chaney et al (2005)- selfselectionofauditors_jeter_chaney

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Self-Selection of Auditorsand Size Nonlinearities in Audit Pricing

Abstract

Prior research has examined audit pricing for publicly held firms and provided some evidenceof a Big 8 premium in pricing. More recent research provides evidence that private firms do not paysuch a premium on average; i.e. a premium is observed using standard OLS regressions, but it vanishesonce self-selection bias is controlled for. This paper returns to the setting of listed U.S. firms andprovides evidence that, on average, the firms in the sample examined also do not pay a Big 5 premium(once self-selection bias and nonlinearities in client size are taken into account). Consistent with thefindings of Chaney, Jeter, and Shivakumar (2004), we find that publicly traded client firms choosingBig 5 auditors generally would have faced higher fees had they chosen non-Big 5 auditors, given their

firm-specific characteristics. Our results are consistent with audit markets for listed firms, as well asfor private firms, being segmented along cost-effective lines. Our findings emphasize the importanceof controlling for self selection and size nonlinearities in any audit fee study using standard OLSregressions to control for client size or auditor size (or quality).


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1. Introduction

Prior audit fee research has demonstrated that model specification is sensitive to firm size

(Francis and Stokes, 1986; Palmrose, 1986; Simunic, 1980; Craswell, Francis, and Taylor, 1995;

among others1), to self-selection bias (Chaney, Jeter and Shivakumar, 2004; Copley, Gaver and

Gaver, 1995; Ireland and Lennox, 2001) and to product and cost differentiation (Chaney, Jeter

and Shivakumar, 2004; Deltas and Doogar, 2003). In this paper, we examine the importance of

these criticisms in the context of audit fee models for publicly traded U.S. firms. Prior studies

have provided mixed evidence with regard to a Big 8(5) fee premium, with Simunic (1980)

suggesting that neither small nor large U.S. clients pay such a premium while Francis (1984)

argues that both small and large Australian firms in their sample paid such a premium.

Francis and Stokes (1986) attempted to reconcile the results by noting that all firms in the

former study were relatively large, while all in the latter were relatively small. One explanation

for the absence of fee premiums in larger clients is that the premiums are offset by economies of

scale in larger clients. This explanation, however, is more of an ex-post rationalization than a

testable hypothesis. The sensitivity of results related to fee premiums with respect to client size

extend to tests of specialist fees and premiums (Craswell et al., 1995) as well as to Big 5/non-Big

5 fee comparisons.

These issuesthe evidence that fee premiums are only observed in a relatively small

subset of clients; and the sensitivity of results to client sizeraise the concern that test

specification in these studies suffers from methodological problems with respect to client size.

This paper revisits the issue of Big 5 fee premiums after considering econometric issues in the

model specification for audit fees. We provide empirical support that these concerns are valid,

and we find that when self-selection and nonlinearities in client size, as well as product


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differentiation, are considered, the Big 5 auditor fee premium, which emerges under standard

OLS regressions, disappears. In fact, we show that most firms choosing Big 5 auditors would in

fact pay higher fees if they make the alternate (non-Big 5) choice.

Although we focus on the existence (absence) of a large fee premium as the setting for

our examination, the econometric problems documented extend to a wide range of accounting

research applications where standard OLS regressions have been the traditional norm for testing

or controlling for client size and auditor size (quality).2 This is most notably the case when the

model specifies audit fees as the dependent variable. Our results indicate that reliance on these

models may lead to erroneous or misleading conclusions and that, at a minimum, studies should

check their results for robustness to the issues of self-selection bias and nonlinearities in client

size.

Craswell, et al. (1995) present evidence that the parameters of their model are inconsistent

between the upper and lower halves of firms in their sample. They conclude that the general

brand-name Big 8 premium observed for the Australian firms examined is significant only for the

bottom half (smaller firms) while the specialist fee premium is significant only for the upper half.

Also using Australian data, Ferguson and Stokes (2002) look at the post-1990 period. They find

evidence of a generalist Big 6(5) fee premium for firms in the smaller half of their sample by

comparing nonspecialist Big 6(5) auditors and nonspecialist non-Big 6(5) auditors; however, they

find little evidence of a specialist premium during this period. These studies have focused almost

exclusively on the differences in the Big 8(6 or 5) or specialist premium across size-sorted

1 Note that whereas these studies focus on the coefficient on the variable of interest, we extend the size sensitivityarguments to all coefficients in the audit fee regression.2 See, for example, Ferguson, Francis, and Stokes (2003), who examine the effects of firm-wide and office-levelindustry experience in audit pricing. Other studies that analyze the effect of auditor quality on dimensions other thanfees include Teoh and Wong (1993, the effect on earnings response coefficients); Petroni and Beasley (1996, theeffect on errors in accounting estimates; Basu, Hwang and Jan (2001, the effect on conservative reporting); Pittmanand Fortin (2004) and Mansi, Maxwell and Miller (2004, the effect on the cost of debt).


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subsamples. We argue that differences in client size will impact almost all the coefficients in

audit-fee regressions, not just the variables of primary interest. Further, when such nonlinearities

are not taken into account, spurious correlations between audit fees and variables of interest may

lead to erroneous conclusions. Although a few prior studies have examined the effects of non-

linearity by estimating regressions within client groups determined using arbitrary size cutoffs,

such an approach is unlikely to be sufficient as the effects of client sizes on regression

coefficients are continuous and not discrete. So, we do not rely on such cutoffs in our analyses.

Client size has the potential to affect audit fees in a variety of ways. Auditors pricing

their services differentially for clients of varying size must consider such issues as risk,

reputation, and economies of scale (Simunic, 1980, for one). For example, because of greater

exposure to media damage and subsequent litigation, an audit failure in a large client firm tends

to be disproportionately more costly for the auditor than an audit failure of a smaller client.

While larger companies generally have more sophisticated internal control systems and more

competent or extensive staff of internal auditors than smaller companies, they may also face

greater pressure to meet or beat analysts expectations (Barton and Simko, 2002). Larger firms

may be argued to have greater bargaining power with auditors (Kim, Liu, and Rhee, 2003), and

auditors may covet the status of auditing the very largest clients in a particular geographic area or

in a particular industry. Moreover, if the audit market is segmented along client size, then some

auditors may be able to offer more efficient or higher quality audits for a particular client group

than another auditor can. Hence nonlinearities in the relation between client size and various

determinants of audit fees are likely.

Using a sample of private U.K. client firms, Chaney, Jeter, and Shivakumar (2004)

present evidence that the Big 5 premium documented with standard OLS regressions disappears

when self-selection bias is controlled for. However, as pointed out by Chaney, et al. (2004), this


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result may not extend to a sample of listed U.S. firms due either to differences in the setting or in

the clientele. Using the two-stage Heckman approach to test for self-selection in a sample of

listed U.S. firms, we reject a null hypothesis that clients are randomly allocated across Big 5 and

non-Big 5 auditors. After controlling for self-selection and size nonlinearities, we find no

evidence of a Big 5 auditor fee premium.

While by no means constituting a direct test of audit quality, an examination of fees paid

to Big 5 versus non-Big 5 auditors does shed some insight into how the respective groups of

auditors are valued by their clientele. Our findings suggest: (a) choice of a Big 5 auditor need

not necessarily signal auditor superiority as the auditor selection may instead be dictated by cost

considerations; and (b) in contrast to the argument that large auditors charge a premium relative

to smaller auditors to cover additional litigation costs (Dye, 1993), audit markets appear to be

segmented along cost-efficient dimensions. In general, the auditor type (Big 5 or non-Big 5) best

equipped to audit a particular client efficiently is usually selected, and audit fee premiums are

most likely to result for those clients that depart from that choice.

The remainder of the paper is organized as follows. Section 2 discusses our theoretical

concerns, including the background for our paper, the arguments in the literature for

differentiated pricing across auditor types (Big 5 and non-Big 5) and methodological issues.

Section 3 describes our model, and Section 4 presents the data and results. Section 5 concludes.

2. Background and Theory

2.1 BACKGROUND

Corporate scandals and alleged audit failures since the turn of the millennium have

brought the accounting and audit professions into the limelight to an extent rarely, if ever, seen

since the stock market crash of 1929. In the wake of Enron, WorldCom, and Tyco, among

others, the investing public has become leery of the value of audits in general and of the


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independence and competence of Big 5 audit firms in particular. Whereas a number of

accounting and auditing studies in the past have assumed Big 5 (or 8 or 6) to be synonymous

with high quality, academics and practitioners alike are now questioning the validity of that

assumption. Recent events have heightened our awareness of a need to understand the working of

audit markets in general and of the value added by Big 5 as well as by non-Big 5 auditors.

Copley, Gaver and Gaver (1995) suggest that prior studies of audit fees and premiums

suffer from potential endogeneity biases as client characteristics (such as size, risk, and leverage)

play important roles in determining both the demand for a particular auditor and the marginal

fees paid. Employing a simultaneous equations approach and using a sample of 162 municipal

audits, they provide mixed support for a Big 5 reputation effect in audit fees.

In this study we compare audit fees across the two auditor groups with the aim of

gleaning some new insights into how audit markets work and along what dimensions the clientele

are segmented into Big 5 and non-Big 5 auditees. We do this largely by pursuing the approach of

prior studies, but in addition, relaxing the following assumptions made in prior studies fee

regressions: (i) slope coefficients are the same across Big 5 and non-Big 5 clients; (ii) the effect

of client size on audit fees is additive and not interactive; and (iii) self-selection of auditors does

not lead to any bias. We discuss below the rationale and the importance of considering these

econometric issues in audit free regressions.

2.2 EXPLANATIONS FOR DIFFERENTIAL PRICING ACROSS AUDITOR TYPES

Several arguments have been presented in the literature to explain observed fee differentials

across Big 5 and non-Big 5 auditors. Although it is difficult to discuss these arguments independently

of client size issues, our emphasis in this section is on the basic premises for a Big 5 auditor fee

premium (or discount). Then, in the following section (2.3), we elaborate on the effects of client size

on the various arguments advanced for fee differentials.


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Various researchers (e.g., Watts and Zimmerman, 1983) argue that the demand for auditing

services arises from conflicts of interest among managers, creditors and outside shareholders. Given

the existence of such agency issues, managers and entrepreneurs have incentives to reduce agency

costs through high quality monitoring. Titman and Trueman (1986) present a model wherein firms

with favorable information signal their quality by selecting auditors that are costly, but that provide

relatively more precise information about the firms final cash flows. Also, DeAngelo (1981) argues

that larger and more prestigious auditors stand to lose more from other clients in the event of an audit

failure and thus are less likely to perform low-quality audits. In the context of these theories, the

Big 5 auditor fee premium could be interpreted as the price paid, by clients signaling their quality, for

an auditor of superior reputation.

Dye (1993) suggests that audit fees may reflect the option value that investors place on a claim

against an auditors wealth in the event of audit failure. Under this argument, financial statement

users perceive auditors as providing insurance in the event of securities litigation; consequently, an

auditors wealth is viewed as a bond posted to ensure the delivery of an audit of appropriate quality.

The higher the bond (or the wealthier the auditor), the higher quality the audit should be. In this

context, the Big 5-auditor fee premium is viewed by client firms as the value of the increased

insurance coverage; alternatively, from the auditor's perspective, it may be viewed as the expected

cost of higher potential litigation losses.

Prior studies have suggested that economies of scale could result in lower audit fees for large

clients of Big 5 auditors (relative to non-Big 5 auditees) (Simunic, 1980; Francis and Stokes, 1986).

In addition, Simunic (1980) suggests that Big 5 auditors may be able to audit virtually all firms with

greater efficiency and at lower cost (though diseconomies are more likely to small auditors auditing

large clients). To the extent that efficiencies and/or economies of scale are passed on to client firms,

Big 5 auditor fees would be expected to be lower than non-Big 5 fees.


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Based on the above arguments, most prior studies restrict the slope coefficients in audit fee

regressions to be the same across Big 5 and non-Big 5 clients, allowing only the intercept to vary

between the two groups.3 However, Chaney, Jeter and Shivakumar (2004) show that such restrictions

are neither theoretically nor empirically justifiable and consequently introduce significant bias in the

analyses. They suggest that auditors structure their businesses in a manner appropriate for targeted

client segments, with Big 5 auditors investing more in technology, training and facilities and, as a

result, carrying out audits more efficiently for large, relatively complex clients. The costs of these

investments result in a relatively high fixed component of audit fees, which may be unattractive (and

costly) for small and less complex clients. Consequently, the slope coefficients as well as the

intercepts are likely to differ across auditor groups. Although the empirical evidence in Chaney,

Jeter and Shivakumar (2004) is for private companies, their arguments for differences in slope

coefficients across auditor types fully carry forward to the case of listed companies.

2.3 IMPACT OF CLIENT SIZE ON AUDIT FEES

Several studies have investigated the effect of client size and also of auditor size on

companies audit fees (e.g., Simunic, 1980; Palmrose, 1986). Initial studies on audit pricing tested

this issue by estimating a cross-sectional regression of audit fees on a set of explanatory variables,

which included both client size and an indicator variable for auditor size (Big 8 or non-Big 8) as

separate additive variables. The studies found strong evidence for the role of client size in

determining audit fees, but mixed evidence for the role of auditor size. However, the framework

presented in Simunic (1980) provides several reasons to suggest that client size and auditor size are

unlikely to be merely additive, but instead are likely to have interactive effects on audit fees. First,

large audit firms enjoy economies of scale in auditing larger clients; or, viewed differently, small

auditors suffer diseconomies of scale when auditing larger clients. Second, due to the small number

3 Although the economies of scale argument discussed in the previous paragraph implies differences in slope


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of audit suppliers in the audit market for larger clients, the assumption of perfect competition for audit

pricing may not apply to audits of larger clients. Thus, if larger auditors charge a premium for their

monopolistic power, such a premium is more likely to be observed among larger clients than among

smaller clients. Yet the opposite has been shown. Francis and Simon (1987), for example, document

that client size and auditor size have an interactive effect on audit fees and that a fee premium for

Big 8 auditors is observed only among small clients. Based on this finding, Francis and Simon

(1987) conclude that Big 8 auditors provide a differentiated audit product relative to smaller (non-Big

8) auditors.

Although Simunic (1980) and others address the interaction between client size and an

auditor indicator variable, the arguments regarding economies of scale and market competition

suggest that client size will have interactive effects with all explanatory variables that capture

either audit effort or monopolistic power rather than merely with a categorical variable for Big 8

vs. non-Big 8 auditor. Moreover, these arguments suggest that such interactive effects will vary

across large and small auditors due to their potential for product differentiation and for taking

advantage of monopolistic opportunities. We extend the arguments from prior literature and

suggest that the interactive effect of size is not limited to differences in the fixed component of

fees for Big 5(8) and non-Big 5(8) auditors but is important for other determinants of audit fees

as well. There are at least four mutually non-exclusive reasons for this: monopolistic

competition, economies of scale, product differentiation and audit risk. We discuss each of these

in turn below.

Monopolistic Competition

Although in the economics of auditing literature it is generally assumed that the audit

market is competitive, regulatory agencies in several countries have questioned the extent to

coefficients across Big5 and non-Big5 auditors, this implication has been largely ignored in prior studies.


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which large and small auditors compete realistically. It has been documented that large auditor

dominance increases significantly with the size of audited clientele (see for e.g., Simunic, 1980),

leading to a conjecture that audit markets are not competitive for larger clients. Consequently,

audit pricing for larger clients is likely to be more discretionary relative to audit pricing for

smaller clients, where the assumption of perfect competition more aptly applies. This suggests

that the relation between audit fees and its determinants is likely to vary as one moves from the

smallest clients to the largest clients (see Shailer, Cummings, Vatuloka and Welch, 2004). In

particular, the coefficients on variables reflecting potential discretionary pricing (e.g., audit risk

and effort, as well as the Big 5 indicator variable) will increase in magnitude with client size if

the large client segment of the audit market is vulnerable to monopolistic pricing. On the other

hand, the possibility cannot be ignored that very large clients exercise power over competing

auditors, even among the Big 5, thus offsetting or even dominating the effects of monopolistic

pricing.

Economies of Scale

Simunic (1980) and Francis and Stokes (1986) suggest that auditors of larger clients may

benefit from economies of scale, in which case audit costs would increase non-linearly with size.

One argument put forth for scale economies is that both internal and external auditing are

sampling-based processes. To the extent that an increase in the measured total assets of an audit

client reflects an increase in the number of individual elements of which those assets are

composed, the sample size necessary to obtain a given level of confidence increases at a

declining rate (Simunic, 1980). In the audit fee model, variables included to capture the costs


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associated with audit effort should thus exhibit coefficients that monotonically decrease with

size.4

Product Differentiation

Although most studies of audit pricing recognize that large auditors and small auditors

provide differentiated products, the implications of such product differentiation on model

specifications have been largely ignored. This sub-section develops the link between product

differentiation and models for audit fees.

The key to a product differentiation strategy is to develop and supply a differentiated

service that clients demand and that competitors find difficult to duplicate. Prior research

generally assumes that large auditors make costly investments both to safeguard their reputation

for superiority and to provide higher quality audits. Implicit in this assumption is the notion that

these costs prevent competitors from easily achieving comparable degrees of perceived quality or

reputation. Researchers argue that these costly investments require a correspondingly higher

return, with the result that Big 8(5) auditors justifiably earn fee premiums over their non-Big 8(5)

counterparts. In contrast, we contend that while such differentiation may indeed require specific

investments by larger auditors, they do not necessarily imply higher fees (see Mayhew and

Wilkins (2003)). Chaney, Jeter and Shivakumar (2004) provide evidence that large and small

auditors of private clients in the U.K. provide differentiated audit services, each of which appeals

to specific segments of privately held audit clients.

Auditors are able to structure their business in a manner targeted to be optimal for specific

client segments. For instance, as argued in Chaney, et al. (2004), Big 5 auditors invest more in

technology, training and facilities and are, consequently, able to carry out audits more efficiently

4 In acknowledgement of this potentially monotonically decreasing relation with size, most prior studies consider alogarithmic transformations of audit fees and client size in the regressions. However, several studies have pointed


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for large, relatively complex clients. The higher fixed costs of these investments are not

attractive to smaller and less complex clients in general.5 Furthermore, such product

differentiation leads to specialization as the audit personnel deal almost exclusively with a

specific client segment. The audit personnel become very adept at identifying and addressing

issues that are unique to their clientele. For instance, auditors that focus on larger clients would

be better able to deal with issues related to public borrowings, since public issues of debt are

predominantly done by larger clients. Such product differentiation and specialization leads to

increases in audit efficiency, as well as to lower audit costs for all auditors involved. Deltas and

Doogar (2003) provide evidence consistent with such product and cost differentiation in the audit

market.

Since an important dimension along which Big 5 and non-Big 5 auditors are segmented is

clearly client size,6 the above arguments imply that client size is likely to affect the relation of

audit fees with either audit effort or audit risk; further, this impact (differential client size) will

vary across Big 5 and non-Big 5 auditors. Because the two basic benefits of product

differentiation and specializationlower costs and higher service quality or efficiencytend to

pull audit fees in opposite directions, the effect of client-size segmentation on audit fees is not

immediately clear. If increased quality is reflected in higher audit fees, then Big 5 auditors will

charge more for larger clients, and the coefficients reflecting the pricing of effort and risk are

likely to increase in magnitude with client size. However, such increases could be offset by cost

efficiencies that arise from specialization.

out that even after logarithmic transformations, there is a non-linear relationship between fees and size (e.g., Carson,Fargher, Simon and Taylor (2004)).5 These arguments differ from arguments based on economies of scale. Under straight-forward economies of scalearguments, there is no reason to expect Big 5 auditors to have a cost disadvantage for less complicated audit clients.Furthermore, economies of scale arguments define clientele groups based only on the size dimension, whereas thisneed not be the case for arguments regarding product differentiation. Under product differentiation arguments, evena small firm, say with significant exports, could find a Big 5 auditor more cost-efficient than a non-Big auditor.


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The precise interactive effect of client size on the relation between audit fees and its

determinants may vary depending on whether client size is interacted with a variable that proxies

for audit risk, audit effort, or monopolistic rents. However, unambiguous separation of audit fee

variables into these categories is not feasible. Moreover, the precise client attributes along which

Big 5 and non-Big 5 auditors differentiate their services is unobservable. Therefore, we do not

hypothesize the direction of the relations between the size-interacted variables and audit fees.

2.4 SELF-SELECTION IN AUDITOR CHOICE

As pointed out in Chaney, et al. (2004),7 companies are not randomly assigned to audit firms,

but rather self select their auditors. Theoretical studies, such as Titman and Trueman (1986) and

Datar et al. (1991) present signaling models to explore the self-selection of auditors by clients. In

these models, clients with favorable private information choose higher quality auditors despite higher

costs. However, from an econometric perspective, self-selection introduces a bias in the standard

OLS regressions.

The self-selection problem arises because fees are observable only after a firm has chosen its

auditor, while the fees under an alternative auditor choice remain unobserved. This causes the

expected error in the standard OLS specification of audit fees to be non-zero and the auditor choice

(Big 5 vs. non-Big 5) variable to be endogenous. To see this, consider the following self-selection

model for audit fees:8

Auditor choice function: Big 5i*

= / Zi + ui (1)

Big 5i = 1 if Big 5i* > 0

Big 5i = 0 if Big 5i* 0

Audit-fee function: F0i = 0/Xi + 0i if Big 5i=0 (2)

7 Much of this section is adapted from Chaney, et al. (2004).


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F1i = 1/Xi + 1i if Big 5i=1 (3)

where Xi and Zi are vectors of exogenous variables and the error terms, ui, 0i and 1i, are assumed to

be normally distributed with mean zero and variance-covariance matrix given by:

Covariance(0i, 1i, ui) =

uuuu

u

u

10

11101

00100

Since F0i is observed only when Big 5i = 0, the expected value of the residuals from estimating

regression (2) on observed data is given by:

E(0i | Big 5i=0) = E(0i | ui - / Zi)

=( )( )

i

iu

Z

Z

0 =

( )( )

10

i

iu

Z

Z

iu 00 ,

where the functions and are the standard normal probability density function and the

cumulative distribution function, respectively.

Similarly, the expected value of the residuals in regression (3) is given by

E(1i | Big 5i=1) = E(0i | ui > -/ Zi)

=( )

( )

i

iu

Z

Z

11 =

( )( )

i

iu

Z

Z

1

iu 11

If either u0 0 or u1 0, then OLS specifications of audit fees are biased as the

expected error in these regressions is non-zero.9 Moreover, the primary parameter of interest in

8 The self-selection model, which is based on Lee (1979), is quite general in that, it allows for simultaneity in theauditor choice and audit-fee equations, as well as for self-selection. The model also allows slope coefficients and theerror terms in the fee equations to vary across auditor types.9 Testing whether0u=0 and 1u=0 is, in fact, the test for self-selection (see Maddala (1983) pg. 259).


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such analyses, namely the average benefit or cost of auditor choice, will also be biased. To see

this, note that the average benefit or cost of auditor choice is essentially measured as average fees

observed for a firm minus the average potential fees that would have been charged if the

alternative auditor choice were made. Formally, this is given by:

For non-Big 5 clients: ( ) 011010 05| uXFBigFEF == (4)

For Big 5 clients: ( ) 100101 15| uXFBigFEF == (5)

where a bar over a variable denotes its cross-sectional average.10 If either u0 0 or u1 0, then

the estimated difference in fees between Big 5 and non-Big 5 auditors from standard OLS

regressions is biased. In particular, if u0 is positive, then the fee differential estimated from

OLS regressions will be biased upward for Big 5 clients as 01 > . Similarly, if u1 is positive,

then the fee differential estimated from OLS regressions will be biased downward for non-Big 5

clients, as 00


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linearities). Next, size interactive variables are included to assess the impact due to non-

linearities in size. These models are as follows:

Traditional fee regression:

Lfeei = 1 + 2Sizei + 3Levi + 4 Sqrtsubti + 5ROAi + 6Sqrtempli

+ 7Yrendi + 8Replagi + 9 Big 5i + i (6)

Traditional fee regression with size interactive variables:

Lfeei = 1 + 2Sizei + 3Levi + 4Sqrtsubi + 5ROAi +

6Sqrtempli + 7Yrendi + B8Replagi + B9Sizei* Sizei +

10Sizei*Levi + 11Sizei*Sqrtsubi +12Sizei*ROAi +

13Sizei*Sqrtempli + 14Sizei*Yrendi + 15Sizei*Replagi

+ 16Big 5i + 17Sizei*Big 5i + i (7)

where:

Lfeei = Logarithm of audit fees;Big 5i = 1 if firm i chose a Big 5 auditor in year t; 0 otherwise;Sizei = Logarithm of end of year total client assets;Levi = long-term debt plus debt in current liabilities divided by market value of

equity plus total liabilities;Sqrtsubit = square root of the number of subsidiaries;ROAi = Earnings before interest and taxes divided by total assets;Sqrtempli = Square root of the number of employees;Yrendi = 1 if the firms year-end occurs in December, 0 otherwise;Replagi = Number of days between the firms year-end and the earnings

announcement date.

Next, we estimate the self-selection model using the two-stage procedure of Heckman

(1979) and Lee (1979). In the first stage, a probit regression is estimated to obtain consistent

estimates for of the indicator variable, Big 5i, on Zi. Using these estimates, the inverse Mills

ratios (IMR), 0i and 1i are computed. Then, in the second stage, the audit fee equation is

estimated by OLS with the inverse Mills ratio included as an additional explanatory variable. Our

self-selection model is given as:


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Probit Regression: Big 5it = 1 + 2Sizeit + 3Levit + 4Sqrtsubit + 5ROAit +

6Sqrtemplit + 7Sizeit* Sizeit + 8Sizeit*Levit +

9Sizeit*Sqrtsubit +10Sizeit*ROAit +

11Sizeit*Sqrtemplit + it (8)

OLS regression: Lfeei = j1 + j2Sizei + j3Levi + j4Sqrtsubi + j5ROAi +

j6Sqrtempli + j7Yrendi + Bj8Replagi + Bj9Sizei* Sizei +

j10Sizei*Levi + j11Sizei*Sqrtsubi +j12Sizei*ROAi +

j13Sizei*Sqrtempli + j14Sizei*Yrendi + j15Sizei*Replagi +

jji + ji (9)

where ji is the inverse Mills ratio for firm i, a client of auditor type j; where j is equal to 0 for

non-Big 5 client firms and equal to 1 for Big 5 client firms; and where size is defined as a

continuous variable in all interactive specifications (log of client assets).

The coefficients, 0 and 1, which are the estimates for u0 and u1 , are the covariances

of the residuals from the non-Big 5 or Big 5 audit-fee equation (9) and the residuals from the

auditor-choice equation (8). The variables have been chosen based largely on previous studies of

audit fee regressions; the rationale for their inclusion is discussed briefly below.

For the auditor fee equation, we expect audit fees to increase with audit effort, risk and

complexity. We use the logarithm of total assets to control for client size, which captures the

amount of audit effort needed to a large degree. To control for audit risk, we include variables for

financial structure (Lev) and profitability (ROA) of the client firm. We include the square root of

the number of subsidiaries and the square root of the number of employees to control for audit

complexity. Other variables likely to affect the audit fee include a year-end indicator variable to

control for peak versus off-peak pricing, and the reporting lag between the end of the year and

the firms earnings announcement date (to capture cross-sectional differences in the timeliness of

the audit or in the time taken to complete the audit). The self-selection model allows the slope


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coefficients and the intercept in the audit fee regression to vary across Big 5 and non-Big 5

clients. This is important since our arguments regarding market segmentation predict differences

in cost functions across these client firms. Specifically, if Big 5 auditors invest more in

technology, training, etc., then the intercept in the fee regression of Big 5 clients will be larger,

reflecting the Big 5 auditors compensation for their increased investments. However, this larger

investment will allow Big 5 auditors to conduct audits more efficiently, particularly for large,

risky and relatively complex clients. In such a case, the slope coefficients on variables associated

with audit effort or risk would be smaller for these clients ifpricing is based on audit costs and

efficiencies rather than monopolistic or reputation advantages. While the year-end dummy

variable is included to control for peak vs. off-peak pricing, the effect of this variable interacted

with client size is somewhat ambiguous. Large clients are often continuously audited throughout

the year, which should reduce the incremental workload at year-end somewhat; however, even

with continuous auditing, the heaviest burden occurs during the auditors busy season for large

clients whose year ends in December.

For the auditor choice equation in the self-selection model, we expect larger companies to

be more likely to hire Big 5 audit firms for various reasons, including the perception that larger

auditors are better equipped to handle the audit efficiently. Also, to the extent that Big 5 auditors

have generally wider experience and arguably better-trained personnel, they may be able to audit

riskier clients more efficiently, especially as size increases. Agency costs tend to be higher in

highly leveraged clients, and such firms may prefer to hire auditors of superior reputation to

reduce agency costs. However, while leverage is a risk variable, as the client firms size

increases, more proactive measures may be taken on the part of lenders and other groups to guard

against firm failure. Large firms with higher ROA are desirable clients and lower fees are likely,

as these firms may be viewed as relatively low-risk and high-profit auditees. In addition, we


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interact all the above variables with client size, as was done for the audit fee regression. The

main motivation behind this is that Big 5 auditors will almost certainly audit very large clients,

due to resource constraints faced by non-Big 5 auditors. Thus, as client size increases, we

expect all variables other than size to decline in importance in determining auditor choice.

4. Data and Results

4.1 DATA

The data source for this study begins with all U.S. listed firms with audit pricing data on S&P

audit pricing database for 2001 (n=5,786). Observations eliminated included 688 observations with

missing data, 1,606 regulated firms, and the top and bottom half percent of continuous variables

(n=151). This resulted in a final sample of 3,341 firms.

Table 1 reports descriptive information for our sample of firms. We present the mean and

medians for each variable used in our regressions, first for all audit clients and then separately for

clients of Big 5 and non-Big 5 auditors. The audit fee for the average Big 5 client is $458.7 thousand,

while the audit fee for the average non-Big 5 client is $122.6 thousand. We test for differences in

means and medians between Big 5 and non-Big 5 clients and present these results in the last two

columns of Table 1. As shown in these columns, virtually all means and medians are significantly

different for Big 5 and non-Big 5 auditees.

The mean of total assets for firms in our sample is $1,013 million. For Big 5 auditees, the

mean is $1,159 million, while for non-Big 5 auditees it is $93.12 million. The mean (median) number

of employees is 6,107 (886) for Big 5 clients and 806 (111) for non-Big 5 clients. The average

leverage, defined as the ratio of current and long-term debt to market value of equity plus total

liabilities, is about 15.7% for Big 5 auditees and 20.3% for non-Big 5 clientele. The mean return on

assets is -9.1% for Big 5 and -13.7% non-Big 5 auditees in our sample. Somewhat surprisingly, the


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number of subsidiaries (reportable segments) is larger for non-Big 5 clients with a mean of 1.6 versus

a mean of 1.5 for Big 5 clients. This differential reflects differences in how companies define a

reportable segment as well as the actual number of segments; thus, it may not be a good proxy for

client complexity. Sixty-five percent of the Big 5 clients reported year-ends in December versus 58

percent for the non-Big 5 clients. Finally, the reporting lag between the year-end and the firms

earnings announcement is significantly longer for non-Big 5 clients versus the Big 5 clients (75 days

versus 48 days), consistent with an argument that Big 5 auditors may be more efficient, on average,

for auditing clients in our sample in a timely fashion.

Correlation coefficients are reported in Table 2. As expected, size is highly correlated with

audit fees. The Big 5 indicator variable is also highly correlated with size. This is expected since most

large firms tend to select Big 5 auditors. ROA and Lev are positively related to audit fees, and

reporting lag is negatively related to both the Big 5 indicator variable and audit fees. ROA is

included as a measure of profitability and is generally expected to be negatively related to fees after

controlling for client size. The positive correlation between ROA and audit fees in this table may be

spuriously induced by the positive correlation between ROA and client size coupled with that

between client size (0.42) and audit fees (0.83).

4.2 RESULTS

OLS Regression Results

For comparison with prior studies, we present the estimates from traditional OLS regressions

of audit fees on the explanatory variables in Table 3. While the results presented in the first two

columns of Table 3 are consistent with prior studies results on fee premiums from an OLS regression


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(with size as an additive explanatory variable), the last two columns include size-interactive variables

for each explanatory variable in the regression.11

Initially, consider the first two columns of Table 3. We see that fees are positively related to

client size (log of assets), the square of the number of employees, a busy-season year-end, the

reporting lag, and the choice of a Big 5 auditor. They are negatively related to the return on assets

and are not significantly associated with the number of subsidiaries or the market to book ratio. The

adjusted R-square value for this specification is 72.1%, which is comparable to those in prior studies.

In the last two columns of Table 3, we present an OLS regression with the addition of

interactive variables between client size and each explanatory variable. An F test indicates that the

inclusion of the interactive terms adds significantly to the model. We find that the coefficient on the

square of the number of subsidiaries is now marginally significant and negative, while the coefficient

on replag, leverage, and year-end are no longer statistically significant. In addition, the interactive

variables for size*log assets, size*year-end, and size*Big 5 are now significant. In particular the

coefficient on size*Big 5 is significantly negative, suggesting that as client size increases, the Big 5

fee premium decreases. This is consistent with prior studies (e.g., Francis and Simon, 1987). The

adjusted R-Square value is 72.9%. Although the increase in the adjusted R-square value is marginal,

the significance of the size-interacted variables indicates that regressions excluding these terms would

be biased.

However, this specification fails to control for the endogeneity of auditor choice and audit

fees, nor does it allow for the interaction between client size and risk or complexity variables in the

auditor choice decision. Thus we next proceed to our two-stage specification.

Regression Results for Auditor Choice

11 The t-statistics reported throughout the paper are based on heteroskedasticity-consistent standard errors. Furtherfor the self-selection model, the standard errors are corrected to account for the fact that an explanatory variable is


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Table 4 presents the results of our estimation of the probit regression described in equation

(8). In predicting auditor choice, we find that firms choosing Big 5 auditors tend to be larger and less

leveraged, but not significantly different from those choosing non-Big 5 auditors in terms of the

square root of the number of subsidiaries or the square of the number of employees. When we

consider the interaction of these attributes with client size, we find, consistent with our expectations,

that as size increases, almost all factors other than size become less important in the choice of

auditors. However, return on assets becomes more important with larger, profitable clients less likely

to choose Big 5 auditors. As client size increases, the negative relation between leverage and Big 5

choice is lessened; i.e., small, highly levered clients are more likely to choose non-Big 5 auditors than

larger, highly levered firms.

To assess the accuracy of our stage one classification, we chose a cut-off level of 50%; i.e., if

the probability of choosing a Big 5 auditor is greater than 50%, we assume the firm would make that

choice. Based on this cut-off, our classification is accurate, on average, 88.5% of the time. Also note

that approximately 86.8% of the firms in our sample chose Big 5 auditors. A Hosmer-Lemeshow chi-

square statistic was computed. This test divides the sample into groups and compares the predicted

values against a perfect model. An insignificant Hosmer-Lemeshow index implies a good model fit.

Thus since the index is insignificant, the model is considered a good fit.12 In addition, a likelihood

ratio test was performed to test the significance of the model (with interactive size variables) to a

model without interactive size variables. The test results indicate that size interactive variables are

significant in predicting auditor type.

To assist in interpreting the coefficients from the probit estimation, we graph the marginal

effects for each independent variable in Figure 1. In the Appendix to the paper, we provide a brief

an estimate from another statistical model. The t-values are based on the method proposed by Greene (1981) toestimate consistent standard errors.


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discussion of the computation of marginal effects for the probit model. At least two significant issues

emerge from an examination of the figure. First, unit changes in the independent variables have a

decreasingeffect in predicting audit fees as firm size increases. This is less surprising in view of the

realization that the probability of auditor choice (being Big 5) cannot exceed one and that very large

firms almost always employ Big 5 auditors. However, it is not suggestive of monopolistic pricing for

large clientele, as the power to affect audit pricing may rest in the hands of very large audit clients in

negotiating within the set of Big 5 auditors. Second, unit changes in leverage, ROA, and size have

the greatest impact on auditor choice prediction.

Regression Results for Audit Fees

Table 5 presents the estimates from our regression of audit fees on the explanatory variables

(the second stage of our estimation). Regression equation (9) is estimated separately for Big 5 and

non-Big 5 auditees. This specification includes the variable lambda (inverse Mills ratio) from stage

one, which controls for potential self-selection bias in the second stage. The significance of the

coefficient on the IMR for the Big 5 sample suggests the importance of controlling for self-selection

bias. Further, by estimating the regressions separately for Big 5 and non-Big 5 auditors, our approach

allows the slope coefficients to vary across the two groups. For illustrative purposes, Figures 2

through 4 present the pricing effects for the variables estimated in the fee regression for various size

cut-offs of the data. For instance in Figure 2, we formed ten portfolios of Big 5 clients based on

size.13 Second, we computed the mean values for all independent variables used in the fee regression.

Then we multiplied the regression coefficients by these mean values to obtain the impact on the

predicted audit fee. Although we recognize that the separation of our sample into size groups is

arbitrary, these figures are presented to aid in the interpretation of the impact of size on audit pricing.

12 A Hosmer-Lemeshow index was computed for the model that did not include interactive size variables. The indexindicated that the model without interactive size variables was a poor model fit.13 Because of the smaller sample size, we form five portfolios for the non-Big 5 sampple.


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The intercept for the Big 5 regression is larger than the intercept for the non-Big 5 regression,

suggesting that Big 5 auditors include a higher fixed component in audit fees. Control variables

exhibiting significance include leverage, ROA, the number of employees, and whether the firms

year-end occurred during December. Reporting lag and the number of subsidiaries were not

significant in either the Big 5 or Non-Big 5 regressions.

Because of the importance of size effects, we discuss the results for our individual variables

along with the interaction of each with client size. In fact, because all firms have a non-zero measure

for size, the coefficients on the variables without size serve merely as intercept effects. The

coefficient on leverage is statistically insignificant for the non-Big 5 subsample but positive and

significant for Big 5 auditees. The interactive term for size and leverage is negative and significant

for Big 5 auditees. In Figure 2, the impact of leverage on audit pricing decreases as firm size increases

(even though the average leverage increases). One possible reason for the insignificance for non-Big

5 clients is that leverage for these clients, given their size and auditor choice, is likely to be private

debt and for such debt, increased monitoring by lenders of smaller clientele could mitigate any

increased risk due to higher leverage in this subsample.

The number of employees picks up another dimension of complexity beyond that of either size

or number of subsidiaries. For both the Big 5 and non-Big 5 samples, the coefficient on Sqemplis

positive and significant and the interactive term is negative and significant. In Figures 2 and 3, the

slope of the predicted fee line forSqemplis positive for the Big 5 sample and relatively flat for the

non-Big 5 sample. For portfolios of smaller non-Big 5 clients, a larger coefficient reflects a greater

impact on fees. Neither the Yrendvariable nor the interactive term (with client size) is statistically

significant for the non-Big 5 sample, while only the interactive term is significant for the Big 5

sample. This implies that year-end does not affect pricing except for the very largest clients that have

December year-ends (also see Figure 2). Fees are higher for these clients, consistent with an


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argument that Big 5 auditors pass the burden of overtime work, etc. during the peak period to some

extent to their large clients with calendar year-ends.

ROA is not significant in the Big 5 regression and is only significant in the non-Big 5 sample

when interacted with size. As size increases (in both samples), average ROA increases (see Figures 2

and 3, and also Table 2). For the non-Big 5 sample, as the firms performance (ROA) increases with

firm size, auditors modify their fees downward. This finding is consistent with an argument that non-

Big 5 auditors offer discounts to attract these large, profitable (low risk) clientele.

As seen throughout the results (tables and figures), the greatest effects on audit fees arise from

client size and the fixed component (intercept). The intercept is larger for the Big 5 than the non-Big

5 sample, consistent with an argument that Big 5 auditors pass along the costs of greater training, etc.

in the fixed component of fees. In contrast, the coefficient on size is greater for the non-Big 5 sample.

As seen in Figure 4, non-Big 5 auditors charge fees that increase at a faster rate than Big 5 auditors.

This may occur because of economies of scale for the Big 5 auditors or diseconomies to non-Big 5

auditors auditing very large clients. A large firm would incur a very large audit fee if it hired a non-

Big 5 auditor.

The results presented thus far are consistent with audit markets being differentiated along

auditor and client factors. They are inconsistent with monopolistic pricing by Big 5 auditors among

large clients; if anything, the results suggest that very large clientele, who virtually always hire Big 5

auditors, may hold increasing levels of power for negotiating audit fees as client size increases.

Given that we allow the slope coefficients to vary across Big 5 and non-Big 5 auditors (and

the evidence of self-selection bias), we next evaluate the existence (absence) of a Big 5 auditor fee

premium in our sample by computing the difference between the actual audit fee paid and the fee that

the firm would have paid, on average, had the alternative choice on auditor-type been made,

[E(Alternate fee)]. We follow Chapter 9 of Maddala (1983) and Section 3.3 of Heckman, Lalonde


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and Smith (1999), both of which provide detailed discussions of self-selection bias and evaluation

problems that require estimation of counterfactuals. We report the mean and median in the last row of

Panel A. We present the comparative data first for firms actually choosing Big 5 auditors, and then

for firms choosing non-Big 5 auditors. The differences are negative in every case, suggesting that if

Big 5 auditees had chosen non-Big 5 auditors, their audit fees would have been higher. Similarly, we

find that if non-Big 5 auditees had chosen to hire Big 5 auditors, their fees [E(Alternate fee)] would

also have been significantly higher on average than the actual fees paid.

These results suggest that firms, on average, self select an auditor type that minimizes their

audit fees. Explanations for a Big 5 auditor fee premium that are based on superior reputation or

deeper pockets of Big 5 auditors imply that firms choosing Big 5 auditors pay higher fees than the

amount they would have paid had they chosen a non-Big 5 auditor. However, our results indicate just

the opposite and do notsupport the view that Big 5 auditors charge more than that which would have

beencharged by non-Big 5 auditors, given the firms' characteristics.

However, our findings are consistent with audit markets being differentiated along dimensions

other than just reputation and deep-pockets. Extending the arguments from Simunic (1980) that Big 5

auditors enjoy economies of scale, we suggest efficiency and differences in audit costs as one likely

dimension. Auditors may structure their businesses in a manner that appeals to specific client

segments. For instance, Big 5 auditors invest more in technology, training and facilities, enabling

them to carry out audits more efficiently for large, relatively complex clients. However, the fixed

costs of these investments may not be attractive to small clients in general. In general, firms self-

select the most cost-effective auditor given their firm-specific characteristics. Further, our results are

inconsistent with monopolistic pricing among large clientele.

Also, in comparing coefficients across Big 5 and non-Big 5 auditors in the audit fee

regressions, we observe Big 5 auditors fee specifications to reveal larger intercepts but smaller slope


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coefficients on most variables associated with client and audit complexity. These findings are

consistent with the above argument, which suggests that Big 5 auditors charge a greater fixed fee

component for audit services, but lower increments for heightened levels of complexity and client

size.

Robustness Tests

We next repeated the auditor choice and audit fee regressions with additional variables or

other modifications to consider the robustness of our results to model specification. First, we

recognize that above a certain size threshold, virtually all listed firms select Big 5 auditors. Thus,

we repeat our tests with extremely large firms eliminated from the sample. We tried various

cutoffs, and our results were remarkably robust. For example, we eliminated all Big 5 firms

larger than the largest non-Big 5 client, thus eliminating 195 Big 5 firms.14 Our coefficients and

their statistical significance are qualitatively similar to those reported in Table 5. When we

evaluate the existence (absence) of a Big 5 auditor fee premium in this sample by computing the

difference between the actual audit fee paid and the fee that the firm would have paid, on

average, had the alternative choice on auditor-type been made, [E(Alternate fee)], we find a

significant difference for both the Big 5 and non-Big 5 samples. For the Big 5 sample, for

example, the difference is -2.3, consistent in direction with the results presented in Table 5. See

Table 6 for the differences between actual and alternative fees for the various robustness tests

described in this section.

Next, we introduced additional variables used in some prior studies of audit fees to see if

their inclusion made any difference in our results. For example, we introduced the quick ratio (as

a measure of audit risk) and the ratio of current to total assets (as a measure of audit or effort

intensiveness), as well as the interaction between each of these new variables and firm size, to

14 We also used a size cut-off that eliminated the top 5% of non-Big 5 firms with similar results.


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both stage one and stage two of our model. This specification of our model had slightly better

predictive power than the one presented (over 89% of the firms were correctly classified), but all

of our main conclusions were unaltered. We chose to present the more streamlined model

(excluding these variables) since our results are already somewhat cumbersome due to the

inclusion of so many size-interactive variables. Once more, the test to evaluate the existence

(absence) of a Big 5 auditor fee premium in our sample by computing the difference between the

actual audit fee paid and the fee that the firm would have paid, on average, had the alternative

choice on auditor-type been made, [E(Alternate fee)] is statistically significant for both Big 5 and

non-Big 5 samples. The mean difference for the Big 5 sample is -0.96, and that for the non-Big 5

sample is -0.94.

In view of the importance of the size effect to our research question, we next wish to

consider the possibility that using a different measure of client firm size might lead to different

conclusions. Thus, we replace client size with the square root of the number of employees in

both stage one and stage two for all interactive variables. Once again, our results remain

qualitatively unchanged. The difference between the actual audit fee paid and the fee that the

firm would have paidunder the alternative choice is -0.61 (p


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firms do not pay such a premium on average; i.e. a premium is observed using standard OLS

regressions, but it vanishes once self-selection bias is controlled for. This paper returns to the

setting of listed U.S. firms and provides evidence that, on average, the firms in the sample

examined also do not pay a Big 5 premium (once self-selection bias and nonlinearities in client

size are taken into account). Consistent with the findings of Chaney, Jeter, and Shivakumar

(2004), we find that publicly traded client firms choosing Big 5 auditors generally would have

faced higher fees had they chosen non-Big 5 auditors, given their firm-specific characteristics.

Our results are consistent with audit markets for listed firms, as well as for private firms, being

segmented along cost-effective lines.

In addition, we extend the research investigating the effect of client size on components

of audit pricing and auditor choice. Auditors pricing their services differentially for clients of

varying size must consider such issues as risk, reputation, and economies of scale. For example,

because of greater exposure, an audit failure in a large client firm tends to be more costly for the

auditor than an audit failure of a smaller client. While larger companies generally have more

sophisticated internal control systems and more extensive staffs of internal auditors than smaller

companies, they may also face greater pressure to meet or beat analysts expectations (Barton and

Simko, 2002). Larger firms may be argued to have greater bargaining power with auditors (Kim,

Liu, and Rhee, 2003), and auditors may covet the status of auditing the very largest clients in a

particular geographic area or in a particular industry. Hence nonlinearities in the relation

between client size and various determinants of audit fees are likely.

Using the two-stage Heckman approach to test for self-selection in a sample of listed U.S.

firms, we reject a null hypothesis that clients are randomly allocated across Big 5 and non-Big 5

auditors. After controlling for self-selection and size nonlinearities, we find no evidence of a

Big 5 auditor fee premium. While by no means constituting a direct test of audit quality, an


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examination of fees paid to Big 5 versus non-Big 5 auditors does shed some insight into how the

respective groups of auditors are valued by their clientele. Our findings suggest: (a) choice of a

Big 5 auditor need not necessarily signal auditor superiority as the auditor selection may instead

be dictated by cost considerations; and (b) in contrast to the argument that large auditors charge a

premium relative to smaller auditors to cover additional litigation costs (Dye, 1993), audit

markets appear to be segmented along cost-efficient dimensions. This cost-segmentation

argument may also explain why Big 5 auditors almost exclusively audit larger clients. Further,

our results are inconsistent with monopolistic pricing among large clients; to the contrary, some

evidence suggests that the power to affect pricing may, to some extent, lie in the hands of very

large clientele. In general, the auditor type (Big 5 or non-Big 5) best equipped to audit a

particular client efficiently is usually selected, and audit fee premiums are most likely to result

for those clients that depart from that choice. Finally, our findings emphasize the importance of

controlling for self-selection and size nonlinearities in any study using standard OLS regressions

to control for client size or auditor size (or quality).


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Appendix

Marginal Effects for Variables estimated using a Probit Model

Define a linear function that determines the probability of an event:

Z = 0 + 1X1 + +kXk.

F(Z), the standardized cumulative normal distribution, gives the probability of the eventoccurring for any value of Z:

pi = F(Zi).

Using maximum likelihood, estimates of the parameters (i) are computed. The marginal effect ofXi is p/Xi. This is computed as

iii

ZfX

Z

dZ

dp

X

p

=

=

)(

Where f (Z) is the derivative of F(Z), the cumulative standard normal distribution, or simply thestandardized normal distribution:

25..

2

1)( zeZf =


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Table 2

Spearman Cross-Correlations(significance level)

Lfee Size Lev ROA Sqempl Sqrtsub Yrend Replag Big 5

Lfee 1.000

Size 0.828 1.000(0.00)

Lev 0.123 0.132 1.000(0.00) (0.00)

ROA 0.231 0.415 0.170 1.000

(0.00) (0.00) (0.00)

Sqempl 0.700 0.752 0.112 0.309 1.000(0.00) (0.00) (0.00) (0.00)

Sqrtsub 0.060 0.079 0.093 0.104 0.122 1.000(0.00) (0.00) (0.00) (0.00) (0.00)

Yrend 0.066 0.033 0.007 -0.104 -0.016 -0.076 1.000(0.00) (0.05) (0.69) (0.00) (0.37) (0.00)

Replag -0.386 -0.537 0.268 -0.185 -0.333 0.047 -0.059 1.000(0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00)

Big 5 0.357 0.396 -0.082 0.045 0.204 -0.044 0.052 -0.389 1.000(0.00) (0.00) (0.00) (0.01) (0.00) (0.01) (0.00) (0.00)

n= 3,341

Lfeei= Logarithm of audit fees; Sizei = Logarithm of end of year total assets;Levi = long-termdebt plus debt in current liabilities divided by market value of equity plus total liabilities;Sqrtsubi= square root of the number of subsidiaries;ROAi= Earnings before interest and taxesdivided by total assets; Sqrtempli = Square root of the number of employees; Yrendi= 1 if thefirms year-end occurs in December, 0 otherwise;Replagi = Number of days between the firms

year-end and the earnings announcement date;Big 5= 1 if firm i chose a Big 5 auditor in year t;0 otherwise.


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Table 3Fee Regressions with Big 5 Indicator VariableWith/without Interactive Size Variables (OLS)

Big 5 Dummy OLSBig 5 Dummy OLSWith Size interactive

variablesVariable Coeff. t-stat Coeff. t-stat

Intercept 2.72 44.15 3.37 20.97

Size 0.41 43.98 0.12 2.41

Lev 0.02 0.45 0.25 1.57

Sqrtsub -0.01 -1.01 -0.07 -1.81

ROA -0.37 -12.25 -0.28 -4.12

Sqrtempl 0.10 12.58 0.10 2.80

Yrend 0.07 3.41 -0.05 -0.89

Replag 0.00 6.95 0.00 1.12

Big 5 0.16 5.07 0.46 5.73

Size*Big 5 -0.07 -3.17

Size*Size 0.03 7.49

Size*Lev -0.04 -1.45

Size*Sqrtsub 0.01 1.26

Size*ROA -0.01 -0.34

Size*Sqrtempl -0.01 -1.58

Size*Yrend 0.02 2.27

Size*Replag 0.00 1.28

F test significanceof interactive terms 13.30

Adj R Sq. (%) 72.1 72.9

No. of obs. 3,341 3,341Where:

Lfeei = Logarithm of audit fees;Big 5i = 1 if firm i chose a Big 5 auditor in year t; 0 otherwise;Sizei = Logarithm of end of year total assets;Levi = long-term debt plus debt in current liabilities divided by market value of equity

plus total liabilities;Sqrtsubi = square root of the number of subsidiaries;ROAi = Earnings before interest and taxes divided by total assets;Sqrtempli = Square root of the number of employees;Yrendi = 1 if the firms year-end occurs in December, 0 otherwise;Replagi = Number of days between the firms year-end and the earnings announcement date.


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Table 4Auditor Demand Equation

Coefficient Chi-sq value Pr > t

Intercept -1.534 31.09 0.00

Size 0.806 38.01 0.00

Lev -2.069 17.40 0.00

Sqrtsub 0.078 0.38 0.54

ROA -0.079 0.12 0.73

Sqrtempl 0.136 0.77 0.38

Size*Size -0.031 3.66 0.06

Size*Lev 0.252 4.97 0.03

Size*Sqrtsub -0.037 1.53 0.22

Size*ROA -0.287 10.78 0.00

Size*Sqrtempl -0.018 0.68 0.41

Model likelihood 791.49 0.00

Hosmer/Lemeshow 8.77 0.36

LR test ofspecification 38.54 0.00

N = 3,341

% CorrectlyClassified 88.5

% Using Big 5 86.3

Pseudo R-square 0.383

The demand equation estimated is:

Big 5i = 1 + 2Sizei + 3Levi + 4Sqrtsubi + 5ROAi + 6Sqrtempli + 7Sizei* Sizei

+ 8Sizei*Levi + 9Sizei*Sqrtsubi +10Sizei*ROAi +11Sizei*Sqrtempli + i

whereBig 5= 1 if firm i chose a Big 5 auditor in year t; 0 otherwise, Sizei = Logarithm of end ofyear total assets;Levi = long-term debt plus debt in current liabilities divided by market value ofequity plus total liabilities; Sqrtsubi= square root of the number of subsidiaries;ROAi=Earnings before interest and taxes divided by total assets; Sqrtempli = Square root of the number

of employees.


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Table 5

Fee Regressions by Auditor Type

Panel A:

Big Five Non-Big FiveCoeff. t-stat Coeff. t-stat

Intercept 4.66 13.56 2.99 7.91Size -0.19 -1.78 0.62 2.00Lev 0.87 3.18 -1.05 -1.35Sqrtsub -0.07 -1.46 0.10 0.97ROA -0.11 -0.99 0.03 0.17Sqrtempl 0.14 3.23 0.49 2.48Yrend -0.08 -1.22 0.03 0.28Replag 0.00 0.46 0.00 0.85Size*Size 0.05 5.98 0.05 2.65Size*Lev -0.13 -2.93 -0.01 -0.05

Size*Sqrtsub 0.01 1.23 -0.05 -1.60Size*ROA -0.02 -0.88 -0.49 -2.53Size*Sqrtempl -0.01 -2.34 -0.07 -1.95Size*Yrend 0.03 2.41 0.01 0.19Size*Replag 0.00 1.35 0.00 0.63Lambda () -0.45 -2.30 1.19 1.76Adj R Sq. (%) 70.2 56.1 No. of obs. 2,883 458

Mean (Actual-

Expected fee) -2.58 -1.04t-value -194.62 -214.20Median (Actual Expected fee) -2.53 -1.02

Where:

Lfeei = Logarithm of audit fees (dependent variable);Big 5i = 1 if firm i chose a Big 5 auditor in year t; 0 otherwise;Sizei = Logarithm of end of year total assets;Levi = long-term debt plus debt in current liabilities divided by market value of equity

plus total liabilities;Sqrtsubi = square root of the number of subsidiaries;ROAi = Earnings before interest and taxes divided by total assets;Sqrtempli = Square root of the number of employees;Yrendi = 1 if the firms year-end occurs in December, 0 otherwise;Replagi = Number of days between the firms year-end and the earnings announcement date;Lambdai() = Inverse Mills Ratio.


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Table 6

Robustness Tests

Counterfactuals: Actual Fees less Expected Fees for Alternative Auditor

Big 5Clients

Non-Big 5Clients

Test 1: Truncated firms larger thanthe largest firm in the non-Big 5sampleMean (Actual-Expected fee) -2.30 -1.22t-value -189.31 -237.90Median (Actual Expected fee) -2.27 -1.21 No. of obs. 2,688 458Adj R Sq. (%) Fee regression 58.3 56.1Percent correctly classified Demand

equation 87.9%

Test 2: Added quick ratio and ratio ofcurrent to total assets to both thedemand and fee regressionsMean (Actual-Expected fee) -0.96 -0.94t-value -128.99 -240.81Median (Actual Expected fee) -0.92 -0.94 No. of obs. 2,784 439Adj R Sq. (%) Fee regression 74.2 58.3

Percent correctly classified Demandequation 89.1%

Test 3: Alternative size variable(replaced asset size with square rootof employees)Mean (Actual-Expected fee) -0.61 -0.26t-value -66.09 -40.26Median (Actual Expected fee) -0.54 -0.29 No. of obs. 2,883 458

Adj R Sq. (%) Fee regression 71.4 57.5Percent correctly classified Demandequation 88.8%


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Figure 1Marginal Effects for the Independent Variables on Auditor Choice

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Rank of Size (10 groups)

MarginalEffectsOnAuditorChoice

Size Lev ROA Employ Sub

Small Large

Size

Leverage

ROA

See appendix for a discussion of the method of computation. For each observation, the marginaleffect for each variable was estimated. Then, ten portfolios were created based on firm size. The plotincludes the average of the marginal effect for each portfolio.

Sizei = Logarithm of end of year total assets;Levi = long-term debt plus debt in current liabilities divided by market value of equity plus

total liabilities;Sqrtsubi = square root of the number of subsidiaries;ROAi = Earnings before interest and taxes divided by total assets;Sqrtempli = Square root of the number of employees.


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Figure 2Effects of Independent VariablesOn the Prediction of Big 5 Audit Fees (Lfee)(Including Size Interactive Terms)

Predicted Fee Effects Big Five

-0.1

-0.05

0

0.05

0.1

0.15

0.2

rank of size

Leverage

ROA

Employee

Sub

Replag

Yrend

Rank of Size Portfolios

Variable 1 2 3 4 5 6 7 8 9 10

Size 2.330 3.408 4.033 4.509 4.976 5.457 5.966 6.502 7.267 8.708

Lev 0.104 0.112 0.130 0.129 0.140 0.145 0.165 0.226 0.214 0.202

ROA -0.484 -0.247 -0.181 -0.128 -0.065 0.010 0.018 0.051 0.049 0.072

Yrend 0.646 0.677 0.644 0.667 0.653 0.640 0.649 0.612 0.594 0.708

Replag 66.823 60.868 53.429 50.278 48.764 44.785 43.059 42.509 37.017 32.097

Sqrtsub 1.014 0.963 0.839 0.845 0.880 0.920 1.072 1.072 1.144 1.205

Sqempl 0.308 0.442 0.578 0.787 0.960 1.233 1.528 2.141 2.893 5.403

n= 288 288 289 288 288 289 288 289 288 288


total liabilities;Sqrtsubi = square root of the number of subsidiaries;ROAi = Earnings before interest and taxes divided by total assets;Yrendi = 1 if the firms year-end occurs in December, 0 otherwise;Replagi = Number of days between the firms year-end and the earnings announcement date;Sqrtempli = Square root of the number of employees.


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Figure 3Effects of Independent VariablesOn the Prediction of Non-Big 5 Audit Fees (Lfee)(Including Size Interactive Terms)

Non-big 5 Predicted Fees

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5

Rank of Size (5 groups)

Leverage

ROA

Employee

Sub

Replag

Yrend

Rank of Size PortfoliosVariable 1 2 3 4 5Size 1.347 2.236 2.874 3.706 5.296Lev 0.152 0.189 0.200 0.225 0.249ROA -0.428 -0.221 -0.084 0.006 0.042Yrend 0.516 0.533 0.598 0.576 0.659Replag 85.967 80.728 78.500 71.413 58.462Sqrtsub 1.177 1.047 1.016 1.024 1.168Sqempl 0.208 0.287 0.417 0.583 1.355n= 91 92 92 92 91


total liabilities;Sqrtsubi = square root of the number of subsidiaries;ROAi = Earnings before interest and taxes divided by total assets;Yrendi = 1 if the firms year-end occurs in December, 0 otherwise;Replagi = Number of days between the firms year-end and the earnings announcement date;


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Sqrtempli = Square root of the number of employees.Figure 4Effects of Size and Size Interactive TermsOn the Prediction of Big 5 and Non-Big 5 Audit Fees (Lfee)

0

0.5

1

1.5

2

2.5

3

3.5

4

Rank of Size (5 Groups)

Big 5

Non Big 5

Rank of SizeAuditor Variable 1 2 3 4 5

Big 5 Size 2.869 4.271 5.217 6.234 7.987n= 576 577 577 577 576

Non-Big 5 Size 1.347 2.236 2.874 3.706 5.296n= 91 92 92 92 91

Sizei = Logarithm of end of year total assets;

chaney et al (2005)- selfselectionofauditors_jeter_chaney

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