Audit fee residuals: Costs or rents?

Fee residuals are computed as the difference between actual audit fees and predicted audit fees from a regression of audit fees on engagement attributes known to affect audit production costs (see Simunic 1980).

We refer to Deloitte LLP, Ernst and Young LLP, KPMG LLP, and PricewaterhouseCoopers LLP collectively as the Big Four auditors and to all other auditors as non-Big-Four auditors. Auditees of Arthur Andersen LLP are excluded from our analyses.

As in DeFond et al. (2002), many of these studies use multiple measures of auditor rents. Our findings speak only to inferences based on the use of audit fee residuals as a measure of auditor rents. Inferences based on other measures are beyond the scope of our present investigation.

Recall that in the framework discussed earlier (Simunic 1980), audit production costs include all normal costs of audit production, including a competitive compensation for any litigation, regulatory, and reputation risk borne by the auditor.

Survey evidence cited in GAO (2003, pp. 27–28) and PCAOB (2011) indicates that these costs can be quite substantial relative to the annual audit fee for a continuing engagement when these costs are not incurred. Respondents indicated that the auditor’s setup costs are usually in excess of 20 % and the auditee’s share in excess of about 17 % of the recurring audit fee. Furthermore, the survey finds that (under the current system of long auditor tenure) both auditors and auditees usually absorb their portion of these setup costs.

Prior research notes that switching costs alone are not sufficient to generate auditor rents. The magnitude of rents also depends on the distribution of bargaining power between the auditor and the auditee (Dye 1991; Kanodia and Mukherji 1994). The distribution of such power is an empirical question, and whether the switching costs documented in GAO (2003) and PCAOB (2011) do in fact give rise to sizeable auditor rents in the U.S. public company audit market is not presently known. Our tests are designed to illuminate the extent to which audit fee residuals from continuing audit engagements contain a material common rent component.

Auditor startup costs associated with new engagements are unlikely to materially impact these coefficient estimates for two reasons. First, as noted earlier, audit firms generally absorb the startup costs associated with the initial year audit (GAO 2003, p. 28). Consequently, such costs are usually excluded from the dependent variable, y _it . Second, even were y _it to contain some element of startup costs, since the predecessor does not have to bear any startup costs, there is little reason to expect the lagged residual fee, ϵ _it−1 , to be systematically correlated with the successor’s startup costs. Consequently, our estimates of γ ^C and γ ^N are unlikely to be affected by the existence of new auditor startup costs.

In this case, note that (3C) and (3 N) both reduce to y_it = a + cc_i + η_it = a + ϵ _it−1  + η_it, which implies γ ^C  = γ ^N  = 1 in Eqs. (4C) and (4N). The coefficients in each of the special cases discussed below follow directly from analogous substitutions of the respective definitions of ϵ_it−1 into Eqs. (3C) and (3N).

Specifically, if the lagged residual fee consists only of common costs and rents, the impact of these two factors on successor’s fee is expected to be 1 × cc−K × cr. When cr/cc ≥ 1/K, the expected coefficient of lagged fee residuals will be nonpositive! For example, when K = 5 and the lagged residual, ϵ_it−1, consists only of cc and cr, whenever the common rent, cr, is >17 % of ϵ_it−1 (i.e., the common cost, cc, is <83 % of ϵ_it−1), the expected value of γ ^N is 1 × 0.83−5 × 0.17 = (−) 0.02. (In this example, we have chosen to set ic _i  = ir _i  = η = 0 and cr _i /ϵ _i,t−1  = 0.17, so that δ = {0 + 0−(5 + 1)cr _i  + 0}/ϵ _i,t−1  = − 6 × cr _i /ϵ_i,t−1. = 1.02 and 1 − δ = (−) 0.02). If fee residuals were to largely be comprised of rents, an priori necessary condition for fee residuals to be a credible proxy for rents, e.g., if 70–80 % of the fee residual were rents, the coefficient of lagged fee residuals can be expected to be in the vicinity of minus 3 to minus 4.

See Appendix 2 for formal variable definitions. Note that this specification includes all of the audit production cost drivers that have consistently been used in prior research to compute fee residuals. As a result, our procedure yields fee residuals that are (a) comparable to residuals used in prior research and (b) exclude factors such as auditor-related and/or audit market effects whose nature (i.e., whether they represent costs or rents) is presently not known. For instance, our model does not include measures of auditor industry specialization the nature of which (i.e., whether they are costs or rents) is presently are not known. Including auditor industry specialization measures would therefore remove from the residual part of the rents that accrue to incumbent auditors. Our approach of excluding variables that represent such unknown fee influences gives our estimate of the fee residual its best shot at capturing any possible auditor rents. However, as noted in footnote 23, including auditor specific variables in the model has no material impact on our findings.

To elaborate, we estimate Eq. (5) using rolling windows. Specifically, we use data from years 2001 and 2002 to estimate the audit fee residual for year 2002. When testing the persistence of lagged fee residuals, the 2002 residual is used as the lagged residual for year 2003. We compute the fee residual for 2003 using data from years 2001, 2002, and 2003 and use the 2003 residual in the lagged residual persistence tests for 2004.

Specifically, we first estimate model (5) for all continuing Big Four engagements and, separately, for all continuing non-Big-Four engagements. We then use the residuals from these estimates as the lagged fee residuals on new engagements. Since the fee residuals are computed separately for Big Four and non-Big-Four engagements, our tests of fee residual persistence across auditor switches are conditioned on both auditee origin and destination (i.e., we conduct separate tests for lateral Big N, for lateral non-Big-N and for Big-N to non-Big N switches).

Note that—by construction—about half of the fee residuals from any well-specified regression model can be expected to be negative. Since economic rents, by definition, represent excess profits, an intrinsically nonnegative construct, it is conceptually difficult to ascribe a meaningful rent-centric interpretation to negative residuals. For instance, especially given the levels of residual fee persistence on continuing engagements that we document in this study, it is difficult to justify why—year after year, on about half of the engagements—auditors would continue to conduct engagements that generate losses (yield negative rents). By contrast, negative residuals are easier to explain from the cost-centric perspective. For example, negative residuals may be driven by an omitted risk factors that makes the auditee less risky than the average firm.

It may also be useful here to note, by way of comparison, the first-order autocorrelation of the residual fees estimated from a (single) pooled-fee model estimated for the period 2001–2011 is about 0.79 for Big Four auditees and 0.83 for non-Big-Four auditees. This comparison indicates that the rolling-window estimation procedure does not materially affect autocorrelation in the fee residual series.

Auditor_fkey, the unique auditor identifier in the AuditAnalytics database tracks firm names rather than the identity of the underlying entity. Such name changes do not, however, result in a change in the underlying entity’s PCAOB auditor registration number. For instance, in 2009, BDO Seidman LLP (auditor_fkey = 7) legally changed its name to BDO USA LLP (auditor_fkey = 11,761). Likewise, in 2011, McGladrey & Pullen (old auditor_fkey = 10) changed its legal name to McGladrey LLP (new auditor_fkey = 16,168). Neither change affected the firms’ PCAOB auditor registration numbers, which respectively remained 243 and 49 after the change. We mitigate against such measurement error in the classification of continuing and new engagements by classifying an observation as an auditor switch only if the auditor’s PCAOB registration number in the auditorsinfo file (available at directory/wrds/audit/sasdata/audit_comp) changes.

In the terminology of Sect. 2, this finding indicates that, in lateral Big Four auditor transition, for positive lagged residual fees, which are considered to be the most likely instances where auditors earn rents, γ ^C (0.678 in column 2) = γ ^N (0.668 in column 5). A formal test for equality of coefficients produces a χ²(1) of 0.00, p > 0.10. This finding provides strong evidence that positive lagged fee residuals consist largely of unobserved production costs common to the predecessor and successor auditor and contain very little by way of auditor rents. Similarly, for negative lagged fee residuals, γ ^C (0.849 in column 2) = γ ^N (0.809 in column 5). In this instance too, we fail to reject the null hypothesis that the two coefficients are equal χ²(1) = 1.97, p > 0.10).

Recall that a successor non-Big-Four auditor is less likely to earn rents than was the successor Big Four auditor in the third test. Fee persistence in the third test can, therefore, be expected to be lower than in the second test. As discussed earlier, however, a non-Big-Four successor is likely to also have lower audit production costs than the Big Four successor auditor in the second test. Consequently, overall, the lateral Big Four auditor transition test is, in our view, the more powerful test.

Columns (5) to (10) report results for auditor switches which are rare events with very few repeat observations involving the same auditee. For consistency, with the results reported in columns (1) to (4), we estimate the models reported in columns (5) to (10) using cluster-robust standard errors as well. However, our results are materially unchanged if we instead use unclustered heteroskedasticity robust standard errors.

To the best of our knowledge, this result has not been reported in prior research. Untabulated analyses show that fees paid to the new non-Big-Four auditor by these auditees are also, on average, about 33 % [100*(1−e ⁻⁰⁴⁰ )] lower than the “counterfactual” fees these auditees would have paid the predecessor Big Four auditor, a finding that is consistent with prior research (cf. Chaney et al. 2004). However, as noted earlier, the finding that such auditees pay more than a similar continuing non-Big-Four auditee would pay its auditor is new.

See Wooldridge (2002, pp. 247–249). GAO (2008) is the first study we know of to estimate a panel-corrected audit fee model. Francis (2011, p. 132) also identifies panel estimation as a useful approach to correct for the influence of firm-specific omitted variables.

To compute 2011 residual fees, Eq. (2) is estimated separately for Big Four and non-Big-Four auditees, using data for all years during the period 2001–2011 when the auditee was a continuing Big Four (or non-Big-Four) auditee. For both estimations, a Hausman test rejects the null hypothesis that the random effects model is the preferred model (Big Four model: χ²(26) = 659.31, p < 0.01; Non-Big-Four model: χ²(26) = 856.17, p < 0.01). For parsimony, we do not tabulate the 2003–2010 residual fee models (all of which yield qualitatively similar coefficient estimates and model fit statistics).

Both definitions of model R² are widely used (see http://​www.​stata.​com/​support/​faqs/​statistics/​areg-versus-xtreg-fe/​ for a brief discussion and http://​www.​stata.​com/​statalist/​archive/​2003-05/​msg00336.​html for details).

As noted in footnote 10, many fee models include measures of auditor-specific factors (such as auditor industry expertise). Since it is not known whether the returns to these factors represent costs or rents and for comparability with most prior research (cf. Hope and Langli 2010; Ball et al. 2012; Hribar et al. 2014), we leave these premia embedded in the fee residual and include in the model only those variables that are known to be cost drivers (inclusive of all expected liability/regulatory and reputation risk costs). This approach gives our estimate of the residual fee its best shot at capturing any auditor rents. However, we re-estimated the model reported in Table 9 after adding auditor fixed effects as well as measures of auditor office size and auditor industry specialization. (Recall that auditee, industry and year fixed effects are already controlled for in Table 9). We find that the coefficient of the lagged residual fee in lateral Big N transitions is about the same as it was in Tables 5 and 9, indicating that controlling for auditor fixed effects does not materially affect the persistence of the fee residual in such transitions. In lateral non-Big-N auditor transitions, in contrast, including auditor fixed effects leads to a much larger decline in fee residual persistence, consistent with the conjecture that the non-Big-N auditors are far more heterogeneous as a group than are the Big N auditors. As noted earlier, whether these auditor fixed effects reflect costs or rents is not presently known. Consequently, in the paper, we focus only on models that leave these auditor fixed effects in the fee residual. Extending the analysis to better understand the impact of auditor—specific factors on fees offers a profitable area for future research, and we thank an anonymous reviewer for drawing our attention to this possibility.

While Gul and Srinidhi (2007) motivate the use of residual audit fees using Kinney and Libby’s economic bonding argument, they find no association between residual audit fees and the magnitude of auditee abnormal accruals (their measure of audit quality), which they interpret as follows: “This implies that when audit fees are unexpectedly high, it is difficult to distinguish whether it reflects an unexpectedly high audit effort (with consequent improvement in accrual quality) or excessive rents (that result in a deterioration of accrual quality).”

The exception, as noted earlier, is Gul and Srinidhi (2007), who do allude, albeit in passing, to a possible cost-centric interpretation when offering an ex post explanation of an observed lack of association between residual audit fees and their measure of audit quality. Asthana and Boone (2009) too allude to the possibility that fee residuals may include the effects of unobserved drivers of audit effort.