weber - 1998 - auditor rotation and retention rules - a theoretical analysis

139 3.4.3 Expected Second Period Fraud Detection Probability in the Deregulated Audit Market...142 3.4.4 Efficiency and Cost Effectiveness o f Rotation / Retention Rules 150 3.5 Summary

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Auditor Rotation and Retention Rules:

A Theoretical Analysis

A DISSERTATION

SUBMITTED TO THE GRADUATE SCHOOL

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

for the degree

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Auditor Rotation and Retention Rules:

A Theoretical Analysis

Eric C Weber Adviser: Professor Ronald A Dye

This dissertation examines the consequences o f restricting firms’ freedom in replacing their auditors While U.S.-based firms can replace their auditors whenever they choose to do so, subject to their shareholders’ approval, many western European countries impose limitations on auditor replacement, and critics o f the audit profession have proposed similar restrictions on U.S.-based firms These restrictions take the form

o f either mandatory rotation or mandatory retention of an auditor for designated time intervals Proponents o f the rules claim that such rules will increase audit quality, while opponents o f the rules assert that the rules will decrease audit quality and increase audit costs

The analytical models in this dissertation address how such rules affect the quality and price o f audit services The dissertation demonstrates that the relative performance o f audit markets with these rules in place relative to laissez faire depends upon whether audit clients can, in the laissez faire regime, credibly threaten to replace their auditor

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demonstrates circumstances under which, when such threats are credible, switching to either a mandatory rotation or mandatory retention regime results in some improvements

In some cases, the dissertation demonstrates that audits o f fixed duration (which entail

both mandatory retention and mandatory rotation) can maximize audit quality, albeit at a

potential increase in audit switching costs However, economic settings in which audits

o f regulated duration uniformly improve the performance o f the audit function are demonstrated to be quite limited, since voluntary resignations and/or replacements of auditors are themselves informative about a client firm’s financial condition Required rotation, or required retention, o f an auditor may result in the suppression o f this source

o f information about a client

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I would like to thank the members o f my dissertation committee for their support and guidance throughout the entire process o f this work: Ronald A Dye (chairman), Larry Jones, Robert P Magee, and Sri Sridharan.

I also thank my fellow doctoral students at Northwestern University, with whom I have spent not only many hours o f work, but also unforgettable moments o f friendship

Finally, I would like to dedicate this dissertation to my family: Maria, Yvonne, Irene, Rafael, and Ana Maria Thank you for your support and never-ending patience

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1 Introduction 1

2 Mandatory Rotation/Retention Rules and Audit Quality 14

2.1 Model Description 14

2.1.1 Use and Consequences o f the Auditor’s Report 18

2.2 Infinite Horizon Model without Retention/Rotation Regulation 20

2.2.1 Model without Credible Threat to Replace Auditors that Report Fraud 20

2.2.2 Model with a Credible Threat to Replace Auditors that Report Fraud 24

2.2.3 Conditions under which the Replacement Threat is Credible 27

2.2.4 Government Preference Ordering 30

2.3 Infinite Horizon Model with Retention/Rotation Regulation 3 5 2.3.1 Two-Period Mandatory Retention Case 36

2.3.2 Two-Period Mandatory Rotation Case 41

2.3.3 Two-Period Mandatory Retention and Rotation 45

2.4 Summary and Discussion o f Chapter 2 48

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Efficiency o f Rotation / Retention Rules 51

3.1 Model Description 5 1 3.1.1 Characterization o f Client Firms 51

3.1.2 Characterization o f Auditors 55

3.1.3 Characterization o f the Audit Technology 60

3.1.4 Characterization o f the Go vermnent 63

3.1.5 Second Period Events 69

3.2 Case I: Fraud is Detected in Period One 74

3.2.1 Second Period Client Programs for Case 1 77

3.2.2 Successor Auditor Second-period Bid 80

3.2.3 Incumbent’s Response 83

3.2.4 Client Opinion Shopping versus Incumbent Resignation 92

3.3 Case II: No Fraud is Detected in Period One 102

3.3.1 Auditor’s Beliefs Regarding Fraudulent Clients in Period Two 103

3.3.2 Second Period Client Programs for Case II 106

3.3.3 Successor Auditor Second-period Bid 108

3.3.4 Incumbent’s Response 108

3.3.5 Client Opinion Shopping vs Incumbent Resignation in Case II 125

3.3.6 Client Opinion Shopping versus Incumbent Resignation: Comparison across Cases 131

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3.4.1 Mandatory Rotation Rules 136

3.4.2 Mandatory Retention Rules 139

3.4.3 Expected Second Period Fraud Detection Probability in the Deregulated Audit Market 142

3.4.4 Efficiency and Cost Effectiveness o f Rotation / Retention Rules 150 3.5 Summary and Discussion o f Chapter 3 158

References 161

Appendix A: Proofs of Lemmas and Propositions of Chapter 2 169

Appendix B: Proofs of Lemmas and Propositions of Chapter 3 196

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3.1 Time-line o f events 73

3.2 Client Opinion Shopping versus Incumbent Resignation in Case 1 99

3.3 Client Opinion Shopping versus Incumbent Resignation in Case II 130

3.4 Auditor switch scenarios 134

3.5 Comparison o f Figures 3.2 and 3.3 135

3.6 Efficiency and Cost Effectiveness o f Rotation / Retention Rules 160

B -1 Decision tree for low type incumbent as response to Fs 200

B-2 Engagement opportunities and expected payoffs for successor auditors 211

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3.1 Summary o f events and results of Case 1 101

3.2 Joint probability o f Triplet Match/Report/2nd Period Fraud 145

B 1 Second period fraud detection probabilities according to scenario 246

B.2 Auditor’s expected second period cost 252

B.3 Second period expected payoff for scenario 1 256

B 5 Second period expected payoff for scenario 3 260

B.7 Second period fee for possible second period scenarios 266

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In this dissertation I explore the effects that mandatory auditor rotation rules and mandatory auditor retention rules have on the audit function Proponents o f this form of audit regulation claim that under such rules audit quality will increase, while the detractors sustain that audit quality will decrease, and that audit costs will increase

In Chapter 2 , 1 first analyze how different auditor rotation and retention regimes affect the quality of audit services when all auditors are homogeneous but must decide

on what effort to exert in performing the audit function I explore under what conditions these mandatory rules are efficient I also determine the governm ent’s preference ordering over these regimes, and analyze the client’s preferred engagement length under each rotation/retention option In Chapter 3, auditor types are introduced together with conditions that allow for both client-initiated and auditor-initiated auditor switches I further explore the effects that mandatory auditor rotation rules and mandatory auditor retention rules have on audit quality, and the impact of these rules on the fee that client firms pay for the audit function

The “benchmark” case against which these mandatory rules are compared, in both setups, is given by a “deregulated” audit market where no restrictions are placed on auditor-client engagements

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This dissertation is motivated by the fact that mandatory rotation and/or mandatory retention of independent auditors has often been proposed, and in some cases enacted, by regulators and professional interest groups The arguments for and against this form of regulation are, however, quite contradictory.

According to Petty and Cuganesan [1996], the commonly-asserted advantages of rotation all relate (either direcdy or indirectly) to the desirability of either enhancing audit independence or improving the quality o f the audit work performed, which allegedly decrease with the length of the auditor’s tenure On the other hand, rotation and/or retention rales have systematically been rejected by the auditing profession The commonly-asserted disadvantages of mandatory auditor rotation or retention relate either to an increased audit cost or the risk of a decline in audit quality Glynn and Ridyard [1992], argue that periodic compulsory rotation of auditors causes potentially high disruption costs and raises questions as to the quality of the audit scrutiny during the transition period Durandez [ 1988a,b], argues that rotation regulation lowers audit quality, eliminates incentives to specialize, and reduces competition among audit firms which could potentially induce them to collude Rutteman [1987], argues that rotation would be both costly and counter-productive in improving audit quality

A bill proposing mandatory rotation of independent auditors was introduced in

1994 in the Senate Commerce Committee (Baliga [1995], and Elitzur and Falk [1996]) The U.S General Accounting Office (GAO [1996]), also raised but then rejected auditor rotation in 1996 (Carmichael [1997]) Standard setters and professional interest groups

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in Australia have recently proposed mandatory rotation o f auditors every seven years (Petty and Cuganesan [1996]) The Cadbury Report on corporate governance has revived the debate concerning mandatory rotation of auditors contained in the European Commission’s Fifth Directive (Paleson [1993]).1 In Italy, Corporations Law requires auditor appointments to be reviewed after three years with compulsory rotation after nine Spain enacted a similar law in 1990, but subsequendy abolished it in 1995.

The underlying assumptions behind these proposals are that: i) audit quality decreases with auditor tenure, and/or, ii) that auditors face increasing pressure from

clients to compromise their independence Both effects, decreasing audit quality and loss of independence, are allegedly caused by the need that auditors have to maintain a good relationship with clients in a competidve environment, an environment where clients can freely switch auditors Kida [1980], finds that auditors may hesitate to give a

qualified or going concern opinion if they believe: a) they will lose the client, b) the client will sue, c) the accounting firm’s reputation would be negatively affected, or d)

the auditor-client relationship will deteriorate

Furthermore, Copley and Doucet [1993] found that the probability of a substandard audit increases with the length of the audit engagement Also, Giroux et al [1995], and Deis and Giroux [1996] find that audit quality tends to decline as independent auditor tenure lengthens

1 See also Dehesa [1987], Bruce [1992], Lea [1992], Mitchell [1992], Accountancy [1993a,b], and Bruce [1993a,b].

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The auditing profession is aware o f these concerns, even though it does not necessarily agree with the findings To this effect, the AICPA Special Committee on Financial Reporting, (Jenkins Committee [1994]), states that users of audited financial statements are concerned that the need to maintain a good relationship with clients in a competitive environment could erode auditor independence over time.

Another common claim is that client-specific quasi-rents, caused by the practice

of low balling, put downward pressure on the quality of audit services See for example, the Cohen Report (The Commission on Auditor’s Responsibilities [1978]), and the Securities and Exchange Commission ASR 250, [1978] Contrary to the claims made

by some accounting regulators, DeAngelo [1981], and Magee and Tseng [1990], have provided a rationale for the practice of low balling showing that client-specific quasirents arise in an equilibrium model of audit-pricing, and do not necessarily lead to a compromise of auditor independence Low balling in this context is a competitive response to the expectation of future quasi-rents to incumbent auditors caused by some technological advantage.2

The SEC has contended that reporting disagreements, anticipated qualifications and opinion shopping often trigger auditor switching (Securities and Exchange Commission [1988]) While there are also other motivations for independent auditor

2 Competing theories o f low balling are given by Dye [1991], Schatzberg [1991], and Kanodia and Mukherji [1992], who show that some form o f informational asymmetry is needed for client-specific quasi-rents, low-balling and auditor replacement to occur in equilibrium, although the three provide a different explanation for the phenomena Jevons and Lin [1992] show, using a principal-agent framework, that low-balling is an efficient mechanism for eliminating moral hazard (collusion between the manager and an external auditor).

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switching,3 such as changes in the demand for audit quality, issues of credibility and reputation, fee reductions, change in management, etc., the relation between auditor opinions and auditor switching has been documented empirically.

Chow and Rice [1982], report a positive association between a firm ’s propensity

to switch auditors and the receipt of a qualified opinion in the year previous to the switch, even though firms that switch auditors do not seem to receive “improved” opinions in the year following the switch.4 Sarhan et al [1991] find that the likelihood

o f management changing auditors after receiving a qualified audit opinion is greater than after a unqualified opinion Lennox [1997], finds that companies use auditor switching to avoid receiving qualified audit reports

Furthermore, the SEC has voiced its concern that opinion shopping raises serious questions about auditor independence.5 In 1976, the Chairman o f the SEC, Harold Williams, stated before the U.S Senate Subcommittee on Reports, Accounting and Management of the Committee on Government Operations (Metcalf Committee [1976]), that:

3 Previous research has noted the inherent difficulties in determining the precise reasons for auditor switches: See for example, Schwartz and Menon [1985], Healy and Lys [1986], Francis and W ilson [1988], Johnson and Lys [1990], and Krishnan [1994],

4 Several studies have searched for empirical evidence consistent with opinion shopping, but generally find no difference in the treatment o f clients who switched in the pre-switch and post-switch years relative

to non-switching clients In addition to Chow and Rice [1982], see also Smith [1986], Krishnan [1994], and Krishnan and Stephens [1995].

5 The SEC, in its Financial Reporting Release No 31, [1998], defines opinion shopping as “the practice o f seeking an auditor willing to support a proposed accounting treatment designed to help a company achieve its reporting objectives even though doing so might frustrate reliable reporting.”

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“T h e m o st ob viou s factor w hich ero d es independence is the fa ct that the auditor’s com pensation and the co n tin u ed utilization o f his se r v ic e s, are

d ep en d en t upon the w ishes o f the c lie n t’s m anagem ent, the sa m e group toward w h ich the auditor is e x p ected to b e im partial”

The same Metcalf Committee in 1976 proposed rotation o f independent auditors

as a means of reducing the effects of eroding auditor independence caused by the practice of opinion shopping by clients The Metcalf Committee’s proposal regarding mandatory rotation of independent auditors did not follow through, but the SEC has consistently increased its monitoring o f independent auditor switches by mandating expanded disclosure requirements for clients who switch auditors See, for example, the SEC Financial Reporting Release No.31, [1988], and the SEC Financial Reporting Release No 34, [1989] Hendrickson and Espahbodi [1991] find, however, that reports

to the SEC of auditor changes and related disagreements on form 8-K do not necessarily disclose the real reasons The public accounting profession has also responded to

concerns related to auditor switches by issuing SAS No 7; Communications Between

Predecessor and Successor Auditors, AICPA [1975], currently under revision, and

issues related to opinion shopping by issuing SAS No 50: Reports on the Application o f

Accounting Principles, AICPA [1986], which provides guidelines about standards of

performance and reporting which should be followed by independent auditors when approached by clients of other auditors concerning appropriate accounting (see Krishnan and Stephens [1995])

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It is clear from the above discussion that issues surrounding the regulation of the auditing profession, be it through self-regulation or through mandatory regulation, are far from solved, and that proposals such as mandatory rotation or mandatory retention of independent auditors are still major concerns of regulatory bodies in many countries.

Previous research has addressed how changes in liability and liability regimes, standards, and wealth constraints affect auditor behavior,6 and how auditors and their clients respond to report-contingent audit contracts,7 but little research exists regarding mandatory rotation and mandatory retention rules Arrunada and Paz-Ares [1997], analyze the effect o f mandatory auditor rotation on audit cost and quality They show that mandatory auditor rotation increases audit cost and price through the destruction of specific assets and the distortion of competition, but their results of the effect on audit quality are inconclusive, even though they hypothesize that a negative impact on audit quality is a highly plausible effect Gietzmann and Sen [1997], analyze the role of mandatory auditor rotation in a setting where a trade-off between auditor reputation and reappointment exists They argue that mandatory rotation could promote auditor independence by removing management’s ability to influence auditors to collude with them by removing reappointment concerns They show that rotation is desirable in markets where any single current assignment constitutes a significant portion of the auditor’s total business

6 See, for example, Penno [1992], D ye [19931, Schwartz [1993], and Shibano [1993].

7 See, for example, Dye at al [ 1990].

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This dissertation proceeds as follows: In Chapter 2, I expand the audit-pricing models of DeAngelo [1981] and Magee and Tseng [1990], by allowing for variable audit effort levels and binding multi-period engagements I assume that truth-telling is uniquely cost-minimizing, which implies that auditors are perfectly independent Once

an accounting breach has been discovered, the auditor will report it The auditor must, however, choose an effort level that will affect the probability of discovering a breach.8 That is, even though truth-telling may always be induced, the auditor can affect the

"truth" to be reported by choosing different effort levels The client, through a credible threat o f termination, for example, can induce the auditor to exert less effort In turn, auditor retention-rotation rules and liability also affect the auditor’s effort choice Audit quality is determined by the effort level that the auditor exerts in detecting a breach in the accounting system, with higher effort levels corresponding to higher quality audits

The government creates the audit market with the sole objective of maximizing the recovery of understated taxes (including fines), net of the government’s cost As a consequence of this assumed government objective, I model the auditor as an agent whose responsibilities are limited to detecting and reporting tax fraud committed by firms The focus of this chapter is on the auditor compliance problem — determining conditions that will induce the auditor to exert effort in detecting fraud— as opposed to the problem of tax compliance by firms, or the determination of an optimal revenue

8 Watts and Zimmerman [1986], refer to these two dimensions o f the audit function as competence (the probability that the auditor discovers a given breach) and independence (the probability that the auditor

reports the discovered breach) These two probabilities, however, are unlikely to be separable.

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collection process by the government (e.g Reinganum and Wilde [1985], [1986], Graetz

et al [1986], Beck and Jung [1989])

I show that when clients cannot credibly threaten to replace an auditor who reports fraud, both the client and the auditor are indifferent to the length of the engagement Furthermore, auditors will never be replaced The government’s revenue, arising from recovery of understated taxes, does not increase when rotation/retention rules are imposed The client is indifferent to mandatory retention rules of any length, but is strictly worse off if any form of mandatory rotation is imposed Thus, rotation rules are not Pareto optimal

W hen auditors face a credible threat of replacement if they detect and report fraud, clients are not indifferent to the engagement length, and will only commit to a single-period engagement As a consequence, auditors will be replaced in equilibrium The expected rate of auditor turnover is inversely related to the magnitude of quasirents, which is consistent with Kanodia and Mukherji [1992] Auditors will exert less effort, compared to the no-threat case, due to the threat of termination That is, client- specific quasi-rents lead an auditor to compromise his competence, with an ensuing audit o f lower quality Thus, the government’s revenue is strictly lower Imposing mandatory retention or mandatory rotation improves the government’s revenue collection, but does not fully eliminate the negative effect of the client’s replacement threat Imposing mandatory retendon and rotation does, however, fully eliminate the negative effects Thus, when there exists a credible threat o f replacement that affects all

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auditors that report fraud, the government will enforce retention and rotation regulation The government is indifferent to the length o f the mandatory retention/rotation period, while the client prefers the longest engagement possible.

In Chapter 3 , 1 offer a multiperiod model where, in the deregulated audit market, auditors compete for the government imposed audit of client firms in each period As in Chapter 2, the auditor’s only function is to detect client fraud.9 Undetected fraud is considered to be socially detrimental and therefore, audit quality in this setup is determined by the likelihood that fraud be detected given that fraud exists Auditors are assumed to be perfectly independent in that they will report fraud if fraud is detected

Contrary to the setup of Chapter 2, client-initiated auditor switches are not exogenously imposed That is, a credible termination threat may not always exist for the incumbent auditor who detects fraud in period one However, comparisons between

an audit market where mandatory rotation or mandatory retention rules are imposed and

a deregulated audit market will only be of interest if in the latter the auditor switching behavior is distinguishable from either form o f regulation If in the deregulated audit market auditor switches always (never) occur, then rotation (retention) rules would have

no meaning To this effect I construct a model, using auditor types, where, in the

absence of rotation or retention regulation, auditors will either: 1) retain the client in the

9 Fraud detection represents only a fraction o f the purposes commonly attributed to the audit function It

is, however, a function that has received much attention lately The SEC has repeatedly taken the stance that auditors should detect certain types o f frauds (see, for example Sack [ 1987], and Rollins and Bremser [1997]) The public accounting profession has also recently revised the role o f the auditor vis-a-

vis fraud in Statement on Auditing Standards No 82: Consideration o f Fraud in a Financial Statement

Audit, AICPA [1997].

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next period, 2) resign the engagement, or 3) be replaced by the client The specific

outcome will depend on the auditor’s fraud detection technology (auditor type), the existence of client fraud in the second period, and the auditor’s first period outcome (a clean or qualified report) The setup is such that in equilibrium all three possibilities can occur Equilibrium conditions and equilibrium audit fees are determined for each of the three possibilities I show that the probability of observing a client-initiated auditor switch after a qualified opinion is always greater than after a clean opinion This is consistent with empirical findings that report a positive association between a firm’s propensity to switch auditors and the receipt of a qualified opinion in the year previous

to the switch (see, for example, Chow and Rice [1982], Sarhan et al [1991], Matsumura

et al [1994], and Lennox [1997])

I also show that the probability of observing an auditor-initiated switch, (i.e., an incumbent resignation) after a clean opinion is always greater than after a qualified opinion I also show that under certain conditions, auditor-initiated switches (i.e., incumbent resignations) produce an efficient realignment of auditors -as measured by a second period increase in the expected fraud detection probability, while under certain conditions, client-initiated auditor switches results in a decrease in the expected second period fraud detection probability

The setup of the deregulated audit market yields four different auditor switching scenarios In scenario one, no auditor switches will be observed in equilibrium In scenario two, auditor switches are observed only after a clean audit opinion Both

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auditor-initiated and client-initiated auditor switches are feasible In scenario three, auditor switches are observed only after a qualified audit opinion Here again, both auditor-initiated and client-initiated auditor switches are feasible In scenario four, auditor switches can be observed both after a clean and a qualified audit opinion, and be caused by both a client-initiated auditor switch or a client-initiated auditor switch.

After completing the analysis of the deregulated audit market, mandatory rotation and mandatory retention rules are introduced I show that no unconditional (not scenario dependent) mandatory auditor rotation or mandatory auditor retention rules exists that increases the expected probability o f fraud detection (i.e., increases audit quality) when compared to the deregulated market That is, when the entire range of possible market conditions is considered, the deregulated audit market is more efficient (higher expected fraud detection probability), and more cost effective (total audit fees are equal or lower) than a market where auditor engagements are mandated by a regulatory body The only instance where mandatory rotation or retention rules increase audit quality and lower the total audit cost, is in scenario three where auditor switches are observed only after a qualified audit opinion, and mostly caused by client-initiated auditor switches To implement mandatory rotation or mandatory retention rules in such a case would, however, require that the rules be contingent on the outcome o f the audit opinion Such conditional mles would allegedly be difficult to justify from an institutional point of view, and even more difficult to control

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This result should be of interest to regulators that claim that these mandatory rotation or retention rules will increase the overall benefits o f independent audits These claims will only be true for specific cases, but in detriment o f the remaining cases in the deregulated audit market where audit quality is higher and the total fees paid by clients equal or lower.

All proofs are in the Appendices, unless otherwise stated

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Mandatory Rotation/Retention Rules and Audit Quality

2.1 Model Description

There are three players in the model: the government, the client, and the auditor The model deals with an infinite horizon, although the auditor-client engagements may be limited to a finite horizon as determined by the regulation in place

The government controls a vast array of policy variables that determine among others, auditor compliance; conditions that induce the auditor to exert effort in detecting fraud and report truthfully.1 The government chooses the specific policy variables related

to the audit market as optimal responses to the strategies o f both the client and the auditor

In this model, there is no time-consistency problem, as in Melumad and Mookherjee [1989], where the government is assumed to be unable to commit to all relevant policy variables.2

The government creates a demand for an audit market by requiring all firms to be audited, in order to aid in the discovery of understated tax liabilities No other value is attributed to the audit; all other uses o f the audited financial statements are assumed away

1 Other policy variables include those related to the revenue collection process by the government, and tax compliance by firms To keep the analysis focused on the auditor compliance problem, I assume that the parameters related to these other policy variables are exogenously given Issues related to their

determination and optimality are outside the scope o f this dissertation.

2 The underlying assumption is that the population o f firms is large and that there is sufficient information about government behavior in the public domain such that audit regulation and/or reputational phenomena enable the government to credibly commit.

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There are two types of clients: Fraudulent clients and non-fraudulent clients Fraudulent clients are those that refuse to comply voluntarily with the tax laws and instead are responding strategically to the enforcement structure of these laws.3 How the client determines his choice regarding the decision whether or not to commit fraud in any given period is not formally modeled in this dissertation I assume that the client’s type is independent across periods.4 Let denote client type, where tF represents afraudulent client and a non-fraudulent one Let h denote the proportion of clients that commit fraud in any given period The client’s type choice is made after retention-rotation regulation is established and after an auditor is hired, and is not publicly observable Fraud consists of filing a tax return with a lower-than-actual tax liability.5 The benefit from fraud,

denoted B, is assumed to be identical for all fraudulent clients I assume that the tax law

is unambiguous and that each client knows the true tax liability he faces The penalty the client faces if tax fraud is discovered is given by 2?*(1+t t), where t t, ( t t > 0), is a fixed (exogenously given) penalty factor to which the government can commit via the tax law.6

As required by the government, the client hires an auditor The length and conditions of the engagement are affected by the regulation in place The client pays the auditor a fixed fee, denoted <5, for his service since contingent audit fees are banned by the

3 These individuals are called the "strategic noncompliers" in the standard econom ics o f crime literature,

as opposed to the "habitual compilers”, see Graetz et al [1986].

4 Despite the exogenous nature o f the client’s decision to commit fraud in my model, fraud should not be

interpreted as a random error, but rather as an irregularity as defined in SAS no 53.

5 A lower tax liability is caused by both tax avoidance (accounting manipulations, such as accruals, that defer taxes to a future period), and permanent tax evasion (through o ff the books sales, for example).

6 This penalty structure is consistent with a tax law where penalties are proportional to evaded taxes as opposed to unreported income.

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government Also, auditor dismissal within a period (as, for example, in Dye [1991] and Teoh [1992]) is not allowed Thus, "opinion-shopping" is precluded I assume that the audit market is perfectly competitive, and thus, the equilibrium fee will be equal to the

auditor’s expected cost In addition to the fee, the client incurs a fixed cost, denoted c, each

time he engages a new auditor

Auditors are homogeneous: They are assumed to be risk-neutral with identical wealth and cost structures The auditor incurs a fixed learning cost, I, every time she

engages with a new client The auditor will exert effort e, ee[g,e], in an attempt to detect

fraud Effort is unobservable and thus, cannot be contracted on The cost of effort, denoted

C(e), is increasing and convex in e, that is, C'(e) > 0, and C"(e) > 0 As a result o f this

effort, the auditor may or may not detect fraud.7

Let D, D eiD pJ)^}, denote the client position as detected by the auditor after exerting effort e, where D? corresponds to detection of fraud and to no detection of

fraud D is unobservable, but can be verified by the government as discussed below.

The auditor’s prior beliefs that the client has committed fraud in any given period are given by Pr(fF) These beliefs are common knowledge to all auditors and the government I assume that Pr(/F) is identical and independent for each client across time,

and equal to the proportion of firms that have committed fraud, that is, Pr(fF) = h.

Let the audit technology be represented by Pr(Dle,/), which is the probability of

7 The auditor cannot produce fake evidence o f fraud by exerting effort There are no intermediate positions or degrees o f fraud; the client has either committed fraud or n o t

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detecting Def-Dp,/)^} conditional on effort e, and client type te f/p ,^ } 8 If the auditor

detects fraud, then with certainty fraud exists; there is no type I I error when fraud is detected; PffDple,/^) = 0, V e However, this audit technology is not perfect That is, Prf-Duple,^) * 0, V e The audit technology is such that dPr(Z)Fle,fF)/de > 0, and,

d^CDjJe./pVde2 < 0 With this structure, the probability o f detecting fraud conditional on

effort e becomes Pr(Dple) = Pr(Dple,rF)-Pr(tF) For notational simplicity, letp{e) = Pr(Z)Fle) The probability that no fraud will be detected when effort e is exerted by the auditor is then given by [1 - pie)] I assume that if fraud is not detected in the period it occurred, it will

not be detected in subsequent periods.9

The auditor’s posterior belief that fraud exists after exerting effort e and observing

D is given by Prf/jJe^D) Given that no type I I error exists, we have that ?x{t)eJD?) = 1 For

notational simplicity, let h(e) = PrC/ple,/),^) By Bayes’ Rule, hie) is given by:

h(e) = [h- pie)] / [1 - pie)], with //'(e) < 0, and his) < h

The auditor will issue a report that will be publicly observed by both the client and the government I assume that the auditor reports what she detects truthfully.10 Even though truth-telling is imposed, the auditor can influence the quality of the message she reports by exerting more or less effort The auditor knows the client’s type with certainty

8 The probability o f detecting fraud in any given period is assumed to be independent of having found fraud or not in a previous period.

9 Given that fraud is due, in part, to tax evasion, an understatement o f earnings in one period does not imply that earnings must be overstated in a subsequent period That is, the sum o f the accounting earnings over the life o f the firm do not have to add up to the economic earnings.

10 The underlying assumption is that the government has no restrictions in selecting an optimal liability structure that always induces truthful reporting.

Reproduced with permission of the copyright owner Further reproduction prohibited without permission.

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only when fraud is detected If no-fraud is observed, there is still a positive probability h{e)

that the client is a fraudulent type Audit quality is determined by the effort level that the auditor exerts in detecting a breach in the accounting system, with higher effort levels corresponding to higher quality audits

The government can verify client type and thus, the auditor’s report, by performing

its own audit of the client at cost AC I assume that the government’s audit is perfect, i.e.,

if fraud exists it will be detected The government will consider an audit to have failed if, subsequent to a no-fraud report by the auditor, a client is found to be a fraudulent type

2.1.1 Use and Consequences of the Auditor's Report

Given that the auditor’s effort level is unobservable, any action against the client or the auditor has to be based exclusively on the auditor’s report This implies that the government can hold the auditor liable for an audit failure, penalizing her accordingly, only

if the auditor failed to detect and report fraud

If the auditor detects and reports fraud, the client is automatically liable for 5-(1+tu) Given that auditors report truthfully and that the audit technology is such that if fraud is detected it exists with certainty, no client will ever dispute an auditor’s fraud report A second audit by the government would just confirm the auditor’s report

If the auditor issues a no-fraud report, the client pays no additional taxes or penalties The government will find it optimal to occasionally verify the claim of no

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fraud.11 It does so because: (z) the auditor’s technology is imperfect and thus, fraud exists with probability [1 - p(e)], even if the auditor has exerted the maximum effort possible and

no fraud is observed, and (//) the auditor may have been negligent, not exerting adequate

effort in detecting fraud Let q denote the probability that the government will audit the

client when the auditor reports no-fraud.12 If fraud is detected in this government audit the client is penalized with i?-(l+7c), and the auditor is held liable for an audit failure Note, however, that the government cannot distinguish between the two cases mentioned above Thus, the penalty imposed on the auditor must be the same in both cases even though the

nature of the no-fraud report on behalf of the auditor is quite different Let L< °°, denote

the penalty imposed on the auditor for an audit failure.13

The auditor’s expected liability, denoted EL{e), is given by:

12 An underlying assumption for both the government and the auditor is that these players only analyze current period data and do not condition their sampling strategy on previous observations o f client type.

13 If the liability imposed on the auditor is not bounded, then the government can always induce any desired behavior by inflicting infinitely large penalties with a very low government audit probability The argument o f maximum fines with corresponding probabilities o f detection at a minimum was first introduced by Becker [1968], and is consistent with the econom ics o f crime literature that habitually allows unbounded penalties that can take on any value required to maximize a given social welfare function As Polinsky and Shavell [1979] point out, however, "this view o f optimal tradeoff between the probability and magnitude o f fines does not seem realistic Individuals are rarely if ever fined an amount approximating their wealth, especially for activities which impose relatively small external costs."

14 Recall that p(e) = PrfDpWjO-PrCfp), which implies that p (e) e [0,h) Thus, EL(e) > 0 V e Also note that E L \e ) < 0.

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2.2 Infinite Horizon Model without Retention/Rotation Regulation

I will first determine the equilibrium behavior and the equilibrium audit prices, when the government imposes no temporal limits on the auditor-client relationship That

is, mandatory retention or rotation rules do not exist Binding multi-period engagements are permitted, but price renegotiation or breach o f contract during the engagement are not allowed The client and the auditor can, however, negotiate renewal o f an engagement after the termination of a binding contracting period If an auditor looses her incumbency, she becomes part of the pool o f auditors competing for an engagement in the next period Ongoing auditor-client engagements of any length are plausible The one-period discount factor is denoted by 5

Two cases are explored: In the first, the client cannot credibly threaten to replace

an auditor who reports fraud In the second case, the client’s replacement threat is credible

I determine the government’s preference over these two cases, and show under which conditions they will arise in equilibrium

2.2.1 Model without Credible Threat to Replace Auditors that Report

Fraud

I first analyze the case where the incumbent auditor faces no report-related threat

o f replacement That is, the client cannot credibly threaten to terminate an auditor who reports fraud The conditions that lead to this scenario will be formally stated in what follows, but the intuition behind this case is straightforward If the increase in audit fees

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and expected switching costs caused by a replacement threat is greater than the increase in benefits to the client obtained by inducing a lower audit effort level, then the client will not announce such a threat, nor will it be credible Thus, the chance that an auditor be engaged

in any given period depends exclusively on the nature of the competitive market, and no past behavior is relevant The incumbent auditor will charge as high a price as possible consistent with remaining the incumbent I assume that if the client is indifferent between retaining the incumbent auditor and hiring a candidate auditor, the client will retain the incumbent I will denote this benchmark case as the no-replacement case

Lemma 2.1 presents the equilibrium effort that will be adopted, and the equilibrium prices that will be charged by the incumbent auditor and by the candidate auditor in the noreplacement case, assuming that the auditor and the client agree to binding engagements with a duration of A^-periods, where M=[l ,«>), is determined endogenously.15 The subscript

nr denotes equilibrium values for the no-replacement case.

Lemma 2.1: In the no-replacement case:

period, i f engaged, regardless o f the contract length N The effort choice

Equivalent expressions can be obtained if we let the contract length vary over time.

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(ii) The price bid, in present value terms, by all candidate auditors fo r an N- period audit, denoted Q j f t ) , is given by:

^(A O = (1-6N) I (1-6) { C ( 0 + L - q ^ h - p ( e j ] } + (1-6NH - 6N-c (2.3)

period audit, denoted & m(N), is given by:

fcUAO = (1-6N) / (1-6) { C (e J + L -q^ih - p ( e j ] } + (l-6 NH<?+c) (2.4)

The above audit-pricing equations are generalizing those of Magee and Tseng [1990] by allowing for variable auditor effort and multi-period engagements The "value

of incumbency" as defined in Magee and Tseng [1990], is independent of the discount rate

and the number of periods N the engagement lasts, and is given by (H+c).16 As expected,

low-balling and price cutting in the first AAperiod engagement do occur The auditor

charges (1-6N)-C in each Af-period engagement to recover the initial learning cost H The

auditor also provides a discount of 6N-c in the first A/’-period, which is recovered in subsequent A-period engagements by raising the price by (l-6 N)-c.17 At the start of the world, all auditors are candidates, and consequendy, the price bid will be ^(A O -

The above pricing relations are set up to leave the client indifferent, in terms of

16 Magee and Tseng [1990] define the value o f incumbency as the present value o f being the incumbent, assuming optimal pricing (and reporting) decisions over the remaining horizon In the current

formulation, the engaged auditor becomes the "incumbent" at the end o f the iV-period relationship The

value o f incumbency, (t+ c), is for the entire N periods.

17 Low-balling in the first iV-period is given by [-6N-(J+c)], followed by an infinite series o f [(l-6 N)-((+c)] every iV periods The //-period discount rate is given by (1-6N)/5 N Thus, the auditor earns zero profits in present value.

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audit price, between the incumbent and candidate auditor In addition, both incumbent and candidate auditors will exert the same effort in every period if engaged Consequently, there will never be any switches between auditors in the no-replacement case.

Note that if the auditor and client engage in binding multi-period contracts of N z 2,

there may be considerable mismatches between current period fees and current period costs, because there is no unique fee for any given period within the iV-period engagement The only equilibrium condition regarding the distribution of fees is that the present value o f fees

quasi-rents within the jV-period engagement will exist, but these "quasi-rents" do not affect

auditor behavior: the auditor will exert em in each period as given in (2.2).

The audit-pricing model of Lemma 2.1 suggests that the engagement length N has some effect on the client’s audit cost, and thus, N will be chosen optimally by the client Lemma 2.2 shows, however, that the client is indifferent to the engagement length N Let

denote the discounted present value of fees in an infinite horizon no-replacement model

Lemma 2.2: The client is indifferent to the engagement length N, in cm infinite

horizon no-replacement model The present value o f fees, T np is given by:

¥ „ = (! + l / ( l - 6 ) [ a e J + L - q ^ lh - p ie J ] } (2.5)

Note that is independent of the engagement length N, and the switching cost c.

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However, each potential auditor switch would increase the client’s cost by c The intuition behind this result is straightforward Once an auditor is engaged, she will remain with the client in perpetuity Thus, how this infinite horizon is partitioned into finite contracts is irrelevant.

2.2.2 Model with a Credible Threat to Replace Auditors that Report

Fraud

I now analyze the case where the auditor faces a credible threat of being replaced

by the client if fraud is detected and reported This replacement threat does not violate the ban on contingent fees The auditor’s incumbency, not the fee, is contingent on the auditor’s

report The client will announce such a replacement threat if it is ex-ante efficient for him

to do so This threat will be credible only if it is also ex-post efficient for the client to

follow-through with it.18 In determining their equilibrium bid prices, auditors must account for the possibility of being replaced The incumbent auditor will charge a price that is as high as possible, but low enough to prevent entry due to price The client, however, does not only consider the magnitude of the comparative equilibrium bids, but also the effect that replacing an auditor has on effort choice, which affects his expected benefits and the probability o f a government audit I will refer to this case as the replacement case

Binding multi-period engagements are permitted However, contrary to the noreplacement case (where contracts of any length are optimal for the client), the optimal

18 The conditions under which it is both ex-ante and ex-post optimal for the client to adopt the replacement

strategy will be determined below.

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contract length, for the client, in the replacement case is one period This is formalized in Lemma 2.3.

Lem m a 2.3: In the replacement case, the client w ill only commit to single-period engagements.

The intuition behind Lemma 2.3 is the following: If the client engages with an auditor for more than one period, the conditions for replacement would occur with positive probability before the end of the engagement The client cannot, however, replace the auditor until the end of the multi-period engagement given the binding nature o f the contract The auditor will have no further threat of replacement in the remaining periods and will revert to the no-replacement effort level, leaving the client worse off.19 If the contract length is set to one period, the auditor will exert the replacement effort level in that one period and thus, in every period, leaving the client better off

Lemma 2.4 presents the equilibrium effort that will be adopted and the equilibrium prices that will be charged, by the incumbent auditor and by the candidate auditor in the replacement case, when the auditor and the client agree to single-period engagements The

subscript r, denotes equilibrium values for the replacement case.

19 Recall that the client will adopt the replacement strategy only if the increase in benefits from inducing a lower effort level is greater than the increase in audit fees and expected switching costs caused by the replacement threat.

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Lemma 2.4: In the replacement case:

period i f engaged The effort choice is given by:

ee[g,e]

given by:

<£r = C(er) + L-q-\h - /?(er)] + (l-6)-£ - 5-c + p(er)-6-({+c) (2.7)

The value of incumbency is independent of the discount rate and is given by (J+c),

as in the no-replacement case The incumbent auditor, however, will lose the incumbency

when fraud is detected, which occurs with probability p(er) In light of this positive

probability event, the auditor’s effort choice is adjusted accordingly as given in (2.6) Thus,

the expected value of incumbency is given by [1 - p(er)]'(H+c).

If we interpret future quasi-rents in expected value terms, low-balling is still obtained in equilibrium The auditor adjusts the fee to account for the possibility of being replaced, by raising the price by/?(er)-8-(fi+c) in each period As in the no-replacement case, the auditor also raises the audit price by (1 -8)*C in each period to recover the initial learning cost C, and provides a discount of 8-c in the first period which is recovered in subsequent

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periods by raising the price by (l-S)-c.20

The client will pay the auditor <&r in the first period With probability [1 - p(er)],

no fraud will be detected and the client will retain the auditor and pay <E>[r in the next period

W ith probability p(er) the client will switch auditors incurring the switching cost c and

paying the new auditor $ r The incumbency fee, <£>',, is equal to <Er + c, which implies that

the client will pay <£r + c, in every subsequent period Let Y r denote the present value of

fees and expected switching costs in an infinite horizon model with a credible replacement threat Y r is given by:21

Yr = fi + 1 / (1-8) (C(er) + L -q ^h -pCeJ] +p(eT)-6-(t+c)} (2.9)

where (C + 1 / (1-8) (C(er) + L-qr-[h - p(er)] + p(e,)'8*6}) corresponds to the present value

o f fees, and [6 / (1-8) p(er)'c] is the present value o f expected switching costs.

2.2.3 Conditions under which the Replacement Threat is Credible

The client does not know his decision regarding type before he engages with an

auditor; with probability h he will choose to be type fF in any given period, and with probability (1 - h), he will be type If the client is a fraudulent type in any given period,

the benefit from undetected fraud is B, while the penalty for detected fraud is 5*(l+rc),

20 Interpreting future quasi-rents in expected value terms, low-balling in the first period is given by {-[1 -p ( e r)]*6-(J+c)}, followed by an infinite series o f {[1 - /?(er)]-(l-8)-({+ c)} TTie discount rate is given

by (l-5 )/5 Thus, the auditor earns zero profits in present value.

21 Using $ r as given in (2.7), and $*r as given in (2.8), we have that:

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