Journal of accounting, auditing finance tập 27, số 03, 2012 7

Reexamining the Relationship
Between Audit and Nonaudit
Fees: Dealing With Weak
Instruments in Two-Stage
Least Squares Estimation

Journal of Accounting,
Auditing & Finance
27(3) 299–324
Ó The Author(s) 2012
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DOI: 10.1177/0148558X11409154


Lilian Chan1, Tai-Yuan Chen2, Surya Janakiraman3, and
Suresh Radhakrishnan3

Abstract
The authors introduce some new econometric tests and techniques for identifying
and overcoming the problem of weak instruments in the context of joint provision of
audit and nonaudit fees. The authors use this context because identifying appropriate
instruments is difficult due to the lack of theoretical guidance as well as due to the difficulty in intuitively identifying instruments that satisfy the econometric requirements. The
authors introduce a battery of empirical tests based on recent developments in econometrics to test for the appropriateness of the instruments. The authors then illustrate
two approaches of using instruments from existing data: the size industry average portfolio approach and the synthetic-instrument approach. Although the approach using
synthetic instruments sidesteps issues of identifying proxies with desirable properties, it
requires some stringent assumptions that cannot be directly tested. However, as a
methodological alternative, this approach can be used for robustness tests. The authors
find that when the instruments are not weak, audit and nonaudit fees are positively
associated. This relationship holds for audit and tax-related nonaudit fees as well. Overall,

the evidence suggests the existence of economies of scope benefits from the joint
supply of audit and nonaudit services. Methodologically, the authors illustrate the importance of testing the appropriateness of the instruments utilized when accounting for
endogeneity.
Keywords
audit fees, nonaudit fees, instruments, two-stage least squares estimation

1

University of Hong Kong, Hong Kong
Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong
3
University of Texas at Dallas, USA
2

Corresponding Author:
Suresh Radhakrishnan, School of Management, SM41, The University of Texas at Dallas, Richardson, TX 75083,
USA
Email:

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A number of studies show a positive association between audit and nonaudit fees, suggesting that knowledge spillovers occur from one service to the other (see, for example, AbdelKhalik, 1990; Bell, Landsman, & Shackelford, 2001; Davis, Ricchiute, & Trompeter, 1993;
DeBerg, Kaplan, & Pany, 1991; Hay, Knechel, & Wongm, 2006; Palmrose, 1986; Simunic,
1984). These studies use the ordinary least squares (OLS) procedure to estimate the association between audit and nonaudit fees. However, Whisenant, Sankaraguruswamy, and
Raghunandan (2003) consider the joint determination of audit and nonaudit fees using the

two-stage least squares (2SLS) procedure and show no association between audit and nonaudit fees. In this study, we reexamine the association of audit and nonaudit fees and reconcile the ‘‘seemingly’’ conflicting results.
Reconciling the conflicting results on the existence of knowledge spillover effects
between audit and nonaudit services is important both for gaining theoretical insights as
well as guiding policy on the provision of nonaudit services. On the theoretical front,
Simunic (1980) considers an analytical model of joint provision of audit and nonaudit services and shows that audit and nonaudit fees should be positively associated when there are
economies of scope, that is, knowledge spillovers.1 The intuition is that with economies of
scope providing audit and nonaudit services, only some of the savings of auditor’s costs
will be passed onto clients. This in turn will enhance the profitability of both segments of
the auditor’s business.2 The empirical audit- and nonaudit-fee models relate the auditors’
supply of effort to the fees. Based on the knowledge spillover hypothesis, in the audit-fee
models, a positive association between audit and nonaudit fees would imply the existence
of a spillover effect, and no association would imply that the audit and nonaudit efforts are
independent and as such imply no knowledge spillover effects. Accordingly, Whisenant
et al. (2003) finding of no association between audit and nonaudit fees lead them to conclude that,
The findings are not consistent with the existence of economies of scope for the joint
performance of audit and non-audit services. Given the ongoing debate over the
level of allowed non-audit services by auditors, the argument for joint provision of
audit and non-audit services is less justified than if the joint-supply benefits had been
documented (p. 722).
In other words, if there are no benefits to the supply of nonaudit services, but only
potential costs in terms of lower audit quality due to loss of audit independence, then limiting the nonaudit services would be a reasonable policy.3 Thus, reconciling the seemingly
conflicting findings of the association between audit and nonaudit services is important.
Reconciling the conflicting results is also important in light of the recent developments
with respect to nonaudit services.4 Although nonaudit fees from management advisory services have been curtailed since 2002, recently the Public Company Accounting Oversight
Board (PCAOB) has initiated efforts to curtail auditors of public companies from supplying
certain types of nonaudit tax services. Reacting to the extensive media coverage and congressional actions pertaining to tax shelters promoted by auditors for their public company
clients, the PCAOB conducted a roundtable in July 2004 and stated that ‘‘the Board has
determined that it is appropriate to consider the impact of tax services on auditor independence’’ (see PCAOB, 2004a). In December 2004, the PCAOB (2004b) proposed rules to
curb certain types of nonaudit tax services for their public company clients.5 To summarize,
although knowledge spillover is the benefit, loss of auditor independence is the cost of

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providing nonaudit services. It is therefore important to document whether there is a knowledge spillover benefit at all.
Audit and nonaudit services/fees are jointly determined because factors such as agency
cost, complexity, size, risk, performance, and auditor characteristics influence the demand
for both (see Whisenant et al., 2003). It is well known that when audit and nonaudit fees
are jointly determined, using the OLS procedure leads to inconsistent/biased coefficient
estimates (Wooldridge, 2002). Accordingly, 2SLS procedure should be used. Recent developments in econometrics show that using weak instruments in 2SLS can lead to inappropriate conclusions (see Ebbes, Wedel, & Bockenholt, 2009, for an excellent summary). As
such, in the context of joint provision of audit and nonaudit fees, we reconcile the mixed
findings by assessing the appropriateness of instruments, that is, whether the instruments
are weak.
We estimate the audit- and nonaudit-fee model using 2SLS with the instruments used in
prior research, that is, reporting lag and new financing activity for audit and nonaudit fees,
respectively. We do this for three separate periods: 2000, 2001, and 2002 to 2006. We consider year 2000 separately so as to provide a benchmark of our sample with that of prior
research that also considers the same year. We consider 2002 onward separately because of
the auditor reforms that went into effect from 2002. We find that audit and nonaudit fees
are not associated with each other, that is, the findings in prior research that use 2SLS are
robust for each period. However, the tests on the strength of the two instruments reveal that
the instruments are ‘‘weak.’’
We thus consider additional instruments to examine the joint determination of audit and
nonaudit fees with 2SLS. We use the industry average audit and nonaudit fees as additional
instruments for audit and nonaudit fees, respectively. There is a rich tradition of using
industry averages as instruments in the financial economics literature: for instance, Lev and
Sougiannis (1996), Bertrand and Mullainathan (2001), Murphy (2000), Hanlon, Rajagopal,

and Shevlin (2003). In particular, we use the mean/median of the 10 closest firms in terms
of total assets operating in the same Fama–French industry group as the instrument. We
show that these instruments are not weak, and with these instruments, audit and nonaudit
fees are positively associated with each other. This suggests that knowledge spillover
effects between audit and nonaudit services exist, that is, there are benefits to the joint provision of audit and nonaudit services. Although our research design does not consider the
cost of such provision of joint services in terms of conflicts of interests and poor accounting quality, our results suggest that the benefits should be compared with the costs in arriving at policy decisions. In other words, it is not the case that there are no benefits and only
costs of allowing such joint provision of audit and audit-related services.
We also consider synthetic instruments as additional instruments for audit and nonaudit
fees—synthetic instruments are instruments derived from the transformation of endogenous
and exogenous variables, that is, the instruments are synthetically derived (see Lewbell,
1997). We do this because even though there is a rich tradition of using industry averages
as instruments in the financial economics literature, recently Larcker and Rusticus (2010)
argue that such methods may not be appropriate.6 It is widely recognized in the econometrics literature that finding suitable instruments may be difficult if not impossible; thus,
creating such synthetic instruments are important for obtaining consistent and efficient estimates. Ebbes et al. (2009) and Lewbell (1997) show that candidates for synthetic instruments are (a) the product of the endogenous and exogenous variables and (b) the second
moment of the endogenous variables. We consider additional synthetic instruments to show
that if instruments are weak then we again obtain the result of no association between audit

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and nonaudit fee. We find that for the calendar year when the synthetic instruments based
on the product of the exogenous and endogenous variables are weak, the positive association between the audit and nonaudit fee is also not statistically significant. When we consider the second moment of the endogenous variables as additional instruments, the
instruments are not weak and the audit and nonaudit fees are positively associated. This
provides indirect evidence on the importance of considering instruments that are not weak
in assessing the relationship between audit and nonaudit services.
Finally, we examine the relationship between audit fees and tax-related nonaudit fees by

considering the industry average–based instruments for these endogenous variables for the
period of 2002 to 2006. We find that audit and tax-related nonaudit fees are positively associated. This shows the existence of knowledge spillover effects across audit and tax services. As discussed earlier, the PCAOB is considering the relationship between the
nonaudit, tax service, and audit independence. Kinney, Palmrose, and Scholz (2004) use
accounting restatements as a proxy for audit quality and show that the provision of nonaudit services is not positively related to accounting restatements. Although our research
design/test does not provide evidence on the relationship between the joint provision of
audit and tax-related services, and auditor independence/quality, our evidence provides
insights into whether there are economies of scope in the provision of such services.
Overall, our objective is to introduce some new econometric techniques using the context of joint provision of audit and nonaudit fees. We use the ‘‘joint provision of audit and
nonaudit’’ service setting because identifying appropriate instruments is difficult due to the
lack of theoretical guidance as well as intuitively identifying instruments that satisfy the
econometric requirements. We use a battery of empirical tests, developed recently in the
econometric literature, to test for the appropriateness of the instruments. We then illustrate
two approaches of using instruments from data that are already available: the industry average approach, which has been used in previous research, and the synthetic instrument
approach. Although the approach using synthetic instruments sidesteps issues of identifying
proxies with desirable properties, it requires some stringent assumptions that cannot be
directly tested.7 However, as a methodological alternative, this approach can be used for
robustness tests. More importantly, we use this approach to demonstrate the importance of
identifying weak instruments.
The rest of the article is organized as follows: Section titled ‘‘Summary of Econometric
Issues with Instruments’’ provides a summary of the econometric issues with weak instruments, section titled ‘‘Empirical Analysis’’ presents the empirical analysis, and section
titled ‘‘Concluding Remarks’’ contains some concluding remarks.

Summary of Econometric Issues With Instruments
In this section, we summarize the issues with instrumental variable (IV) methods drawing
on literature from statistics and econometrics. To highlight the issues with IV methods,
consider the following equation
y5a0 1a1 x1v;

ð1Þ

where y is the dependant variable, x is the explanatory variable, and v is the structural error
term. If y is the audit fee and x is the nonaudit fee, and audit and nonaudit fees are jointly
determined, then the nonaudit fee and the structural error are potentially correlated: the
explanatory variable x is not independent of the structural error term v. It is well known

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that estimating Equation 1 using OLS leads to an inconsistent estimate of a1. One approach
to mitigate this problem is to choose an IV, z, that is not correlated with the structural error
term, v, and is correlated with the explanatory variable, x. The 2SLS uses the IV approach.8
In the first step, the endogenous variable x is regressed on an instrument z as follows:
x5b0 1b1 z1u:

ð2Þ

In the second stage, Equation 1 is estimated with x being replaced by the predicted
value of the explanatory variable from Equation 2, x^ The probability limit (plim) of the
estimator is given by (see Wooldridge, 2002) plimð^
a1 Þ5a1 1½covðz; vÞ=covðx; zފ where
cov(a, b) is the covariance of a and b. It follows that if the instrument z is correlated with x
but not with v then the second term converges to zero for sufficiently large samples. In
other words, we can obtain consistent estimates of a1, if cov(z, v) is close to zero and
cov(x, z) is nonzero and sufficiently large. Correspondingly, an inappropriate instrument
would have large cov(z, v) and/or sufficiently small cov(x, z), and such weak instruments
will not provide consistent estimates. The probability limit of the coefficient estimate provides the basis for establishing the appropriateness of the instruments. For this purpose,

recently, various tests have been developed in the econometrics literature to validate the
appropriateness of the instruments. We provide a brief discussion of these tests.

Relevance of Instruments
Partial R2. The bias introduced in the estimate using the 2SLS procedure depends on the
covariance of the IV and the endogenous variable (see Equation 1). Specifically, Larcker
and Rusticus (2007) show that the IV method is valid only if the following inequality is
satisfied: R2zv\R2xz Á R2xv , where R2ij is the squared population correlation between variables i
and j. It follows that a necessary condition for good instruments is R2xz should be sufficiently large. The R2 obtained from the regression of the endogenous variable x on the IV z
provides a measure of the potential improvement that the IV method provides over the
OLS procedure in correcting the bias and is called partial R2. In the case of one endogenous
variable and one instrument, the corresponding measure is the correlation coefficient. In
the case of a multivariate version of Equation 1 with many exogenous variables, the corresponding measure is the partial R2. It follows that if the partial R2 is small, then the instruments are not appropriate.9
Partial F test. Estimates based on the 2SLS procedure are likely to have larger standard
errors than estimates obtained from the OLS procedure (Bartels, 1991). The asymptotic
standard error of the estimates obtained from the 2SLS procedure is greater than that
obtained from the OLS procedure: the difference in the asymptotic standard error increases
with decreases in the correlation between the endogenous variable x and the instrument z.
In other words, as the correlation between x and z approaches zero, the standard error using
the 2SLS procedure approaches infinity.10 To see this, consider the following equation in
place of Equation 1: y5ao 1a1 x1 1a2 x2 1 . . . 1ak xk 1u, where xk is the endogenous variable. Let a
^ to be the vector of 2SLS estimators using instruments Z. The asymptotic var^ k , where SSR
^ k is the sum of
iance (Avar) of the 2SLS estimator is Avarð^
aÞ’ s2 =SSR
residuals of the first-stage regression, that is, the regression of the endogenous variable on
^ k 5SST
^ k ð1 À R^2 Þ where
all exogenous variables (Wooldridge, 2002). The denominator SSR
k

2
2
^ k is the total sum of squares of x^k and R^ is the R of the regression of the predicted
SST
k
value of the endogenous variable x^k on the exogenous variables in the second stage. It

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follows that if (1 À R^2k ) is small, Avar can be very high (Wooldridge, 2002). Simply put, if
the endogenous variable is only weakly associated with the instruments over and above the
^ k is small leading to higher standard errors in the
other exogenous variables, then SST
second-stage regression. Weak instruments lead to small (1 À R^2k ) and, most importantly, a
nonzero correlation between the endogenous variable, and the instruments alone is not sufficient to ensure that (1 À R^2k ) is not small. The partial correlation in the first-stage regression
between the endogenous variable and the IV, that is, the correlation between the endogenous
variable and the instruments, after accounting for the correlation between the endogenous
variable and all other exogenous variables in the model needs to be sufficiently large. Thus,
good instruments need to have a sufficiently large partial F statistic in the first-stage regression: the partial F statistic measures the strength of the correlation between the endogenous
variable and the instruments over and above that of all other exogenous variables.
The partial R2 and partial F tests do not provide an indication of how much correlation
is good enough. Although Staiger and Stock (1997) provide F values that are considered
desirable for different sizes of finite samples, recently there have been various test statistics
developed for validating the appropriateness of the instruments. These tests are described
briefly below.

Underidentification Test
The underidentification test provides a canonical correlation version of the partial R2 and F
statistic tests. That is, the endogenous variable x must be correlated with the IV z, when
there are more than one endogenous and IVs. The canonical correlations represent the correlations between the endogenous variable x and linear combinations of z. The squared
canonical correlations with multiple endogenous variables and instruments are calculated as
the eigenvalues, and the underidentification test requires that all canonical correlations are
different from zero. Conversely, if one or more of the canonical correlations is zero, then
the model is underidentified. For the case where the errors are independent and identically
distributed (i.i.d.), the Anderson’s (1951) canonical correlation LM statistic is computed.
For the case where the errors are non-i.i.d., Kleibergen and Paap (2006) propose a robust
error correction for the Anderson’s statistic. A failure to reject the null of zero correlation
indicates that the model is underidentified.

Weak Identification Tests
When the correlation between the endogenous variable and the IV is nonzero but small, the
weak instrument problem arises (see discussion above). Staiger and Stock (1997) show that
for large samples, the weak instrument problem can arise even when the correlation
between x and z is significant at conventional levels of 5% and 1%. Stock and Yogo (2005)
develop an F statistic based on the Cragg and Donald (1993) F statistic for i.i.d. errors, and
Kleibergen and Paap (2006) extend this, if the i.i.d. assumption is violated. The test statistic
is based on the rejection rate of various percentages, if the true rejection rate is 5%. Stock–
Yogo’s critical values are available for a range of the number of endogenous variables and
instruments. If the computed F statistic is below the critical value, then the instruments are
weak. In our reported results, we use the rejection rate of 20%.

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Weak Identification Robust Inference Tests
The Anderson and Rubin (1949) test is used by substituting the relationship between the
endogenous variable and the IV from Equation 2 in Equation 1. Thus, Equation 1 is estimated in its reduced form, and if the test fails to reject that the coefficient estimate on the
IV is zero, then the instrument is likely to be weak. The idea with this test is that as the
instruments become weak, the relationship between the endogenous variable and the IV
must be weak, and thus, the relationship between the IV and dependant variable must also
be weak. The beauty of this test is that it is robust to implicit weakness of the instruments.
The Anderson and Rubin F statistic and the Stock and Wright (2000) S statistic provide
tests for the weak identification tests, when errors are non-i.i.d.

Overidentifying Restrictions Test
In choosing instruments, we need to be reasonably assured that the covariance of the IV z
with the structural error term v in Equation 1 is zero. In general, demonstrating this is difficult because the structural error term is unobservable. When the Generalized Method of
Moments (GMM) estimation is used, the Hansen’s J test can be used. The null hypothesis
is that the instruments are not correlated with the structural error term in the second-stage
regression. That is, rejection of the null hypothesis provides evidence that the instruments
are correlated with the error term. In general, for large samples this test would lead to
rejection of the null hypothesis (see Larcker & Rusticus, 2007).

The Hausman Test
Hausman (1978) provides a formal test to assess whether the OLS estimates are significantly different from the 2SLS estimates: the Hausman test. The Hausman test is a test for
the difference in OLS and 2SLS coefficients under the maintained assumption that the
instruments are not weak. From the discussion of the partial R2 and partial F statistic
above, it follows that the Hausman test could reject the null or no joint determination of
the endogenous variables if the instruments are weak. Thus, the Hausman test should be
conducted only if the instruments are not weak (also see Larcker & Rusticus, 2007).
In summary, we compute the following test statistics when we use the 2SLS estimation:

(a) the partial R2, (b) the partial F statistic, (c) Anderson’s canonical correlation LM statistic for underidentification, (d) Cragg and Donald’s (1993) Wald F statistic for weak identification, (e) Anderson–Rubin F statistic and Stock and Wright’s S statistic for weak
instrument robust inference, and (f) Hansen’s J statistic for the overidentification. We use
the GMM estimation when we consider additional instruments: We substitute the
Kleibergen and Paap’s (2006) rk LM statistic and F statistic for Anderson’s canonical correlation LM statistic and Cragg and Donald F statistic, respectively (see Stock & Wright,
2000; Stock, Wright, & Yogo, 2002).

Empirical Analysis
Following Whisenant et al. (2003), we consider estimate Equations 3 and 4: These models
draw on a rich literature on the determinants of audit fees.11

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Empirical Model
LogðAudit feeÞ5a1a1 LogðNonAudit feeÞ1aD 9 Determinants1e;

ð3Þ

LogðNonaudit feeÞ5b1b1 LogðAudit feeÞ1bD 9 Determinants1e;

ð4Þ

where Log(Audit fee) is the natural logarithm of fees paid to the auditor for audit and auditrelated services, and Log(Nonaudit fee) is the natural logarithm of fees paid to the auditor
for nonaudit services (fee data are obtained from Audit Analytics databases). Lag is the
number of days between current fiscal year-end and earnings announcement date
(Compustat report date of quarterly earnings). New Finance is an indicator variable that

equals one if the firm issues equity (Compustat Item 108 . US$10 million) or long-term
debt (Compustat Item 111 . US$1 million) in either the current or subsequent fiscal year
and is zero otherwise. Assets is the natural logarithm of total assets (Compustat Item 6).
Segments is the square root of the number of segments (Compustat Segment database).
Employees is the square root of the number of employees (Compustat Item 29). DA ratio is
total debt (Compustat Item 181) divided by total assets (Compustat Item 6). Liquidity is the
ratio of current assets (Compustat Item 4) divided by current liabilities (Compustat Item 5).
Inventory and AR turnover is inventory (Compustat Item 3) plus accounts receivable
(Compustat Item 2), divided by total assets (Compustat Item 6). ROA is return on assets
defined as operating income (Compustat Item 178) divided by total assets (Compustat Item
6). Institutional ownership is the percentage of institutional holdings at the beginning of the
year. Initial is an indicator variable that equals one if the auditor has been the firm’s auditor
for less than 2 years (Compustat Item 149) and is zero otherwise. BIG5 is an indicator variable that equals one when the auditor is a member of the Big 5, and zero otherwise.
Foreign Operations is an indicator variable that equals one if the firm has foreign operations as indicated by foreign currency adjustments to income (Compustat Item 150) and is
zero otherwise. Loss is an indicator variable that equals one if the firm reported negative
net income (Compustat Item 172) in either of the two previous years and is zero otherwise.
Sales growth is the growth rate in sales (Compustat Item 12) compared with the previous
year. Volatility is variance of the residual from the market model over the current fiscal
year. Opinion is an indicator variable that equals one if the firm received a modified goingconcern audit opinion in either the current or previous fiscal year (Audit Analytics) and
equal to zero otherwise. Employee plans is an indicator variable that equals one if the
firm’s pension or postretirement plan assets or cost is greater than US$1 million and is zero
otherwise. Book to market is the book-to-market ratio at the beginning of the year.
Discontinued operations is an indicator variable that equals one if the firm reports extraordinary items or discontinued operations (Compustat Item 48) and is zero otherwise.
Distress probability is the 1-year change in Zimjewski’s (1984) probability of bankruptcy
score. Stock return is the raw return for the fiscal year. Restate is an indicator variable that
is one if net income or assets were restated and zero otherwise (data obtained from
Government Accountability Office [GAO] list of restatements’’).
Based on the knowledge spillover, we expect that a1 and b1 in Equations 3 and 4 will
be positive, and based on Whisenant et al.’s (2003) results of no knowledge spillover
across audit and nonaudit fees, we expect a1 and b1 to be statistically no different from

zero (the null hypothesis). Note that if only a1 (b1) is positive then theoretically speaking,

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if we have the ‘‘correct and complete’’ model, the knowledge spillover is only from nonaudit to audit (audit to nonaudit). This of course is a conclusion of tall order to draw from
our empirical analysis.
The instruments are Lag for audit fee and New Finance for nonaudit fee. As discussed
in the previous section, the instruments Lag and New Finance should be correlated with
audit and nonaudit fees, respectively, and should not be correlated with the structural error
term in the audit and nonaudit fee models, respectively.12

Sample and Initial Results
The sample contains all firms not in the financial services industry with data available in
Compustat and Center for Research in Security Prices for fiscal years 2000 to 2006. We
stop at 2006 because the instrument New Finance requires 1-year-ahead data. The audit
and nonaudit fees data are from Audit Analytics. We consider three subsamples: year 2000,
year 2001, and years 2002 to 2006. In particular, we consider year 2000 separately to provide a benchmark for comparing our results with those of prior research. We consider 2002
to 2006 together because there were regulatory changes involving nonaudit fees in 2002
(see Sarbanes-Oxley Act [SOX] of 2002 and Securities and Exchange Commission Release
No. 33-8183).13 As such, year 2001 is also considered separately. There are 2,768; 3,812;
and 20,173 observations for the subsamples 2000, 2001, and 2002 to 2006, respectively.
Table 1, Panel A provides the descriptive statistics for the three subsamples. Compared
with the prior research that is typically based on hand collected data, the companies in our
sample pay lower audit and nonaudit fees in 2000. This could be due to Audit Analytics
coverage of many smaller firms compared with the sample of earlier studies. The mean

audit fee increases from about US$0.5 million in 2001 to about US$1.2 million in 2005;
the median shows a similar substantial increase. This suggests that the SOX requirements
have substantially increased audit fees in the later years of our sample. Correspondingly,
the nonaudit fees have substantially decreased. The audit fees have increased over time,
whereas the nonaudit fees have decreased reflecting changes in the regulatory environment.
It is also interesting to note that even though the sample of firms covered in Audit
Analytics has increased over time, the fundamental firm characteristics are roughly stable,
that is, the mean and median total assets, lag, segments, employees, debt to asset ratio,
liquidity, turnover ratios, and institutional ownership are similar over the years, whereas
profitability, growth, and financial distress measures exhibit macroeconomy-wide trends.
Table 2 contains the estimation of Equations 3 and 4. Panel A reports the results of the
OLS estimation: similar to prior research, we find that the coefficients of Log(Audit fee)
and Log(Nonaudit fee) are positive and significant, suggesting the presence of knowledge
spillover effects. Although statistically speaking the results are qualitatively similar to
those of prior research, compared with Whisenant et al. (2003), in our 2000 sample, for
Equation 3 the coefficient estimate is a little more than twice as large; these differences are
clearly attributable to differences in the sample.
Table 2, Panel B reports the results of using 2SLS estimation for Equations 3 and 4. For
the 2002-to-2006 sample, we use the robust standard errors to compute the t statistic, with
Fama–French 48 industry groups as the cluster.14 Here again, as with the discussion of
Table 2, Panel A above, the results for year 2000 are qualitatively similar to those of prior
research. Most importantly, the OLS results and the 2SLS results together are consistent
with the conclusion that audit and nonaudit fees are not associated when we consider their
joint determination. This conclusion extends to the later years: 2001 and 2002 to 2006.

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M

Median

Fee variables
Audit fees
458,519
148,000
Nonaudit fees
1,027,149
124,000
Log(Audit fees)
11.7471
11.9050
Log(Nonaudit fees)
10.8211
11.7280
Audit-related fees
69,718
0
IT fees
141,872
0
Benefit fees
1,943
0
Other fees
768,957

96,000
Continuous determinants of audit and nonaudit fees
Ln(total assets)
5.5019
5.4801
Lag
53.40
46.00
Sqrt(segments)
1.1894
1.0000
Sqrt(employees)
1.3784
0.7064
Debt to asset ratio
0.5441
0.5378
Liquidity
2.3885
1.2693
Inventory & AR turnover
0.2806
0.2162
ROA
20.2042
0.0223
Institutional ownership
0.3285
0.2750
Sales growth

0.4491
0.1195
Volatility
0.0473
0.0399
Book to market
0.2823
0.3839
Distress probability
20.0030
0.0000
Stock Return
20.0966
20.1457

Variables

Year = 2000

Table 1. Sample Descriptive Statistics by Year

461,889
958,129
11.8530
10.7505
146,974
106,964
13,381
522,096
5.3171

54.98
1.2124
1.4387
0.5701
2.2088
0.2826
20.3584
0.3386
0.0724
0.0392
0.3526
0.0382
0.0864

2.2724
32.46
0.3984
1.9388
0.3515
3.8302
0.2500
0.6098
0.2659
1.6745
0.0299
1.0278
0.2872
0.7262

M

1,570,272
4,366,506
2.2716
4.0000
551,064
1,482,143
84,257
3,367,652

SD

5.3485
46.00
1.0000
0.7032
0.5303
1.2985
0.2262
0.0184
0.2911
0.00885
0.0327
0.4928
0.0000
0.0194

153,225
101,000
11.9397

11.5229
0
0
0
49,000

Median

Year = 2001

2.4016
38.02
0.4152
2.0746
0.4586
3.2757
0.2477
0.9895
0.2780
0.7913
0.0269
1.7003
0.2725
0.7905

1,405,892
4,151,136
1.9514
3.8989
866,296

1,427,372
392,877
2,439,960

SD

5.3234
69.10
1.2360
1.5601
0.8335
2.1667
0.2567
20.1134
0.3738
0.0876
0.0268
20.8743
20.0082
0.1656

1,191,363
523,539
12.3656
9.9360
195,412
6,939
1,119
97,402

M

2.9206
57.27
0.4339
2.2980
1.9668
3.6536
0.2455
3.1607
0.3150
0.8843
0.0224
5.9135
0.2411
1.2482

255,837
59,565
12.4523
10.9948
6,500
0
0
0

Median

SD

(continued)

5.5878
58.00
1.0000
0.7308
0.5372
1.2493
0.1857
0.0249
0.3168
0.0514
0.0211
0.3436
0.0000
0.0414

3,953,775
2,268,502
2.2159
4.2076
1,001,379
378,590
43,670
926,998

Years = 2002 to 2006


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M

Median

Year = 2000

0.3755
0.3211
0.4966
0.2478
0.3654
0.4323
0.3771
0.3971
0.0847

SD

Note: AR = accounts receivable; IT = income tax; ROA = return on assets.

Categorical determinants of audit and nonaudit fees
Initial
0.1698
NR
BIG5
0.8833
NR

Loss
0.4417
NR
Opinion
0.0657
NR
Employee plans
0.1587
NR
Discontinued operations
0.2488
NR
New finance
0.1716
NR
Foreign operations
0.1961
NR
Restate
0.0072
NR

Variables

Table 1. (continued)

0.1658
0.8583
0.4249
0.0931

0.1504
0.2744
0.1431
0.2051
0.0157

M
NR
NR
NR
NR
NR
NR
NR
NR
NR

Median

Year = 2001

0.3719
0.3488
0.4944
0.2905
0.3575
0.4462
0.3502
0.4038
0.1242

SD

0.2667
0.7194
0.4480
0.1296
0.1668
0.2657
0.2326
0.2731
0.0224

M

NR
NR
NR
NR
NR
NR
NR
NR
NR

Median

Years = 2002 to 2006

0.4422

0.4493
0.4973
0.3359
0.3728
0.4417
0.4225
0.4456
0.1479

SD


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2001

2002 to 2006

2000

2001

2002 to 2006

Equation 4 Dependant variable = Log(Nonaudit fees)

Note: AR = accounts receivable; ROA = return on assets.
Significance level of coefficients is indicated by * for p \ .05, ** for p \ .01, and *** for p \ .001.

a
Estimation includes year-fixed effects that have not been tabulated.

Test variables
Log(Nonaudit fees)
0.3501*** (34.77)
0.1795*** (26.83)
0.0895*** (38.33)
Log(Audit fees)
0.8684*** (34.50)
0.8890*** (26.62)
0.7519*** (37.74)
Other variables
Lag
0.0063*** (4.46)
0.0027** (3.13)
0.0016*** (7.31)
New Finance
0.0353 (0.23)
20.0547 (–0.43)
0.0725 (1.16)
Assets
0.1705*** (5.53)
0.2827*** (15.74)
0.3780*** (55.89)
0.5590*** (11.93)
0.4591*** (11.44)
0.3283*** (15.51)
Segments
0.1910** (2.67)

0.1044** (2.58)
0.1403*** (9.25)
20.0335 (–0.30)
20.0589 (–0.65)
20.0527 (–1.18)
Employees
0.0432* (2.12)
0.0480*** (4.37)
0.0451*** (11.37)
20.0653* (–2.03)
20.0160 (–0.65)
20.0041 (–0.35)
DA ratio
0.0478 (0.36)
20.1739* (–2.53)
20.0611* (–2.47)
20.9757*** (–4.83)
20.2058 (–1.36)
20.1883** (–2.61)
Liquidity
20.0310*** (–3.62)
20.0219*** (–3.74)
20.0199*** (–8.42)
0.0086 (0.63)
0.0155 (1.18)
20.0027 (–0.39)
Inventory and AR turnover
0.4251* (2.51)
0.3973*** (4.05)
0.3604*** (8.97)

0.4133 (1.54)
0.3859 (1.75)
0.9083*** (7.71)
ROA
20.2024 (–1.59)
0.0132 (0.21)
20.3383*** (–12.36)
20.4042* (–2.01)
20.6579*** (–4.71)
20.0702 (–0.87)
Institutional ownership
0.0107 (0.08)
0.0128 (0.19)
0.3887*** (15.97)
0.5120* (2.55)
0.6041*** (4.11)
0.1759* (2.48)
Initial
0.0724 (0.82)
0.0977* (1.98)
0.0462** (2.64)
20.4010** (–2.89)
20.4830*** (–4.37)
20.5579*** (–10.92)
BIG5
20.0101 (–0.09)
20.0032 (–0.05)
0.2883*** (13.96)
0.5253** (3.16)
0.9732*** (7.39)

0.1943** (3.21)
Foreign operations
0.0709 (0.83)
0.1653*** (3.44)
0.1472*** (9.37)
20.0552 (–0.41)
0.1416 (1.31)
0.0869 (1.89)
Loss
20.0104 (–0.15)
0.1224** (2.93)
0.2152*** (13.57)
0.0779 (0.69)
0.0288 (0.31)
0.0801 (1.72)
Sales growth
0.0032 (0.18)
20.0541* (–2.25)
20.0139 (–1.36)
20.0421 (–1.47)
0.1140* (2.11)
20.0017 (–0.06)
Volatility
20.3182 (–0.21)
2.2311* (2.34)
21.1819** (–3.12)
20.5047 (–0.21)
0.4814 (0.23)
23.4965** (–3.16)
Opinion

0.1686 (1.13)
0.1777* (2.19)
20.1652*** (–4.50)
20.1111 (–0.47)
20.2317 (–1.29)
20.1913 (–1.78)
Employee plans
0.1711 (1.79)
0.3044*** (5.61)
0.1610*** (7.87)
20.0410 (–0.27)
20.0611 (–0.50)
0.2139*** (3.58)
Book to market
20.0719 (–1.78)
20.0050 (–0.31)
20.0289*** (–9.13)
20.3530*** (–5.63)
20.1872*** (–5.29)
20.0205* (–2.21)
Discontinued operations
0.0499 (0.71)
0.0008 (0.02)
0.0946*** (5.55)
0.0584 (0.53)
0.1156 (1.22)
0.0515 (1.03)
Distress probability
0.2512* (2.06)
0.1950* (2.49)

20.2766*** (–7.13)
20.3651 (–1.89)
0.2350 (1.34)
20.0181 (–0.16)
Stock Return
0.0713 (1.67)
0.0083 (0.35)
0.0128 (1.66)
20.2231*** (–3.30)
0.0984 (1.89)
0.0394 (1.74)
Restate
0.2320 (0.83)
0.0278 (0.25)
0.2015*** (5.57)
0.5691 (1.28)
0.3982 (1.57)
20.0470 (–0.45)
Number of observations
2,768
3,812
20,173
2,768
3,812
20,173
.4894
.5271
.6399
.5326
.4707

.3135
Adjusted R2

2000

Equation 3 Dependant variable = Log(Audit fees)

Panel A: Ordinary Least Squares (OLS) Procedure

Table 2. Ordinary Least Squares (OLS) Benchmark and Two-Stage Least Squares (2SLS) With Instruments Used in Prior Research


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2001

2002 to 2006

2000

2001

2002 to 2006

Equation 4 Dependant variable = Log(Nonaudit fees)

Notes: Fixed-year effects are included for the subsample 2002 to 2006, and as such, the intercept is not reported.
Significance level of coefficients is indicated by * for p \ .05, ** for p \ .01, and *** for p \ .001. In Panel B, the critical value for the weak instrument test based on a rejection

rate of 20% is 6.66 (see Stock & Yogo, 2005).

Results for endogenous variables
Log(Nonaudit fees); z statistics in parenthesis
0.8055 (0.87) 20.1315 (–0.08)
0.4789 (1.57)
Log(Audit fees); z statistics in parenthesis
21.0543 (–1.23) 268.301 (–0.22) 210.954** (–3.26)
Tests for relevance of instruments
First-stage F statistic; p values in parenthesis
0.57 (.45)
0.10 (.75)
2.79 (.09)
7.35* (.01)
0.05 (.83)
12.85* (.00)
Partial R2
.0002
.0000
.0001
.0027
.0000
.0006
Underidentification test
Kleibergen–Paap rk LM statistic (x2); p values in parenthesis
0.572 (.45)
0.103 (.75)
2.793 (.09)
7.396 (.01)
0.05 (.83)

12.862 (.00)
Weak identification test
Kleibergen–Paap Wald rk F statistic; critical value is 8.75
0.567
0.103
2.790
7.352
0.047
12.852
Weak instrument robust inference test
Anderson–Rubin Wald test (F statistic); p values in parenthesis
0.92 (.34)
0.01 (.93)
5.43* (.02)
3.27 (.07)
44.61*** (.00) 181.61*** (.00)
Stock–Wright LM S statistic (x2); p values in parenthesis
0.93 (.34)
0.01 (.93)
5.44* (.02)
3.30 (.07)
44.37*** (.00) 180.23*** (.00)
Overidentification test
Hansen J statistic (x2); p values in parenthesis
NR
NR
NR
NR
NR
NR

2000

Equation 3 Dependant variable = Log(Audit fees)

Panel B: Two-Stage Least Square (2SLS) Procedure With Lag and New Finance as Instruments

Table 2. (continued)


312

Journal of Accounting, Auditing & Finance

Thus, the results of prior research are robust and carryover to different samples and different periods.
We test the validity/appropriateness of the instruments. The F statistic for New Finance
as the instrument of Log(Nonaudit fee) are 0.57, 0.10, and 2.79 for the 2000, 2001, and
2002 to 2006 subsamples, respectively; the partial R2s are .02%, .00%, and .01% for the
three subsamples. This suggests that the instrument New Finance is not appropriate for
Log(Nonaudit fee). The F statistic for Lag as the instrument of Log(Audit fee) are 7.35,
0.05, and 12.85, and the partial R2 are .27%, .00%, and .06% for the 2000, 2001, and 2002
to 2006 subsamples, respectively. Although the partial F statistic is statistically significant
for Lag as the instrument for Log(Audit fee), the partial R2 indicates a close to zero correlation between the instrument and the endogenous variable. This suggests that the instruments are not appropriate (see Larcker & Rusticus, 2007, 2010).15
We provide tests based on recent advances in econometrics for the appropriateness of
the instruments (see discussion in section titled ‘‘Summary of Econometric Issues With
Instruments’’). The Anderson canonical correlation test for underidentification shows that
New Finance is not appropriate for Log(Nonaudit fee), whereas Lag is reasonable for
Log(Audit fee) for 2000 and 2002 to 2006. The Cragg-Donald F statistic for the weak identification test for the instrument New Finance are considerably below the critical cutoff
values for a rejection rate of 20%, whereas Lag is above the cutoff critical value for 2000
and 2002 to 2006 subsamples. The Weak Instrument Robust inference tests statistics show

that New Finance is marginally significant for 2002 to 2006, and Lag is strongly significant
in 2001 and 2002 to 2006. In summary, the tests of appropriateness of Lag as an instrument
for Log(Audit fee) for 2000 and 2001 provide mixed support and show reasonable support
for being an appropriate instrument for 2002 to 2006. For the instrument New Finance, the
tests of appropriateness suggest that the instrument is weak.16 Because these instruments
are weak, we next look for additional instruments that can alleviate the problem of weak
instruments.

Additional Instruments
Although the existing audit literature supports the notion that audit and nonaudit fees are
jointly determined, there is no theoretical model to guide our choice of instruments. For
instance, in the economics literature when the price and quantity of a commodity are considered to be jointly determined, there is rich theory of demand and supply for the commodity that guides the structural equation that needs to be estimated, which can guide the
choice of instruments. Even with a rich theory, it is sometimes difficult to identify appropriate instruments.
We consider additional instruments based on two approaches used in the financial economics literature. First, we consider the industry average as the instrument (see Bertrand &
Mullainathan, 2001; Hanlon et al., 2003; Lev & Sougiannis, 1996; Murphy, 2000). Second,
we consider a method developed for mitigating the difficulty of identifying appropriate
instruments by creating synthetic instruments with higher moments of the combination of
endogenous and exogenous variables developed by Lewbell (1997). This approach has
been used in financial economics papers (Nagar & Rajan, 2005).
Industry average–based instruments. In addition to Lag, we consider the industry average
of log of audit fee as an additional instrument for Log(Audit fee), and correspondingly, in
addition to New Finance, we consider the industry average of log of nonaudit fee as an
additional instrument for Log(Nonaudit fee). The instruments are developed using the

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Chan et al.

313

companion portfolio approach. Industry groups are based on the Fama–French 48 industry
groups.17 For each firm-year observation, we identify the 10 closest firms in the same
industry group in terms of total assets/size: thus the companion portfolio of firms belong to
the same industry group and are of similar size. We choose size as the matching criteria
because research in audit fees show that most of the variation in audit fees are explained
by the size variable. The mean and median Log(Audit fee) and Log(Nonaudit fee) of the
companion portfolio firms are the instruments for Log(Audit fee) and Log(Nonaudit fee).
Larcker and Rusticus (2010) discuss two drawbacks of using industry averages: first is
the implicit assumption that the endogenous portion of the audit- and nonaudit fees only
vary within the size industry, and second is the preclusion of the use of industry-fixed
effects, which are likely to be important in the audit- and nonaudit-fee context. We try to
overcome the first concern, by using the size-matched industry average. Given that firm
size explains more than half the variation in audit fees, it appears reasonable that the endogenous portion of the audit fees is contained in the size industry–matched portfolio.
However, this may not be true for the nonaudit fees. For the second concern, because we
use the size industry–matched portfolio approach, we can use the industry-fixed effects.
Table 3, Panel A provides the results using Industry Mean as the additional instrument.
For these estimations, we use the GMM procedure, with industry cluster robust estimator
of the variance and covariance matrix for computing the z statistics of the coefficient estimates. The GMM procedure is appropriate for our purpose because in the IV estimation,
there is an implicit restriction that the errors are expected to be zero if and only if the coefficient estimate is the ‘‘true’’ estimate (see Amemiya, 1974). The Kleinbergen-Paap F statistic of the instruments for Log(Nonaudit fee), that is, New Finance and Industry mean
Log(Nonaudit fee) for year 2000 is 8.72, which is slightly below the critical value of 8.75.
Thus, we cannot reject the hypothesis that the instruments are not weak. Other than this the
underidentification, weak identification, and weak instrument robust inference tests all
show that the instruments for Log(Audit fee) and Log(Nonaudit fee) are not weak. For the
overidentification test, the Hansen’s J statistic shows that the instruments for Log(Nonaudit
fee) are orthogonal to the structural error term, but the instruments for the Log(Audit fee)
are not so. As discussed before, for large samples, rejection of the null hypothesis is more
likely with the overidentification tests (see Larcker & Rusticus, 2007). In balance, the tests
indicate that the industry mean–based additional instruments along with Lag and New
Finance are not weak. In unreported analysis, the Hausman test indicates that Log(Audit

fees) and Log(Nonaudit fees) are jointly determined.
Given that the set of instruments are not weak, the top rows of Table 3, Panel A shows
the coefficient estimates of the endogenous variables and the associated z statistic computed, correcting the standard error using industry groups as the cluster. In Equation 3 with
Log(Audit fee) as the dependant variable, the coefficient estimates of Log(Nonaudit fee) are
0.6313, 0.6329, and 0.5020, for the subsamples 2000, 2001, and 2002 to 2006, respectively,
and all these estimates are statistically significant. In Equation 4 with Log(Nonaudit fee) as
the dependant variable, the coefficient estimates of Log(Audit fee) are 0.4458, 0.8593, and
0.9175, for the subsamples 2000, 2001, and 2002 to 2006, respectively, and all these estimates are statistically significant. This suggests that audit and nonaudit fees are positively
associated, indicating the presence of knowledge spillovers. More interestingly, in Equation
3, the estimated coefficient of Log(Nonaudit fee) for 2002 to 2006 is lower than that in
2000 and 2001, which may be due to SOX provisions relating to nonprovision of nonaudit
services.

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Results for endogenous variables
Log(Nonaudit fees); z statistics in parenthesis
Log(Audit fees); z statistics in parenthesis
Tests for relevance of instruments
First-stage F statistic; p values in parenthesis
Partial R2
Underidentification test
Kleibergen–Paap rk LM statistic (x2); p values in parenthesis

Panel B: Additional Industry Median-Based Instruments

Results for endogenous variables
Log(Nonaudit fees); z statistics in parenthesis
Log(Audit fees); z statistics in parenthesis
Tests for relevance of instruments
First-stage F statistic; p values in parenthesis
Partial R2
Underidentification test
Kleibergen–Paap rk LM statistic (x2); p values in parenthesis
Weak identification test
Kleibergen–Paap Wald rk F statistic; critical value is 8.75
Weak instrument robust inference test
Anderson–Rubin Wald test (F statistic); p values in parenthesis
Stock–Wright LM S statistic (x2); p values in parenthesis
Overidentification test
Hansen J statistic (x2); p values in parenthesis

Panel A: Additional Industry Mean–Based Instruments

2001

2002-2006

0.079 (.78)

14.84*** (.00)
9.53*** (.01)

32.21

12.73** (.02)

32.21*** (.00)
0.0238

7.74** (.02)

5.69 (.06)

12.10*** (.00)

25.40*** (.00)
.0206

8.49*** (.00)
.0126

5.68*** (.01)
.0091

2002-2006

0.5284*** (10.01)

2001

0.6047*** (4.51) 0.5898*** (6.29)

2000

Equation 3 Dependant variable = Log(Audit fees)

0.001 (.97)

0.447 (.50)

10.75

8.72
14.95*** (.00)
9.54*** (.01)

8.66** (.01)

7.60* (.02)

12.81*** (.00)
7.83** (.02)

10.75*** (.00)
0.0158

8.72*** (.00)
0.0110

0.6313*** (4.94) 0.6329*** (6.93) 0.5020*** (9.22)

2000

Equation 3 Dependant variable = Log(Audit fees)

Table 3. Two-Stage Least Squares (2SLS) Procedure With Additional Instruments

2001

2002-2006

5.49* (.02)

13.28*** (.00)
11.70*** (.00)

47.82

17.22*** (.00)

8.92*** (.00)

20.74*** (0.00)
11.01*** (.00)

29.68

17.94*** (.00)

29.68*** (.00)
0.0559

0.8029*** (6.15)

2001

14.40*** (.00) 17.88*** (.00)

21.00*** (.00) 47.78*** (.00)
.0303
.0433

0.3442 (1.91)

2000

(continued)

17.85*** (.00)

28.27*** (.00)
.0539

0.8539*** (8.78)

2002-2006

Equation 4 Dependant variable = Log(Nonaudit fees)

5.87* (.02)

4.93** (.01)
7.22* (.03)

19.05

14.15** (.00)

19.05*** (.00) 47.82*** (.00)
0.0308
0.0496

0.4458* (2.37) 0.8593*** (6.57) 0.9175*** (8.58)

2000

Equation 4 Dependant variable = Log(Nonaudit fees)


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8.49
9.45*** (.00)
7.88* (.02)
0.00 (.96)

7.90*** (.00)
5.82* (.05)
0.43 (.51)

2001

5.68

2000

0.11 (.75)

14.62*** (.00)
9.70*** (.00)

25.40

2002-2006

Equation 3 Dependant variable = Log(Audit fees)

4.46* (.03)

3.50* (.04)
5.35 (.07)

21.00

2000

5.27* (.02)

13.17*** (.00)
10.38*** (.01)

47.78

2001

8.43*** (.00)

19.50*** (.00)
10.89*** (.00)

28.27

2002-2006

Equation 4 Dependant variable = Log(Nonaudit fees)

Note: Fixed-year effects are included for the subsample 2002 to 2006. The critical value for the weak instrument test based on a rejection rate of 20% is 8.75 (see Stock &
Yogo, 2005). Equations 3 and 4 are estimated using the Generalized Method of Moments with industry cluster-robust estimator of the variance-covariance matrix for computing
the z statistics.
In Panel A, the instrument for Log(Audit fee) are Lag and Industry Mean of Log(Audit fee) and the instrument for Log(Nonaudit fee) are New Finance and Industry Mean of
Log(Nonaudit fee). The industry mean instruments are constructed based on a companion portfolio approach. Each firm-year is matched with the 10 firms in the same Fama–
French 48 industry group in terms of total assets. The mean value of the endogenous variable of the companion 10 firms is the instrument for the respective endogenous
variable.
In Panel B, the industry mean is replaced by the industry median. The industry medians are also computed using the companion portfolio approach.
Significance level of coefficients is indicated by * for p \ .05, ** for p \ .01, and *** for p \ .001.

Weak identification test
Kleibergen–Paap Wald rk F statistic; critical value is 8.75
Weak instrument robust inference test
Anderson–Rubin Wald test (F statistic); p values in parenthesis
Stock–Wright LM S statistic (x2); p values in parenthesis
Overidentification test

Hansen J statistic (x2); p values in parenthesis

Panel B: Additional Industry Median-Based Instruments

Table 3. (continued)


316

Journal of Accounting, Auditing & Finance

Table 3, Panel B provides the results of estimating Equations 3 and 4 with additional
instruments based on industry medians. The results are qualitatively similar to that discussed in Table 3, Panel A. Overall, the results are consistent with the existence of knowledge spillovers between audit and nonaudit services.
Synthetic instruments: Higher moment (HM) estimators. Erickson and Whited (2002),
Lewbell (1997), and Dagenais and Dagenais (1997) show that for models with measurement error, appropriate instruments can be constructed from available data by using higher
order moments. Following Lewbell, we call the HM estimator as synthetic instrument to
emphasize that the observations for the instruments are derived from transformations of
endogenous and exogenous variables, that is, the instruments are synthetically derived.
Ebbes et al. (2009) shows that such higher order moment methods are applicable for IV
methods as well. In particular, Ebbes et al. and Lewbell show that candidates for appropriate instruments are (a) the product of the endogenous and exogenous variables and (b) the
second moment of the endogenous variable. Lewbell shows that the HM estimators are sensitive to outliers. As such, Ebbes et al. suggest using robust estimators and GMM. Nagar
and Rajan (2005) use Lewbell’s HM estimator as the instrument. The performance of the
method depends on the skewness of the endogenous variable, and the method can yield
weak instruments.18
Table 4, Panel A provides the results of estimating Equations 3 and 4 when the additional instruments are based on the second moment of the endogenous variables: the instrument for Log(Audit fee) is the second moment of the demeaned Log(Audit fee) and Lag,
and the instrument for Log(Nonaudit fee) is the second moment of the demeaned
Log(Nonaudit fee) and New Finance19. The weak instrument tests shows that the second
moment is a valid instrument: this is because the Log(Audit fee) and Log(Nonaudit fee) are
skewed. Lewbell (1997) shows that the HM method is likely to be appropriate if the endogenous variable is skewed. However, the overidentification test largely fails to reject the
null hypothesis of no correlation between the instrument and the structural error term. As

discussed earlier, the overidentification test, especially in large samples, is likely to reject
the null hypothesis. Overall, the synthetic instrument is appropriate. In this case, both the
audit and nonaudit fees are positively correlated for each of the subsample periods.
Table 4, Panel B provides the results of estimating Equations 3 and 4 when the additional instruments are based on the product of the endogenous variables and an exogenous
variable and the second moment of two exogenous variables. In particular, the instruments
for audit fee are Lag, product of the demeaned log of total asset times demeaned Log(Audit
fee), square of demeaned log of total assets, and square of demeaned square root of segments, and the instruments for nonaudit fee are New Finance, product of the demeaned log
of total asset times demeaned Log(Nonaudit fee), square of demeaned log of total assets,
and square of demeaned square root of segments. The instruments for nonaudit fee are
below the critical value of 10.27 for the weak identification test for all subsample periods,
whereas the instrument for audit fee is below the critical value for the subsample period
2002 to 2006. Here, we observe the relationship between the endogenous variables and the
appropriateness of the instruments. As suggested by Staiger and Stock (1997), in large samples even if the F statistic and the partial R2s are reasonably high, the instrument may still
be weak. The weak identification test demonstrates this point. For nonaudit fee, the synthetic instruments are weak for 2001: in this subsample, we find no association between
nonaudit and audit fee. For the 2002 to 2006 period, the Kleibergen and Paap (2006) test
shows that the instruments are weak, but the Anderson and Rubin (1949) and Stock and
Wright (2000) tests show that they are not weak. Here the z statistic of the coefficient

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2001

2002 to 2006

2000

2001

2002 to 2006

Equation 4 Dependant variable = Log(Nonaudit fees)

Results for endogenous variables
Log(Nonaudit fees); z statistics in parenthesis
Log(Audit fees); z statistics in parenthesis
Tests for relevance of instruments
First-stage F statistic; p values in parenthesis
Partial R2
Underidentification test
Kleibergen–Paap rk LM statistic (x2); p values in parenthesis
Weak identification test
Kleibergen–Paap Wald rk F statistic; critical value is 10.27

15.11*** (.00)

9.51** (.05)

9.22

9.22*** (.00)
.2678

9.71*** (.00)
.2225

9.71

0.0913 (1.54)

2001

0.3286*** (7.63)

2000

7.90

9.67* (.05)

7.90*** (.00)
.1290

0.0636* (2.18)

2002 to 2006

Equation 3 Dependant variable = Log(Audit fees)

Panel B: Additional Synthetic Instruments Based on Exogenous and Endogenous Variables

19.40

13.09** (.01)

19.40*** (.00)

.2672

0.7268*** (11.23)

2000

18.60

7.82 (.10)

1.86 (.13)
.1034

0.7726*** (5.65)

2001

(continued)

5.37

10.43* (.03)

5.37*** (.00)
.1033

0.3528 (1.82)

2002 to 2006

Equation 4 Dependant variable = Log(Nonaudit fees)

Results for endogenous variables
Log(Nonaudit fees); z statistics in parenthesis
0.3716*** (10.94) 0.1636*** (5.96) 0.0608*** (5.62)
Log(Audit fees); z statistics in parenthesis
0.8892*** (48.15)
0.9037*** (66.84) 0.8039*** (47.13)
Tests for relevance of instruments
First-stage F statistic; p values in parenthesis
4.467*** (.00)
2.384*** (.00) 13.865*** (.00)
7.995*** (.00)
3.094*** (.00)
2.275*** (.00)
Partial R2
.8329
.7907
.7949
.8839
.7427
.5479
Underidentification test
Kleibergen–Paap rk LM statistic (x2); p values in parenthesis 14.12** (.00)
19.05*** (.00)
16.44***(.00)
11.74*** (.00)
8.35** (.02)
12.18*** (.00)
Weak identification test

Kleibergen-Paap wald rk F statistic; critical value is 8.75
4.467
2.384
13.685
7.995
3.094
2.275
Weak instrument robust inference test
Anderson–Rubin Wald test (F statistic); p values in parenthesis57.07*** (.00)
15.61*** (.00)
19.79*** (.00)
837.44*** (.00)
1,084.04*** (.00)
579.04*** (.00)
Stock–Wright LM S statistic (x2); p values in parenthesis
11.34*** (.00)
9.02** (.01)
9.64** (.01)
15.19*** (.00)
8.77** (.01)
12.26** (.00)
Overidentification test
0.57 (.45)
0.11 (.75)
6.25* (.01)
11.19*** (.00)
8.17*** (.00)
14.28*** (0.00)
Hansen J statistic (x2); p values in parenthesis

2000

Equation 3 Dependant variable = Log(Audit fees)

Panel A: Additional Synthetic Instruments–Based on Second Moments of Endogenous Variables

Table 4. Two-Stage Least Squares (2SLS) Procedure With Additional Synthetic Instruments


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1.49 (.21)
5.85 (.21)
6.81 (.08)

2.94* (.03)
9.09 (.06)
7.04 (.07)

2001

12.06** (.01)

5.31*** (.00)
12.23** (.02)

2002 to 2006

15.66*** (.00)

7.85*** (.00)
12.80** (.01)

2000

14.98*** (.00)

18.63*** (.00)
11.99** (.02)

2001

14.37*** (.00)

16.40*** (.00)
13.20*** (.00)

2002 to 2006

Equation 4 Dependant variable = Log(Nonaudit fees)

Note: Fixed-year effects are included for the subsample 2002 to 2006. The critical value for the weak instrument test based on a rejection rate of 20% is 8.75 (see Stock & Yogo,
2005). Equations 3 and 4 are estimated using the Generalized Method of Moments with industry cluster-robust estimator of the variance-covariance matrix for computing the z
statistics.
In Panel A, the instruments for Log(Audit fee) are Lag and second moment of demeaned Log(Audit fee), and the instruments for Log(Nonaudit fee) are New Finance and second moment of
demeaned Log(Nonaudit fee) (see Lewbell, 1997).
In Panel B, the instruments for Log(Audit fee) are Lag, product of the demeaned log of total asset times demeaned Log(Audit fee), square of demeaned log of total assets, and square of
demeaned square root of segments, and the instruments for Log(Nonaudit fee) are New Finance, square of demeaned log of total assets, and square of demeaned square root of segments (see Lewbell, 1997).

Significance level of coefficients is indicated by * for p \ .05, ** for p \ .01, and *** for p \ .001.

Weak instrument robust inference test
Anderson–Rubin Wald test (F statistic); p values in parenthesis
Stock–Wright LM S statistic (x2); p values in parenthesis
Overidentification test
Hansen J statistic (x2); p values in parenthesis

2000

Equation 3 Dependant variable = Log(Audit fees)

Panel B: Additional Synthetic Instruments Based on Exogenous and Endogenous Variables

Table 4. (continued)


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29.68*** (.00)
.0559
17.94*** (.00)
29.68
20.74*** (.00)
11.01*** (.00)
8.92*** (.00)

12.73*** (.00)

32.21
14.84*** (.00)
9.53*** (.00)
0.08 (.78)

0.9175*** (8.58)
32.21*** (.00)
.0238

0.5020*** (9.22)

Dependant variable =
Log(Tax fees)

0.11 (.75)

14.62*** (.00)
9.70*** (.01)

25.40

12.10*** (.00)

25.40*** (.00)

0.5284*** (10.01)

Dependant variable =
Log(Audit fees)

8.43*** (.00)

19.50*** (.00)
10.89*** (.00)

28.27

17.85*** (.00)

28.27*** (.00)

0.8539*** (8.78)

Dependant variable =
Log(Tax fees)

Additional instruments based
on industry median

Note: Fixed-year effects are included for the subsample 2002 to 2006. The critical value for the weak instrument test based on a rejection rate of 20% is 8.75 (see Stock &
Yogo, 2005). Equations 3 and 4 are estimated using the Generalized Method of Moments with industry cluster-robust estimator of the variance-covariance matrix for computing
the z statistics.
In Panel A, the instrument for audit fee are Lag and Industry Mean Audit Fee and the instrument for tax-related, nonaudit fee are New Finance and Industry Mean Tax-Related
Nonaudit Fee. The industry mean instruments are constructed based on a companion portfolio approach. Each firm-year is matched with the 10 firms in the same Fama–French
48 industry group in terms of total assets. The mean of the companion ten firms is the instrument for industry mean.
In Panel B, the industry mean is replaced by the industry median. The industry medians are also computed using the companion portfolio approach.
Significance level of coefficients are indicated by * for p \ .05, ** for p \ .01, and *** for p \ .001.

Results for endogenous variables
Log(Tax fees); z statistics in parenthesis

Log(Audit fees); z statistics in parenthesis
Tests for relevance of instruments
First-stage F statistic; p value in parenthesis
Partial R2
Underidentification test
Kleibergen–Paap rk LM statistic (x2); p value in parenthesis
Weak identification test
Kleibergen–Paap Wald rk F statistic; critical value is 8.75
Weak instrument robust inference test
Anderson–Rubin Wald test (F statistic); p value in parenthesis
Stock–Wright LM S statistic (x2); p value in parenthesis
Overidentification test
Hansen J statistic (x2); p value in parenthesis

Dependant variable =
Log(Audit fees)

Additional instruments
based on industry mean

Table 5. Determinants of Audit Fees and Tax-Related Nonaudit Service Fees (2002 to 2006)


320

Journal of Accounting, Auditing & Finance

estimate on nonaudit fee is 2.18, which is considerably lower than that when the instrument
is not weak. A similar pattern can be observed in Equation 4: When the instrument for
audit fee is not weak, that is, for 2000 and 2001, the endogenous variables are positively

associated, but when the instruments are weak, that is, for 2002 to 2006, the z statistic indicates an association that is not significantly different from zero.

Audit Fees and Tax-Related Nonaudit Fees
Although nonaudit fees from management advisory services have been curtailed since
2002, recently the PCAOB has initiated efforts to curtail auditors of public companies from
supplying certain types of nonaudit tax services. Reacting to the extensive media coverage
and congressional actions pertaining to tax shelters promoted by auditors for their public
company clients, the PCAOB conducted a roundtable in July 2004 and stated that ‘‘the
Board has determined that it is appropriate to consider the impact of tax services on auditor
independence’’ (see PCAOB, 2004a, p. 3). In December 2004, the PCAOB (2004b) proposed rules to curb certain types of nonaudit tax services for their public company clients.
We thus examine the relationship between audit fee and tax-related nonaudit fee for the
period 2002 to 2006. For this purpose, we use the instruments based on the companion
portfolio approach, that is, industry mean and industry median as in Table 3. We find that
the instruments are not weak, but as with large samples, the overidentification test rejects
the null hypothesis of no association between the instrument and the structural error term.
The results of this analysis are reported in Table 5. The association between the audit fee
and tax-related nonaudit fee is positive and statistically significant, which shows the presence of knowledge spillover effects between tax-related services and audit services.

Concluding Remarks
We examined the joint determination of audit and nonaudit fees using the 2SLS estimation
method. We utilized tests to validate the appropriateness of the instruments. We find that
when the instruments are not appropriate, that is, the instruments are weak, there is no relationship between audit and nonaudit fees. However, when we use instruments that are not
weak, then audit and nonaudit fees are positively associated. This shows the presence of
knowledge spillover effects across audit and nonaudit services. We also show the existence
of such knowledge spillover effects across audit and tax services. We thus document the
benefits arising from economies of scope, which in turn needs to be balanced with the cost
of loss of auditor’s independence (if any) for policy decisions on regulating nonaudit
services.

Acknowledgments

The authors gratefully acknowledge comments and suggestions from an anonymous reviewer, Ashiq
Ali, Ferdinand Gul, Clive Lennox, Bin Srinidhi and Scott Whisenant.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interests with respect to the research, authorship, and/
or publication of this article.

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Chan et al.

321

Funding
The author(s) received no financial support for the research, authorship, and/or research of this
article.

Notes
1. Joint provision of audit and nonaudit services has been extensively debated in the literature. The

2.

3.

4.
5.

6.
7.

8.

9.

benefits from providing audit and nonaudit services arise due to economies of scope, driven
largely by knowledge spillovers (Antle & Demski, 1991). To the extent that auditors capture
rents from such spillovers, economic bonding between the auditor and the client could lead to
auditor independence being compromised, which can be viewed as the cost of joint provision of
services. For instance, Arthur Levitt, the former chairman of Securities and Exchange
Commission stated, ‘‘How can auditors remain independent when the audit fee is just 30% of
their firms’ total revenues?’’ Although evidence on auditor independence being compromised
due to the joint supply of services is lacking, the proponents of this view cite isolated cases such
as Waste Management’s US$3.54 billion write-down of 1992 to 1997 profits and Micro
Strategy’s US$55.8 million earnings restatement. Economic bonding leading to loss of auditor
independence is not the focus of the research design used in this article. Our objective is to
examine the presence of economies of scope benefits.
Other explanations posited for the positive association between audit and nonaudit fees are (a)
nonaudit services could lead to extensive changes in organization structure that require additional
audit effort, (b) clients that get nonaudit services are ‘‘problematic,’’ and (c) the noncompetitive
audit market enables auditors to charge premiums (see Hay, Knechel, & Wongm, 2006).
A rich stream of literature examines the effect of nonaudit services on various proxies of audit
quality and provides insights into the impact of such services on auditor independence. DeFond,
Raghunandan, and Subramanyam (2002) use the auditor’s going-concern qualification as a proxy
for audit quality and show that the provision of nonaudit services does not adversely impact the
auditor’s propensity to issue going-concern opinion. Kinney, Palmrose, and Scholz (2004) show
that audit quality is not impaired but improved by the provision of tax-related services: they use
restatements as the proxy for audit quality. Kinney et al.’s finding indicates the presence of
knowledge spillover. Other studies such as Ashbaugh, LaFond, and Mayhew (2003) document
similar findings when they measure audit quality using abnormal accruals.
Concurrent research by Francis and Lennox (2008) shows that results obtained from selfselection models of audit fees are not robust.

Although this issue has been placed in the back burner, recent conflict of interest concerns
regarding the Lehman collapse has reignited such discussions. In addition, accounting firms are
developing their corporate governance and International Financial Reporting Standards–related
consulting practices in recent years; of course, their target market is not their current audit
clients.
Industry averages contain both the endogenous and the exogenous portions. As such, Larcker
and Rusticus (2010) state, ‘‘This approach will only work when the exogenous part of the original variable varies across industry, whereas the endogenous part varies only within industry.’’
Larcker and Rusticus (2010) summarize the challenge when they state, ‘‘There is no fool-proof
way of dealing with the problem of endogeneity.’’ The synthetic-instrument approach for all its
‘‘heroic’’ assumptions is an additional method that we bring to the forefront.
Even though the discussion is couched in terms of the two-staged least squares (2SLS) procedure, the econometric problems apply to all methods that use the instrument (IV) approach. We
thus refer the 2SLS and IV methods interchangeably. In Equation 1, x is referred to as an endogenous variable.
A nice interpretation of the partial R2 is provided by Shea (1997) and Godfrey (1999). They
show that the partial R2 is the ratio of the asymptotic variance of the coefficient estimate
obtained from ordinary least squares (OLS) and IV, times the ratio of one minus the residual

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10.

11.
12.

13.
14.
15.
16.

17.
18.

19.

Journal of Accounting, Auditing & Finance
sum of squares over the total sum of squares obtained from the second stage of IV and OLS.
This demonstrates that the downside of using the IV method compared with the OLS method is
the increased standard error of the estimated coefficient. In other words, improving the consistency of the estimate comes at a cost of increased standard errors.
Kennedy (1992, p. 137) states, ‘‘The major drawback to instruments (IV) estimation is that the
variance-covariance matrix of the IV estimator is larger than that of the OLS estimator, by an
amount that is inversely related to the correlation between the instrument and the regressor. This
is the price paid for avoiding the asymptotic bias of OLS; the OLS estimator could be preferred
on the MSE criterion.’’
For example, see Ezzamel, Gwilliam, and Holland (1996), Felix, Gramling, and Maletta (2005),
Ferguson, Francis, and Stokes (2003), Francis (1984), and Francis and Stokes (1986).
See Whisenant, Sankaraguruswamy, and Raghunandan (2003) for arguments on why Lag would
not be correlated with nonaudit fee and New Finance would not be correlated with the audit-fee
model. However, as in any context without a solid theoretical underpinning (see Larcker &
Rusticus, 2007, 2010), it could be argued that higher Lag would lead to more nonaudit opportunities so as to improve the accounting information system. Similarly, it could be argued that New
Finance would be associated with higher audit fees because the auditors would be ‘‘more careful’’ due to legal liability concerns.
The release is available at />All the results are qualitatively similar when we use years as the cluster.
Theoretically speaking, the negative coefficients are difficult to interpret, and likely are indicative of problems with the instruments.
The overidentification test is not applicable because Equations 3 and 4 are exactly identified.
See />The consistency of the higher moment approach requires that the exogenous portion of the audit
and nonaudit fees, that is, the endogenous variables have a skewed distribution, and the endogenous portion has a symmetric distribution and is uncorrelated to the structural error term. These
assumptions cannot be directly verified and is one major limitation of this approach.
The distribution of all the synthetic instruments is highly skewed (the mean of these variables
exceed the third quartile of their respective distributions. The pairwise Spearman correlation
coefficients for all the IVs are highly significant (at less than 1% significance level). Additional

tables giving the distribution of the synthetic instruments and the correlation between the synthetic instruments are available from the authors.

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