A Positive Theory of Accounting-Based Management by Exception

A Positive Theory of Accounting-Based
Management by Exception
By
Mark Penno

The University of Iowa
Tippie College of Business
W324 Pappajohn Business Building
Iowa City, IA 52242-1000
USA
mark-penno@uiowa.edu
May 2017

This paper has benefitted from comments made by Peter Demerjian, Brad Hepfer, Doug DeJong,
Mehmet Ozbilgin, Doug Stevens and an accounting seminar held at the University of Iowa.

Electronic copy available at: https://ssrn.com/abstract=2978180

A Positive Theory of Accounting-Based
Management by Exception
ABSTRACT

Management by exception (MBE) is widely used to allocate scarce managerial expertise on the
basis of exception reports. I model MBE as a rule that triggers a management intervention if-andonly if accounting thresholds are not met. While the resulting MBE rule economizes on valuable
expertise, its mechanical structure creates a mismatch between the rule and the underlying
phenomena (i.e., under- and overinclusion). I show that relevant accounting measures are
optimally excluded from the exception report as a way to compensate for these mismatches, even
when they are costless (violating an informativeness maxim). Furthermore, individual thresholds
may not be uniquely determined, clouding the issue of threshold tightness. The model is used to
evaluate a number of accounting practices, including management control systems (tightness of
standards, moral hazard), auditing independence (waived adjustments), and debt contracting
(using covenants as tripwires).
Key Words: Positive theory; Management by exception; Informativeness; Auditor independence;
Debt covenants; Moral hazard.

Electronic copy available at: https://ssrn.com/abstract=2978180

1. Introduction

Management by exception (MBE) is used by firms, auditors and private lenders, among others, to
simplify the utilization of complex accounting information. In particular, multidimensional
accounting data must be grouped and diagnosed before problems can be addressed, and a major

purpose of MBE is to efficiently allocate the valuable time spent by the experts who make these
evaluations. In his seminal book, Bittel (1964) describes MBE this way (p. 5):

Management by exception, in its simplest form, is a system of identification and
communication that signals the manager when attention is required; conversely it remains
silent when his attention is not required. The primary purpose of such a system is of course,
to simplify the management process itself – to permit a manager to find the problems that
need his action …
Accordingly, I model MBE as a two-step process beginning with an exception report that triggers
a managerial intervention if and only if its underlying accounting thresholds are not met. While an
exception report provides a way to economize on the expertise spent addressing the state of
controls, its mechanical structure may result in a mismatch between the if-and-only-if rule
governing the report and the underlying phenomena. This mismatch means either that i) an
exception report triggers interventions for a state that does not need correction (overinclusion), or
ii) that an out-of-control state is ignored (underinclusion). Mismatches have long been of concern
to scholars such as Ehrlich and Posner (1974), Simons (1989), Diver (1989), and Sunstein (1995),
who discuss the under- and overinclusions of rules. To counter the effects of these mismatches, I
demonstrate that certain accounting measures must be optimally excluded from the exception
report even when they are informative and costless, and in spite of being given strict consideration
when (and if) an intervention is subsequently triggered.

At a specific level, this study provides a perspective on a number of accounting practices. For
example, there has been an ongoing debate in managerial accounting over the setting of cost and
revenue standards (e.g., Bedford et al., 2016; Simons, 1988). The results here may indicate why
that debate remains unresolved. In particular, the result that informative and costless measures may

1

not be assigned cost or revenue standards runs contrary to an informativeness maxim holding that
otherwise costless and informative measures should be recognized in a formal report.1 Nontrivial
under- and overinclusion helps to explain a literature that has focused on the alleged dysfunctional
consequences of budgets.2 And the result that standards may not be uniquely determined in
multidimensional settings with performance evaluation may help to further explain the mixed
results from field studies.

A second instance is the practice of using materiality thresholds to identify proposed adjusted
journal entries (PAJEs) by external auditors. Because the process is initiated (finalized) by less
(more) experienced staff, it may also be regarded as an instance of MBE. For example, Hicks
(1964, p. 168) comments:

Materiality at the execution level merits more detailed consideration; here, knowing when
to deal with immaterial items is important. Although these decisions are often initially
made by staff assistants, they may have significant audit consequences and must be
carefully reviewed.
PAJEs are waived at least one-half of the time, and this practice has generated a concern that
auditors are rubber-stamping their client’s wishes, indicating a loss of auditor independence.3 The
results here demonstrate, instead, that a cost-efficient auditor will generate more MBE-type
overinclusions, which end up being waived. Noting that incumbent auditors tend to have lower

costs, these results are also consistent with empirical findings indicating that proposed audit
adjustments are more likely to be waived for clients with whom the audit firm has had a longer
relationship (see Section 5). Relatedly, the AICPA (1983, AU 312.02) defines “audit risk” as “the
risk that the auditor may unknowingly fail to appropriately modify his opinion on financial
statements that are materially misstated.” This study makes notion of ‘unknowingly’ more precise.
Simply put, those professionals who are assigned to make final evaluations will not be aware of

1 Decision theory maintains that costless information should not be ignored if it changes beliefs. The term,
informative, is frequently associated in the accounting literature with Holmström (1979), who uses it to label a
maxim for principal-agent settings.
2 See Hansen and Van der Stede (2004) for a discussion of this focus.

3 See Messier et al. (2005) for a review, and Coffee (2001) for a discussion of PAJEs and auditor independence.

2

an overall material misstatement if the MBE system does not properly alert them to it
(underinclusion).

To the extent that the technical defaults triggered by bond covenant violations are threshold-based
exceptions, and an expert’s valuable time (in this case, a bank executive) is consumed by default
management, conventional debt contracting represents yet another instance of MBE.4 Technical
defaults provide a flow of information to the lender, helping to keep it informed about the status
of the loan. Consequently, technical defaults in themselves do not necessarily signify that financial
distress is on the horizon (see section 5). That said, covenant tightness has not received extensive
attention in the analytical literature,5 and an explanation for why banks waive technical default has
not been fully fleshed out.6 Consistent with empirical findings, this study suggests why waivers of
technical defaults in private lending are common, and why the frequency of waivers may increase
with the strength of the lending relationship.
Beyond the specific applications noted above, the study contributes to a conceptual ‘unpacking’
of control systems. For example, Evans and Tucker (2015, p. 347) suggest that:

failing to view control as a package as comprising both formal and informal elements
makes it difficult to identify how findings may be integrated and assimilated; how they
refute, complement or extend existing theory …
If one were to describe an exception report as a formal component, and management evaluations
as a more informal (i.e., a judgement-based assessment) component of a larger management
control system, then the finding that relevant measures are sometimes (but not always) excluded
from the former but referenced during latter, suggests how accounting measures themselves can
transition between different roles.7

4 In addition to the three applications discussed here, the use of red flags by analysts, regulators and investors
constitutes further uses of MBE-style data filters. Furthermore, Hicks (1964) cautions the reader to remember that
MBE “is not solely an accounting consideration, as some of the literature on the subject would seem to suggest.”
Accordingly, conclusions from this study may be applied to certain non-accounting settings as well.
5 See Gârleanu and Zwiebel (2009).
6 See HassabElnaby (2006).
7 See Chenhall (2003) for a comprehensive review of field studies that distinguish between the formal and informal
aspects of management control systems while taking context into consideration (contingency-based research).

3

Finally, and most importantly, this study introduces the idea of how if-and-only-if rules serve as
the fundamental building blocks for a range of accounting applications, and explains the
implications of doing so. This is at odds with the view which casts rules as choice-constraining
factors, similar to the conventional income and price constraints found in economics (Vanberg,
1994, p. 15). Under that perspective, it would be irrational to use rules if they restricted one’s
choices. In fact, Baiman and Demski (1980a) have proven that a literal application of this view
implies, contrary to common practice, that there is no economic demand for variance
computations.8 Nonetheless, MBE is remains recognizable as a set of rule-like thresholds; and its
widespread use confirms, contrary to what is generally assumed by standard normative theory, that
managerial expertise is not freely available, but rather is a valuable resource to be conserved and
allocated.9 Accordingly, this study is positive in nature because it is concerned with the description
and explanation of readily identifiable accounting-based practices.

Section 2 reviews related analytical literature, Section 3 models an MBE rule and Section 4
provides results. Sections 5 and 6 apply and extend the model to the specific accounting practices
described above, and Section 7 concludes.

2. Related Analytical Literature

An early approach to accounting-based MBE applies industrial statistical quality control

techniques to actual standard cost accounting settings, featuring algorithms which compute
numerical limits signaling whether a process is in “in control” or “out of control,” in order to
determine when corrections are necessary.10 Kaplan (1975) reviews this literature, but cautions (p.

8 See next section for a discussion.
9 A Google Scholar search (3/1/17) for the joint use of “management by exception,” “simplify” and “accounting,”
yielded almost 2,000 results.
10 Attention is directed in these studies to the complexity of proposed algorithms aimed resolving control issues in
real-world settings. For example, Dittman and Prakash (1978. p. 25) offer an algorithm for the “practicing
accountant” for which the “critical limit is simple to calculate, and the resulting policy yields much of the benefits of
the policies based upon more sophisticated cost control models.”

4

312) that in practice, managers rarely use the sophisticated mathematical procedures in specified
by these algorithms, and instead use their judgment to determine MBE thresholds, by citing
Anthony’s (1973) review article, who notes that “few if any managers believe that statistical
techniques … are worth the effort to calculate [cost standards].” Kaplan (p. 312) further suggests
that exception report be simple in the following manner:

There are reasons to believe, however, that some form of screening model would be
beneficial to managers by eliminating the need for them to examine extensive variance
reports item by item in order to detect a significant variance.
The model presented here captures Kaplan’s stated view by representing an exception report as a
binary indicator that simply flags whether or not an intervention is called for.

Holmstöm (1979) demonstrates that as long as information is costless, any marginally informative
measure will benefit a principal when contracting with a risk-averse and self-interested agent.
Similarly, a fundamental implication of decision theory (for cases where moral hazard is absent)
is that marginally informative data will improve decisions, as well. Holmstöm (p. 86) warns,
however, that:
If, for administrative reasons, one has restricted attention a priori to a limited class of
contracts (e.g., linear price functions or instruction-like step-functions), then
informativeness may not be sufficient for improvements within this class.

Similarly, this study examines the effect of the administrative restrictions placed on the use of
accounting information by MBE filters, and confirms that a measure’s relevance11 may not be
sufficient for improvements – even when that information is costless.
Baiman and Demski (1980a) refine Holmstöm’s normative model to implicitly demonstrate
(Proposition 1.1) that there will be no economic demand for the computations that give rise to

11 The FASB (2008, COB2-2) defines relevant accounting information as “capable of making a difference in a
decision.”

5

variances.12 Baiman and Demski (1980a, 1980b) go on to define variance investigation more
narrowly by modeling a setting where a principal designs a contract for a self-interested agent
based on a costless primary performance measure plus a costly second measure produced
conditionally upon the realization of the first measure. The ‘investigation’ studied by these authors
differs from the ‘intervention’ examined here in that the purpose of an investigation is not to correct
any out-of-control states, but rather the threat of a conditional investigation is used to improve on
ex ante managerial incentives. An important finding for this type of model is that realizations of

the primary measure found in the tails of the distribution may not always trigger an investigation,
and that the results are sensitive to the agent’s utility function and the probability distribution
assumed by the model.13 Consequently the explanatory power of this approach is limited to the
extent that, unlike MBE practice, the model does not necessarily single out exceptional
observations for investigation.

Similar to this study, Garicano (2000) models an organizational hierarchy that specifies a handful
of knowledgeable individuals at its top and less knowledgeable members at its bottom. For this
setting, he shows that it is optimal for the knowledge of solutions to the most common or easiest
problems to be located on the production floor, whereas the knowledge about how to solve more
exceptional or harder problems is located in higher layers of the hierarchy. This result requires an
information system that is capable of distinguishing exceptional from common problems, thereby
establishing a rationale for a management by exception policy. The study here is similar to
Garicano’s in that I assume the need for experts, but differs by identifying a readily recognizable
report structure specifically designed to minimize the expected sum of intervention costs and the
costs of not correcting out-of-control states.14

12 Suppose that q , q  reflects a computation based on accounting measures q and q . Then Baiman and
1
2
1
2

Demski note that any contract of the form s q1 , q 2 , q1 , q 2  can be replaced by an equivalent contract s q1 , q 2 
without the need for  , where s q1 , q 2   s q1 , q 2 , q1 , q 2  . The reasoning may be then extended to any

decision d q1 , q 2 , q1 , q 2 .
13 For example, Lambert (1985) shows that in general, neither the extremeness nor the unusualness of the cash
flows provides a measure of the benefits of conducting an investigation. Also see Young (1986) for an analysis of
two tailed requirements.
14Similar to Sections 3-5 presented here, Garicano does not consider moral hazard.

6

3. Basic Model
The accounting system produces two measures, q1 and q 2 , where q1 , q 2  is the realization of a
random variable that is uniformly distributed over the unit square. The exception report is based
on these measures, but indicates only whether or not a managerial intervention will be called for
(i.e., its report is binary). The exception report calls for an intervention by an expert evaluator if-

and-only-if q1  t1 or q2  t 2 , where t1 and t 2 are the thresholds underlying the exception report.

The expert’s specialized knowledge is summarized by , k  , which along with q1 , q 2  is used by
the expert to determine whether the state is in control. The state is in control when q1  q 2  k,
and out of control when q1  q 2  k . Assume that 0  k  1 and 0    1. 15

Without an intervention, the firm has a net payoff, q1  q 2  k . If we view q1  q 2  k  0 as
the ‘damage’ caused by being out of control, then I assume that an intervention allows the

organization to mitigate that damage by ex post resetting any net loss to zero. Let c  0 represent
the cost of the evaluator’s time spent in assessing, and resetting if necessary, the state of control.

Then given an intervention, the organization’s payoff is q1  q 2  k  c if the state is in control,

and  c if the state is out of control and then corrected. The following summarizes the net payoff
to the organization for each possible event:

Event

Net payoff

The expert intervenes and q1  q 2  k

q1  q2  k  c

The expert intervenes and q1  q 2  k

The expert does not intervene

c

q1  q 2  k

Note that the model assumes that an intervention provides an incremental benefit (eliminating a
loss) only when the state is sufficiently unfavorable, thereby assigning a trouble-shooter’s role to
15 Assuming that

k  1 limits the number of required the geometric representations (e.g., Figure 1 below).

7

the evaluator. This assumption is reflected in descriptions of MBE practice. For example, Kohler
(1975, p. 301), in A Dictionary for Accountants: Fifth Edition, asserts that
these [exception] reports bring out “favorable” and “unfavorable” variances, the latter
being the basis for “management by exception.”
Similarly Brownell (1983, p. 456) observes that MBE practice reduces to “a preoccupation with
unfavorable variances,” and more recently, Arnold and Artz (2015, p. 66), also conclude that
academic field studies tend to focus on unfavorable variances as well.

Figure 1 summarizes an MBE rule.

--Place Figure 1 about here-The diagonal line maps the q1 , q 2  pairs such that q1  q 2  k, and defines the boundary between
being in control and being out of control. This boundary captures the pattern of classifications that

an expert with knowledge of k and  would make based on available evidence, q1 and q 2 . If,

instead, the organization had a costless algorithm which could analyze q1 , q 2  based on k and  ,

that generates understandable instructions for lower level personnel or machines, then there would
be no economic demand for MBE. Consequently, a sufficient condition for a strict demand for
MBE is that an automated self-correcting process not exist, or that management must be personally
involved to identify and reset out-of-control processes (as required by MBE).

Outcomes above the diagonal represent in-control states which will not benefit from correction,
diagonal’s slope expresses the interaction between q1 and q 2 . Note that because q1 , q 2  is
while those below the diagonal represent outcomes that will benefit from correction. The

uniformly distributed on the unit square, the area corresponding to a particular event also
those outcomes that will not be evaluated, with an ex ante probability (area) ANE = 1  t1 1  t 2 ,

represents the probability of that event. The dotted areas (both light and dark together) represent
and where AE 1  ANE , represents the ex ante probability that an intervention will occur. The ex

ante probability of not evaluating and correcting an out-of-control state corresponds to the triangle

8

 k  t2

1
 t1  . The expected of value of
with dark dotted fill, with an area, ANC   k  t1   t 2 
2
 


q1 , q 2  conditioned on an out-of-control state not being evaluated and corrected is the centroid of

the dark dotted triangle, or

q

NC
1

, q2NC





k  t2 

  2t1 

  2t 2  k  t1  


,
,



3
3





Which, in turn, implies that the expected loss of not correcting a state that is out of control is:
1
E NC  k  q1NC  q 2NC  k   2k  t1  t 2  .
3

Bittel (1964, p. 13) goes on to note that
[MBE’s] big advantage lies in the fact that much of the time-consuming process of thinking
and decision making can be done in advance.
Accordingly, I assume that the MBE rule is designed by an expert (again a member of
management) who understands AE , ANC and E NC as described above and chooses t1 and t 2 to
minimize the overall expected loss associated with investigations and underinclusions, which is
the expected sum of intervention costs and the costs of not correcting out-of-control states
expressed as :16
AE c  ANC E NC ,

(1)

16 Minimizing (1) is equivalent to maximizing expected profit.

9

where the minimization of (1) approximates the exercise of an expert’s intuition.17
4. Results
As a useful benchmark, Figure 2 depicts a rule where t1  0. When t1  0, threshold t 2 alone
dictates whether an intervention will be called for by the exception report, which is equivalent to
saying that t1 has been omitted from the exception report.

--Place Figure 2 about here-Proposition 1a (Case 1) below indicates that as long as   k  1 , then the optimal t1  0 ,
regardless of c . In particular, as long as the importance of q1 is sufficiently low (as reflected by

a small  ) or the ex ante likelihood that the state is an in-control state is sufficiently high (as
reflected by a small k ), then a threshold for q1 will not be specified in the exception report, and
q1 is not needed. This proves that whether a relevant measure is included in the exception report

is not dictated by the cost of the intervention alone, but is also due to the under- and overinclusion
effects of the MBE rule itself. While omitted from the exception report, q1 continues to be relied
upon by the evaluator (as long as   0 ) for making control classifications whenever an
intervention is called for (q2  t 2 ).

Proposition 1a:
Case 1: If   k  1 , then the optimal t1  0 and

17 While humans sometimes underperform as intuitive statisticians, they do quite well in other settings (Hogarth,
2001, Chapter 4) . I assume that the thresholds chosen by the experts approximate the minimizing ones identified by
(1).

10


k2
k
c
if
c
2




2

t2  

2
0 if c  k

2

(2)

Optimal t 2 thresholds for Case 1 are illustrated by Figure 3:

--Place Figure 3 about here-MBE ceases to provide a net benefit to the organization when t 2  0, or c exceeds

k2
and
2

interventions do not occur because they are too expensive.18
Next, consider the Case 2 where   k  1, and Figure 1 applies:
Proposition 1b:
Case 2: If   k  1, then the optimal









2
 1  2

k    1
2

 2  2   2k  c  2    2 2c 2  c  2k  2    if c 
2
 4
t1  

2
0 if c  k    1

2

(3)

and the optimal

 extend this range, and they do so because the misfit between the MBE rule based
on q 2 alone and the in/out of control boundary becomes smaller as well.

18 Note that smaller values of

11





1
k    12
c
k
if
c







2
2
2

2
4
2
2

k    1  c  k
t 2  k  2c if
2
2

2

k
0 if c 
2


(4)

where   4c  c 2  4ck  4c
Optimal thresholds for Case 2 are illustrated by Figure 4:

--Place Figure 4 about here--

Figure 4 shows how the cost of a managerial intervention affects whether an accounting measure
will be included in the exception report. Because, by assumption,   1; measure q1 is dropped

first ( t1  0) as c increases, eventually followed by dropping q 2 ( t 2  0). Again, if both thresholds
equal zero, then MBE ceases to provide a net benefit.
Corollary 1: When   0, then the optimal t1 , t 2  is located strictly below the diagonal
q1  q 2  k .

Mismatches are ex post inefficient, and Corollary 1 suggests a reason for why field studies find a
threshold pair t1 , t 2  is located strictly below the diagonal, MBE produce both under- and

variety of seemingly dysfunctional results. An examination of Figure 1 reveals that when the
overinclusion. In contrast, when   0, q1 is out of the picture, effectively creating a

unidimensional setting. If this occurs, t 2  k and there is no under- or over inclusion.

Consequently multidimensionality (  0) leads to ambiguity (the rule is sometimes inconsistent
with the underlying phenomena), and one might, in turn, allege a causal connection between
complexity and dysfunctionality.

12

Next note that Figure 4 depicts thresholds that are declining in c. More generally,

Corollary 2 (Slack): The optimal thresholds, t1 and t 2 are decreasing in c.

Declining thresholds reflect an increase in overall (budgetary) slack, and Corollary 2 provides the
intuitive result that slack increases as the cost of managerial intervention increases.
1 depicts a scenario where an exception is waived whenever q1 , q 2  lies within one of the polygons

A waiver occurs when the expert determines that an exception is actually an overinclusion. Figure

with checkered fill. Note from Corollary 2 that both optimal thresholds are decreasing in c.
Imagine decreasing t1 and/or t 2 while holding k constant. Then, by inspection of Figure 1, it is
clear that the area devoted to waivers decreases as t1 and/or t 2 decrease (and c increases).

Corollary 3 (Waivers): The probability of a waiver increases as c decreases.

Given the informational constraints imposed by the MBE filter, the organization insures itself
against uncorrected out of control states by increasing the probability of waivers, which in turn,
decreases the probability of a missed out of control state (underinclusion).

Corollaries 2 and 3 together summarize the role of c in determining how the MBE rule functions.
To the extent that a lower value of c indicates more efficient interventions, a lower value of c
represents a higher level of managerial expertise. This observation is useful in discussing
applications of the model to specific accounting settings in Section 5.

5. Applications and Extensions

Materiality

13

Because external auditors use materiality thresholds to identify proposed adjusted journal entries
(PAJEs), excessive waivers of PAJEs may create the impression that the auditor’s independence
has been impaired. For example, Coffee (2001, p. 23) suggests that:

auditors often are aware that earnings management is being attempted, but nonetheless
waive any audit adjustment on a variety of grounds, including the practice’s asserted
immateriality…
Alternatively, Braverman et al. (1997) suggest the auditor’s impairment may be an unconscious
one, by proposing a less-than-noticeable differences explanation, where auditors’ judgment is
gradually captured by their clients’ wishes.
It turns out that waivers of PAJEs are quite common. Houghton and Fogarty (1991) and Wright
and Wright (1997) separately find that auditors waive 65 to 75 percent of all audit detected
misstatements, whereas Icerman and Hillison (1991) find that auditors waive approximately onehalf of detected errors. To reconsider the issue of PAJEs, suppose that t1 and t 2 represent
individual materiality thresholds. To remain consistent with the model, suppose that the

cumulative misstatement is decreasing in q1  q 2 , and k represents the allowable cumulative

misstatement such that q1  q 2  k is not materially misstated. This relation would hold, for
example, if understatements of total expense were the investors’ concern. A decreasing relation

might also be expected where q1  q 2 represents an auditor’s assessment of company-wide

internal control, which the auditor issues in a separate report.19
Consider a modification of (1), and restate the auditor’s objective as

AE c  ANCE NC ,

(5)

19 U.S. Sarbanes Oxley (SOX) Act of 2002 requires both management (Section 302) and external auditors (Section
404) to perform top-down assessments of an organization’s ability to identify and prevent fraud and to safeguard
assets. SOX has been followed by similar laws in Australia, Canada, France, Germany, Israel, Italy, India, Japan,
and South Africa. See Weiss (2014, p. 463).

14

where the first component represents the expected direct cost of a review, and parameter  now
scales the expected loss borne when the auditor unknowingly fails to modify its opinion given an
underlying misstatement.20 Define c  by
c 

c
.


The expression, AE c  ANC E NC , has the same minimum as (5), and has the same form as (1), with

the exception that c  replaces c . Consequently, we may apply the results previously derived for
(1). In particular, increasing  has the same general effect as decreasing c. Consequently,
increasing  increases the probability of a waiver (Corollary 3).

If the regulator’s concern were to stem from the frequency of waivers in the first place, then

increasing the auditor’s general liability for ignoring material errors,  , could backfire – if the

regulator responds to concerns about auditor independence by increasing  , then the imposition
of regulation increases the probability of a waiver even more, potentially prompting a repeated
regulatory action. If, on the other hand, the frequency of waivers, itself, were used by the regulator
to target penalties, then the optimal MBE policy will be compromised if auditors adjust (i.e., relax)
their thresholds in order to reduce the frequency of waivers (overinclusions) and with the goal of
classifying fewer items as PAJEs. (See Figure 1). This would then increase audit risk (the dark
dotted area) – which was the regulator’s ultimate concern to begin with. In summary, by giving in
to political and other pressures by treating outward symptoms with coarse responses, the regulator
could actually worsen audit quality.

Corollary 3 also implies that an incumbent auditor will generate more waivers than a new auditor
who is at the beginning of its learning curve, and for whom the cost of an intervention will be
higher.21 Joe et al. (2011) confirm this conjecture by finding that PAJEs are more likely to be

20 AICPA (1983, AU 312.02).
21 The assumption that incumbents have lower costs than new auditors can be traced back (at least) to DeAngelo
(1981).

15

waived for clients with whom the audit firm has had a longer relationship, but conclude that the
pattern does not reflect favoring such clients. Similarly, the model provides an explanation against
the charge that auditors intentionally give in to clients from whom they extract quasi-rents.22

Debt Covenants

Debt covenants frequently contain thresholds that trigger technical defaults.23 Dichev and Skinner
(2002) argue that private lenders set debt covenants tightly and use them as “trip wires” for
borrowers. While empirical work has begun to examine the corresponding tightness of accountingbased thresholds,24 the rationale for how and why these trip wires are set is not well understood.
Furthermore, technical defaults are frequently waived. For example, Beneish and Press (1995, p.
346) indicate that 51% of their default firms reported waivers. To that end, the model here provides
a simple rule-based explanation of why a lender would go through the trouble of designing
accounting-based thresholds, only to waive technical defaults.25
To apply the model, let q1  q 2 represent the expected cash flow available to pay off the debt, k,

and k  q1  q 2   0 the expected loss incurred conditioned on an cash shortfall.26 Suppose that
upon technical default, the lender waives technical defaults for otherwise profitable loans, and
restructures unprofitable loans to restore the expected cash flow back to k. If we assume that the
net cost of investigating/resolving a technical default is c, then the MBE model applies.

22 See Magee and Tseng (1990). Levitt (1998) suggests that “auditors who want to retain their clients are under
pressure not to stand in the way.”
23 The thresholds discussed here are affirmative covenants which require borrowers to maintain specified levels of
accounting-based ratios. Smith (1993) notes that extant evidence suggests that borrowers more frequently violate
affirmative covenants. The breach of negative covenants (which limit certain investment and financing activities) is
rare.
24 See for example, Demiroglu and James, (2010), or Demerjian and Owens (2016). Demerjian and Owens note that
while many studies refer financial covenant “slack,” “tightness,” or “strictness,” they prefer the term “probability of
violation.”
25It is notable that the common usage of the term, technical, suggests a faulty assessment, and referring to a default
as ‘technical’ serves to downplay the event. For example, Merriam Webster (online) describes ‘technicality’ as “a
small detail in a rule, law, etc., and especially one that forces an unwanted or unexpected result.” (Emphasis added.)
See http://www.merriam-webster.com/dictionary/technicality
26 Demerjian (2011) finds that the use of balance sheet covenants (such as net worth) has decreased over time (from
more than 80% in 1996 to 32% in 2007), while inclusion of income statement covenants (such as interest coverage)
has remained constant (between 74% and 82%) during the same period.

16

Corollary 3 indicates that the probability of a waiver is highest when c is low. To the extent that
relationship banking lowers the cost of intervention, we might expect waivers to be common in
private debt. In that regard, Gopalakrishnan and Parkash’s (1995) survey indicates private contains
more restrictive debt covenants than public debt. If lenders learn more about borrowers over time,
we might also expect waivers to increase with the length of the borrower-lender relationship as c
declines. This is consistent with HassabElnaby (2006) who finds that strong bank-firm business
ties are more likely to be associated with a higher level of waivers.

6. Moral Hazard (Management Control Systems)

Hopwood (1972, p. 158) suggests that because organizations require their accounting reports to
address multiple issues, they may end up failing to address any specific issue very well:
accounting systems are also trying to serve many purposes. … However, in trying to satisfy
a series of purposes, the reports may fail to perfectly satisfy the requirements for any single
purpose – the appraisal of managerial performance, for instance.
To examine the question of performance, and in particular, the role of incentives, this section
extends the model to include moral hazard. The extension indicates that an exception report with
moral hazard may look quite different than one without moral hazard. In particular, the mixed
findings from field studies are consistent with the result that thresholds may no longer be uniquely
determined when moral hazard is present.27
As before, the exception report is based on q1  0,1 and q 2  0,1 where q1 , q 2  is uniformly
distributed over the unit square. The extension assumes that a risk-neutral agent’s effort directly
contributes to control, but that it is not directly measured. Let a  0, aˆ represent a risk-neutral

27 Collectively, textbooks and practice produce mixed guidance for the appraisal of managerial performance. On the
one hand, Merchant and Manzoni (1989) note that the prescription made in most management accounting textbooks
is that, for optimum motivation, budget targets should be achievable less than 50 percent of the time. On the other
hand, Merchant and Manzoni conclude that no comprehensive field evidence exists about the actual levels of budget
target achievability at profit center levels within corporations

17

agent’s effort choice, for which the agent suffers disutility a , where aˆ  0 and   0. The state
is now considered to be in control if q1  q2  a  k and out-of-control if q1  q 2  a  k . In this

extension, the evaluator observes the state of control (the sum), q1  q 2  a , which along with
q1 , q 2 and knowledge of  , permits the evaluator to infer a. If the evaluator infers that a  aˆ

(work), then the agent receives the bonus, B . If the evaluator infers that a  0 (shirk), then the
agent receives no bonus. If an intervention is not performed (there is no evidence to indicate that
the agent did not work), I assume that the agent receives bonus, B. Consequently, the
compensation arrangement ensures that an agent who works obtains the bonus.

The agent considers the consequences of working and shirking before deciding what to do. An

agent who works has utility B  aˆ , while an agent who shirks receives no bonus with probability
1  1  t1 1  t 2  ,

(9)

and will have an expected utility of 1  t1 1  t 2 B . Assume that the agent has an opportunity
utility of zero. Then the agent will work for this organization if B  aˆ  1  t1 1  t 2 B , or:
B

aˆ
.
t1  t 2  t1t 2

(10)

If the organization were to prefer that a  0 , then there is no need to incentivize B  0 , and the
model and results from Section 3 apply. Accordingly, I assume that the organization wishes the
agent to work and provides the incentive to do so. This implies that if the organization wishes to
minimize expects costs, then (10) is an equality.28 Then the right-hand side of (10) decreases in
either t1 or t 2 , which means that tighter thresholds require lower bonuses, but more costly
intervention. Because the organization wishes to motivate effort, one would expect tighter
thresholds than were indicated in the previous sections.
28 If B 
can reduce

aˆ

t1  t 2  t1t 2

, then the organization is not minimizing expected costs. Because t1  t 2  t1t 2  1, we

B while maintaining (10) while guaranteeing at least a zero opportunity utility.

18

Given that incentives are in place for the agent to choose aˆ, the following represents the net payoff
to the organization of each possible event:

Event

The expert intervenes and q1  q 2  aˆ  k
The expert intervenes and q1  q 2  aˆ  k
The expert does not intervene

Net payoff

q1  q2  aˆ  k  B  c
 Bc

q1  q 2  aˆ  k  B

See Figure 5.

--Place Figure 5 about here-Because kˆ  k  aˆ effectively determines the q1 , q 2  demarcated boundary between in-control

ˆ and Eˆ equal the analogs of A and E given that kˆ  k  aˆ
and out-of-control,29 let A
NC
NC
NC
NC
replaces k in the respective expressions. Then the organization’s expected cost equals

1  1  t1 1  t 2 c  Aˆ NC Eˆ NC 

1  1  t1 1  t 2 c 

aˆ
, if t1  t 2  kˆ , or
t1  t 2  t1t 2

aˆ
, if t1  t 2  kˆ .
t1  t 2  t1t 2

(11a)
(11b)

Both (11a) and (11b) imply that the agent works and is (always) paid B , but (11b) also indicates
that when t1  t 2  a  k (see Figure 5), there are no cases where an out-of-control state is ignored

ˆ Eˆ ,
(underinclusions) , and the expected cost associated with ignoring out-of-control cases, A
NC NC
drops out of the analysis.
29 That is, q  q  aˆ   k implies q  q   k  aˆ .
1
2
1
2

19

Figure 5 differs from Figure 1 in that t1 , t 2  is now located above the boundary for in-control and
out-of-control, rather than below the boundary (as previously established by Corollary 1). This will
occur when moral hazard becomes a sufficiently prominent factor. This guarantees that all out-ofcontrol states will be corrected as a consequence of the organization’s incentive-related vigilance.30
That is, addressing one problem may automatically solve the other. Also note that once an optimal
threshold pair is located above the diagonal, numerous threshold combinations will be optimal as
case, the optimal t1 , t 2  is not unique, and Proposition 2 indicates when this happens:

long as the threshold pairs provide the same probability (and expected cost) of intervention. In that

Proposition 2 (Moral Hazard): Suppose that the organization prefers that the agent work.31 If
aˆ
 kˆ , then there exist optimal t1 , t 2  thresholds such that t1  t 2  kˆ . In particular, these
c

thresholds obey

ti 

4
2
3
aˆc 1  t j   ct j  2ct j  ct j



c 1 t j



3

for t j  t i ,

(12)

and the optimal probability of intervention,
1  1  t1 1  t 2 

(13)

is unique and decreasing in c.

30 Lazear (1989) describes a related phenomenon when he notes that folklore has it that tuna fishermen sometimes
throw a shark into the holding tank with live tuna to keep them active (and fresh) until the ship reaches the cannery.
31 If aˆ is too large, then it becomes uneconomical to incentivize the agent to work. The worked-out examples
below have been checked (see Appendix) to verify that work is preferred by the organization.

20

Example 1 illustrates a case where

aˆ
 kˆ . In particular, it demonstrates that when   0, q1
c

may be optimally included in the exception report, even though it is irrelevant to assessing the
state of controls.
Example 1: Suppose that   0 , c  .3 ,   .2 , k  1 , aˆ  .5 and kˆ  .5 . Then both

t1 , t 2   0, . 58 and t1 , t 2   .1, . 53 are optimal, the probability of intervention is .58 , the bonus

payment equals .17 , and the expected intervention cost equals .17.
worked, done with probability p , where p  1  1  t1 1  t 2   .58. This policy of random

It may at first appear that MBE could be simply replaced by random check whether the agent

checking would maintain the incentive to work without changing the bonus, but using MBE to link
the interventions to accounting outcomes also guarantees that the state is always corrected when
necessary. This benefit would be lost by pure randomization. Thus, the control issue is still
indirectly addressed by employing MBE with even a seemingly irrelevant threshold, and we see
that the addition of moral hazard has dramatically changed the way that we describe the operation
of MBE.
Example 2 continues Example 1 by reducing the agent’s disutility,  from .2 to .15, so that
aˆ
 .5  kˆ . In this case there is for only one solution to be optimal.
c

Example 2: Suppose that   0 , c  .3 ,   .15 , k  1 , aˆ  .5 and kˆ  .5 . Then the unique
optimal t1 , t 2   0, . 5 , the probability of intervention is .5, the bonus payment equals .15, and the
expected intervention cost equals .15.
Simons (1991) identifies a “diagnostic” style where senior managers intervene only when formal
measures deviate from the expected targets, but he also identifies an “interactive” style which is

21

characterized by frequent personal attention from top management levels.32 A diagnostic style
might apply to the settings examined in the previous sections, while an interactive style may be
motivated by concern for moral hazard.

7. Conclusions

Management by exception (MBE) is widely used to allocate scarce managerial expertise on the
basis of exception reports. The model provides a novel and coherent view of MBE by reducing it
to a small, yet salient, set of factors which explore the fundamental rule-like nature of an exception
report.33 In particular, the study demonstrates how alleged dysfunctions of accounting practice
might be simply explained as under- or overinclusions. While these mismatches may be ex post
inefficient , they are optimal, ex ante. The model provides insight into a number of specific
accounting-based applications which, in turn, constitute a subset of a larger set of accounting
practices.34 As Holmström (1979) has indicated, administrative realities may entail a violation of
an informativeness maxim. Because MBE filters information, it constrains how that information
is used. In some cases, relevant measures may be excluded from exception reports; and in other
cases, irrelevant measures may be included in the exception report.

As a final note, Gjesdal (1981) makes the distinction between accounting information as used for
investment decisions and accounting information as used for stewardship. This study suggests even
finer distinctions. When restricted to stewardship itself, the use to which accounting information
is put depends on whether its main purpose is to control moral hazard or to address the expected
cost of managerial interventions, and addressing one problem may automatically resolve the other.

32 See Shen and Perera (2012) for a review of the accounting literature on the diagnostic and interactive uses of
budgets.
33 Contrast this to Fisher (1995, p. 24) who notes that “one of the major weaknesses of contingent control research
[a dominant method for organizing field studies] is the piecemeal way in which it is done.”
34 A Google Scholar search (5/19/17) for the joint use of “accounting,” ”investigate,” “threshold,” “financial
statement,” and “red flag,” yielded almost 500 results.

22

Appendix

Lemma 0: The optimal t1 , t 2  is located weakly below the diagonal, or t1  t 2  k.

Proof: If instead, the optimal t1 , t 2  were located above the diagonal, the organization could
general an expected cost savings (intervention) by reducing t1 , t 2  so that t1  t 2  k .
Proof of Proposition 1:
Proof : Objective function (1) equals

� −� � − � − �� � + �� −� − � � −�+� − �� − �+� + �−� � +�
6�

.

(A1)

(A1) is convex in t1 for a given t 2 whenever t1  t 2  k , and (A1) is convex in t 2 for a given t1

whenever t1  t 2  k , with strict convexity following from strict inequalities. Assume that the

organization picks one threshold first and then the other one second. Lemma 0 ensures that t1 , t 2 
is a minimum. Corollary 1 (below) shows that for   0, k  t1  t 2 holds for the optimal t1 , t 2 
pair, which means that the optimal t1 , t 2  will be unique.

I will represent the optimal thresholds by their first-order conditions. The first-order condition of
(A1) with respect to t1 is:

� =

��−�� −√ √�� −�� �
�

.

(A2)

Insert (A2) back into (A1) to find that the first-order condition of (A1) with respect to t 2 is:
� =

2 − � + 2� − 2� − √4� + � − 4�� + 4�� .

(A3)

Insert (A3) back into (A2) to get
t1 

� +� − +�+ �+√�

+�− �+ � − √ √��
�

+�− �+ �+√�

+�− �+ �

It can be verified that (A4) is declining in c , and equals zero whenever c 
negative whenever c 
2

k    1
c

k    12 , or we have a corner solution ( t
2

1

2

.

k    12
2

(A4)

and is

 0) whenever

(A5)

23

In this case ( t1  0) , condition (A1) reduces to
� − � − �� � + �� −�
6�

.

(A6)

And the first order condition with respect to t 2 equals
t 2  k  2c ,

(A7)

which is less than one, declining in c , and equals zero (corner solution) when c 
t1  0 , when

2

k    1
c

2

k2
. Note that
2

 0 , or when k    1. This proves both Case 1 and Case 2.

Proof of Corollary 1: Lemma 0 shows that t1  t 2  k (a weak inequality). For Case 1, t1  0,
which
=−

√��

means

that

+�− �+ �+√�

t1  t 2  k  2c  k ,

+�− �+ �

and

for

Case

2,

t1  t 2  k

< 0 , which again implies that t1  t 2  k , completing the

proof that optimal t1 , t 2  is located strictly below the diagonal.
�

Proof of Corollary 2: By inspection, t 2 is strictly decreasing in c for both Case 1 and Case 2 of

Proposition 1 for c 



k2
. It can be verified that the expression for t1 in Case 2:
2







1  2
2   2k  c  2    2 2c 2 2  c  2k  2   
2 

4 
is