Fixed Costs, Audit Production, and Audit Markets: Theory and Evidence

by

Tracy Gu1, University of Hong Kong Dan A. Simunic2, University of British Columbia Michael T. Stein3, Old Dominion University

November, 2016 version

1

Assistant Professor, E-mail: [email protected] Professor, E-mail: [email protected] 3 Professor, E-mail: [email protected] 2

Acknowledgements: We thank workshop participants at the University of Technology-Sydney, and Rutgers University, New Jersey for their comments on an earlier version of this paper.

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Fixed Costs, Audit Production, and Audit Markets: Theory and Evidence Abstract We analyze the role of fixed costs in audit production. Our motivation is to better understand the

interaction of the production and supply of audit services and audit market outcomes. We conjecture that fixed costs are associated with the technology and other types of fixed investments used by the auditor to transform audit effort (hours) into assurance. We assume that such investments (and resulting fixed costs) influence production primarily through the efficiency of audit effort (process improvements). Efficiency increasing investments can result in either lower cost audits or higher assurance levels. We formally analyze the audit production problem from simple to more complex specifications, and use examples and simulation methods as well as explanatory figures to try to understand the pricing and market implications of various formulations. We rely on examples and simulation results, since the complexity of audit production with technology investments and fixed costs when an accounting firm has a portfolio of diverse clients doesn’t allow us, in general, to obtain closed-form solutions. The assumption that fixed costs are an important feature of audit service production yields a rich mix of interesting insights into the audit service market that are not found in the existing auditing literature. Based on these analyses, we develop four testable hypotheses concerning the relations between audit quality and (1) the magnitude of client-specific possible losses from servicing a client; (2) the average client losses in an audit firm’s portfolio; (3) the number of client’s in an audit firm’s portfolio; and (4) the variability of client losses in an audit firm’s portfolio. Using the absolute value of discretionary accruals as the proxy for audit quality, we find evidence supporting the four hypotheses.

Keywords:

Audit services, client portfolios, production, investments, fixed costs

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1.

Introduction and prior literature In this paper we analyze the role of fixed costs in audit production. Our motivation is to

better understand the interaction of the production and supply of audit services and audit market outcomes. Outcomes of interest include audit quality, audit costs and fees, and audit firm market shares. Fixed costs can be associated with a variety of investments that are made by a public accounting firm to facilitate audit production, including location specific investments (e.g. local offices), firm-wide training programs for staff, and investments in audit technology. We conjecture that such investments affect the transformation of audit effort (hours) into assurance, and that investments (fixed costs) influence production primarily through the efficiency of audit effort (process improvements). Efficiency increasing investments can result in either lower cost audits or higher assurance levels, or these outcomes could be combined. The investments and associated costs that we analyze are those that affect the audit of more than a single client. Considered over multiple time periods, such costs are constant for a given period of time, and joint across audits (of at least a subset) of clients serviced in that period. We do not consider client-specific set-up costs that may be incurred when performing an audit. A key implication of our focus on these fixed, joint costs is that the investment decision and the production of audit services cannot be analyzed on a client-by-client basis but must consider a portfolio of clients. Existing research (e.g. O’Keefe, Simunic and Stein 1994; Bell, Doogar and Solomon 2008; Akono and Stein 2014) models audit production as a simple transformation of variable labor inputs into audit assurance, without explicitly considering how (if at all) efficiency enhancing investments and associated fixed costs enter into that transformation. In the absence of significant fixed costs, the production of audit services for a specific client is largely separable from audit 3

production for other clients in an audit firm’s client portfolio. Of course, this greatly simplifies the audit production problem. When investments and resulting fixed costs are an important feature of production, then audits are no longer separable since investments will typically improve the efficiency of production of all audits, or at least a subset of the firm’s audits (e.g. clients in certain industries). These effects need to be aggregated when making the investment decision. As noted above, process improvements can be general and/or limited to specific clienteles. General investments improve the efficiency of audit effort for all of the auditors’ clients, while investments in specific clienteles improve the efficiency of production for a limited subset of the auditors’ clients. The modeling strategy we employ appears to be flexible insofar as it can be extended to cover a multitude of auditing scenarios, at least to a first approximation. The model does not encompass investments that target the demand side of the auditing market such as investments in advertising or customer relations. Our focus on the supply side of the auditing market follows from our interest in understanding how cost conditions affect the market for audit services. Since a large portion of the audit market operates under conditions of mandatory audits and unobserved ex ante audit quality, we believe there is considerable insight to be obtained from an improved understanding of supply conditions. The fact that a well specified and calibrated audit fee model (Simunic 1980; Hay, Knechel and Wong 2006) is able to explain 80% or more of the cross-sectional variation in logged U.S. audit fees using supply-side variables measuring client size, complexity, and risk suggests that supply-side factors are of critical importance in understanding audit production, pricing, and the market for audit services. As noted above, virtually all existing research has treated audit production as simply involving variable labor inputs which are (somehow) transformed into audit assurance, i.e., the

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probability that a client’s financial statements are not materially misstated. A significant exception is the paper by Sirois and Simunic (2011) which applies the endogenous fixed cost (EFC) model developed by Sutton (1991) to the auditing industry. In Sutton’s model as applied to auditing, audit technology plays a central role in determining the level of audit quality and audit fees. Sirois and Simunic further argue that Big 4 auditors make differentially greater technology investments than non-Big 4 auditors, and strategically compete on both quality and price through these investments in technology, the level of which is increasing in market size. Ferguson, Pinnuck and Skinner (2016) also apply Sutton’s EFC model to explain audit market structure and the emergence of the two-tier audit market (Big 4 vs. non-Big 4) in Australia. While Sutton’s EFC model is useful in that it incorporates technology investments and fixed costs, its application to the auditing industry has been mostly verbal and ad hoc. By contrast, in this paper we formally analyze the long-run audit production problem when fixed investments and resulting fixed costs are important. We set up an auditor’s expected audit cost minimization problem, obtain some analytical results, and then use examples, simulations, and graphic analysis to try to understand the observable implications of various formulations. These analyses lead to several testable hypotheses concerning relationships between audit quality, and the characteristics of individual clients and auditors’ portfolios of clients. We then test these hypotheses using the absolute value of discretionary accruals as the proxy for audit quality and four definitions of audit markets ranging from the broad U.S. national market (all publicly listed companies) to companies operating in specific U.S. Metropolitan Statistical Areas (MSAs) in specific 2-digit Standard Industrial Classification (SIC) industries. The results of these various empirical tests suggest that audit investments and related fixed costs that affect the production of some (or all) of an audit firm’s portfolio of clients are an important, hitherto unexamined feature of audit production which

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can help explain auditor-specific and client-specific systematic variations in audit quality, as well as audit pricing. The remainder of the paper is organized as follows. In section 2, we set up a basic formulation of the audit production problem where production requires variable labor input(s) but fixed costs are not explicitly considered – either because they do not exist or because technology and other investments associated with fixed costs are given, and not a choice variable. This formulation is consistent with the way audit production has been conceived and modeled in the existing literature. We use the initial formulations to motivate our foundational model, since the fact that an audit is a client-specific service and audit assurance is a state of mind of the service provider and service consumers, distinguishes audits from the typical production of tangible goods. In section 3, which is the conceptual / theoretical core of our paper, we introduce investments as a choice variable and resulting fixed costs into the analysis. We set up models that incorporate audit firms and their clients as described by several exogenous parameters, and study the characteristics of optimal production including levels of investment, variable labor hours used, assurance levels provided, and average total costs. We also extend our analysis of the behavior of individual audit firms to consider the implications for market characteristics and market equilibrium. We conclude this section by developing four testable hypotheses that follow from our analyses. In section 4 we develop and report the results of empirical tests of our hypotheses. The last section summarizes and concludes the paper.

2.1

Basic Set-Up - Single Client Optimization It is commonly assumed that competition in the market for audits and/or the production of

audits given a fixed audit fee motivates auditors to minimize the costs of audit production. This insight can be formalized in a number of ways. For example, an auditor planning the audit of a 6

single client using audit hours of various types (i.e. a choice among junior, senior, manager and partner hours) might solve (in concept) the following program: 1)

Minimize c(h) = w∙h + L • [1 - q(h, a) ] s.t.

where, c(•),

q(h, a) = 𝑞 𝑝 is the total cost function, h, is a vector of audit hours of various types (e.g. junior, senior etc.), w, is a vector of factor costs of various types of audit hours, L, is the potential loss an auditor may incur through association with a client’s financial statements q(•), is the audit transformation function in which audit hours are transformed into assurance, where assurance is the auditor assessed probability that the post-audit financial statements are free of material misstatement. 𝑝 𝑞 , is the planned level of assurance, a, is a fixed audit investment (e.g. technology) parameter affecting audit efficiency, and (1 - q), is the probability of a post audit loss.

Imposing appropriate structure to assure a solution and emphasizing that a is fixed and not a choice variable, then the auditor’s problem is to pick the cost minimizing h, i.e.

𝒉∗ = arg min 𝑐(𝑎, 𝒘, 𝐿, 𝑞 𝑝 , 𝒉) ℎ

If there is an interior solution to this problem then it would be characterized by the usual equalities between the ratios of the marginal rates of transformation and the ratios of the factor costs (prices). This model carries the essence of the cost structure implicit in most empirical cross-sectional audit fee or audit hour studies involving multiple labor inputs and was used to motivate the empirical analysis of audit hours utilized by a major public accounting firm in O’Keefe, Simunic and Stein (1994) and Bell, Doogar and Solomon (2008).

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If we specify an appropriate audit hour transformation function (see end note one) and substitute in parameter values then, in theory, we could write down an audit cost function relative to the parameters as:

2)

c(𝒉∗ | a, w, L, 𝑞 𝑝 )

We can view 2) as a foundational model used to motivate archival audit fee studies where w, the vector of wage rates, is assumed to be exogenous, and a represents the fixed investment in technology and other factors utilized by the auditor. Since a is unobserved (unobservable?) by the researcher, it is often assumed to be a pre-determined characteristic of the audit firm. L, the potential loss, varies across clients and is likely a function of the size, complexity, and risk of the client as well as the legal and institutional environment associated with the audit. We expect the potential loss to increase as client size, risk, and complexity increase, and as the legal and institutional regime becomes more onerous to auditors. Since liability is ultimately constrained by the financial resources of the audit firm and / or its professional liability insurance, L is finite and bounded from above. Also, to focus on the essential features of audit service production and to simplify our analyses, we assume that auditors are strictly liable for failing to detect material misstatements in financial statements (i.e. there is no “negligence defense” based on adherence to auditing standards) or the combination of auditing standards toughness and vagueness is such that the auditor is motivated to ignore the standards (Ye and Simunic, 2013). The treatment of the planned level of assurance appearing in 1) and 2) as a fixed parameter is somewhat problematic. Often 𝑞 𝑝 is assumed to be fixed either by GAAS or by audit firm policy. If 𝑞 𝑝 is fixed or predetermined then there is no guarantee that c(𝒉∗ | a, w, L, 𝑞 𝑝 ) satisfies the condition that c(𝒉∗ | a, w, L, 𝑞 𝑝 ) < c(𝒉, 𝑞 |a, w, L) for all allowable combinations of {h, q}. That 8

is, fixing q in advance potentially conflicts with cost minimization. If, on the other hand, q is assumed to vary audit by audit then the program 1) would need to be changed to reflect optimization over both h and q. Assuming , 𝑞 𝑝 is fixed, c(•) represents the (usually unobserved) cost of the audit and (1+π) c(•) represents the audit fee, where (1+π) is the markup on cost. We can then write the audit fee as: 3)

Fee = (1+ π) c(𝒉∗ | a, w, L, 𝑞 𝑝 )

Equation 3) can be transformed into the commonly used cross-sectional audit fee model by adding an error term and appropriate client subscripts. If the audit market is competitive (1+π) should trend towards a constant representing a normal return on investment. As mentioned above, w is exogenous and variation in wages would follow price levels in local labor markets. In our model L is the main driver of audit costs and varies with client characteristics. It is a matter of debate whether variation in planned assurance, 𝑞 𝑝 , tracks the auditor’s brand name (an observable that can be used for contracting in the audit market) or potentially varies systematically with client or environmental factors. What role is played by the fixed costs in this structure? Program 1) is a short-run cost minimization problem and fixed costs are treated as both predetermined and sunk. The lack of controls for fixed investment may not be too problematic empirically. If the fixed costs vary across providers than a provider fixed effect potentially captures the cross-sectional differences. If there is no across provider variation in investment (due, perhaps to competition), the rental costs of fixed investments are included in the mark-up on cost. This mechanism is consistent with the normal practice in service firms to add mark-up on direct labor costs to bill overhead and earn profits.

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We represent any fixed investments by the parameter a in the assurance transformation function. Higher levels of a imply larger fixed investments. In turn, these investments change the efficiency (marginal physical product) of the various classes of labor. Then continuing the chain, changes in the marginal product of labor hours impact the vector of labor required to achieve the planned level of assurance, 𝑞 𝑝 .

2.2

Analysis with Multiple Clients Program 1) can be easily extended to incorporate a portfolio of clients:

5)

Minimize ∑𝑐𝑖 (𝒉𝑖 ) = ∑w𝒉𝑖 + ∑𝐿 (1 - 𝑞 𝑝 ) s.t.

q(𝒉𝑖 , a) = 𝑞 𝑝 , for all i ∊ 𝑛𝑡

where 𝑛𝑡 is auditor t’s set of clients. To conserve on notation we set 𝑛𝑡 equal to the set number of clients in auditor t’s portfolio. If audit production is separable in the sense that 𝒉𝒊 is independent of any other 𝒉j, then program 5 is a simple adding up of model 1). However, interdependencies might enter the cost functions either through the loss function (see Simunic and Stein, 1990) or through the assurance transformation function, as would occur if learning increased the efficiency of labor. In these cases, the optimal vectors of 𝒉𝑖 ’s might be jointly determined rather than determinable on an audit by audit basis. Further, if there is a fixed level of planned assurance as in 5) then dependencies are built into the problem. It is worth noting that if an audit firm were to audit to a fixed level of assurance, 𝑞 𝑝 , across clients, it would make sense for the firm to solve for the optimal 𝑞 𝑝 at the portfolio level.

3.0

Production with Investments and Related Fixed Costs

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As noted above, we treat the technology and other investments that are associated with fixed costs, the parameter a, as an input to the auditor’s assurance transformation function. We assume that such fixed investments do not directly provide assurance, but rather affect the various types of labor hours needed to produce a level of assurance. That is, they operate indirectly through the relationship between the usage of hours and the production of assurance. As a consequence of this assumption, fixed investments and costs are inherently efficiency oriented. An auditor investing in technology and other fixed investments and incurring fixed costs reduces the marginal use of labor hours for any target level of assurance. Of course, by reducing the marginal cost of producing assurance it is possible that the auditor with higher fixed costs offers a higher level of assurance, but whether or not that outcome occurs depends upon other supply parameters and demand conditions. We rewrite program 5) to emphasize that the problem is solved for each auditor at the client firm level. In addition, to simplify notation and because the mix of labor types is not important to our analyses, we assume a single type of labor going forward. Finally, and most important, we drop the constraint which characterizes the prior literature that the assurance level produced must equal some planned, target level. If there are T auditors in the market and each auditor has nt clients, we denote auditor t’s choice of investment as 𝑎t. Thus:

6)

Minimize ∑𝑐𝑖 (𝑎𝑡 , ℎ𝑖 ) = ∑wℎ𝑖 + ∑𝐿 (1 - qi) + f(𝑎𝑡 ) s.t.

q(ℎ𝑖 , 𝑎𝑡 ) = 𝑞𝑖 , for all i ∊ 𝑛𝑡

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where f(𝑎𝑡 ) is the fixed rental cost of 𝑎𝑡 , We assume df/da > 0 and d2f/da2 > 0; that is, the fixed costs of investing in technology and other factors increase at an increasing rate.. The auditor chooses a parameter value 𝑎𝑡 and a vector of client-specific labor hours, hi , that minimize the total (expected) cost of auditing her portfolio. Since q(ℎ𝑖 , 𝑎𝑡 ) = 𝑞𝑖 is a function of 𝑎𝑡 and ℎ𝑖 through the constraint, 𝑞𝑖 varies across audits and a firm level of assurance is only achieved in terms of a portfolio average.

3.1

Fixed Costs with n Identical Clients To obtain some intuition into the solution of program 6), suppose that an auditor, t, has 𝑛𝑡

identical clients and is considering a new fixed investment, say in technology, that improves the efficiency of production for each client. We rewrite program 6) to incorporate the identical client assumption and specify an audit hour transformation function: 7a)

c(ℎ𝑡∗ , 𝑎𝑡∗ ) = Min 𝑐𝑖 (ℎ𝑡 , 𝑎𝑡 ) = 𝑛𝑡 wℎ𝑖 + 𝑛𝑡 𝐿 (1 - 𝑞 ) + f(𝑎𝑡 ) s.t.

q = 𝑎𝑡 h1/2

∀ i ∊ 𝑛𝑡 and 0 ≤ q ≤ 1

Given the symmetry of having identical clients we can divide 7a) by 𝑛𝑡 to minimize the average cost per client: 7b)

c(ℎ𝑡∗ , 𝑎𝑡∗ ) / 𝑛𝑡 = Min 𝑐𝑖 (ℎ𝑡 , 𝑎𝑡 ) / 𝑛𝑡 = wℎ𝑖 + 𝐿 (1 - 𝑞 ) + f(𝑎𝑡 ) / 𝑛𝑡 s.t.

q = 𝑎𝑡 h1/2

∀ i ∊ 𝑛𝑡 and 0 ≤ q ≤ 1

To derive an algebraic solution to this problem we also need to specify a functional form for f(•), the cost of the fixed factor 𝑎𝑡 . We let 8)

f(𝑎𝑡 ) = (𝑘𝑡 • 𝑎𝑡 )3.

Importantly, the cost of 𝑎𝑡 increases quickly enough to offset the concavity of the assurance transformation function q(•).Also, we allow the cost of the fixed factor to vary across audit firms. Working through the math and solving in terms of the parameters: 12

𝑞𝑡∗ = (L5 𝑛𝑡2 ) / (72 𝑘𝑡6 w3),

𝑎𝑡∗ = (L2 𝑛𝑡 ) / (6 𝑘𝑡3 w),

and

ℎ𝑡∗ = (L6 𝑛𝑡2 ) / (144 𝑘𝑡6 w4)

The results are qualitatively as expected: 𝑞𝑡∗ , 𝑎𝑡∗ , and ℎ𝑡∗ , each increase in L and 𝑛𝑡 and decrease in w and 𝑘𝑡 . To get a better sense for these results we next fix the parameter values for four cases and then plot the average cost as 𝑎𝑡 ranges over the set of values such that the corresponding q lies in the range 0 < q < 1. Given that we have fixed the values of 𝐿𝑖 , 𝑘𝑡 w, and 𝑛𝑡 , then q = q(𝑎𝑡 ) uniquely for each 𝑎𝑡 . We label the four cases HB (High Risk / Big Firm), HS (High Risk / Small Firm), LB (Low Risk / Big Firm), and LS (Low Risk / Small Firm). The parameter values we use are given in the following table: HB:

L = 50,000;

𝑘𝑡 = 2,150;

w = 100;

𝑛𝑡 = 150

HS:

L = 50,000;

𝑘𝑡 = 2,150;

w = 50;

𝑛𝑡 = 50

LB:

L = 30,000;

𝑘𝑡 = 1,450;

w = 100;

𝑛𝑡 = 150

LS:

L = 30,000;

𝑘𝑡 = 1,450;

w = 50;

𝑛𝑡 = 50

Risky clients pose a greater potential loss, L, to the auditor. Small firms are defined as having fewer clients than large firms. We also assume small firms pay a lower wage. With low risk clients we reduced the cost constant 𝑘𝑡 . The intuition is that the cost of implementing more efficient technologies is likely reduced for less complex, less risky clients. The results are seen in Figure 1. The curves shown are analogous to long run average costs curves (the envelope of short run average costs where 𝑎𝑡 is fixed) for producing various levels of assurance, q. The values of 𝑞 ∗ , 𝑎∗ , and ℎ∗ are the long-run average cost-minimizing values given the parameterization of each audit firm. Comparing HB and HS we see the firm with the greater number of clients makes a larger investment in technology, obtains a smaller average cost, and provides a higher level of assurance despite using fewer labor hours. FIGURE 1 about here 13

HB:

𝑞 ∗ = .987

𝑎∗ = .0628

ℎ∗ = 246

AC = 41,760

HS:

𝑞 ∗ = .882

𝑎∗ = .0444

ℎ∗ = 394

AC = 42,676

In Figure 2 we compare the LB and LS scenarios. FIGURE 2 about here

LB:

𝑞 ∗ = .817 𝑎∗ = .0738

ℎ∗ = 123

AC = 25,915

LS:

𝑞 ∗ = .726 𝑎∗ = .0521

ℎ∗ = 194

AC = 26,369

Again the firm with the larger portfolio makes a greater technology investment, provides higher assurance, uses fewer labor hours, and does so at lower average cost. Comparing the high risk and the low risk cases we see that the high risk portfolios use more labor and provide higher assurance. That the 𝑎𝑡∗ are higher in the low risk cases is due to the decrease in kt from 2,150 to 1,450. If the kt had been held constant across the scenarios the results would be qualitatively similar, however the level of assurance, 𝑞 ∗ , and the level of technology, 𝑎𝑡∗ , would be much lower in the low risk examples. Additional insight into the optimum solution can be obtained by considering how the size of an audit firm’s portfolio (number of clients) affects AC, 𝑞 ∗ , 𝑎∗ , and ℎ∗ . As shown in Alternative Figures A, increasing the number of clients in an audit firm’s portfolio motivates a reduction in average audit cost, an increase in technology investments, an increase in audit hours, and an increase in assurance levels, but these effects are all much more pronounced for large loss clients than for small loss clients. This is interesting and suggests that auditors will behave differently in their technology investments and assurance production if they have a large portfolio of small clients vs. a smaller portfolio of large clients. Also, note that the third and fourth alternative figures look similar and show that the usage of more audit hours per client is associated with providing more assurance. When maximum assurance (q = 1) for the largest clients (𝐿𝑖 = $45,000) is reached, 14

then adding more clients to the portfolio induces a pure efficiency substitution of technology (𝑎∗ for labor ℎ∗ ). ALTERNATIVE FIGURES A about here Another way to look at the model is shown in Figure 3 which focuses on the trade-offs being made by the HB auditor in minimizing costs. The figure shows that different combinations of labor hours (vertical axis) and fixed investments (horizontal axis) will yield various levels of assurance, q. The least-cost solution for the HB auditor, who recall has 150 identical high risk clients, is the green dot on the 𝑞 ≈ .99 iso-assurance curve which yields the minimum average cost of $41,760 per client. Non-optimal, higher iso-cost combinations of hours, fixed investments, and assurance are shown in brown, blue and red. Finally, the figure also shows a constrained cost minimization if the value of fixed investments, 𝑎𝑡 , is arbitrarily set at .0565. Then the constrained least-cost solution is the point of tangency with the blue iso-cost curve. Since the HB auditor in this example has identical clients, a constrained optimization is not particularly relevant. However, the example illustrates that when clients are heterogeneous, a fixed investment that is optimal for the whole portfolio would not necessarily be cost minimizing for a particular client. FIGURE 3 about here Overall, the initial analysis points towards two major trends that emerge within our framework. First, the assurance level is driven by the dollar amount of possible losses associated with a client and the number of such clients, and second, investment in technology is driven largely by economies of scale. Also, while the four cases are only illustrative examples of optimal production under different parameter values and not market equilibrium results, we note that the operations of HB strictly dominate HS, and LB dominate LS, in the sense that the large firms can offer the same or higher assurance levels at a lower cost to clients of a given size. 15

3.2

Portfolio Simulation 1 - Fixed Costs and Varying Portfolio Characteristics In section 3.1, we assume each audit firm has 𝑛𝑡 identical clients. In this section we

generalize the results by assuming the firm’s 𝑛𝑡 clients possess varying audit relevant characteristics. To keep the analysis uncluttered we assume these characteristics can be summarized by the client’s scalar loss, 𝐿𝑖 . To form a portfolio of clients random values of Li are drawn from a uniform distribution. As before we vary some of the parameters as well as the distribution of 𝐿𝑖 . Below is psuedo code (algorithm) describing our simulation process: 1.

Set the parameter values for w, 𝑘𝑡 , 𝑛𝑡 and 𝐿𝑖 ~ U[Lmin, Lmax]

2.

Select a random sample of nt values of 𝐿𝑖 from the interval (Lmin, Lmax)

3.

For each client, i, calculate the minimum cost given wt0, 𝑘𝑡0 , nt0, 𝐿𝑖 by optimizing over 𝑎𝑡 , and qi. s.t. 0 ≤ qi ≤ 1

4.

Average the minimum client costs over the portfolio of clients.

5.

Repeat steps 3 and 4, 50 times.

The next table shows the parameter values for the first set of simulations: 𝐿𝑖 ~ U[40,000, 60,000];

𝑘𝑡 = 2,150;

w = 100;

𝑛𝑡 = 150

Large n HV: 𝐿𝑖 ~ U{30,000, 70,000];

𝑘𝑡 = 2,150;

w = 100;

𝑛𝑡 = 150

𝐿𝑖 ~ U[40,000, 60,000];

𝑘𝑡 = 2,150;

w = 50;

𝑛𝑡 = 50

Small n HV: 𝐿𝑖 i~ U[30,000, 70,000];

𝑘𝑡 = 2,150;

w = 50;

𝑛𝑡 = 50

Large n:

Small n:

HV refers to higher variance as we increase the range of the possible values of 𝐿𝑖 . A table of outcomes is given below along with a graph (Figure 4) of the average cost and 𝑎𝑡 for each simulation (each simulation is repeated 50 times and the reported results are the averages over the repetitions). 16

As with the case of 𝑛𝑡 identical clients we find that smaller portfolios result in lower investment, lower assurance, and higher average costs. In our high variance samples the means of the distribution are not changed, but nonetheless we find decreases in investment, hours, assurance, and cost relative to the smaller variance counter-parts. These results are likely due to the nonlinearity of the assurance transformation function. Clients with low values of 𝐿𝑖 are lightly audited relative to clients with high values of 𝐿𝑖 . FIGURE 4 about here It is worth repeating that in these simulations 𝑞𝑖∗ varies significantly by client and that from the firm’s point of view an average level of assurance is delivered. This is in contrast to the usual way audit services are conceptualized (e.g. O’Keefe, Simunic, and Stein, 1994) where a planned level of assurance is delivered for each client. The idea that assurance varies client by client around a firm mean is consistent with an economic approach to the auditor’s problem in which auditors maximize their profits. In contrast, if the assurance level is set as a constraint to be equaled or bettered, then it is hard to see that strategy as being consistent with profit maximizing. It might be more consistent, perhaps, with the traditional professionalism approach to audit planning. Our research does not take up normative arguments for the precedence of one approach over the other,

𝑎𝑡∗

Ave. q*

Ave. Cost

Large n:

0.061

0.913

41,519

Large n HV:

0.059

0.846

40,862

Small n:

0.042

0.880

42,404

Small n HV

0.041

0.828

41,696

but we note that the economic argument for allowing assurance to vary with risk and potential losses is straightforward as the economic agent internalizes the costs and benefits of their decision17

making. The professionalism approach may also be economically consistent but requires a more comprehensive (less realistic?) model of auditor decision making in which externalities are taken into account. The fact that adding variance to a client portfolio has a relatively minor impact on optimal auditor behavior – with the important exception that assurance levels vary and are client specific is further seen in ALTERNATIVE FIGURE B which shows that the dollar amount of optimal fixed investment, 𝑎∗ , increases with the number of clients each associated with a given potential loss, L, of 35,000 (the straight line) vs. an increase in the number of clients which vary in potential loss but where the average potential loss is 35,000 (the curvy line). Note that these lines are roughly co-incident; that is optimal investment behavior is essentially the same.

3.3

Portfolio Simulation 2 - Fixed Costs, Varying Portfolios, and an Incremental Client In this set of simulations we consider four auditors with different client portfolios and then

look at the cost of adding a new audit to each portfolio. We start by assuming each auditor type has an initial endowment of clients. The auditor optimizes the investment in technology to minimize the average cost of producing its initial portfolio. We then calculate the cost to each auditor type of adding a client with a given 𝐿𝑖 . The auditor parameters are given in the following table. Clients

𝑘𝑡

w

n

𝑎𝑡∗

High Large:

𝐿𝑖 ~ U[40,000, 80,000];

𝑘𝑡 = 2,150;

w = 100;

𝑛𝑡 = 150

.062

Low Small:

𝐿𝑖 ~ U[20,000, 50,000];

𝑘𝑡 = 2,150;

w = 75;

𝑛𝑡 = 100

.029

High Small:

𝐿𝑖 ~ U[40,000, 80,000];

𝑘𝑡 = 2,150;

w = 100;

𝑛𝑡 = 100

.056

Low Large:

𝐿𝑖 ~ U[20,000, 50,000];

𝑘𝑡 = 2,150;

w = 75;

𝑛𝑡 = 150

.043

18

Note that the High and Low portfolios overlap in the range 40,000 ≤ 𝐿𝑖 ≤ 50,000, but the High auditors “specialize” in providing audits to larger clients than Low auditors. Thus the High Large auditor could be thought of as a Big 4 firm, while the Low Small auditor might be a nonBig 4 firm. In this simulation all auditors have the same technology unit cost, 𝑘𝑡 , but Low auditors pay a somewhat reduced wage rate relative to High auditors. Large auditors have 150 clients while Small auditors have 100 clients. Ceteris paribus, both High and Large clienteles lead to increased investment. Next we specify a collection of new clients from the set, 𝐿𝑖 = {40,000, 42,500,…,60,000} and calculate the average cost of adding a client of that size to the above portfolios. Figure 5 shows a comparison of High Large with Low Small. Note that the High Large auditor is more costly with respect to the audit of a new client until about 𝐿𝑖 = 44,000, then becomes less costly for larger Li. The greater technology investment improves audit efficiency enough to overcome the wage differential for sufficiently large clients. The High Large auditor also provides a higher level of assurance uniformly across the range (assurance levels are untabulated). Figure 5 about here In Figure 6, which shows a comparison of High Small and Low Large, the High Small auditor is uniformly more expensive than the Low Large auditor. While the High Small auditor provides a higher level of assurance than the Low Large auditor, The differences in assurance levels are much smaller than in the cases depicted in Figure 4 (again the assurance levels are untabulated). Figure 6 about here In Figure 5 the High auditor takes advantage of its large size to make a significantly greater investment in technology. This investment pays off in terms of assurance in general and efficiency for large clients. In contrast, the comparison in Figure 6 shows the Low Large auditor using its 19

size to invest almost as much as the High Small auditor in technology. Nonetheless the lower technology investment results in lower levels of assurance while the increased size and lower wage rate results in reduced average costs. 3.4

Discussion of the Analyses Up to This Point in Section 3 An audit is a client-specific service, not a tangible product. When audit production

incorporates investments that generate fixed costs, we need to specify how such investments combine with labor to produce audit assurance. Since assurance is an auditor’s (e.g. engagement partner’s) and/or a financial statement user’s subjective belief that the client-prepared, post-audit financial statements are free of material misstatements, we model audit technology investments as increasing the efficiency of audit labor hours. That is, investments do not produce assurance directly, but only through their effects on labor effort required. Enhanced efficiency allows an auditor to produce a fixed level of assurance with fewer hours, or to produce a higher assurance level with a fixed number of hours, or a combination of both. Fixed costs are not client specific, but are amortized over (at least part) of a client portfolio. When investment level ( 𝑎𝑡 ) is a choice variable for an audit firm, audit production is interdependent across clients, which vary in nature (i.e. size, complexity, and risk). The nature of clients is captured in our analyses through the potential dollar amount of losses (𝐿𝑖 ) that an auditor may incur by being associated with a client’s post-audit financial statements. Heterogeneous clients and interdependent production suggest that a fixed assurance level for each audit is not likely to be cost-minimizing over a client portfolio. Therefore, an assurance level describing an audit firm can be thought of as a portfolio average assurance level. For example, there is a wealth of evidence that Big 4 firms provide higher average assurance levels than non-

20

Big 4 audit firms. But the client-specific assurance level for a high risk non-Big 4 audit client could well be greater than the client-specific assurance level for a low risk Big 4 client. The problem of finding an optimal 𝑎𝑡 together with the optimal client-specific ℎ𝑖 for a portfolio of heterogeneous clients (with varying 𝐿𝑖 ) is too complex (impossible?) to solve analytically without fairly strong assumptions. However, the auditor’s optimization problem assuming constant loss exposure (L) with the number of such clients allowed to vary is manageable. In addition, we have shown that adding pure variance in client losses has relatively little impact on the optimum solution which largely depends on mean client size and the number of clients, although larger portfolio variance does reduce average audit quality levels. In addition, we have solved a number of examples and run simulations with assumed specific functional forms (i.e. for q(•) and f(𝑎𝑡 ) ) and parameter values. These analytical results, examples and simulations suggest the following: 

Audit firms with more clients and/or clients with higher 𝐿𝑖 ‘s make larger fixed investments, and audit firms can be differentiated by their levels of fixed investments.



Audit firms making larger optimal fixed investments can obtain a lower average cost per unit of assurance, even those auditors who pay a higher wage rate (per labor hour). These firms can supply a given level of assurance at a lower cost, or can supply greater assurance at the same cost as audit firms with lower levels of investment.



Optimal assurance levels vary by client, such that clients with low values of L are audited to a lower assurance level than clients with high L values.



Audit firms with more total clients and/or higher L clients will tend to produce higher average assurance levels than audit firms with fewer clients and/or lower L clients.

21



Audit hours are not a good proxy measure of total auditor effort nor audit assurance levels across audit firms when there are varying levels of productive fixed investments.



Given a level of technology investment (and resulting fixed costs) that is optimal for servicing a given client portfolio, an auditor with a high level of investment is potentially the least cost producer for clients with both high values of Li and low values of 𝐿𝑖 . However, our model cannot speak to whether or not a high investment auditor would choose to compete for low 𝐿𝑖 audits.

3.5

Production with Fixed Investments and Audit Markets In this section, we analyze and discuss how audit firms might interact in a market when

fixed investments are important. We begin with two examples which illustrate the optimum solution with respect to 𝑎𝑡 , ℎ𝑖 , 𝑞𝑖 , and average total cost as the number of clients in an audit firm’s portfolio increases for two audit firms, where one firm specializes in relatively high loss (𝐿𝑖 ) clients and the other firm specializes in low loss clients. One might think of the former as representing a Big 4 firm and the latter as a non-Big 4 firm. The solution values for the large client firm are shown in Table 1 and the solution values for the small client firm are shown in Table 2 (w=75 and 𝑘𝑡 = 2000 in these examples). Insert Tables 1 and 2 about here Note that for any portfolio size, the high loss firm has higher average cost, a higher investment in technology, a higher assurance level, and uses more audit hours per client. In addition, increasing portfolio size has a relatively large impact on the (optimal) operations of the “high loss” firm (i.e. changes in AC, 𝑎𝑡∗ , ℎ𝑡∗ , 𝑞𝑡∗ ) relative to the “low loss” firm. The trade-offs made by an audit firm in response to the two parameters, client losses (L) and portfolio size (𝑛𝑡 ), 22

are illustrated in Figure 7, which shows various levels of investment, 𝑎𝑡 , that are consistent with combinations of L and 𝑛𝑡 . Note that higher values of 𝑎𝑡 are also consistent with the production of higher assurance levels, 𝑞𝑖 (which are untabulated). Could the two audit firms described in Tables 1 and 2 co-exist in a market place? Initially, it would seem so as the firms specialize in different types of clients and deliver different qualities of service at a different cost (price). However, Table 1 and 2 don’t answer the question of whether, in a frictionless competitive market, the clients of the “high loss” audit firm are motivated to switch to the “low loss” audit firm, and/or vice versa, simply to minimize their audit costs (i.e. obtain the same assurance at a lower cost or obtain more assurance at the same cost). To answer this question, we need to consider the market equilibrium that would obtain given our characterization of audit production. 3.6

Static Market Equilibrium with Fixed Investments Since our model focuses upon the supply of audit assurance through fixed cost investments

(demand is not relevant) we are limited in what we can say about market equilibrium. Probably the most significant market implication that follows from our set of (highly restrictive) assumptions is that, in equilibrium, all audit firms would choose the same level of investment, 𝑎𝑡∗ . Interestingly, this condition does not require all audit firms in the market to have the same number of clients or client portfolios with the same magnitude of potential post audit losses. Thus, the “high loss” firm and the “low loss” firm illustrated above could not co-exist in a frictionless competitive marketplace. The intuition for this result rests upon the assumptions that: i) increased investment decreases the amount of labor required to achieve any level of assurance; ii) the investment does this in a generalized way, i.e., the technology is not specific to limited subsets of clients; iii) all 23

audit firms face the same factor prices and agree upon the potential loss for each client in the market; iv) clients treat assurance as a normal good, i.e., at a given price more assurance is preferred to less; and v) firms price audits competitively. As a consequence, the audit firm with the highest 𝑎𝑡∗ can produce assurance more cheaply than any of its competitors. In turn, this implies either the most efficient audit firm sweeps the market (natural monopoly) or if multiple firms coexist then each has equal levels of investment and audit efficiency. To see how this works more concretely we revisit our solution to the auditor cost minimization problem where each auditor has nt identical clients of size L. We determined earlier that the optimal solution is: 𝑞𝑡∗ = (L5 𝑛𝑡2 ) / (72 𝑘𝑡6 w3),

𝑎𝑡∗ = (L2 𝑛𝑡 ) / (6 𝑘𝑡3 w),

and

ℎ𝑡∗ = (L6 𝑛𝑡2 ) / (144 𝑘𝑡6 w4)

The auditor’s portfolio cost is: 9)

𝑐𝑡 (𝑎𝑡 , ℎ𝑡 | 𝑛𝑡 , 𝐿𝑡 , w, 𝑘𝑡 ) = 𝑛𝑡 w ℎ𝑖 + 𝑛𝑡 𝐿𝑡 • (1- 𝑞𝑡 ) T+ (𝑘𝑡 𝑎𝑡 )3

The t subscript indicates that these variables and parameters are tied to a specific auditor. If we substitute in the optimal values from above into 9) and simplify the resulting expression we get the minimum cost: 10)

𝑐𝑡 (𝑎𝑡∗ , ℎ𝑡∗ | 𝑛𝑡 , 𝐿𝑡 , w, k) = 𝑛𝑡 𝐿𝑡 – ((𝐿6𝑡 𝑛𝑡3 ) / (432 𝑘 6 w3))

To simplify the exposition we assume there are only two auditors in the market and that each auditor has a unique clientele with differing values for 𝐿𝑡 and 𝑛𝑡 . If each audit firm minimizes the cost of its portfolio, then the least cost solutions are: 11)

∗ 𝑐1 (𝑎1∗ , ℎ11 | 𝑛1 , 𝐿1 , w, k) = 𝑛1 𝐿1 – ((𝐿16 𝑛13 ) / (432 𝑘 6 w3))

12)

∗ 𝑐2 (𝑎2∗ , ℎ22 | 𝑛2 , 𝐿2 , w, k) = 𝑛2 𝐿2 – ((𝐿26 𝑛23 ) / (432 𝑘 6 w3))

∗ ∗ The notation ℎ11 (and ℎ22 ) indicates the optimal number of hours per client used by auditor 1 (2)

for a client with loss, 𝐿1 (𝐿2 ). Suppose 𝑎1∗ > 𝑎2∗ , then from the optimal solution for 𝑎𝑡∗ we 24

know 𝐿12 𝑛1 > 𝐿22 𝑛2 . (This condition also implies that if 𝑎1∗ = 𝑎2∗ then it is not necessary the client portfolios are identical w.r.t. 𝐿𝑡 and 𝑛𝑡 .) With investment fixed and these costs considered sunk we can ask what would be the cost for auditor 1 to audit a client from auditor 2’s portfolio? First we solve for the minimum cost of an incremental audit with an arbitrary loss, 𝐿𝑖 , for either auditor given a level of investment set at the auditor’s existing portfolio’s optimum as: 13)

∗ 𝑐𝑡 (𝑎𝑡∗ , ℎ𝑡𝑖 | 𝐿𝑖 , w, k) = 𝐿𝑖 – ((𝐿𝑖2 𝑎𝑡∗2 ) / (4w))

So the cost to auditor 1 of auditing a client from auditor two’s portfolio is: 14)

∗ 𝑐1 (𝑎1∗ , ℎ12 | 𝐿2 , w, k) = 𝐿2 – ((𝐿22 𝑎1∗2 ) / (4w))

And the cost to auditor 2 of providing the same (incremental audit) is: 15)

∗ 𝑐2 (𝑎2∗ , ℎ22 | 𝐿2 , w, k) = 𝐿2 – ((𝐿22 𝑎2∗2 ) / (4w))

Subtracting 15) from 14) we get: 16)

𝐿2 – ((𝐿22 𝑎1∗2 ) / (4w)) - 𝐿2 + ((𝐿22 𝑎2∗2 ) / (4w)) = (𝐿22 / 4 w) (𝑎2∗2 - 𝑎1∗2 ) < 0

Since 0 < 𝑎2∗ < 𝑎1∗ by assumption, this implies that auditor 1 has a lower cost of producing the audit for auditor 2’s client, 𝐿2 , and could undercut auditor 2’s price. Notice the only assumption on the 𝐿2 is that it is greater than 0. From this type of argument, we can conclude, under our assumptions, that if a frictionless competitive market equilibrium exists with more than one provider, then each provider would have a common level of investment. This does not imply that each auditor provides the same level of assurance to their clients (they have different portfolio L’s). The condition for optimal assurance is: 𝑞𝑖∗ = (𝐿5𝑖 𝑛𝑡2 ) / (72 𝑘 6 w3) s.t. 0 ≤ 𝑞𝑖∗ ≤ 1 and the condition for common investment is: 𝐿12 𝑛1 = 𝐿22 𝑛2 25

Clearly, by inspection, the common investment condition doesn’t imply equality of the 𝑞𝑖∗ ′𝑠. However, 13) implies that for an incremental audit, suppliers with a common level of investment have the same cost. Given this and a common 𝑎𝑡∗ they will audit to the same level of assurance for this particular client.

3.7

Testable Empirical Implications Based on the various analyses in this paper, it is possible to develop a number of testable

empirical implications. Specifically: 1. For a given audit firm, audit quality is client specific and increases with the size of the potential client specific losses (𝐿𝑖 ). This is more of an assumption rather than an implication of our analysis since a fixed level of assurance is not likely to be cost minimizing when an auditor services heterogeneous clients, and we assume cost minimization. 2. In any market, average audit quality produced by an audit firm increases as average client Li

in the firm’s portfolio of clients increases (as 𝐿𝑖 increases, 𝑎∗ increases, and

𝑞 ∗ increases). We note that, in a frictionless competitive equilibrium, 𝐿2 𝑛𝑡 will equalize across audit firms since 𝑎𝑡 is proportional to 𝐿2 𝑛𝑡 . But this equilibrium result does not necessarily describe any specific audit market at any particular time when there are market frictions (e.g. transaction costs of auditor change are positive and significant). 3. In any market, average audit quality produced by an audit firm increase as the number of clients (nt ) in the firm’s portfolio increases (as nt increases, 𝑎∗ increases, and 𝑞 ∗ increases). 4. In any market, average audit quality decreases as the variability of client losses (Li ) in the firm’s portfolio increases.

26

Note that these predictions derive solely from production, supply-side considerations and do not make any assumptions about demand except that audits are normal goods (i.e. more assurance is preferred to less, given audit cost).

4.

Empirical Tests

4.1

Regression Models The four empirical implications in section 3.7 predict that audit quality of a specific client

increases with the potential client-specific losses, the audit firm’s potential average client-specific losses, the number of clients in the audit firm’s client portfolio, and decreases with the variability of the potential client-specific losses. To test the four empirical implications, we use the absolute value of performance-matched discretionary accruals (AbsoluteDAC) (Kothari et al. (2005)) as the proxy for audit quality. We use the natural logarithm of clients’ total assets (Ln(Asset)) as the proxy for client-specific losses (𝐿𝑖 ). Accordingly, the potential average client losses are proxied by the average value of the natural logarithm of clients’ total assets, i.e. the average client size (AvgClientsize). The variability of the potential client-specific losses is proxied by the standard deviation of client size (StdClientsize). To construct an audit firm’s client portfolio, we define four categories of audit market: (1) the broad U.S. national market, which includes all publicly listed companies; (2) U.S. public companies operating in specific 2-digit Standard Industrial Classification (SIC) industries; (3) companies operating in specific U.S. Metropolitan Statistical Areas (MSAs); and (4) companies operating in specific U.S. MSAs in specific 2 digit SIC industries. The four categories of audit market are denoted as M1, M2, M3, and M4, respectively.

27

We follow Kothari et al. (2005) in constructing performance-matched discretionary accruals by requiring at least 10 observations in each 2-digit SIC industry to calculate discretionary accruals. Specifically, we build the following model to test our four empirical implications: 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒𝐷𝐴𝐶𝑖,𝑡 = 𝛼0 + 𝛼1 𝐿𝑛(𝐴𝑠𝑠𝑒𝑡)𝑖,𝑡 + 𝛼2 𝐴𝑣𝑔𝐶𝑙𝑖𝑒𝑛𝑡𝑠𝑖𝑧𝑒𝑖,𝑡 + 𝛼3 𝐶𝑙𝑖𝑒𝑛𝑡𝑛𝑢𝑚𝑖,𝑡 + 𝛼4 𝑆𝑡𝑑𝐶𝑙𝑖𝑒𝑛𝑡𝑠𝑖𝑧𝑒𝑖,𝑡 + 𝛼5 𝐵𝑖𝑔4𝑖,𝑡 + 𝛼6 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔𝐶𝑦𝑐𝑙𝑒𝑖,𝑡 + 𝛼7 𝑅𝑂𝐴𝑖,𝑡 + 𝛼8 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡 + 𝛼9 𝐿𝑜𝑠𝑠𝑖,𝑡 + 𝛼10 𝐺𝑜𝑖𝑛𝑔_𝐶𝑜𝑛𝑐𝑒𝑟𝑛𝑖,𝑡 + 𝛼11 𝑀𝐵𝑖,𝑡 + 𝛼12 𝑆𝑡𝑑_𝐶𝑓𝑜𝑖,𝑡 + 𝛼13 𝑆𝑡𝑑_𝑆𝑎𝑙𝑒𝑖,𝑡 + 𝛼14 𝐿𝑛(𝐴𝑔𝑒)𝑖,𝑡 + 𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑦 𝑓𝑖𝑥𝑒𝑑 𝑒𝑓𝑓𝑒𝑐𝑡 + 𝑌𝑒𝑎𝑟 𝑓𝑖𝑥𝑒𝑑 𝑒𝑓𝑓𝑒𝑐𝑡 + 𝜀𝑖,𝑡

(1)

where the absolute value of performance matched discretionary accruals capture audit quality. As defined above, Ln(Asset) and AvgClientsize are proxies for client-specific losses and the potential average client losses, and they are key variables of interest for our first (H1) and the second (H2) empirical predictions. Clientnum and StdClientsize are key variables of interest for the third (H3) and the fourth (H4) empirical implications. H1 predicts that the greater the client-specific loss exposure, the higher the assurance level provided by auditors, and accordingly the coefficient (𝛼1 ) on Ln(Asset) is predicated to have a negative sign. H2 and H3 predict that the coefficients (𝛼2 and 𝛼3 ) on AvgClientsize and Clientnum both have a negative sign. H4 predicts that the coefficient (𝛼4 ) on StdClientsize has a positive sign. Among the four key independent variables, client size (Ln(Asset)) is a client-specific variable, and the other three variables are measured using auditors’ client portfolios based on the audit market we defined. Corresponding to the four categories of audit market defined, for each client-year, AvgClientsize, Clientnum, and StdClientsize have four values. We denote the four 28

values with the prefixes M1, M2, M3 and M4, respectively, to represent the four categories of audit market. To empirically test model (1) for the four categories of audit market, we apply the values of AvgClientsize, Clientnum, and StdClientsize calculated based on the four categories in four regressions. We draw from the prior literature to include other control variables (e.g., e.g., Gu, Lee, and Rosett (2005) and Zang (2012)). The controls include a Big 4 indicator (Big4) variable and a battery of other variables that capture the client’s business risk which affects the estimation difficulty of accruals: the natural logarithm of the firm’s operating cycle (OperatingCycle), the ratio of net income and total asset (ROA), the leverage ratio (Leverage), the loss (Loss) indicator variable, going concern opinion (Going_Concern), the market to book ratio (MB), the standard deviation of cash flow across the previous 7 years (Std_Cfo), the standard deviation of the firm’s sales across the previous 7 years (Std_Sale), and the natural logarithm of the firm’s age (Ln(Age)). Complementing the regression model that includes all of the four independent variables, i.e. Ln(Asset), AvgClientsize, Clientnum, and StdClientsize as specified in model (1), we also test the four empirical implications by separately adding AvgClientsize, Clientnum, and StdClientsize to a regression model that includes Ln(Asset) and other control variables drawn from model (1). Ln (Asset) is included in each of the separate regression models because our empirical implication that audit quality is client specific and increases with the size of the potential client specific losses (i.e. H1) is more of an assumption rather than an implication of our analysis.

4.2

Data and Sample To construct our sample for the analysis, we start with the year 2000, the first year for

which Audit Analytics provides an expanded set of audit related information, such as the location

29

of the auditors’ office, audit fee, and going concern opinions, none of which are available in Compustat. Our sample ends in 2014. We constrain our sample to listed companies that are operated and incorporated in the U.S. to ensure that all firms in the sample are subject to the same U.S. legal and institutional environment. We also require that firms have U.S. auditors so that the auditors are from the same labor market and are subject to the U.S. legal environment. We remove firms in the financial industry (SIC codes from 6000 to 6999) because financial firms are regulated and auditors’ loss exposure associated audits of the financial industry can be substantially different from audits of other industries. By requiring firms to have auditor choice, auditor location information, and accounting data necessary to calculate discretionary accruals, be able to be classified in to U.S. Metropolitan Statistical Areas, and have other variables in the regression models, our final sample contains 39,519 firm-years. The sample covers 6291 firms. Firms’ accounting data are obtained from Compustat and are winsorized at 1th percentile and 99th percentile. The absolute value of abnormal discretionary accruals is winsorized at the 99th percentile. Table 1 Panel A reports the summary statistics of the variables used in this paper and Panel B reports the Pearson correlation matrix of these variables. 4.3

Regression Results Tables 2 – 5 report the results of the regressions estimated using the four categories of audit

market. The coefficients on all variables in the four tables are standardized for better comparison. In each table, columns (1) – (5) report estimation results for five regressions. Column (5) of each table reports regression results for model (1), which is specified to test the four empirical implications in one model. Before running the regression as specified in model (1), we start with a simple regression in column (2) that regresses the audit quality measure (AbsoluteDAC) on our

30

first key variable of interest Ln(Asset) and the control variables drawn from model (1), while excluding AvgClientsize, Clientnum, and StdClientsize from the regression. In columns (2) – (4), Ln(Asset)is retained as a control variable, and we regress AbsoluteDAC on AvgClientsize, Clientnum, and StdClientsize, respectively, in each column, while controlling for the battery of control variables drawn from model (1). In Table 2, the audit market is the broad U.S. national market, which includes all publicly listed companies. An audit firm’s client portfolio in this market consists of all of the firm’s clients that are operated and incorporated in the U.S. M1(AvgClientsize), M1(Clientnum), and M1(StdClientsize) are the audit firm’s average client size, number of client, and standard deviation of client size in the U.S. national market. Note that as defined earlier, the prefix M1 refers to the first category of audit market, i.e. national level market. As reported in column (5), the coefficient on Ln(Asset) is significantly negative (coefficient estimate=-0.089, t-statistic=-9.22). This result suggests that as client size increases audit quality increases. The evidence is consistent with the prediction of the first empirical implication. The coefficient on M1(AvgClientsize) is -0.111 (tstatistic=-5.39), suggesting that audit quality increases with the audit firm’s average client size in the national market. Furthermore, the coefficients on M1(Clientnum) and M1(StdClientsize) are consistent with the third and fourth empirical implications in section 3.7, with the coefficient on M1(Clientnum) being -0.043 (t-statistic = -4.29) and the coefficient on M1(StdClientsize) being 0.018 (t-statistic = -1.80). These results suggest that audit quality increases as the number of clients in the audit firm’s client portfolio increases and decreases as the variability of client size increases. The results in columns (1) – (4) are all consistent with results in column (5), and they provide supporting evidence for the four empirical implications.

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In Table 3, an audit market covers U.S. public companies operating in specific 2-digit Standard Industrial Classification (SIC) industries. For each client-year in the five regressions, M2(AvgClientsize) is calculated as the audit firm’s average size of clients operating in the specific client’s 2-digit SIC industry. In a similar vein, M2(Clientnum) is the number of clients in the specific client’s 2-digit SIC industry and M2(StdClientsize) is the standard deviation of client size for the specific industrial client portfolio. Columns (1) to (5) report regression results of the five regressions. The set of regression results estimated using audit client portfolios constructed based on the national industrial market are consistent with results we obtain in Table 2. In Table 4, the audit market is defined as companies operating in specific U.S. Metropolitan Statistical Areas (MSAs). For each client-year, M3(AvgClientsize) is calculated as the audit firm’s average size of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. Accordingly, M2(Clientnum) is the number of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. M3(StdClientsize) is the standard deviation of the size of clients within the specific MSA. In column (5), where the results for the main regression is reported, the coefficients on Ln (Asset), M3(AvgClientsize), and M2(Clientnum) are all significantly negative, and the coefficient on M3(StdClientsize) is significantly positive. These results further support our four empirical predictions. In Table 5, the audit market are companies operating in specific U.S. MSAs in specific 2digit SIC industries. Specifically, for each client-year, M4(AvgClientsize)is calculated with the average size of clients in the specific 2-digit SIC industry in the specific MSA area. M4(Clientnum) and M4(StdClientsize) are also calculated using the auditor’s client portfolio within the specific industry in the MSA the audit firm is located. As reported in column (5), the coefficients on all the key variables of interest are consistent with the predicted sign. The coefficients on Ln(asset),

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M4(AvgClientsize), M4(StdClientsize) are all significant at the 1% level. Even though the coefficient on M4(Clientnum) is not statistically significant (t-statistic=-0.99), the sign of the coefficient does not go against our empirical prediction. Collectively, the regression results estimated using the four levels of market provide empirical evidence for your predictions based on our theory developed in this paper.

5.

Concluding Comments In this paper, we study audit service production when fixed investments (e.g. in audit

technology) that are associated with fixed costs are important. A key feature of such investments and associated fixed costs are that they affect the production of audit services for multiple clients. As a result, choosing an optimal level of investment requires the analysis of production over a client portfolio, rather than on a client-by-client basis as has been done in essentially all existing literature in the economics of auditing since Simunic (1980), Dye (1993), and O’Keefe, Simunic and Stein (1994). Another feature of our analysis is that we assume auditor investments influence the production of audit assurance (which exists in the minds of auditors and financial statement users) through their impact on the efficiency of labor. That is, technology investments do not produce assurance directly, but make the auditor and her staff more efficient in producing assurance. Our paper is in the spirit of Sutton’s (1991) endogenous fixed cost model. However, we build up our analysis from basic elements that reflect our understanding of key features of the production of an audit - a client-specific service that is specifically tailored to suit the characteristics (e.g. size, complexity, and riskiness) of each client.

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While our focus is almost exclusively on supply-side (not demand side) considerations, we believe that this emphasis is appropriate to understand both audit production and the market for audit services. The fact that supply-side variables measuring the size, complexity, and riskiness of client companies are able to explain about 80% of the cross-sectional variation of U.S. listed companies’ audit fees implies that the supply-side is critically important, particularly for listed companies where audits are mandatory. As seen in the empirical implications of our analysis discussed in section 3.7, the assumption that fixed costs are an important feature of audit service production yields a rich mix of interesting insights into the audit service market that are not found in the existing literature. For example, Blokdijk, Drieenhuizen, Simunic and Stein (2006) tried to test whether audit quality was higher for the (then) Big 5 firms compared to non-Big 5 firms by studying total audit hours, and how those hours were utilized (e.g. risk analysis, substantive testing, etc.) for a sample of about 100 Dutch audits. They concluded that any audit quality differences were subtle and associated with the details of how audits were conducted rather than with differences in total audit hours, since total audit hours of the Big 5 firms and non-Big 5 firms were virtually the same, ceteris paribus, in their sample. However, if Big 5 firms have higher fixed investments in the Netherlands than non-Big 5 firms, then they would be expected to utilize fewer audit hours, ceteris paribus. So the fact that the total audit hours of the Big 5 and non-Big 5 were the same is consistent with a higher audit quality by the Big 5. Another example of a different perspective from our analysis relates to the large literature on auditor-industry specialization that originates with Craswell, Francis and Taylor (1995). That literature argues that audit firms that have a high market share in a client industry (e.g. banking, manufacturing, etc.) are necessarily associated with the production and sale of differentially higher quality audit services than auditors with lower market shares. Presumably, the development of industry expertise requires some type

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of fixed investment, so that our analysis applies to that setting. We (indirectly) show that high market share itself is not sufficient to claim that audit quality is higher than average. A high market share that is based on servicing (perhaps) a relatively small number of large clients is likely to have this effect, since large clients motivate higher fixed investments which are associated with higher assurance levels. However, a market share derived from servicing a large number of small clients, is much less likely to have this effect. Moreover, even the audit firm that services large clients and has large fixed investments will provide an assurance level that is positively correlated with client size. That is, the assurance provided to small clients of a high market share auditor is not expected to be high; the effect is client-specific. In conclusion, modeling audit production to incorporate both fixed and variable resources and costs yields a different perspective on the market for audit services than exists in the current auditing literature. We believe that further research to develop and extend this perspective is likely to be both interesting and highly productive of new insights.

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TABLE 1 Panel A Summary Statistics AbsoluteDAC Ln(Asset) M1(AvgClientsize) M2(AvgClientsize) M3(AvgClientsize) M4(AvgClientsize) M1(Clientnum) M2(Clientnum) M3(Clientnum) M4(Clientnum) M1(StdClientsize) M2(StdClientsize) M3(StdClientsize) M4(StdClientsize) Big4 LogCycle ROA Leverage Loss Going_Concern MB Std_Cfo Std_Sale Ln(Age)

N 39519 39519 39519 39519 39519 39519 39519 39519 39519 39519 38422 33961 37252 20493 39519 39519 39519 39519 39519 39519 39519 39519 39519 39519

Mean 0.15 5.48 5.43 5.42 5.43 5.44 454.09 32.22 21.01 3.61 1.87 1.64 1.71 1.47 0.71 4.59 -0.21 0.19 0.40 0.08 2.77 0.14 0.55 2.77

STD 0.28 2.44 1.78 1.96 1.94 2.23 292.40 37.25 21.62 5.21 0.33 0.53 0.54 0.82 0.45 0.83 1.21 0.25 0.49 0.27 7.49 0.30 1.14 0.71

P25 0.03 3.81 4.84 4.54 4.45 4.08 159.00 4.00 6.00 1.00 1.86 1.37 1.41 0.92 0.00 4.13 -0.10 0.00 0.00 0.00 1.10 0.04 0.13 2.20

Median 0.07 5.53 5.87 5.62 5.74 5.55 503.00 16.00 13.00 2.00 1.91 1.67 1.73 1.44 1.00 4.62 0.02 0.11 0.00 0.00 1.51 0.07 0.25 2.71

P75 0.15 7.21 6.71 6.79 6.85 7.02 686.00 50.00 30.00 4.00 2.00 1.91 2.02 1.92 1.00 5.08 0.07 0.29 1.00 0.00 2.41 0.13 0.52 3.30

This table presents summary statistics for the main variables used in the empirical analysis. See Appendix B for variable definitions.

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Panel B Correlation Table (1)AbsoluteDAC (2)Ln(Asset) (3)M1(AvgClientsize) (4)M2(AvgClientsize) (5)M3(AvgClientsize) (6)M4(AvgClientsize) (7)M1(Clientnum) (8)M2(Clientnum) (9)M3(Clientnum) (10)M4(Clientnum) (11)M1(StdClientsize) (12)M2(StdClientsize) (13)M3(StdClientsize) (14)M4(StdClientsize) (15)Big4 (16)LogCycle (17)ROA (18)Leverage (19)Loss (20)Going_Concern (21)MB (22)Std_Cfo (23)Std_Sale (24)Ln(Age)

(1) 1.00 -0.37 (0.00) -0.34 (0.00) -0.37 (0.00) -0.34 (0.00) -0.37 (0.00) -0.22 (0.00) -0.07 (0.00) -0.07 (0.00) -0.01 (0.01) -0.00 (0.42) 0.05 (0.00) 0.04 (0.00) 0.04 (0.00) -0.24 (0.00) 0.01 (0.21) -0.45 (0.00) 0.05 (0.00) 0.23 (0.00) 0.37 (0.00) 0.36 (0.00) 0.40 (0.00) 0.13 (0.00) -0.15 (0.00)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

1.00 0.69 (0.00) 0.79 (0.00) 0.76 (0.00) 0.91 (0.00) 0.47 (0.00) 0.15 (0.00) 0.16 (0.00) 0.06 (0.00) 0.16 (0.00) 0.07 (0.00) 0.06 (0.00) 0.06 (0.00) 0.58 (0.00) -0.09 (0.00) 0.37 (0.00) 0.16 (0.00) -0.41 (0.00) -0.41 (0.00) -0.31 (0.00) -0.40 (0.00) -0.21 (0.00) 0.35 (0.00)

1.00 0.86 (0.00) 0.91 (0.00) 0.76 (0.00) 0.67 (0.00) 0.34 (0.00) 0.28 (0.00) 0.16 (0.00) 0.18 (0.00) 0.13 (0.00) 0.03 (0.00) 0.03 (0.00) 0.82 (0.00) -0.07 (0.00) 0.32 (0.00) 0.04 (0.00) -0.27 (0.00) -0.40 (0.00) -0.28 (0.00) -0.37 (0.00) -0.20 (0.00) 0.17 (0.00)

1.00 0.85 (0.00) 0.87 (0.00) 0.59 (0.00) 0.17 (0.00) 0.19 (0.00) 0.05 (0.00) 0.19 (0.00) 0.05 (0.00) 0.06 (0.00) -0.04 (0.00) 0.72 (0.00) -0.13 (0.00) 0.38 (0.00) 0.12 (0.00) -0.32 (0.00) -0.41 (0.00) -0.33 (0.00) -0.40 (0.00) -0.21 (0.00) 0.25 (0.00)

1.00 0.83 (0.00) 0.61 (0.00) 0.25 (0.00) 0.19 (0.00) 0.07 (0.00) 0.17 (0.00) 0.09 (0.00) 0.04 (0.00) 0.02 (0.01) 0.75 (0.00) -0.09 (0.00) 0.32 (0.00) 0.10 (0.00) -0.32 (0.00) -0.39 (0.00) -0.28 (0.00) -0.37 (0.00) -0.20 (0.00) 0.24 (0.00)

1.00 0.51 (0.00) 0.15 (0.00) 0.16 (0.00) 0.05 (0.00) 0.17 (0.00) 0.05 (0.00) 0.05 (0.00) 0.04 (0.00) 0.63 (0.00) -0.12 (0.00) 0.36 (0.00) 0.16 (0.00) -0.37 (0.00) -0.40 (0.00) -0.31 (0.00) -0.40 (0.00) -0.21 (0.00) 0.31 (0.00)

1.00 0.54 (0.00) 0.50 (0.00) 0.30 (0.00) 0.39 (0.00) 0.22 (0.00) 0.19 (0.00) 0.10 (0.00) 0.87 (0.00) -0.05 (0.00) 0.18 (0.00) 0.03 (0.00) -0.15 (0.00) -0.25 (0.00) -0.15 (0.00) -0.22 (0.00) -0.11 (0.00) 0.00 (0.51)

1.00 0.42 (0.00) 0.55 (0.00) 0.21 (0.00) 0.23 (0.00) 0.11 (0.00) 0.11 (0.00) 0.46 (0.00) 0.01 (0.13) 0.05 (0.00) -0.08 (0.00) 0.05 (0.00) -0.12 (0.00) -0.05 (0.00) -0.06 (0.00) -0.01 (0.01) -0.12 (0.00)

1.00 0.69 (0.00) 0.20 (0.00) 0.13 (0.00) 0.17 (0.00) 0.14 (0.00) 0.39 (0.00) 0.02 (0.00) 0.05 (0.00) -0.05 (0.00) 0.04 (0.00) -0.11 (0.00) -0.05 (0.00) -0.06 (0.00) -0.01 (0.01) -0.12 (0.00)

1.00 0.11 (0.00) 0.12 (0.00) 0.04 (0.00) 0.12 (0.00) 0.23 (0.00) 0.01 (0.02) 0.01 (0.12) -0.06 (0.00) 0.10 (0.00) -0.06 (0.00) -0.01 (0.03) 0.00 (0.59) 0.00 (0.55) -0.16 (0.00)

1.00 0.33 (0.00) 0.55 (0.00) 0.21 (0.00) 0.42 (0.00) -0.03 (0.00) -0.05 (0.00) 0.06 (0.00) -0.04 (0.00) -0.02 (0.00) 0.07 (0.00) -0.03 (0.00) -0.01 (0.01) -0.02 (0.00)

1.00 0.22 (0.00) 0.49 (0.00) 0.25 (0.00) 0.04 (0.00) -0.06 (0.00) 0.01 (0.03) 0.05 (0.00) 0.02 (0.00) 0.07 (0.00) 0.04 (0.00) -0.02 (0.00) -0.02 (0.00)

1.00 0.37 (0.00) 0.19 (0.00) -0.02 (0.00) -0.07 (0.00) 0.05 (0.00) 0.01 (0.02) 0.04 (0.00) 0.08 (0.00) 0.02 (0.00) 0.02 (0.00) -0.00 (0.82)

1.00 0.10 (0.00) 0.04 (0.00) -0.06 (0.00) -0.02 (0.00) 0.01 (0.07) 0.03 (0.00) 0.07 (0.00) 0.04 (0.00) 0.02 (0.01) 0.03 (0.00)

1.00 -0.07 (0.00) 0.19 (0.00) 0.07 (0.00) -0.20 (0.00) -0.28 (0.00) -0.16 (0.00) -0.26 (0.00) -0.14 (0.00) 0.06 (0.00)

1.00 -0.03 (0.00) -0.11 (0.00) 0.06 (0.00) 0.03 (0.00) 0.00 (0.39) 0.00 (0.61) -0.09 (0.00) 0.08 (0.00)

1.00 -0.10 (0.00) -0.29 (0.00) -0.43 (0.00) -0.71 (0.00) -0.42 (0.00) -0.10 (0.00) 0.13 (0.00)

1.00 0.05 (0.00) 0.07 (0.00) 0.08 (0.00) 0.02 (0.00) -0.04 (0.00) 0.04 (0.00)

1.00 0.32 (0.00) 0.13 (0.00) 0.24 (0.00) 0.12 (0.00) -0.28 (0.00)

1.00 0.30 (0.00) 0.35 (0.00) 0.13 (0.00) -0.13 (0.00)

1.00 0.37 (0.00) 0.08 (0.00) -0.09 (0.00)

1.00 0.34 (0.00) -0.17 (0.00)

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1.00 -0.21 (0.00)

1.00

This paper presents the Pearson correlation matrix for the main variables used in the empirical analysis. See Appendix B for variable definitions

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TABLE 2 Client Portfolio Characteristics in the National Market and Audit Quality M1_H1 M1_H2 M1_H3 M1_H4 M1_All (1) (2) (3) (4) (5) -0.113*** -0.093*** -0.110*** -0.107*** -0.089*** Ln(Asset) [-11.38] [-9.79] [-11.04] [-11.00] [-9.22] -0.122*** -0.111*** M1(AvgClientsize) [-5.92] [-5.39] -0.050*** -0.043*** M1(Clientnum) [-4.97] [-4.29] 0.032*** 0.018* M1(StdClientsize) [3.23] [1.80] -0.045*** 0.043*** -0.005 -0.061*** 0.062*** Big4 [-7.28] [2.66] [-0.50] [-8.19] [3.45] -0.033*** -0.034*** -0.034*** -0.028*** -0.029*** LogCycle [-3.61] [-3.70] [-3.66] [-3.09] [-3.21] -0.232*** -0.228*** -0.232*** -0.243*** -0.242*** ROA [-8.35] [-8.25] [-8.35] [-8.60] [-8.57] 0.031*** 0.028*** 0.030*** 0.033*** 0.030*** Leverage [3.53] [3.28] [3.41] [3.80] [3.50] 0.005 0.007 0.006 0.003 0.005 Loss [0.86] [1.15] [1.06] [0.49] [0.85] 0.127*** 0.118*** 0.126*** 0.120*** 0.112*** Going_Concern [11.49] [10.82] [11.38] [10.97] [10.30] 0.042* 0.035 0.042* 0.047* 0.042 MB [1.66] [1.40] [1.66] [1.82] [1.63] 0.175*** 0.168*** 0.175*** 0.177*** 0.171*** Std_Cfo [10.31] [9.93] [10.31] [10.67] [10.34] -0.009 -0.010 -0.009 -0.006 -0.008 Std_Sale [-0.86] [-0.95] [-0.90] [-0.65] [-0.76] -0.015** -0.017*** -0.016*** -0.012** -0.015** Ln(Age) [-2.42] [-2.73] [-2.61] [-2.07] [-2.51] N 39519 39519 39519 38422 38422 adj. R-sq 0.3080 0.3104 0.3084 0.3191 0.3214 This table reports regression results for the audit quality model. An audit market is defined as the national audit market, covering all U.S. public companies. Ln(Asset)is the natural logarithm of a client’s total assets. M1(AvgClientsize)is an audit firm’s average client size in the national market. M1(Clientnum)is an audit firm’s number of clients in the national market. M1(StdClientsize)is an audit firm’s standard deviation of client size in the national market. Other variables are defined in Appendix B. Year and industry (SIC two digit) fixed effects are included. t-statistics (in parentheses) are computed using heteroskedasticity-consistent standard errors that are corrected for clustering at the industry level. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively, using twotailed tests.

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TABLE 3 Client Portfolio Characteristics in the National Industrial Market and Audit Quality M2_H1 M2_H2 M2_H3 M2_H4 M2_All (1) (2) (3) (4) (5) -0.113*** -0.081*** -0.112*** -0.093*** -0.078*** Ln(Asset) [-11.38] [-8.78] [-11.30] [-9.10] [-7.63] -0.108*** -0.080*** M2(AvgClientsize) [-5.50] [-3.42] -0.045*** -0.028** M2(Clientnum) [-4.75] [-2.50] 0.019** 0.015* M2(StdClientsize) [2.20] [1.74] Big4 -0.045*** 0.009 -0.025*** -0.052*** 0.004 [-7.28] [0.76] [-3.68] [-6.92] [0.27] -0.033*** -0.034*** -0.034*** -0.031*** -0.032*** LogCycle [-3.61] [-3.69] [-3.63] [-3.04] [-3.11] -0.232*** -0.227*** -0.231*** -0.268*** -0.266*** ROA [-8.35] [-8.16] [-8.37] [-8.05] [-8.01] 0.031*** 0.029*** 0.029*** 0.031*** 0.030*** Leverage [3.53] [3.35] [3.34] [3.33] [3.17] 0.005 0.007 0.007 0.008 0.010 Loss [0.86] [1.22] [1.21] [1.09] [1.36] 0.127*** 0.120*** 0.126*** 0.091*** 0.088*** Going_Concern [11.49] [11.07] [11.41] [7.42] [7.21] 0.042* 0.034 0.042* 0.038 0.034 MB [1.66] [1.35] [1.66] [1.24] [1.10] 0.175*** 0.170*** 0.175*** 0.155*** 0.152*** Std_Cfo [10.31] [9.97] [10.33] [7.79] [7.65] -0.009 -0.010 -0.008 0.010 0.009 Std_Sale [-0.86] [-0.99] [-0.78] [0.89] [0.86] -0.015** -0.016*** -0.017*** -0.013** -0.014** Ln(Age) [-2.42] [-2.66] [-2.74] [-2.02] [-2.19] N 39519 39519 39519 33961 33961 adj. R-sq 0.3080 0.3098 0.3086 0.2751 0.2763 This table reports regression results for the audit quality model. An audit market is defined as the national industrial audit market, covering U.S. public companies operating in specific 2-digit Standard Industrial Classification (SIC) industries. Ln(Asset)is the natural logarithm of a client’s total assets. M2(AvgClientsize)is an audit firm’s average size of clients operating in the specific client’s 2-digit SIC industry. M2(Clientnum)is an audit firm’s number of clients operating in the specific client’s 2-digit SIC industry. M2(StdClientsize)is an audit firm’s standard deviation of the size of clients operating in the specific client’s 2-digit SIC industry. Other variables are defined in Appendix B. Year and industry (SIC two digit) fixed effects are included. t-statistics (in parentheses) are computed using heteroskedasticity-consistent standard errors that are corrected for clustering at the industry level. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively, using two-tailed tests.

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TABLE 4 Client Portfolio Characteristics in the MSA Market and Audit Quality M3_H1 M3_H2 M3_H3 M3_H4 M3_All (1) (2) (3) (4) (5) -0.113*** -0.094*** -0.112*** -0.106*** -0.088*** Ln(Asset) [-11.38] [-9.45] [-11.31] [-10.73] [-8.81] -0.060*** -0.058*** M3(AvgClientsize) [-4.51] [-4.52] -0.007 -0.013*** M3(Clientnum) [-1.64] [-2.89] 0.019*** 0.017*** M3(StdClientsize) [3.12] [2.87] -0.045*** -0.012 -0.043*** -0.053*** -0.015 Big4 [-7.28] [-1.29] [-6.73] [-8.37] [-1.54] -0.033*** -0.033*** -0.033*** -0.030*** -0.030*** LogCycle [-3.61] [-3.61] [-3.61] [-3.22] [-3.22] -0.232*** -0.231*** -0.232*** -0.245*** -0.245*** ROA [-8.35] [-8.34] [-8.35] [-8.56] [-8.57] 0.031*** 0.031*** 0.030*** 0.033*** 0.034*** Leverage [3.53] [3.61] [3.48] [3.79] [3.81] 0.005 0.005 0.006 0.003 0.004 Loss [0.86] [0.79] [0.97] [0.51] [0.62] 0.127*** 0.124*** 0.127*** 0.120*** 0.117*** Going_Concern [11.49] [11.27] [11.47] [10.80] [10.56] 0.042* 0.039 0.042* 0.050* 0.047* MB [1.66] [1.54] [1.67] [1.89] [1.80] 0.175*** 0.172*** 0.175*** 0.172*** 0.170*** Std_Cfo [10.31] [10.15] [10.32] [10.23] [10.09] -0.009 -0.009 -0.009 -0.006 -0.006 Std_Sale [-0.86] [-0.88] [-0.85] [-0.56] [-0.59] -0.015** -0.014** -0.015** -0.014** -0.014** LN(Age) [-2.42] [-2.29] [-2.52] [-2.41] [-2.41] 39519 39519 39519 37252 37252 N 0.3080 0.3088 0.3080 0.3184 0.3193 adj. R-sq This table reports regression results for the audit quality model. An audit market is defined as companies operating in the U.S. Metropolitan Statistical Area where the audit office is located. Ln(Asset)is the natural logarithm of a client’s total assets. M3(AvgClientsize)is an audit firm’s average size of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. M3(Clientnum)is an audit firm’s number of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. M3(StdClientsize)is an audit firm’s standard deviation of the size of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. Other variables are defined in Appendix B. Year and industry (SIC two digit) fixed effects are included. t-statistics (in parentheses) are computed using heteroskedasticity-consistent standard errors that are corrected for clustering at the industry level. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively, using twotailed tests.

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TABLE 5 Client Portfolio Characteristics in the MSA Industrial Market and Audit Quality M4_H1 M4_H2 M4_H3 M4_H4 M4_All (1) (2) (3) (4) (5) -0.113*** -0.076*** -0.113*** -0.090*** -0.064*** Ln(Asset) [-11.38] [-5.80] [-11.36] [-6.89] [-4.39] -0.052*** -0.055*** M4(AvgClientsize) [-3.74] [-3.33] -0.006 -0.008 M4(Clientnum) [-1.12] [-0.99] 0.017** 0.019** M4(StdClientsize) [2.32] [2.49] Big4 -0.045*** -0.035*** -0.044*** -0.059*** -0.038*** [-7.28] [-5.17] [-7.01] [-6.33] [-3.76] -0.033*** -0.034*** -0.034*** -0.029** -0.030** LogCycle [-3.61] [-3.70] [-3.62] [-2.33] [-2.41] -0.232*** -0.231*** -0.232*** -0.287*** -0.287*** ROA [-8.35] [-8.34] [-8.35] [-7.65] [-7.66] 0.031*** 0.031*** 0.030*** 0.034*** 0.035*** Leverage [3.53] [3.56] [3.49] [2.66] [2.71] 0.005 0.005 0.005 0.004 0.004 Loss [0.86] [0.91] [0.95] [0.46] [0.49] 0.127*** 0.126*** 0.127*** 0.099*** 0.098*** Going_Concern [11.49] [11.43] [11.48] [6.45] [6.41] 0.042* 0.040 0.042* 0.039 0.037 MB [1.66] [1.59] [1.66] [1.02] [0.96] 0.175*** 0.174*** 0.175*** 0.133*** 0.132*** Std_Cfo [10.31] [10.24] [10.32] [5.75] [5.69] -0.009 -0.009 -0.009 0.008 0.008 Std_Sale [-0.86] [-0.88] [-0.85] [0.59] [0.59] LN(Age) -0.015** -0.015** -0.015** -0.021*** -0.021*** [-2.42] [-2.41] [-2.53] [-2.60] [-2.66] N 39519 39519 39519 20493 20493 adj. R-sq 0.3080 0.3083 0.3080 0.2798 0.2805 This table reports regression results for the audit quality model. An audit market is defined as companies operating in a specific 2-digit SIC industry in a specific MSA area. Ln(Asset)is the natural logarithm of a client’s total assets. M4(AvgClientsize)is an audit firm’s average size of clients in a specific 2-digit SIC industry in a specific MSA area. M4(Clientnum)is an audit firm’s number of clients in a specific 2-digit SIC industry in a specific MSA area. M4(StdClientsize)is an audit firm’s standard deviation of the size of clients in a specific 2-digit SIC industry in a specific MSA area. Other variables are defined in Appendix B. Year and industry (SIC two digit) fixed effects are included. t-statistics (in parentheses) are computed using heteroskedasticity-consistent standard errors that are corrected for clustering at the industry level. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively, using two-tailed tests.

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End Notes: 1.

The auditor transformation function maps auditor effort (hours) and technology (a) into assurance (q). A simple assurance function is: q = a • √h

=>

h = ( q / a )2

Assurance increases in both the technology parameter and effort. One problem with this functional specification is that q is unbounded from above. A lower bound of zero is a consequence of non-negativity constraints on a and h, however, an upper bound must be imposed as a constraint. In our simulations it is not uncommon for q*, the optimal q, to take on the value of the upper bound for multiple observations.

An alternative specification of the assurance transformation function is: q = 1 - b Exp[ - a • h] =>

h = Ln[(1-q) / b ] / a

While this looks ungainly, it also has the property that assurance increases in both effort and technology. Further, assurance has a natural upper bound of one as effort goes to infinity. One problem with this functional form is that if we impose the natural non-negativity constraints on effort and technology the lower bound goes to 1 - b, which is most likely negative.

We think of b as an environmental parameter that effects how quickly assurance approaches the upper bound. In our simulations, setting the value of b allows some control over the variability of the assurance levels. For a given set of client-specific losses, higher values of b result in greater variation in q*. We note that for any fixed b1 ≥ 0 and a1 ≥ 0, there exists some h1 ≥ 0 such that q(a1, b1, h1) = 0. h1 could be interpreted as a set-up cost, in terms of effort, associated with the technology and an

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environmental parameter. In our simulations, negative levels of assurance do not appear to be an issue when this functional form is used.

2.

We argue that audit markets are characterized by client-specific levels of assurance. Audit firm technology investments make some firms more efficient in delivering high levels of assurance than others. In our model the level of assurance is not determined by client preferences, but by client characteristics as encapsulated in the potential loss associated with the client. While the optimal level of assurance for a given client could vary from audit firm to audit firm (based on technology differences), every audit firm would choose a higher level of assurance for a client with a high potential loss compared to a client with a low potential loss. As a consequence, the quantity of service provided is the product of the client’s potential loss and the audit firm’s level of assurance. Price is then measured in terms of units of service and revenues can be represented as: Ri(p, Li, qi,) = p•Li•qi . Equilibrium is enforced by profitability and free entry constraints. In operational terms, the balance between these two forces is determined by the cost of delivering the optimal level of assurance. Since amortized fixed costs depend upon the size of the market (i.e., number of clients) and the number of firms providing services the equilibrium depends upon these market parameters as well as firm technology and client characteristics.

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FIGURE 1

45

FIGURE 2

46

ALTERNATIVE FIGURES A

47

48

FIGURE 3

49

FIGURE 4

ALTERNATIVE FIGURE B

50

FIGURE 5

FIGURE 6

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Table A-1

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TABLE 2

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APPENDIX B VARIABLES Key variable AbsoluteDCA Independent variables Ln(Asset)

M1(AvgClientsize) M1(Clientnum) M1(StdClientsize) M2(AvgClientsize)

M2(Clientnum)

DEFINITIONS The performance-matched discretionary accruals measured following Kothari, Leone, and Wasley (2005). The natural logarithm of a client’s total assets (AT). An audit firm’s average client size in the national market. An audit firm’s number of clients in the national market. An audit firm’s standard deviation of client size in the national market. An audit firm’s average size of clients operating in the specific client’s 2-digit SIC industry. An audit firm’s number of clients operating in the specific client’s 2-digit SIC industry.

LogCycle

An audit firm’s standard deviation of the size of clients operating in the specific client’s 2digit SIC industry. An audit firm’s average size of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. An audit firm’s number of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. An audit firm’s standard deviation of the size of clients operating in the U.S. Metropolitan Statistical Area where the audit office is located. An audit firm’s average size of clients in a specific 2-digit SIC industry in a specific MSA area. An audit firm’s number of clients in a specific 2-digit SIC industry in a specific MSA area. An audit firm’s standard deviation of the size of clients in a specific 2-digit SIC industry in a specific MSA area. An indicator set to 1 when a firm uses one of the Big 4 auditors (PricewaterhouseCoopers, Ernst & Young, Deloitte & Touche, or KPMG) and 0 otherwise. Source: Audit Analytics The natural logarithm of firms’ operating cycle.

ROA

Net income (NI) over total assets (AT).

Lag_Assetgrw

Asset growth in the past year, where assets denotes total assets (AT).

Leverage

The ratio of year-end total liabilities (DLTT) to total assets (AT).

Loss

An indicator variable that is set to 1 when income before extraordinary items (IB) is less than zero and 0 otherwise. An indicator variable that is set to 1 if the auditor opinion for the fiscal year includes a going concern qualification and 0 otherwise. The ratio of the market value of total assets to the book value of total assets (AT+CSHO*PRCC_F-CEQ- TXDB)/AT). Firm-specific standard deviation of the cash flow from operations deflated by average total assets from years t-5 to t-1 (cash flow = 2*OANCF/ (AT+LAG(AT)). We require at least three years of data available for standard variation calculation. Firm-specific standard deviation of the sales deflated by average total assets from years t-5 to t-1 (sales = 2*SALE/ (AT+LAG(AT)). We require at least three years of data available for standard variation calculation. The natural logarithm of firm-specific age. Age is calculated as the difference between the current year and the first year the firm appears in Compustat.

M2(StdClientsize) M3(AvgClientsize) M3(Clientnum) M3(StdClientsize) M4(AvgClientsize) M4(Clientnum) M4(StdClientsize) Big4

Going_Concern MB Std_Cfo

Std_Sale

Ln(Age)

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