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School of Accounting

Seminar – Session 1, 2012

Meta-Regression Analysis and the Big Firm


David Hay

University of Auckland


Friday 20



3:00 to 4:30 pm





Meta-regression analysis and the Big firm premium

David Hay, The University of Auckland Business School

November 2011


This paper uses meta-regression analysis to take stock of the results of research examining the premium charged by the Big audit firms. It shows that the Big firm premium is overstated in research taken as a whole, partly due to the publication bias that is inherent in the system of research publication, and that if there is any underlying effect it is smaller than is generally believed. The extent to which Big firm premiums occur is more consistent with product differentiation explanations for the premium than with monopolistic pricing explanations. Examining measures of the research and the researchers, including publication quality, university status and Big firm affiliation shows that publication bias occurs to a greater extent in research settings that are regarded as higher quality. Meta-regression analysis has potential to lead to revised views of many areas of accounting and auditing research.

Key words: Auditing; Audit fee research; Meta-analysis; Big 4; Audit quality JEL Descriptors M40, M42



I appreciate helpful comments made by Jean C. Bedard, Chris Doucouliagos, Neil Fargher, Janto Haman, Fabian Homberg, Debra Jeter, Alan Kilgore, Robert Knechel, Mark Kohlbeck, Clive Lennox, David Lont, Ingram Olkin, Martin Paldam, Jacques Poot, Kevin Simpkins, Tom

Stanley, Jenny Stewart, Tracy Wang and the participants at the Deakin University Workshop on Meta-analysis in Economics and Commerce, the Auckland Region Accounting Conference, the Accounting & Finance Association of Australia & New Zealand Conference, the Meta-Analysis in Economics Research Network Colloquium, the Asia-Pacific Conference on International Accounting Issues, the American Accounting Association Auditing Section Mid-Year Meeting, the International Symposium on Audit Research and seminars at the University of Waikato, Monash University, the Australian National University, Victoria University of Wellington and the University of Auckland.


Meta-regression analysis and the Big firm premium

1. Introduction

This paper applies meta-regression analysis to examine evidence from published research about whether the Big audit firms1 are able to charge a premium for their services. Although it is widely believed that there is a Big firm premium, the results of previous studies have been very mixed, and indeed this area of research commenced with a study reporting results that show no overall premium (Simunic 1980). Since then, published studies show almost as many results where the premium is not significant as results where it is highly significant. Choi et al. (2008) describe the existing results as “mixed at best.” Accounting and auditing research is known to be subject to publication bias, so there is reason for some concern that the body of published research may give a misleading impression that could overstate whether any premium exists and (if it does) its extent. Meta-regression analysis contains techniques for assessing whether publication bias is present in a body of research literature, and for estimating the extent of any remaining effect after taking account of publication bias. Meta-regression analysis also allows multivariate testing of other factors that could influence the results, such as the setting of the research, the period and factors relating to the research and the researchers themselves. This study tests whether the Big firm premium exists and examines issues about the research and the researchers.

The existing research about the Big firm premium is motivated by continuing concerns about domination of the market for audit services by the Big firms. These concerns have led to investigations by government and regulatory bodies since the 1970s (e.g., US Senate 1977) and continuing up to the present (GAO 2003; Oxera 2006; GAO 2008; US Treasury 2008; European

1 The Big firm premium currently applies to the Big 4 audit firms; in earlier periods they were the Big 8, Big 6 or


Commission 2010; House of Lords 2011).2 There is also an extensive body of published research over almost as long a period, commencing with Simunic (1980) and including more than 121 published papers.

A number of recent narrative literature reviews of research observe that research in auditing lacks influence over public policy and practice (e.g., Francis 2004, DeFond and Francis 2005, Carcello 2005, Kinney 2005, Simunic 2005 and Humphrey 2008). Carcello (2005 37) states that a reason why auditing research does not have more effect on public policy is that “as is the case with most social science work, findings across different studies are often inconsistent. These inconsistent results reflect the realities of using different samples, different models and different variable definitions”. Carcello (2005) calls for research to synthesize the conflicting findings of research. Meta-regression analysis provides a way to synthesize research results, and potentially to increase the impact of auditing research. In this case meta-regression analysis shows an overall conclusion about a body of research where there are mixed results, and provides evidence about the alternative explanations for the results.

The results of the meta-regression analysis show that, while there is some uncertainty, there is a significant premium in the overall body of research. However, the underlying effect is much smaller than is generally believed.

As well as the existence of the premium itself, the study considers alternative explanations for it. Two explanations are well-established in the literature, namely monopolistic pricing and product differentiation. If the monopolistic pricing explanation applies, it is likely


The US Treasury (2008) reported that “As the result of mergers and the demise of Arthur Andersen, there are fewer large auditing firms with particular concentration amongst large global public companies. Audit committees and those who engage auditors desire choice and a competitive environment, which stimulates excellence and innovation.” The European Commission (2010) observed that “The market appears to be too concentrated in certain segments and deny clients sufficient choice when deciding on their auditors.” In July 2011 the UK Office of Fair Trading announced that it has provisionally referred the audit market to the Commerce Commission for an investigation that could culminate in what have been called “potentially nuclear measures to reduce Big Four dominance” (Orlik 2011).


that market dominance by the Big firms will manifest itself as a premium in all sectors of the market, including listed companies, other entities and public sector entities. If auditees are voluntarily paying a premium for a higher-quality product that meets their needs, then it is more likely that the Big firm premium arises in only some settings, where there is more need for greater assurance. The results show that the Big firm premium is a private sector phenomenon and is not associated with the public sector, consistent with the product differentiation explanation and not with the monopolistic pricing explanation.3 The Big firm premium is also not associated with Big firm market share in a country.

The results also suggest that publication bias is present in the existing research. Publication bias occurs because authors, reviewers and editors all regard significant results as more interesting, and are all more likely to persevere with studies that find significant results (see, e.g., Stanley et al. 2008). It is possible that pressure to obtain more interesting results is higher when submitting papers to higher-quality publications, and at better universities, and among higher-ranked faculty. The study also examines the incidence of publication bias to assess whether there is greater bias in these higher-quality settings. The results show that there is extensive publication bias, raising the possibility that despite many years of extensive high-quality research, the Big firm premium might be a mere mirage. Publication bias is frequently worse in research that would be regarded as higher-quality – based on whether the authors include a full professor and the status of their universities. However, top-ranked journals are able to avoid publication bias while lower-ranked journals are not. Auditing faculty members also have many close affiliations with the Big audit firms (such as named chairs) and it is worth investigating whether these affiliations systematically influence their results. Affiliation of a researcher with a Big firm is not associated with greater publication bias,.


This study adds to the literature by critically reviewing research on the Big firm premium, and showing that there is doubt about the premium‟s existence. In addition, it finds that the premium is more consistent with product differentiation than with monopolistic pricing, and is associated with certain investor protection measures. The study introduces meta-regression analysis to auditing and accounting research; and further contributes by examining the extent of publication bias and finding that it is stronger in some research environments than others. Meta-regression analysis could be valuable in many areas of accounting and auditing research, as other well-known findings may be influenced by publication bias or other issues concerned with the research setting or the researchers. The paper now proceeds to discuss previous research in this area, followed by the need for meta-regression analysis and an explanation of the technique used, and the results of the study. These are followed by discussion of the findings, limitations and a conclusion.

2. Previous research on the Big firm premium and issues for investigation Previous research

There are more than 121 published research papers on the Big firm premium, starting with Simunic (1980). The results include a large number of studies reporting a significant premium, but also many studies finding no significant result. Francis (2004 352) states that, “on average, the Big firm premium has been around 20%”, but there is a very wide range of reported results (and this estimate could be overstated due to publication bias). Sometimes the Big firm premium is the issue of importance in a research study; at other times it is a control variable in a research study investigating another issue (this difference is useful in investigating publication bias). Research about the premium has focused on the two alternative explanations for it, namely monopolistic pricing or product differentiation.


Simunic (1980 167) presents arguments that where there is monopoly pricing, then audit fees will be higher. Simunic also notes that product differentiation may also take place. Francis (1984) also recognizes that both monopoly pricing and product differentiation can apply, while developing arguments that the Big firm firms have invested in developing brand name capital, and that they receive higher fees because their audits are recognized as being of higher quality (Francis 1984 135). The issue of monopolistic pricing is examined by considering segments of the audit fee market, namely large clients versus small. Simunic (1980) argues that small clients have a wide choice of auditor but large clients do not, so that if there was monopoly pricing by Big firms then there would be an audit fee premium paid by large but not small clients. In his study, there was no overall premium for either group, consistent with a competitive market and product differentiation. Causholli et al. (2010) report that a large number of other studies using a similar approach have reported a wide variety of results, including no premium in either group (e.g., Firth 1985; Chung and Lindsay 1988; Rubin 1988; Firth 1997), premiums in both large and small segments (e.g., Francis 1984; Gul 1999; Su 2000), and premiums for small clients only (e.g., Francis and Stokes 1986; Palmrose 1986; Lee 1996). Very few studies show evidence consistent with monopoly pricing.

Recent calls for more research about the Big firm premium include Simunic (2004 5) who provides a number of argumentsthat suggest more investigation is needed. He states, “given the recent problems and changes in the profession, and the many unanswered questions, revisiting this issue seems worthwhile.” Simunic (2004 5) suggests that, “the underlying „theory‟ is sketchy”; most practitioners do not accept the quality ranking of Big firms higher than small firms; and that “there is good reason for concern that audit quality of Big firms may become (be) no higher than some minimum (e.g., GAAS audit).” He also notes that recent audit failures have


frequently involved the Big firms4, and raises the issue that the audit market now might be quite different from that in the past due to such changes as firm mergers. Calls for further research have also been made by Watkins et al. (2004 168); Choi et al. (2008 56); and Clatworthy et al. (2009 163). In addition to mixed evidence about the premium in prior studies, there are other reasons to be skeptical about its existence, including self-selection effects (caused by the selection of a Big firm auditor being driven by similar factors to those that influence audit fees).5

The issue of the Big firm premium is thus worthy of further investigation. I synthesize audit fee research on the Big firm premium, using meta-regression analysis to take account of issues about the research settings and the researchers. The questions under examination are whether the Big firm premium exists; if it does, how large it is; and the extent to which the results of these studies vary according to factors about the research setting and the researchers. Issues about the research setting include the country in which a study is set; country variables such as its institutional arrangements and the market share of the Big firms; the private sector or public sector setting of the study; and the time period from which the data are collected. Issues about the researchers include the purpose of the research (to investigate the Big firm premium, or some other issue); issues concerning the quality of the research; and the affiliations of the researchers with a Big firm. Meta-regression analysis provides techniques for investigating those issues and developing overall conclusions based on the accumulated evidence from research studies and thus making them more useful. The major issues for examination, aside from whether there is a robust evidence of a premium after taking account of publication bias, include market


There is also recent evidence that any premiums are not supported by differences in quality. Lawrence (2011 259) find no significant difference in audit quality between Big firm and non-Big firm auditors and argue that any differences observed reflect client characteristics, particularly size.


Studies that examine self-selection have very mixed results. Ireland and Lennox (2002) find that controlling for self-selection shows higher premiums for Big firms, while Chaney et al. (2004 51) find that “the premium vanishes once we control for selection bias”. Lennox and Francis (2008) and Clatworthy et al. (2009) note that self-selection models are highly sensitive to changes in model specification.


structure and whether premiums are consistent with monopolistic pricing or product differentiation.

Issues about the research settings

Meta-regression analysis allows the setting of the various research studies to be controlled for. Whether a study involves listed companies or some other type of entities could have an effect due to variations in user needs. Many public sector organizations do not raise funds from capital markets, so there may be less value in the signal provided by a high-quality auditor. The private sector or public sector setting of the research is an issue that is likely to make a difference. In view of changes over time in the regulatory environment and in practices such as corporate governance, the premium could also vary over time.

It has also been suggested that country-level institutional factors may be another issue that explains differences in fee levels (Choi et al. 2008 56). In this regard, there is also an opportunity for this research to contribute to an unresolved issue in the literature, namely whether auditors play a stronger role in environments where there is weak governance or where it is strong. There are two alternative views stated in recent papers: Choi and Wong (2007) call these the strong governance and weak governance views. Under the strong governance view, auditors play a stronger governance role in weak environments. In that case, companies that are issuing debt or equity in weak investor protection environments are more likely to appoint Big firms (this is supported by the results of Choi and Wong 2007) and the Big firm premium decreases in strong environments (this is supported by the results of Choi et al. 2008). Francis and Wang (2008) suggest that the opposite will apply – Big firms are more likely to enforce higher earnings quality as investor protection regimes become stronger (and this is supported by their results). Both arguments are plausible and there is evidence to support each view. Choi et


al. (2008) and Francis and Wang (2008) both draw attention to this inconsistency and note that further research is needed.

Issues about the research and the researchers

An issue of particular concern is potential publication bias. It is widely believed (e.g., Stanley et al. 2008 279) that studies with statistically significant results are much more likely to be published than those with “no results”.6

Authors, reviewers and editors all regard significant results as more interesting, so that it is more likely that a researcher will lose the motivation to persevere with a study that does not find significant results (or will keep on trying variations in the tests reported). The outcome of this effect is that the overall results in published research will frequently overstate the underlying effects simply because of the publication bias that is inherent in the system. 7

Publication bias in accounting research has been discussed in earlier papers. Lindsay (1994 33) argued that publication bias was impeding the progress of accounting research. This is consistent with Bamber et al.‟s (2000 123) argument that “the placement of the first research bricks affected the whole wall” – initial studies of an issue in accounting are very influential and there are barriers to publishing work that challenges previous published accounting research. Pomeroy and Thornton (2008 319) argue that “prior research suggests that publication bias is particularly acute in accounting.” Publication bias will be apparent if the research results show systematically different results for more precise studies than for less precise studies. Hay et al. (2006 163) note that publication bias might be affected by journal quality – top journals may be less likely to publish studies with insignificant results than lower level journals, and thus the

6 Publication bias is commented upon by Sutton et al. (2000), Ashenfelter and Greenstone (2004), and Egger et al.


7 Goldacre (2008, 215) points out that “not only has publication bias been found in many fields of medicine, but a

paper has even found evidence of publication bias in studies of publication bias. . . This is what passes for humor in the field of evidence-based medicine.” The paper is Dubben and Beck-Bornhold (2005).


system under which research is published may inflict top journals with even greater publication bias. I therefore look at measures of journal quality, and other measures of research quality including the status of the researchers and of their universities.

Several auditing papers have asked whether affiliation to an auditing firm through an endowed chair affects research results (Francis 2004; DeFond and Francis 2005; Carcello 2005; Bazerman et al. 2006). The idea that Big firm audits are valued for their high quality might appeal particularly to researchers who are associated with the Big firms in some way, and it is worth investigating whether these affiliations could be associated with greater publication bias. In addition, therefore, I consider the association between Big firm affiliations by the researchers and publication bias.

To summarize: I examine whether the results of research into the Big firm premium are associated with variables related to the research and the researchers. These include country setting, the type of entities being researched, Big firm market share, investor protection, status of the researchers, and publication bias. The Big firm premium is a particularly appropriate issue to examine in this meta-regression analysis because it was the starting point for audit fee research (Simunic 1980); there is widespread research either examining the issue or using it as a control variable; the results of previous studies are mixed; and it is a topic on which certain issues (such as the affiliations of academic researchers) are particularly relevant.

3. Meta-regression analysis

Meta-analysis is a quantitative literature review, which can synthesize existing research and contribute in making sense of previous research in order that research may become more useful to practitioners and policymakers. Papers applying meta-analysis techniques in auditing and accounting include Christie (1990), Trotman and Wood (1991), Kinney and Martin (1994)


and Ahmed and Courtis (1999). Recent examples in auditing-related areas include Hay et al. (2006) on audit fee research in general; Sánchez-Ballesta and García-Meca (2007) examining corporate governance; Pomeroy and Thornton (2008) examining audit committee effectiveness; and Lin and Huang (2010) on earnings management.

Meta-regression analysis is a further development from meta-analysis which has the advantage that more than one variable at a time can be examined and that research can consider issues related to the research setting and the researchers. Meta-regression analysis allows for tests for publication bias (the funnel asymmetry test) and the precision of the estimated effect (the precision effect test) while taking account of the other variables (e.g., Stanley et al., 2008). Publication bias is first examined graphically, and then the tests for it are discussed.

Publication bias and other issues can be examined by meta-regression analysis.8 A preliminary approach to examining the effect of publication bias is to draw the reported results and their precision in a funnel plot (Egger et al. 1997; Sutton el. 2000; Stanley et al. 2008). Effect size is plotted against precision (defined as 1 divided by standard error). In the absence of publication bias, the result should resemble an inverted funnel. More precise studies (those with lower standard errors) form the top of the funnel, and tend to cluster together. Less precise studies form the lower part of the funnel chart and are more widely dispersed – but if publication selection bias exists, those with unexpected results will be truncated, and one half of the funnel will not be present, leaving an asymmetrical funnel. Publication bias thus results in the precise studies and imprecise studies reporting different results from each other. Such a funnel plot of studies of the elasticity of demand for water appears in Dalhuisen et al. (2003), and the authors

8 Meta-regression analysis was proposed and discussed by Stanley and Jarrell (1989, 161). They described

meta-regression analysis as “the meta-regression analysis of meta-regression analyses . . . it studies the processes that produce empirical economic results as though they were any other social scientific phenomenon”. “Meta-regression analysis can see through the murk of random sampling error and selected misspecification bias to identify the underlying statistical structures” (Stanley 2005, 309).


observe that the mean elasticity in reported studies is overstated by a factor of three to four times, because of the inclusion of less precise studies in the expected direction, but not those whose results are in the opposite direction.

Figure 1 shows a funnel plot of research results from studies of the Big firm audit firm premium, and it shows a pattern similar to previous studies of research in which publication bias was evident.9 The funnel is asymmetrical, with extreme observations in the expected positive direction associated with low precision, and a comparative absence of low-precision results in the opposite direction. The most precise studies (usually those with very large sample sizes) form the top of the funnel. The less precise studies are widely dispersed, but many are on the right hand side of the funnel. The mean Big firm effect estimated using this published data might well overstate the underlying premium. The most extreme observation suggests a Big firm premium of over 100%; the most precise study indicates a 5% premium.

Insert Figure 1 here

The apparent publication bias shown in the funnel plot can be investigated by statistical tests using meta-regression analysis. Stanley et al. (2008) explain meta-regression analysis. In economics research (and audit fee research) there is usually a regression model of this form:

Y = X +  (1) Where Y is the dependent variable vector (audit fees in this case), X is the vector of explanatory variables and  is the error vector. Often the significance of one particular regression coefficient (in this case, the significance of the coefficient on the Big firm variable) is the key issue. Differences in reported findings may be due to differences in the research setting, the time period


or other effects. Stanley et al. (2008) suggest that such differences can be examined using a meta-regression model like this:

Where bj isthe reported estimate of  (the coefficient on the Big firm premium) in the jth study,

is the underlying value of the coefficient on the Big firm premium, Zjk is the matrix of meta-independent variables which explain the relevant characteristics of the study and its systematic variation from other studies, αk are the meta-regression coefficients and ej is the meta-regression disturbance term (Stanley and Jarrell, 1989 164; Stanley et al. 2008 279). The moderator (or meta-independent) variables Zjkshould include model specification characteristics of Equation (1), quality measures of the study, characteristics of the authors (such as institutional affiliations10) and characteristics of the data (Stanley and Jarrell 1989 165).

A meta-regression analysis test for publication bias, and the existence of an underlying effect, can be conducted using the following model (Stanley et al 2008 280).

This equation is as equation (2) with the addition of the standard error Se to measure precision. If there is no publication bias, the reported effect bj will vary randomly around the underlying effect, , with other factors that affect the results taken account of by the Zjk variables. If there is publication bias, the standard error of the study will affect of the results, and

0 will be significant. This occurs because studies with smaller standard errors obtain significant results with smaller coefficients, and are likely to be published even with relatively small

10 Stanley et al. (2008, 278) suggest “gender, experience, income, ideology, funding source, etc.” Not all of these are


reported effects. Less precise studies are likely to have a wider range of results, and those with significant effects in the expected direction are more likely to be published. The funnel asymmetry test examines this issue. The same equation also allows a test of whether there is a significant underlying effect, which is indicated by  ≠ 0 (the precision effect test) (Stanley et al 2008 280).

Since equation (3) suffers from heteroscedasticity with regard to Se, in practice the following version of the equation is usually estimated, with both sides of the equation divided by Sej (so that the dependent variable now becomes bj/Sej, the t-statistic):

As a result of dividing through, the intercept 0 now becomes the funnel asymmetry test variable, and a significant result indicates publication bias. Explanatory variables (Zk) that relate to factors about the setting of the study are also divided by Se. The significance of the sum of β and the coefficients the Zk variables is the precision effect test variable for an underlying effect, free of publication selection bias (Stanley et al. 2008 281; Doucouliagos and Stanley 2009 421).

4. Data and descriptive statistics

A list of published audit fee studies was identified from the papers in Hay et al. (2006), supplemented with papers in Thirty Years of Audit Research (Brazel 2006), and then extended by electronic searches using ABI/Inform and EBSCO Host with the key words „audit‟ or „auditing‟, and followed by a detailed review of the tables of contents of journals which publish research on auditing.11 The search examined publications up to December 31, 2007.

11I did not include conference papers or unpublished papers listed in SSRN as these papers may not have been subject to a review and editorial process, and are usually published with some variation at a later date.


I examined observations from 121 papers that included a Big firm variable in 28 journals. The papers are listed in Appendix 1. In many cases, papers include more than one set of observations (for example, results from different countries, or different years reported separately) so that there are 182 analyses of separate sets of data available. Where more than one analysis of the same data is presented, I selected the main observation that features in each paper (or where this was not identifiable, the observation from the most comprehensive analysis). Papers were excluded if they did not use log of audit fee as the dependent variable, if they did not report sufficient data about the coefficient, standard error and t-statistic or if a measure of Big firm market share is not available, leaving 160 observations. Table 1 shows the number of observations included.

Insert Table 1

The results are summarized in Table 2. There are a large number of highly significant results (70 results are significant at 1% or better) , but there are also many that do not find a significant premium (59 are not significant).

Insert Table 2

Table 3 shows the descriptive statistics for continuous variables, which examine the effect size from each study, and its precision. The mean coefficient on the Big firm variable is .180. This unadjusted mean coefficient is equivalent to a premium12 of 19.7%. This level is consistent with the 20% premium discussed in Francis (2004) after adjustment to take account of publication bias. The mean t-statistic is 2.47, suggesting that published studies on average find a significant coefficient.

Insert Table 3 here


Table 4 shows the descriptive statistics for the coefficient on Big firm broken down by binary variables for countries where there are large numbers of observations (the US, the UK and Australia), categories of entity (other entities versus listed companies, and public sector versus private sector) and categories of research. Table 4 also shows the results of univariate tests which show some evidence that the Big firm premium is higher in the US than in other countries, and lower in the UK and Australia. Non-standard entities (such as municipalities, schools, insurance companies and pension funds) are not significantly different from companies. However, public sector entities have significantly lower Big firm premiums than the other entities. Premiums were lower in the 1990s than before or after. Premiums reported in US journals are higher than in other journals. Other variables related to the research process (whether the Big firm premium was the topic of interest in the paper, publication in a top journal, the status of the authors and their universities, and Big firm affiliation of the authors) did not show significant differences. The multivariate tests reported below will provide more useful information about the relationships.

Insert Table 4 here

5. Meta-regression analysis results

A preliminary meta-regression model is reported in Table 5, Panel A. This panel shows a model with only two variables, precision and the intercept, in order to carry out the funnel asymmetry test for publication bias and the precision effect test for an underlying effect. The results show a significant coefficient on the intercept (indicating that the funnel asymmetry test shows the presence of publication bias). The results (reported with robust standard errors) show no significant coefficient on the measure of precision (1/Se) indicating that the precision effect test suggests that there is no underlying Big firm premium after controlling for publication bias.


In Table 5, Panel B, results are reported after adding explanatory variables. These include measures for the period from which the data are collected; country measures (for the three countries in which the most audit fee studies have been conducted, the US, the UK and Australia), and for the setting in which the research was conducted (public sector or other). Each of these variables is divided by Se as shown in Equation (4) above. The coefficient on the variable indicating data from the 1990s is significant and negative. None of the separate country measures is significant. The dummy for the public sector has a significant and negative coefficient, consistent with the Big firm premium being a private sector phenomenon.13 The combination of precision plus the period, country and setting variables (i.e., the Zjk variables from Equation (4)) is the precision effect test and measures whether there is a significant overall effect after taking account of publication bias. The combined effect is (just) not significant (F=3.41, p=.067), suggesting doubt over the existence of an underlying Big firm premium. Despite the univariate test results suggesting that US premiums are higher, and those in the UK and Australia are lower, these results do not hold when other variables are controlled for.14 The intercept is significant, again consistent with publication bias.

In order to further investigate the premium, I replace the country variables with measures of the institutional environment that could be expected to affect auditing. It could be expected that if the Big firm premium is driven by dominant market positions, it will be higher in countries where the Big firms have higher market share; and that if it is driven by demand, then it will be associated with investor protection at the country level. I use the index measures for disclosure, enforcement and liability from La Porta et al (2006) for measures of investor


I also examine whether non-standard entities (i.e., all except listed companies) were different from the remaining observations of listed companies and found no significant difference.

14 In additional tests, English-speaking countries are also not significantly different from all others, and developing


protection, and the Big firm market share measure from Bushman et al. (2004). Panel C shows that when the individual country measures are replaced by measures for Big firm market share and investor protection (divided by Se as above), the coefficient on Big firm market share is not significant. Replacing the country measures with measures of investor protection, the results show that enforcement is significantly associated with a Big firm premium but disclosure and enforcement are not. The relationship is negative, consistent with the arguments in Choi et al. (2007) but not with Francis and Wang (2008). The coefficient on public sector is still negative, and publication bias is present. A precision effect test of the effect of the sum of the explanatory variables in Panel C is significant and positive, consistent with an underlying premium after allowing for publication bias.15

In Table 6, summary results of models using partitions of the data according to issues about the research and the researchers are reported. I first investigate publication bias by separate examination of those studies that were examining whether Big firm premiums apply and other studies that were using Big firm as a control variable in a study of other issues. The results (Models 1 and 2 in Table 6) show that publication bias is present in studies where the Big firm premium is the issue under investigation (p=.023) and not where the study is investigating some other issue (p=.089). This provides further evidence of publication bias.

Insert Table 6 here

I also partition the data using other variables that are relevant to the research and the researchers. These include journal quality, measured by SSCI impact factor (Models 3 and 4);


For sensitivity, I examined a number of alternative measures of investor protection including the Wingate index of litigation (Wingate 1997), rule of law (La Porta et al. 1997), overall earnings opacity (Bhattacharya et al. 2003), the CIFAR measure of disclosure intensity (Bushman et al. 2004 248) and Transparency International‟s Corruption Perceptions Index (Transparency International, 2010). As with the La Porta (2006) measures, the results showed either significant and negative relationships with investor protection or insignificant relationships.


and other factors about the journals represented by whether the journal is based in the US or not (Models 5 and 6). Top journals (measured by journals with SSCI impact factors greater than 1 in 2010, and including JAR, AR, JAE, CAR, AOS, AJPT and EAR) do not show publication bias, while lower-ranked journals show publication bias (significant at .003). I also examine publication quality using a measure for the top 5 journals and find similar results. The US journals are subject to publication bias (p=.000), but not the non-US journals. Standards for publication are very high in the US, but there is also very strong pressure to publish or perish and that might lead to greater pressure on authors to produce significant results.

The remaining models in Table 6 measure the effects of variables concerned with the researchers. These include whether full professors report different results from other academic grades (Models 7 and 8); whether researchers at top 100 universities report different results from those at other universities (Models 9 and 10); and whether researchers who are affiliated with Big firms report different results from those who are not (Models 11 and 12). Publication bias is evident (p=.001) in papers where at least one author was a full professor,16 but not in papers where this was not the case. Publication bias is substantially influenced by whether the authors are motivated to spend time on a particular study, or transfer their efforts to one with more significant results. Full professors are likely to have more opportunity to choose among projects to pursue and are likely to choose top focus on those with the most interesting results. I also measured seniority by the status of the university. I examined whether authors who were affiliated with a top 100 university (using any of four classifications, the US News and World Report listing of top 100 US universities17; and the listings of top 100 world universities

16 At the time of publication as shown in the paper‟s author details. 17 Obtained 15 November 2010 from


published by the Times Higher Education Supplement,18 Quacquarelli Symonds19 and Shanghai Jiao Tong University (also known as Academic Ranking of World Universities20). Publication bias was evident (p=.025) in papers with an author from a top 100 university, but not in those with no author from a top 100 university21 (this is again consistent with greater pressure to publish).

It is intriguing to consider, in the light of comments that audit researchers are sometimes seen as apologists for the accounting profession (Francis 2004), whether papers by authors with a Big firm affiliation are more likely to report a Big firm premium. If a Big firm premium is explained as indicating higher quality, then researchers affiliated with Big firms may find results that show a Big firm premium more plausible and be more inclined to pursue publishing them. I partitioned the data by Big firm affiliation of an author to test whether this is the case. I used the Hasselback Accounting Faculty Directory22 for the appropriate year to identify Big firm affiliations. There are 20 papers where the author is a Big firm professor (or fellow) at the time of the study. In this case publication bias is evident in the studies where no author is affiliated with a Big firm (p=.005) and no publication bias is observed where there is an affiliation. The result is consistent with affiliation not influencing the results reported. However, there are limitations to the use of this Big firm affiliation variable, because it provides an incomplete measure of Big firm associations. Almost all auditing academics have close links of some kind with professional firms through former colleagues or former students.


Obtained 18 November 2010 from:


Obtained 18 November 2010 from:


Obtained 18 November 2010 from:

21 University rankings have limitations (Enserink 2007), and unintended consequences (Diver 2005), but using a

broad range of top 100 measures gives a reasonable opportunity for any highly regarded university to be recognized.


The size of the underlying empirical effect in the absence of publication bias can be estimated in several ways. Computing the mean of the reported results suggests a premium of 19.7% (as reported above), but this estimate is affected by publication bias. Methods that take account of publication bias include computing the mean of the most precise 10% of estimates (Stanley 2005, 316); or using the PEESE (precision-effect estimate with standard error) method set out by Stanley (2008).23 The mean coefficient using the most precise 10% of observations is .093, a premium of 9.7%. The PEESE method provides a similar result (.063 and 6.5%). These methods suggest that any underlying Big firm premium is within the range of 5% to 10%.

I conducted a variety of diagnostic tests. These included a Ramsey RESET test, which found no significant result, consistent with the hypothesis that there are no omitted variables. The Breusch-Pagan test for heteroscedasticity showed some indication of heteroscedasticity, and as a result the tests reported above are carried out using White‟s heteroscedasticity-consistent t-statistics. I also repeated testing excluding extreme observations and again obtained very similar results. I also computed variance inflation factors to test for multicollinearity. I used a large number of alternative measures for investor protection, journal quality, author seniority, top universities, and period. As an alternative measure to for entity type I examined whether listed companies show different results from all other entities (as well as from public sector entities). Other entities (apart from the public sector) do not show significantly different results. Where possible, I partitioned the data and examined separately the results for the major countries (US, UK and Australia), and for Europe generally, English-speaking countries and non-English speaking countries, developing countries and other countries. In each case the results were consistent with those reported in the paper.

23 Estimating the equation t

i = β0Sei + α(1/Sei) + vi, wherethe estimate of α is the empirical effect corrected for


6. Summary and conclusions

In this paper, meta-regression analysis is applied to the Big firm premium. The results show that the publication bias that is inherent in published research appears to exist in this area of research, and the apparent premium is overstated. This suggests doubt about whether the Big firm premium exists, although further tests suggest that there is a significant remaining underlying premium after adjusting for publication bias. The results also show that the Big firm premium is negatively associated with the public sector. This finding contributes to resolving the issue of whether the Big firm premium represents monopolistic pricing or product differentiation – as there is more demand from private sector firms for a differentiated higher quality audit, and the premium is much more significant in this setting. (If monopoly pricing occurred, any premium would be more likely to apply across both settings). However, this result is not entirely conclusive, as there may be other factors, such as more widespread use of public tendering, that influence public sector audit fees. There is also some evidence that the premium is negatively associated with investor protection and no evidence that it is associated with higher Big firm market share. These results are again more consistent with product differentiation than with monopolistic pricing. The paper provides evidence that could reduce concern by policymakers about domination of the market for audit services by the Big firms, at least so far as audit fees are the issue.

The tests show that publication bias is widespread. There is a remaining Big firm premium evident overall in the subset of studies that set out to examine Big firm effects, but not in the studies that are examining other issues and using the Big firm measure as a control. This result is also consistent with publication bias. Publication bias is avoided by top journals, but not by lower-ranked journals; is more prevalent in US-based journals, in papers where authors come


from top 100 universities and in papers authored by full professors. Big firm affiliation by the authors is not associated with greater publication bias.

In common with similar studies, the limitations of the study include the relatively small number of published research papers available (121 papers). While studies such as Chaney et al. (2004) have argued that it is necessary to control for self-selection, and that the literature using simple OLS models is misspecified, there are not sufficient studies for the meta-analysis to study this issue and assess whether the premium is different when self-selection is controlled for. A further limitation is the difficulty of taking account of changes over time, such as changes in regulations or business practices such as corporate governance as the small number of papers means there are not usually sufficient to test results before and after a change. In developing this area of research, and other research areas concerned with issues of public importance, it would be helpful if journals published a wider range of papers, including papers with insignificant results. Other limitations include some inconsistency in the results regarding investor protection measures, and there are probably not sufficient studies in a wide enough variety of settings for evidence on this issue to be conclusive.

Meta-regression analysis may also help to provide clearer conclusions, and mitigate the effects of publication bias, in other controversial areas of auditing (such as the effect of consulting services on auditor independence, or the incidence of going concern opinions) and thus be capable of providing guidance for policy makers. Future research could also extend to other areas where audit fees provide useful information, such as corporate governance or audit specialization. Other well-known findings may also be influenced by publication bias or issues about the research setting or the researchers. Meta-analysis has potential as to allow diverse


results of research in auditing to be synthesized, and to result in research findings having greater influence on policy.



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0 20 40 60 80 100 120 140 160 -1.5 -1 -0.5 0 0.5 1 1.5

Big firm effect (coefficient)

Big firm effect and precision (1/Se)



Table 1: Number of papers included in the meta-regression analysis

Number of papers 121

Plus additional years reported 39

Plus additional countries reported 13

Plus separate analyses of size 2

Plus separate analyses of categories 7

Total number of studies 182

Minus studies not using ln(fee) as dependent variable

5 Minus studies not reporting sufficient data 6 Minus studies for which no Big firm share

measure available


Studies reporting sufficient data 160

Table 2: Summary of significance of results

Positive and highly significant (1% or less) 70 Positive and somewhat significant (from 1% to 5%) 29

Not significant 59

Negative and somewhat significant (from 1% to 5%) 1 Negative and highly significant at 1% or less 1

Total 160

Table 3: Descriptive statistics of continuous variables (160 observations)

Variable Mean Std. Dev. Min Max Median

COEFFICIENT .180 . 179 -.50 1.01 .151

TSTATISTIC 2.472 2.941 -3.66 28.86 2.085

STDERROR .107 .183 .01 2.17 .074

PRECISION 16.841 16.840 .46 136.00 13.58

COEFFICIENT = reported coefficient on Big firm variable TSTATISTIC = t-statistic of coefficient Big firm variable STDERROR = standard error of coefficient of Big firm variable PRECISION = 1 divided by STDERROR


Table 4: Descriptive statistics and univariate testing: number of observations and mean coefficient for study characteristics Frequency and mean of the coefficient on Big firm in studies with and without selected characteristics (160 observations) Characteristic Frequency - with characteristic Mean coefficient – observations with characteristic Frequency – without characteristic Mean coefficient – observations without characteristic t-stat Wilcoxon rank-sum test (Z-statistic) US 43 .219 117 .185 -1.692 -2.500* UK 48 .131 112 .200 2.248* 2.307* AUST 22 .119 138 .189 1.703 1.997* NONSTANDARD 27 .127 133 .190 1.661 1.793 PUBLICSECTOR 17 .091 143 .190 2.161* 1.780 PRE90 43 .235 117 .159 -2.387* -2.362* NINETIES 91 .146 69 .225 2.815** 2.705** POST2000 26 .208 134 .174 -.872 -.793 ISBIG 97 .189 63 .165 -.837 -.024 TOP5JOURNAL 42 .175 118 .181 .191 -.741 SSCI 88 .179 72 .180 .037 -.652 USJOURNAL 64 .223 96 .151 -2.535* -2.715** FULLPROF 112 .182 48 .175 -.220 -.689 TOP100UNI 82 .187 78 .172 -.536 .442 BIG4AFFIL 29 .207 131 .174 -.902 -1.192 Significance: * 5%, ** 1%

US = 1 for US data, 0 otherwise; UK = 1 for UK data, 0 otherwise; AUST = 1 for Australian data, 0 otherwise; NONSTANDARD = 1 for non-standard entities including pension funds, municipalities, schools, and pension funds) etc, 0 for listed companies; PUBLICSECTOR = 1 for public sector entities, 0 otherwise; PRE90 = 1 for data before 1990, 0 otherwise; NINETIES = 1 for date from 1990-2000, 0 otherwise; POST2000 = 1 for data after 2000, 0 otherwise

ISBIG = 1 if the Big firm premium was an issue being investigated by the research, 0 otherwise; TOP5JOURNAL = 1 if published in Accounting Review, Journal of Accounting Research, Accounting, Organisations and Society, Contemporary Accounting Research or Auditing: A Journal of Theory and Practice, 0 otherwise; SSCI: 1 for studies published in journals with SSCI Impact factor >1, 0 otherwise; USJOURNAL: 1 for studies published in journals in the US, 0 otherwise; FULLPROF: 1 for studies where at least one author is a full professor, 0 otherwise; TOP100UNI: 1 for studies where at least one author is attached to a Top 100 university, 0 otherwise; BIG4AFFIL = 1 if least one author holds a named chair or other named position affiliated to a Big firm, 0 otherwise.


Table 5: regression models of study effect on precision and study characteristics Panel A: Model including intercept and precision only

Variable Coef. Robust Std. Err. t Sig. 1/Se .064 .043 1.48 .140 INTERCEPT 1.382 .601 2.30 .023 Observations 160 F-statistic 2.20 .140 R-squared .137 Adj. R-squared .132


Panel B: Model including period and country measures and public sector Coef. Robust Std. Err. t Sig. Zk variables 1/Se .121 .040 3.02 .003 NINETIES/Se -.066 033 -2.01 .046 POST2000/Se -.006 .068 -0.08 .934 US/Se -.017 .041 -.41 .685 UK/Se -.016 .046 -0.34 .733 AUST/Se -.036 .037 -.96 .337 PUBLICSECTOR/Se -.087 .041 -2.16 .033 Intercept INTERCEPT 1.487 .251 5.93 .000 Observations 160 F-statistic 4.59 .000 R-squared .228 Adj. R-squared .197

Precision effect testa:

F-statistic 3.41 .067

1/Se = Precision (1 divided by standard error); NINETIES = 1 for date from 1990-2000, 0 otherwise; POST2000 = 1 for data after 2000, 0 otherwise; US = 1 for US data, 0 otherwise; UK = 1 for UK data, 0 otherwise; AUST = 1 for Australian data, 0 otherwise; PUBLICSECTOR = 1 for public sector entities, 0 otherwise.


Panel C - Model including decade dummies, investor protection and Big firm market share Coef. Robust Std. Err. t Sig. Zk variables 1/Se .149 .114 1.30 .194 NINETIES/Se -.056 .030 -1.86 .065 POST2000/Se .007 .064 .10 .919 DISCLOSURE/Se 22.850 19.030 1.20 .232 LIABILITY/Se -2.174 14.244 -.15 .879 ENFORCEMENT/Se -2.121 .784 -2.70 .008 PUBLICSECTOR/SE -.089 .039 -2.32 .022 BIG4SHARE/Se -.015 .032 -.47 .642 Intercept INTERCEPT 1.695 .508 3.34 .001 Observations 160 F-statistic 4.81 .000 R-squared .255 Adj. R-squared .216.

Precision effect testa:

F-statistic 6.54 .012

1/Se = Precision (1 divided by standard error); NINETIES = 1 for date from 1990-2000, 0 otherwise; POST2000 = 1 for data after 2000, 0 otherwise; DISCLOSURE = Disclosure requirements index; LIABILITY = Liability standard index; ENFORCEMENT = Public enforcement index (INDEX measures ALL from La Porta et al. 2006);

PUBLICSECTOR = 1 for public sector entities, 0 otherwise; BIG4SHARE = measure of Big firm market share from Bushman et al. (2004).



Table 6: summary results of regression model partitioned to examine issues regarding research and researchers

Model Funnel asymmetry test for publication bias

Precision effect test for an underlying effect free of publication bias

Overall model

Coeff. t-stat p F-statistic p Number of Observations F-statistic p. R-squared Adj. R-squared (1) ISBIG = 1 .843 2.32 .023 4.14 .045 97 21.11 .000 .274 .226 (2) ISBIG = 0 2.865 1.73 .089 2.51 .119 63 9.82 .000 .287 .211 (3) SSCI = 1 .816 1.48 .142 4.55 .036 88 18.42 .000 .577 .546 (4) SSCI = 0 2.352 3.04 .003 5.61 .021 72 3.25 .004 .173 .097 (5) USJOURNAL = 1 2.126 3.79 .000 .58 .451 64 5.39 .000 .290 .215 (6) USJOURNAL = 0 -1.772 -.95 .343 8.55 .004 96 4.58 .000 .622 .596 (7) FULLPROF = 1 1.609 3.31 .001 694 .009 112 7.95 .000 .253 .210 (8) FULLPROF =0 1.402 1.63 .112 1.59 .215 48 10.44 .000 .412 .326 (9) TOP100UNI = 1 1.201 2.29 .025 3.21 .078 82 6.05 .000 .298 .242 (10) TOP100UNI = 0 .555 .72 .476 4.19 .044 78 7.16 .000 .694 .668 (11) BIG4AFFIL = 1 1.129 .35 .727 .20 .660 29 38.49 .000 .778 .717 (12 BIG4AFFIL = 0 1.593 2.87 .005 8.60 .004 131 3.27 .002 .251 .215

ISBIG: indicator variable for studies where Big firm is the issue of research interest; SSCI: indicator variable for studies published in journals with SSCI Impact factor >1; USJOURNAL: indicator variable for studies published in journals in the US; FULLPROF: indicator variable for studies where at least one author is a full professor; TOP100UNI: indicator variable for studies where at least one author is attached to a Top 100

university; BIG4AFFIL: indicator variable for studies where at least one author holds a named chair or other named position affiliated to a Big firm.




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