 addresses the changes in E( δ ). Proposition 6: The auditor s expected audit effort E( δ ) : 6

29 1. is unaffected by changes in expected earnings µ π ;. increases in the manager s expected payoff-type µ ε, 3. increases as relatively more is known about the manager s payoff type (σ π increases or σ ε decreases), 4. increases in the manager s benefit multiplier on priceτ, 5. decreases in the manager s cost multiplier on bias q, 6. increases in the auditor s liability cost multiplier L, and 7. decreases in the auditor s cost multiplier on effort k. The auditor s expected audit effort E( δ ) is equal to L EB and consequently changes in k expected audit effort are the same as those for EB when L and k are fixed. E( δ ) decreases in the manager s cost multiplier q and corresponds to a decrease in EB. The manager reduces EB with higher costs associated with bias, and the auditor responds to the reduction with a decrease in E( δ ). Likewise, as relatively more is known about the manager s payoff-type, EB increases and the auditor responds by increasing E( δ ). Note that despite the effects of EB on market price, the auditor and manager play a sub-game where the auditor would like to avoid costly undetected bias. For changes in E( δ ) with respect to L, E( δ ) and EB change in opposite directions. We have de( δ ) dl = d L k EB dl = EB k + L deb k dl > 0. 7

30 Despite expected bias decreasing in the auditor liability multiplier, the auditor increases expected audit effort because it directly affects his expected payoff. In this case the manager reacts to the auditor s increase in expected effort by decreasing expected bias when γ > 1/. 17 The amount of increase in expected audit effort is lessened by the associated decrease in expected bias times L/k and increased by the amount of expected bias times 1/k. For decreases in audit efficiency (increases in k), the opposite is true. 5. Empirical Implications and Applications In this section we provide some intuition about how the comparative statics in Propositions 3 through 6 might be applied to empirical studies. The drivers of change in these propositions include k, L, σ π, σ ε,µ ε, τ and q. The auditor s cost of effort k is often linked to audit quality because, in most studies, k is inversely related to audit effort, which in turn is positively correlated to the probability of detecting and correcting misstatements. 18 More broadly, k is a technology factor that is related to audit efficiency and effectiveness. 19 As k increases, a given level of detection probability is more expensive to employ. Thus, k decreases in auditor independence because audit procedures are less effective and k is smaller for larger audit firms because they have more resources, which is likely to result in a more efficient audit technology. In addition, if audit tenure improves audit effectiveness, then tenure should also be linked to a decrease in k. 0 On the other hand, audit tenure may be associated 17 While γ > 1/ is a sufficient condition and our proof of deb/dl < 0 requires this condition, we can find no numerical examples where deb/dl > See for example, Newman and Noel (1989), Newman, Patterson, and Smith (001), and Newman, Patterson, and Smith (005), among others. 19 Effectiveness is either due to the nature of the audit procedure itself or the person applying the procedure. 0 See Myers, Myers, and Omer (003) and Johnson, et. al (00) who provide evidence that longer audit tenure reduces the cost of auditing. Beck and Wu (006) provide a theoretical explanation for this decrease in costs. 8

31 with declining independence when the auditor has engaged in low-balling or is attempting to retain a client for non-audit service fees. Thus, based on our analysis we would predict that as auditor independence declines, the market s weight on reported earnings decreases, the amount of report-contingent auditing decreases, expected bias increases and expected audit effort decreases. 1 We would make the same predictions for smaller audit firms verses larger audit firms. We designate the auditor s expected litigation costs for an audit failure as L. Our predictions related to L are consistent with several empirical studies. First, large national audit firms have larger litigation costs and deeper pockets. Thus, large firms have both smaller k and larger L, which implies that larger audit firms are associated with an increase in the market s weighting on reported earnings (for example, see Teoh and Wong (1993)). Second, several empirical studies have investigated how varying litigation environments across countries affect the quality of reported earnings. DeFond, Hung, Trezevant (007) document that stronger investor protection increases the market s reaction to earnings (higher L). Leuz, Nanda and Wysocki (003) suggest that controlling shareholders have incentives to hide firm performance in order to maintain their control benefits. They find evidence that earnings quality is positively correlated with the level of investor protection across countries. However, they cannot rule out 1 See Gul, Tsui, and Dhaliwal (006) (GTD) who study the effect of non-audit services (NAS) on the market s weighting of reported earnings. They find that, overall, there is a negative effect of NAS on the market s weighting of reported earnings because, based on their hypothesis, NAS result in less auditor independence but the negative effect is weaker for Big 6 auditors. There are two possible effects associated with NAS. They may provide scope economies for the auditor (reduce k) while also impairing independence (increase k) or diverting the auditor s attention away from fundamental audit tasks. GTD imply that the net effect of NAS is to lessen the audit s effectiveness but the effect is less for bigger audit firms. See Teoh and Wong (1993) who find that the market s weighting on reported earnings is larger for larger audit firms. 9

32 other institutional factors that may correlate with investor protection and drive their results. For example, there may be less consensus about ethical norms regarding reporting bias where σ ε is negatively correlated to the size of L. Countries with higher levels of investor protection may also have more common agreement on the personal costs of bias. Francis and Wang (010) posit that legal environments alone do not determine earnings quality. Rather, earnings quality depends both on the legal environment and audit quality. Their data suggest that the level of investor protection has no impact on earnings quality if the auditor is low quality. Rather investor protection is meaningful only if the auditor is a high quality auditor. This result is understandable if k is sufficiently large (low audit quality) so as to mute the effects of L (higher for better investor protection). In our model, the market s weight on reported earnings increases in the parameter combination L/k. With regard to σ π / σ ( π +σ ε ) = γ, we predict that the market s weighting on reported earnings increases in γ. Collins and DeAngelo (1990) find that during a proxy contest, the market is more responsive to earnings. Dechow, et. al (010) note on page 370 that: This finding rejects one proposed hypothesis, which is that earnings during this period are less precise because they are likely to be opportunistically managed, in which case the ERC should be lower. Rather, they interpret their finding as evidence that a proxy contest is a period of heightened uncertainty and that the earnings number is especially useful for valuation. This evidence suggests that ERCs as a proxy for earnings quality may be specific to an event-period. Our model helps interpret this effect. As γ increases due to an increase in σ π, the market has better information about management incentives than they do about earnings and are more able to undo any anticipated bias in reported earnings. Thus, while the 30