lu - 2006 - does opinion shopping impair auditor independence and audit quality

DOI: 10.1111/j.1475-679X.2006.00211.x
Journal of Accounting Research
Vol. 44 No. 3 June 2006
Printed in U.S.A.
Does Opinion Shopping
Impair Auditor Independence
and Audit Quality?
TONG LU
∗
Received 7 October 2004; accepted 22 October 2005
ABSTRACT
This study investigates how companies’ threats to dismiss auditors and their
engagement in opinion shopping influence auditor independence and au-
dit quality, which in turn affect misstatements in financial statements. It also
examines how outsiders’ reactions to auditor switching influence opinion
shopping. The results indicate that neither the predecessor auditor’s nor the
successor auditor’s independence is compromised by dismissal threats and
opinion shopping. Further, the successor auditor’s audit quality exceeds the
predecessor auditor’s audit quality. In addition, auditor switching decreases
potential understatements and increases potential overstatements in finan-
cial statements, and the capital market’s and the successor auditor’s reac-
tions to auditor switching reduce the benefits of opinion shopping to com-
panies. Additionally, the study sheds some light on the potential effects of
both the Sarbanes-Oxley’s restriction on non-audit services and mandatory
auditor rotation or retention. The paper also derives a rich set of empirical
implications.
∗
University of Houston. This paper is based on my dissertation at the University of
Minnesota. I am very grateful to my advisor, Chandra Kanodia, for his guidance. I also thank
the members of my dissertation committee, Regina Anctil, Andrea Moro, and especially Frank
Gigler, for their advice. I gratefully appreciate the constructive comments by the anonymous

referee. Thispaper hasalso benefitedfrom thecomments ofPhilip Berger(the editor),Haresh
Sapra, Raghu Venugopalan, and workshop participants at the University of Minnesota.
561
Copyright
C

, University of Chicago on behalf of the Institute of Professional Accounting, 2006
562 T.
LU
1. Introduction
The recentexplosivegrowth inauditor switching isexemplified by thefact
that in 2004, more than 1,600 companies changed their outside account-
ing firm, an increase of 78% over 2003. Moreover, 61 companies changed
auditors at least twice in 2004, and the 2,514 changes during 2003 and
2004 represents more than one-fourth of all U.S. publicly traded companies
(Taub [2005]). Whereas some auditor switches occur for legitimate reasons
like client firm growth, others are driven by opinion shopping, which “is
generally understood to involve the search for an auditor willing to sup-
port a proposed accounting treatment designed to help a company achieve
its reporting objectives even though that treatment might frustrate reli-
able reporting” (SEC [1988]). To date, debate continues in the financial
community, academic literature, and popular press as to the most effective
way of curbing opinion shopping. Whereas the Sarbanes-Oxley Act of 2002
required the General Accounting Office to study the potential effects of
mandatory auditor rotation in strengthening auditors’ resistance to opin-
ion shopping threats, some scholars advocate a policy of mandatory auditor
retention to mitigate companies’ opinion shopping opportunities (Lennox
[1998]).
Legislators’ and regulators’ attention to auditor switches apparently re-
sults from two concerns: (1) impairment of the reliability of reported ac-

counting numbers because of auditors’ failure to detect misstatements in
financial statements (an issue of “audit quality”) and (2) expansion of op-
portunities for earnings management by unscrupulous managers because
of auditors’ failure to deal appropriately with detected misstatements (an is-
sue of “auditor independence”). Audit quality refers to the probability that
the auditor will detect misstatements, while auditor independence refers to the
probability that the auditor will refuse to support detected misstatements.
The concern is that companies’ threats to dismiss auditors and their engage-
ment in opinion shopping might damage auditor independence and audit
quality, thereby precipitating materially misstated financial statements and
ultimately harming capital market investors.
Most debate over opinion shopping has so far revolved around manda-
tory auditor rotation versus mandatory auditor retention. However, before
answering the questions of whether and how the government should inter-
vene, the status quo free market setting in which companies can voluntarily
switch auditors should be investigated first. Therefore, several more prim-
itive economic questions must precede the issue of public policy: Are the
predecessor auditor’s and the successor auditor’s independence impaired
by dismissal threats and opinion shopping? Is the successor auditor’s audit
quality lowerthan the predecessorauditor’saudit quality?Are misstatements
in financial statements increased by opinion shopping? Can companies fool
the capital market and the successor auditor and reap the full benefits of
opinion shopping? This paper contributes to the research stream by ad-
dressing these crucial questions.
OPINION SHOPPING
563
Dye [1991] and Teoh [1992] are important forerunners of this paper in
that they too investigate auditor switches resulting from auditor-client dis-
agreements ina capital market setting. However, thereare two important dif-
ferences between those studies and this study. Whereas Dye [1991] presents

what might be termed a “vindication seeking” view of auditor switches in
which auditor replacement is done by “good” firms, my theory integrates
both “vindication seeking” and “opinion shopping.” Similarly, whereas
Teoh [1992] focuses on auditor switching after public disclosure of audit
opinions, my investigation concentrates on firms’ shopping for opinions
before their public release.
My model introduces two opposing forces that influence auditors’ de-
cisions: auditor fee and legal liability. Auditor fees are potential auditor
benefits from repeat audit business and non-audit services, while legal li-
abilities are those that may be imposed on auditors when the rosiness
of a client’s portrayal turns out to be gloomy. Auditors are assumed to
choose their audit quality and attestation so as to maximize the differ-
ence between the expected auditor fee and legal liability, less the audit
cost. The firm is assumed to maximize its price in the capital market, less
the auditor fee, by choosing the proposed accounting report, the audi-
tor fee, and the auditor switching strategy, thereby influencing its audi-
tor’s audit quality and attestation, and thus misstatements in audited ac-
counting reports. The price in the capital market depends on inferences
that traders make from audited accounting reports; the beliefs of traders
are consistent with the firm’s and the auditor’s equilibrium choices. Infor-
mational differences in reports induce a change in the behavior of mar-
ket prices, which in turn induces changes in the firm’s and the auditor’s
decisions. The results in my paper depend on informational differences
in audited accounting reports caused by different directions and degrees
of misstatements, which are affected by auditor independence and audit
quality.
The study’s primary findings are as follows. First, neither the predeces-
sor auditor’s nor the successor auditor’s independence is compromised by
dismissal threats and opinion shopping. Second, the successor auditor’s
audit quality exceeds the predecessor auditor’s audit quality. Third, auditor

switching decreases potential understatements and increases potential over-
statements in financial statements. Fourth, both the capital market’s and the
successor auditor’s reactions to auditor switching reduce the benefits of opin-
ion shopping to companies.
The first twofindings contrast starkly with the popular beliefthat dismissal
threats and opinion shopping impair auditor independence and audit qual-
ity, which implies that a policy of mandatory auditor rotation or retention
is called for. Rather, my analysis suggests that proponents of such public
policies fail to recognize the corporate governance role of capital market
prices in disciplining excessive client pressure.
Nevertheless, the results on auditor independence and audit quality
do not necessarily imply that opinion shopping is innocuous. Rather,
564 T.
LU
as the third finding asserts, auditor switching may decrease one type of
misstatement (understatements) but increase the other (overstatements).
On the other hand, a policy of mandatory auditor retention, which forbids
auditor switching for a fixed duration, may prevent correction of under-
statements. Furthermore, I show that, when auditor switching is feasible,
in the preswitching period, firms prefer auditor conservatism; however, as a
result of mandatory retention, firms with better prospects would prefer audi-
tor aggressiveness instead. Thus, in evaluating alternative policy proposals,
legislators and regulators must carefully investigate the trade-off between
understatements and overstatements.
The fourth finding extends the points made earlier and implies that
mandatory auditor rotation may take away valuable information from out-
siders. In a free market, auditor switching is voluntary and so is itself in-
formative to outsiders: the capital market and the successor auditor extract
useful information from auditor switching to assess the firm’s financial con-
dition. This finding shows that outsiders’ assessments and consequent re-

actions reduce the benefits of opinion shopping to companies; in some
cases, they even preclude opinion shopping. In contrast, mandatory rota-
tion, which forces all types of firms to switch auditors after a fixed duration,
suppresses the information content of auditor switching, thereby possibly
providing a cover for opinion shopping and encouraging overstatements.
Thus, my analysis suggests that requiring mandatory auditor rotation may
be dysfunctional.
The analysis also sheds some light on the potential effects of banning
most auditor-provided non-audit services, which is required by the Sarbanes-
Oxley Act of 2002. I show that, (1) given auditor conservatism, the ban im-
pairs audit quality; (2) given auditor aggressiveness, the ban improves audit
quality; and (3) a severe restriction on non-audit services makes attestations
conservative.
In addition to the above main results, the analysis provides a framework
to both explain systematically many extant empirical findings and derive
a rich set of new empirical predictions. These empirical implications in-
clude (1) the likelihood, behavior, and consequences of auditor switching;
(2) the properties of and the asymmetric price responses to audited ac-
counting reports; (3) the determinants and consequences of auditor con-
servatism and audit quality; and (4) comparisons of the predecessor and
successor auditor’s fees and their impacts on auditor conservatism and audit
quality.
The remainder of the paper is organized as follows. Section 2 de-
scribes the model. Section 3 characterizes equilibrium reporting, attes-
tation, and capital market price, and section 4 characterizes audit qual-
ity in the absence of auditor switching. Section 5 outlines both the
equilibrium in the presence of auditor switching and the firm’s equi-
librium auditor switching strategy. Section 6 investigates auditor fees
before and after auditor switching. Finally, section 7 presents possible
extensions of the model. Proofs of propositions are contained in the

appendix.
OPINION SHOPPING
565
2. The Model
I studya financial accounting and auditingsetting inwhich a firmprovides
the capital market audited financial statements on its profitability. The firm
hasa decreasingreturnsto scaletechnologythat producesstochastic returns.
Specifically, by investing k in the firm’s technology, capital market investors
receive a positive return of 2
√
k with probability p and a zero return with
probability 1 − p. The profitability parameter p takes the value p
G
with
probability 1 −x and the value p
B
with probability x, where 1 ≥ p
G
> p
B
≥ 0
and 1 >x > 0. Because the value of p is unobservable to investors, the firm
is required to publish report G or B to indicate whether p is p
G
or p
B
. Based
on the report and other available information, the capital market prices the
firm at m.
To ensure its consistency with the firm’s underlying financial condi-

tion, the accounting report must be audited by an auditor before its re-
lease. The auditor’s audit technology produces audit evidence on the
firm’s profitability parameter p. The audit evidence can be either con-
clusive or uninformative. Uninformative evidence, denoted by p
0
, where
p
0
= Pr(p
G
)p
G
+ Pr(p
B
)p
B
, provides no incremental information, and it
can also be interpreted as two pieces of conflicting evidence. In contrast,
conclusive evidence, either p
G
or p
B
, unmistakenly identifies the value of
p and so can be used to check for misstatements in the client’s proposed
report. In the real world, the audit technology is not always able to pro-
duce conclusive evidence, a feature that the model captures by assuming
that the conclusive evidence is produced with probability q and the unin-
formative evidence is produced with probability 1 − q. The probability of
obtaining conclusive evidence—or equivalently, the probability of detecting
misstatements, q—is referred to as “audit quality.” This audit quality q can

be increased by devoting more resources to the audit technology. Letting
C(q) denote the audit cost required to achieve a certain level of q, C(q)is
increasing and convex in q with C(0) = 0, C

(0) = 0, and C

(1) =∞.
Audit evidence helps auditors make informed attestations. The auditor
must give either an unmodified audit opinion, U , in support of the client’s
report or a modified audit opinion, M, stating disapproval of it. The prob-
ability that the auditor refuses to support detected misstatements is here
termed “auditor independence.” Thus, auditor independence would be com-
promised if an auditor with the audit evidence p
B
supported the report G.
However, no issue of auditor independence exists when the audit evidence
is uninformative because such evidence cannot reveal any misstatement.
To induce an unmodified opinion on its preferred report, the firm lures
the auditor with future audit and non-audit services. The total auditor fee
from these businessopportunities isdenoted byF .
1
If the auditoris unwilling
1
F does not include the fee for the current audit engagement. The current period audit fee
is required to be noncontingent on the current period audit opinion and so it is not modeled
here. Results from a setting in which the current period audit fee is formally modeled are
available upon request.
566 T.
LU
to support its report, the firm may threaten to take away the business oppor-

tunities and appoint a new auditor. As a countervailing force against client
pressure, a legal liability, L, is imposed on any auditor giving an unmodified
opinion, U, on the firm’s report G when the subsequently realized return
to investment turns out to be zero.
The sequence of events is as follows:
1) The firm chooses an auditor fee, F .
2) The firm’s profitability parameter, p, is realized.
3) The auditor chooses an audit quality, q, and then receives the audit
evidence.
4) The firm and the auditor decide on the accounting report, G or B,
and the audit opinion, U or M.
5) The firm decides whether to switch auditors. If the firm switches
auditors, it chooses an auditor fee, F , for the new auditor and the
sequence of events goes back to stage 3 and continues onward; if the
firm does not switch auditors, the accounting report and the audit
opinion are released.
6) Capital market investors price the firm at m and make an investment
of k.
7) The return to investment is realized, and legal liability, if any, is
imposed on the auditor.
Regarding observability of information, the profitability parameter, p,is
private to the firm; the audit quality, q, and the audit evidence are private
to the auditor; and all else are public information.
In terms of the decision-makers’ objectives, the firm maximizes its expec-
tation of themarket price less theauditor fee by choosing the report, the fee,
and whether to switch auditors; the auditor chooses his or her audit quality
and attestation to maximize the expected auditor fee less the expected legal
liability, net of the audit cost; and the capital market investors choose their
investments to maximize their expected return on investments.
3. Reporting, Attestation, and Capital Market Price

The characterization of equilibrium in the absence of auditor switching
begins with an outline of the firm’s reporting strategy, the auditor’s attesta-
tion decision, and the capital market’s pricing rule.
Letting
ˆ
p denote theinvestors’assessment ofthe firm’sprofitabilityparam-
eter, p,on thebasis oftheaccounting reportand otheravailable information,
an investment of k will produce a positive return of 2
√
k with probability
ˆ
p
and a zero return otherwise. Therefore, the investors’ objective function—
their expected return on investments—is 2
√
k
ˆ
p − k. The first-order condi-
tion with respect to k implies that the optimal level of investment is
ˆ
p
2
.
Inserting this value of k into the objective function yields
ˆ
p
2
, which equals
the equilibrium price in a competitive capital market:
m =

ˆ
p
2
. (1)
OPINION SHOPPING 567
Equation (1) expresses the market price as a function of the market belief.
How the market forms its belief,
ˆ
p, depends on its understanding of the
auditor-client interactions that produce audited accounting reports, which
the following text elaborates.
Recall that the auditor is torn between auditor fee and legal liability when
facing the client’s favorite report, G: disapproving G jeopardizes the auditor
fee, F , whereas supporting G risks legal liability, L. Thus, the auditor assesses
the litigation risk on the basis of the audit evidence. When the evidence is
conclusive (p
G
or p
B
), the auditor’s expected legal liability when supporting
G is (1 − p
G
)L or (1 − p
B
)L. When the evidence is uninformative, the
auditor uses the prior expectation of p, p
0
, to assess the expected legal
liability, which is (1 − p
0

)L. Comparing the expected legal liability with
the expected auditor fee, the auditor decides whether to support the client
firm’s preferred report, G. Because (1 − p
G
)L < (1 − p
0
)L < (1 − p
B
)L,
only four cases need be considered: (1) F ≤ (1 − p
G
)L, (2) (1 − p
G
)L ≤
F ≤ (1 − p
0
)L, (3) (1 − p
0
)L ≤ F ≤ (1 − p
B
)L, and (4) (1 − p
B
)L ≤ F .
Case (1): F ≤(1 −p
G
)L. In this extreme case, the auditor fee is too small
to cover even the smallest expected legal liability; so the auditor refuses
to approve report G regardless of audit evidence. Therefore, the firm is
forced to issue report B no matter what its profitability. Yet such a report
B contains no information whatsoever about p and is thus ignored by the

capital market, which then uses its prior belief about p, p
0
, to price the firm
according to equation (1): m = p
2
0
.
Case (4): (1 − p
B
)L ≤ F . In this other extreme case, the auditor fee is
so large that it can cover even the largest expected legal liability; therefore,
the auditor approves whatever report the client prefers regardless of audit
evidence. However, once again, such a report, either G or B, contains abso-
lutely no information about p and is therefore ignored by the market. Thus,
as in case (1), the market uses its prior belief, p
0
, to price the firm: m = p
2
0
.
Cases (1) and (4) indicate that excessive legal liability or excessive auditor
fee leads to “uninformative accounting,” in which accounting reports pro-
vide no incremental information on the firm’s financial condition.Thus, the
market’s belief given uninformative accounting is the same as the market’s
belief prior to the release of accounting reports:
p
0
= (1 − x)p
G
+ xp

B
. (2)
Additionally, by equation (1), the market price prior to the release of ac-
counting reports is
m
0
= [(1 − x)p
G
+ xp
B
]
2
. (3)
Because reports from uninformative accounting make no impression on the
capital market, the firm will not choose a fee, F , to induce uninformative
accounting. Thatis, uninformative accountingis not an equilibrium. Rather,
if informative reports are to be produced, the tension between auditor fee
and legal liability must not be lopsided, as shown in the two remaining
568 T.
LU
G
p
q
1 –
q
q
1 –
q
0
p

0
p
B
p
firm
type
audit
evidence
G
p
B
p
GG
G
G
B
B
BB
conservative
accounting
aggressive
accounting
1 –
x
x
F
IG. 1.—Conservative and aggressive accounting.
cases.
Case (2): (1 − p
G

)L ≤ F ≤(1 − p
0
)L. In this case, audit evidence matters
to theauditor. Recall that the favorableevidence, p
G
, impliesthat theclient is
a high-profitability firm, whereas the unfavorable evidence, p
B
, implies that
the client is a low-profitability firm; while the uninformative evidence, p
0
,
may correspond toeither ahigh- or low-profitabilityfirm. Whenthe evidence
is favorable (p
G
), the auditor fee exceeds the legal liability ((1 − p
G
)L ≤
F ), so the auditor approves report G. When the evidence is unfavorable
(p
B
) or uninformative (p
0
), the legal liability exceeds the auditor fee (F ≤
(1 − p
0
)L < (1 − p
B
)L), so the auditor disapproves G and the firm has
to issue B. Clearly, in case (2), a high-profitability firm’s financial condition

(p
G
) might be understated (reported as B), whereas a low-profitability firm’s
financialcondition wouldnot.This typeofaccounting, withsuch asymmetric
understatements—here termed “conservative accounting”—is illustrated in
figure 1.
Based on its understanding of the auditor-client interaction, the market
makes its rational inferences. If report G is issued, the market believes that
the auditor has identified the firm as a high-profitability type, p
G
, so its belief
given G is
ˆ
p
G
= p
G
. If report B is issued, the market believes that either the
firm is a high-profitability type, p
G
(the probability of which is 1 −x), not so
identifiedby theauditor(the probabilityofwhich is1−q) or thefirm is alow-
profitability type, p
B
(the probability of which is x). Therefore, the market’s
belief given B is, by Bayes’ Theorem,
ˆ
p
B
=

(1 −x)(1−q)p
G
+xp
B
1 −(1 −x)q
.
2
Inserting the
expressions for the market’s beliefs,
ˆ
p
G
and
ˆ
p
B
, into equation (1) yields the
2
Section 4 provides an explanation of how the market rationally infers audit quality, q,on
the basis of observable information.
OPINION SHOPPING
569
market prices given G and B, denoted by m
c
G
and m
c
B
, respectively. (The
superscript c denotes conservative accounting.)

Case (3): (1 − p
0
)L ≤ F ≤ (1 − p
B
)L. The analysis for this case is similar
to that for case (2). The auditor’s attestations in case (3) differ from those
in case(2) only when the evidence is uninformative (p
0
)—because auditor
fee exceeds legal liability ((1 − p
0
)L ≤ F ), the auditor approves G. Clearly,
in case (3), a low-profitability firm’s financial condition (p
B
) might be over-
stated (reportedas G),whereas ahigh-profitability firm’sfinancial condition
would not. This type of accounting with such asymmetric overstatements,
here referred to as “aggressive accounting,” is illustrated in figure 1. From
figure 1, given aggressive accounting, the market’s rational belief given B
is
ˆ
p
B
= p
B
, and its belief given G is
ˆ
p
G
=

(1 −x)p
G
+x(1 −q )p
B
1 −xq
. Inserting the
expressions for
ˆ
p
G
and
ˆ
p
B
into equation (1) yields the market prices given
G and B, denoted by m
a
G
and m
a
B
, respectively. (The superscript a denotes
aggressive accounting.)
The above results are summarized in the following proposition.
P
ROPOSITION 1. a) (Conservative accounting). When (1 −p
G
)L ≤ F ≤ (1 −
p
0

)L, a high-profitability firm p
G
publishes report G if it is detected by the auditor
but B otherwise, a low-profitability firm, p
B
, publishes B, and the market prices given
G and B, respectively, are
m
c
G
= p
2
G
and m
c
B
=

(1 − x)(1 −q)p
G
+ xp
B
1 − (1 − x)q

2
. (4)
b) (Aggressive accounting). When (1 − p
0
)L ≤ F ≤ (1 − p
B

)L , a low-profitability
firm, p
B
, publishes report B if it is detected by the auditor but G otherwise, a high-
profitability firm, p
G
, publishes G, and the market prices given G and B, respectively,
are
m
a
G
=

(1 − x)p
G
+ x(1 −q)p
B
1 − xq

2
and m
a
B
= p
2
B
. (5)
c) Regardless of the accounting type, the auditor approves G when the audit evidence
is p
G

and disapproves G when the audit evidence is p
B
; when the audit evidence is
p
0
, the auditor disapproves G given conservative accounting and approves G given
aggressive accounting.
Proposition 1 and figure 1 directly imply the following results:
C
OROLLARY 1. a) Auditor independence is not compromised.
b) A lower (higher) F relative to L results in auditor conservatism (aggressiveness).
c) Pr (misstatements) is decreasing in q.
d) Pr (misstatements |conservative accounting) < Pr (misstatements |aggressive ac-
counting) if and only if Pr(p
G
) is sufficiently low.
e) The report G produced from conservative accounting ismore informative than G pro-
duced from aggressive accounting; the report B produced from aggressive accounting
570 T. LU
is more informative than B produced from conservative accounting.
f) Pr (G |conservative accounting) < Pr (G |aggressive accounting).
Corollary (1a) states that auditor independence is maintained in equi-
librium: the auditor approves G when the audit evidence is favorable and
disapproves G when the audit evidence is unfavorable. That is, the audi-
tor refuses to support detected misstatements. This important conclusion
results from the corporate governance role of market prices. Supposing
that a low-profitability firm is identified by the auditor, to induce the au-
ditor’s attestation to its favored report—that is, to compromise auditor
independence—the low-profitability firm must offer a huge auditor fee to
allay its auditor’s legal liability concern (F ≥ (1 − p

B
)L). However, such a
huge fee destroys the financial report’s credibility in the eyes of the capi-
tal market, which then ignores these rosy reports in its pricing of the firm.
Consequently, anticipating the market’s rational pricing, the firm does not
find it worthwhile to offer its auditor a huge fee in return for nothing ex-
tra from the market. Thus, the market’s pricing regulates excessive client
pressure on the auditor, and auditor independence is maintained in equilib-
rium. In equilibrium, misstatements in financial statements may only survive
when the auditor receives uninformative evidence; however, as discussed
in section 2, this issue is not one of auditor independence but of audit
quality.
A poorer audit quality implies a greater likelihood of uninformative evi-
dence and consequently a greater likelihood of errors in attestations. When
the auditor fee is small relative to the legal liability, litigation risk concerns
provide incentives for auditors to err on the side of conservatism. Specif-
ically, when in doubt, the auditor disapproves the client’s more favorable
report and may unknowingly force a high-profitability firm to issue a less
favorable report. Thus, auditor conservatism may result in understatements
in financial statements, leading to conservative accounting. On the other
hand, when the auditor fee is large relative to the legal liability, lucrative
business opportunities provide incentives for auditors to err on the side
of aggressiveness. That is, when in doubt, the auditor approves the client’s
more favorable report and may unknowingly allow a low-profitability firm
to issue a more favorable report. Thus, auditor aggressiveness may lead to
overstatements, causing aggressive accounting. Overall, as Corollary (1b)
shows, the tension between the auditor fee and legal liability determines
auditor conservatism/aggressiveness and in turn leads to accounting con-
servatism/aggressiveness.
3

Clearly, conservative accounting may hurt “good” firms and aggressive
accounting may hide “bad” firms. Thus, the less likely the firm is to be a
3
Even though many factors contribute to accounting conservatism/aggressiveness, this
study focuses on one factor: auditor conservatism/aggressiveness. Whereas Gigler and Hem-
mer [2001] and Venugopalan [2004] study cases in which these two types of accounting are
exogenous systems, this paper addresses a case in which they are endogenous outcomes.
OPINION SHOPPING 571
“good” firm, the fewer misstatements conservative accounting will produce
(Corollary (1d)). Because aggressive accounting may produce overstate-
ments, a rosy report from aggressive accounting is not as reliable as a rosy
report from conservative accounting. By the same token, because conser-
vative accounting may produce understatements, a gloomy report from
conservative accounting is not as reliable as a gloomy report from aggressive
accounting (Corollary (1e)).
Proposition 1 also directly impliesthe following results concerning capital
market prices.
C
OROLLARY 2. a) (price ranking) m
a
B
≤ m
c
B
≤ m
0
≤ m
a
G
≤ m

c
G
.
b) (asymmetric price responses) |m
c
G
− m
0
|≥|m
c
B
− m
0
| and |m
a
B
− m
0
|≥
|m
a
G
− m
0
|.
c) (asymmetric price responses) |m
c
G
− m
0

|≥|m
a
G
− m
0
| and |m
a
B
− m
0
|≥
|m
c
B
− m
0
|.
d) The asymmetries in (b) and (c) are decreasing in q.
Corollary (2b) states that, (i) given conservative accounting, the magni-
tude of the price response to good news is larger than that to bad news,
and (ii) given aggressive accounting, the magnitude of the price response
to bad news is larger than that to good news. Corollary (2c) states that, (i)
given good news, the magnitude of the price response given conservative
accounting is larger than that given aggressive accounting, and (ii) given
bad news, the magnitude of the price response given aggressive accounting
is larger than that given conservative accounting. These asymmetries result
from the differential information content ofaudited financial reportscondi-
tional on the type of accounting (Corollary (1e)). Specifically, conservative
accounting produces asymmetric understatements, and aggressive account-
ing produces asymmetric overstatements. Thus,asymmetric accounting trig-

gers asymmetric price responses. Because a higher audit quality decreases
the asymmetric misstatements in reports (Corollary (1c)), it decreases the
asymmetries of price responses (Corollary (2d)).
As previously mentioned, legislators and regulators have two concerns
related to auditor’s decisions: (1) how the auditor deals with detected mis-
statements (an issue of auditor independence) and (2) how likely the audi-
tor is to detect misstatements (an issue of audit quality). Therefore, having
established that auditor independence is maintained in equilibrium, the
discussion now turns to audit quality.
4. Audit Quality
A higher audit quality increases the chances of informative audit evidence
and helps the auditor make more informed attestations. Nevertheless, a
higher audit quality necessarily comes at a higher audit cost. In view of this
trade-off, the auditor chooses the audit quality, q, to maximize the antici-
pated payoff from the subsequent attestation, less the audit cost, C(q). Be-
cause the auditor’s anticipated payoff from attestations depends on the type
572 T. LU
of accounting induced by the tension between auditor fee and legal liability,
two cases are relevant for the determination of audit quality: conservative
accounting and aggressive accounting.
Given conservative accounting, the auditor approves G only when the
client is a high-profitability firm, p
G
(the probability of which is 1 − x), and
the auditor detects this fact (the probability of which is q) (see figure 1). In
this event, the auditor receives an auditor fee, F, but bears a litigation risk
of (1 − p
G
)L. Hence, the auditor’s objective function is
Max

q
(1 − x)q[F − (1 − p
G
)L] −C(q). (6)
Given aggressive accounting, the auditor’s expected payoff from attesta-
tions can be thought of as the payoff from approving G regardless of audit
evidence, less the payoff from approving G when the audit evidence is p
B
(see figure 1). If the auditor were to approve G regardless of audit evidence,
he or she would definitely receive fee F but would be exposed to an av-
erage litigation risk of (1 − p
0
)L. On the other hand, if the client were a
low-profitability firm, p
B
(the probability of which is x), and the auditor de-
tected this fact (the probability of which is q), by approving G, the auditor
would receive the auditor fee, F, but bear a litigation risk of (1 − p
B
)L.
Hence, the auditor’s objective function is
Max
q
[F − (1 − p
0
)L] − xq[F − (1 − p
B
)L] −C(q). (7)
The incumbent auditor’s optimal audit quality, q
1

, in both cases is char-
acterized by the first-order conditions in equation (8) and equation (9)
below. Using equation (8) and equation (9), the capital market and non-
incumbent auditors can infer the incumbent auditor’s audit quality on the
basis of observable information.
P
ROPOSITION 2. The incumbent auditor’s optimal audit quality, q
1
, is charac-
terized as follows:
a) Given conservative accounting,
C

(q
1
) = (1 − x)[F − (1 − p
G
)L], (8)
and
dq
1
dF
> 0.
b) Given aggressive accounting,
C

(q
1
) = x[(1 − p
B

)L − F ], (9)
and
dq
1
dF
< 0.
Figure 2 illustrates the auditor’s optimal audit quality as a function of the
auditor fee. Clearly, depending on the type of accounting, a larger auditor
fee may cause a higher or lower audit quality, which implies that the popular
belief that auditor fee depresses audit quality is not always correct.
The relation between audit quality and auditor fee is driven by the type
of errors that auditors may make in attestations. Recall that, given conserva-
tive accounting, auditors in doubt disapprove report G and may therefore
OPINION SHOPPING 573
Lp
G
)1( −
Lp
B
)1( −
Lp )1(
0
−
q
F
expected liability
given favorable
audit evidence
expected liability
given unfavorable

audit evidence
expected liability
given uninformative
audit evidence
auditor
fee
audit
quality
uninformative
accounting
uninformative
accounting
conservative
accounting
aggressive
accounting
FIG. 2.—The auditor’s optimal audit quality.
unknowingly disapprove a high-profitability firm’s report G, thereby losing
that firm’s auditor fee F . The larger the opportunity cost of F , the greater
the incentive for the auditor to increase the chances of receiving informa-
tive evidence by increasing audit quality, q. Therefore, given conservative
accounting, a larger auditor fee will result in a higher audit quality.
The case of aggressive accounting, however, isquite different. Here, an au-
ditor in doubt approves report G and may therefore unknowingly approve
a low-profitability firm’s report G, thereby bearing an excessive litigation
risk. However, the auditor fee, F , dampens this litigation risk concern. The
larger the fee, F—and consequently the more bearable the litigation risk—
the smaller the incentive for the auditor to raise the audit quality, q. There-
fore, given aggressive accounting, a larger auditor fee causes a lower audit
quality.

Overall, the tension between auditor fee and legal liability not only affects
auditor independence but also affects audit quality. It might seem that if this
tension were just right, either kind of attestation error would be precluded,
meaning that neutral accounting would be achieved. However, in the real
world, audit technologies are neither perfect nor costless; there is always a
chance that inconclusive evidence may lead to the auditor’s failure to detect
misstatements.When thisisthe case,even thebestintentioned auditormight
make errors in attestations, and misstatements might survive.
Figure 2 sheds some light on the implications of the Sarbanes-Oxley Act
of 2002. The Act prohibits a broad spectrum of auditor-provided non-audit
services. It is clear from figure 2 that such restrictions on auditor fees have
574 T. LU
three impacts: (1) given conservative accounting, a restriction on auditor
fees will impair audit quality; (2) given aggressive accounting, a restriction
will improve audit quality, but with a higher audit cost; and (3) a severe
restriction might eliminate aggressive accounting and make accounting
conservative.
Sections 3 and 4 have addressed a situation in which auditor turnover is
absent; however, when auditor switching is introduced, significant changes
occur.
5. Auditor Switching
This section begins with outsiders’ (the capital market’s and nonincum-
bent auditors’) perceptions of and reactions to auditor switching and then
characterizes the firm’s auditor switching strategy given these perceptions
and reactions. In equilibrium, outsiders’ perceptions are consistent with the
firm’s actual switching strategy.
When an auditor change takes place, it is natural for outsiders to ask what
type of firm switches auditors. Given that a firm whose auditor supports its
favorite report, G, has no incentive to switch auditors, it seems likely that
the capital market and nonincumbent auditors view auditor switching as

a “red flag” signal: they perceive that switching firms have failed to secure
their predecessor auditors’ approval of report G. Later in this section, this
conjecture is confirmed in equilibrium.
Given this conjecture, a switching firm that has induced aggressive ac-
counting before switching is perceived to be a low-profitability type, p
B
,
because, given aggressive accounting, only this type might fail to receive its
auditor’s approval of G (see figure 1). Thus, because of the damaging signal
a switch would send to the capital market, such firms would not switch audi-
tors. Hence, in the case of aggressive accounting, the capital market fulfills
a perfect corporate governance role in the sense that it precludes opinion
shopping.
On the other hand, outsiders cannot perfectly infer the identity of switch-
ers that have induced conservative accounting before switching because,
given conservative accounting, both a high-profitability firm, p
G
, and a low-
profitability firm, p
B
, may fail to secure their auditors’ approval of G. The
likelihoods of such failure are (1 − x)(1 − q
1
) and x, respectively (see fig-
ure 1). Because, in contrast to low-profitability firms, high-profitability firms
can sometimes obtain their auditors’ approval, outsiders view the former
as having a greater tendency than the latter to switch auditors. Therefore,
on observing auditor switching, outsiders adjust upward the perceived prior
probability of a low-profitability type, p
B

:
Pr(p
G
|switching) =
(1 − x)(1 −q
1
)
1 − (1 − x)q
1
, Pr(p
B
|switching) =
x
1 − (1 − x)q
1
.
(10)
OPINION SHOPPING 575
Hence, outsiders’ prior expectation of p given auditor switching is
p
0
=
(1 − x)(1 −q
1
)p
G
+ xp
B
1 − (1 − x)q
1

. (11)
Outsiders’ skepticism about auditor switching considerably affects the
successor auditor’s audit quality and capital market prices. Like that of the
predecessor auditor, the successor auditor’s independence is unimpaired
in equilibrium because of the corporate governance role of market prices
(discussed in detail in section 3). Regarding audit quality, like the prede-
cessor auditor’s problem described in the preceding section, the successor
auditor’s objective functions are
Max
q
(1 − x)(1 −q
1
)
1 − (1 − x)q
1
q[F − (1 − p
G
)L] −C(q) (12)
given conservative accounting, and
Max
q
[F − (1 − p
0
)L] −
x
1 − (1 − x)q
1
q[F − (1 − p
B
)L] −C(q) (13)

given aggressive accounting. The only difference between the predecessor’s
objective functions, expressions (6) and equation (7), and the successor’s
objective functions, expressions (12) and equation (13), is the perceived
prior probabilities that the firm is a high- or low-profitability type. For the
predecessor, the perceived prior probabilities are 1 − x and x, respectively;
for the successor, the perceived prior probabilities are given by equation
(10). The successor auditor’s optimal audit quality is characterized by the
first-order conditions in equation (14) and equation (15) below. A compari-
son of equilibrium audit qualities before and after auditor switching is made
in the next section.
P
ROPOSITION 3. The successor auditor’s optimal audit quality, q
2
, is character-
ized as follows:
a) Given conservative accounting,
C

(q
2
) =
(1 − x)(1 −q
1
)
1 − (1 − x)q
1
[F − (1 − p
G
)L], (14)
and

dq
2
dF
> 0.
b) Given aggressive accounting,
C

(q
2
) =
x
1 − (1 − x)q
1
[(1 − p
B
)L − F ], (15)
and
dq
2
dF
< 0.
Turning to the capital market’s pricing, it should first be noted that, as
described in equation(11), uponlearning the newsof auditorswitching (but
before the release of any accounting report audited by the new auditor),
the market updates its belief. Inserting this belief into the pricing rule given
576 T. LU
in equation (1) yields the market price prior to the release of accounting
reports given auditor switching:
M
0

=

(1 − x)(1 −q
1
)p
G
+ xp
B
1 − (1 − x)q
1

2
. (16)
Characterizations of market prices given accounting reports released after
auditor switching are obtained in Proposition 4.
P
ROPOSITION 4. Given auditor switching,
a) the market prices given G and B produced from conservative accounting are,
respectively,
M
c
G
= p
2
G
and M
c
B
=


(1 − x)(1 −q
1
)(1 − q
2
)p
G
+ xp
B
1 − (1 − x)q
1
− (1 − x)(1 − q
1
)q
2

2
, (17)
and
b) the market prices given G and B produced from aggressive accounting are,
respectively,
M
a
G
=

(1 − x)(1 −q
1
)p
G
+ x(1 −q

2
)p
B
1 − (1 − x)q
1
− xq
2

2
and M
a
B
= p
2
B
. (18)
(The lower case m denotes the market price without auditor switching; the
upper case M denotes the price given switching.)
Comparing equations (16), (17), and (18) with their respective counter-
parts, equations (3), (4), and (5), yields the following corollary.
C
OROLLARY 3. a) M
a
B
= m
a
B
; M
c
B

≤ m
c
B
; M
0
≤ m
0
; M
a
G
≤ m
a
G
; M
c
G
= m
c
G
.
b) |M
c
G
− M
0
|−|M
c
B
− M
0

|≥|m
c
G
− m
0
|−|m
c
B
− m
0
|; |M
a
B
− M
0
|−
|M
a
G
− M
0
|≤|m
a
B
− m
0
|−|m
a
G
− m

0
|.
c) |M
c
G
− M
0
|−|M
a
G
− M
0
|≥|m
c
G
− m
0
|−|m
a
G
− m
0
|; |M
a
B
− M
0
|−|M
c
B

−
M
0
|≤|m
a
B
− m
0
|−|m
c
B
− m
0
|.
Corollary (3a) states that, in general, the market’s skepticism about audi-
tor switching depresses the firm’s market value.
4
Corollary (3b) states that
auditor switching increases the first asymmetry of price responses described
in Corollary (2b) and decreases the second asymmetry. Corollary (3c) states
that auditor switching increases the first asymmetry of price responses de-
scribed in Corollary 2(c) and decreases the second asymmetry.
As discussed earlier, at the time of auditor switching, the market cannot
discern a switching firm’s type if it has induced conservative accounting
before switching. This opens up the possibility that both high- and low-
profitability firms may switch auditors. The switching firm chooses an au-
ditor fee for the new auditor to induce its preferred type of accounting.
4
Switching does not affect m
c

G
and m
a
B
because report G from conservative accounting
and report B from aggressive accounting unmistakenly reflect the firm’s underlying financial
conditions.
OPINION SHOPPING 577
G
p
q
1 –
q
q
1 –
q
0
p
0
p
B
p
firm
type
audit
evidence
G
p
B
p

GG
G
G
B
B
BB
conservative
accounting
aggressive
accounting
1 –
x
x
switching
switc
hing
FIG. 3.—Auditor switching and conservative/aggressive accounting.
A high-profitability firm that has not obtained its incumbent auditor’s ap-
proval of G heartily dislikes the understatement possibility imbedded in
conservative accounting and so changes from conservative to aggressive ac-
counting, which guarantees that report G will be sanctioned by the new
auditor. Such auditor switching by high-profitability firms is termed “vindi-
cation seeking.” On the other hand, a low-profitability firm unable to obtain
its incumbent auditor’s approval of G very much likes the overstatementpos-
sibility afforded by aggressive accounting and so changes from conservative
to aggressive accounting in the hope of receiving an approval of G from the
new auditor. This kind of switching constitutes “opinion shopping.” There-
fore, both types of firms, if they switch auditors, change from conservative
accounting to aggressive accounting—but for different reasons. Overall, the
firm’s auditor-switching strategy confirms outsiders’ conjecture as described

at the beginning of this section.
Figure 3 illustrates auditor switching. Proposition 5 summarizes the firm’s
switching strategy described above.
5
PROPOSITION 5. a) The firm switches auditors if and only if it has induced
conservative accounting and failed to secure its incumbent auditor’s approval of
report G.
b) The switching firm induces aggressive accounting after switching.
Nevertheless, even though switching auditors increases the firm’s chances
of publishing its favorite report, the capital market casts a suspicious eye
5
Further switching of auditors is not an equilibrium. This is because once aggressive ac-
counting is induced after switching, a further switching would only reveal to the market that
the switcher is a low-profitability firm (see figure 3). Therefore, further switching is pointless.
578 T. LU
on such reports: for the same kind of accounting report, a switching
firm’s market price is not as high as a nonswitching firm’s market price
(Corollary (3a)). Thus, the capital market’s pricing reduces the benefits of
opinion shopping.
Proposition 5 and figure 3 have the following implications for the likeli-
hood and consequences of switching.
C
OROLLARY 4. a) Pr(switching |p
B
) > Pr(switching |p
G
).
b) Pr (switching |conservative accounting ) > Pr(switching |aggressive accounting).
c) Pr (switching) decreases in q
1

.
d) Auditor switching increases the probability of publishing report G.
e) With auditor switching, a high-profitability firm can secure an auditor’s approval
of its report G, whereas a low-profitability firm cannot always do so.
f) Auditor switching decreases the possibility of understatements but increases the
possibility of overstatements.
Corollary (4f ) identifies an important trade-off: auditor switching may de-
crease one type of misstatements (understatements) but increase the other
(overstatements). This outcome is a direct consequence of the switching
firm’s moving from conservative to aggressive accounting (Proposition 5).
On the other hand, a policy of mandatory auditor retention, which forbids
auditor switching for a fixed duration, may prevent correction of under-
statements. This result suggests that regulators must carefully investigate
the trade-off between understatements and overstatements in evaluating
alternative policy proposals.
6. Auditor Fee
This section wraps up the analysis by studying the determination of the
successor auditor’s fee and the predecessor auditor’s fee. As evidenced by
figure 2, the auditor fee affects both the auditor’s attestation (conservative
or aggressive) and the audit quality (q). Thus, when choosing the auditor
fee, the firm takes into account both effects of the fee.
6.1 DETERMINATION OF THE SUCCESSOR AUDITOR’S FEE, F
2
By Proposition 5, the switching firm induces aggressive accounting after
auditor switching. Thus, the auditor fee should be chosen from the range
[(1 − p
0
)L,(1− p
B
)L] (see figure 2). Because a high-profitability firm

p
G
can publish report G for sure given aggressive accounting, its expected
payoff is π
p
G
≡ M
a
G
− F . It can be easily verified that π
p
G
is decreasing in F .
This is due to two reasons. First, a lower auditor fee pushes up audit quality
and so makes the report G less likely to contain overstatements, thereby
increasing the market price, M
a
G
. Second, a lower auditorfee directlyreduces
the firm’s out-of-pocket cost. Taken together, a high-profitability firm, p
G
,
will choose theminimal amountof auditor feenecessaryto induceaggressive
accounting, which implies that F
2
= (1 − p
0
)L. A low-profitability firm, p
B
,

has two options: mimicking the high-profitability firm by choosing the same
amount of auditor fee, or choosing a different level of fee. Clearly, any
OPINION SHOPPING 579
level of fee that is different from the one chosen by the high-profitability
firm reveals the low-profitability firm’s identity to the market. Therefore,
mimicking is the best strategy. For later reference, both types’ expected
payoffs given auditor switching are listed below:
π
p
G
≡ M
a
G
− (1 − p
0
)L and
π
p
B
≡ (1 − q
2
)

M
a
G
− (1 − p
0
)L


+q
2
M
a
B
.
(19)
6.2 DETERMINATION OF THE PREDECESSOR AUDITOR’S FEE, F
1
Anticipating the auditor switching option, the firm sets the predecessor
auditor fee. In principle, the firm can induce either conservative or ag-
gressive accounting. If conservative accounting is induced and the firm is
unhappy with its incumbent auditor, it will switch auditors; if aggressive ac-
counting is induced, the firm will not switch auditors (Proposition 5). So the
firm’s expected payoff given conservative accounting (W
c
) and its expected
payoff given aggressive accounting (W
a
) are, respectively,
W
c
= (1 − x)q
1

m
c
G
− F
1


+ (1 − x)(1 − q
1
)π
p
G
+ xπ
p
B
and W
a
= (1 − xq
1
)

m
a
G
− F
1

+ xq
1
m
a
B
. (20)
To shed some light on the effect of mandatory auditor retention, the case in
which auditor switching is infeasible is also worth investigating. In that case,
the firm’s expected payoff given conservative accounting and its expected

payoff given aggressive accounting are, respectively,
W
c
= (1 − x)q
1

m
c
G
− F
1

+

1 − (1 − x)q
1

m
c
B
and W
a
= (1 − xq
1
)

m
a
G
− F

1

+ xq
1
m
a
B
. (21)
P
ROPOSITION 6. a) When auditor switching is feasible, the firm prefers conser-
vative accounting to aggressive accounting before switching.
b) When auditor switching is infeasible, the firm prefers conservative accounting to
aggressive accounting if and only if Pr(p
G
) < Pr(p
B
).
The intuition for the above results is straightforward. If auditor switching
is feasible, the firm would like to start with conservative accounting because
a favorable report G produced from conservative accounting is regarded as
the best possiblereport by the market(Corollary (2a)). If,unfortunately, the
firm does not receive its incumbent auditor’s approval of G, it can engage in
auditor switching. However, if the firm starts with aggressive accounting, the
best it can get (report G) is not viewed as good as report G produced from
conservative accounting. Even worse, the firm does not dare to engage in
auditor switching, because a switching would send a damaging signal to the
market, not to mention the auditor fee for thenew auditor. Things arediffer-
ent when auditor switching is banned. In that scenario, if understatements
are produced by conservative accounting, firms cannot switch auditors to
fix them. Therefore, those firms that are more likely to be hurt by under-

statements prefer aggressive accounting. Clearly, such firms are those with
580 T.
LU
better prospects (with a sufficiently large Pr (p
G
)). In brief, mandatory audi-
tor retention induces those firms with better prospects to prefer aggressive
accounting.
6.3 COMPARISONS OF AUDITOR FEES AND THEIR CONSEQUENCES
The next proposition compares the auditor fees and their impacts on
attestation and audit quality before and after auditor switching.
P
ROPOSITION 7. a) F
1
< F
2
.
b) The firm induces conservative accounting before auditor switching and aggressive
accounting after.
c) q
1
< q
2
.
Proposition (7a) results directly from Proposition (7b) because a higher
auditor fee is required to induce aggressive accounting. Proposition (7c)
states that the successor auditor’s audit quality exceeds thepredecessor audi-
tor’s audit quality. Thisimprovement occurs because,since alow-profitability
firm has a greater tendency to switch auditors than a high-profitability firm,
the successor bears a higher litigation risk than the predecessor. To make

matters worse, the switching firm offers the successor auditor only the mini-
mal amount of auditor fee necessary to induce aggressive accounting. Taken
together, the successor auditor deals with a riskier client with insufficient
fee. This stimulates the successor auditor to choose a higher audit quality
than that of the predecessor auditor.
The successor auditor’s high audit quality implies that a low-profitability
firm’s overstatements are very likely to be detected. Because auditor inde-
pendence is maintained in equilibrium, the detected overstatements will
not survive; therefore, opinion shopping is very likely to be frustrated.
Proposition (7c) seems to lend support to mandatory auditor rotation, the
proponents of which believe that it enhances audit quality. However, there
is a considerable difference between the voluntary rotation regime studied
here and a mandatory rotation regime. In the former, the common percep-
tion ofauditor switchingas a“red flag”signal alertsthe successor auditor and
stimulates audit quality. A mandatory rotation, on the other hand, forces all
types of firms to switch auditors and therefore eliminates the information
content of auditor switching. As a result, it may not enhance audit quality
but may encourage overstatements by providing a good cover for opinion
shopping. Therefore, my theory questions the wisdom of mandatory auditor
rotation.
In sum, the capital market’s and the successor auditor’s reactions to audi-
tor switching reduce the benefits of opinion shopping to the firm. First, the
market’s rational perception precludes opinion shopping when the firm has
induced aggressive accounting (Proposition (5a)). Second, when the firm
has induced conservative accounting before switching, for the same kind
of accounting reports, the switching firm’s market price is not as high as
the nonswitching firm’s market price (Corollary (3a)). Third, the successor
OPINION SHOPPING
581
auditor’s choice of a higher audit quality than that of the predecessor audi-

tor (Proposition (7c)) makes opinion shopping less likely to succeed.
7. Conclusion
My results contradict the conventional wisdom that opinion shopping
impairs auditor independence and audit quality. I study a plausible capital
market setting in which (1) firms have information superior to the market
and auditors regarding their financial conditions, and (2) firms are con-
cerned about how they are priced in the capital market. I show that neither
auditor independence nor audit quality is impaired by dismissal threats and
opinion shopping. In addition, auditor switching decreases potential under-
statements and increases potential overstatements in financial statements,
and because of the capital market’s and the successor auditor’s reactions to
auditor switching, firms cannot reap the full benefits of opinion shopping.
The study also sheds some light on the effects of banning most auditor-
provided non-audit services by the Sarbanes-Oxley Act of 2002. Further-
more, thepaper derives empiricalimplications for accounting conservatism,
attestation, audit quality, capital market price, auditor fee, and auditor
switching.
Based on the analysis of voluntary auditor switching in this paper, future
research can address three important normative economics questions in a
capital market setting in which auditors conduct financial statements audits.
Should a policy of mandatory auditor rotation be adopted? Should a pol-
icy of mandatory auditor retention be adopted? Or would a combination of
both policies be more desirable? As discussed in the paper, voluntary auditor
switching may decrease understatements but increase overstatements. On
the other hand, mandatory retention may prevent correction of understate-
ments, whereas mandatory rotation may encourage overstatements. Inves-
tigation of these trade-offs would shed some light on the conditions under
which a particular policy is most desirable.
APPENDIX
Proofof Proposition 4. In figure 1,replacing 1 −x and x by Pr(p

G
|switching)
and Pr(p
B
|switching) described in equation (10), respectively, then by
Bayes’ Theorem, the market’s beliefs given G and B produced from con-
servative accounting are, respectively,
ˆ
p
G
= p
G
and
ˆ
p
B
=
(1 − x)(1 −q
1
)(1 − q
2
)p
G
+ xp
B
1 − (1 − x)q
1
− (1 − x)(1 − q
1
)q

2
,
and themarket’sbeliefs given G and B produced from aggressiveaccounting
are, respectively,
ˆ
p
G
=
(1 − x)(1 −q
1
)p
G
+ x(1 −q
2
)p
B
1 − (1 − x)q
1
− xq
2
and
ˆ
p
B
= p
B
.
582 T.
LU
Inserting these beliefs into equation (1) yields the market prices described

in equations (17) and (18), respectively.
Proof of Proposition 6. Inserting the expressions for π
p
G
and π
p
B
given
in equation (19) into W
c
in equation (20) and comparing it with W
a
in
equation (20) yield W
c
≥ W
a
if and only if
x
1 − x
≥
q
1
−q
2
q
1
(1 − q
2
)

.
This condition is satisfied because, in equilibrium, q
1
≤ q
2
, which is proved
in the proof of Proposition (7c). This proves Proposition (6a).
Comparing W
c
and W
a
in equation (21) yields W
c
≥ W
a
if and only if
x
1 − x
≥ 1 ⇐⇒ Pr(p
B
) ≥ Pr(p
G
).
This proves Proposition (6b).
Proof of Proposition 7. Proposition (7b) results directly from Proposi-
tion (6a) and Proposition (5b). Then, it is clear from figure 2 that Proposi-
tion (7a) holds.
The result q
2
> q

1
in Proposition (7c) comes from two facts: (1) q
2
in-
creases in q
1
and (2) when q
1
takes its minimal value (q
1
=0), q
2
attains the
maximal value of q
1
, denoted by
¯
q
1
.
From Proposition 5, the switching firm induces aggressive accounting
after switching. Therefore, the successor auditor’s optimal audit quality, q
2
,
is characterized by equation (15). It follows from equation (15) that a higher
q
1
implies a higher q
2
.

To prove the second fact, it should first be noted that, because the switch-
ing firm changes from conservative to aggressive accounting, the prede-
cessor auditor’s optimal audit quality is characterized by equation (8) and
the successor auditor’s optimal audit quality by equation (15). The maxi-
mal value of q
1
,
¯
q
1
, is attained at F = (1 − p
0
)L (see figure 2). Inserting
this value of F into equation (8) yields C

(
¯
q
1
) = (1 − x)(p
G
− p
0
)L; more-
over, inserting the predecessor’s prior belief, p
0
, given by equation (2) into
the preceding equation yields C

(

¯
q
1
) = x(1 − x)(p
G
− p
B
)L. Turning to q
2
,
the successor auditor’s fee is F = (1 − p
0
)L. Inserting this value of F into
equation (15) yieldsC

(q
2
) =
x
1 −(1 −x)q
1
(p
0
− p
B
)L; moreover, inserting the
successor auditor’s prior belief, p
0
, given by equation (11) into the preced-
ing equation yields C


(q
2
) =
x(1 −x)(1 −q
1
)
1 −(1 −x)q
1
(p
G
− p
B
)L. In particular, at q
1
=
0, C

(q
2
) = x(1 − x)(p
G
− p
B
)L, which equals C

(
¯
q
1

), as described above.
Thus, at q
1
= 0, q
2
=
¯
q
1
.
REFERENCES
DYE, R. “Informationally Motivated Auditor Replacement.” Journal of Accounting & Economics
14 (1991): 347–74.
G
IGLER,F.,AND T. HEMMER. “Conservatism, Optimal Disclosure Policy, and the Timeliness of
Financial Reports.” The Accounting Review 76 (2001): 471–93.
OPINION SHOPPING
583
LENNOX, C. “Audit Quality and Auditor Switching: Some Lessons for Policy Makers.” Working
paper, Hong Kong University of Science and Technology, 1998.
S
ECURITIES AND EXCHANGE COMMISSION (SEC). “Disclosure Amendments to Regulation S-K,
Form 8-K and Schedule 14A Regarding Changes in Accountants and Potential Opinion
Shopping Situations.” Washington, DC: SEC, 1988.
T
AUB, S. “Auditors Rotating at a Dizzying Pace.” February 18, 2005 <>.
T
EOH, S. “Auditor Independence, Dismissal Threats, and the Market Reaction to Auditor
Switches.” Journal of Accounting Research 30 (1992): 1–25.
V

ENUGOPALAN, R. “Conservatism in Accounting: Good or Bad?” Working paper, University of
Chicago, 2004.