Competition in the audit market∗
Joseph Gerakos
Chad Syverson
July 11, 2012
Abstract
We estimate the demand of publicly traded firms for the Big 4 auditors. Using these demand
estimates, we calculate the expected changes in consumer surplus arising from the disappearance
of one of the Big 4 audit firms and from the implementation of mandatory audit firm rotation.
Our conservative estimated decreases in consumer surplus range from $1.48 billion for the disappearance of Deloitte Touche to $1.85 billion for the disappearance of PriceWaterhouseCoopers.
These are the total amount of transfers clients would require to compensate them for losing the
ability to hire one of these firms as an auditor. Such losses are substantial; for comparison, total
audit fees for public firms were $11 billion in 2009. Regarding mandatory audit firm rotation,
we find similarly large impacts. Firms would lose $3.5 billion in consumer surplus if rotation
were required after ten years and $5.6 billion if mandatory rotations were required after only
four years.
1
Introduction
An audit is a necessary input for a publicly traded firm. Set against the mandatory nature of this
input demand is the fact that the market’s supply side is highly concentrated. Among publicly
traded companies in the U.S., for example, the majority of audit engagements and almost all
audit fees involve just four audit firms (the “Big 4”: Ernst & Young, Deloitte Touche, KPMG,
and PriceWaterhouseCoopers). In 2009 the Big 4 handled 67 percent of audit engagements and
collected over 94 percent of audit fees. (For a breakdown of market shares, see Table 1.) Similar
concentration is observed in the audit markets of many other developed economies.
This combination of mandated purchase and concentrated supply raises two major questions for
academics and policy makers. First, what would be the effects of continued concentration in the
∗
Affiliations: Joseph Gerakos, University of Chicago Booth School of Business; Chad Syverson, University of
Chicago Booth School of Business and NBER. We thank Ray Ball, J.P. Dubé, Ron Goettler, Bobby Gramacy, Günter
Hitsch, Doug Skinner, Anne Vanstraelen, and workshop participants at Maastricht University for their comments.
1
audit industry, say if one of the Big 4 audit firms disappeared? Second, imposition of mandatory
audit firm rotation has recently been a topic of considerable debate. How would implementation of
such a policy affect market participants?
Both questions have likely already played roles in policy toward the industry. There have
been several recent cases in which a Big 4 audit firm could arguably have been criminally indicted
but the Department of Justice decided to not file charges, probably because of concerns about
further increasing concentration.1 For example, in 2007 KPMG admitted criminal wrongdoing by
creating tax shelters that helped clients evade $2.5 billion in taxes. Nevertheless, the Department of
Justice did not indict KPMG and instead entered into a deferred prosecution agreement. Moreover,
according to the Lehman Brothers bankruptcy examiner’s report, Ernst & Young assisted Lehman
Brothers in implementing its Repo 105 transactions, which allowed Lehman to temporarily reduce
its leverage when preparing its financial statements. Nonetheless, the Department of Justice did
not pursue criminal charges against Ernst & Young.2
With regard to mandatory auditor rotation, the Public Company Accounting Oversight Board
(the “PCAOB”) is in active discussions about implementing such a policy for SEC registrants.
During the PCAOB’s recent hearings in March 2012 on mandatory audit firm rotation, panelists
voiced opposing views about the costs and benefits of mandatory audit firm rotation. For example,
the executive director of the AICPA’s Center for Audit Quality stated that mandatory audit firm
rotation would hinder audit committees in their oversight of external auditors, while former SEC
chairman Arthur Levitt supported mandatory rotation because “investors deserve the perspectives of
different professionals every so often, particularly when an auditor’s independence can be reasonably
called into question” (Tysiac (2012)).
Addressing these questions satisfactorily requires, at the very least, measurements of the willingness of firms to substitute among individual auditors and the value firms place (if any) on extended
relationships with auditors. However, prior research on the structure of the audit market has focused primarily on either correlations between audit fees and firm characteristics or substitutability
between the Big 4 and non-Big 4 auditor groups. While this work has offered insights to several
questions, its focus has left a gap that we seek to begin to fill with this study.
1
A criminal indictment virtually prohibits an audit firm from carrying out audits of SEC registrants.
In contrast, the New York attorney general Andrew Cuomo sued Ernst & Young claiming that the audit firm
helped Lehman “engage in a massive accounting fraud.”
2
2
Our empirical approach treats the audit market like any other differentiated product market.
We model firms seeking audit services as choosing from among several producers of those services
(i.e., the audit firms), with each producer offering different aspects of service that are differentially
valued by each firm.3 Each firm considers how well the attributes of each auditor’s product match
its needs (these attributes include price—the audit fees) and hires the auditor offering the best
match.
With this factor demand framework, we can use data on publicly listed firms’ choices of auditors
to measure via revealed preference how firms view the audit services provided by each of the Big
4 auditors as well as by smaller audit service providers. Importantly, we can measure a firm’s
willingness to substitute among auditors. That is, we can compute the dollar transfer necessary to
make a client switch to a different auditor, and in particular what transfers would be necessary to
compensate clients of a disappearing Big 4 auditor for having to switch to one of the remaining Big 3.
Moreover, we can also gauge clients’ willingness to pay for longer-term relationships with a particular
auditor, and hence what value the firms would lose if forced to break such relationships because
of auditor rotation. As mentioned above, knowing these values is critical to be able to answer the
questions of the effects of further industry concentration and mandatory auditor rotation.
Our preliminary analyses indicate large losses in firms’ expected consumer surplus (i.e., the value
to firms of their purchased audit services in excess of the fees they pay for them) if any of the Big
4 auditors disappear, though some would create losses larger than others. Based on estimates of
demand from firms’ recent choices of auditors, our conservative estimated decreases in consumer
surplus range from $1.48 billion for the disappearance of Deloitte Touche to $1.85 billion for the
disappearance of PriceWaterhouseCoopers. These are the total amount of transfers clients would
require to compensate them for losing the ability to hire one of these firms as an auditor. Such losses
are substantial; for comparison, total audit fees for public firms were $11 billion in 2009. Regarding
mandatory audit firm rotation, we find similarly large impacts. Firms would lose $3.5 billion in
consumer surplus if rotation were required after ten years and $5.6 billion if mandatory rotations
were required after only four years.
These estimates carry several caveats. First, the Big 4 audit firms operate worldwide, while our
3
Because audits are inputs into firms’ production activities, these are differentiated factor markets, but the economics are essentially the same as in markets for differentiated outputs.
3
estimates are based only upon their U.S. public clients. Second, given a lack of publicly available
data we are also unable to include private firms in our analysis. Finally, our estimates are limited to
audit fees and services and do not take into account non-audit and audit-related fees and services.
Nevertheless, these estimates provide preliminary information to regulators about the costs that
could arise from changes in market structure and from the implementation of mandatory rotation.
In addition, they provide some of the first estimates of the value of audit firm-client matches. Such
estimates are missing in the academic literature.
In future drafts we will extend this analysis in multiple directions. We will investigate the impact
of reduced concentration in the industry, say if one of the smaller auditors experienced considerable
growth, or if one of the Big 4 were broken up. Additionally, we will characterize the supply side
of the audit industry. This will allow us to see, for instance, how remaining auditors might change
their fee-setting behavior if the industry were to become more concentrated due to exit or merger.
This supply-side response, as it is likely to lead to an increase in market power among surviving
auditors and higher fees, is likely to exacerbate the aforementioned losses in value suffered by firms
seeking audit services.
Our analysis is structured as follows. We first discuss how we model firms’ auditor choices.
We then discuss estimation of the demand model, including our approaches for dealing with the
standard price endogeneity issue. We also discuss how we handle a more atypical situation in
demand estimation—the fact that we do not observe prices (fees) for producers (auditors) that a
firm does not hire. After reporting and discussing our demand estimates, we use them to calculate
the effects of increasing audit industry concentration (we compute separate effects for disappearance
of each of the Big 4) and mandated auditor rotation. We conclude with a discussion of how we plan
to model the extensions to this analysis in future versions of the paper.
2
Demand side
We model publicly listed firms’ demand for audit services as a choice among several auditors (each
of the Big 4 and an amalgam outside good that includes all other audit firms). Each firm makes
its choice based on the expected benefit it obtains from each of the possible auditors. This benefit
includes the effects of both firm-, auditor-, and match-specific attributes and is net of the fees the
4
auditor charges the firm for its service.
While the model we lay out below is in many ways standard in the industrial organization
literature, our approach differs from prior literature on auditor choice in that this work has typically
examined the determinants of the simple dichotomous choice between using a Big 4 versus a nonBig 4 auditor. Our analytical structure allows us to both characterize much more fully the patterns
of substitution among the individual audit firms, but just as importantly lets us tie firms’ choices
directly to parameters of firms’ factor demands that can be interpreted in terms of dollar values.
2.1
Utility specification
For each firm’s choice of auditor, we specify the inside goods as the Big 4 auditors (Ernst & Young,
Deloitte Touche, KPMG, and PriceWaterhouseCoopers) and the outside good as the aggregation
of all other auditors who provide audits to public firms (BDO Seidman, Grant Thornton...). We
assume that each year a publicly traded firm chooses whether to keep its existing auditor or switch
to another audit firm. We assume that when making this choice the client forms expectations about
the fees that each of the Big 4 and the non-Big 4 composite auditor would charge for an audit.
We model each client firm i’s utility from the choice of auditor j as taking the following linear
form
Uij = δj − αi ln(pij ) + βij xij + ij
(1)
in which δj is an auditor (or brand) fixed-effect that represents the mean utility that clients receive
for each auditor j, pij is the auditor j’s price (i.e., audit fees) for an audit of firm i, αi represents
firm i’s marginal willingness to pay for a log-dollar of audit fees, xij are observable non-price
characteristics of the client-auditor pair, βij are the utility loadings on these characteristics, and ij
represents an unobserved client-auditor specific component of utility assumed to be independently
and identically distributed.4 In our specification, audit fees enter in logarithm form. The logarithm
form implies that an additional dollar of audit fees matters less to a large client than a small client.
This is consistent with the common practice of clients negotiating with their existing auditors over
percentage changes in audit fees rather than absolute dollar changes.
To model the interactions between non-price characteristics of the client and the audit firm, we
4
While we have labeled equation (1) as describing a client firm’s utility, it can be interpreted more broadly as any
objective function of the client’s with respect to its audit firm choice.
5
expand βij xij as follows. First, we interact the auditor fixed effect, δj , with the natural logarithm
of the client’s size ln(T otalAssetsi ). This interaction allows us to capture audit firm preferences
that vary with client size. For example, smaller firms may prefer non-Big 4 auditors, and there
can be heterogeneous size-based preferences for each of the Big 4 auditors. Second, we include the
client’s past history with the audit firm. To do so, we include the natural logarithm of the number
of years that firm i has been a client of auditor j, ln(Y earsClientij ) and an indicator variable coded
as 1 if the firm was not a client of the auditor in the prior year, and 0 otherwise, 1(N ot clientij ).
These variables allow demand preferences to vary with the history of the client-audit firm match.
This captures any influence of client-auditor specific capital that might be built over the audit
relationship.
The overall specification for utility of firm i for choosing auditor j is therefore
Uij = δj − α1 ln(pij ) + β1j δj ln(T otalAssetsi ) + β2j ln(Y earsClientij ) + β3j 1(N ot clientij ) + ij .
(2)
Client i calculates Uij for each of the Big 4 firms and the outside good and then chooses the
audit firm j that provides the maximum Uij . This linear specification is standard in the industrial
organization and marketing literatures for modeling the demand for discrete differentiated products.
2.2
Estimation
Utility for client i and auditor j can be specified as Uij = Vij + ij in which Vij ≡ βij xij − αi pij + δj
is the observable portion of utility and ij is the unobserved portion of utility. If we assume that
ij is distributed type 1 extreme value, the predicted probability that client i chooses audit firm j is
Pij =
eVij
.
Σj eVij
(3)
This specification is referred to as the conditional logit and is commonly used in the industrial
organization and marketing literature to estimate demand for discrete differentiated products.5
Conditional logit is similar to a fixed effect regression in that any characteristic of client i that does
not vary across the audit firm choices drops out of equation (3). For example, firm-size on its own
drops out of equation (3), but interactions between the auditor fixed-effects and firm size remain.
5
For a discussion, see Train (2009).
6
If yij = 1 represents that client i chooses auditor j and zero otherwise, then the log likelihood is
as follows:
LL(α, β, δ) =
XX
i
yij ln Pij =
j
XX
i
j
yij ln
eVij
Σj eVij
(4)
We maximize this log likelihood to obtain estimates of the preference parameters α, β, and δ.
2.3
Prices
One issue with equation (2) is that we only observe prices (audit fees) for actual matches between
clients and auditors. This is unusual situation in most demand estimation settings; the researcher
typically observes the prices of each item of the available choice set. We must therefore estimate
what fees a client would have expected to pay had it hired an audit firm other than the one it ended
up choosing.
We implement this estimation using a predictive model estimated from the relationships between
the fees in observed client-auditor matches and client-, auditor-, and match-specific characteristics.
We considered several prediction methods including ordinary least squares, lasso regression, ridge
regression, partial least squares, and several regression tree approaches (random partitioning, conditional inference trees, and random forest).6 Based on root mean squared error derived from
cross-fold validation, we found that regression trees (specifically, random forest) best predict dollar
audit fees using the following set of predictor variables: total assets, the number of industrial segments, foreign sales, long term debt, short term debt, return on assets, loss indicator, receivables,
inventory, market value of equity, indicator for accelerated filer, indicator for going concern in prior
year, and indicators to capture whether and for how long the firm was a client of the auditor. We
include polynomials up to the fourth power for both total assets and the natural logarithm of total assets. For the number of industrial segments, foreign sales, long term debt, short term debt,
receivables, inventory, and market value of equity, we also include the natural logarithm of these
variables.7
It is important to note that in our demand estimations, we use predicted fees for all auditors,
including for the audit fees charged by the actual audit firm chosen by the client. We do so because
6
For discussion of these methods, see Hastie, Tibshirani, and Friedman (2009).
Although this is a large predictor set, over fitting is not an issue given that we use cross-fold validation. Moreover,
most of the prediction methods we considered include a penalty for each additional predictor.
7
7
it is likely that the prices associated with actual choices include a negative price shock that could
bias our estimated price coefficients toward zero. For a discussion of this issue, see Erdem, Keane,
and Sun (1999).
2.3.1
Price endogeneity
A major concern with estimating equation (2) is the possibility of price endogeneity (e.g., cov(pij , ij ) 6=
0). For example, if price is correlated with unobserved audit quality, then the coefficient on price
will be positively biased (toward zero, given that theory predicts the coefficient should be negative).
As a result, the demand estimates would make it appear that firms are less sensitive to audit fees
than they really are. A way to avoid this bias is to identify firms’ price sensitivity using fee variation
that is driven by supply-side factors that are uncorrelated with demand shifts. We include two sets
of supply shifters in our audit fee prediction regressions to aid in this identification: one uses the
change in supply structure induced by the disappearance of Arthur Andersen and the second uses
increases in auditor supply created by client mergers and acquisitions.
Disappearance of Arthur Andersen We assume that the collapse of Arthur Andersen was
an exogenous shock to supply in the audit market. Namely, the collapse of Arthur Andersen
reduced competition among auditors, leading to increased audit fees, and this competitive effect
was orthogonal to shocks to demand for the audit firms. Moreover, given the prior research on
auditor specialization, we assume that the shock varied with Andersen’s share of client industries,
thereby providing cross-industry variation in the reduction of supply.
To validate the disappearance of Arthur Andersen as a supply shifter, Table 2 presents ordinary least squares regressions that regress the log growth in the client’s total audit fees on the
natural logarithm of the total assets in each four-digit SIC audited by Arthur Andersen in 2001,
ln(Andersen0 s Share in 2001). If our assumption is correct that Andersen’s disappearance is an
inward shift in audit supply, the coefficient on Andersen’s 2001 share should be positive.
We estimate these regressions for each year between 2002 and 2009. We include as additional
controls indicator variables for the firm’s auditor in 2001 to capture differences in fee growth that
are driven by the client’s auditor in 2001. For example, the fee growth for Andersen clients could
differ from the fee growth for firms that were Ernst & Young clients in 2001. We also include the
8
change in the client’s logged total assets over each period, as the prior literature has found that
total assets is the major predictor of audit fees. We cluster the standard errors by four-digit SIC.
Because we require that the data is available over each change, the sample size drops monotonically
from 4,970 clients for 2002–2001 to 2,809 clients for 2009–2001.
The results in Table 2 indicate that the supply shift measure ln(Andersen0 s Share 2001) is
indeed positive and significant at each horizon. That is, industries in which Andersen had a larger
market share experienced greater growth in audit fees. Importantly, this effect lasted through 2009.
With respect to the audit firm indicators that capture average growth in fees, these coefficients
are, in general, similar in magnitude for the clients of Arthur Andersen and Big 4 in 2001. One
exception is that for 2002, clients of Arthur Andersen experienced a decrease in fees, which was
probably due to the Big 4 offering aggressive prices to lure former Andersen clients. Clients of the
non-Big 4 experienced lower fee growth over all horizons. Consistent with the documented levels
relation between total assets and audit fees, the coefficients on the log change in total assets are
positive and significant for each year between 2002 and 2009.
An alternative explanation for these results is that Arthur Andersen charged lower prices and
provided lower quality audits, thereby leading to greater increases in audit fees for Andersen clients.
We do not believe that such an effect drives the results presented in Table 2 for two reasons.
First, Cahan, Zhang, and Veenman (2011) find that prior to the Enron scandal, Arthur Andersen
provided audits of similar quality to the audits provided by the other major audit firms. Second, in
untabulated tests, we find similar effects if we limit the regressions to firms that were not Andersen
clients.
Given the results presented in Table 2, we include in the annual audit fee prediction regressions
the natural logarithm of the total assets in each four-digit SIC audited by Arthur Andersen in 2001,
ln(Andersen0 s Share 2001). This variable offers variation in audit fees due to supply shocks that
should be uncorrelated with clients’ relative demand for surviving auditors.
Client mergers and acquisitions Our second source of supply-driven audit fee variation exploits
mergers and acquisitions among client firms. The notion is that a merger in an industry increases
the available supply of auditors to the industry. Primarily this increased supply would arise when
the pre-merger client firms each have separate auditors but will drop one after. The audit firm
9
that loses a client due to merger or acquisition will find itself with excess capacity that should put
downward pressure on audit fees. Supply can also shift even if both pre-merger client firms have
the same auditor, because even though the merged firm requires greater auditing, the elasticity of
audit fees to total assets is approximately 0.3–0.4. This also creates excess audit capacity for the
merged firm’s auditor and the resulting price effects. These supply shifts will be orthogonal to audit
demand shocks as long as client-level mergers and acquisitions are driven by neither auditor choice
nor audit fee considerations.
To test whether mergers and acquisitions have the expected effects on audit fees, we regress
logged fees on the natural logarithm of total client assets in the client’s respective four-digit SIC
level that were lost by audit firms in the prior year due to mergers or acquisitions, ln(M ergers).
For control variables, we include the ratio of receivables to assets, the ratio of inventories to assets,
the return on assets, an indicator variable for whether the client experienced a loss, the percent of
foreign sales, the natural logarithm of the number of industrial segments, an indicator for whether
the firm is an accelerated filer, and an extensive set of fixed effects. We cluster standard errors at
the client level and estimate the regressions over the sample period 2002–2009.
Table 3 presents the results. Columns (1) and (3) include audit firm fixed effects and columns
(3) and (4) include client fixed effects. All four regressions include year fixed-effects.
Consistent with ln(M ergers) representing an increase in the supply of auditing, its coefficient
is negative and statistically significant in all four specifications, implying that greater mergers and
acquisitions of clients are associated with the audit firm charging lower audit fees in the subsequent
year. We therefore include this variable in the audit fee prediction regressions.
With regard to the controls, as prior literature typically specifies audit fee regressions using
pooled cross-sections, it’s worth noting the similarity between the coefficients presented in columns
(1) and (2) and those in prior audit fee research. These are similar in sign, magnitude, and significance to those in earlier work. For example, the elasticity with respect to firm size ranges from 0.409
with auditor fixed-effects to 0.454 without auditor fixed-effects. In addition, fees increase in losses,
inventory, foreign sales, accelerated filers status, and a going concern. They decrease in receivables
and inventory.
10
2.3.2
Fit of predicted audit fees
The within-sample fitted values from our random forest prediction specification are highly correlated
with actual audit fees. The Pearson product moment correlations between actual and predicted fees
are as follows: Ernst & Young, 0.976; Deloitte Touche, 0.967; KPMG, 0.970; PwC, 0.968; all other
auditors, 0.967. Figure 1 presents plots of actual versus predicted audit fees for our sample. The
left figure presents the plot for the entire distribution of actual fees and the right figure presents
the plot for actual fees between the 1st and 99th percentiles. These plots show that the prediction
model does well over most of the distribution of actual audit fees. The exception is that the model
underpredicts fees above the 99th percentile. In untabulated tests, we estimated demand while
excluding clients with actual audit fees above the 99th percentile. Results for this restricted sample
are qualitatively and quantitatively similar to those presented in the tables.
3
Demand estimation
3.1
Sample
Our sample consists of SEC registrants with available data. It starts in 2002 and ends in 2009.
We start in 2002 because, as explained above, we rely on exogenous variation created by the disappearance of Arthur Andersen. We pull audit fee data from Audit Analytics, which provides audit
fee data starting with the mandatory disclosure of audit fees in 2000. We use Compustat to obtain accounting-based control variables and the histories of auditor-client matches for prior to 2000.
Finally, we use SDC Thomson to identify client-level mergers and acquisitions.
3.2
Conditional logit results
Table 4 presents the results from the annual conditional logit regressions that estimate clients’ preference parameters for auditor choice. These form the basis for our estimates of clients’ willingness to
pay for audit services and willingness to substitute among audit firms. We estimate the conditional
logit regressions annually over the period 2002–2009 and include the variables listed in equation (2).
Across the annual estimates several patterns emerge. First, for each of the Big 4 audit firms,
the interactions between the audit firm fixed-effects and client size are positive and significant each
11
year, implying that larger clients prefer the Big 4 compared to the non-Big 4. For each of the
Big 4 auditors the largest coefficients on the size interactions are in 2005, which was the first year
subsequent to the implementation of the Sarbanes-Oxley internal control requirements. Second,
the coefficients on the interactions with 1(N ot clientij ) are negative and significant for each of the
Big 4 auditors in each annual regression and the interactions with ln(Y ears clientij ) are positive
and significant for many of the years. These results imply that either there are significants costs
associated with switching from your current auditor or that there are heterogeneous preferences for
audit firms that lead to long-term matches between auditors and clients.
The coefficient on ln(Audit f eesij ) is negative and significant for each year in the sample, with
the coefficient having the smallest absolute magnitude in 2004, which was the first year of the
Sarbanes Oxley internal control requirements. A lower coefficient on price for that year implies
that non-price characteristics of an audit increased in importance relative to price. While as noted
we focus on the post-2001 period in order to exploit exogenous variation created by the implosion
of Arthur Andersen, we found in untabulated tests that the coefficient on ln(Audit f eesij ) is also
negative and significant for 2000 and 2001.
Given that we are estimating a non-linear model, the coefficients on the interactions do not
represent marginal effects. In Table 5, we therefore present for comparison marginal effects for size
and the history of the match between the client and audit firm. These computed values measure
the changes in choice probabilities associated with a change in the demand shifter. We use the
preference parameter estimates for 2009 to calculate the marginal effects in the table.
Panel A presents marginal effects over various points in the client size distribution. Several
patterns emerge in the marginal effects of size. First, there is heterogeneity across the audit firms.
Starting at the 10th percentile of client size, the marginal effects are greatest for Ernst & Young,
rising from 0.0078 at the 10th percentile to 0.1337 at the 99th percentile. Below the 10th percentile,
the smallest marginal effects are for PriceWaterhouseCoopers. Above the 10th percentile, PriceWaterhouseCoopers’ marginal effects are the second largest. In contrast, for KPMG and Deloitte
the marginal effects with respect to client size are smaller than for Ernst & Young and PriceWaterhouseCoopers starting at the first quartile and begin to taper off at the 90th percentile of client
size.
Panel B presents marginal effects based on the length of the match between the client and
12
audit firm. Once again these effects vary across the Big 4 audit firms. A client that has been with
Ernst & Young for 10 years is only about three percentage points more likely to choose Ernst &
Young again than one that has been with E&Y for 1 year. On the other hand, a 10-year client of
PriceWaterhouseCoopers is over 13 percentage points more likely to stick with PwC than a first-year
client.
Table 6 Panel A presents annual mean estimates of the audit firms’ own price elasticities—the
percentage change in the probability of choosing the auditor for a one percent increase in price. In
general, the estimates are close to unit elastic for the Big 4. Across the years, Deloitte appears
to have the most elastic demand of the Big 4, while Ernst & Young has the least elastic demand.
Across all of the years, non-Big 4 firms have on average less elastic demand than the Big 4. Of the
years, in 2004 the mean elasticities across all of the audit firms are smallest in absolute magnitude.
Interestingly, 2004 was the first year that audit firms carried out Sarbanes Oxley 404 internal control
inspections. Although the mean estimates are in general elastic or close to elastic, as shown in Panel
B the mean elasticities for the client’s prior auditor are almost always inelastic. This appears to be
driven by either switching costs or heterogeneous brand preferences.
3.3
3.3.1
Additional items
Auditor overlap with competitors
Aobdia (2012) documents the empirical regularity that large firms in concentrated industries are
less likely to share auditors, presumably because of concerns about the transmission of proprietary
information through the auditor.8 We therefore created the variable CompetitorOverlapij which is
coded as the product of an indicator for whether firm i is within the top three firms in its industry
as defined by four digit SIC, an indicator for whether auditor j audited at least one other top three
firm in the industry, and a measure of the industry’s concentration (the percentage of industry
sales controlled by the top three firms). When we include CompetitorOverlapij in our conditional
logit specification, the coefficients are negative and therefore consistent with the findings of Aobdia
(2012). The coefficients are not, however, statistically significant. This lack of significance appears
to be driven by the fact that prior history of the match between the audit firm and client soaks up
8
Asker and Ljungqvist (2010) find a similar effect for firm-bank matches.
13
variation related to CompetitorOverlapij . For example, when we estimate demand but exclude the
history of firm-client match, CompetitorOverlapij enters significantly for many of the years.
3.3.2
Nested logit
An alternative model of audit firm choice is that clients first choose whether to use a non-Big 4 or
Big 4 auditor and then, conditional on choosing a Big 4 auditor, choose which of the Big 4 to engage.
To explore this possibility, we re-estimated our demand system using a nested logit specification.
For these estimates, the substitution parameter between Big 4 and non-Big 4 is not significantly
different than the parameters that arise under the conditional logit model. Therefore for the sake
of parsimony we stick with the conditional logit model.
3.3.3
Dollar fees
In addition to the log price specification in equation (2), we also tried a dollar price specification. A
dollar price specification assumes that a dollar of audit fees is equally important to large and small
firms. For the dollar price specification, the non-price preference parameter estimates are similar
to those presented in Table 4. The elasticity estimates are, however, about half the magnitude of
those based on the log price specification. The log price specification appears to be better able to
handle the heterogeneity in audit fees driven by firm size differences.
4
Counterfactuals
We next use the parameter estimates presented in Tables 4 and 6 to calculate the expected changes
in consumer surplus arising from two sets of counterfactuals: the (separate) disappearance of each
of the Big 4 audit firms and the implementation of mandatory audit firm rotation at various tenures.
To estimate these counterfactuals, we use the methodology outlined by McFadden (1999). This
methodology involves calculating the expected change in consumer surplus for each audit client as
the expected dollar transfer required to make the client indifferent between the unrestricted choice
set of the status quo and the restricted choice set arising under the counterfactuals. We then sum
the individual client estimates to come up with the expected total change in consumer surplus.
For example, suppose that under the status quo client i chooses the auditor j that leads to
14
maximized utility maxj U (Audit f eesij , xij, ij ), and under the counterfactual firm i chooses auditor
m from a restricted choice set that leads to maximized utility maxm U (Audit f eesim , xim, im ). The
change in consumer surplus, Cijm , is the dollar transfer (or reduction in audit fees) required to
equate the client’s maximum utility under the unrestricted choice set with the client’s maximum
utility based on the restricted choice set:
max U (Audit f eesij , xij , ij ) = max U (Audit f eesim − Cijm , xim , im ).
j
m
(5)
To calculate the total change in consumer surplus for the counterfactual, one can add up the Cijm s
across client firms.
Under each counterfactual, we estimate Cijm for each firm i. To do so, we draw vectors of type
1 extreme value error terms—one for each of the Big 4 auditors and one for the outside good. For
each vector draw, we combine in equation (2) the parameter estimates from the demand estimation
along with the the observed firm and auditor characteristics and the error term draw to calculate
the utility that the client firm would receive from choosing each of the Big 4 auditors and the
outside good. We then pick the audit firm that leads to maximum utility under this unrestricted
choice set. We next restrict the choice set for each client (i.e., remove one of the Big 4 auditors
or remove the client’s prior auditor based on tenure) and calculate the maximum utility that the
client would receive under the restricted choice set. Then we solve for the Cijm that equates these
two maximized utilities. We repeat this procedure 1,000 times for each client and take the average
of the required dollar transfer over these error draws to create E[Cijm ]. For each counterfactual we
add these estimates across client firms to calculate the expected total change in consumer surplus.
4.1
Loss of a Big 4 audit firm
The first set of counterfactuals is based on the loss of a Big 4 audit firm. Using the demand estimates
for 2009, we estimate the total expected changes in consumer surplus if each of the Big 4 disappears.
We do so by removing from each client’s choice set each of the Big 4 firms one at a time.
Table 7 presents the estimates along with each firm’s total audit fees for our sample in 2009. The
estimated total changes in consumer surplus range from a loss of $1.48 billion for the disappearance
of Deloitte Touche to a loss of $1.85 billion for the disappearance of PriceWaterhouseCoopers. These
15
are substantial values; for all of the Big 4, the estimated changes in consumer surplus are over 60
percent the firm’s total audit fees for our sample. The largest change relative to total fees is for
KPMG, 77 percent, and the smallest is for PriceWaterhouseCoopers, 63 percent.
These estimates are subject to several caveats. One that would mitigate the size of the estimated
losses is the possibility that audit teams from the disappearing audit firm could move en masse with
their clients to the remaining audit firms. This would reduce switching costs or maintain matches
based on heterogeneous preferences even if an audit firm disappears as a legal entity.9 On the other
hand, there are several reasons why these estimates might understate the true loss in client firms’
consumer surplus. For one, the estimates do not include losses in consumer surplus that could arise
from non-audit services (such as consulting and tax services) provided by the Big 4 firms to their
clients. Additionally, the estimates exclude any effect that the disappearance of a Big 4 firm would
have on that firm’s domestic private and international clients. Finally, as we discuss in Section 5,
these estimates do not account for potential strategic price responses by the remaining audit firms
that could lead to higher audit fees and further losses in consumer surplus.
4.2
Introduction of mandatory audit firm rotation
The second set of counterfactuals is based on the implementation of mandatory audit firm rotation.
To estimate the total expected change in consumer surplus that would occur if mandatory rotation
were to be implemented, we calculate the dollar transfer that would be required to make clients
indifferent to the removal of their current auditor from their choice set after four through 10 years
of tenure. We again base these estimates on the demand parameters for 2009.
Table 8 presents these expected total changes in consumer surplus. They are significantly larger
than expected changes that arise from the disappearance of one of the Big 4 and range from a $3.47
billion loss if rotation is mandatory after 10 years to a $5.60 billion loss if rotation is mandatory
after four years. The fact that these estimated total changes in consumer surplus are significantly
larger than the changes in consumer surplus arising from the disappearance of a Big 4 audit firm is
to a certain extent not surprising given that mandatory rotation has potential to affect any client,
not just the clients of the disappearing firm. These estimates provide policy makers with estimates
9
Consistent with this possibility, Blouin, Grein, and Rountree (2007) find that some Arthur Andersen clients
followed their Andersen audit teams to the remaining Big 4 auditors.
16
of the minimum dollar benefits required to justify mandatory audit firm rotation.
As with the counterfactuals in the prior section, these estimates are subject to the caveat that
they do not take into account strategic price responses by the audit firms in response to the introduction of mandatory rotation.
5
Supply response
Our estimated changes in consumer surplus are based only on our demand estimates of client
firms’ willingness to substitute among audit firms and do not take into account any strategic price
responses that audit firms might make in the counterfactual scenarios. In other words, ours is a
partial equilibrium analysis. In future drafts, we will estimate a model of the supply side of the
audit industry. This will allow us to calculate the counterfactual price responses that would further
impact the expected changes in consumer surplus. Moreover, this will let us estimate the gross
profits of the Big 4 auditors.
To model the supply side we assume that each client represents a static oligopoly market in
which each auditor offers the client a differentiated product. Audit firms price strategically based
on client firms’ demand and the expected pricing decisions of competing auditors. For each potential
audit client, the audit firm maximizes the following profit function
Πij (pi ) = qij (pi )(pij − mcij )
(6)
in which qij (pi ) is the quantity sold which depends on the vector of prices of all audits offered to
the client, pi , mcij represents the audit firm j’s marginal cost of providing an audit to client i, and
pij represents the price of audit firm j providing an audit to client i.
Using our demand parameter estimates, we can solve for the strategic price responses under
the counterfactuals by either inverting the first order conditions of equation (6) or by calculating
iterated best responses.
17
6
Conclusion
Using estimates of the demand for the Big 4 audit firms, we calculate the expected changes in
consumer surplus arising from changes in industry structure. Our conservative estimated decreases
in consumer surplus range from $1.48 billion for the disappearance of Deloitte Touche to $1.85
billion for the disappearance of PriceWaterhouseCoopers. These are the total amount of transfers
clients would require to compensate them for losing the ability to hire one of these firms as an
auditor. Under the implementation of mandatory audit firm rotation, firms would lose $3.5 billion
in consumer surplus if rotation were required after ten years and $5.6 billion if mandatory rotations
were required after only four years.
We plan to extend this analysis in multiple directions. First, we will investigate the impact of
reduced concentration in the industry, say if one of the smaller auditors experienced considerable
growth, or if one of the Big 4 were broken up. Second, we will characterize the supply side of the
audit industry. This will allow us to see, for instance, how remaining auditors might change their
fee-setting behavior if the industry were to become more concentrated due to exit or merger. Finally,
we further plan to examine whether audits as a product are vertically or horizontally differentiated
and what are the industry characteristics that led to the current level of concentration.
18
References
Aobdia, D., 2012. Proprietary information spillovers and auditor choice, Unpublished working paper,
UCLA.
Asker, J., Ljungqvist, A., 2010. Competition and the structure of vertical relationships in captial
markets. Journal of Political Economy 118 (3), 599–647.
Blouin, J., Grein, B., Rountree, B., 2007. An analysis of forced auditor change: The case of former
Arthur Andersen clients. The Accounting Review 82 (3), 621–650.
Cahan, S., Zhang, W., Veenman, D., 2011. Did the waste management audit failures signal lower
firm-wide audit quality at Arthur Andersen? Contemporary Accounting Research 28 (3), 859–891.
Erdem, T., Keane, M., Sun, B., 1999. Missing price and coupon availability data in scanner panels:
Correcting for self-selection bias in choice model parameters. Journal of Econometrics 89, 177–196.
Hastie, T., Tibshirani, R., Friedman, J., 2009. The Elements of Statistical Learning, 2nd Edition.
Springer, New York, NY.
McFadden, D., 1999. Computing willingess to pay in random utility models. Trade, Theory, and
Econometrics: Essays in honour of John S. Chipman 15, 253–274.
Train, K., 2009. Discrete Choice Methods with Simulation. Cambridge University Press, New York,
NY.
Tysiac, K., 2012. PCAOB panelists say mandatory firm rotation could be harmful, helpful. Journal
of Accountancy 213 (4).
19
20
These figures plot predicted versus actual audit fees. The left figure plots predicted fees against actual fees for the full distribution of
actual audit fees. The right figure drops the 1st and 99th percentiles of actual audit fees. We predict dollar audit fees using random forest
regression trees with the following set of predictor variables: total assets, the number of industrial segments, foreign sales, long term debt,
short term debt, return on assets, loss indicator, receivables, inventory, market value of equity, indicator for accelerated filer, indicator for
going concern in prior year, and indicators to capture whether and for how long the firm was a client of the auditor. For total assets, we
include polynomials up to the fourth power for both total assets and the natural logarithm of total assets. For the number of industrial
segments, foreign sales, long term debt, short term debt, receivables, inventory, and market value of equity, we also include the natural
logarithm of these variables.
Figure 1: Actual versus predicted audit fees
21
Andersen
20.42
15.51
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Andersen
19.75
17.76
Panel B:
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Panel A:
E&Y
21.42
21.54
25.35
24.94
22.90
21.17
20.82
20.62
20.75
20.89
E&Y
18.97
19.58
23.27
23.98
22.22
23.71
23.72
24.27
22.99
24.09
Deloitte
13.00
13.62
18.37
18.06
18.02
16.51
15.71
15.33
15.49
15.61
Deloitte
15.86
16.61
19.21
20.12
21.68
21.60
21.37
22.87
23.01
21.77
KPMG
14.39
14.47
18.57
17.81
17.36
15.99
15.18
14.17
13.94
14.52
KPMG
15.30
14.34
23.35
20.68
20.57
20.26
20.37
19.86
19.98
19.53
PwC
21.26
21.45
24.21
23.77
21.79
18.00
16.71
15.70
15.77
15.88
PWC
26.72
31.21
31.25
31.63
32.33
29.48
29.06
26.77
28.11
28.74
BDO
1.97
2.00
2.03
2.46
3.23
3.65
3.61
3.63
3.58
3.26
BDO
0.87
0.83
0.76
0.70
0.91
1.27
1.24
1.29
1.15
1.01
GT
1.87
2.68
2.99
3.22
4.07
4.52
4.88
5.08
4.81
5.06
GT
0.49
0.76
0.64
0.74
0.84
1.29
1.43
1.60
1.47
1.49
All others
6.35
6.49
8.47
9.74
12.64
20.16
23.09
25.47
25.67
24.80
All others
1.37
1.16
1.51
2.15
1.44
2.39
2.81
3.34
3.29
3.38
Total clients
3,955
4,560
5,416
5,721
5,673
6,334
6,231
6,000
5,676
5,222
Total fees
2.1
2.7
4.9
6.3
10.2
11.7
13.0
12.7
12.6
11.2
This table presents a breakdown of market shares of public audits. Panel A presents percentage market shares based on fees. Total fees
are presented in the last column and are in billions of US Dollars. Panel B presents a breakdown of market shares based on number of
clients.
Table 1: Market Shares
22
Observations
Adjusted R-squared
Change Ln(Assets) 2009-2001
Change Ln(Assets) 2008-2001
Change Ln(Assets) 2007-2001
Change Ln(Assets) 2006-2001
Change Ln(Assets) 2005-2001
Change Ln(Assets) 2004-2001
Change Ln(Assets) 2003-2001
Change Ln(Assets) 2002-2001
Other Client in 2001
PwC Client in 2001
KPMG Client in 2001
Deloitte Client in 2001
E&Y Client in 2001
Andersen Client in 2001
Ln(Andersen’s Share 2001)
4,970
0.158
0.032***
(0.007)
-0.551***
(0.051)
0.196***
(0.021)
0.142***
(0.026)
0.155***
(0.030)
0.178***
(0.021)
0.043
(0.035)
0.347***
(0.044)
2002
0.451***
(0.025)
0.049***
(0.017)
0.824***
(0.056)
0.753***
(0.052)
0.696***
(0.045)
0.684***
(0.085)
0.819***
(0.052)
0.429***
(0.061)
2004
0.442***
(0.025)
0.052***
(0.017)
0.899***
(0.058)
0.840***
(0.052)
0.828***
(0.046)
0.765***
(0.091)
0.911***
(0.055)
0.545***
(0.051)
2005
4,680
4,353
3,992
0.351
0.595
0.655
*** p<0.01, ** p<0.05, * p<0.1
0.337***
(0.036)
0.030***
(0.010)
0.400***
(0.037)
0.354***
(0.036)
0.273***
(0.030)
0.268***
(0.055)
0.311***
(0.032)
0.205***
(0.035)
2003
3,664
0.700
0.413***
(0.025)
0.050**
(0.020)
0.984***
(0.072)
0.948***
(0.065)
0.917***
(0.061)
0.797***
(0.102)
0.963***
(0.070)
0.628***
(0.062)
2006
3,324
0.762
0.438***
(0.024)
0.047***
(0.017)
1.008***
(0.063)
0.963***
(0.059)
0.956***
(0.058)
0.856***
(0.096)
0.975***
(0.051)
0.658***
(0.064)
2007
3,040
0.787
0.402***
(0.025)
0.050***
(0.017)
1.032***
(0.064)
0.983***
(0.066)
0.964***
(0.053)
0.932***
(0.104)
1.025***
(0.053)
0.753***
(0.051)
2008
2,809
0.788
0.393***
(0.021)
0.036**
(0.015)
1.024***
(0.058)
0.948***
(0.061)
0.966***
(0.051)
0.900***
(0.068)
1.008***
(0.047)
0.796***
(0.051)
2009
This table presents regressions that test the validity of the use of the disappearance of Arthur Andersen as a shifter of audit firm supply.
The dependent variable in the regressions is the difference between the natural logarithm of total audit fees in 2001 and the natural
logarithm of audit fees in the relevant year. ln(Andersen0 s Share 2001) is the natural logarithm of the total assets in each four digit SIC
audited by Arthur Andersen in 2001. Robust standard errors clustered at the four-digit SIC level are in parentheses.
Table 2: Disappearance of Arthur Andersen
Table 3: Client mergers and acquisitions
This table presents ordinary least squares regressions that test the validity of using audit client
mergers and acquisitions as shifters of audit supply. The dependent variable in all four regressions
is the natural logarithm of total audit fees. Columns (1) and (3) include audit firm fixed-effects and
columns (3) and (4) include client-level fixed effects. All four regressions include year fixed-effects.
ln(M ergers) represents the exogenous shift in audit supply and demand arising from client-level
mergers and acquisitions. It is calculated at the four digit SIC level and is the natural logarithm of
total assets of clients that disappeared due to either mergers or acquisitions in the prior fiscal year.
Robust standard errors clustered at the client level are in parentheses.
Ln(Mergers)
Ln(Assets)
Receivables to Assets
Inventory to Assets
Return on Assets
Loss
Percent Foreign Sales
Ln(Segments)
Accelerated Filer
Going Concern Opinion
Constant
(1)
(2)
(3)
(4)
-0.017***
(0.002)
0.409***
(0.004)
-0.355***
(0.036)
0.592***
(0.049)
-0.537***
(0.025)
0.081***
(0.014)
0.395***
(0.017)
0.195***
(0.009)
0.169***
(0.017)
0.082***
(0.019)
9.902***
(0.031)
-0.013***
(0.002)
0.454***
(0.004)
-0.695***
(0.039)
0.637***
(0.051)
-0.555***
(0.027)
0.097***
(0.014)
0.447***
(0.017)
0.216***
(0.009)
0.328***
(0.018)
0.032
(0.020)
9.393***
(0.025)
-0.003***
(0.001)
0.248***
(0.008)
0.236***
(0.043)
0.150**
(0.072)
-0.247***
(0.019)
0.033***
(0.007)
0.025
(0.016)
0.029***
(0.007)
0.046***
(0.010)
0.043***
(0.013)
10.956***
(0.046)
-0.002**
(0.001)
0.261***
(0.008)
0.232***
(0.044)
0.131*
(0.073)
-0.262***
(0.019)
0.032***
(0.007)
0.030*
(0.017)
0.035***
(0.007)
0.045***
(0.010)
0.044***
(0.013)
10.748***
(0.044)
Observations
51,823
51,823
51,823
Adjusted R-squared
0.793
0.772
0.518
Firm fixed effects
No
No
Yes
Auditor fixed effects
Yes
No
Yes
Year fixed effects
Yes
Yes
Yes
Industry fixed effects
No
No
No
Number of firms
9,576
*** p<0.01, ** p<0.05, * p<0.1
23
51,823
0.502
Yes
No
Yes
No
9,576
Table 4: Demand estimation
This table presents annual conditional logit estimates of demand. E&Y, Deloitte, KPMG, and PwC
are auditor brand fixed-effects. Ln(Total assets) is the natural logarithm of the client’s total assets.
Ln(Years client) is the natural logarithm of the number of years that the firm was a client of the
audit firm and 1(Not client) is an indicator variable coded as 1 if the firm was not a client of the
audit firm, and 0 otherwise. Standard errors are in parentheses.
E&Y
E&Y * Ln(Total assets)
E&Y * Ln(Years client)
E&Y * 1(Not client)
Deloitte
2003
2004
2005
2006
2007
2008
2009
0.433
-0.799***
-1.294***
-1.058***
0.714
0.781*
0.377
(0.275)
(0.280)
(0.350)
(0.348)
(0.449)
(0.427)
(0.491)
0.570***
0.563***
0.671***
0.530***
0.438***
0.325***
0.536***
(0.042)
(0.042)
(0.038)
(0.043)
(0.054)
(0.052)
(0.062)
0.191
0.339***
0.451***
0.656***
0.282
0.418**
0.259
(0.121)
(0.112)
(0.157)
(0.141)
(0.191)
(0.166)
(0.205)
-5.089***
-4.726***
-4.154***
-4.091***
-5.896***
-5.186***
-6.125***
(0.247)
(0.267)
(0.318)
(0.278)
(0.400)
(0.354)
(0.457)
0.040
-0.783**
-1.028***
-1.488***
-0.592
-0.008
0.302
(0.310)
(0.371)
(0.339)
(0.395)
(0.457)
(0.480)
(0.506)
Deloitte * Ln(Total assets)
0.558***
0.646***
0.678***
0.582***
0.448***
0.394***
0.373***
(0.049)
(0.048)
(0.040)
(0.050)
(0.056)
(0.062)
(0.060)
Deloitte * Ln(Years client)
0.256**
0.307*
0.113
0.726***
0.509***
0.540***
0.532***
Deloitte * 1(Not client)
KPMG
KPMG * Ln(Total assets)
KPMG * Ln(Years client)
KPMG * 1(Not client)
PwC
PwC * Ln(Total assets)
PwC * Ln(Years client)
(0.128)
(0.166)
(0.142)
(0.153)
(0.165)
(0.175)
(0.198)
-5.231***
-4.752***
-4.710***
-4.515***
-4.775***
-5.319***
-5.154***
(0.270)
(0.324)
(0.300)
(0.294)
(0.349)
(0.382)
(0.417)
0.839***
-0.313
-1.917***
-0.071
-0.642
-0.478
1.089*
(0.312)
(0.333)
(0.325)
(0.407)
(0.441)
(0.540)
(0.611)
0.527***
0.599***
0.715***
0.465***
0.430***
0.460***
0.326***
(0.047)
(0.046)
(0.038)
(0.047)
(0.056)
(0.060)
(0.064)
0.108
0.206
0.536***
0.297**
0.744***
0.670***
0.416*
(0.138)
(0.144)
(0.141)
(0.143)
(0.166)
(0.202)
(0.223)
-5.630***
-5.222***
-3.823***
-5.146***
-4.964***
-5.017***
-6.085***
(0.500)
(0.287)
(0.308)
(0.276)
(0.313)
(0.340)
(0.421)
-0.087
-0.621*
-2.226***
-1.822***
-0.291
0.368
-0.354
(0.339)
(0.353)
(0.375)
(0.421)
(0.475)
(0.593)
(0.606)
0.624***
0.521***
0.819***
0.604***
0.396***
0.478***
0.483***
(0.049)
(0.047)
(0.044)
(0.048)
(0.057)
(0.067)
(0.068)
0.260
0.569***
0.321**
0.520***
0.526***
0.291
0.584***
(0.159)
(0.148)
(0.155)
(0.148)
(0.168)
(0.229)
(0.223)
PwC * 1(Not client)
-5.172***
-4.759***
-4.788***
-4.377***
-4.801***
-5.829***
-5.262***
(0.303)
(0.308)
(0.342)
(0.337)
(0.374)
(0.512)
(0.489)
Ln(Audit fees)
-1.362***
-0.980***
-1.343***
-1.157***
-1.274***
-1.338***
-1.434***
(0.130)
(0.110)
(0.099)
(0.105)
(0.139)
(0.155)
(0.165)
30,970
30,075
29,585
27,815
25,675
24,160
23,020
Observations
24
25
Panel B: Predicted
1 year
E&Y
0.9382
Deloitte 0.8263
KPMG 0.9075
PwC
0.8079
Median
0.0501
0.0200
0.0164
0.0240
Q3
0.0882
0.0280
0.0217
0.0414
90th
0.1166
0.0330
0.0240
0.0562
10 years
0.9645
0.9418
0.9624
0.9416
99th
0.1337
0.0333
0.0213
0.0734
client
9 years
0.9641
0.9387
0.9607
0.9382
95th
0.1269
0.0343
0.0241
0.0631
audit firm conditional on tenure as a
5 years 6 years 7 years 8 years
0.9584 0.9602 0.9617 0.9630
0.9180 0.9250 0.9305 0.9350
0.9504 0.9539 0.9566 0.9589
0.9150 0.9229 0.9291 0.9341
to client size
10th
Q1
0.0078 0.0205
0.0056 0.0108
0.0057 0.0100
0.0044 0.0160
Probabilities of choosing the
2 years 3 years 4 years
0.9478 0.9528 0.9560
0.8731 0.8951 0.9087
0.9290 0.9394 0.9458
0.8631 0.8887 0.9043
Panel A: Marginal effects with respect
Mean
1st
5th
E&Y
0.0467 0.0006 0.0035
Deloitte 0.0184 0.0010 0.0033
KPMG 0.0156 0.0013 0.0036
PwC
0.0220 0.0005 0.0022
This table presents marginal effects by Big 4 audit firm. Panel A presents marginal effects at various point in the distribution of client
size. Panel B presents the predicted probabilities of remaining a client of the audit firm at various tenures. The marginal effects and
predicted probabilities are based on the parameter estimates for 2009 and are calculated at the mean values of the other independent
variables.
Table 5: Marginal effects for firm size and auditor tenure
26
2005
−1.090
−1.152
−1.131
−1.118
−0.878
2006
−0.945
−0.994
−0.981
−0.978
−0.729
2007
−1.036
−1.101
−1.088
−1.087
−0.783
2008
−1.089
−1.159
−1.147
−1.137
−0.819
the prior year
2009
−0.0500
−0.0790
−0.0514
−0.0601
−0.0865
2009
−1.164
−1.243
−1.225
−1.220
−0.886
Panel B: Mean elasticities conditional on being a client of the audit firm in
2003
2004
2005
2006
2007
2008
E&Y
−0.0898 −0.1123 −0.1132 −0.0796 −0.0445 −0.0668
Deloitte −0.1004 −0.0694 −0.1361 −0.0905 −0.0930 −0.0809
KPMG −0.0765 −0.0766 −0.1379 −0.0809 −0.0872 −0.0696
PwC
−0.0773 −0.0793 −0.1432 −0.1112 −0.0869 −0.0499
Other
−0.1203 −0.0635 −0.2259 −0.0858 −0.0769 −0.0801
Panel A: Mean elasticities
2003
2004
E&Y
−1.068 −0.791
Deloitte −1.158 −0.837
KPMG −1.140 −0.828
PwC
−1.089 −0.797
Other
−0.993 −0.665
This table presents mean price elasticities for a one percent change in dollar audit fees by audit firm and year. Panel A presents mean
elasticities by audit firm for all clients. Panel B presents mean elasticities by audit firm conditional on being a client of the audit firm in
the prior year.
Table 6: Price elasticities
Table 7: Expected total changes in consumer surplus arising from the disappearance of a Big 4
audit firm
This table presents expected changes in consumer surplus if one of the Big 4 auditors disappeared.
We base these estimates on the Table 4 coefficient estimates for 2009. The expected total changes
are denominated in billions of US dollars. For the disappearance of each of the Big 4 audit firms, we
estimate the expected change in consumer surplus, Cijm , for each firm i. To do so, we draw vectors
of type 1 extreme value error terms—one for each of the Big 4 auditors and one for the outside
good. For each vector draw, we combine in equation (2) the parameter estimates from the demand
estimation along with the the firm-auditor characteristics and the error term draw to calculate the
utility that client would receive from choosing each of the Big 4 auditors and the outside good.
We then pick the audit firm that leads to maximum utility under this unrestricted choice set. We
next restrict the choice set for each client (i.e., remove one of the Big 4 auditors) and calculate the
maximum utility that the client would have received under the restricted choice set. Then, we solve
for the Cijm that equates the maximum utilities. For each client, we repeat this procedure 1,000
times and take the average of the required dollar transfer to create E[Cijm ]. For each counterfactual
we add up these estimates to calculate the expected total change in consumer surplus.
E&Y
Deloitte
KPMG
PwC
Expected total change in consumer surplus
−$1.76
−$1.48
−$1.52
−$1.85
27
Firm’s total fees in 2009
$2.37
$2.14
$1.96
$2.93
Table 8: Expected total changes in consumer surplus arising from the implementation of mandatory
audit firm rotation
The table presents expected changes in consumer surplus if mandatory audit firm rotation were to
be implemented after four through 10 years. Estimates are based on Table 4 coefficient estimates
for 2009 and are denominated in billions of US dollars. For the implementation of mandatory audit
firm rotation at various tenures, we estimate the expected change in consumer surplus, Cijm , for
each firm i. To do so, we draw vectors of type 1 extreme value error terms—one for each of the
Big 4 auditors and one for the outside good. For each vector draw, we combine in equation (2) the
parameter estimates from the demand estimation along with the the firm-auditor characteristics
and the error term draw to calculate the utility that client would receive from choosing each of the
Big 4 auditors and the outside good. We then pick the audit firm that leads to maximum utility
under this unrestricted choice set. We next restrict the choice set for each client (i.e., remove the
client’s audit firm based on tenure) and calculate the maximum utility that the client would have
received under the restricted choice set. Then, we solve for the Cijm that equates the maximum
utilities. For each client, we repeat this procedure 1,000 times and take the average of the required
dollar transfer to create E[Cijm ]. For each counterfactual we add up these estimates to calculate
the expected total change in consumer surplus.
Mandatory rotation
4 years
5 years
6 years
7 years
8 years
9 years
10 years
Expected change in consumer surplus
−$5.60
−$5.35
−$5.21
−$4.37
−$4.02
−$3.71
−$3.47
28