gietzmann and sen - 2002 - improving auditor independence through selective mandatory rotation [mar]

International Journal of Auditing
Int. J. Audit. 6: 183-210 (2002)
Received 2001
ISSN 1090–6738 Revised September 2001
Copyright © 2002 Management Audit Ltd. Accepted March 2002
Improving Auditor Independence
Through Selective Mandatory
Rotation
Miles B. Gietzmann
1
*, Pradyot K. Sen
2
1
Department of Economics, University of Bristol, UK
2
Department of Accounting and Information Systems, University of
Cincinnati, US
When an auditor receives signicant fee income from one
client it has often been suggested that reappointment concerns
may dilute auditors incentives to maintain independence from
management. A possible response to this issue could be to
mandate the rotation of auditors. However this is costly since
new auditors must repeatedly invest in learning a new clients
accounting system. In this research we build a model to
formally analyze this trade-off. We nd that the desirability of
rotation depends critically upon characteristics of the audit
market structure and to what extent an individual client
dominates an auditors’ client portfolio dened in terms of total
fees. We show that although rotation is costly, in audit markets
with relatively few large clients (thin markets), the resulting
improved incentives for independence outweigh the

associated costs. Our research is timely because although
historically it may not have been economically desirable to
adopt mandatory rotation, currently with increased corporate
merger activity taking place, for instance in the oil sector,
markets may now have become sufciently thin to warrant the
introduction of rotation.
Key words:
Auditor rotation, auditor independence, dominant
client, multi-period game, sequential equilibrium.
Correspondence to: Department of Economics, University of
Bristol, 8 Woodlands Road, Bristol, BS8 1TN. E-mail:

SUMMARY
A number of commentators on auditor rotation
often quote the US report of the Quality Control
Committee of the Securities and Exchange
Commission (SEC) Practices section of the
AICPA (1992). The study concluded that the
frequency of audit failure was three times
greater after the rst or second periodic audit
than in successive periods. An additional
inference from the study is that whether or
not the auditor changes, defalcations going
undetected are more likely in early years. The
study has been used by some commentators to
conclude that mandatory rotation is therefore
more likely to expose the nancial community to
more ‘new auditor ’ failures and hence on
184 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)

grounds of efciency and effectiveness should
not be adopted. We question attempts to draw
such conclusions on the basis of the AICPA
report for the following reasons. It is our
understanding that none of the sample rms in
the US study changed their auditor in a
systematic fashion as would be the case under a
condition of mandatory rotation. Therefore, the
audit failures occurred in rms where auditors
were changed in the prior period for some non-
legislative (non-mandatory) reason. The extant
audit literature, see for example Teoh (1992)
would suggest that at least some of these
changes were motivated by weaker firms
conducting opionion shopping or auditors
dropping their high risk clients. For instance, it
is conceivable that the reason there were
increased failures in the early years is because
the previously incumbent auditor recognized
serious problems with the client (such as the
going concern assumption) or, the observation
of auditor change simply indicates audit rms
removing the perceived ‘lemons’ from their
portfolio. That is, the increased failure rate may
not simply be the result of new auditor failures
per se,
but instead also the result of previous
incumbents lack of desire to stay with certain
risky clients.
With these issues in mind we develop a model

of auditor rotation which focuses upon the
economic trade-offs facing auditors. We focus
upon the incentives for a new auditor to provide
sufcient effort to understand a client and the
incentives for an incumbent auditor to be
inuenced by reappointment concerns. We then
define a set of circumstances which are
supportive for the case for mandatory rotation.
1. INTRODUCTION
‘Another suggestion contained in the European
Union’s Fifth Directive was that there should be
an upper limit on the number of years for which
an accounting rm could act as auditors to any
given company. After a maximum of ve years,
the company would have to find another
auditor. This would mean the auditor would not
have to worry about the effects of upsetting the
directors because he would know he was going
to be replaced after ve years anyway This
proposal was also considered unacceptable by
the accountancy profession on the grounds of
time and cost. It could also be argued that an
auditor is more likely to miss something during
the early years of an appointment when he is
relatively unfamiliar with the client. The
proposal was certainly unpopular, although is
not totally unworkable. In Italy, for example, an
auditor cannot serve the same client for more
than nine years. After this period has elapsed, he
cannot be reappointed by the company for at

least ve years.’ (Dunn pp.32, (1991)).
‘Independence is of paramount importance to
the effectiveness of the audit function.
Representatives of regulatory agencies, as well
as critics of the public accounting profession and
ineffective corporate governance, have
questioned whether private sector auditors are
sufciently independent of their clients in fact
and appearance. To insure independence in
Canada, among other controls, (1) the regulators
may review the public accountants’ working
papers and (2) two outside auditors are required
to share responsibility for the audit with one of
the two being rotated every two years.’ US
GAO/AFMD-91-43 p48-49.
A recent report by the Maastricht Accounting
and Auditing Research Center (Buijink
et al.
(1996)) illustrated that within Europe, there
exists a rich set of regulatory control
mechanisms for auditors. This is in contrast to
North America where the literature has
predominantly focused upon auditors’ legal
liability exposure (Nagarajan (1994),
Balachandran (1993)), looking at whether the
liability levels of US auditors may have become
problematic in recent times. One of the principal
research ndings of this paper is to argue that
given structural changes in the market for audit
services, it may now be benecial for another

regulatory instrument (mandatory auditor
rotation) to be given simultaneous consideration
along with legal liability. Specically, consistent
with informal arguments (Shank 1979,
DeAngelo 1981a,b,) we establish that in audit
markets with relatively few new client
opportunities (thin markets), the application of
rotation is economically desirable since the
improved incentives for independence
outweigh the additional cost associated with
understanding a new client’s auditing system
upon rotation. The simple intuition for this
result is that when one client forms a signicant
element of total fee income for an auditor, the
auditor becomes more susceptible to managerial
influence, endangering maintenance of
Improving Auditor Independence Through Selective Mandatory Rotation 185
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
independence. Thus, in our view, the problem of
auditor independence is not a systematic
auditor-specic problem, rather it is embedded
in the incentives of the specic auditor-client
relationship and the entire audit market
structure. If only liability levels are used to
ensure independence, the best auditors which
maintain independence, but which sometimes
fail (for other reasons) face greater liability than
is required to maintain their independence.
Thus, under some circumstances, even the better
auditors may prefer mandatory rotation if it led

to a lower legal liability. Furthermore, we note
that auditor rotation is used in a number of
countries and these countries have lower legal
liabilities for auditors
1
. For instance in Italy
mandatory rotation exists for stock exchange
listed companies and in Belgium and Canada for
banks. In each of these cases it seems reasonable
to argue that the audit markets could be
characterized as thin
2
.
In situations where independence is a concern,
one possible alternative to rotation, would be to
further increase the legal liability of the auditors.
However, it is only recently that legislators in
the US have enacted the Private Securities
Litigation Reform Act 1995, which lowers the
liability regime of auditors. This suggests that
proposing increases in liability to further
improve independence may not be constructive
at this time. Instead, after the application of
mandatory rotation in certain well defined
situations, we show that auditors’ liability
could in fact be further lowered without
compromising independence, or increasing the
cost to the client, while at the same time
retaining sufcient incentives for better auditors
to invest in learning costs for new clients. Our

analysis provides a basic framework within
which to better understand the performance of
mandatory rotation so that its efcacy can be
appraised relative to other policy instruments
such as rotation of audit partners within
partnerships and the use of audit committees to
monitor the auditors to improve auditor
independence.
The paper is organized as follows. In Section 2
we characterize a representative client rm’s
investment project that is subject to audit.
Then we present a characterization of audit
technology, along with managerial and auditor
incentives. We characterize information
processing in the dynamic setting and provide
the equilibrium concepts used for our analysis.
We, then analyze the case of period by period
mandatory rotation in Section 3. In Section 4, we
analyze the two-period audit game that
represents a non-rotational regime and
characterize the equilibria. Our main results are
contained in Section 5. We establish that if audit
markets are thin, independence can be
maintained with a lower level of legal liability
under mandatory rotation than when rotation
is not mandated. The intuition here is that
in thin markets without rotation, auditors’
reappointment concerns are so strong that
liability levels need to be signicant to maintain
independence. In contrast, in more developed

audit markets with many potential new clients,
auditors’ potential gains from maintaining a
reputation for independence outweigh the gains
from reappointment with a specific client.
Exploiting this incentive, regulators can reduce
liability, relying on auditors’ self-interested
concern to maintain independence. Our results,
therefore, arise because in a sufciently thin
market, self-interested reputation concerns are
muted by the fact that there are relatively few
new clients and that opportunities to replace the
existing client base are limited no matter how
good an auditor’s reputation. In such a setting
without mandatory rotation, the legal liabilities
must not only balance the cost of effort, it must
also balance the auditors’ compromising
incentives associated with the loss of current
business, lest the report becomes unfavorable.
Indeed, if overall liability reduction is deemed to
be desirable from a societal perspective,
mandatory rotation is clearly benecial where
the market for audit services is dominated by a
few large clients who are solicited by all the
audit firms. In Section 6 we outline some
empirical evidence from countries where
auditor rotation is in effect and discuss
regulators current policy debate on mandatory
auditor rotation in Section 7. We present our
concluding comments in Section 8.
2. THE AUDIT GAME: A STOCHASTIC

INVESTMENT PROJECT AND
STRATEGIC INCENTIVES
In the following subsections we develop our
model of the audit game using standard game
theoretic constructs which help us understand
how the strategic behavior of an auditor is
186 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
determined. However, before presenting the
formal modelling assumptions we shall set out
some of the conceptual limitations of this
economic approach. We argue that although the
model makes somewhat simple assumptions
about the motivation of auditors, the derived
model provides us with predictions which allow
us to clearly identify regulatory implications
under one polar extreme assumption about self-
interested selfish auditors. That is while
ultimately research needs to be conducted to
capture more complex auditor behavior, the
results with the simplied assumptions need to
be established so that one can then see how
sensitive they are to subsequent behavioral
modications.
Modelling the auditor as an economic
agent
In the following model we shall assume that
auditors’ desire to maintain independence is
determined by economic forces such as present
and future fee income. However, it has

sometimes been argued that some auditors lack
independence for no apparent economic reasons
and that conversely some other auditors have
historically made signicant nancial sacrices
to maintain independence. Obviously there is a
complex mix of economic, pschological and
other reasons why an auditor behaves in a
particular fashion and hence our model should
be seen as a polar extreme which simply
concentrates on economic factors. While
admitting therefore that the model only captures
part of the setting in which auditors actually
operate, we think it is also important to stress
that with the increasing size, internationaliza-
tion and commoditization of auditing, economic
factors have become increasingly important to
auditors working in the eld. In fact some
would argue that it is the dominant factor.
Indeed, factors such as fee income and repeat
business have become increasingly applied in
internal performance appraisal when auditors
look to be promoted within an audit
partnership. Thus given this increasing use of
such economic performance measures at every
stage of the promotion and renumeration phases
of an auditor’s career, it is hard to defend any
assumption that such economic factors are of
minor importance
3
.

Another concern reects whether an auditor’s
desire to maintain independence is a fixed
binary choice or determined more on a case by
case basis related to economic factors. That is, is
an auditor always independent no matter how
important the client is, or could the auditor
consider compromising his or her independence
only if a client was ‘sufciently’ important. We
try to address this complex issue by developing
a model of implicit collusion in which an auditor
does not simply flip from being totally
independent to alternatively conspiring with a
client to hide information once some critical
economic cutoff is reached. Instead in our model
the auditor switches from diligently looking for
defalcation to not looking so hard for
defalcation. However, if it is found in the latter
case it is immediatedly acted upon. That is we
do not assume that auditors switch from being
completly independent to completly non
independent but instead that at the margin they
simply don’t try as hard when they are under
increasing nancial pressure.
Finally it is sometimes argued that a (fee) size
based metric for independence is problematic.
One possible reason for this is that taking the
economic model to its extreme it should be client
assignment protability that is the driving force,
not fee, since some large assignments may be so
complex and labour intensive that the

assignment is not as protable as a medium
sized niche sector assignment. However, while
recognizing that this is a limitation of the model,
basing the model on assignment protability
will severly limit empirical testability since such
profitability is not disclosed. Moreover, the
magnitude of client by client fees is often seen as
a good proxy for the ability of an audit
partnership to sell on lucrative consulting
services such as management consulting and
taxation advice. Thus while it is true to say that
size alone does not soley determine an auditor’s
incentives to maintain independence it is an
important factor
4
. Thus given these important
caveats let us now turn to the formal model
specication.
We assume there are three risk-neutral players
in the game; an owner (shareholder), manager
and an (external) auditor. The owner has an
investment project which the manager oversees
(manages) on a day-to-day basis. Since some
auditors need to invest in client-relation specic
skills that augment their audit technology
Improving Auditor Independence Through Selective Mandatory Rotation 187
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
(outlined below), we shall forthwith describe the
owners’ investment project simply as ‘the
project’ and reserve ‘investment’ for the

auditor’s technological investment required to
understand the accounting system of a specic
client.
The essential strategic interaction in the game
is as follows. We assume that a conict of
interest exists between the manager and the
owner because the manager is an empire
builder
5
who wants the project always to
continue and the owner only wants the project
to continue, if it is expected to be protable.
Given the stochastic nature of the project and the
owners awareness of the managers’ incentives,
the owner may nd it valuable to employ an
independent auditor to attest
6
the ‘state’ of the
project. However, the independence of the
auditor may be compromised since economic
incentives exist such that the auditor may
also prefer the project to continue and be
reappointed as the auditor again. That is, rather
than suggest that the auditor would ever collude
directly with management, we propose a model
in which the auditor simply may not ‘try too
hard’ to nd evidence which casts the project in
a negative light; which we describe as implicit
collusion by the auditor. Thus in our model
setting

7
we dene an auditor as
maintaining
independence
as an auditor that does not
implicitly collude.
The formal analysis is presented as follows. In
the rst subsection we shall concentrate only
upon the nature of the project, temporarily
assuming that the manager is non selsh and
carries out duties purely in the interests of the
owner. In the second subsection we will relax the
naive incentives assumption and focus upon the
economic incentives of management and
auditors and how self interest may lead them to
behave strategically in their own interests
resulting in non-maintenance of independence
by the auditor.
The project
We shall assume the project can be classied as
intrinsically either a good, g project or a bad, b
project, and at the beginning of the game the
owner assumes that the (unconditional)
probability that the project is good is p(g) (bad
with probability (1-p(g))). We shall assume that
the project has just generated an annual return
of Y and at issue is whether to continue with the
investment project or liquidate it and also
whether to continue with the incumbent auditor
or not. If the state of the project were good, it

will generate an annual return of Y for the next
two periods
8
, which has a net present value (to
the owner) of V
g
. If the project were bad it would
generate an annual return Y each period if it
remained in progress. However, in every period,
there is a probability w that it will suffer
nancial distress
9
and this is evaluated by the
owner as having an expected net present value
of V
b
. We further assume that all period project
state realizations are independent. That is:
Y Y
V
g
= Y + ––––– + ––––––
1 + r (1 + r)
2
’
and
1 – w 1 – w
2
V
b

= Y + –––––– Y + –––––– Y.
1 + r
(
1 + r
)
In order to generate a potential demand for an
auditor to attest the state of the project we shall
also assume that if the owner was informed that
the project state was bad (before it suffered
nancial distress), market opportunities exist
such that the owner can immediately liquidate
the project for a value L by diverting the assets
of the project to some alternative unrelated use
such that:
V
g
> L > V
b
(1)
i.e., the owner would prefer to keep with good
projects and liquidate bad ones. However,
without any audit, the owner stays with the
project because:
p(g)V
g
+(1 – p(g))V
b
> L, (2)
that is, without any information about the state
of the project, it is not desirable to liquidate it.

The audit technology, liability, direct and
reputational fees
We shall assume that since audit technology is
imperfect, audits do not perfectly reveal the
underlying project state. To reflect this we
introduce
tilda
notation to differentiate the
auditors’ report on the state of the project, from
the intrinsic states, g and b. That is we let:
~
g = auditor reports the project is good
~
b = auditor reports the project is bad.
Furthermore we assume a good project never
generates a bad signal
10
but a bad project can
generate a good signal.
Next in order to generate the possibility of
different strategic responses by different
188 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
auditors, we need to introduce auditor
heterogeneity into our model. Recalling that it is
often argued in the literature that initial audit
engagements may involve signicant relation
specic start-up costs (Arens and Loebbecke
1976 p. 100, De Angelo 1981 p. 35), we assume
there are two (unobservable) types of auditors.

These two types of auditors are labelled M and N
and they differ as follows. At the beginning of an
audit assignment, type M auditors make a client-
specific investment in detection technology,
denoted I, that is not observable to the investor
11
resulting in the chance of an audit detecting a
bad project being d
M
. In contrast, the type N
auditors do not have the ability to improve their
audit detection probability which remains xed
at d
N
. The relation specific investment is
productive in the sense that it increases the
probability of an auditor detecting a bad state,
with:
1 > d
M
> d
N
> 0. (3)
Then let the proportion of Type M auditors in
the economy be denoted m
Î
(0,1) and for
notational convenience we shall subsequently
write the detection probability to be d
m

, where
d
m
Î
[d
M
, d
N
]. We further assume that the
auditor is independent in the sense of Magee
and Tseng (1990) such that the auditors report
what they observe and do not strategically
misrepresent their findings
12
. What they
however do provide strategically is their effort.
That is auditors always report what they see but
when they do not maintain independence they
do not provide (extra) effort
13
to detect whether
the state is bad.
We assume the auditor is paid an audit fee F
per period for performing the audit
14
. We also
assume that the audit fee F is sufciently large to
cover the auditor’s operating costs so that both
types of auditors can participate and the market
for audit services does not break down with the

decision to collude following in a trivial fashion.
Furthermore, when performing audit-detection
duties, auditors incur (xed) effort cost of e
every period regardless of their type.
If the project fails (suffers nancial distress)
after the auditor reports
~
g then the auditor
expects to incur litigation liability of
a
, that is,
nancial distress acts as a trigger
15
for litigation
(Alexander (1991)) and the auditor just breaks
even on other assignments
16
.
At this stage it is important to stress that if we
assumed that direct liability concerns were the
only force incentivizing auditors to maintain
independence, we may be criticized for being
too severe on auditors. Indeed auditors are also
motivated by a concern to maintain their
reputation and not simply by litigation costs.
Since developing a fully endogenized model
of formation and maintenance of auditor
reputation is outside the scope of this research,
we concentrate only on one aspect of the entire
reputational concerns: the concern to protect the

future fees. We assume existence for such a
concern, and denote the additional fees
(possibly through additional assignments) to a
‘reputed’ auditor as f. Our analysis then allows
f to vary parametrically so as to be applicable to
different market settings which give rise to
different values for reputation maintenance f.
Also note that the process that generates the
reputational fees f in our model is economically
rational. We assume the total audit market per
surviving auditor to grow in period 2. Since
the independence and type of auditors are
unobservable, investors in the second period
select only from those auditors who have a good
‘track record’ in that their clients did not suffer
nancial distress in the rst period. Since d
M
>
d
N
, type M auditors are more likely to survive in
the second period. Therefore, it is rational for the
clients to impute a reputation of competence
(better audit detection technology) on the
average to the surviving auditors, who are
rewarded with incremental business
(reputational gain) of f in the second period
17
.
Having established the payoff variables, let us

now characterize the auditor’s strategy. Both the
auditor types, i.e., who do and do not invest in
additional audit detection technology
respectively, have a choice whether or not to
provide some minimum effort (which we shall
normalize to take the value 0 ) or alternatively
provide additional (xed) effort e > 0 when
trying to ascertain the state
18
, that is:
e > 0 = personal (xed) cost to the auditor of
providing effort to ascertain the state
in every period
e = 0 = normalized cost of providing
minimum effort.
We assume the manager is an empire builder
deriving positive utility from project
continuance and faces limited liability
19
. When
the state is good, the manager is indifferent
about auditors’ behavior. When the state of the
world is bad, the manager prefers the auditor to
Improving Auditor Independence Through Selective Mandatory Rotation 189
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
provide minimum detection effort
20
and hence
the decision to set e = 0 can be described as
auditor collusion with management, whereas

setting e > 0 maintains independence
21
, that is:
e > 0
Þ
auditor maintains independence (4)
e = 0
Þ
auditor implicitly colludes.
There now remains one necessary detail; the
length of the audit game. We shall consider two
possibilities. In the immediately following
section we assume that mandatory rotation is in
place and hence we model the audit game as a
one-period game. In the next section we assume
that the auditors of rms, who do not suffer
nancial distress, can be reappointed. We model
the simplest setting in which reappointment can
occur, a two-period setting
22
.
3. MANDATORY ROTATION: THE
SINGLE PERIOD AUDIT GAME
Mandatory auditor rotation can be viewed as
an arrangement where the auditor-client
relationship is limited by law to a nite number
of years. For mathematical simplicity we shall
dene the length of time of such a limitation as
one period. Thus, whether or not the client
experiences nancial distress, the engagement

comes to an end. In a mandatory rotation
setting, since rehiring cannot take place, a
reputation based upon observation of rehiring
can not now be established. Thus, by
construction, there is no possibility of a
reputational gain
23
of f.
We assume that the sequence of strategic
moves and the associated pay-offs of the
players
(game tree) are summarized in Figure 1. Note
that the nodes A and A’ (equivalently B and B’)
are informationally equivalent. Similarly, nodes
1, 2, 3 and 4 are informationally equivalent to the
nodes 1’, 2’, 3’, and 4’ respectively.
Starting from the left assuming the project has
just commenced:
 Nature chooses the state of project
s Î
[g, b],
g for good and b for bad, with respective prior
probabilities p(g) and 1 – p(g).
 Nature also chooses the auditor types
whereby m
Î
(0, 1) is the proportion of type M
auditors who are capable of investing an
amount I in the client-specic skills.
PERIOD 1

F
–
I
–
e
F
–
I
F
–
e
F
F
–
I
–
e
F
–
I
–
e
–
a
F
–
I
–
e
F

–
I
F
–
I
–
a
F
–
e
F
–
e
–
a
F
–
e
F
F
–
a
Project g
Project b
Invest m
Not
Invest (1-m)
Invest m
Not
Invest (1-m)

Work (1 – C
1
)
Collude C
1
Work (1 – C
1
)
Collude C
1
Work
(1 – C
1
)
Not Detect 1 – d
1
Not Detect 1 – d
1
Detect d
1
Survive 1 - W
Fail W
Survive 1 - W
Fail W
Survive 1 - W
Fail W
Survive 1 - W
Fail W
Detect d
1

Collude
C
1
Work
(1 – C
1
)
Collude
C
1
B’
A’
A
B
1
2
3
4
1’
2’
3’
4’
Figure 1:
190 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
 The investors decide to hire an auditor
24
and
pay a fee F, provided that the auditor produces
decision-relevant information (that is, satises

the conditions of Observation 1 to be set out).
Since investors can not observe the auditor type,
it is as if nature assigns auditors to projects.
 The auditor chooses an implicit collusion
strategy l
Î
[c, nc] where c stands for colluding
(e = 0) and nc stands for not colluding (e > 0).
Let c
M
, c
N
denote the probability of colluding
with management by investing types M and N
respectively. For the sake of notational
convenience, we write the collusion probability
to be c
m
, where c
m
Î
[c
M
, c
N
].
 The auditor reports the audit nding non-
strategically
25
, denoted as

~
s Î
[
~
g,
~
b].
 In the case the auditor colludes and nature
chose b, there is a probability w that the project
will then suffer nancial distress and end in the
period. However, there is also a 1–w probability
that the project will not suffer nancial distress
in the period.
 In the case the auditor does not collude and
nature chooses b, there is a probability d
m
that
the auditor will detect the state is bad and hence
the project is ended as a result of the auditors’
discovery. However, there is also a probability of
1 – d
m
that the bad state is not detected and
hence following the audit report there is a
probability of w that the project then suffers
nancial distress and probability 1 – w that it
will not.
 The investor decides to act after receiving
the audit report (continues or divests from the
project); the nancial distress is determined then

through nature’s move. We denote this event as
the (imperfect) state realization and denote it
as
q
.
Although we discuss the above game in
continuous strategies, we restrict our analysis
only to pure strategies, i.e., whether the auditors
collude or not. That is, the admissible values of
c
m
for this analysis are either 0 or 1. Before we
characterize the equilibria, we need another
consistency check. In any equilibrium, the
investors must have a demand for auditing,
such that the information generated by audit has
a strictly positive value. We establish such a
condition in Observation 1 below.
Investors demand for audit information
We assume that investors decision of whether or
not to hire an auditor is based upon an
evaluation of whether the auditor generates
decision relevant information. In this particular
context this pertains to the extent to which audit
information leads investors to revise beliefs
concerning the state of the investment project g
or b. Thus letting
r
(g|
~

g) denote the (Bayesian)
revised belief of the investor after observing a
good audit report
~
g for the rst period but
before the nature’s draw determining nancial
distress, we rst note that if the state is bad the
probability that the auditor will not detect it is
given by:
n
(d
m
, c
m
, m) = {m[1 – d
M
(1 – c
M
)] +
(1 – m) [1 – d
N
(1 – c
N
)}
and hence the unconditional probability of a
good report p(
~
g) is given by:
p(
~

g) = p(g) +
n
(d
m
, c
m
, m)(1 – p(g))
For instance in the case of type M auditors and
c
M
= 0 (implying no collusion takes place) the
chance of
non detection
is simply given by (1 –
d
M
). In contrast with collusion c
M
= 1, this
probability becomes 1. Thus the required
conditional expectation for investors is given by:
p(g)
r
(g|
~
g) = –––––––––––––––––––––––– (5)
p(g) +
u
(d
m

, c
m
, m)(1 – p(g))
.
and so when an investor is considering the
incremental benet of employing an auditor,
this necessitates a comparison between:
the expected payoff with an audit information
conditioned strategy:
– if receive audit report
~
g continue with the
investment expecting to earn
r
(g|
~
g)V
g
+
(1 –
r
(g|
~
g))V
b
– F
=
[
(6)
– if receive audit report

~
b, liquidate the
investment earning L – F
to
the expected payoff without audit information (given
by (2))
p(g)V
g
+ (1 – p(g))V
b
.
Thus we have:
Observation 1: (Condition for positive
demand for auditors under rotation)
Audit information has value to investors
provided:
p(
~
g)(
r
(g|
~
g)V
g
+ (1 –
r
(g|
~
g))V
b

) + (1 –
r
(
~
g))L – F>p(g)V
g
+ (1 – p(g))V
b
(7)
Proof: Follows from the denition of the value
of information.
Improving Auditor Independence Through Selective Mandatory Rotation 191
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
Turning now to consider the characterization
of equilibria, we note that for every equilibrium,
we need to verify that (7) holds given the
parameters specied under that equilibrium.
Equilibrium Under Mandatory Rotation
It is clear that there are three possible candidates
for equilibrium in the above one-period game. A
pooling equilibrium, where both (investment)
types do not collude which we denote as the
Full Compliance (FC) Equilibrium. A separating
equilibrium where only type M auditors do not
collude but type N auditors collude, which we
denote as the Partial Compliance (PC)
equilibrium. Another pooling equilibrium
candidate is where both types collude, which we
denote as the No Compliance (NC) Equilibrium.
We use the concept of the Bayesian-Nash-

sequential equilibrium (Kreps and Wilson 1982)
adapted to our situation
26
. We show that the
only two possible equilibria that can exist in the
game described above are a PC equilibrium and
a FC equilibrium. An NC equilibrium cannot
exist because under the belief structure induced
by NC strategies, there is no demand for
auditing. Theorem 1 sets out the conditions for
existence of the FC and the PC equilibria.
Theorem 1 (Existence of FC and PC
equilibria)
Let the fee in the audit market be set to at least
offset the operating costs of a Type M auditor.
Let
a
R
denote the legal liability under the
mandatory rotational regime. The only possible
equilibria of the single period audit game
discussed above are a PC equilibrium and an FC
equilibrium. An NC equilibrium cannot exist.
A PC equilibrium would exist if:
p
M
a
R
º
d

M
w(1 – p(g))
a
R

e

d
N
w(1 –
p(g))
a
R
º p
N
a
R
. (8)
Alternatively, a FC equilibrium would exist, if
instead,
p
N
a
R
º
d
N
w(1 – p(g))
a
R


e. (9)
and,
I 
(d
M
– d
N
) (1 – p(g))w
a
R
. (10)
Proof: See Appendix.
From (8) we see that assuming type M auditors
have no incentive to collude, if effort cost for a
type N auditor is large relative to the probability
of liability
p
N
, such auditors will collude.
However once (9) is satised, they would not.
Notice also that improved audit technology of
type M auditors requires that d
M
> d
N
, which
precludes the possibility that a type M auditor
would collude when a type N auditor nds it
optimal to maintain independence (not collude).

The condition (10) ensures that whenever a type
M auditor nds it economical to work, a type N
auditor also nds it economical to work. That is,
if fees are set to just make type M auditors
indifferent about participation we need to
ensure that type N auditors’ participation
constraint is also satised. In the Appendix we
show that this corresponds to requiring that the
differential gains from investment are not too
large relative to the cost of investment and leads
to the condition (10). In other words, one cannot
separate the types by offering a differential fee
schedule and ‘pricing out’ the less efficient
auditor. In this respect, it is interesting to note
that in economies characterized by a high level
of good projects (p(g)
®
1), the right-hand side
of (10) would tend to get smaller and the
participation condition for the Type N auditor
are more likely to be satised.
The intuition of Theorem 1 is that for a type m
auditor, the benet of providing costly effort e is
that the expected liability (1 – p(g))w
a
R
is
reduced by a factor d
m
, that is, the reduction in

expected liability compensates for the additional
personal effort cost where
p
m
is the probability of
liability reduction. Depending on how large is
the d
N
parameter compared to d
M
, we will have
either a PC or an FC equilibrium. It also follows
that everything else being equal, the liabilities
required to induce an FC equilibrium will be
greater than that required to induce a PC
equilibrium, as discussed in Corollary 1 below.
Corollary 1 (Liability needs to be higher to
insure
FC
existence as compared to what is
required for
PC
existence)
If
a
R
is chosen to satisfy:
e e
––– >
a

R
> ––– (11)
p
N
p
M
a PC equilibrium will follow. However, if
a
R
is
increased so that the left inequality of (11) is
violated, then an FC equilibrium will follow.
Proof: Follows straightforward from
Theorem 1.
The importance of Corollary 1 is that it allows
us to examine bounds on the liability level
a
R
which, under mandatory rotation, induces
desirable auditor behavior completely or at
least, partially. The intuition for the (11)
192 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
requirement is that if liability levels are
sufciently high, an auditor will always provide
maximum effort no matter what their type is
and an FC equilibrium will follow. However, the
liability required to induce an FC equilibrium
will always be more than adequate for the type
M auditors. This is somewhat undesirable since

the legal system may not want to appear too
harsh to the most skilled service providers. If the
legal liability is set just about to induce
independence from the type M auditors, a PC
equilibrium will result because the liability will
not be adequate to preclude collusion by the
type N auditors. Thus, our conjecture is that
under mandatory rotation, if liability was set to
insure existence of a FC equilibrium, the type M
auditors would complain about ‘excessive’ legal
liability.
It is also worth noting that apart from the
systemic operating risk characteristics w and
p(g), the required liability level under
mandatory rotation is functionally dependent
upon only two sets of parameters: the audit
technology d
m
and effort cost e. This is
important because in the following subsection
when rotation is no longer mandated, a third set
of parameters, current fees F relative to future
fees f (that can be earned only through survival
and building of reputation), also effect the
determination of necessary liability levels in the
various equilibria. In particular, we will focus
upon when the interaction between these two
parameters reinforces auditors’ incentives to
maintain independence (as is often claimed by
the profession) or alternatively weakens

incentives. It will then be in the later class of
cases that mandating rotation will have a role to
play.
4. NO MANDATORY ROTATION:
THE TWO-PERIOD AUDIT GAME
In this section, we allow auditors to be
reappointed for another term and hence
potentially extend the auditing game to a second
period. In so doing, we specifically bring
attention to the fact that auditors’ behavioral
strategy [c, nc] may be inuenced by a desire for
reappointment. In particular if management is
inuential in the reappointment decision, an
auditor may balance the trade-off between loss
of reputation and legal liability and the
improved prospects of continuation of future
audit fees when deciding to collude
27
.
Therefore we need to consider carefully
whether the incentive effects of a xed level of
legal liability are reduced when such additional
reappointment concerns arise. As we shall see, it
will depend upon characteristics of the audit
market, and liability levels may need to be
increased or alternatively could be decreased in
order to maintain incentives.
Before commencing the formal analysis, it is
important to stress that an addition of a second
period,

per se,
does not necessarily give rise to
different conclusions concerning auditor
strategic behavior. In particular, if the
participants were certain that one more period
exists in the game, they would play the second
period as if it were a one period game, and by
backward induction, arrive at the solution of the
rst period, which would be no different. What
makes a difference in our model is that the
likelihood that the auditor may ‘enter’ a second
period game is in part influenced by the
strategies and inferences adopted by the auditor,
the investor, and the manager in the rst play of
the game. That is, the auditor can never be
certain that a second period will take place.
As before, let us commence by setting out the
circumstances under which the audit game will
continue
28
to a second period. This will of course
depend on the underlying state of the project
hence:
 if the state of the project is good:
regardless of what the auditor does, the game
continues to a second period provided the
investor values a second audit report.
 if the state of the project is bad:
the game progresses to the second period if the
investor values a second audit report and if in

the rst period the auditor:
– colludes and the project survives;
– does not collude, does not detect the state
and the project survives;
[
– does not collude, detects the state and the
investor liquidates.
In the last alternative, although the auditor
loses the current assignment fee F, it would
continue to earn its normal fee f during the
second period.
Clearly the remaining possibilities are that the
game does not proceed to a second period
because the firm suffers financial distress
without any warning from the auditor. Our
Improving Auditor Independence Through Selective Mandatory Rotation 193
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
assumption (3) ensures that non-colluding type
M auditors are more likely to enter the second
period. Therefore, it is rational for the market to
assign a reputation to the auditors of the
surviving rms.
These possibilities can be summarized by
referring back to the game tree in Figure 1,
where we see that for 8 out of the 14 possible
branches, there will be a second period, and in
the remaining 6 branches, the game ends after
the rst period. Again we stress that since the
auditors do not have complete control over the
probability of the second period play, they do

not know
ex-ante
whether they will be in a single
period game or in a two-period game, that is,
they do not have available a strategy which will,
with probability one, insure that they are
reappointed. Thus the characterization of the
equilibria in the rst period of the two-period
game will be qualitatively different from that of
a single period game because of the possible
interaction between the rst period behavior
(choice of collusion strategy) and the second
period net fees and liabilities
29
. Another
important difference in the two-period game is
that assuming conditions are such that investors
always value costly rst period audits ((7) is
satised), it need not then be the case that they
will also value second period audits. Specically
given a good audit report
~
g at the end of the rst
period, they may in the second period assign a
probability to the underlying state being g that is
sufciently close to 1 such that there is no
demand for a second period audit. Therefore, we
shall first outline the conditions needed to
ensure that even with updated beliefs, investors
have a demand for the second period audit.

The dynamic demand for audit with
updated investors’ beliefs
Clearly when basing inferences in part upon
audit reports, the investors will take into
account how information is gathered by
auditors. For the non-colluding auditors,
information about the state can arrive in two
ways. First, the auditor’s own discovery process
provides information. Second, regardless of the
auditor’s strategy, the survival of the project
itself provides additional information. Thus,
assuming reappointment, at the commencement
of the second period, a non-colluding auditor is
better informed than a colluding auditor whose
only information comes from the observation of
the project’s survival (
q
). It is important to stress
early on that as the auditor acquires ‘improved
inferences’ this could increase the auditors’
incentive to collude since the more and more
convinced the auditor is that the true state is
good, the less the incentive to provide
subsequent (litigation-reducing) effort, since in
the limit litigation can not occur with a good
project. This subtlety of argument explains why
the two-period game is not a simple
generalization of the one period (rotational)
game.
Allowing the possibility for such multi-period

interactions to occur, we now assume that belief
revision occurs according to a Bayesian system
and integrate such belief formation as part of the
denition of equilibrium. To simplify notation,
given survival of the project up until period t,
we denote
p
t
m
(g) = revised belief at the end of period t of
non-colluding auditor of type m that
the state is g, having issued a
~
g audit
report in every period up to t
Thus, p
1
M
(g) and p
1
N
(g) become the respective
non collusive inferences (probabilities) for the
type M and type N auditors at the end of the rst
period. Similarly we dene:
s
t
(g) = revised belief at the end of period t of a
colluding auditor that the state is g
having issued a

~
g audit report in every
period up to t.
Concentrating upon the revised inferences
concerning the state held at the end of period 1
(t = 1), we note that the exact (Bayesian)
expressions for the revised beliefs
30
are:
p
1
M
(g) = p(g|
~
g, e; I,
q
) =
p(g)
–––––––––––––––––––––––––––
p(g) + (1 – d
M
)(1 – w)(1 – p(g))
p
1
N
(g) = p(g|
~
g, e;
q
) =

p(g)
–––––––––––––––––––––––––––
p(g) + (1 – d
N
)(1 – w)(1 – p(g))
s
1
(g) = s(g|
~
g,
q
) =
p(g)
––––––––––––––––––––
p(g) + (1 – w)(1 – p(g)) (12)
Observation 2 (Incremental auditor belief
revision):
The revised beliefs satisfy the ordering p
1
M
(g) >
p
1
N
(g) > s
1
(g) > p(g).
Proof: Follows straightforwardly from concavity
of the Bayesian belief revision process.
194 M. B. Gietzmann and P. K. Sen

Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
Now returning to investors’ inferences, given
that neither the auditor type (hence his or her
investment in client specic audit technology)
nor collusion can be observed outside the audit
relationship, the investors rationally anticipate
the auditor’s strategy and form beliefs
accordingly, which (in equilibrium) will be a
weighted average of the three probabilities: the
weights arising out of the probabilities of
collusion and investment (in equilibrium). Thus
given survival of the project, we denote
31
:
r
1
(g|
~
g;
q
) = revised belief at the end of the rst
period of an investor that the state
is g given the auditor issued a
~
g
audit report
with:
r
1
(g|

~
g;
q
) =
p(g)
–––––––––––––––––––––––––––––––
p(g) +
u
(d
m
, c
m
, m)(1 – w)(1 – p(g)) (13)
In a similar way, we can also dene
r
2
(g|
~
g,
~
g;
q
) as the revised probability of a good state at
period t = 2 given two good audit reports and
inter period survival.
For the audit report to have value, the
investors must react to the audited reports in the
same consistent fashion as they would with
intrinsic state reports, that is liquidate the
project after receiving

~
b and continue after
receiving
~
g. However, the audit reports are
costly to generate with the auditor charging the
client F each period for producing the report.
Thus, the condition under which it is rational for
the investor to reemploy a costly, imperfect
auditor who may or may not invest in audit
technology is given by the following
generalization of the static demand conditions
of Observation 1:
Observation 3: (Positive demand for a
second audit after a rst period
~
g
report)
Audit information has value to investors in the
second period if:
p(
~
g){
r
1
(g|
~
g,
~
g;

q
) V
g
1
+ (1 –
r
1
(g|
~
g,
~
g;
q
))V
b
1
}
+ (1 – p(
~
g))L – F
>
r
1
(g|
~
g;
q
)V
g
1

+ (1 –
r
1
(g|
~
g,
~
g;
q
))V
b
1
(14)
where V
g
1
and V
b
1
are the net present values of
the good and the bad project respectively, at the
end of period 1.
Proof: Similar to Observation 1.
The above expression essentially puts a limit
on the scale of audit fees F and the cash ow Y
incorporated within the present values V, such
that the audit does not become valueless just
because one period has elapsed
32
. Having

specied how inferences are constructed, we can
now turn to the identication of equilibrium
conditions for the two-period game.
The Equilibrium Solution of the Two-
period Game
When solving for the equilibrium strategies in
the nal period of the two-period game, it is
important to recognize two key differences from
the analysis in the single period game. First,
player beliefs at the beginning of the second
period (after rst period’s survival) will differ
from the beginning of the rst period prior
beliefs and will depend upon the strategy an
auditor adopted during the rst period. Second,
there is no cost of client-specic investment in
the second period for type M auditors. However,
though the set of second period equilibrium
candidates remain unaltered
33
; a partial
compliance equilibrium (PC-2), a no compliance
equilibrium (NC-2) and a full compliance
equilibrium (FC-2), may follow either a PC-1,
FC-1 or an NC-1 equilibrium in the rst period.
Thus, there are 3 X 3 = 9 candidates for
equilibrium. However, we have already noted
that an NC-1 equilibrium cannot exist, thus
eliminating three candidates (NC-1 followed by
any of the three equilibria in the second period).
Note also that an NC-2 equilibrium cannot exist

for exactly the same reason; the demand for
auditing disappears when NC-2 strategy is
anticipated. Thus, two more candidates (NC-2
proceeded by either PC-1 or FC-1 equilibrium in
the rst period) get eliminated. We have seen in
the one-period game that existence of a PC-1
equilibrium requires insufcient penalty for the
type N auditors. However, in a two-period
game, allowing for insufcient penalty in the
nal period (given costly investment does not
take place in that period) seems rather counter
intuitive since an assumption of insufcient
penalty in the second period would imply that
liability levels are even lower than what is
required in the rst period. For this reason, we
do not focus on any equilibrium involving PC-2,
thus eliminating two more candidates
34
. In the
following Theorem 2, we characterize the
remaining two equilibria (FC-1,FC-2 and PC-
1,FC-2) that now become the principal focus of
Improving Auditor Independence Through Selective Mandatory Rotation 195
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
our analysis. Before doing so we note that since
we are now in a two-period game we need to
drop the R superscript on the liability level
a
for
this non-rotational regime and instead add a

subscript 2 to indicate that it is the second period
liability.
Theorem 2 (Existence of FC-1,FC-2 and PC-
1,FC-2 equilibria in the two-period setting)
FC-1,FC-2 equilibrium conditions:
Let the audit fees be set to at least offset the
operating costs of the Type M auditors. Let
a
1
and
a
2
denote that legal liability levels in period
1 and period 2 respectively. An FC-1,FC-2
equilibrium occurs if:
both types of auditors nd it economical to
maintain independence (not collude) in the
terminal second period, i.e.,
p
2
N
a
2
º
d
N
w(1 – p(g))
a
2


{p(g) + (1 – d
N
)(1 – w)(1 – p(g))}
––––––––––––––––––––––––––––e, (15)
(1 – d
N
)(1 – w)
p
2
M
a
2
º
d
M
w(1 – p(g))
a
2

{p(g) + (1 – d
M
)(1 – w)(1 – p(g))}
––––––––––––––––––––––––––––e; (16)
(1 – d
M
)(1 – w)
and, in anticipation of that strategy, both types
of auditors also nd it economical to maintain
independence (not collude) in the rst period,
i.e.,

d
M
[ f(p
1
M
(g) – p(g)) – F(1 – p
1
M
(g))]
––––
1 + r
+ (1 – p(g))d
M
w
a
1
+ {(1 - p
1
M
(g))d
M
+
w
a
2
(p
1
M
(g) – s
1

(g)) ––––––}
1 + r (17)
d
M
(1 – p
1
M
(g))
> e[1 – –––––––––––– ]
1 + r
and
d
N
[ f (p
1
N
(g) – p(g)) – F(1 – p
1
N
(g))]
––––
1 + r
+ (1 – p(g))d
N
w
a
1
+ {(1 - p
1
N

(g))d
N
+ (p
1
N
(g)
w
a
2
– s
1
(g)) ––––––}
1 + r (18)
d
N
(1 – p
1
N
(g))
> e[1 – –––––––––––– ].
1 + r
A PC-1, FC-2 equilibrium occurs where both
types of auditors maintain independence in the
final period, but only the type M auditors
maintain independence in the rst period and
the type N nds it economical to collude, i.e., if
(15), (16) and (17) hold but (18) holds with the
inequality reversed.
For both the equilibria, a Type N auditor will
always participate in the game if,

d
M
I

[ f (p
1
M
(g) – p(g)) – F(1 – p
1
M
(g))] –––––
1 + r
d
N
– [ f (p
1
N
(g) – p(g)) – F(1 – p
1
N
(g))] –––––
1 + r
+ (1 – p(g))d
M
w
a
1
+ {(1 - p
1
M

(g))d
M
+
w
a
2
(p
1
M
(g) – s
1
(g)) ––––––}
1 + r (19)
– (1 – p(g))d
N
w
a
1
+ {(1 - p
1
N
(g))d
N
+
w
a
2
(p
1
N

(g) – s
1
(g)) ––––––}
1 + r
e
+
––––
[ d
N
(1 – p
1
N
(g)) – d
M
(1 – p
1
M
(g))].
1 + r
Proof: See Appendix.
The proof follows in line with Theorem 1 and
essentially consists of setting up the appropriate
pay-off inequalities under the specified
equilibrium beliefs and verifying that
simultaneous existence of the inequalities
violate neither any technical assumption made
nor the demand for auditing condition.
In all the equilibrium payoff conditions, the
left-hand side of the inequality represents the
(appropriately probability weighted discounted)

benet of spending the effort and the right hand
side is the cost of providing the effort.
Furthermore, the expressions of benets on the
left-hand side have two components; one related
to the fees and the other related to the liabilities,
indicating that legal liabilities in the rst period
cannot be set without regard to the fees earned
by the auditors in both periods. This is in
marked contrast with the one-period game
where legal liabilities could be set without
reference to fee levels. We have so far assumed
that the level of legal liabilities could differ
between periods. If, for whatever reasons, the
liability levels must be the same over the two
periods, either the condition involving
a
1
or
a
2
will be binding, and an auditor will be over-
penalized in one of the two periods.
Next we need to formally recognize that in the
two-period game, auditors’ incentive to
maintain independence need not only come
from liability pressures but also will be
inuenced by the ratio of current audit fees to
future reputational based fees. We shall dene
the relative reputational value of an audit
market by the ratio:

196 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
F
––
º n
=
relative reputational value of an
f audit market
that is, when the ratio is large for a client, that
client dominates the auditors’ overall fee
portfolio of current and future reputational
based fees. The converse when the ratio is small.
This naturally gives rise to the following two
observations.
Observation 4 (Reputation as a substitute
of legal liability in well developed audit
markets)
Provided the reputational value of an audit
market is below a critical value
~
u
, the reputation
effect reinforces the liability needed to maintain
independence.
Proof: Notice that in the equilibrium conditions
(18) and (17), the net fees term can only act as a
substitute for legal liability if the term involving
the net effect of fees has a positive sign.
Therefore, it must be true that in any such
equilibrium,

f (p
1
m
(g) – p(g)) – F(1 – p
1
m
(g)) > 0. (20)
or,
F p
1
m
(g) – p(g)
– < –––––––––––
f (1 – p
1
m
(g))
Dene
F
f
=
u
as the characterization of the
audit market such that there exists a critical
cutoff
~
u
, dened as:
p
1

m
(g) – p(g)
~
u º
–––––––––––
(1 – p
1
m
(g))
at which an audit market switches from being
well ‘developed / diversied’ with (an in built
desire by auditors to maintain a reputation for
independence) to being described as ‘thin’ when
such self-regulatory incentives are not in place.
To understand the choice of terminology, we see
that for
u
<
~
u
the fee of the client in question is
small relative to other reputational driven fees
and hence characterizing the audit market as
developed follows from the fact that the auditor
is concerned about (many) other client
opportunities arising from a maintenance of
reputation. In contrast when
u
>
~

u
we describe
the market as thin because the existing clients
dominate the fee portfolio.
It follows from Observation 4 that a reputation
for independence cannot form in a thin audit
market where
F p
1
m
(g) – p(g)
u
= –– > ––––––––––– =
~
u.
f (1 – p
1
m
(g))
That is reputational incentives for protecting
independence, will reinforce legal liability
effects, only if the audit market is developed,
with fees from any individual client not
exceeding a certain proportion of the total future
fees as dened by
~
u
. We use this denition of
thin market in our subsequent discussions.
The signicance of Observation 4 is that a

reputation for independence can only form if the
concern for future fees f sufciently outweighs
the current fee F concerns. Anticipating the
following section’s results we can see that
rotation may then have a positive role to play
when we are in the converse setting; a thin audit
market in which current fee concerns are so
large that liability needs to be increased to insure
independence in the first period. Before
addressing these specific issues we briefly
outline a number of related observations which
are of indirect interest.
Observation 5 (Second-period (terminal)
liability needs to be higher than the
necessary liability in a single period
(rotational) setting)
The second-period liability
a
2
needs to be
greater than the one-period liability
a
R
.
Proof: Follows from direct comparison of (8) and
(16).
The intuition of Observation 5 is that to induce
the same level of effort, the liability level
a
is

increasing in the beginning probability of good
news p(g) or p
1
m
(g). Since the probability of
being good increases with rst-period survival,
the liability level must increase correspondingly
in order to induce compliance.
Next we turn to consider the effects on
investment participation incentives in the case
that the level of investment is a free variable.
Observation 6 (Rotation makes
participation of type M auditors more
difcult)
Given the same level of legal liability, the
maximum level of investment I supported by
mandatory rotation regime is lower than the
investment supported in the reappointment
regime.
Proof: It is sufcient if we prove our claim in the
case with zero concern for reputation, i.e., where
the concern for reputation exactly offset the
Improving Auditor Independence Through Selective Mandatory Rotation 197
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
concern for reappointment for both types.
Notice that it is never possible to hold the net
reputational concern for both types to zero.
However, with zero concern for reputation for
type N and ignoring the incremental concern for
type M, the condition (19) can be re-written as

I > (1 – p(g))d
M
w
a
1
+ {(1 – p
1
M
(g))d
M
+
w
a
2
(p
1
M
(g) – s
1
(g)) –––––} (21)
1 + r
– (1 – p(g))d
N
w
a
1
+ {(1 – p
1
N
(g))d

N
+
w
a
2
(p
1
N
(g) – s
1
(g)) –––––}
1 + r
e
+ ––––– [d
N
(1 – p
1
N
(g)) – d
M
(1 – p
1
M
(g))].
1 + r
By direct comparison with (10), it can be seen
that if
a
R
=

a
1
, the right-hand side of (19) must be
greater than the right-hand side of (10).
This is consistent with the ‘costly rotation’
argument to which the industry and academics
refer. The intuition of Observation 6 is straight
forward. In a two-period game, the investment
must justify the net present value of future
benets over the two years, whereas, under
mandatory rotation, investment needs to be
justified in one period. Therefore, being
balanced by the present value of two periods’
benets, the reappointment regime can allow for
some audit technologies that may prove to be
‘too expensive’ under mandatory rotation. In
those cases, either the audit fee has to increase,
or the liability has to come down in order to
induce all auditors to participate in the market
for audit services. However, as we shall see in
the next section; there are compelling reasons to
think that legal liability under a mandatory
rotation regime can be lowered (relative to a non
rotational regime) in certain cases and hence the
overall comparison is more complex.
In the next section, we compare the liability
levels of the two alternative regimes, rotation
versus non-rotation, and examine more
completely the role of the current and the
future period’s fee in determining auditors’

independence.
5. MINIMUM LEVELS OF LIABILITY
THAT INSURE AUDITOR
INDEPENDENCE, WITH AND
WITHOUT ROTATION
In this section we compare the equilibria under
the two regimes and derive implications
pertaining to auditors’ independence in each of
the two regimes. Specically, we compare the
minimum levels of legal liability needed to
support the equilibrium with and without
mandatory rotation.
Relative Liability Levels
We have already established in Observation 5
that
a
2
>
a
R
. However, whether
a
1
is greater than
a
R
or not depends on the size of the reputation
(net fees f ) term on the left-hand side of (18) and
(17). In Observation 4 we have noted that in a
market where the size of the reputation effect

f is signicant, it may be possible to induce
auditors’ incentives with a relatively low level of
legal liability of
a
1
. To the contrary, in a ‘thin’
audit market, the legal liability must not only
balance the cost of effort, but it also must rectify
the negative incentives associated with
reappointment concerns with a dominant client.
Thus, in a ‘thin’ audit market, it is possible that
legal liability can be lowered by introducing
mandatory rotation, thereby neutralizing the
negative incentive effect of auditors’
reappointment concern. We formalize this
intuition in the following Proposition 1.
Proposition 1 (Legal liability is lower with
mandatory rotation when audit markets
are thin)
A necessary condition for
a
1
>
a
R
is that the
audit market is thin in the sense that the
reputation effect is negative, i.e.,
f ( p
1

m
(g) – p(g)) – F (1 – p
1
m
(g)) < 0.
Proof: It is sufcient if we can prove our claim
where the above condition holds with an
equality. Substitution and simplication of (17)
yields:
p
3
a
1
º
(1 – p(g))d
M
w
a
1
+ {(1 – p
1
M
(g))d
M
+
w
a
2
(p
1

M
(g) – s
1
(g))
–––––
} (22)
1 + r
d
M
(1 – p
1
M
(g))
> e[1 – ––––––––––––]
1 + r
Similarly, simplication of (18) yields
p
4
a
1
º
(1 – p(g))d
N
w
a
1
+ {(1 – p
1
N
(g))d

N
+
w
a
2
(p
1
N
(g) – s
1
(g))
–––––
} (23)
1 + r
d
N
(1 – p
1
N
(g))
> e[1 – ––––––––––––]
1 + r
if it is an (FC-1, FC-2) equilibrium, and with
the inequality reversed if it is a (PC-1, FC-2)
equilibrium.
198 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
Consider the (FC-1, FC-2) equilibrium rst.
Direct comparison of (8) and (22) establishes that
the right-hand side of (22) is smaller than that of

(8) whereas on the left-hand side, the coefcient
of
a
1
needed in (22) is greater than the coefcient
of
a
R
in (8). Therefore, with a zero net reputation
effect, the required
a
R
must be greater than the
required
a
1
. The only reason why
a
1
may exceed
a
R
is that the net reputation effect must be
negative. A similar conclusion can be arrived at
by comparing (9) and (23).
In the (PC-1, FC-2) equilibrium, the conditions
for the type M auditors remain identical while
a
1
needs to be even smaller than that under (FC-1,

FC-2) so that (23) can hold with the inequality
reversed. Further, given d
M
> d
N
, even if the net
reputation concern for the Type N is zero, there
will be a small mass of reputational payoff
attached to the left-hand side of (22), thus
making the incentives for the Type M even
stronger. Therefore, in any equilibrium, for
a
1
>
a
R
to hold, the underlying audit market must be
thin.
Conversely, it can be argued that non-negative
reputation is sufcient to induce
a
1
<
a
R
. Thus,
in a thin market, mandatory rotation reduces the
liability by removing the reappointment
concerns. In a developed audit market, however,
that would not be true because mandatory

rotation would not allow development of
reputation, which supports auditor
independence. Introducing mandatory rotation
in such a situation would also lead to increased
legal liability, a consequence that would not be
preferred by an audit profession looking for
liability reduction and or may be considered to
be socially wasteful. On the other hand, in thin
audit markets where
u
is sufciently large (
u
>
~
u
), introduction of mandatory rotation may help
reduce legal liability of auditors. (Thus, if
auditor’s legal liability is of concern, mandatory
rotation can reduce the legal liability in thin
markets, but will tend to increase the legal
liabilities in a developed market.)
The Effect of Current Fee and Future Fee
Levels on Auditors’ Incentives to Maintain
Independence.
Observation 4 highlights that unlike a single-
period audit game, the auditor’s incentive not to
collude (and maintain independence) are
inuenced by the current fee level F for the
current assignment, as well as the fee of the
future reputational-driven assignments f, in

addition to the legal liability. It is therefore,
important to investigate how absolute and
relative changes in these fees affect auditor
independence. We note below two propositions
in this regard.
Proposition 2: (Higher current fee levels
F
tend to compromise auditor independence).
An increase in the current fees F,
ceteris paribus,
will increase the auditor’s incentives to collude.
Proof: Notice that the coefcient of F in the
left-hand side of the expressions in Theorem 2 is
negative. Thus,
ceteris paribus
, increasing F will
make the inequality harder to satisfy, thus
increasing the propensity to collude.
Proposition 3: (Higher reputational fees
f
tend to mitigate collusive incentives).
An increase in reputation based future fees f,
ceteris paribus,
will decrease the auditor ’s
incentives to collude.
Proof: Since the coefcient of f in the left-hand
side of the expressions in Theorem 2 is positive,
the higher the value of f the easier it is to satisfy
the required inequality.
Propositions 2 and 3 highlight the economic

process behind building reputation where the
concern for future business outweighs current
reappointment concerns. The higher the second-
period fees compared to the rst period’s fees,
regardless of the equilibrium, the bigger is the
incentive for the auditor to maintain her
independence. Therefore, it is internally
consistent for the clients to believe that auditors
in more developed markets are more likely to
maintain their independence, thus further
enhancing their reputation. It is, however,
important to note that the reputation for
independence is not independent of the
auditor’s (competence) type and that a more
efcient (Type M) auditor is expected to have a
higher concern for reputation than a less
efficient type. We note this result in the
following Proposition 4.
Improving Auditor Independence Through Selective Mandatory Rotation 199
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
Proposition 4: (Type
M
auditors have more
incentives to protect reputation for
independence).
Whenever a Type N auditor has a non-zero
incentive to protect her reputation for
independence, so will a Type M auditor.
Proof: The non-zero incentive implies that for
both the types, the condition (20) must hold with

strict inequality. From Observation 2, it follows
that:
F p
1
N
(g) – p(g) (p
1
M
(g) – p(g))
–– < ––––––––––– < ––––––––––––
f 1 – p
1
N
(g) 1 – p
1
M
(g)
Therefore, whenever the reputation condition
(20) is satised for the Type N auditor, it must be
satised for the Type M auditor, signifying a
greater incentive to protect their reputation for
independence.
Within one market, if we interpret the fee ratio
F
f
as the relative importance of a single client in
the auditor’s portfolio, it is interesting to note
that the above results identify a critical limit on
that ratio, depending upon the environment and
the audit technology, for any positive reputation

formation
35
. Thus in principle, our results
provide the basis for an empirical test to identify
the maximum allowable proportion of fees that
a single client should command if a desire for
positive reputation formation is viewed as
desirable.
Our results also indicate another rationale for
large (client) rms using large auditors. Such a
size-matched appointment need not only arise
because of any claimed or extant differences in
audit (detection) technology, it may instead be
necessary for the auditor to maintain his or her
reputation and be believed.
It also follows that, if the market structure
were to change in that client rms go through
signicant economic consolidation and merge to
form larger economic entities, protection of
reputation may require that the reputed audit
firms, auditing these client firms, also
consolidate their markets, perhaps through a
series of mergers of their own, thereby
maintaining the
F
f
ratio. If, in addition, the
audit market were very diverse in the ratio
F
f

between auditors, incentives could exist for the
lower
F
f
ratio auditor to acquire the high
F
f
ratio
auditor, thereby consolidating the industry and
its reputation. This phenomenon could occur
across international borders or within any
particular country; however, detailed exam-
ination of such a scenario is clearly beyond the
scope of the present work. Leading on from this
argument, we see that an interesting indirect
implication of our work on rotation is to show
that from a regulatory perspective, mergers of
audit rms should not be viewed in isolation
from what is happening in their client market.
More directly, we see that if auditors do not
want to see increases in legal liability in the
future, regulatory incentives exist to introduce
selective mandatory rotation in sectors of the
economy which become dominated by large
F
f
ratio auditors
36
.
6. INITIAL OVERVIEW OF EMPIRICAL

EVIDENCE
In our preceding discussion, we developed an
analysis of the theoretical efcacy of auditor
rotation. Given the fact that some member states
within the European Union have either
implemented or have been considering
implementing mandatory rotation of auditors, it
is interesting to consider whether the audit
markets in such countries
37
are consistent with
those predicted by our theory. In this subsection,
we introduce a brief discussion of the issues to
hopefully motivate more detailed systematic
empirical work being carried out in the area.
We note that auditor rotation has recently been
an active topic of debate (particularly in
Germany) as will be detailed. Almost invariably
the auditing profession has been rmly against
the introduction of rotation. The grounds on
which they argue the case is usually in terms of
claimed excessive costliness of implementation
and operation of mandated rotation, also
claiming that the quality of the audits will fall. A
question therefore arises as to whether or not
these proposed arguments are simply an
attempt to protect self interest (in the form of
continued audit and consultancy opportunities),
disguised in a politicized form of a public
interest debate (Power (1993)). In this respect,

our research has an important bearing on this
debate since it establishes that it is not self
evident that rotation is excessively costly or
gives rise to lower quality audits. Instead we
argue a case for more judicious consideration.
Specically, we argue that if the audit markets
are thin, rotation is desirable. In our following
200 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
discussion we will focus upon this aspect of the
various member state audit services markets.
The member state with the most experience
with auditor rotation is Italy. In 1974, legislation
was enacted to establish the National
Commission for Listed Companies and the
Stock Exchange (CONSOB). In the subsequent
year this was followed by a Presidential Decree
(DPR 136/75) which established a limitation on
the length of time for which an (external)
auditing firm may hold the auditing
engagement for a particular company. The
engagement may be given for a maximum of
three years and may only be renewed twice
(art.2.4 DPR 136/75), (see Andrei (1991)). Before
considering empirical data, it is important to
stress that the system of overall corporate
governance in Italy is quite different from other
member states. Key identifying components of
the Italian system include pyramidal group
holdings, active intervention by the state and

transacting, based upon strong familial ties.
Barca (1995) presents an overview of these issues
and comments that in Italy the degree of
separation between ownership and control ‘is
certainly low by US standards’ (p.16). Given
this, in part, will inuence the way the role of
(statutory) auditing may be dened, it is further
complicated by the fact that in Italy two forms of
auditors conduct investigations of companies
listed on the stock exchange. Mauri (1995) gives
a detailed account of the concurrent nature of
audits performed by the Collegio Sindacale and
external auditors (Società di revisione). No
direct equivalent exists for the Collegio
Sindacale elsewhere and the simplest analogy is
to consider the Collegio as essentially a hybrid
between a board of internal auditors and non
executive directors (see Mauri (1995) for details).
He explains how in Italy all public limited
companies (plus certain others) must have a
statutory audit performed by the Collegio
Sindacale and that only those companies listed
upon the Stock Exchange, Investment Firms and
Funds, Insurance Companies and certain State
related organizations need also ‘submit their
annual accounts for examination to an auditing
rm to obtain a
certication
of the balance sheet’
(p.4). Furthermore it is interesting to note that

the Italian
rotational requirement
only applies to
the external auditors and thus in an attempt to
relate our theoretical results to the Italian
situation, we need to evaluate whether the
market for external auditors could be described
as thin.
As the above discussion makes clear, only a
restricted set of companies for which audits are
compulsory actually require external auditors to
provide certication. Mauri indicates that of
the approximately one hundred thousand
companies that require statutory audits (by
the Collegio Sindacale) no more than two
thousand are required to seek certication by an
external auditor. He notes additionally that
approximately thirteen thousand companies
seek voluntary audits but even including these
in the total, less than fifteen percent of
companies employ an external auditor for
certication. Hence it seems at least suggestive
that the Italian situation could be characterized
as having a relatively thin market for (external)
auditors. Thus in order to test the applicability
of our theory to the Italian situation an
interesting issue is how could one operationalize
the measure of thinness or the ratio
F
f

so that an
empirical testing procedure could be developed.
Motivated by the Italian experience, one way to
commence would be to measure the proportion
of the total rms for whom mandatory audit is
required, however, as we shall argue below,
more sophisticated empirical procedures need to
be developed given the complexity of the issues.
The second member state to have experience
with rotation is Greece. However it should
immediately be noted that in Greece rotation
only applied to the audit of public (state) bodies.
Again since the number of state bodies is a much
reduced subset of the total rms, it is again
conceivable that the necessary conditions for
auditor rotation were met. However, recently
moves have taken place to repeal the rotational
requirement.
More recently the German legislature has
embarked on an active consideration of reform
regarding the regulation of auditors. One topic
that was actively debated was the possible
introduction of auditor rotation. As our opening
quotation in the paper demonstrates, the Italian
implementation of auditor rotation is sometimes
proffered as providing evidence that rotation is a
workable proposition. Our above discussion
suggests that before the German legislature
passed judgement on the possibility of adoption
of rotation (in order to enhance independence),

an analysis of the relative thinness (concen-
tration) of the audit market should have rst
Improving Auditor Independence Through Selective Mandatory Rotation 201
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
been considered. What is particularly interesting
when looking at the German regime is that
potentially it too could conceivably be
characterized as a relatively thin market since
relatively few companies are publicly limited
(AG’s). The predominant organizational form
being privately limited companies (GmbH),
with only a subset
38
of this later group requiring
statutory audits.
Outside Europe, mandatory rotation of
auditors exists in India, where the government’s
Standing Committee on Public Enterprises
requires the Comptroller and Auditor General of
India (CAG) to rotate auditors every three years
for all government owned and controlled public
enterprises (Dugar
et. al.
1995). Motivated
by concerns regarding economic wealth
distribution and also for political reasons, CAG
tends to hire relatively small auditors and the
public sector enterprises become dominant
clients themselves. Given the capacity restriction
of the small auditors, such an arrangement may

essentially create a condition of thinness in the
audit market populated by the small Indian
audit rms. If so, an efcient arrangement of
auditor rotation would be consistent with our
results in this paper.
Our study shows how any analysis of the
relative efcacy of audit rotation should instead
be based upon a fundamental analysis of audit
services’ market concentration. Our analysis has
shown that under certain dened conditions,
legal liability and fees can be lower under
rotation and still the same quality of audits can
be achieved.
7. ELEMENTS OF THE PUBLIC POLICY
DEBATE
Given the empirical evidence, a question
concerns why we do not see more widespread
use of rotation. Our ndings suggest that an
empirical study of thinness of audit markets
should have been conducted to supplement any
other evidence that was considered. However,
instead it appears the recent decision not to
introduce rotation was heavily inuenced by a
report of the Quality Control Committee of the
SEC Practices section of the AICPA (1992) in the
US. This study concluded that the frequency of
audit failure was three times greater after the
rst or second periodic audit than in successive
periods
39

. Allegedly this sample statistic was
used by some commentators to conclude that
mandatory rotation was therefore more likely to
expose the nancial community to more ‘new
auditor’ failures and hence on grounds of
efficiency and effectiveness should not be
adopted in Germany. We question attempts to
draw such conclusions on the basis of the AICPA
report for the following reasons. It is our
understanding that none of the sample rms in
the US study changed their auditor in a
systematic fashion as would be the case under a
condition of mandatory rotation. Therefore, the
audit failures occurred in rms where auditors
were changed in the prior period for some non-
legislative (non-mandatory) reason. The extant
audit literature
40
would suggest that at least
some of these changes were motivated by
weaker rms conducting opinion shopping or
auditors dropping their high risk clients. For
instance, it is conceivable that the reason there
were increased failures in the early years is
because the previously incumbent auditor
recognized serious problems with the client
(such as the going concern assumption) or, the
observation of auditor change simply indicates
audit rms removing the perceived ‘lemons’
from their portfolio. That is, the increased failure

rate may not simply be the result of new auditor
failures
per se,
but instead also the result of
previous incumbents lack of desire to stay with
certain risky clients.
If we were to observe the rst-period audit
failure rate in all firms regardless of their
motivation to change the auditor, would we
observe a higher than average audit failure rate?
We have no evidence yet. However, it is
interesting to note that to the extent voluntary
auditor change is initiated by the weaker rms;
in contrast with mandatory rotation we would
expect the proportion of failures in early years to
reduce, since the proportion of lemons in the
new client set will be reduced. Overall, the
above arguments fundamentally calls into
question the ability to generalize the US audit
failure studies to a regime of mandated auditor
rotation. It is, however, possible that some
auditors (working under an indefinite
reappointment regime) are slow to invest in
client-specic understanding and therefore have
early failure. Our model cannot capture this
feature because the investment in client-specic
skills in our model happens instantaneously.
However, if the auditor could control this
202 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)

investment rate, given proper incentives, in a
rotational regime, they may invest in client-
specic skills at a rate faster than that under the
indenite regime. Thus it is conceivable that
failures under rotation could be lower. On the
other hand, it may also be possible that the
minimum learning period about a client’s
business with the client specic investment is
say, two years. If so, one could correctly argue
that even with no collusion, rotation would
increase this cost. However, as our analysis
suggests, this outcome may be the better of the
two evils in a thin audit market, because while
saving the investors from initial erratic reporting
during the learning period, non-rotation may
lead to a long-term collusive situation where
inaccurate reporting would persist over a longer
period of time, possibly resulting in overall
higher costs. The fact that there could at this
time exist near unanimous belief that mandatory
rotation is not cost-effective in the United States,
does not justify the use or lack of use of
mandatory rotation in any other country.
Consistent with our study, if the US audit
market is characterized by a developed audit
market, rotation would indeed be wasteful;
whereas if some audit markets (in Europe, Asia
or Latin America) can be characterized as thin,
mandatory rotation can lower auditors’ legal
liability and improve welfare in those markets.

Thus, it is far from self evident that the data
supports the assertion that audit rotation should
not be introduced in Germany, or anywhere else
in Europe. Moreover given signicant corporate
merger activity in the US it may be that there is
a case to argue for the introduction of rotation in
specic sectors, such as for instance pharmaceu-
ticals or oil.
Furthermore, it needs to be recognized that the
public policy options for the alternative regimes,
may differ in fundamentally substantive ways.
For instance, with mandatory rotation with a
known rotation date, it would be possible to
mandate for the forthcoming auditor to be
chosen in time for the incumbent to include an
observer (from the audit rm elect) during the
nal audit, or at least to enter into a dialogue
and possibly share working papers as is the
practice in Canada in the banking industry. In
this way the number of audit failures occurring
shortly after audit switching may be reduced
41
.
It is interesting to note that this sort of
constructive policy presumably was not in place
during the AICPA study and it is conceivable
that some failures could have occurred because
the outgoing auditor chose not to cooperate with
the following auditor.
8. CONCLUSION

Much of the discussion about the potential
efficacy of rotation is couched in terms of
the benefits of improved incentives for
independence set against possible additional
costs in terms of lower quality audits and fees.
We have formally modelled how removing the
ability of management to influence the
likelihood of the reappointment of incumbent
auditors can improve the incentives for auditors
to maintain independence. This is clearly an
ongoing concern for regulators as evidenced by
the GAO recognition that ‘criticism (of auditor
independence) has focused on ineffective
audit committees, the concept of privity of
client information, on long-standing audit
relationships spanning several decades,
auditor independence being compromised by
economic pressures to maintain clients, ’
(emphasis and bracket added)
42
.
We nd that rotation does have a positive
public policy role in certain well-defined
circumstances. If audit markets are sufciently
thin, mandatory rotation of auditors is a
desirable policy instrument because in thin
markets, auditors who can be indefinitely
reappointed are very concerned about
holding on
to

their existing client base and this makes them
more susceptible,
ceteris paribus,
to colluding
with management. Thus, in this setting, rotation
may have a positive role to play. However, if the
audit market is sufficiently developed, the
reputation effect associated with potential loss
of future business is sufciently strong to deter
implicit collusion, and mandatory rotation could
lead to additional unnecessary costs. Our work
adds additional insight to the policy debate
because we show how the policy switching
debate should not be based upon the
assumption that rotation
always
improves
auditors’ incentives to maintain independence
and
always
decreases audit quality.
Additional research into a number of related
topics will further rene our understanding of
the potential efcacy of mandated rotation. For
instance, consideration of whether rotating
partners or audit teams within audit rms may
Improving Auditor Independence Through Selective Mandatory Rotation 203
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
be sufcient, is a topic of some interest. Critical
to such considerations is a need to understand

the internal incentive structures and general
rent-seeking behavior of audit partnerships.
Another possible extension would be to model
the dynamics of client-specic investment. In
our model setting, investment occurs instanta-
neously and a dynamic model would allow us to
explicitly consider learning rates induced under
the two regimes. Additionally, our theoretical
analysis suggests that consideration be given to
developing empirical testing procedures for
audit market thinness. Such measures may
provide an important tool in public policy
debate concerning the desirability of mandatory
auditor rotation. Finally, we also want to suggest
that further research be applied to
understanding the link between the need for
relation / client specic investment and the
denition of an audit market. If, for instance,
audit staff were trained mainly in one sector
such as bank auditing, or public sector
institutions, it may be more appropriate to
consider the number of banks or the public
sector bodies when developing a measure of
thinness rather than the total number of all audit
clients. Thus, although creation of specialized
skills or expertise may lead to short-term gains
in terms of reduced errors, such an emphasis, in
time, would fragment the audit market, possibly
creating dominant clients and thin markets.
Our results suggest that with increasing

market concentration of clients, proposals for
mandatory rotation in thin markets for audit
services may be justiable.
ACKNOWLEDGEMENTS
We gratefully acknowledge the comments of
Nick Dopuch, Ron Dye, Bob Magee, Arijit
Mukherjee, two annonymous referees and the
seminar participants at the American
Accounting Association Annual Meeting
(Philadelphia), 2nd EIASM Workshop on
Auditor Regulation (Copenhagen), European
Economic Association Annual Congress
(Toulouse), 3rd International Conference on
Accounting Issues (Rutgers), London School of
Economics, Georgia State University, SUNY
Buffalo and University of Cincinnati. The second
author acknowledges partial funding from the
European Union Center of the University
system of Georgia.
NOTES
1. Proposals to mandate rotation in the US go
back to at least the 1970’s when Ralph Nader
proposed the use of instrument.
2. However, whether the audit institutions in
different countries with different
institutional arrangements are equally
strong and effective or not, remains an
empirical question.
3. In addition other factors that may affect
independence such as former employment

ties and friendship are indeed important but
probably vary on a case by case basis
whereas the base economic factors may be
common in most cases.
4. A related concern is what is the unit of
analysis since if a client is 50% of the fee
income of a sole partnership but would only
be 0.5% of the fee income of a large
partnership BUT this being 50% of the fee
income of one of the partners of the large
partnership, is there a material difference in
partner incentives. Our model does not
consider this important issue of comparing
the relative incentives of a multi-agent audit
partnership to that of a sole agent auditor.
Indeed a worthy topic of future research is to
develop an understanding of the
performance appraisal and incentives
within multi-hierarchy audit partnership. To
date however relatively little information
has been disclosed to researchers on how
audit partnerships set internal promotion
and incentive pay awards.
5. There exists a significant literature on
managerial empire building; see for instance
Hart and Moore (1990). We could revise our
model so that the manager does not want the
project always to continue and instead the
manager simply applies a lower required
rate of return for project continuance than

the owner. It is this fundamental conict of
interest that drives our model, rather than
the exact cutoff values. Our assumption is
the simplest form of conict which allows us
to model the auditor’s problem in the most
transparent fashion.
6. In our model auditors have imperfect
detection technology, so by attestation we
mean a professional opinion (report) rather
than an exact observation of the project state.
204 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
The investor then updates beliefs in a
Bayesian fashion and a principal concern is
whether the costly imperfect information is
valuable. We shall make precise statements
on this matter.
7. We will make precise statements dening
the terms implicit collusion and
independence. At this stage our intent is
simply to give an overview of the principal
elements of the model.
8. In an earlier version of this work the authors
developed a model of a project which if
intrinsically good would produce an innite
horizon of returns Y. Though additional
insights can be generated from such a
model, so far as auditor rotation is
concerned, they are minimal.
9. That is the state will be revealed

unequivocally to be bad.
10. We assume this because since the manager
knows the state to be unequivocally g, the
manager can take additional steps to
demonstrate to the auditor what the true
state is.
11. This is consistent with the literature in that
while it may be relatively straight forward to
observe cost incurrence, it may be far more
difficult to evaluate whether costs were
incurred solely with understanding a
specic client in mind or for some other
purpose.
12. Thus, when the project state is good the
auditor never reports it to be bad. There are
several instutional barriers for the auditors
to trivially mis-represent their ndings. For
instance in the case of litigation, they need to
produce their working papers.
13. The formal denition of independence is
given in (4) below.
14. That is, we assume that auditors do not earn
report-contingent fees. Theoretical support
for this assumption is provided by
Acemoglu (1997) who considers the design
of the optimal contract for the auditor
allowing for report-contingent and whistle-
blowing fees. He develops a multi-task
agency model which assumes that in
addition to reporting the state of the project,

the auditor is also required to perform some
other task such as checking internal controls,
for which management and shareholders are
in joint agreement needs critically to be
conducted. However, only management can
observe whether the auditor has performed
this other task and hence this creates a
problem with using report-contingent or
whistle-blowing fees. In fact in the model,
Acemoglu shows that the optimal contract is
to offer the auditor a at fee contract plus the
threat of legal liability if found guilty of
negligence, with no report-contingent or
whistle-blowing fees being paid. This agrees
with what we commonly observe in practice.
15. In our model setup, the occurrence of
nancial distress unambiguously indicates
that the state was bad. However, this does
not lead to us concluding that the auditor is
unambiguously guilty of negligence because
regardless of type, there is still a chance that
the auditor may not have detected a bad
state. Given the complex additional legal
issues of appraising standards of care on a
case by case basis, we interpret
a
as the
expected liability. Thus we do not assume
that in practice given nancial distress the
auditor is automatically found guilty and is

liable for
a
. Instead we assume that since the
owner has little information about the
auditor’s performance, the observation of
financial distress prompts (triggers) the
owner to consider gathering evidence on the
performance of the auditor and thus the
rational expectation of
a
is that which exists
at the beginning of the game.
16. Note that for parsimony our model just
considers a single audit assignment. An
obvious extension would be to consider
multiple assignments. However, then the
reputational model would need to be much
more complex to capture how failure on one
audit assignment influences continuance
decisions by other audit clients.
17. A good example of how nancial distress of
an audit client can endanger earnings from
other opportunities is given by the UK case
of the Arthur Anderson audit of Delorean.
Following the failure of the automotive
project, Arthur Anderson faced not only
potential litigation from investors in the
venture, but was also banned for a period
from bidding for any consulting projects
with the UK government which in our

notation corresponds to a loss of f.
Improving Auditor Independence Through Selective Mandatory Rotation 205
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
18. The effort variable attempts to capture the
complexity of the auditors’ task rather
crudely, yet it captures some important
features. To the extent that auditors’
activities are governed by the respective
auditing standards, auditors need to
generate a standard set of work papers and
paper trail regardless of what they believe
to be the true state and the efciency of
their audit technology. This minimum
requirement we summarize as resulting
from provision of e = 0.
19. Legal scholars such as Finch (1992) have
outlined how in practice, legislation insures
that most managers face only limited
liability in the work place.
20. It is important to clarify the type of b signal
that we have in mind. If for example the b
signal related to bad internal controls under
which an employee was able to steal money
from the rm, clearly the manager would
benefit from the auditor disclosing the
signal. However, what we have in mind here
is a signal which for instance relates to
perquisite consumption by management, for
instance the use of a company aircraft for
vacation travel. In such a case the manager

already knows the state is b and does not
want it disclosed whereas in the former case
the audit was valuable because it revealed
new information to the manager. Acemoglu
and Gietzmann (1997) provide an extended
model of this point.
21. In a two-period game the auditor must also
consider whether or not to provide effort in
the second period. We defer discussion of
two-period auditor strategies until section 4
were we introduce the formal model and the
existence conditions.
22. As indicated earlier, the authors have also
developed a multi-period t > 2 model of
strategic interaction which is available upon
request. The central results of this paper still
remain, however, in a more complex form.
The main difference with arbitrary more
periods is that if an auditor in the non
mandated rotational environment keeps on
nding g (for the given project) they will
eventually believe there is a sufficiently
small chance of the actual state being b and
so they stop providing effort. Realistically
this may not happen because through time
new projects are embarked upon and so
there is something new for the auditor to
attest.
23. Note we are not saying that the only
source of reputation is from observed

reappointment just that f relates to this
specic component of reputation.
24. Note we will be assuming that auditors earn
the same fee F in the mandatory rotational
environment and the non mandated
environment. We do not model the type of
‘bare bones’ auditing which can occur in the
public sector where rotation is always to the
lowest bidder leading to a disincentive for
investment.
25. We consider this assumption to be
descriptive of real life. Regardless of the
game auditors may play, legal liabilities and
associated requirements of a defensible
paper trail preclude their trivial or strategic
misreporting. That is, they never lie about
evidence they have found, the problem
instead is they may simply not look for the
evidence with any great zeal: hence the use
of the term
implicit
to capture that auditors
collude by providing minimum effort e = 0,
which reduces the chance of them detecting
the state of a project is bad.
26. The formal denition of the equilibrium
appears in the Appendix.
27. Informally the situation auditors face is that
if they work hard (do not collude), they may
detect the state to be bad and lose future fees

from the project because the project is
liquidated when
~
b is reported. However, if
they believe there is ‘little’ chance of the bad
state being indicated by other means (the w
process) they may decide not to work hard
(collude) and hence increase the chance of
reappointment.
28. At this point, for clarity we are just mapping
out the possibilities on the game tree. We
will soon also establish the dynamic
equivalent of Observation 1 which
establishes that an investor will value a
second audit report.
29. This interaction would not be material if the
auditor was indifferent between receiving
second period fees from the current
assignment or not. However, adopting such
a modelling assumption ignores the benet
in the second period that an auditor gains
206 M. B. Gietzmann and P. K. Sen
Copyright © 2002 Management Audit Ltd. Int. J. Audit. 6: 183-210 (2002)
from prior period investment in audit
technology to understand the client.
30. Of course given the Magee and Tseng
assumption, we also have p(g|
~
b) = 0 and
p(b|

~
b) = 1.
31. Clearly we could have dened the investors’
beliefs at an arbitrary time t; however such
generality is not required for our purposes
here.
32. However, it should be clear that if the game
were to continue beyond the second period
for a potentially innite number of periods,
given concavity of belief revision and the
xed nature of the fees F, the condition (14)
will eventually be violated in some period.
For a complete discussion of such a horizon
limiting problem of an audit contract, see
Gietzmann and Sen (1999). In reality
however, rms may engage in a portfolio of
investment projects. Thus when a firm
continuously takes on new projects through
time, whereas the audit eventually fails to be
a cost-effective means upon which to revise
beliefs for an ‘old’ project, it may still be cost
effective for new projects.
33. We use the notation -2 and -1 to indicate
what period we are considering and to
distinguish the fact that we are not
considering the static rotational equilibria.
34. It however, may be possible that existence of
such an insufcient penalty for one type of
auditors is a descriptive reality. If so,
analysis of such a situation could be of

particular interest. Our model is robust
enough to generate such an analysis.
Specically, it is true that a PC-2 equilibrium
can exist following a PC-1 equilibrium.
However, a PC-2 equilibrium following a
FC-1 cannot exist for reasonable range of
parameter values (such as p(g)

0.5). Our
main conclusions in such a (PC-1, PC-2)
equilibrium do not change signicantly or
qualitatively. However, absent any specic
evidence, we refrain from speculating as to
the possibility of such arrangements that
may lead to a PC-2 equilibrium.
35. In reality such limits do exist but they have
sometimes been described as arbitrary,
unlike in our analysis where they are
derived endogenously.
36. We see this occuring in practice at an
international level, for instance bank audits
in Belgium have been rotated. However, it is
not clear that this is occuring with any
systematic rationale. The intention of this
research is to potentially provide one.
37. We gratefully acknowledge the Fédération
des Experts Compatables Européens for
providing information on this topic.
38. We thank the referee for pointing out that
Paragraph 316 of the Handelsgesetzbuch

(German Commercial Code) requires that
medium sized and large AG’s and GmbH’s
require audits plus all credit institutions and
certain other sorts of specically dened
organization.
39. An additional inference from the study is
that whether or not the auditor changes,
defalcations going undetected are more
likely in early years.
40. See, for example Teoh(1992).
41. An off-setting factor may be that under
mandatory rotation if an auditor knows they
have the client assignment say for six years,
the fact that they do not need to rebid for the
contract after the rst year as under the non
rotational environment may weaken
incentives in subsequent periods.
42. GAO Report on Failed Banks, AFMD-91-43,
Chapter 3, p48. 1991.
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APPENDIX
Denition of Equilibrium
We adopt the notion of sequential equilibrium
as dened by Kreps and Wilson (1982) and offer
the following denition as it applies to our
model setting. An equilibrium of the one-period
auditing game is given by:
(EqC1) A set of strategies such that
(a)
u Î
[0, 1] is the strategy of the investor,
denoting the probability of appointing the
auditor, such that
u
maximizes rm value.
(b) c
m
º

>
[c
M
, c
N
]
Î
[0, 1] is the strategy of the
auditor denoting the probability with which the
auditor decides to collude (not providing
detection effort) with the management, with or
without the investment in detection technology
subscripted M and N respectively. The auditor’s
message space is characterized by
~
q Î
[
~
g,
~
b],
which non-strategically communicate the
auditor’s nding.
(EqC2) c
m
Î
Arg max E [A(m, c
m,
s
] where

A(.,.,.) denotes the auditor’s payoff function at
the beginning of the period, for each state and E
is the expectation operator, m refers to auditor’s
type and
s
refers to the state (g or b).
(EqC3) The strategy c
m
is sequentially rational
in the sense of Kreps and Wilson (1982).
(EqC4) The auditors’ belief about the true state
in the equilibrium path are determined by
Bayes’ rule.
(EqC5) The investors’ belief about the true
state in the equilibrium path
r
(
s
|
~
s
), for all [
s
,
~
s
]
Î
[g, b] are determined by Bayes’ rule.
(EqC6) The beliefs on an off equilibrium path

can be characterized by a set of mixed strategies
such that
r
(
s
|
~
s
)
Î
{0, 1} for all [
s
,
~
s
]
Î
[g, b].
For the two-period game we need, in addition,
that:
(EqC3a) The strategy c
m
is sequentially
rational in the sense of Kreps and Wilson (1982)
in the second period.
(EqC4a)The auditors’ beliefs about the true
state in the equilibrium path are based on all
available actual information from successive
evidence and survival. For a non-colluding type
M auditor, this path is denoted by p

M
m
(g) and for
a colluding auditor this path is denoted by s(g).