Technical Inefficiency,Allocative Inefficiency,and Audit Pricing

Abstract

The critical global role of audit firms, combined with the scarcity of qualified staff and downward pressure on fees, has increased the importance of understanding efficiency in this industry. This article examines the technical and allocative inefficiencies of audit firm staffing using data from 165 audit engagements performed by a Big 4 international certified public accountant (CPA) firm. Prior research has shown that the technical inefficiency of audit engagements leads to lower billing realization rates on audit engagements. We complement and extend this research by examining whether there are inefficiencies in allocating staff for audit engagements in addition to technical inefficiency, and whether each of these inefficiencies leads to lower billing realization rates. We find that there are differences in both technical and allocative inefficiencies across audit engagements, and that both inefficiencies lead to lower billing realization rates after controlling for other characteristics that could affect the realization rates of the audit engagements.

Keywords

technical inefficiency allocative inefficiency audit pricing Big 4 DEA

Introduction

Independent auditing firms play a critical role in the global economy due to the high cost of audit failures. Skilled staff is a significant scarce resource for audit firms. The American Institute of Certified Public Accountants (AICPA; 2013) sponsored Private Companies Practice Section (PCPS) CPA Firm Top Issues Survey reports that staffing concerns were one of the top issues for certified public accountant (CPA) firms. Hence, the efficiency with which an audit firm manages its staffing is a prominent issue in a highly competitive market. The mandatory disclosure of audit fees in the United States has provided more opportunity for clients to benchmark and negotiate their fees. The resulting downward pressure on fees has increased the need for firms to utilize their resources more efficiently.

Overall, managerial efficiency typically consists of two major components—technical efficiency, which reflects the ability of a business unit to use the minimal inputs for a given level of output, and allocative efficiency, which represents the ability of the unit to use the inputs in optimal proportions, given their respective prices and the production technology (Farrell, 1957). An audit engagement can be considered technically efficient if it is operating on the production frontier irrespective of relative wage rates of audit staff. Prior research has examined the role of technical efficiency of audit engagements (Bell, Knechel, & Willingham, 1994; Dopuch, Gupta, Simunic, & Stein, 2003; Knechel, Rouse, & Schelleman, 2009; O’Keefe, Simunic, & Stein, 1994). For example, Dopuch et al. (2003) show that technical inefficiencies do exist in the audit production process. Furthermore, they conclude that these inefficiencies result in lower average billing realization rates per hour, and hence are economically costly to audit firms.

Even if an audit engagement were technically efficient, though, the audit firm may not be using the appropriate mix of audit staff, given their relative wage rates. That is, the engagement may be allocatively inefficient, even if it is technically efficient. Hence, an examination of both technical and allocative components simultaneously provides a better understanding of sources of overall managerial inefficiency in performing audit engagements. In this article, we examine if there are technical and allocative inefficiencies in audit production and if these inefficiencies affect billing realization rates of audit engagements.

We utilize hourly data per professional staff category obtained from audit engagement billing runs of an international Big 4 CPA firm office to draw conclusions about the optimal assignment of audit staff to audit engagements. Audit engagements are performed by audit teams composed of three major levels of audit professional staff: partners, managers, and other audit professionals.¹ Senior-level audit staff plan and supervise the activities for those at lower levels. Although different roles and responsibilities are assigned by job description to each of the staff levels, the training, experience, and promotion flow of the firm allows for some effort substitution possibilities among the different levels. Firms use billing (charge-out) rates to differentiate staff into various categories. The relative billing or charge-out rates between staff in the different categories reflect the differences in their abilities, experience, and cost to the firm. Assessing allocative efficiency requires detailed information on the costs of the different inputs—namely staff resources, which is not easily accessible due to the proprietary and confidential nature of such data. To the best of our knowledge, no prior study has examined an auditor’s allocative efficiency of audit engagements. Our access to cost and hourly data of 165 audit engagements from a Big 4 international CPA firm enables us to complement prior research on auditor efficiency in allocating staff resources and, to examine how allocative efficiency can affect audit realization rates.

We utilize data envelopment analysis (DEA) to examine the efficiencies of different audit engagements. DEA is a nonparametric performance evaluation technique that has been applied in the context of accounting in different ways. For instance, Chang, Chang, Das, and Li (2004) evaluate operational efficiencies of hospitals using DEA, whereas Mensah and Li (1993) use DEA to estimate inefficiencies of budgeting systems in a not-for-profit setting. Banker, Lee, Potter, and Srinivasan (2010) utilize DEA to compute relative productivity of retail outlets, and then use the productivity scores to examine the impact of supervisory monitoring on retail sales productivity. Feroz, Kim, and Raab (2005) apply DEA in their analytical procedure to determine audit scope and to assess the preliminary risk level of a client. Dopuch et al. (2003) estimate the auditor’s production (technical) efficiency in performing audit engagements by DEA, and suggest that audit inefficiencies lead to auditor’s discounts on its normal billing rates. Banker, Chang, and Natarajan (2005) use DEA to estimate productivity change, technical progress, and efficiency change in the public accounting industry. Knechel et al. (2009) adopt DEA to evaluate the relative efficiencies of audit engagements. Chang, Chen, Duh, and Li (2011) use DEA to evaluate the contributions of information technology and human capital in the productivity growth of public accounting firms. More recently, Demerjian, Lev, and McVay (2012) utilize DEA to quantify a measure of managerial ability, while Demerjian, Lewis, Lev, and McVay (2013) examine the relation between this DEA-based measure of managerial ability and earnings quality.

Our analysis is conducted in two stages: In the first stage, we utilize DEA to estimate the technical and allocative inefficiencies of each audit engagement. Following a conventional assumption in the audit literature that the assurance level of audit engagements by the same auditor is constant,² in our first-stage analysis, we consider client characteristics as output variables with staff hours of three audit professional categories as input variables to estimate technical inefficiencies. We then use the costs and hours of these audit professional categories to derive their corresponding wage rates to estimate aggregate technical and allocative inefficiencies. Finally, we follow Banker and Maindiratta (1988) in estimating allocative inefficiencies by dividing the aggregate inefficiencies by the technical inefficiencies.

Client managers are able to observe at least some aspects of the audit production process. If these managers spot inefficiencies in the audit process, they are likely to negotiate with the audit firm to reduce the audit fee component associated with these inefficiencies (Dopuch et al., 2003). This would result in a positive association between the fee discount and these inefficiencies. In the second-stage analysis, we examine whether billing realization rates of individual audit engagements are associated with technical and allocative inefficiencies obtained from the first-stage analysis. We also include four characteristics of individual engagements that are likely to be associated with realization rates, namely auditor tenure, industry specialization, restatements, and off-peak pricing, in our empirical models. The results indicate that both technical and allocative inefficiencies are useful in explaining realization rates, even after including auditor tenure, industry specialization, restatements, and off-peak pricing in our regressions. While not being the primary focus of our study, these results provide interesting insights on how characteristics such as auditor tenure and specialization affect realization rates.

The rest of this article is organized as follows: The next section describes the research site and hypotheses. This is followed by a description of the estimation models, including the DEA methodology used to calculate technical and allocative inefficiencies, and the ordinary least squares (OLS) regression models. We next present the empirical results and robustness checks used in the analyses. Our concluding remarks appear in the final section.

Research Site and Hypotheses

Our research site is the branch office of a Big 4 international public accounting firm (hereafter referred to as the AUDITOR). We collect data pertaining to 165 audit engagements performed by the AUDITOR for its largest clients during a recent fiscal year. The single data source allows us to control for audit firm characteristics that may influence audit engagement quality and performance. In addition, using data on engagements from a single office enables controlling for unmeasured auditor characteristics, such as audit technology and style, which may influence the audit production processes.

For each engagement, we collect data on AUDITOR’s staffing hours (PTNRHRS, MNGRHRS, STAFFHRS) and costs for three audit professional staff categories, that is, partners, audit managers, and other audit professionals, recorded in the AUDITOR’s internal cost system. We also collect the actual fee charged for each engagement and the AUDITOR’s standard billing rates of the three professional categories (PTNRBILLRATE, MNGRBILLRATE, STAFFBILLRATE). The standard total fee of an engagement is calculated as staff hours weighted by standard billing rates (= PTNRBILLRATE × PTNRHRS + MNGRBILLRATE × MNGRHRS + STAFFBILLRATE × STAFFHRS). The price realization rate (RLZRATE) for the audit work performed for each client is derived as actual fee charged divided by standard total fee. When there is unanticipated work negotiated in the middle of an audit engagement year, the actual fee charged for an engagement and the actual professional work hours increase from what was initially agreed and planned, but the professional billing rates remain the same.

We utilize the collected data to estimate the technical and allocative inefficiencies for each of the audit engagements, and evaluate how they affect the realization rates of these engagements. As prior research documents that technical inefficiencies lead to lower realization rates for audit engagements (Dopuch et al., 2003), we specify our first research hypothesis, stated in null form, to re-examine this issue in the context of our research setting:

Hypothesis 1 (H1): There is no association between technical inefficiency and realization rates of audit engagements.

Once a firm begins an audit, it must expend all the time necessary to meet professional standards, or incur substantial monetary and professional risks. The total staffing cost is the sum of the wages paid to employ each of the different levels of professional staff. To minimize the total staffing cost charged to the billing run on an audit engagement, the firm needs to optimally assign different professional staff among the staffing categories by taking into account the requirements of the engagement, the expected realization rate for the engagement, availability of staff, and wage rates for each staff level.

An audit firm must continually hire new juniors, and then through training and on-the-job experience keep the pipeline full with the appropriate mix of staff. Substitution of some tasks between staff categories is possible. As the personnel gain experience at each level, they are expected to obtain the competencies necessary to move to the next level. This progression provides flexibility in assigning tasks as staff who are nearing the end of their current level often perform duties categorized as the next level. Nevertheless, sometimes such flexibility is attained at the cost of incurring a greater number of input hours. In addition, if senior staff spend more time on planning and supervision, lower level staff may perform their tasks more efficiently. This represents another possibility of effort substitution between different staff levels. Thus, the firm needs to be aware of the substitutability between different staff levels and their relative costs to allocate the audit inputs efficiently to each individual audit assignment.

The challenges of staffing are growing as audit firms and alliances deal with increasing globalization and scrutiny by regulatory agencies such as the Public Company Accounting Oversight Board (PCAOB). Delivering an audit engagement is a complex task that involves meeting the client’s expectations, maximizing the expected realization rate on costs charged to the billing run, and meeting professional auditing standards. The availability of staff at the planned level is a significant constraint on delivering the audit product. Both quantitative and qualitative factors must be considered. Quantitatively, work pushed down from the ideal level may result in increased time to complete the task along with an increase in supervision and review time. This increase may initially seem to be offset by the lower wage rate of the lower level staff but qualitatively, the risk of errors may increase. The staff at the lower level may not have the professional skills and experience to understand and identify certain issues. These issues, when caught on review, result in rework that increases the number of hours required to complete the audit. As client managers are an integral part of at least some parts of the audit production process, they would be able to discern some of these inefficiencies. To the extent that the client can observe these inefficiencies, the client can be expected to negotiate to lower the incremental audit fee due to the “excess” hours. In this situation, the client would pressure the audit firm to lower the audit fee, leading to lower price realizations for the audit firm.

The ability of the client to negotiate a lower fee would depend on the relative bargaining power of the client vis-à-vis the auditor. This is contingent on the price competitiveness that exists in that particular client segment. In early studies of the audit market, a common assumption has been that there is perfect competition in the audit market (Simunic, 1980). However, several recent studies show that auditors compete along a number of dimensions such as industry expertise, implied audit quality, location, geographic reach, scope of services, and not just based on price (see, for example, Bills & Stephens, 2015; Keune, Mayhew, & Schmidt, 2015; Mayhew & Wilkins, 2003; Numan & Willekens, 2012). These dimensions provide an opportunity for audit firms in some client segments to differentiate themselves from competing firms, such that they are not simply price takers.

Interviews with the senior management at our research site indicated that price negotiations are based on several engagement-specific factors, including the costs of the engagement. During the initial audit engagement, when the audit firm first takes on a new client, a company receives bids from multiple auditors and purchases audit services from the auditor who offers the lowest price for the company’s required services (Johnstone & Bedard, 2001). This stage of the audit engagement process can be very competitive. However, once the client has retained a particular audit firm, on an ongoing basis, the dynamics of audit pricing can be quite different. At the beginning of each fiscal year, the audit firm estimates the audit cost for each existing client based on its prior experience with the client, and any changes in the client’s characteristics over the past year. The firm negotiates with each client an engagement price based on the estimated audit cost. Hence, in subsequent years of an audit relationship the audit firm is less likely to be a price taker, with the audit cost being a significant determinant of the engagement price. This is consistent with the results of prior studies that document that audit fees tend to be lower in the first couple of years of an audit relationship, and tend to increase in subsequent years (Baber, Brooks, & Ricks, 1987; Rubin, 1988; Simon & Francis, 1988).

In addition, for some audit engagements, the audit firm may negotiate additional fees with the client during the year when it anticipates the actual cost for the audit will exceed the initially estimated cost due to unanticipated exigencies, such as changes in mandated requirements, and other significant events. Our discussions with senior management at our research site revealed that the fees for additional work that arises during the year are based on the same billing rates negotiated at the beginning of the year, and the additional hours required to complete the unanticipated work at the agreed-upon billing rates. The client would reasonably expect to pay for any additional work assuming that the audit firm is able to make the optimal allocation of resources for this additional work. If unanticipated work is required in the middle of an audit engagement, the audit firm needs to find, or reallocate, staff to the extra work after the original allocation of resources has already been made. This tends to be difficult as the firm does not tend to have unscheduled hours available at all staff levels, especially during peak periods. Staff are allocated to audits in blocks of time and expected to move to the next audit as prescheduled. This sometimes results in the unanticipated work being done using overtime hours or by staff not previously assigned to the engagement. Any staff added to a new engagement require time to get up to speed on the client. Even if the firm had made the optimal allocation of resources for the original amount of work, the firm has less flexibility in staff available to do any additional work that would need to be completed by the filing deadline. Any less than optimal allocation of staff would lead to either technical inefficiencies, allocative inefficacies, or both. To the extent that clients are able to identify these inefficiencies, this will lead to lower realization rates on the audit engagement.³

As is apparent from the discussion above, regardless of whether the auditor was a price taker at the beginning of the engagement, the final fees charged will reflect at least some of the actual costs incurred for the engagement. Ultimately, the discount reflected in the realization rate will depend on whether the client feels any deviation from the agreed-upon price is justified or not, and the relative bargaining power of the client vis-à-vis the auditor. Our tests in the second stage of the article examine whether inefficiencies in the audit engagement process get reflected in a lower realization rates for the engagement.

However, it is also possible that a nonoptimal allocation of audit staff could be the result of a reallocation of audit staff with more senior audit personnel substituting for lower level staff. In this case, the client may actually value this inefficiency in allocating audit staff. To the extent that allocative inefficiency is valued by the client, in our empirical tests we should not expect to find any positive association between the fee discount and the allocative inefficiency. Our second hypothesis below examines this issue (stated in null form):

Hypothesis 2 (H2): There is no association between allocative inefficiency and the realization rates of audit engagements.

In addition to technical and allocative inefficiencies, we consider the effects of engagement characteristics such as auditor tenure, industry specialization, restatements, and off-peak pricing on the realization rates of individual engagements. Recent interest in mandatory rotation has prompted research investigating the relation between auditor tenure and audit quality (Davis, Soo, & Trompeter, 2009; Knechel & Vanstraelen, 2007; Stanley & DeZoort, 2007). While regulators are concerned that long tenures negatively affect auditor independence, most studies have found that longer tenure results in higher audit quality leading to higher fees and realization rates over time (Baber et al., 1987; Rubin, 1988; Simon & Francis 1988). These studies argue that fees and realization rates may be lower for newer clients due to audit firms low balling their services to win new business. In addition, as the audit firm learns and accumulates knowledge about a particular client over time, this is likely to lead to higher quality audits for which the audit firm may charge a premium. Hence, we expect to find that the longer the tenure, the higher will be the realization rate. As this remains an issue of interest to researchers in the area, we present this as our third research hypothesis (stated in null form):

Hypothesis 3 (H3): There is no association between auditor tenure and the realization rates of audit engagements.

Several papers have examined whether auditor specialization affects audit fees (e.g., Carson 2009; Ferguson, Francis, & Stokes, 2003; Francis, Reichelt, & Wang, 2005; Lowensohn, Johnson, Elder, & Davies, 2007). Some have argued that industry specialization leads to higher quality audits due to greater knowledge of business and accounting practices in the industry than nonspecialists (Dopuch & Simunic, 1982). As a result, clients would be willing to pay a premium for the expertise of these specialized audit firms. Also, industry specialization reduces the costs for the client as less effort is needed in explaining industry-specific trends and processes to the auditor (Mayhew & Wilkins, 2003). As a result of lower costs, then, the client would be more willing to pay a higher price for the audit, all else remaining equal.

However, some have argued that industry specialization can lead to lower realization rates. If the audit firm possesses a competitive advantage due to industry specialization, it will likely be able to achieve a lower cost as a result of economies of scale. However, if the client segment in which it specializes is price competitive, then the audit firm may be forced to pass on these cost savings to clients (Mayhew & Wilkins, 2003). Under this scenario, the audit firm would have to discount their services for clients in their specialization industry from their standard billing rates resulting in lower realization rates (DeFond, Francis, & Wong, 2000). Thus, it remains an open question whether industry specialization leads to higher or lower realization rates. We present this as our fourth research hypothesis as follows (stated in null form):

Hypothesis 4 (H4): There is no association between industry specialization and the realization rates of audit engagements.

The pricing of individual audit engagements may depend on the client’s year-end (Chaney, Jeter, & Shivakumar, 2004; Francis, 1984; Gul, 1999). If the client has a year-end during the peak season, that is, December, it is less likely that discounts would be offered for such engagements. However, most prior studies find an insignificant, or a negative relationship between busy season and audit fees (Hay, Knechel, & Wong, 2006). Hence, we include peak season as a control variable to explain realization rates but without a directional prediction.

Finally, accounting restatements are required to correct any material misstatements in a company’s previous financial statements. Restatements represent auditor’s failures in detecting material errors in the previous time period and are a direct measure of actual (rather than perceived) audit quality (DeFond & Zhang, 2014). Prior audit research shows a mixed relationship between restatements and audit fees. Some studies find that restatements are associated with higher audit fees (e.g., Kinney, Palmrose, & Scholz, 2004; Stanley & DeZoort, 2007) perhaps because restatement firms are riskier clients. However, other studies (e.g., Blankley, Hurtt, & MacGregor, 2012) find that restatements are negatively associated with audit fees, presumably indicating that auditors in these cases may have provided less effort by skipping some procedures that could have detected the errors (Lobo & Zhao, 2013). We include the restatement variable in our second-stage analysis to control for the possible effects of audit quality on audit fee realization rates.

In the next section, we describe our two-stage methodology which consists of calculating the technical and allocative inefficiencies of the audit engagements in the first-stage analysis, and then examining how these inefficiencies relate to the pricing of audit services in the second stage of the analysis.

Estimation Models

Measuring Technical and Allocative Inefficiencies Using DEA

We employ DEA to measure technical and allocative inefficiencies of audit engagements. DEA is a nonparametric approach for measuring the relative efficiency of decision-making units (DMUs). It has been used previously in the audit literature (e.g., Chang et al., 2011; Dopuch et al., 2003; Knechel et al., 2009). Two commonly used models for DEA are the Charnes, Cooper, and Rhodes (1978; CCR) and the Banker, Charnes, and Cooper (1984; BCC). The CCR model assumes constant returns to scale, whereas the BCC model enables variable returns to scale. Banker, Chang, and Cunningham (2003) analyze the underlying production function of audit firms, and find that it is not characterized by constant returns to scale. Knechel et al. (2009) similarly conclude that a variable-returns-to-scale model is more appropriate for the analysis of audit production. Hence, we utilize the BCC model that incorporates variable returns to scale into our analysis.

To see what is involved in the BCC model, let Y_j = (y _1j,y _2j, . . . y_Rj ) ≥ 0 and X_j = (x _1j,x _2j, . . . x_Ij ) ≥ 0, j = 1, . . . N be the observed output and input vectors generated from an underlying production possibility set S = {(Y,X)| outputs Y can be produced from inputs X} for a sample of N audit engagements. The technical inefficiency $θ_{j}^{T}$ ≥ 1 of an engagement (y_j, x_j ) ∈ S is measured as the reciprocal of $ϕ_{j}^{T}$ , which can be obtained by solving the following DEA model:

ϕ_{j}^{T} = \min ϕ,

s . t . \sum_{j = 1}^{N} λ_{j} y_{r j} \geq y_{r j} \forall r = 1, . . R,

\sum_{j = 1}^{N} λ_{j} x_{i j} \leq ϕ x_{i j} \forall i = 1, . . I,

\sum_{j = 1}^{N} λ_{j} = 1,

ϕ, λ_{j} \geq 0,

where ϕ is scalar, and the $λ_{j}$ optimize the value of $ϕ_{j}^{T}$ under which audit engagement j is being evaluated.

Following Banker and Maindiratta (1988), we define allocative inefficiency as aggregate inefficiency divided by technical inefficiency in the following two steps: In Step 1, we use the following DEA model to estimate aggregate technical and allocative inefficiency $θ_{j}^{A}$ , relative to the minimum input cost given the input prices $p_{i}$ :

\max θ_{j}^{A} = \frac{\sum_{i = 1}^{I} p_{i} x_{i j}}{\sum_{i = 1}^{I} p_{i} {\hat{x}}_{i j}},

s . t . \sum_{j = 1}^{N} λ_{j} y_{r j} \geq y_{r j} \forall r = 1, R,

\sum_{j = 1}^{N} λ_{j} x_{i j} \leq {\hat{x}}_{i j} \forall i = 1, \dots I,

\sum_{j = 1}^{N} λ_{j} = 1,

θ_{j}^{A}, {\hat{x}}_{i j}, λ_{j} \geq 0,

where ${\hat{x}}_{i j}$ are minimum inputs required for the given outputs. As described earlier, we have audit hours and costs by staff category. We can calculate the input prices by dividing the individual input costs by the corresponding input hours. In Step 2, we calculate the allocative inefficiency $θ_{j}^{V}$ by dividing aggregate technical and allocative inefficiency $θ_{j}^{A}$ in (2) by technical inefficiency $θ_{j}^{T}$ in (1); that is, $θ_{j}^{V}$ = $θ_{j}^{A}$ / $θ_{j}^{T}$ .

Similar to Dopuch et al. (2003), we consider audit production inputs as effort from different categories of audit professionals. We define inputs of our DEA methodology to be the staff hours for each category of professionals, that is, partners, managers, and other audit professionals. We assume, as in earlier studies, such as O’Keefe et al. (1994) and Dopuch et al. (2003), that the fundamental audit output, the level of assurance provided for all the audit engagements, is constant across our sample clients. This is a reasonable assumption, given that all engagements are carried out by the same office of an audit firm under the same brand in the same year. The auditor exerts labor hour inputs to provide the desired level of audit assurance, which in turn depends on client characteristics. Hence, the outputs in the DEA model consist of client characteristics that have been identified by the literature. We consider 11 client characteristics that describe the size, ownership, complexity, riskiness, and other features of the client (Bell, Doogar, & Solomon, 2008; Ghosh & Lustgarten, 2006; Hackenbrack & Knechel, 1997; Hay et al., 2006; Palmrose, 1986; Schelleman & Knechel, 2010; Seetharaman, Gul, & Lynn, 2002; Simon & Francis, 1988).

Prior literature has shown that size of the client affects the audit effort required to complete the audit (O’Keefe et al., 1994). We capture the size of the client using logged total assets (lnASSETS) of the client. We consider the ownership structure of clients as public clients (PUBLIC) demand more audit professional input to produce audit engagements that meet statutory requirements. Similar to prior studies, we measure client complexity using the number of subsidiaries (SUBSIDIARY) and the proportion of foreign assets (FOREIGN) as a determinant of audit effort. Finally, we capture various aspects of risk using the variables LEVERAGE, RECEIVABLE, INVENTORY, ZSCORE, LITIGATION, LOSS, and MARGIN. As LEVERAGE, defined as the ratio of long-term debt to total assets, is tied to client’s business risk, this would also be associated with audit risk. High proportions of receivables (RECEIVABLE) and inventory (INVENTORY) in total assets require additional subjective judgment on valuation, implying a higher probability of misstatement and an increase in audit risk. The Altman Z score (ZSCORE) has been used in the extant literature to measure a client’s bankruptcy risk, where a lower Z score indicates a higher likelihood of bankruptcy. A client with higher bankruptcy risk has more incentive to misrepresent its financial information, and thus represents higher audit risk. LITIGATION is an industry proxy based on Francis, Philbrick, and Schipper (1994) to measure securities litigation risk. It is coded 1 if the client is in the biotechnology, computers, electronics, or retail industries, and 0 otherwise. Finally, a client’s profitability is measured by two variables: LOSS and MARGIN. LOSS is coded 1 if the client had a loss in any of the past 3 years, and 0 otherwise. MARGIN is the profit-to-revenue ratio. A client with low profitability has high business risk, thereby increasing the risk that management might try to misrepresent the firm’s financial position.

The DEA estimation assumes a monotonically increasing relationship between inputs and outputs. All of the variables that we use as outputs have been extensively studied in the literature in the context of audit effort, so the relationships between these variables and audit effort are well understood. Nonetheless, we conduct OLS regressions of staffing hours on these client characteristics to ensure that there is a positive association between them and also to identify which client characteristics should be included as production outputs in our DEA model. The OLS regressions use partner hours, manager hours, other audit professional hours and total professional hours as dependent variables explained by client characteristics as independent variables. Any characteristics that are significantly associated with at least one of these four dependent variables are retained as output variables in our DEA estimation. Our empirical analysis identifies seven DEA output variables: lnASSETS, PUBLIC, SUBSIDIARY, LEVERAGE, RECEIVABLE, ZSCORE,⁴ and LITIGATION, which are used subsequently in the DEA as outputs.

Evaluating the Effects of Technical and Allocative Inefficiencies on Realization Rates

We use the technical and allocative inefficiency scores obtained from our first-stage DEA to evaluate whether they affect the realization rates of audit engagements. In our second-stage regressions, we include auditor tenure (TENURE), industry specialization (SPECIALIST), misstatements (RESTATEMENT), and busy season (PEAK) to control for audit engagement characteristics likely to affect the realization rates.⁵ TENURE is measured as the number of years the AUDITOR has been associated with the client, ranging from 1 to 4, where 4 represents a relationship that lasts for 4 or more years.⁶ The AUDITOR’s senior management identifies its own audit specialty in computer and electronic product manufacturing (NAICS Code 334).⁷ Therefore, we utilize SPECIALIST as a dummy variable where a value of 1 indicates a client in a specialized industry, and 0 otherwise. RESTATEMENT is coded 1 if the client issued a restatement in the sample year, and 0 otherwise. As the predominant fiscal year-end of the clients of our research site is in December, PEAK is assigned 1 if the client has a December year-end, and 0 otherwise. In addition, for control purposes, we include the four variables that were excluded in the first-stage analysis—INVENTORY, FOREIGN, LOSS, and MARGIN, as they can potentially affect audit production even though they were not found to be significant in explaining audit effort for our sample. Thus, we estimate the following OLS model to capture the effect of technical and allocative inefficiencies on realization rates:

\begin{array}{l} R L Z R A T E = α_{0} + α_{1} T E C H I N E F F + α_{2} A L L O I N E F F + α_{3} T E N U R E + α_{4} S P E C I A L I S T \\ + α_{5} R E S T A T E M E N T + α_{6} P E A K + α_{7} I N V E N T O R Y + α_{8} F O R E I G N + α_{9} L O S S + α_{10} M A R G I N + ε, \end{array}

where RLZRATE is the realization rate of audit fees, TECHINEFF is the technical inefficiency $θ^{T}$ , ALLOCINEFF is the allocative inefficiency $θ^{V}$ , and all other variables are as defined earlier.

Results

In Table 1, we present the descriptive statistics for all the variables used in our analysis. As can be seen from Table 1, the mean realization rate is 69% which denotes the ratio of the actual audit fee to the standard total fee. This realization rate includes any planned discount taken at the time the audit fee is agreed upon between the firm and the client, as well as any additional discount taken at the time the client is actually billed for the work. During the audit, costs are accumulated as the audit is performed by taking professional hours and recording costs on a billing run. The standard audit fee is computed by multiplying the hours worked by each professional member’s billing rate. As audit fees are normally bid in advance, the audit firm may choose to have a planned variance between the total standard fee that will appear on the billing run and the amount that will be billed to the client as the audit fee. In 2000, the Securities Exchange Commission mandated that companies disclose the amount of payments to their audit firms in response to concerns that audit firms may have independence issues, given the amount of nonaudit services they were performing.

Table 1.

Descriptive Statistics of Variables (N = 165).

Variables	Definition	M	SD	25%	Median	75%
RLZRATE	Ratio of actual audit fee^a to standard total fee^b	0.69	0.11	0.62	0.68	0.75
lnASSETS ^c	Logarithm of total assets	14.61	1.61	13.45	14.25	15.44
PUBLIC	Coded 1 if the client is a public company, and 0 otherwise	0.35	0.48	0	0	1
SUBSIDIARY	Logarithm of number of subsidiaries	0.74	0.73	0	0.69	1.39
FOREIGN	Proportion of foreign assets in total assets	0.02	0.05	0	0	0.03
RECEIVABLE	Proportion of receivables in total assets	0.14	0.13	0.03	0.12	0.22
INVENTORY	Proportion of inventory in total assets	0.11	0.14	0.01	0.08	0.17
LEVERAGE	Ratio of long-term debt to total assets	0.14	0.19	0.02	0.08	0.18
LOSS	Coded 1 if the client had a loss in any of the past 3 years, and 0 otherwise	0.43	0.50	0	0	1
ZSCORE	Altman’s Z score	2.46	3.52	0.85	1.71	2.97
LITIGATION	Coded 1 if the client is in the biotechnology, computers, electronics, or retail industry, and 0 otherwise	0.30	0.46	0	0	1
MARGIN	Profit-to-revenue ratio	0.08	0.94	−0.06	0.06	0.16
SPECIALIST	Coded 1 if the client is in the AUDITOR’s specialized industry,^d Computer and Electronic Product Manufacturing (NAICS Code 334), and 0 otherwise	0.26	0.44	0	0	1
TENURE	Number of years the AUDITOR has performed audit engagements for the client. 1 = first-year client, 2 = second-year client, 3 = third-year client, 4 = clients that have associated with the AUDITOR for 4 or more years.	3.65	0.79	4	4	4
RESTATEMENT	Coded 1 if the client issued a restatement for the sample period, and 0 otherwise	0.07	0.26	0	0	1
PEAK	Coded 1 if the client’s year-end falls in December, and 0 otherwise	0.69	0.46	0	1	1

Actual audit fee charged to client.

The standard total fee is calculated using staff hours weighted by standard billing rates for each staff category.

The numbers in this row are scaled by a constant as per confidentiality agreement with the AUDITOR.

As described by the AUDITOR’s senior management during field interviews, and verified by the portfolio share approach. The clients in the computer and electronic product manufacturing industries generated the highest share of revenue for the AUDITOR during our sample period.

As described earlier, only seven of the 11 client characteristics were found to be consistently significant in at least one of the regressions. We present the results of these regressions in Table 2. Thus, in our application of DEA estimation models we utilize only these seven client characteristics as output variables, namely client size (lnASSETS), ownership (PUBLIC), organizational complexity (SUBSIDIARY), proportion of receivables in assets (RECEIVABLE), business risk (LEVERAGE), bankruptcy risk (ZSCORE), and litigation risk (LITIGATION).⁸

Table 2.

Identification of Client Characteristics as Outputs in Estimating Inefficiencies.

Variables	lnPTNRHRS	lnMNGRHRS	lnSTAFFHRS	lnTOTALHRS
lnASSETS	0.143** (.015)	0.132*** (.001)	0.082** (.024)	0.099*** (.002)
PUBLIC	0.783*** (<.001)	0.630*** (<.001)	0.554*** (<.001)	0.561*** (<.001)
SUBSIDIARY	0.167 (.099)	0.241*** (<.001)	0.257*** (<.001)	0.249*** (<.001)
FOREIGN	1.381 (.467)	0.587 (.648)	−0.117 (.920)	0.125 (.903)
RECEIVABLE	1.867*** (<.001)	1.558*** (<.001)	0.896*** (.005)	1.089*** (<.001)
INVENTORY	0.112 (.807)	0.131 (.673)	0.289 (.306)	0.241 (.332)
LEVERAGE	0.276 (.485)	0.312 (.244)	0.386* (.094)	0.335 (.119)
LOSS	−0.083 (.549)	−0.083 (.381)	−0.115 (.181)	−0.100 (.186)
ZSCORE	−0.011 (.549)	−0.006 (.653)	−0.238** (.041)	−0.020** (.052)
LITIGATION	0.455*** (.001)	0.099 (.286)	0.167** (.049)	0.165** (.028)
MARGIN	0.001 (.458)	0.001 (.888)	−0.001 (.827)	−0.001 (.920)
Adjusted R²	.48	.61	.59	.66

Note. The p values are reported in parentheses. Other variable definitions are provided in Table 1. lnPTNRHRS = logarithm of partner work hours; lnMNGRHRS = logarithm of manager work hours; lnSTAFFHRS = logarithm of other audit staff (including senior auditors and junior auditors) work hours; lnTOTALHRS = logarithm of total professional work hours exerted by partners, managers, and other audit staff.

, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively (two-tailed test).

It is interesting that we find that both LOSS and MARGIN are not significant in determining audit effort in our first-stage estimations. In a meta-analysis of audit fee research, however, Hay et al. (2006) report that a majority (69%) of prior studies find client loss to be insignificant, whereas 49% find client profitability to be insignificant. Our results seem consistent with these studies. Hay et al. (2006) speculate that this could be because auditors may not be as finely calibrated to differences in the profitability metrics as the fee model would suggest. In addition, a loss may not reflect the threshold at which auditors actually begin to perceive increased risk. It is also possible that the relationship between profitability ratios and effort may be nonlinear.

In the first stage of our analysis, we compute the technical and allocative inefficiencies of the audit engagements using DEA. Specifically, we apply DEA to calculate two inefficiency measures for each engagement. The first is the technical inefficiency $θ^{T}$ obtained using the program in (1), which is based on seven client characteristics as outputs and the three professional staff hours as inputs. We then calculate the aggregate inefficiency estimate $θ^{A}$ using the program in (2). Finally, we calculate the allocative inefficiency $θ^{V}$ for each engagement as $θ^{V}$ = $θ^{A}$ / $θ^{T}$ .

The results of the DEA are presented in Panel A of Table 3. The mean technical inefficiency score is 1.481, which shows that there is considerable technical inefficiency in the audit engagements with 102 of them having a technical inefficiency that is greater than 1. This is consistent with earlier studies such as Dopuch et al. (2003). Besides, the mean allocative inefficiency is 1.191, which shows that there are allocative inefficiencies as well, and a total of 124 engagements have an allocative inefficiency greater than 1. Note that there are 41 engagements that are both technically and allocatively efficient. We also empirically test the existence of allocative inefficiencies using three DEA-based statistical tests following Banker (1993) and Banker, Chang, and Natarajan (2007). Assuming that the logarithm of inefficiency is exponentially distributed over [0, $\infty$ ), the first test statistic is computed as $\sum_{j = 1}^{N} \ln (θ_{j}^{A}) / \sum_{j = 1}^{N} \ln (θ_{j}^{T})$ and evaluated against the F-distribution with (2N, 2N) degrees of freedom. The second test statistic is based on the assumption that the logarithm of inefficiency follows a half-normal distribution over the range [0, $\infty$ ), and is computed as $\sum_{j = 1}^{N} \ln (θ_{j}^{A}) / \sum_{j = 1}^{N} \ln (θ_{j}^{T})$ . The statistic is then evaluated against the F-distribution with (N, N) degrees of freedom. If no assumption is imposed on the distribution of the logarithm of inefficiency score, a Kolmogorov–Smirnov type test statistic based on the maximum vertical distance between the empirical cumulative distributions of ln( $θ_{j}^{A}$ ) and ln( $θ_{j}^{T}$ ) is constructed to test the existence of allocative inefficiency. As reported in Panel B of Table 3, all the three test statistics are significant at the 1% level, suggesting that AUDITOR exhibited significant allocative inefficiency while performing the audit engagements.

Table 3.

Technical and Allocative Inefficiencies.

Panel A: Descriptive Statistics for Technical and Allocative Inefficiencies.
Variables	Definitions	M	SD	25%	Median	75%	Number of $θ s > 1$
TECHINEFF	Technical inefficiency score $θ_{j}^{T}$	1.481	0.711	1.000	1.149	1.728	102
ALLOCINEFF	Allocative inefficiency score $θ_{j}^{V}$	1.191	0.282	1.004	1.108	1.246	124

Note. Number of engagements that are both technically and allocatively efficient (i.e., $θ_{j}^{T}$ = $θ_{j}^{V}$ = 1): 41.

Panel B: Tests of Existence of Allocative Inefficiency in the Audit Firm (N = 165).
	F _2N,2N = $\sum_{j = 1}^{N} \ln (θ_{j}^{A}) / \sum_{j = 1}^{N} \ln (θ_{j}^{T})$	F_N,N = $\sum_{j = 1}^{N} {(\ln (θ_{j}^{A}))}^{2} / \sum_{j = 1}^{N} {(\ln (θ_{j}^{T}))}^{2}$	Kolmogorov–Smirnov statistic comparing $θ_{j}^{A}$ and $θ_{j}^{T}$ distributions
Test statistic	1.453***	1.562***	0.097***
p value	<.001	.002	.004

Note. $θ_{j}^{T}$ and $θ_{j}^{A}$ are obtained from Equations 1 and 2, respectively.

***

Statistical significance at the 1% level.

We next examine the relationship between the inefficiency scores and the realization rates as described in Equation 3. The correlations between the variables used in Equation 3 are presented in Table 4. The results show a significantly negative association between billing realization rates (RLZRATE) and technical inefficiency scores (TECHINEFF). Consistent with our expectation, we find a significantly negative correlation between price realization rates and allocative inefficiency scores (ALLOCINEFF).

Table 4.

Pearson’s Correlation Coefficients for the Regression Variables.

Variables	RLZRATE	TECHINEFF	ALLOCINEFF	TENURE	SPECIALIST	PEAK	RESTATEMENT	INVENTORY	FOREIGN	LOSS	PROFITMARGIN
RLZRATE	1.000	−.208*** (.007)	−.146* (.061)	.183** (.019)	−.168** (.031)	.148* (.058)	−.150* (.053)	.411 (.618)	−.022 (.775)	.015 (.852)	.133 (.865)
TECHINEFF		1.000	−.102 (.193)	.027 (.726)	−.068 (.384)	.106 (.176)	−.082 (.291)	−.028 (.737)	.001 (.994)	.059 (.455)	−.041 (.605)
ALLOCINEFF			1.000	.027 (.733)	.148* (.057)	−.037 (.630)	−.012 (.880)	−.014 (.863)	−.012 (.879)	.069 (.373)	.106 (.176)
TENURE				1.000	−.051 (.517)	.186** (.016)	.124 (.112)	−.001 (.989)	−.041 (.604)	−.125 (.108)	.039 (.614)
SPECIALIST					1.000	−.0533 (.495)	.238* (.082)	.0865 (.293)	.123 (.115)	−.042 (.593)	.126 (.116)
PEAK						1.000	.166** (.03)	−.044 (.579)	.100 (.201)	−.066 (.398)	.039 (.614)
RESTATEMENT							1.000	.132* (.091)	.478*** (.001)	−.104 (.182)	−.025 (.746)
INVENTORY								1.000	−.071 (.367)	.069 (.376)	−.060 (.442)
FOREIGN									1.000	−.071 (.367)	−.022 (.775)
LOSS										1.000	−.077 (.326)
MARGIN											1.000

Note. N = 165 audit engagements. The p values are reported in parentheses. See Table 1 for variable definitions.

, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

The OLS regression results of Equation 3 are presented in Table 5. In Model A, we examine the effect of technical inefficiency on realization rates. Consistent with Dopuch et al. (2003), we find that the coefficient for technical inefficiency is negative and statistically significant at the 5% level (p = .023 in Model A). This confirms findings of earlier studies which show that technical inefficiencies result in lower realization rates. In Model B, we include allocative inefficiency as an additional explanatory variable, and find that the coefficient on ALLOCINEFF is significantly negative (p = .006), while that on TECHINEFF remains significantly negative (p = .004) as well. That is, allocative inefficiencies result in lower realization rates, even after controlling for the technical inefficiency score. This shows that like technical inefficiencies, the existing allocative inefficiencies are costly to AUDITOR as they lead to discounts in audit pricing. Thus, we are able to reject H1 and H2.

Table 5.

OLS Regression of Realization Rates on Inefficiencies and Other Contextual Variables.

	Estimated coefficients (p values)
Variables	Model A	Model B	Model C	Model D
Intercept	0.745*** (<.001)	0.889** (<.001)	0.779*** (<.001)	0.785*** (<.001)
TECHINEFF	−0.039** (.023)	−0.042** (.004)	−0.057*** (<.001)	−0.058*** (<.001)
ALLOCINEFF		−0.117*** (.006)	−0.113*** (.005)	−0.117*** (.004)
TENURE			0.033*** (.007)	0.032** (.013)
SPECIALIST			−0.072** (.006)	−0.075*** (.005)
PEAK			0.063** (.012)	0.067*** (.010)
RESTATEMENT			−0.099** (.015)	−0.099** (.032)
INVENTORY				0.009 (.911)
FOREIGN				0.0233 (.949)
LOSS				−0.003 (.893)
MARGIN				0.001 (.381)
Adjusted R²	.03	.06	.19	.17

Note. F-statistic to compare Models A and B = $[(R S S_{Model A} - R S S_{Model B}) / (P_{Model B} - P_{Model A})] / [R S S_{Model B} / (N - P_{Model B})]$ = 7.743**. OLS = ordinary least squares. Variable definitions are provided in Table 1.

, **, and *** indicate statistical significance at 10%, 5%, and 1% levels, respectively.

To test whether the inclusion of the allocative inefficiency variable significantly increases the model’s explanatory power for billing realization rates, we compare the fit of Model B with that of Model A by computing the test statistic as $[(R S S_{Model A} - R S S_{Model B}) / (P_{Model B} - P_{Model A})] / [R S S_{Model B} / (N - P_{Model B})]$ , where P = number of parameters in the model. Model B represents an unrestricted model, while model A is akin to restricting the coefficient on allocative inefficiency to 0. The test statistic is then evaluated against the F-distribution with (P _{Model B} – P _{Model A}, N − P _{Model B}) degrees of freedom. A significant F-statistic would imply that allocative inefficiency adds significantly to the explanatory power of the model. The F-statistic is found to be significant at the 1% level, indicating that allocative inefficiency score is incrementally informative in determining the billing realization rate.

In Model C, we include TENURE, SPECIALIST, PEAK, and RESTATEMENT to test their respective impacts on the billing realization rate. As shown in Model C, TENURE has a significantly positive impact on realization rates (p = .007). Thus, we are able to reject H3, indicating that the longer the auditor has audited a client, the higher the realization rate it earns on the engagement. This result is relevant to the current debate on mandatory auditor rotation. Our findings are consistent with those that argue that there are potential gains from longer auditor–client tenures, possibly through client-specific knowledge that is gained over time.

Unlike some prior studies, we find that SPECIALIST has a significantly negative impact on realization rates (p = .006), and hence are able to reject H4. While at first glance this result might seem surprising, Mayhew and Wilkins (2003) argue that an audit firm may gain efficiencies due to the economies of scale in the specialist client group. However, if this client segment is price competitive, the audit firm may be forced to pass on any cost savings to the clients. As a result, the realization rates will be lower than those for nonspecialist clients. This is also consistent with results found in a recent study by Bills, Jeter, and Stein (2015) that documents that industry specialists charged lower audit fees than nonspecialists because of cost efficiencies. Our discussions with AUDITOR management seem to suggest that this may be true in the case of AUDITOR as well. However, in the absence of empirical evidence on potential causes, we refrain from drawing any definitive conclusions from this finding.

PEAK has a significantly positive (p = .012) impact on realization rate, which indicates a better realization rate (i.e., a lower discount) for work performed during the busy season. RESTATEMENT is negatively associated with realization rate at a significance level of 5%. The result supports Blankley et al.’s (2012) speculation that auditors actually receive abnormal and lower audit fee from clients that subsequently restate their financial statements. In Model D, we include INVENTORY, FOREIGN, LOSS, and MARGIN as control variables but find that they do not have any significant impact on realization rates. In the empirical results of Models C and D, the coefficients on technical and allocative inefficiency scores remain significant and negative, and hence we are able to reject both H1 and H2.

Note that a critical assumption that we make in our study that is common among studies in this area is that there is no difference in the unobservable quality of audit engagements across clients (Dopuch et al., 2003; O’Keefe et al., 1994). We follow the prescriptions suggested by DeFond and Zhang (2014) by utilizing different ways of controlling for audit quality. As our sample is taken from the local office of a single firm, we expect quality to be fairly uniform across engagements, consistent with the firm’s stated policies. We also conduct a field interview with a senior partner who is in charge of the audit practice at our research site. He explained that every time a decision is made to accept or retain a client, the audit firm estimates the audit effort required to achieve a defensible level of assurance, given the client’s characteristics and estimated level of client riskiness. If they feel that it would be difficult to achieve this acceptable assurance level, then a decision is made to drop the client. Thus, within the same branch office we expect all engagements to at least achieve a minimum acceptable assurance level.

Even so, it is possible that there are other client characteristics that affect the quality level of an audit engagement, either due to client type or due to the risk of litigation. Differences due to client type are likely to be mitigated by our inclusion of client characteristics such as PUBLIC, TENURE, and SPECIALIST. We also include two variables that capture business risk of the client, namely bankruptcy probability (ZSCORE) and client profitability (MARGIN). In addition, we capture litigation risk using an industry proxy based on Francis et al. (1994). In addition to all the client risk factors included in our model, we include RESTATEMENT which is a direct measure of audit quality. By including these variables, we hope to capture much of the difference in audit quality that may exist among audit engagements.

We conduct an additional robustness test to ensure that our results are not affected by any residual effects of audit quality in our measures of audit efficiency. Accounting accruals are widely used in the extant literature as indirect proxies of audit quality (DeFond & Zhang, 2014). We divide our research sample into two subsamples based on above-median and below-median values of accounting accruals.⁹ We rerun our main regression models for realization rates using the two subsamples. Our results (not reported) show that the main results for allocative inefficiency remain significant and in the predicted direction for both subsamples. An F test is unable to reject the null hypothesis that the coefficients from the two estimations are equal (p < .001). This provides further reassurance that our main results are not driven by residual effects of audit quality. However, like other studies in this area, we cannot completely rule out this possibility.

Given that the inefficiencies scores are truncated below at 1, we re-estimate Regression Model 3 using Tobit regression. The regression results (not reported) are very similar to those presented in Table 5. Furthermore, we conduct several econometric tests of our model specification to evaluate the robustness of our empirical results. We use Belsley, Kuh, and Welsch’s (1980) diagnostics for collinearity and do not find evidence of collinearity between explanatory variables in our Regression Model 3. White’s (1980) test does not indicate heteroskedasticity. We also employ the criteria proposed by Belsley et al. (1980) to identify influential observations. Results (not reported) remain substantially unchanged when the model is re-estimated after removing the identified outliers. Finally, we use super-efficiency procedures to screen out three outliers (Banker & Chang, 2006; Knechel et al., 2009) and obtain results (not reported) that are qualitatively similar to those discussed earlier.

Conclusion

In this study, we extend the findings of earlier studies that examine the relationship between audit inefficiency and fee realization rates of audit services. Prior work has shown that technical inefficiencies exist in audit work, and that these inefficiencies result in lower pricing. We build on this literature by examining whether audit engagements are technically and allocatively inefficient using data on 165 audit engagements performed by a large international accounting firm in a recent fiscal year. In the first stage of our analysis, we use the DEA methodology to calculate the technical and allocative inefficiencies of these audit engagements. We find that both allocative and technical inefficiencies do exist which implies that audit staff are not being utilized in an efficient manner in all engagements. More importantly, we find that these inefficiencies actually resulted in lower realization rates for audit engagements.

While our results are obtained from analyzing data from a Big 4 audit firm, they may generalize to other firms as well. International networks and alliances of CPA firms are growing in size and importance as these firms deal with increasingly sophisticated clients, international issues, and staffing constraint problems (Chang et al., 2011). As Big 4 firms have a history of dealing with complex, global clients, the lessons learned from their experience will provide insights for other firms as well as they grow, expand internationally, manage their constrained professional resources, and try to identify aspects of the audit engagement that add value to the client while being efficient in providing the level of services. These results are of import to regulators as well. One of the priorities of the PCAOB has been to develop input-based measures of audit quality to assist in their regulatory processes and policy making for improving audit quality and protecting investors. Such input-based measures include the experience levels of audit firm staff on individual engagements, the average ratio of auditing firm professional staff to audit firm partners, and annual staff retention (U.S. Department of the Treasury, 2008). Our measurement of allocative inefficiency would be potentially useful to the regulators such as PCAOB as an input-based measure of internal processes of audit firms.

This study underlines the importance of technical and allocative inefficiencies of audit production in audit fees as they tend to result in lower realization rates for the audit firm. Identifying factors that may affect these inefficiencies will aid audit firms in better understanding the production function of audit activities and help firms be more efficient in utilizing constrained personnel resources. Understanding the causes of these inefficiencies, thus, provides a fruitful endeavor for future research in the area. An examination of other engagement and audit firm characteristics would provide additional guidance to the audit industry, so that it can more efficiently utilize its constrained professional pipeline resources.

Footnotes

Declaration of Conflicting Interests

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

Funding

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

Notes

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