Competition in the audit market

Transcription

1 Competition in the audit market Joseph Gerakos Chad Syverson July 11, 2012 Abstract We estimate the demand of publicly traded firms for the Big 4 auditors. Using these demand estimates, we calculate the expected changes in consumer surplus arising from the disappearance of one of the Big 4 audit firms and from the implementation of mandatory audit firm rotation. Our conservative estimated decreases in consumer surplus range from $1.48 billion for the disappearance of Deloitte Touche to $1.85 billion for the disappearance of PriceWaterhouseCoopers. These are the total amount of transfers clients would require to compensate them for losing the ability to hire one of these firms as an auditor. Such losses are substantial; for comparison, total audit fees for public firms were $11 billion in Regarding mandatory audit firm rotation, we find similarly large impacts. Firms would lose $3.5 billion in consumer surplus if rotation were required after ten years and $5.6 billion if mandatory rotations were required after only four years. 1 Introduction An audit is a necessary input for a publicly traded firm. Set against the mandatory nature of this input demand is the fact that the market s supply side is highly concentrated. Among publicly traded companies in the U.S., for example, the majority of audit engagements and almost all audit fees involve just four audit firms (the Big 4 : Ernst & Young, Deloitte Touche, KPMG, and PriceWaterhouseCoopers). In 2009 the Big 4 handled 67 percent of audit engagements and collected over 94 percent of audit fees. (For a breakdown of market shares, see Table 1.) Similar concentration is observed in the audit markets of many other developed economies. This combination of mandated purchase and concentrated supply raises two major questions for academics and policy makers. First, what would be the effects of continued concentration in the Affiliations: Joseph Gerakos, University of Chicago Booth School of Business; Chad Syverson, University of Chicago Booth School of Business and NBER. We thank Ray Ball, J.P. Dubé, Ron Goettler, Bobby Gramacy, Günter Hitsch, Doug Skinner, Anne Vanstraelen, and workshop participants at Maastricht University for their comments. 1

2 audit industry, say if one of the Big 4 audit firms disappeared? Second, imposition of mandatory audit firm rotation has recently been a topic of considerable debate. How would implementation of such a policy affect market participants? Both questions have likely already played roles in policy toward the industry. There have been several recent cases in which a Big 4 audit firm could arguably have been criminally indicted but the Department of Justice decided to not file charges, probably because of concerns about further increasing concentration. 1 For example, in 2007 KPMG admitted criminal wrongdoing by creating tax shelters that helped clients evade $2.5 billion in taxes. Nevertheless, the Department of Justice did not indict KPMG and instead entered into a deferred prosecution agreement. Moreover, according to the Lehman Brothers bankruptcy examiner s report, Ernst & Young assisted Lehman Brothers in implementing its Repo 105 transactions, which allowed Lehman to temporarily reduce its leverage when preparing its financial statements. Nonetheless, the Department of Justice did not pursue criminal charges against Ernst & Young. 2 With regard to mandatory auditor rotation, the Public Company Accounting Oversight Board (the PCAOB ) is in active discussions about implementing such a policy for SEC registrants. During the PCAOB s recent hearings in March 2012 on mandatory audit firm rotation, panelists voiced opposing views about the costs and benefits of mandatory audit firm rotation. For example, the executive director of the AICPA s Center for Audit Quality stated that mandatory audit firm rotation would hinder audit committees in their oversight of external auditors, while former SEC chairman Arthur Levitt supported mandatory rotation because investors deserve the perspectives of different professionals every so often, particularly when an auditor s independence can be reasonably called into question (Tysiac (2012)). Addressing these questions satisfactorily requires, at the very least, measurements of the willingness of firms to substitute among individual auditors and the value firms place (if any) on extended relationships with auditors. However, prior research on the structure of the audit market has focused primarily on either correlations between audit fees and firm characteristics or substitutability between the Big 4 and non-big 4 auditor groups. While this work has offered insights to several questions, its focus has left a gap that we seek to begin to fill with this study. 1 A criminal indictment virtually prohibits an audit firm from carrying out audits of SEC registrants. 2 In contrast, the New York attorney general Andrew Cuomo sued Ernst & Young claiming that the audit firm helped Lehman engage in a massive accounting fraud. 2

3 Our empirical approach treats the audit market like any other differentiated product market. We model firms seeking audit services as choosing from among several producers of those services (i.e., the audit firms), with each producer offering different aspects of service that are differentially valued by each firm. 3 Each firm considers how well the attributes of each auditor s product match its needs (these attributes include price the audit fees) and hires the auditor offering the best match. With this factor demand framework, we can use data on publicly listed firms choices of auditors to measure via revealed preference how firms view the audit services provided by each of the Big 4 auditors as well as by smaller audit service providers. Importantly, we can measure a firm s willingness to substitute among auditors. That is, we can compute the dollar transfer necessary to make a client switch to a different auditor, and in particular what transfers would be necessary to compensate clients of a disappearing Big 4 auditor for having to switch to one of the remaining Big 3. Moreover, we can also gauge clients willingness to pay for longer-term relationships with a particular auditor, and hence what value the firms would lose if forced to break such relationships because of auditor rotation. As mentioned above, knowing these values is critical to be able to answer the questions of the effects of further industry concentration and mandatory auditor rotation. Our preliminary analyses indicate large losses in firms expected consumer surplus (i.e., the value to firms of their purchased audit services in excess of the fees they pay for them) if any of the Big 4 auditors disappear, though some would create losses larger than others. Based on estimates of demand from firms recent choices of auditors, our conservative estimated decreases in consumer surplus range from $1.48 billion for the disappearance of Deloitte Touche to $1.85 billion for the disappearance of PriceWaterhouseCoopers. These are the total amount of transfers clients would require to compensate them for losing the ability to hire one of these firms as an auditor. Such losses are substantial; for comparison, total audit fees for public firms were $11 billion in Regarding mandatory audit firm rotation, we find similarly large impacts. Firms would lose $3.5 billion in consumer surplus if rotation were required after ten years and $5.6 billion if mandatory rotations were required after only four years. These estimates carry several caveats. First, the Big 4 audit firms operate worldwide, while our 3 Because audits are inputs into firms production activities, these are differentiated factor markets, but the economics are essentially the same as in markets for differentiated outputs. 3

4 estimates are based only upon their U.S. public clients. Second, given a lack of publicly available data we are also unable to include private firms in our analysis. Finally, our estimates are limited to audit fees and services and do not take into account non-audit and audit-related fees and services. Nevertheless, these estimates provide preliminary information to regulators about the costs that could arise from changes in market structure and from the implementation of mandatory rotation. In addition, they provide some of the first estimates of the value of audit firm-client matches. Such estimates are missing in the academic literature. In future drafts we will extend this analysis in multiple directions. We will investigate the impact of reduced concentration in the industry, say if one of the smaller auditors experienced considerable growth, or if one of the Big 4 were broken up. Additionally, we will characterize the supply side of the audit industry. This will allow us to see, for instance, how remaining auditors might change their fee-setting behavior if the industry were to become more concentrated due to exit or merger. This supply-side response, as it is likely to lead to an increase in market power among surviving auditors and higher fees, is likely to exacerbate the aforementioned losses in value suffered by firms seeking audit services. Our analysis is structured as follows. We first discuss how we model firms auditor choices. We then discuss estimation of the demand model, including our approaches for dealing with the standard price endogeneity issue. We also discuss how we handle a more atypical situation in demand estimation the fact that we do not observe prices (fees) for producers (auditors) that a firm does not hire. After reporting and discussing our demand estimates, we use them to calculate the effects of increasing audit industry concentration (we compute separate effects for disappearance of each of the Big 4) and mandated auditor rotation. We conclude with a discussion of how we plan to model the extensions to this analysis in future versions of the paper. 2 Demand side We model publicly listed firms demand for audit services as a choice among several auditors (each of the Big 4 and an amalgam outside good that includes all other audit firms). Each firm makes its choice based on the expected benefit it obtains from each of the possible auditors. This benefit includes the effects of both firm-, auditor-, and match-specific attributes and is net of the fees the 4

5 auditor charges the firm for its service. While the model we lay out below is in many ways standard in the industrial organization literature, our approach differs from prior literature on auditor choice in that this work has typically examined the determinants of the simple dichotomous choice between using a Big 4 versus a non- Big 4 auditor. Our analytical structure allows us to both characterize much more fully the patterns of substitution among the individual audit firms, but just as importantly lets us tie firms choices directly to parameters of firms factor demands that can be interpreted in terms of dollar values. 2.1 Utility specification For each firm s choice of auditor, we specify the inside goods as the Big 4 auditors (Ernst & Young, Deloitte Touche, KPMG, and PriceWaterhouseCoopers) and the outside good as the aggregation of all other auditors who provide audits to public firms (BDO Seidman, Grant Thornton...). We assume that each year a publicly traded firm chooses whether to keep its existing auditor or switch to another audit firm. We assume that when making this choice the client forms expectations about the fees that each of the Big 4 and the non-big 4 composite auditor would charge for an audit. We model each client firm i s utility from the choice of auditor j as taking the following linear form U ij = j i ln(p ij )+ ij x ij + ij (1) in which j is an auditor (or brand) fixed-effect that represents the mean utility that clients receive for each auditor j, p ij is the auditor j s price (i.e., audit fees) for an audit of firm i, i represents firm i s marginal willingness to pay for a log-dollar of audit fees, x ij are observable non-price characteristics of the client-auditor pair, ij are the utility loadings on these characteristics, and ij represents an unobserved client-auditor specific component of utility assumed to be independently and identically distributed. 4 In our specification, audit fees enter in logarithm form. The logarithm form implies that an additional dollar of audit fees matters less to a large client than a small client. This is consistent with the common practice of clients negotiating with their existing auditors over percentage changes in audit fees rather than absolute dollar changes. To model the interactions between non-price characteristics of the client and the audit firm, we 4 While we have labeled equation (1) as describing a client firm s utility, it can be interpreted more broadly as any objective function of the client s with respect to its audit firm choice. 5

6 expand ij x ij as follows. First, we interact the auditor fixed effect, j, with the natural logarithm of the client s size ln(t otalassets i ). This interaction allows us to capture audit firm preferences that vary with client size. For example, smaller firms may prefer non-big 4 auditors, and there can be heterogeneous size-based preferences for each of the Big 4 auditors. Second, we include the client s past history with the audit firm. To do so, we include the natural logarithm of the number of years that firm i has been a client of auditor j, ln(yearsclient ij ) and an indicator variable coded as 1 if the firm was not a client of the auditor in the prior year, and 0 otherwise, 1(Not client ij ). These variables allow demand preferences to vary with the history of the client-audit firm match. This captures any influence of client-auditor specific capital that might be built over the audit relationship. The overall specification for utility of firm i for choosing auditor j is therefore U ij = j 1 ln(p ij )+ 1j j ln(t otalassets i )+ 2j ln(yearsclient ij )+ 3j 1(Notclient ij )+ ij. (2) Client i calculates U ij for each of the Big 4 firms and the outside good and then chooses the audit firm j that provides the maximum U ij. This linear specification is standard in the industrial organization and marketing literatures for modeling the demand for discrete differentiated products. 2.2 Estimation Utility for client i and auditor j can be specified as U ij = V ij + ij in which V ij ij x ij i p ij + j is the observable portion of utility and ij is the unobserved portion of utility. If we assume that ij is distributed type 1 extreme value, the predicted probability that client i chooses audit firm j is P ij = ev ij j e V ij. (3) This specification is referred to as the conditional logit and is commonly used in the industrial organization and marketing literature to estimate demand for discrete differentiated products. 5 Conditional logit is similar to a fixed effect regression in that any characteristic of client i that does not vary across the audit firm choices drops out of equation (3). For example, firm-size on its own drops out of equation (3), but interactions between the auditor fixed-effects and firm size remain. 5 For a discussion, see Train (2009). 6

7 If y ij =1represents that client i chooses auditor j and zero otherwise, then the log likelihood is as follows: LL(,, )= X i X y ij ln P ij = X j i X y ij ln ev ij j j e V ij (4) We maximize this log likelihood to obtain estimates of the preference parameters,, and. 2.3 Prices One issue with equation (2) is that we only observe prices (audit fees) for actual matches between clients and auditors. This is unusual situation in most demand estimation settings; the researcher typically observes the prices of each item of the available choice set. We must therefore estimate what fees a client would have expected to pay had it hired an audit firm other than the one it ended up choosing. We implement this estimation using a predictive model estimated from the relationships between the fees in observed client-auditor matches and client-, auditor-, and match-specific characteristics. We considered several prediction methods including ordinary least squares, lasso regression, ridge regression, partial least squares, and several regression tree approaches (random partitioning, conditional inference trees, and random forest). 6 Based on root mean squared error derived from cross-fold validation, we found that regression trees (specifically, random forest) best predict dollar audit fees using the following set of predictor variables: total assets, the number of industrial segments, foreign sales, long term debt, short term debt, return on assets, loss indicator, receivables, inventory, market value of equity, indicator for accelerated filer, indicator for going concern in prior year, and indicators to capture whether and for how long the firm was a client of the auditor. We include polynomials up to the fourth power for both total assets and the natural logarithm of total assets. For the number of industrial segments, foreign sales, long term debt, short term debt, receivables, inventory, and market value of equity, we also include the natural logarithm of these variables. 7 It is important to note that in our demand estimations, we use predicted fees for all auditors, including for the audit fees charged by the actual audit firm chosen by the client. We do so because 6 For discussion of these methods, see Hastie, Tibshirani, and Friedman (2009). 7 Although this is a large predictor set, over fitting is not an issue given that we use cross-fold validation. Moreover, most of the prediction methods we considered include a penalty for each additional predictor. 7

8 it is likely that the prices associated with actual choices include a negative price shock that could bias our estimated price coefficients toward zero. For a discussion of this issue, see Erdem, Keane, and Sun (1999) Price endogeneity A major concern with estimating equation (2) is the possibility of price endogeneity (e.g., cov(p ij, ij ) 6= 0). For example, if price is correlated with unobserved audit quality, then the coefficient on price will be positively biased (toward zero, given that theory predicts the coefficient should be negative). As a result, the demand estimates would make it appear that firms are less sensitive to audit fees than they really are. A way to avoid this bias is to identify firms price sensitivity using fee variation that is driven by supply-side factors that are uncorrelated with demand shifts. We include two sets of supply shifters in our audit fee prediction regressions to aid in this identification: one uses the change in supply structure induced by the disappearance of Arthur Andersen and the second uses increases in auditor supply created by client mergers and acquisitions. Disappearance of Arthur Andersen We assume that the collapse of Arthur Andersen was an exogenous shock to supply in the audit market. Namely, the collapse of Arthur Andersen reduced competition among auditors, leading to increased audit fees, and this competitive effect was orthogonal to shocks to demand for the audit firms. Moreover, given the prior research on auditor specialization, we assume that the shock varied with Andersen s share of client industries, thereby providing cross-industry variation in the reduction of supply. To validate the disappearance of Arthur Andersen as a supply shifter, Table 2 presents ordinary least squares regressions that regress the log growth in the client s total audit fees on the natural logarithm of the total assets in each four-digit SIC audited by Arthur Andersen in 2001, ln(andersen 0 ssharein2001). If our assumption is correct that Andersen s disappearance is an inward shift in audit supply, the coefficient on Andersen s 2001 share should be positive. We estimate these regressions for each year between 2002 and We include as additional controls indicator variables for the firm s auditor in 2001 to capture differences in fee growth that are driven by the client s auditor in For example, the fee growth for Andersen clients could differ from the fee growth for firms that were Ernst & Young clients in We also include the 8

9 change in the client s logged total assets over each period, as the prior literature has found that total assets is the major predictor of audit fees. We cluster the standard errors by four-digit SIC. Because we require that the data is available over each change, the sample size drops monotonically from 4,970 clients for to 2,809 clients for The results in Table 2 indicate that the supply shift measure ln(andersen 0 sshare2001) is indeed positive and significant at each horizon. That is, industries in which Andersen had a larger market share experienced greater growth in audit fees. Importantly, this effect lasted through With respect to the audit firm indicators that capture average growth in fees, these coefficients are, in general, similar in magnitude for the clients of Arthur Andersen and Big 4 in One exception is that for 2002, clients of Arthur Andersen experienced a decrease in fees, which was probably due to the Big 4 offering aggressive prices to lure former Andersen clients. Clients of the non-big 4 experienced lower fee growth over all horizons. Consistent with the documented levels relation between total assets and audit fees, the coefficients on the log change in total assets are positive and significant for each year between 2002 and An alternative explanation for these results is that Arthur Andersen charged lower prices and provided lower quality audits, thereby leading to greater increases in audit fees for Andersen clients. We do not believe that such an effect drives the results presented in Table 2 for two reasons. First, Cahan, Zhang, and Veenman (2011) find that prior to the Enron scandal, Arthur Andersen provided audits of similar quality to the audits provided by the other major audit firms. Second, in untabulated tests, we find similar effects if we limit the regressions to firms that were not Andersen clients. Given the results presented in Table 2, we include in the annual audit fee prediction regressions the natural logarithm of the total assets in each four-digit SIC audited by Arthur Andersen in 2001, ln(andersen 0 sshare2001). This variable offers variation in audit fees due to supply shocks that should be uncorrelated with clients relative demand for surviving auditors. Client mergers and acquisitions Our second source of supply-driven audit fee variation exploits mergers and acquisitions among client firms. The notion is that a merger in an industry increases the available supply of auditors to the industry. Primarily this increased supply would arise when the pre-merger client firms each have separate auditors but will drop one after. The audit firm 9

10 that loses a client due to merger or acquisition will find itself with excess capacity that should put downward pressure on audit fees. Supply can also shift even if both pre-merger client firms have the same auditor, because even though the merged firm requires greater auditing, the elasticity of audit fees to total assets is approximately This also creates excess audit capacity for the merged firm s auditor and the resulting price effects. These supply shifts will be orthogonal to audit demand shocks as long as client-level mergers and acquisitions are driven by neither auditor choice nor audit fee considerations. To test whether mergers and acquisitions have the expected effects on audit fees, we regress logged fees on the natural logarithm of total client assets in the client s respective four-digit SIC level that were lost by audit firms in the prior year due to mergers or acquisitions, ln(mergers). For control variables, we include the ratio of receivables to assets, the ratio of inventories to assets, the return on assets, an indicator variable for whether the client experienced a loss, the percent of foreign sales, the natural logarithm of the number of industrial segments, an indicator for whether the firm is an accelerated filer, and an extensive set of fixed effects. We cluster standard errors at the client level and estimate the regressions over the sample period Table 3 presents the results. Columns (1) and (3) include audit firm fixed effects and columns (3) and (4) include client fixed effects. All four regressions include year fixed-effects. Consistent with ln(mergers) representing an increase in the supply of auditing, its coefficient is negative and statistically significant in all four specifications, implying that greater mergers and acquisitions of clients are associated with the audit firm charging lower audit fees in the subsequent year. We therefore include this variable in the audit fee prediction regressions. With regard to the controls, as prior literature typically specifies audit fee regressions using pooled cross-sections, it s worth noting the similarity between the coefficients presented in columns (1) and (2) and those in prior audit fee research. These are similar in sign, magnitude, and significance to those in earlier work. For example, the elasticity with respect to firm size ranges from with auditor fixed-effects to without auditor fixed-effects. In addition, fees increase in losses, inventory, foreign sales, accelerated filers status, and a going concern. They decrease in receivables and inventory. 10

11 2.3.2 Fit of predicted audit fees The within-sample fitted values from our random forest prediction specification are highly correlated with actual audit fees. The Pearson product moment correlations between actual and predicted fees are as follows: Ernst & Young, 0.976; Deloitte Touche, 0.967; KPMG, 0.970; PwC, 0.968; all other auditors, Figure 1 presents plots of actual versus predicted audit fees for our sample. The left figure presents the plot for the entire distribution of actual fees and the right figure presents the plot for actual fees between the 1st and 99th percentiles. These plots show that the prediction model does well over most of the distribution of actual audit fees. The exception is that the model underpredicts fees above the 99th percentile. In untabulated tests, we estimated demand while excluding clients with actual audit fees above the 99th percentile. Results for this restricted sample are qualitatively and quantitatively similar to those presented in the tables. 3 Demand estimation 3.1 Sample Our sample consists of SEC registrants with available data. It starts in 2002 and ends in We start in 2002 because, as explained above, we rely on exogenous variation created by the disappearance of Arthur Andersen. We pull audit fee data from Audit Analytics, which provides audit fee data starting with the mandatory disclosure of audit fees in We use Compustat to obtain accounting-based control variables and the histories of auditor-client matches for prior to Finally, we use SDC Thomson to identify client-level mergers and acquisitions. 3.2 Conditional logit results Table 4 presents the results from the annual conditional logit regressions that estimate clients preference parameters for auditor choice. These form the basis for our estimates of clients willingness to pay for audit services and willingness to substitute among audit firms. We estimate the conditional logit regressions annually over the period and include the variables listed in equation (2). Across the annual estimates several patterns emerge. First, for each of the Big 4 audit firms, the interactions between the audit firm fixed-effects and client size are positive and significant each 11

12 year, implying that larger clients prefer the Big 4 compared to the non-big 4. For each of the Big 4 auditors the largest coefficients on the size interactions are in 2005, which was the first year subsequent to the implementation of the Sarbanes-Oxley internal control requirements. Second, the coefficients on the interactions with 1(Notclient ij ) are negative and significant for each of the Big 4 auditors in each annual regression and the interactions with ln(yearsclient ij ) are positive and significant for many of the years. These results imply that either there are significants costs associated with switching from your current auditor or that there are heterogeneous preferences for audit firms that lead to long-term matches between auditors and clients. The coefficient on ln(audit fees ij ) is negative and significant for each year in the sample, with the coefficient having the smallest absolute magnitude in 2004, which was the first year of the Sarbanes Oxley internal control requirements. A lower coefficient on price for that year implies that non-price characteristics of an audit increased in importance relative to price. While as noted we focus on the post-2001 period in order to exploit exogenous variation created by the implosion of Arthur Andersen, we found in untabulated tests that the coefficient on ln(audit fees ij ) is also negative and significant for 2000 and Given that we are estimating a non-linear model, the coefficients on the interactions do not represent marginal effects. In Table 5, we therefore present for comparison marginal effects for size and the history of the match between the client and audit firm. These computed values measure the changes in choice probabilities associated with a change in the demand shifter. We use the preference parameter estimates for 2009 to calculate the marginal effects in the table. Panel A presents marginal effects over various points in the client size distribution. Several patterns emerge in the marginal effects of size. First, there is heterogeneity across the audit firms. Starting at the 10th percentile of client size, the marginal effects are greatest for Ernst & Young, rising from at the 10th percentile to at the 99th percentile. Below the 10th percentile, the smallest marginal effects are for PriceWaterhouseCoopers. Above the 10th percentile, Price- WaterhouseCoopers marginal effects are the second largest. In contrast, for KPMG and Deloitte the marginal effects with respect to client size are smaller than for Ernst & Young and PriceWaterhouseCoopers starting at the first quartile and begin to taper off at the 90th percentile of client size. Panel B presents marginal effects based on the length of the match between the client and 12

13 audit firm. Once again these effects vary across the Big 4 audit firms. A client that has been with Ernst & Young for 10 years is only about three percentage points more likely to choose Ernst & Young again than one that has been with E&Y for 1 year. On the other hand, a 10-year client of PriceWaterhouseCoopers is over 13 percentage points more likely to stick with PwC than a first-year client. Table 6 Panel A presents annual mean estimates of the audit firms own price elasticities the percentage change in the probability of choosing the auditor for a one percent increase in price. In general, the estimates are close to unit elastic for the Big 4. Across the years, Deloitte appears to have the most elastic demand of the Big 4, while Ernst & Young has the least elastic demand. Across all of the years, non-big 4 firms have on average less elastic demand than the Big 4. Of the years, in 2004 the mean elasticities across all of the audit firms are smallest in absolute magnitude. Interestingly, 2004 was the first year that audit firms carried out Sarbanes Oxley 404 internal control inspections. Although the mean estimates are in general elastic or close to elastic, as shown in Panel B the mean elasticities for the client s prior auditor are almost always inelastic. This appears to be driven by either switching costs or heterogeneous brand preferences. 3.3 Additional items Auditor overlap with competitors Aobdia (2012) documents the empirical regularity that large firms in concentrated industries are less likely to share auditors, presumably because of concerns about the transmission of proprietary information through the auditor. 8 We therefore created the variable CompetitorOverlap ij which is coded as the product of an indicator for whether firm i is within the top three firms in its industry as defined by four digit SIC, an indicator for whether auditor j audited at least one other top three firm in the industry, and a measure of the industry s concentration (the percentage of industry sales controlled by the top three firms). When we include CompetitorOverlap ij in our conditional logit specification, the coefficients are negative and therefore consistent with the findings of Aobdia (2012). The coefficients are not, however, statistically significant. This lack of significance appears to be driven by the fact that prior history of the match between the audit firm and client soaks up 8 Asker and Ljungqvist (2010) find a similar effect for firm-bank matches. 13

14 variation related to CompetitorOverlap ij. For example, when we estimate demand but exclude the history of firm-client match, CompetitorOverlap ij enters significantly for many of the years Nested logit An alternative model of audit firm choice is that clients first choose whether to use a non-big 4 or Big 4 auditor and then, conditional on choosing a Big 4 auditor, choose which of the Big 4 to engage. To explore this possibility, we re-estimated our demand system using a nested logit specification. For these estimates, the substitution parameter between Big 4 and non-big 4 is not significantly different than the parameters that arise under the conditional logit model. Therefore for the sake of parsimony we stick with the conditional logit model Dollar fees In addition to the log price specification in equation (2), we also tried a dollar price specification. A dollar price specification assumes that a dollar of audit fees is equally important to large and small firms. For the dollar price specification, the non-price preference parameter estimates are similar to those presented in Table 4. The elasticity estimates are, however, about half the magnitude of those based on the log price specification. The log price specification appears to be better able to handle the heterogeneity in audit fees driven by firm size differences. 4 Counterfactuals We next use the parameter estimates presented in Tables 4 and 6 to calculate the expected changes in consumer surplus arising from two sets of counterfactuals: the (separate) disappearance of each of the Big 4 audit firms and the implementation of mandatory audit firm rotation at various tenures. To estimate these counterfactuals, we use the methodology outlined by McFadden (1999). This methodology involves calculating the expected change in consumer surplus for each audit client as the expected dollar transfer required to make the client indifferent between the unrestricted choice set of the status quo and the restricted choice set arising under the counterfactuals. We then sum the individual client estimates to come up with the expected total change in consumer surplus. For example, suppose that under the status quo client i chooses the auditor j that leads to 14

15 maximized utility max j U(Audit fees ij,x ij, ij ), and under the counterfactual firm i chooses auditor m from a restricted choice set that leads to maximized utility max m U(Audit fees im,x im, im ). The change in consumer surplus, C ijm, is the dollar transfer (or reduction in audit fees) required to equate the client s maximum utility under the unrestricted choice set with the client s maximum utility based on the restricted choice set: max U(Audit fees ij,x ij, ij ) = max U(Audit fees im C ijm,x im, im ). (5) j m To calculate the total change in consumer surplus for the counterfactual, one can add up the C ijm s across client firms. Under each counterfactual, we estimate C ijm for each firm i. To do so, we draw vectors of type 1 extreme value error terms one for each of the Big 4 auditors and one for the outside good. For each vector draw, we combine in equation (2) the parameter estimates from the demand estimation along with the the observed firm and auditor characteristics and the error term draw to calculate the utility that the client firm would receive from choosing each of the Big 4 auditors and the outside good. We then pick the audit firm that leads to maximum utility under this unrestricted choice set. We next restrict the choice set for each client (i.e., remove one of the Big 4 auditors or remove the client s prior auditor based on tenure) and calculate the maximum utility that the client would receive under the restricted choice set. Then we solve for the C ijm that equates these two maximized utilities. We repeat this procedure 1,000 times for each client and take the average of the required dollar transfer over these error draws to create E[C ijm ]. For each counterfactual we add these estimates across client firms to calculate the expected total change in consumer surplus. 4.1 Loss of a Big 4 audit firm The first set of counterfactuals is based on the loss of a Big 4 audit firm. Using the demand estimates for 2009, we estimate the total expected changes in consumer surplus if each of the Big 4 disappears. We do so by removing from each client s choice set each of the Big 4 firms one at a time. Table 7 presents the estimates along with each firm s total audit fees for our sample in The estimated total changes in consumer surplus range from a loss of $1.48 billion for the disappearance of Deloitte Touche to a loss of $1.85 billion for the disappearance of PriceWaterhouseCoopers. These 15

16 are substantial values; for all of the Big 4, the estimated changes in consumer surplus are over 60 percent the firm s total audit fees for our sample. The largest change relative to total fees is for KPMG, 77 percent, and the smallest is for PriceWaterhouseCoopers, 63 percent. These estimates are subject to several caveats. One that would mitigate the size of the estimated losses is the possibility that audit teams from the disappearing audit firm could move en masse with their clients to the remaining audit firms. This would reduce switching costs or maintain matches based on heterogeneous preferences even if an audit firm disappears as a legal entity. 9 On the other hand, there are several reasons why these estimates might understate the true loss in client firms consumer surplus. For one, the estimates do not include losses in consumer surplus that could arise from non-audit services (such as consulting and tax services) provided by the Big 4 firms to their clients. Additionally, the estimates exclude any effect that the disappearance of a Big 4 firm would have on that firm s domestic private and international clients. Finally, as we discuss in Section 5, these estimates do not account for potential strategic price responses by the remaining audit firms that could lead to higher audit fees and further losses in consumer surplus. 4.2 Introduction of mandatory audit firm rotation The second set of counterfactuals is based on the implementation of mandatory audit firm rotation. To estimate the total expected change in consumer surplus that would occur if mandatory rotation were to be implemented, we calculate the dollar transfer that would be required to make clients indifferent to the removal of their current auditor from their choice set after four through 10 years of tenure. We again base these estimates on the demand parameters for Table 8 presents these expected total changes in consumer surplus. They are significantly larger than expected changes that arise from the disappearance of one of the Big 4 and range from a $3.47 billion loss if rotation is mandatory after 10 years to a $5.60 billion loss if rotation is mandatory after four years. The fact that these estimated total changes in consumer surplus are significantly larger than the changes in consumer surplus arising from the disappearance of a Big 4 audit firm is to a certain extent not surprising given that mandatory rotation has potential to affect any client, not just the clients of the disappearing firm. These estimates provide policy makers with estimates 9 Consistent with this possibility, Blouin, Grein, and Rountree (2007) find that some Arthur Andersen clients followed their Andersen audit teams to the remaining Big 4 auditors. 16

17 of the minimum dollar benefits required to justify mandatory audit firm rotation. As with the counterfactuals in the prior section, these estimates are subject to the caveat that they do not take into account strategic price responses by the audit firms in response to the introduction of mandatory rotation. 5 Supply response Our estimated changes in consumer surplus are based only on our demand estimates of client firms willingness to substitute among audit firms and do not take into account any strategic price responses that audit firms might make in the counterfactual scenarios. In other words, ours is a partial equilibrium analysis. In future drafts, we will estimate a model of the supply side of the audit industry. This will allow us to calculate the counterfactual price responses that would further impact the expected changes in consumer surplus. Moreover, this will let us estimate the gross profits of the Big 4 auditors. To model the supply side we assume that each client represents a static oligopoly market in which each auditor offers the client a differentiated product. Audit firms price strategically based on client firms demand and the expected pricing decisions of competing auditors. For each potential audit client, the audit firm maximizes the following profit function ij (p i )=q ij (p i )(p ij mc ij ) (6) in which q ij (p i ) is the quantity sold which depends on the vector of prices of all audits offered to the client, p i, mc ij represents the audit firm j s marginal cost of providing an audit to client i, and p ij represents the price of audit firm j providing an audit to client i. Using our demand parameter estimates, we can solve for the strategic price responses under the counterfactuals by either inverting the first order conditions of equation (6) or by calculating iterated best responses. 17

18 6 Conclusion Using estimates of the demand for the Big 4 audit firms, we calculate the expected changes in consumer surplus arising from changes in industry structure. Our conservative estimated decreases in consumer surplus range from $1.48 billion for the disappearance of Deloitte Touche to $1.85 billion for the disappearance of PriceWaterhouseCoopers. These are the total amount of transfers clients would require to compensate them for losing the ability to hire one of these firms as an auditor. Under the implementation of mandatory audit firm rotation, firms would lose $3.5 billion in consumer surplus if rotation were required after ten years and $5.6 billion if mandatory rotations were required after only four years. We plan to extend this analysis in multiple directions. First, we will investigate the impact of reduced concentration in the industry, say if one of the smaller auditors experienced considerable growth, or if one of the Big 4 were broken up. Second, we will characterize the supply side of the audit industry. This will allow us to see, for instance, how remaining auditors might change their fee-setting behavior if the industry were to become more concentrated due to exit or merger. Finally, we further plan to examine whether audits as a product are vertically or horizontally differentiated and what are the industry characteristics that led to the current level of concentration. 18

19 References Aobdia, D., Proprietary information spillovers and auditor choice, Unpublished working paper, UCLA. Asker, J., Ljungqvist, A., Competition and the structure of vertical relationships in captial markets. Journal of Political Economy 118 (3), Blouin, J., Grein, B., Rountree, B., An analysis of forced auditor change: The case of former Arthur Andersen clients. The Accounting Review 82 (3), Cahan, S., Zhang, W., Veenman, D., Did the waste management audit failures signal lower firm-wide audit quality at Arthur Andersen? Contemporary Accounting Research 28 (3), Erdem, T., Keane, M., Sun, B., Missing price and coupon availability data in scanner panels: Correcting for self-selection bias in choice model parameters. Journal of Econometrics 89, Hastie, T., Tibshirani, R., Friedman, J., The Elements of Statistical Learning, 2nd Edition. Springer, New York, NY. McFadden, D., Computing willingess to pay in random utility models. Trade, Theory, and Econometrics: Essays in honour of John S. Chipman 15, Train, K., Discrete Choice Methods with Simulation. Cambridge University Press, New York, NY. Tysiac, K., PCAOB panelists say mandatory firm rotation could be harmful, helpful. Journal of Accountancy 213 (4). 19

20 Figure 1: Actual versus predicted audit fees These figures plot predicted versus actual audit fees. The left figure plots predicted fees against actual fees for the full distribution of actual audit fees. The right figure drops the 1st and 99th percentiles of actual audit fees. We predict dollar audit fees using random forest regression trees with the following set of predictor variables: total assets, the number of industrial segments, foreign sales, long term debt, short term debt, return on assets, loss indicator, receivables, inventory, market value of equity, indicator for accelerated filer, indicator for going concern in prior year, and indicators to capture whether and for how long the firm was a client of the auditor. For total assets, we include polynomials up to the fourth power for both total assets and the natural logarithm of total assets. For the number of industrial segments, foreign sales, long term debt, short term debt, receivables, inventory, and market value of equity, we also include the natural logarithm of these variables. 20

21 Table 1: Market Shares This table presents a breakdown of market shares of public audits. Panel A presents percentage market shares based on fees. Total fees are presented in the last column and are in billions of US Dollars. Panel B presents a breakdown of market shares based on number of clients. Panel A: Year Andersen E & Y Deloitte KPMG PWC BDO GT All others Total fees Panel B: Year Andersen E & Y Deloitte KPMG PwC BDO GT All others Total clients , , , , , , , , , ,222 21

22 Table 2: Disappearance of Arthur Andersen This table presents regressions that test the validity of the use of the disappearance of Arthur Andersen as a shifter of audit firm supply. The dependent variable in the regressions is the difference between the natural logarithm of total audit fees in 2001 and the natural logarithm of audit fees in the relevant year. ln(andersen 0 sshare2001) is the natural logarithm of the total assets in each four digit SIC audited by Arthur Andersen in Robust standard errors clustered at the four-digit SIC level are in parentheses Ln(Andersen s Share 2001) 0.032*** 0.030*** 0.049*** 0.052*** 0.050** 0.047*** 0.050*** 0.036** (0.007) (0.010) (0.017) (0.017) (0.020) (0.017) (0.017) (0.015) Andersen Client in *** 0.400*** 0.824*** 0.899*** 0.984*** 1.008*** 1.032*** 1.024*** (0.051) (0.037) (0.056) (0.058) (0.072) (0.063) (0.064) (0.058) E&Y Client in *** 0.354*** 0.753*** 0.840*** 0.948*** 0.963*** 0.983*** 0.948*** (0.021) (0.036) (0.052) (0.052) (0.065) (0.059) (0.066) (0.061) Deloitte Client in *** 0.273*** 0.696*** 0.828*** 0.917*** 0.956*** 0.964*** 0.966*** (0.026) (0.030) (0.045) (0.046) (0.061) (0.058) (0.053) (0.051) KPMG Client in *** 0.268*** 0.684*** 0.765*** 0.797*** 0.856*** 0.932*** 0.900*** (0.030) (0.055) (0.085) (0.091) (0.102) (0.096) (0.104) (0.068) PwC Client in *** 0.311*** 0.819*** 0.911*** 0.963*** 0.975*** 1.025*** 1.008*** (0.021) (0.032) (0.052) (0.055) (0.070) (0.051) (0.053) (0.047) Other Client in *** 0.429*** 0.545*** 0.628*** 0.658*** 0.753*** 0.796*** (0.035) (0.035) (0.061) (0.051) (0.062) (0.064) (0.051) (0.051) Change Ln(Assets) *** (0.044) Change Ln(Assets) *** (0.036) Change Ln(Assets) *** (0.025) Change Ln(Assets) *** (0.025) Change Ln(Assets) *** (0.025) Change Ln(Assets) *** (0.024) Change Ln(Assets) *** (0.025) Change Ln(Assets) *** (0.021) Observations 4,970 4,680 4,353 3,992 3,664 3,324 3,040 2,809 Adjusted R-squared *** p<0.01, ** p<0.05, * p<0.1 22

23 Table 3: Client mergers and acquisitions This table presents ordinary least squares regressions that test the validity of using audit client mergers and acquisitions as shifters of audit supply. The dependent variable in all four regressions is the natural logarithm of total audit fees. Columns (1) and (3) include audit firm fixed-effects and columns (3) and (4) include client-level fixed effects. All four regressions include year fixed-effects. ln(mergers) represents the exogenous shift in audit supply and demand arising from client-level mergers and acquisitions. It is calculated at the four digit SIC level and is the natural logarithm of total assets of clients that disappeared due to either mergers or acquisitions in the prior fiscal year. Robust standard errors clustered at the client level are in parentheses. (1) (2) (3) (4) Ln(Mergers) *** *** *** ** (0.002) (0.002) (0.001) (0.001) Ln(Assets) 0.409*** 0.454*** 0.248*** 0.261*** (0.004) (0.004) (0.008) (0.008) Receivables to Assets *** *** 0.236*** 0.232*** (0.036) (0.039) (0.043) (0.044) Inventory to Assets 0.592*** 0.637*** 0.150** 0.131* (0.049) (0.051) (0.072) (0.073) Return on Assets *** *** *** *** (0.025) (0.027) (0.019) (0.019) Loss 0.081*** 0.097*** 0.033*** 0.032*** (0.014) (0.014) (0.007) (0.007) Percent Foreign Sales 0.395*** 0.447*** * (0.017) (0.017) (0.016) (0.017) Ln(Segments) 0.195*** 0.216*** 0.029*** 0.035*** (0.009) (0.009) (0.007) (0.007) Accelerated Filer 0.169*** 0.328*** 0.046*** 0.045*** (0.017) (0.018) (0.010) (0.010) Going Concern Opinion 0.082*** *** 0.044*** (0.019) (0.020) (0.013) (0.013) Constant 9.902*** 9.393*** *** *** (0.031) (0.025) (0.046) (0.044) Observations 51,823 51,823 51,823 51,823 Adjusted R-squared Firm fixed effects No No Yes Yes Auditor fixed effects Yes No Yes No Year fixed effects Yes Yes Yes Yes Industry fixed effects No No No No Number of firms 9,576 9,576 *** p<0.01, ** p<0.05, * p<0.1 23