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

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NORTHWESTERN UNIVERSITY
Auditor Rotation and Retention Rules:

A Theoretical Analysis
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
DOCTOR OF PHILOSOPHY
Field of Accounting and Information Systems
By
Eric C. Weber
EVANSTON, ILLINOIS
June 1998
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DM! Number: 9832711
Copyright 1998 by
Weber, Eric C.
Ail rights reserved.
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© Copyright by Eric C. Weber 1998
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ABSTRACT
Auditor Rotation and Retention Rules:

A Theoretical Analysis
Eric C. Weber
Adviser: Professor Ronald A. Dye
This dissertation examines the consequences of 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 of 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 of 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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when the auditor proposes to release an unfavorable audit report. The dissertation
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 of 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, of an auditor may result in the suppression of this source
o f information about a client.
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ACKNOWLEDGEMENTS
I would like to thank the members of 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 of 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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Table o f Contents
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 of Chapter 2

48
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3 Client Opinion Shopping, Auditor Resignation and the
Efficiency of 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 Mandatory Rotation and Retention Rules

136

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 of 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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List o f Figures
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 of 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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List o f Tables
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.4 Second period expected payoff for scenario 2

258
B .5 Second period expected payoff for scenario 3

260
B.6 Second period expected payoff for scenario 4

262
B.7 Second period fee for possible second period scenarios

266
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Chapter 1
Introduction
In this dissertation I explore the effects that mandatory auditor rotation rules and
mandatory auditor retention rules have on the audit function. Proponents of 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 government’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.
1
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2
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 of 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 of 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 of 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 quasi
rents 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 of 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

of 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 of 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 Wilson
[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 he m ost obviou s factor which ero des independence is the fact that the
auditor’s com pensation and the co n tin ued utilization o f his se rv ice s, are
dep enden t upon the w ishes o f the c lie nt’s managem ent, the sam e group
toward w hich the auditor is exp ected to be impartial”
The same Metcalf Committee in 1976 proposed rotation of 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 of 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], Dye [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.
When 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 quasi
rents, 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 of 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 of 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 of 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 of 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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