Discussion Paper No.

587

THE MARKET FOR LIARS:
REPUTATION AND AUDITOR HONESTY

Andrew McLennan
andIn-Uck Park

June 2003

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

The Market for Liars:
Reputation and Auditor Honesty *byAndrew McLennan
Department of Economics
University of Minnesota
271 19th Avenue South
Minneapolis, MN 55455
mclennan@atlas.socsci.umn.edu
andIn-Uck Park
Department of Economics
University of Pittsburgh
4S01 W.W. Posvar Hall
Pittsburgh, PA 15260
ipark@pitt.edu

June 2003
Journal of Economic Literature Classification Numbers M41, D82, G14.

* This project was initiated when the first author was a Benjamin Meaker Visiting Professor at Bristol
University. Both authors are grateful for the hospitality of the Institute for Social and Economic Researchof Osaka University. We have benefitted from conversations with Ian Jewitt, detailed remarks by Jennifer Ireland, and the comments of seminar participants at the Institute for Social Economic Research(University of Osaka) Keio University, the University of Pittsburgh, the University of Illinois, the Midwest Economic Theory Meetings (Spring 2003) and the Canadian Economic Theory Conference (Spring2003). The second author gratefully acknowledges the research support of the ESRC, U.K. (Grant Number
R000222716).

The Market for Liars: Reputation and Auditor Honesty
byAndrew McLennan and In-Uck Park
“The National Association, representing the majority of its members’ views, always has held firmly to the belief that all human nature is
weak at best, and that that weakness extends even to Public Accountants,
certified or otherwise.”
W.R. Anderson, “The Surety Bond,” The Certified Public Accountant Bulletin, IV-4, 1925.
Abstract: In the model there are two types of financial auditors with identical technology, one of whichis endowed with a prior reputation for honesty. We characterize conditions under which there exists a“two-tier equilibrium” in which “reputable” auditors refuse bribes offered by clients for fear of losing
reputation, while “disreputable” auditors accept bribes because even persistent refusal does not create agood reputation. The main findings are: (a) honest auditors charge higher fees, and have economic profits
accruing to reputation; (b) as the fraction of auditors who are honest increases, the premium charged
by reputable auditors eventually decreases, which diminishes the incentive to refuse bribes; (c) if thefraction of honest auditors exceeds an upper bound, there does not exist a two-tier equilibrium; (d) thus
the reputation mechanism may be undermined by entry into the honest segment of the industry, if it ispossible; (e) increasing auditor independence increases the upper bound. (JEL M41, D82, G14)
Keywords: auditing, reputation, adverse selection, auditor independence

During the first three decades of the twentieth century the auditing industry grew
rapidly, and several audit firms opened branches in multiple cities(1) . Since that period
most observers have recognized a clear distinction between a small number of large firms,
described as the Big Eight, the Big Six, the Big Five, or the Big Four, depending on the era,
who are generally acknowledged to have a special status within the industry. (Herein thesewill usually be described as the Big n firms.) Various studies suggest that smaller audit
firms charge lower fees and their clients received less favorable treatment from financial
markets in connection with IPOs and perhaps other transactions. (The empirical literature
is surveyed in Section IV.) The membership of this group seems to be very stable: twobilateral mergers in 1989 reduced the number from eight to six, and a merger in 1998
reduced the number to five(2) . Although the collapse of Arthur Anderson provides anexample of departure from this group, it seems to be very hard to enter the Big n(3) : all(1)

This process in described in Edwards (1960).

(2)

Arthur Anderson, Deloitte & Touche, Ernst & Young, KPMG, and PricewaterhouseCoopers constituted the Big 5 in 1999.
(3)

E.g., “Too Few Accountants,” The Economist, January 31, 1998.

1

of its current members are descended from the firms that expanded on a national scale
during the early part of the last century. These firms have also undergone considerable
internal expansion in recent decades.
This paper presents a model in which there are two types of audit firms, which we
describe as “reputable” and “disreputable.” These firms have identical technology, butbehave differently in equilibrium. The reputable audit firms are more fearful of losing
their reputation and less easily induced to misreport the condition of the client. As aresult their reports are, in fact, more credible, and more valuable because of the impact
on the client firms’ valuations on asset markets, or because they allow new financing to be
secured on more favorable terms. For this reason reputable firms are able to charge higher
fees, and the capitalized value of expected future fees is what makes them more reluctant
to jeopardize their reputations.
In contrast to earlier theoretical studies (DeAngelo (1981) and Dye (1993)) we findthat this form of reputation depends on an entry barrier to the reputable segment of theaudit industry that prevents competition from eroding the profits of the reputable auditors.
Perhaps the most important conclusion is that the value of reputation, and thus the ability
to obtain a credible audit, can be jeopardized if the size of the reputable segment of theindustry grows beyond a certain point. Some data suggests that the market share of the
top audit firms has, indeed, increased substantially during recent decades. Reforms aimed
at strengthening “auditor independence” may postpone the collapse of the reputation
mechanism, but we know of no proposed reform that would arrest the internal expansionof the Big n firms. Events such as the collapse of Arthur Anderson probably diminish thesize of this segment, even though many former Arthur Anderson employees have foundemployment at other Big n firms, but such exits from the Big n also create antitrust
concerns.
In another paper (McLennan and Park (2003)) we present a quite general modelthat describes conditions under which market forces lead to full disclosure of relevant
information by parties to financial contracts. Applied to this paper’s model, the import isthat in any equilibrium in which reputable and disreputable auditors coexist, the reputable
auditors are providing a more valuable service, so they must be charging higher fees,
since otherwise the demand for the services of disreputable audit firms would dry up.
Concretely, the audit reports of disreputable auditors are uninformative, so that the firms
hiring such auditors are “pooled.” The “best” client firms in this pool receive worse
treatment from financial markets, on average, than they would if they hired a reputable
auditor, so they would switch if the two types of auditors charged identical fees. An
important finding of McLennan and Park (2003) is that, although this conclusion depends
2

on well functioning markets, it is very robust with respect to the nature and details of thefinancial arrangements being pursued by the client firms.
We regard this work as a contribution to the theoretical literature on reputation inindustrial organization and game theory. In contrast with some other models of reputation(e.g., Kreps and Wilson (1982), Milgrom and Roberts (1982), Rogerson (1983)) there is no
hidden state variable, e.g., a “commitment type” or capital suitable for making productsof a particular quality, that persists across periods. In this sense ours is a model of“pure” reputation: agents of different reputation do not differ in other ways, so that thedesire to preserve one’s reputation is the only motivation for behaving in the manner one’s
reputation predicts. Klein and Leffler (1981), Shapiro (1983), and Allen (1984) are alsomodels of pure reputation in this sense. Unlike those papers (but like Rogerson (1983)) in
our model behavior is monitored infrequently and imperfectly.
The remainder has the following structure. Sections I and II present and analyze theformal model of financial auditing. Section III contrasts our model with related theoreticalresearch on the auditing profession. Section IV reviews related empirical literature, andSection V concludes.
I. The Model
This section describes the formal model of the auditing industry, and the different
types of equilibria that are possible.
In each period there is a continuum of client firms with total measure one. A client
firm cannot stay in business unless it succeeds in obtaining financing in the form of a loan
whose amount ` is fixed and exogenous. The firm has an unknown state, which may beeither “good” or “bad,” so the set of possible states is S := {G, B}. The firm hires anauditor who investigates the firm’s condition, and this investigation reveals the state of
the firm to both the firm and the auditor, but not to the financial market. The auditor
then publicly states whether the firm is good or bad. The auditor must state that thecondition of the firm is good when that is in fact the case. If the state is found to be bad,the audit firm may state this (in the terminology of the industry, the audit firm “qualifies
the accounts”) but there is also the possibility that the client may offer inducements tothe audit firm to not qualify the accounts, as we explain in more detail below. Thus, when
the auditor reports that the firm’s state is bad, that is certainly the case, but in response
to a favorable report the financial market must assess the probability that the state is, infact, good.

After the auditor issues her report, the repayment promise r required for the firm’s
loan is determined in the financial market. (It may happen that there is no repayment
3promise sufficient to induce lenders to make the loan.) If the firm obtains financing, iteither succeeds or fails. The probability of success is either pG or pB , according to whether
the firm’s state is G or B. (The state is a sufficient statistic for the probability of successin the sense that, conditional on it, the firm’s type is uninformative.) We assume thatpB < pG . In the event that the firm succeeds its value is h (which is fixed and exogenous)
so that the profits resulting from the attempt at survival, net of the audit fee f and theloan repayment, areh − f − r.
If it fails, then its value is zero and it makes no repayment of the loan(4) . Regardless ofthe outcome, we assume that the firm and the auditor have no dealings in later periods.
In the event that the firm fails, there is an investigation that reveals whether thestate was actually G or B. The auditor is forced to leave the industry if she is revealed tohave failed to qualify the accounts when the state was bad.
Although, in the equilibria we emphasize, different auditors will have different reputations, all auditors have the same cost of performing an audit, which is assumed to be zerofor the sake of notational simplicity. Each auditor is capable of auditing one firm in eachperiod. The interaction between the auditor and the client firm is assumed to be governedby a contract, specifying a payment prior to the audit, and there is also the possibilityof a renegotiation leading to a bribe once the actual state has been revealed. Since theauditor is bound to report that the state is good when the actual state is good, there isno possibility of renegotiation in this circumstance.
We assume that the contractual fee cannot depend on the reported state. An agreement to pay a higher fee when the state is bad amounts to a vehicle for shifting a greater
fraction of the expected fee onto the firm’s creditors when the firm is bankrupt, so it isnatural to expect that such an arrangement would be disallowed by the bankruptcy court.
On the other hand an agreement to pay a higher fee when the state is good is
disadvantageous from at least two points of view. First, in practice, though not in the modeldue to the assumption of rational expectations, if the financial markets can observe theterms of such a contract, they will tend to have doubts about the auditor’s independence.
Second, the effect of such a contract is to shift some of the auditor’s expected payments into
events in which the firm does not declare bankruptcy, which is unnecessarily generous to
the firm’s creditors. In the equilibria we study a disreputably audited firm always receives
financing. The creditors end up paying the audit fee when the firm fails, and the equity(4)

That is, we are assuming that f is treated as an operating expenses, hence is paid regardless ofwhether the firm succeeds, but in the bankruptcy proceedings of a failed firm the assets are insufficient to
repay all debt more senior than the loan under consideration.

4

holders pay when the firm succeeds. Under a contract in which an auditor’s fee was lower
in the bad state, and the expected fee was equilibrated, hence higher in the good state, theexpected payment of the creditors would be less, and the expected payment of the equity
holders would be more, to the extent that the probability of success was lower in the badstate.
There is a continuum of auditors with total measure one. Of these, measure mR < 1
are reputable auditors. In the equilibria we focus on reputable auditors do not accept bribes
because the maximum bribe a firm in a bad state would be willing to pay is insufficient
to compensate for the risk to a reputable auditor’s reputation. The constant fee charged
by reputable auditors is denoted by fR . All auditors value expected audit fees and bribes
in future periods by applying the discount factor δ ∈ (0, 1), so the value of a reputable
auditor’s future stream of fees is δfR /(1 − δ). The minimum bribe that a reputable auditor
would accept is (1 − pB )δfR /(1 − δ), which is the probability of being caught times theloss in that event.

The prior reputation for honesty of reputable auditors is an exogenously given (i.e.,
historically determined) fact: reputable auditors retain their reputation unless they arecaught, and the model does not permit an auditor to acquire a reputation for honesty.
Thus the quantity mR is given and fixed, instead of being determined by equilibration(5) .
The essence of reputation is a coordination of intentions and inclinations on the part of
the audit firm and expectations on the part of the financial markets. In general one cantry to create a reputation, in the sense of inducing desired expectations concerning one’s
behavior, by taking steps to make honest behavior attractive and dishonest behavior risky
or irrational. The implicit hypothesis of our model is that the expectations of financial
markets are unresponsive to publicly available information suggesting honest behavior, sothat creating “a Big n reputation” from scratch is either infeasible or excessively costly. We
should stress that the reputable auditor’s behavior is an equilibrium phenomenon, not amatter of inherent honesty; an incentive compatibility condition will state that she declines
bribes only because they are insufficient to compensate for the risk to her reputation.
The other auditors are described as disreputable. Prior to each period new auditors(5) One might ask whether there could be a third class of auditors with an intermediate reputation.
Since they sometimes accept bribes and sometimes refuse, a client in a bad state must be unwilling to
induce sure acceptance by slightly increasing the bribe. Thus the client’s option of offering a bribe has
no value, so the difference between this auditor’s fee and the fee of the reputable auditor must exactly
offset the difference in reputation. Varying the intermediate reputation between the two extremes, theintermediate value theorem implies the existence of a reputation at which the client firm is indifferent about
offering the minimum bribe the auditor would accept, so such equilibria exist. But such an equilibrium ishighly unstable: a small improvement (decline) in the intermediate auditor’s reputation results in refusal(sure acceptance) of bribes, due to the increased (decreased) value of future fees, after which this groupwould merge with the reputable (disreputable) auditors.

5

can enter the disreputable segment of the industry by paying a fixed cost C. The fee
actually paid to the disreputable auditor will be fDG or fDB according to the state. HerefDG is the contractual fee, and the differenceb := fDB − fDG
is the amount of the bribe. (In practice such payments are difficult to identify as such,since they are embedded in the continuing relationship between the firm and the auditor,
which may involve purchases of consulting services or other interactions.) Our definitionof equilibrium specifies that the bribe should be the minimum amount that is acceptable
to the auditor as compensation for the risk of getting caught(6) .
The possibility of entry is the mechanism that equates the total supply for auditorswith total demand, and it also determines the expected revenue of disreputable auditors.
The value of a disreputable auditor’s business is equal in equilibrium to the cost C of entry
into the industry, and a client firm whose state has been found to be bad is willing to
pay a bribe that is sufficient to compensate a disreputable auditor for the risk of being
forced to leave the industry. The value of being an undiscredited disreputable auditor isthe discounted value of the entry cost C, so b + pB δC = δC, i.e,b = (1 − pB )δC.
Therefore free entry implies that the value of receiving fDG in every subsequent period isC, sofDG = (1 − δ)C and fDB = (1 − pB δ)C.
The type of the auditor is the only information available to the financial market
at the time the financial contract is negotiated. The financial market is competitive andrisk neutral, so that the firm will receive a loan if there is a repayment amount that
does not exceed the value of the firm in the event of success (net of the audit fee andbribe) such that the expected repayment is equal to `. Let rR and rD be the repayment
amounts for firms who receive unqualified reports from reputable and disreputable auditors
respectively. Since reputable auditors always report truthfully, in equilibrium pG rR = `,so that rR = `/pG . We assume that pG h > `, so that a firm that is known to be good is aworthwhile gamble(7) .
(6)This assumption can be justified by the following bargaining protocol. Prior to performing the audit,
the firm pays the auditor a sum that is necessarily independent of the state. After the audit, if the stateis bad, the firm may make a take-it-or-leave-it offer of a bribe to the auditor. Naturally, other bargaining
protocols imply different outcomes. It may be of interest to investigate other possibilities along these lines.
(7)

Since (1 − δ)C is the minimum audit fee that could be observed in equilibrium, it would be natural
to assume that pG (h − (1 − δ)C) > `, but this strengthening of the assumption would not simplify the
analysis by ruling out obnoxious and irrelevant special cases.

6

The repayment amount for a firm receiving an unqualified audit from a disreputable
auditor (in equilibria where this happens) is rD . Equilibrium requires that
Prob(G|D)pG + Prob(B|D)pB rD = `,(1)

where Prob(G|D) and Prob(B|D) are the probabilities of the good and bad state conditional on receiving an unqualified audit from a disreputable auditor. We assume that,regardless of the audit fee, there is no repayment amount satisfying this condition when
the state is known to be bad. That is, pB h < `, i.e., the expected revenues from continued
operation are less than the loan amount.
For the most part we will focus on equilibria in which firms found to have a bad state
are willing to pay the bribe that suffices to elicit a false report from a disreputable auditor,
but are not willing to pay the amount required to induce a false report from a reputable
auditor. We describe such an outcome as a two-tier equilibrium. Another outcome thatmight be described as an equilibrium is a collapse of the reputation mechanism, resulting
in a situation in which formerly reputable auditors accept bribes, so that, in effect, there
are only disreputable auditors.
A firm that is audited by a disreputable auditor and is found to be bad must decide
whether it is worthwhile to pay the bribe. Since, in our model, all firms who have beenfound to be in a bad state are, at that point in time, identical, either all firms bribe ornone do. The profit of such a firm, in the event that it succeeds, is h − fDB − rD .
Prior to choosing which auditor to hire, the firm is privately informed of its type,which is the probability t ∈ T := (0, 1) that the state will be good. If the firm hires a
reputable auditor its expected payoff is

tpG (h − fR − rR ) = t(pG (h − fR ) − `).

(2)

Provided that it is worthwhile to bribe a disreputable auditor, the expected payoff resulting
from hiring a disreputable auditor istpG (h − fDG − rD ) + (1 − t)pB (h − fDB − rD ).

(3)

Comparing the results of hiring the two sorts of auditors, we find that the reputable
auditors are hired by firms with favorable types.
Lemma 1: Assume that h − fDB − rD > 0, and suppose there is a probability t̃ such thata firm of type t̃ is indifferent between hiring a reputable auditor and hiring a disreputable
auditor. Then firms of type t > t̃ strictly prefer hiring a reputable auditor to hiring adisreputable auditor, and the opposite is the case for firms of type t < t̃.
7

Proof: Since h − fDB − rD > 0, the equalityt̃pG (h − fR − rR ) = t̃pG (h − fDG − rD ) + (1 − t̃)pB (h − fDB − rD )implies that h − fR − rR > h − fDG − rD .
The distribution of firm types (and thus the prior beliefs of the financial markets)are given by a probability distribution µ on (0, 1). We assume that µ is atomless andhas full support. These assumptions imply that there is a unique number t∗ such thatµ((t∗ , 1)) = mR . Now Lemma 1 implies that, in equilibrium, all types in (0, t∗ ) either hire
disreputable auditors or do not attempt to stay in business, and all types in (t∗ , 1) hire
reputable auditors. (Since µ is atomless, what a firm of type t∗ does is inconsequential.)
We now explain the determination of the repayment terms of clients of disreputable
auditors and the fees of reputable auditors. Under the assumptions that (a) all typesof firm hire auditors and attempt to stay in business, and (b) the set (t∗ , 1) of types
hiring reputable auditors is known, when a firm hires a disreputable auditor, the financial
market’s beliefs about its probability τ (t∗ ) of being good will be the average type of firms
with types in (0, t∗ ): set
R t∗
t dµ
τ (t∗ ) := 0.
µ((0, t∗ ))The equilibrium value of rD is now determined by (1):rD = ρD (τ (t∗ )),where, for 0 ≤ α ≤ 1

ρD (α) :=`αpG + (1 − α)pB

is the equilibrium repayment amount when the probability of a good state is α.
If t∗ is small, so that rD is large, it may happen that h − fDB − rD < 0, in which caseeven disreputable auditors refuse the largest bribes that the client firm can afford. The

outcome seems indeterminate: if the financial market came to believe that all auditors
were refusing bribes, the repayment amount rD would fall, restoring the bribability ofdisreputable auditors.
An even more extreme possibility is that h−fDG −rD < 0, in which case disreputable
auditors will not be hired since hiring one cannot lead to a situation in which continued
operation of the firm is worthwhile. One might expect the fee of reputable auditors to riseto the point where all firms are indifferent between immediate bankruptcy and hiring a8

reputable auditor, so that h − fR − `/pG = 0, hence fR = h − `/pG . At this fee all firms are

indifferent as to whether to hire a reputable auditor, and which firms actually hire auditors
is indeterminate. Moreover, a firm whose state has been found to be bad is unwilling to
pay any bribe, since all the surplus has already gone into the audit fee. Such equilibria

are quite extreme, with very high audit fees and bankruptcy of many firms for which it
would be worth the expense of an audit if there could be a credible report in the eventthat the state was found to be good, so they might be regarded as unrealistic in the sensethat there would be pressure for institutional reforms that would undermine the featuresof the model leading to this outcome. In any event we will not give further consideration
to these possibilities. Henceforth we will assume thath − fDB − rD > 0.

(4)

In view of Lemma 1, the fee of reputable auditors will be determined by the condition
that a firm of type t∗ is indifferent between the two types of auditors. Equating (2) and(3) and isolating fR yields:
fR = fDG + rD − rR −(1 − t∗ )pB (h − fDB − rD )
.
t∗ pG

(5)

At this point we have shown how to determine the equilibrated variables—fR , fDG , fDB ,rR , and rD —in a two-tier equilibrium.
II. Equilibrium Analysis
This section presents the analysis of parameter values for which two-tier equilibria
exist. In such an equilibrium a disreputably audited firm must be willing to pay the bribeb, which will be the case if (4) holds. Note that τ (t∗ ) is an increasing function of t∗ , andρD (τ (t∗ )) is a decreasing function of τ (t∗ ), so there is a unique number t > 0 such that
ρD (τ (t)) = h − fDG − b = h − fDB = h − (1 − pB δ)C.

(6)

Disreputably audited firms will be able to obtain financing that justifies paying a bribe
when t∗ ≥ t and not otherwise.

We now examine the incentive compatibility condition under which reputable auditors cannot be bribed. A firm whose state has been found to be bad by a reputable auditor
would be willing to pay up to h − fR − rR to obtain an unqualified audit report. Thus

the maximum bribe plus the probability of success in the bad state times the value of the9stream of future audit fees must be less than the value of having the future audit fees withcertainty:
h − fR − rR + pB
or fR ≥ fRmin wherefRmin :=

δ
δ
fR <
fR ,
1−δ
1−δ

h − rR.
δ
1 + (1 − pB ) 1−δComparing this with (5), an equilibrium in which reputable auditors do not accept
bribes exists if and only if t∗ ≥ t andfDG + ρD (τ (t∗ )) − rR −(1 − t∗ )pB (h − fDB − ρD (τ (t∗ )))≥ fRmin .
∗t pG

Isolating ρD (τ (t∗ )), this inequality is equivalent to ρD (τ (t∗ )) ≥ ρ(t∗ ) where, for t ∈ (0, 1),
ρ(t) :=

fRmin − fDG + rR − (h − fDB )B
1 + (1−t)ptpG+ h − fDB

(7)

is the repayment amount for disreputably audited firms that results in a fee for a reputable
auditor that makes her indifferent about whether to accept the maximum bribe a client
firm would be willing to pay.
Lemma 2:
Proof:

fRmin − fDG + rR < h − fDB , so that ρ is a decreasing function.

Above we assumed the existence of t satisfying (6), so that h − fDG − rR >h − fDG − ρD (τ (t)) = b. Thus h − rR − b > fDG . Since b is just sufficient to compensate

an auditor for the risk of losing a stream of revenues of fDG in each future period, b is
not sufficient to induce acceptance by an auditor who could receive a fee of h − rR − b ineach future period. Since b would be the maximum possible bribe if fR = h − rR − b, this
implies that fRmin < h − rR − b = h − rR + fDG − fDB .
Note that ρ(t∗ ) decreases from h − fDB to fRmin − fDG + rR as t∗ increases from 0 to

1, and that ρD (α) = `/(αpG + (1 − α)pB ) decreases monotonically from `/pB to `/pG asα increases from 0 to 1. We claim that``< h − fDB <
pG
pB

and

`
`
< fRmin − fDG + rR <,pG
pB

so that the image of ρ is contained in the interior of the image of ρD , which means that we∗may define τ : (0, 1) → (0, 1) by τ (t∗ ) := ρ−1
D (ρ(t )). Of the four asserted inequalities, thefirst follows from (4) and rD > rR = `/pG , while the second follows from h < `/pB . The
10third follows from `/pG = rR and fRmin > fDG , while the fourth follows from fRmin < h − rR
and h < `/pB . Since ρD and ρ are both decreasing functions, we have:
Lemma 3:τ is an increasing function.

Summarizing the discussion above:
Theorem 1: There exists a two-tier equilibrium if and only if t∗ ≥ t and ρD (τ (t∗ )) ≥ ρ(t∗ ),i.e., τ (t∗ ) ≤ τ (t∗ ).

The inequality τ (t∗ ) ≤ τ (t∗ ) holds whenever τ (t∗ ) ≥ t∗ , since t∗ ≥ τ (t∗ ). The

case τ (t∗ ) < τ (t∗ ) ≤ t∗ corresponds to an exotic possibility: the distribution of firmtypes is so heavily concentrated near t∗ , and t∗ is so close to one, that the financial
markets extend loans to disreputably audited firms at terms that are only slightly worse
than the repayment terms for reputably audited firms, with reputable auditors receivinga premium that is insufficient to dissuade them from accepting a bribe from a firm that isrevealed to be bad. Assuming that the reputation mechanism collapsed, the distributionof types of disreputably audited firms would become even more favorable. The parametervalues leading to this outcome are extreme, and this aspect of the model seems both
unrealistic and unproblematic, but it leads to a certain qualification of our comparative
statics: changing δ has an unambiguous effect on t, but we are not able to say that it has
a monotonic (in the sense of set inclusion) effect on the set of values of t∗ supporting a

two-tier equilibrium.
To prepare for the discussion of the possible consequence of changes in mR and δ wedevelop a sufficient condition (Theorem 2 below) for the existence of a two-tier equilibrium.
This will have the implication that for any specification of h, `, C, pB , pG , and δ such thatfirms known to be good receive financing and those known to be bad do not, there is anonempty interval such that a two-tier equilibrium exists whenever mR is in this interval.
Lemma 4: There is a unique number 0 < t̂ < 1 such that τ (t̂) = t̂.
Proof: Since τ : (0, 1) → (0, 1) is continuous, existence follows from the intermediate value

theorem. It is easy to see that a function from (0, 1) to (0, 1) cannot have more than one
fixed point if it is either convex or concave, so uniqueness is a consequence of the next
result.

Lemma 5: Either τ is concave or τ is convex.
11

Proof: The definitions of τ and ρD , together with (7), imply that`f min + rR − h + b= R p +t(p −p )+ h − fDB
B
B
G
pB + τ (t)(pG − pB )
=

tpG
min
tpG (fR + rR − h + b)

pB + t(pG − pB )+ h − fDB .

To simplify notation let α = pG (fRmin + rR − h + b), β = h − fDB and ∆p = pG − pB .
Substituting, then rearranging, yields
τ (t)∆p =`(pB + t∆p)
− pB .
t(α + β∆p) + βpB(8)Differentiating (8) with respect to t twice, we gett(α + β∆p)∆p + βpB ∆p − (pB + t∆p)(α + β∆p)·`2t(α + β∆p) + βpB
βpB ∆p − pB (α + β∆p)= 
2 · `t(α + β∆p) + βpB
−`αpB
=
2
t(α + β∆p) + βpB

τ 0 (t)∆p =

and



(α + β∆p)
β∆p)
+
2`αp
t(α
+
βp
B
B
τ 00 (t)∆p =4t(α + β∆p) + βpB
2`αpB (α + β∆p)=
3 .
t(α + β∆p) + βpB

(9)

(10)

Note from (8) that, for all t ∈ (0, 1), t(α + β∆p) + βpB > 0, since otherwise τ (t) < 0

contrary to the definition of τ . Hence, for all t, τ 00 (t) has the same sign as the constantα(α + β∆p).
If τ (1) > t̂ let t := τ −1 (t̂), and otherwise set t := 1. We now have the following
result:Theorem 2: If µ((t, 1)) ≤ mR ≤ µ((t, 1)), i.e., t ≤ t∗ ≤ t, then there is a two-tierequilibrium.

Proof: We wish to show that t ≤ t∗ ≤ t implies that τ (t∗ ) ≤ τ (t∗ ). For 0 ≤ t∗ ≤ t̂ wehave τ (t∗ ) ≤ t∗ ≤ τ (t∗ ). For t̂ ≤ t∗ ≤ t we have τ (t∗ ) ≤ t̂ = τ (t̂) ≤ τ (t∗ ).
The interval (t, t) is always nonempty:
12

Lemma 6: t < t.
Proof: If τ (1) ≤ t̂, then t := 1 > t. Otherwise t̂ = τ (t), so that the claim follows from themonotonicity of τ once we show that τ (t) < t̂. From Lemma 2 we have fRmin − fDG + rR <−1
h − fDB , so (7) implies that ρ(τ (t)) < h − fDB , whence ρ−1
D (ρ(τ (t))) > ρD (h − fDB )−1
because ρD
is decreasing. The definition of τ gives τ (τ (t)) = ρ−1
D (ρ(τ (t))), and (6) implies−1
that ρ−1
D (h − fDB ) = ρD (ρD (τ (t))) = τ (t). Therefore τ (τ (t)) > τ (t), and consequently

τ (t) < t̂ since t̂ is the unique fixed point of τ .

The picture developed by these results is shown in Figure 1.
[Insert Figure 1 near here.]
To understand the graphical derivation of t observe that, by (7), ρ(0) = h − fDB . From−1−1(6), therefore, τ (t) = ρ−1
D (h − fDB ) = ρD (ρ(0)), and τ (0) = ρD (ρ(0)) = τ (t) follows fromthe definition of τ . It is possible for t to be less than, equal to, or greater than t̂. The
graph of τ can cross the graph of τ , perhaps more than once, as shown, or it may happen
that τ (t) < τ (t) for all 0 ≤ t ≤ 1. If the graph of τ moved up when δ increased, increasing

δ would unambiguously expand the set of values of t∗ for which a two-tier equilibrium
exists by virtue of the next result. But examples show that it is possible that an increasein δ can result in the graph of τ moving down in some intervals.
Although we treat δ as a discount factor, it can be construed more generally asa measure of auditor independence, insofar as its function in the model is primarily tomeasure the relative importance of the auditor’s expected fees from other clients in comparison with the temptations offered by the current client. Note that the definition of τ isindependent of δ.
Lemma 7: t is a decreasing function of δ.
Proof: From (6) we havet = τ −1 (ρ−1
D (h − (1 − pB δ)C)).
Since τ is an increasing function, ρD is a decreasing function, and neither function changes
when δ varies, this quantity decreases when δ increases.

III. Related Theoretical Work
This section compares our model to two other models of how the Big n auditors
might be different, in equilibrium, from other auditors. The first paper, due to DeAngelo
13

(1981), proposes that large auditors have a larger client base, hence more to lose in theevent of a scandal, due to the phenomenon known as “lowballing.” The second paper, Dye(1993), proposes what has come to be known as “the deep pockets hypothesis.” The mainidea is that large firms have more wealth, hence are at greater risk in the event of law suits
by creditors or investors.
Another possibility that is sometimes mentioned, but is not considered in our modelor by DeAngelo or Dye, is that Big n auditors may simply have superior technology andmore talented employees, so that (independent of incentives arising out of moral hazard
considerations) their reports are more reliable because they are, in effect, more precise
instruments for examining client firms. While it may be true that Big n firms are morecapable, the apparent difficulty of entering the Big n, and the continued existence of lessreputable auditors, seem difficult to explain in terms of these factors alone.
DeAngelo was responding to industry critics who argued that large audit firms benefitted unfairly and unjustifiably from discrimination by underwriters and other actors
in financial markets. Those critics maintained that large and small audit firms provided
essentially the same service, and that the preference of customers for large audit firms
was the result of discriminatory practices unrelated to any underlying difference in quality.
She countered by arguing that large firms had more to lose in the event that they were
found to have failed to honestly report the condition of one of their clients, and that thismade their reports more reliable. Thus large and small audit firms were selling different
products which could reasonably be expected to be regarded as distinct by customers andthose who might be influenced by auditors’ reports.
DeAngelo describes a world in which competition in the market for new clients drives
expected profits, at the time of first audit, to zero. Since the costs of performing an audit
for a new client are greater than the costs of auditing a client one has audited before, audit
firms can extract quasi-rents from existing clients who would incur costs if they switchedauditors. Since these quasi-rents are anticipated, competition leads auditors to offer a fee
for the initial audit that is below cost. This practice, which is known as lowballing, implies
that relationships with existing clients are valuable to the audit firm, and the value ofthese relationships is placed at risk whenever the audit firm behaves dishonestly. Largefirms have more clients, hence more to lose.
Our results suggest that one should not expect to observe both large and small audit
firms if the capitalized value of existing accounts is the only force motivating differential
honesty and there is free entry into the high quality tier of the auditing industry, so thatthe two types of auditors have equal expected fees. In equilibrium the firms that choose
disreputable auditors must be precisely those who prefer to do so, given the signal to14

financial markets that results from this choice. The “best” type in the pool choosing adisreputable auditor would prefer to be audited by a reputable auditor, if the fees were thesame, since the alternative is to be treated as an average member of the pool. A processof continued expansion of the high quality tier, and the best firms in the low quality tierswitching, would lead eventually to the evaporation of the market for disreputable auditors.
(As mentioned earlier, this inference is strengthened by the analysis of McLennan and Park
(2003).)Dye (1993) develops the deep pockets hypothesis in a model in which wealthier audit
firms are more strongly motivated to be diligent in their investigations of client firms
because their greater wealth makes them more vulnerable to lawsuits. Even if both large
and small auditors are incorporated, hence protected by limited liability(8) , smaller firms
may be presumed to have much less wealth, so that a favorable verdict in a lawsuit might
be a hollow victory. One significant point emerges from Dye’s model: if the deep pockets
hypothesis was the only important factor, large auditors would dominate small ones, anddrive them out of the market, unless small auditors enjoyed a cost advantage. Dye (1993,
p. 890) mentions that liability can arise out of failure to follow proper procedures, and thatsuch failure can result in lower costs. For example, Generally Accepted Auditing Standards
require that auditors inspect warehoused inventories. But one might expect (we have no
specific information) that to a large and increasing extent the relevant data is alreadyavailable to the auditor in electronic form, and can be manipulated with no more effort
than is required to modify a spreadsheet. In addition, the hypothesis that wealthy firms
use more expensive procedures is counter to the usual presumption of scale economies. On
the other hand, even prior to the Enron affair there was substantial anecdotal evidence (e.g.
Grout et. al. (1994)) concerning the importance of pressure to give a favorable presentationof the client firm’s accounts. In the contemporary popular press there is little discussionof costs of diligence. We do not know of formal studies supporting the view that such costdifferentials are substantial, but possibly this is due to difficulty in obtaining data.
IV. Empirical Literature
In this section we give a brief guide to relevant empirical literature. We organize
our discussion around four issues: a) Is it actually the case that the audit reports of large
and/or reputable audit firms lead to better treatment of client firms on financial markets?
b) Do large firms charge higher fees? c) What is the relative importance of reputation incomparison with deep pockets? d) Have the answers to these questions changed over time,(8)

In fact Arthur Anderson was a partnership.

15

and has the market share of the Big n been expanding?
A. Does Auditor Reputation Benefit Clients?
Balvers et. al. (1988) study the impact of auditor reputation on underpricing of IPO’s.
In their model the audit firms’ reputations are common knowledge, but the reputationsof investment bankers are less well known. In equilibrium high reputation auditors matchwith high reputation bankers, which acts as a signal to the markets conveying information concerning bankers’ quality. Using a data set consisting of 1182 IPOs between 1981
and 1985, they find support for the following propositions: a) high reputation auditors
are matched with high quality investment bankers; b) there is less underpricing of IPOs
associated with high quality audit firms; c) there is less underpricing of IPOs associatedwith high quality investment banks.
Using data on 103 IPOs in New Zealand between 1983 and 1986, Firth and Smith(1992) find that IPO firms that are less well positioned to give credibility to their accounts(e.g., firms whose management has low level of share ownership in the company, firms withhigh debt to equity ratio, and firms with short history) tends to hire Big 8 audit firms. In
a separate regression with underpricing of IPO as the dependent variable, they find that
reputation of the underwriter is a significant explanatory variable, but that whether theauditor is a Big n firm is not significant.
Beatty (1989) raises doubts about the classification of Big 8 as having reputation
capital and non Big 8 as entirely without reputation, because “it appears that smaller Big
8 and larger non-Big 8 exhibit similar reputations in the IPO market.” Using two-stage
least squares, he first measures reputation as excess compensation for the auditor, thentests the relation between reputation capital, measured in this way, and underpricing of
IPOs. He finds that auditors’ reputation is inversely related to underpricing of IPOs.
Beatty’s finding may also be construed as supporting the view that high reputation auditors charge higher fees, but since fees are used to measure reputation, the morecautious interpretation would seem to be that, for some reason, there is an inverse relationship between the fees charged by auditors and underpricing. Reputation is one possible
explanation, but Beatty’s finding is potentially consistent with other theories of auditor“quality.”
B. Is There a Big n Premium?
The literature on the existence of a Big n premium is large, with few conclusions
that are robust across all studies. Simunic (1980) and Chaney et. al. (2002) are studies
that fail to find a Big n premium. Studies that find a positive Big n premium include
Francis (1984), Francis and Stokes (1986), Palmrose (1986), Francis and Simon (1987),
16

Simon and Francis (1988), Ettredge and Greenberg (1990), Chan et. al. (1993), Pong andWhittington (1994), Craswell et. al. (1995), and Ireland and Lennox (2002)
In some cases, such as Francis and Stokes (1986) and Palmrose (1986), there is apremium for smaller client firms, but not for large clients. On the other hand, Rubin(1988) finds a Big 8 premium for large clients (which are city governments in his study)
but not for small clients.
Any measurement of a Big n premium depends on some measure of auditor costs, andpotentially other factors that might affect either the choice of auditor or the relationshipbetween auditor and client. While the studies that we are aware of do not present structuralmodels, they attempt to various extents, and in various ways, to incorporate additional
explanatory variables, and to correct for phenomena that could bias regression analysis. In
particular, Ireland and Lennox (2002) and Chaney et. al. (2002) are explicitly concernedwith biases resulting from the possibility that, for whatever reason, the client firms choosing
large firms might be “easier” to audit, in which case the actual premium over costs enjoyedby Big n firms might be larger than it appeared. Ireland and Lennox (2002) find a Bign premium, and argue that correction for selection bias results in a larger estimate of thepremium, but Chaney et. al. (2002) find no premium.
While the accumulated evidence does not seem to resolve the question definitively, it
seems that most of the studies to date find that there is a Big n premium. In addition, thereis the possibility that some authors’ failure to find a premium is due to biased statisticalmethods, but with respect to this point as well, the literature has not yet reached a clear
consensus.
C. Deep Pockets vs. Reputation
Although we have not done so, it seems reasonable to suppose that one could construct a theoretical model incorporating both reputation and the deep pockets hypothesis.
Similarly, it seems reasonable to suppose that both effects are present in reality. In addressing the empirical literature, probably the correct attitude is to try to assess the relative
importance of the two effects.
The empirical literature is not especially large, nor does it point clearly in a particular
direction.
Using litigation data during 1960-85 for the largest 15 audit firms in the US (whoaudit more than 90% of US public companies) Palmrose (1988) found that the “Pretty Big
9-15,” as a group, had higher litigation occurrence rates than the Big 8. She interprets
this as evidence that the Big 8 provide, in some sense, higher quality service, but she
does not take a position concerning the nature or source of this quality differential. Using17multivariate regression (earlier studies used univariate regression) Stice (1991) studies theeffects of 9 characteristics of the client and auditor on the likelihood of lawsuits against
auditors. The variables that were found to be significant concern the client firm: theclient’s asset structure (higher ratio of accounts receivable and inventory to total assets)financial condition, variability of its returns, and market value. In contrast to Palmrose(1988), he did not find that a Big 8 dummy variable was significant.
Firth (1990) examines the effects of auditor criticisms reported by the UK Department of Trade after investigations, finding that i) there is a small but significant reduction
in stock prices of other clients of the criticized auditor immediately after the criticism, andii) relative to comparable uncriticized auditors, the criticized auditors experienced loss ofclients and a reduction in new clients’ fees, but no reduction of existing clients’ fees. As
Firth points out, these findings are consistent with the reputation hypothesis(9) . Similarly,
Chaney and Philipich (2002) find significant negative returns of Arthur Anderson clientsduring the three days following the disclosure that documents had been shredded, and ofcourse the damage to Arthur Anderson went far beyond lost clients and lower fees. Insofar as criticism does not directly result in diminished auditor wealth, it seems difficult to
explain these phenomena using only the deep pockets hypothesis.
In contrast to Palmrose (1988), Lennox (1999) finds that large auditors are more
likely to be sued and/or criticised. In contrast to Firth (1990) and Chaney and Philipich(2002), he finds that criticised auditors did not suffer drops in demand as a result ofcriticism. This paper presents complicated issues concerning the data—reports in the UK
financial press—which may be biased in the direction of emphasizing large events. One
point of interest is that, whereas his discussion treats reputation as a continuous variable,
so that increased criticisms should lead to eroded reputation and demand, in our model it isa binary variable. That is, our model is consistent with “run-of-the-mill” criticism having
slight or no effect on demand, while “decisive” events result in occasional catastrophic
losses of reputation, as in the case of Arthur Anderson.
D. Evidence of a Changing Environment
One of our important theoretical findings is that incentives to maintain reputation
will diminish if the Big n premium is eroded as a result of competition. While entry into
the Big n seems to be very difficult, all these firms are now very different creatures from
(9)

Strictly speaking, these findings relate to a different model of reputation than the one consideredherein, in which reputation is nothing more than the belief that the audit firm is motivated to behave
in a way that will tend to sustain its reputation, and does not represent a belief about an unobserved
persistent feature of the auditor. Since all agents in our model have rational expectations concerning
auditor behavior, a loss of reputation by an auditor would not be interpreted as revealing a hidden statevariable, and consequently it would not result in new doubts about that auditor’s other clients.

18

the firms that opened branches in multiple cities during the first quarter of the twentiethcentury. (See Edwards (1960) for a description of the evolution of the auditing industry
during this period.) In particular, there is the possibility that internal expansion of thesefirms could erode the Big n premium, and for this reason it is interesting to examine theevolution of their market share over time. Most of the studies cited above deal with aparticular time period, and comparison across studies is complicated by differences in thenation from which the data is taken, and the criteria used to select the sample of audit
clients.
We know of two studies that are explicitly focused on the evolution of market sharein the US. Using a sample of 299 S&P firms drawn from a selection of industries chosen
to include both regulated and unregulated industries, and industries with both high andlow propensity to use Big n auditors, Danos and Eichenseher (1986) find that the Big 8
market share increased from 51.8% in 1965 to 58.2% in 1972 and then to 66.6% in 1980.
For all audit clients listed in the NYSE, NASDAQ, or AMEX (excluding those that wereacquired, went private, or for which there was inadequate information) Wolk, Michelson
and Wootton (2001) find that the Big n market share was well over 80% in the years 1988,
1991, 1996, and 1999.
V. Conclusion
This paper develops a model in which the audit firms previously endowed with areputation for honesty do, in fact, behave honestly, because they are afraid to jeopardize
their reputation. The value of reputation is proportional to the difference between the fees
charged by reputable auditors and those charged by auditors without prior reputation.
In equilibrium this fee differential leaves the marginal client firm indifferent between the
two types of auditors. High quality client firms have a stronger preference for reputable
auditors, so that expansion of the reputable segment of the market leads to a marginal
client firm with lower willingness to pay for a high quality audit. Lowering the quality ofthe marginal firm also results in a lower average quality, and less favorable financing, fordisreputably audited firms. We find that the former effect is dominant, except in unusual
and unrealistic circumstances, so that expansion of the supply of high quality auditing
leads to a reduction of the fee differential. If the supply of high quality auditing passes
a certain threshold, the fee differential will be so small that the value of reputation is
insufficient to motivate honest behavior.
Our model shares various features with the models of DeAngelo (1981) and Dye(1993). Unlike those models, our model has equilibria in which reputable and disreputable
auditors coexist in spite of the disreputable auditors having equal or greater costs.
19

A large body of empirical research examines the hypotheses that large audit firms
charge higher fees and are viewed as more reliable by actors in financial markets. Several
studies support these conclusions, but the evidence is mixed, suggesting that the work todate has not settled these questions definitively. The data of Danos and Eichenseher (1986)
and Wolk, Michelson and Wootton (2001) suggest that, as a result of internal expansion of
the top firms, the market share of Big n auditors has increased substantially during recent
decades.
Our comparative statics result may be viewed as supportive of policy reforms (e.g.,
prohibitions on auditors supplying consulting services or periodic mandatory rotation ofauditors) that enhance auditor independence by diminishing anticipated revenues from theclient firm, as a fraction of the auditor’s current and future business. But such reforms
are a stop gap response to the erosion of the value of reputation that results from anincrease in the market share of the top firms. This suggests giving consideration to more
drastic reforms, such as requiring publicly traded firms to purchase audit insurance, withthe auditor hired by the insurer, in order to align the auditor’s incentives with its true
“customers,” namely those who base financial decisions on audit reports.
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22

Figure 11

τ

45% line

τ

0

tˆ

t

t

23

1

t