Accounting Research Center, Booth School of Business, University of Chicago
Information Rents and Preferences among Information Systems in a Model of Resource
Allocation
Author(s): Rick Antle and John Fellingham
Reviewed work(s):
Source: Journal of Accounting Research, Vol. 33, Studies on Managerial Accounting (1995), pp.
41-58
Published by: Blackwell Publishing on behalf of Accounting Research Center, Booth School of Business,
University of Chicago
Stable URL: http://www.jstor.org/stable/2491373 .
Accessed: 12/06/2012 09:39
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .
http://www.jstor.org/page/info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact support@jstor.org.
Blackwell Publishing and Accounting Research Center, Booth School of Business, University of Chicago are
collaborating with JSTOR to digitize, preserve and extend access to Journal of Accounting Research.
http://www.jstor.org
Journal of Accounting
Research
Vol. 33 Supplement
1995
Printed in US.A.
Information Rents
and Preferences among
Information Systems in a Model
of Resource Allocation
RICK
ANTLE*
AND
JOHN
FELLINGHAMt
1. Introduction
Using a model in which private information and self-interested behavior induce a socially inefficient allocation of resources, we analyze
the effects of introducing a public information system. A manager of
productive resources has an informational advantage over the owner of
the resources, as in Antle and Eppen [1985]. In this setting, mutually
beneficial production is foregone as the owner attempts to limit the
manager's information rent. We consider the possibility of introducing
a public information system that reduces the manager's information advantage. In particular, we describe conditions under which the social
efficiency of production is enhanced or reduced by the introduction of a
public information system.
In three scenarios, public information is exogenously given, chosen
by the owner and influenced by the manager, and stochastically determined by the manager's actions. We find that regardless of who chooses
* Yale University; tThe Ohio State University. We thank Michael Alles, Anil Arya, Stan
Baiman, Peter Bogetoft, Joel Demski, Harry Evans, Mitch Farlee, Jonathan Feinstein, Jon
Glover, Michael Maher, Nandu Nagarajan, John Persons, Suresh Radhakrishnan,
Doug
Schroeder, Richard Sansing, Andy Stark, Shyam Sunder, Bin Srinidhi, Rick Young; and
Rutworkshop participants at Iowa, Ohio State, Maryland, Stanford, Carnegie-Mellon,
Association
gers, North Carolina, and Yale universities; the 1994 American Accounting
Convention; and two anonymous referees for useful comments.
41
Copyright
?, Institute
of Professional
Accounting,
1996
42
JOURNAL
OF ACCOUNTING
RESEARCH, SUPPLEMENT
1995
a costless, public information system, productive efficiency is attained.
However, the manager's preferred public information system differs in
substantive and describable ways from the owner's choice. By restricting
the analysis to a particular density function for the private information,
we can entirely describe each person's optimal information system.
The existence of contrary preferences over public information systems
raises another set of questions. Will the owner and manager engage in
activities designed to skew the public information system and production schedule toward their private self-interests? Furthermore, will these
activities disrupt the social efficiency results?
We consider the possibility of activities which affect the public information system choice and its use. For example, in one scenario we allow
the owner to commit to ignore information. In another scenario, we allow the manager to coarsify the partitions in the public information system. With these tools at their disposal, we give conditions under which
the actors will attempt to affect the public information system choice for
personal benefit and under which these attempts destroy the efficiency
properties of the resulting allocation of resources. In addition, we characterize conditions under which the actors will engage in more vigorous
influence activities. The greater the profit margins, the greater the incentives for actions which affect the public information system.
While our results are derived using a general characterization of a public information system of varying fineness, some insight can be obtained
about particular accounting systems. For example, an argument in favor
of activity-based costing (ABC) systems is that they supply finer cost information.1 If that is an important attribute of ABC systems, our results
shed some light on when and why it is difficult, from an organization
structure perspective, to design, install, and maintain an ABC system in an
organizations Furthermore, even if a perfectly good system is in place, it
may be economically rational for some users to commit to ignore some of
the output of even a well-functioning
information system.
Section 2 presents the model and section 3 provides the solution to a
benchmark case. Section 4 examines the efficiency consequences
of introducing public information. Section 5 introduces and analyzes two
important special cases. Section 6 contains analyses of two models of
activities that affect the public information
are
system. Conclusions
offered in section 7. Appendix A contains proofs.
1 It is probably more accurate to say that ABC systems are more detailed than traditional
costing systems. As is pointed out in Datar and Gupta [1994], more detail does not guarantee more accuracy or finer information.
2 The textbook literature recognizes
the difficulties involved in changing organizations'
discuss individual
information systems. For example, Atkinson et al. [1995, pp. 592-600]
and organizational
defensive responses, the investment of money and time required to
balance of power as sources of
make changes, and potential shifts in the organization's
difficulties encountered
when installing information systems. We contribute to this literaof
ture by providing explicit assumptions and solutions, as well as a formal exploration
efficiency effects.
INFORMATION
SYSTEMS IN RESOURCE ALLOCATION
43
time
Contract
signed
Manager
reports cost
Manager
learns cost, c
FIG.
Owner
supplies
resources,
x produced
y
time line: no public information.
1.-First
2. The Model
model with linear
The model is an extension of the owner-manager
production technology in Antle and Eppen [1985]. In that model3 the
owner of a production function has the property rights to the cash it
produces. The owner hires a manager whose comparative advantage is
required to implement production.
Production requires cash in addition to the manager's presence. If a
cash flow of x is to be produced, cash of cx is required, where c < 1 is the
cost per dollar of cash flow. Only the manager can put the cash into
production. At the time he does so, he knows the cost, c. The owner
does not. The owner believes c E C, some set of possible costs. Sometimes we take C = {cl, . . . ,cq}, with cl < c2 < . . . < cn < 1. The probability
c= ciis pi. At other times, we take C = [0, 1], with probabilities given by
the densityf
All cash must come from the owner.4 Let y denote the amount of cash
transferred from the owner to the manager. The manager consumes cash
above what he puts into production. Therefore, the manager's utility for
cash transferred, y, production requirement, x, with cost per dollar c is
U(y, x; c) = y - cx. The time line in figure 1 shows the sequencing of
events depicted thus far.
It can be shown that a participative budget scheme is the optimal form
x
}?=, such
of contracting. The owner designs a menu of contracts, {xi,
that the manager selects (xi, yi) when he knows the per dollar cost is ci.5
The owner's objective in choosing among alternative budgets is to maxf7
imize expected
profits:6
E
Pi [xi- Yi.
i= 1
There are five types of constraints on the owner's choice of schemes.
First, the manager must receive an expected utility at least as high as his
next-best alternative. The contract is entered into before the manager
3We use the Antle and Eppen [1985] model, with a finite set of per dollar costs, for
some of our analysis, but we also use a model with per dollar costs from an interval of the
real line. Therefore, we present footnotes that extend the Antle and Eppen model to the
case. Also see Farlee, Fellingham, and Young [1995].
continuous
4 This rules out the manager implementing
on his own and capturing all
production
the rents.
5 In the continuous
version of the model, the owner designs a pair of functions, x(.)
and y(.), that map per dollar cost reports into required output and resources provided,
1
respectively.
- y(c))f(c)dc.
case, the objective function is: f(x(c)
6In the continuous
0
44
RICK ANTLE AND JOHN FELLINGHAM
learns the cost and we assume his beliefs are the same as the owner's.
Let 0 be the manager's opportunity cost in utility terms. Then the contract must satisfy:7
n
E
pi [yi - ci xi]
2
0. To ensure a distributional
issue,
i= 1
we assume throughout that 0 = 0. Second, the contract must respect the
manager's lack of cash,8 so that yj - cixi 2 0, i = 1, . . . n. Third, the
contract must induce a manager who knows the cost is ci to select
(xi, yi):9 y - cixi 2 yj- cixj, i, j = 1. . * * n. Fourth, to ensure a solution
exists we must assume the production of cash flows is bounded. If xmax
denotes the maximum cash,10 xi < Xmax, i= 1, ... ,n. Finally, cash produced must not be negative:11 xi > 0, i = 1 . . . ,n.
3. Solution of Benchmark Case
Antle and Eppen [1985] showed that the optimal amounts of production and resources transferred are given by a simple hurdle strategy. If
the reported cost is above some amount, say c^, nothing is produced and
no resources are given. If the reported cost is cz or below, Xmaxis produced and cash of CzXmaxis given to the manager.
This solution displays the trade-off between productive efficiency and
distributional consequences
that forms the basis of our analysis. Lowering the critical hurdle cost gives up valuable production. But it allows the
owner to capture more of the surplus by reducing the resources he provides when production does occur. Raising the critical hurdle cost increases valuable production but gives more of the surplus to the manager
in the form of excess resources. The owner reduces the manager's surplus
(a distributional effect) by reducing the amount of resources available,
but this reduces the amount of resources produced (an efficiency effect).
The optimal policy strikes the best balance between these factors.12
Consider a candidate for the critical hurdle cost, say ck. The expected
profit with this hurdle must be higher than that with the next lower or
next higher hurdle. If the hurdle is lowered to ck-l, production with an
expected gross revenue to the owner of Pkxmax is lost. But the expected
resources allocated decline by pkCkX1ax +
_________
7 The constraint
in the continuous
case is:
f
k- I
p
- Ck_1)Xmax. If the hurP(Ck
~~
= 1
~~~~~~~~i
(y(c)
-
cx(c))f(c) dc
2
0.
0
8 In the continuous
9 In the continuous
10In the continuous
1 In the continuous
12 In the continuous
tion of the first-order
F is the cumulative
case:
case:
case:
case:
case,
y(c) - cx(c )
y(c)
- cx(c)
x(c)
2
0
Vc E C.
y(~) - cx(C)
x(c) < xmax Vce C.
0
VcE
for the optimal
function
V c, & E C.
C.
the analysis that follows
condition
distribution
2
2
cutoff,
associated
in the text is replaced
ct, where c* =
with the densityf
1-
by examina)
and
INFORMATION
45
SYSTEMS IN RESOURCE ALLOCATION
dle is raised to Ck+1, production with an expected gross revenue to the
owner of Pk + IXmax is created. But the expected resources allocated increase by Pk + 1 Ck+ 1 XIax +
k
E
Pi (ck + 1 -
Xmax. The optimal hurdle is such
COk)
that the value of the decreased production associated with a lower hurdle
offsets the savings in resources allocated, and the additional resources
allocated offset the increased production of a higher hurdle.
The ck hurdle produces
ck)xmaX.The manager's
an expected
expected
profit to the owner of
slack is
k
E
3
pi(1 -
i= 1
p1(c;-
ci)Xlax.
Summing
i= 1
the owner's expected
the total expected
profits and the manager's
expected
slack, we see
surplus produced with a ck hurdle strategy is
k
E
pi(3
-
i= 1
ci) X~nx
The total expected surplus, a measure of productive efficiency, is maximized by the cn hurdle strategy. The difference between the total expected surplus under the optimal hurdle strategy and the total expected
surplus under the cn hurdle strategy is the social cost of the owner's attempts to acquire a higher net expected profit. Thus, it represents a loss
due to concerns over distribution.
Figure 2 depicts the trade-off between productive efficiency and distributional consequences for the special case of costs uniformly distributed
on [0, 1] and maximum production equal to one. Since production cost
is always less than or equal to revenue derived from production, it is productively efficient to produce in all cases, i.e., set the hurdle cost equal to
one. The owner's profits would be zero because the hurdle cost of one
will always be the amount of resources transferred to the manager. All the
gains from production are captured by the manager in the form of slack.
To retain some of the surplus, the owner can reduce the hurdle cost
below one. Figure 2 shows the effects of setting the hurdle costs equal to
the hurdle is set at 4, the owner's expected profits are16
4. When
This is greater than the zero expected profits obtained with a hurdle of
one but is less than the maximum achievable expected profits. The hurdle
contract which maximizes the owner's expected profits sets the hurdle cost
1
I
equal to and achieves owner's expected profits of
To further improve the situation, note that the initial probabilities enter
into the determination of the optimal hurdle strategy and the resulting
level of the manager's expected slack.13 A system that conveys information
about costs alters these probability assessments. The next section expands
the model to allow the owner and manager to receive information before
13 This may be clearest
in the case of a finite set of possible
costs.
RICK ANTLE AND JOHN FELLINGHAM
46
Example Hurdle Contract
Expected Profit and Expected Slack
1
E(profit)
=
0.25 x (1 - 0.25)
=
0.1875
0.8
0.6
0.4
E(slack) = 0.25 x 0.25 = 0.0625
0.2
45degrees
0
0.25
0.5
cost (uniformly distributed)
0.75
1
FIG. 2.-Expected
profits and expected slack under a contract with a hurdle cost of 4,
on [0, 1], and maximum production
costs uniformly distributed
equal to one. The
of cumulative probability,
horizontal axis plots cost. The vertical axis plots a combination
amount produced, and resources transferred. The amount of resources transferred is equal
to both the probability that costs are less than or equal to the hurdle costs and hurdle cost
itself. Therefore, the 45-degree line gives both the cumulative distribution function of costs
under uniformity and the resources allocated under all possible hurdle costs. The owner's
expected profits are equal to the difference between resources returned, 1, and resources
allocated, I, weighted by the probability that production occurs, 4. The owner's expected
profits of $ p6 are given by the area of the indicated rectangle with base 4 and height -. The
manager's expected slack (assessed before the manager knows the cost) of Il is the area
of the indicated isosceles right triangle with base and height each equal to 4.
the manager learns the cost.14 This information
plans, but because it also alters the distribution
may have incentives to subvert the system.
allows better production
of surplus, the manager
4. Exogenous Public Cost Information
Public information, a subpartition of the initial set of possible costs, C,
is observed by the owner and manager before the manager learns the
14
We model the introduction
of a cost system as producing public information for the
owner and manager. Thus, we assume the owner has access to the output of the organization's formal cost accounting
system but not the system that ultimately generates the
takes place. The manager's primanager's perfect knowledge of cost before production
vate information
system can inprovides his rents. We show that the public information
crease or decrease the value of the manager's private information.
INFORMATION
SYSTEMS IN RESOURCE ALLOCATION
47
time
Public information
structure
revealed
Contract
signed
Public information
observed
FIG. 3.-Second
Manager
learns
cost, c
time line: exogenous
Manager
reports
cost
Owner
supplies
resources,
x produced
y
public information.
exact value of the costs. This model corresponds to the basic setting for
each element of the subpartition, where beliefs over the costs in each
subpartition are derived by Bayes' rule. Thus, a hurdle strategy is optimal
in each element of the subpartition. The time line in figure 3 depicts the
sequence of events.
It is easy to show that the arrival of such information cannot decrease
the owner's expected net profits. Imposing the restriction of the optimal
no-information
hurdle strategy on the set of subpartitions of C is feasible and produces the same expected profits as in the no-information
case. Also, in some cases the only use of the information would be distributive: introduce perfect information (i.e., the subpartition consisting
of singleton elements) into the case in which a cn hurdle strategy is optimal with no information. Total surplus remains the same, but the manager's slack is driven to zero.
However, the manager is not always adversely affected by the arrival of
information, and information does not always result in improved productive efficiency, as manifested in the expected total surplus. Consider
the following examples.
EXAMPLE1. The set of possible costs is C= {0.65, 0.7, 0.71, 0.8, 0.85,
0.91, each element of which is equally likely. Xmax= 100. With no information, the solution is to set the hurdle at 0.71, which yields expected
profits of 141 expected slack to the manager of 1I, and expected total
surplus of 152. Now introduce the partition {{0.65, 0.7, 0.711, {0.8, 0.85,
0.9} 1. In the first element of the partition, the solution is to set the hurdle
at 0.71, which yields conditional expected profits of 29, conditional expected slack of 23, and conditional expected total surplus of 313. In
the second element of the partition, the solution is to set the hurdle at
0.9, which yields conditional expected profits of 10, conditional expected
slack of 5, and conditional expected total surplus of 15. Thus, with information the expected profits are 191, expected slack is 32, and expected
total surplus is 23k.
EXAMPLE2. The set of possible costs is {0.65, 0.7, 0.75, 0.8, 0.85, 0.9},
with corresponding probabilities {0.01, 0.06, 0.01, 0.01, 0.01, 0.9}. With
no information, the ex ante optimal solution is to set the hurdle at 0.9,
which produces expected profits of 10, expected slack of 143, and expected total surplus of 113. Now introduce the partition {{0.65, 0.7,
0.75}, {0.8, 0.85, 0.9} }. In the first element of the partition, the solution is
to set the hurdle at 0.7, which yields conditional expected profits of 261,
conditional expected slack of 5, and conditional expected total surplus
48
RICK ANTLE AND JOHN FELLINGHAM
of 267. In the second element of the partition, the solution is to set the
hurdle at 0.9, which yields conditional expected profits of 10, conditional expected slack of 1S, and conditional expected total surplus of
10 15 . In this example, the expected profits with public cost information
3
are 11 , expected slack is 10, and expected total surplus is 11.
In example 1, the introduction of information increased the owner's
expected net profits, the manager's expected slack, and (consequently)
total expected surplus; there is no conflict between the productive and
distributional consequences
of the information. Both the owner and
manager have incentives to seek out such an information system and
have no incentives to sabotage it.
In example 2, information lowers the cost of reducing production to
increase expected net profits. With no information, full production is
achieved in all circumstances. But the manager captures all the profits
from costs lower than 0.9. With the information, the owner can raise expected net profits, in part by not producing when the cost is 0.75. This is
the familiar use of rationing to reduce slack, now made profitable by the
information system's altering of the probability structure. The effect is
lower total surplus. Also, the manager has incentives to oppose or sabotage this information system, and certainly would not have incentives to
discover and reveal it to the owner.
5. Uniform Distributions and Regular Partitions
Before taking up these incentive issues in more detail in the next section, we present two special cases of interest. The uniform case is described
by Xmax = 1, C = [0, 1], and uniform distribution of the per dollar costs,
c. The regular case is the uniform case under all regular partitions: { [0, 1] },
The uniform case
[1,
{[0,
1]},
{[0,
1),
4),
[4, 1),
[2, 4),
[4, 1]} .
will be analyzed in detail in later sections. We take up the regular case
here, as it allows a precise characterization of when conflicts of interest
exist as a function of the number of elements in the partition.
In the regular case, it can be shown that if there are m elements in a
partition, the total expected surplus is: TS(m) =
surplus is increasing
lim
m
Ts
TSi (m)
in the number
of elements
I. The manager's expected
214-
E[Slack(m)]
2-
12 The total
2 8i2
in the partition,
and
slack is:
= 4m 3(1)
8m2
At m = 1, the manager's expected slack is 8. In this regular case, it
rises to 32 at ma= 2, after which it falls. Its limit is 0.
The owner's expected profits when there are m elements in the partition are equal to the expected total surplus minus the manager's expected slack. This works out to:
INFORMATION
SYSTEMS IN RESOURCE ALLOCATION
E[7 (rm)] =
49
I
- 2m-1
2
4m
E[7(m)] is increasing in m and tends to the total surplus of 2 as m goes
to infinity. We have shown:
PROPOSITION1. In the regular case there is a conflict of interest between the owner and manager if and only if m is greater than 2.
If costs are uniformly distributed and the manager could select any
partition of [0, 1], he will choose a partition that provides some information, as shown in Proposition 2.
PROPOSITION2. (Proof in Appendix A.)The partition of C = [0, 1] in
slack is:
the uniform case that maximizes the manager's expected
=
isfies:
{[2,
2),
lim
,
[4
[2, -),
E[Slack(m)]
liMEE[(i(m)]
mum value of
=
3.
87, ...
}.
= 6.
The
The manager's
owner's
expected
expected
utility sat-
profits
In the limit, the total surplus approaches
satisfies:
its maxi-
2.
As this proposition shows, the manager has natural incentives to provide some information to the owner, because with no information, the
owner allows no production above c = i. The manager gets slack from
the low-cost states, while the owner's expected profits are the same for
all costs for which production takes place. In choosing an information
system, the manager would like to keep the slack from lower costs while
providing information that induces the owner to produce in higher-cost
circumstances. This thinking yields the structure of the manager's most
preferred partition, which pools the most low costs possible without incurring restricted production. Thus, the manager is interested in information systems that only coarsely describe low-cost circumstances and
more accurately describe costs close to the point where production is
not profitable
(c = 1).15
The proposition also implies the manager may be better or worse off
as the result of public cost information and productive efficiency may or
may not be enhanced. Consider starting from a partition of the form:
0, 2),
is better off with
{=[
,
48),
[8, 1]}. The manager
[2, [4),
any subpartition of 's that only subdivides the highest interval and does
that at values greater than or equal to 16. Any subpartition that divides
any other element of 's makes the manager worse off. Also, further partitioning of 'M increases the owner's expected profits by the same
amount it decreases the manager's expected slack. That is, further partitions of 'M have only distributional consequences.
'is
15As an example, in a field study of cost systems in a health-care facility, Maher and
manager,
Marais [1994] suspect the head nurse, whom we would consider a production
has reason to prefer a less precise costing system. Their reasoning is consistent with ours:
A more precise system would provide less opportunity to create slack through careful disclosure of local conditions to higher-level
management.
50
RICK ANTLE AND JOHN FELLINGHAM
We can also characterize the partitions preferred by the owner. In the
limit, the owner prefers perfect information, but his preferences over partitions with two elements, three elements, four elements, etc., take a wellstructured form.
3. The m element partition that maximizes the owner's
PROPOSITION
expected
L
2
profits
3
m+
m+
1 1
in the
rn-i,
uniform
m~+1
case
is: LI?
]. The owner's expected
E[n(m)]
=
jmIjL
'172ii'
profits are:
i
2 (rn + 1)
2 m
2
2 (m + 1)2
Comparing special cases of Propositions 2 and 3 illustrates the conflict
of interest over information systems. For m = 3, the manager's most preferred partition is {[0, I), [2, 3), [3, 111. The owner's most preferred
partition is {[0, ,[,
1), [1, 1]}. As discussed above, the manager prefers to pool the most low costs possible without incurring a loss of production. The owner prefers more accurate identification of low costs and
is more tolerant of restricted production than is the manager.
We can use the characterization of the owner's and manager's most
preferred information systems to gain some insight into how their preferences vary across economic environments. Consider the effects of having per dollar costs uniformly distributed over [0, I], instead of [0, 1].
The important change is not that costs are lower, but that profits are
higher. With no information the owner will select the contract that always produces $1 and gives the manager $0.50. The owner gets the surplus from the excess of price, $1, over the $0.50 maximum total cost,
and the manager gets all the rent from information about costs. The
manager has no incentives to supply information in this very profitable
situation, because restricting output is too costly a way for the owner to
control the manager's slack. Full production always occurs: Information
can only allow the owner to make a more favorable (to him) distribution
of the benefits of producing.
Now consider the effects of moving the upper bound on the distribuI
tion of per dollar costs from to 1. The closer we get to an upper bound
of 1, the lower the profits. Without additional information, the owner's
optimal contract restricts production when the upper bound on cost is
greater than 9. This restriction imposes a cost on the manager, so he
would like to avoid this lost production by supplying information that reveals more when costs are high. For example, when the per dollar cost is
uniformly distributed over [0, 3], an uninformed owner will ration at
2 The manager would like to preserve his slack for costs less than 2
and induce production between 2 and 3. The best (from the manager's
this is {[0, 9), [2, 3]1. The
point of view) partition that accomplishes
The manager's expected
slack is: E[Slack(m)]
INFORMATION
SYSTEMS IN RESOURCE ALLOCATION
51
owner with this information will produce fully for all costs. Continuing
this process leads to thinking of the manager's optimal information system in Proposition 2 as the limit of the optimal information systems as
the upper bound on the distribution of per dollar costs goes to 1 from
below. Our interpretation is that in less profitable situations, the manager has incentives to provide information about costs close to the margin.
As mentioned above, this shows that from the manager's point of view,
"good" information systems for decision making are also "good" from
the point of view of maximizing his slack.
Put somewhat more abstractly, factors external to the firm affect the
information preferences of the participants in the firm to the extent
that they affect the distributional consequences of whatever information
is supplied. Managers typically play a role in designing, implementing,
and maintaining information systems. It seems reasonable, then, to introduce opportunities
for the manager to influence the information
generated. This is the purpose of the next section.
6. Incentives for Influencing Information
This section introduces opportunities for the manager to influence the
information structure he and the owner install before production takes
place. We study two different models of information influencing. They
differ in the owner's ability to observe and provide incentives for the manactivities.16 In model 1, the manager can
ager's information-influencing
join adjacent elements of any given information partition. For example,
if C = {0.6, 0.7, 0.8, 0.9} and the information partition is {{0.6}, {0.7, 0.81,
{0.911, the manager can alter the partition to any one of the following
three: {{0.6, 0.7, 0.81, {0.9}}; {{0.6}, {0.7, 0.8, 0.9)1; {{0.6, 0.7, 0.8, 0.911.
Although the owner observes the results of the manager's informationinfluencing activities, we assume the owner cannot commit to provide incentives for these activities. The time line in figure 4 depicts the sequence
of events.
Model 2 parallels standard moral hazard models. Information production is uncertain, and the manager has an action choice that influences
the probability distribution over information structures. For instance,
consider a set of costs, C, and the two partitions fi and 2. The manager
has two available influence activities, denoted I, and I2. Under II, fi is
realized with probability 1. Under I2, fi is realized with probability p and
12 is realized with probability 1 - p.
In contrast to the first model, the owner is assumed to be able to commit to a contract that depends on the realized partition, thus allowing
for the provision of incentives for information-influencing
activities. The
16 Information
is not the only focus of influence activities in organizations.
Milgrom
[1988] and Milgrom and Roberts [1988; 1992] discuss a wide range of influence activities and organizations'
attempts to limit them.
52
RICK ANTLE AND JOHN FELLINGHAM
S
S
}
Q
Q
M
bl)a sM C
C
b)
X
.C
b
Q
Q
Ct
5o
C
C
CD
CDa
_
C
;
.
bX
OC<a
c) C.
.;~~~~~~~~
t
.2h
,
S
5J
CE
Gn S4 sv
h?
:~~~~~~~~~~~
U~~~~~~
C
hC
t
bb~~~~~~~~~~~~~l
INFORMATION
SYSTEMS IN RESOURCE ALLOCATION
53
time line in figure 5 depicts the sequence of events. We proceed to an exploration of these two models.
In principle, model 1 is straightforward. Given any partition, say Al,we
derive the set of all partitions that are coarsifications of rA.Call this set
set for information
systems. The
H(fl), the manager's opportunity
manager's expected utility for any element in this set is the expected
slack it generates. Since the owner will choose the hurdle strategy optimal
for each member of a given partition, the manager's expected utility for
any member of H(f) is easily calculated. We have the following result for
the regular case:
PROPOSITION 4. In the regular case, if the manager starts from a regular partition with m elements, he will construct:
~(rl)
=
2L0'
The manager's
2
L
21
4
expected
L m-2
~
2
' i2
n-li'
2
L
im-i
2
slack is:
E[Slack((rn(n))]
1-
(2)
The gain from influencing the information is (2) - (1).
In model 1, the owner cannot provide incentives for the manager's information-influencing
activities, even though he would prefer to let the
manager start from the finest possible regular partition. In model 2,
however, the owner can commit to providing information incentives by
restricting production and manipulating the manager's slack.
Specifically, when the owner can commit to contracts before the information partition is received, the payments to the manager and production
targets can depend on the partition observed as well as the manager's subsequent cost report. If the manager controls the partition, information
incentives could be costlessly provided by withholding production unless
the manager chooses the desired partition. Therefore, just as in ordinary
incentive problems, uncertainty in production is a key element of nontrivial analysis, where here information is what is being produced. We report preliminary analysis of two examples from the uniform case.
EXAMPLE
3. Suppose the owner can commit to a contract before the partition is realized. Also, suppose there are two possible partitions: [40, I),
0),
[2, 1]} and {[O,
[3, 111. The first of these is the two-element
partition
most preferred by the manager and the second is the two-element partition most preferred by the owner. Call them rL2 and r2, respectively. We
have already shown there is a conflict of interest. We assume I, leads to
9
with probability 1, and I2 leads to il with probability I.
Because the action is costless, the manager will take the action that
yields the highest probability of his preferred partition, unless given incentives to do otherwise. The most efficient way to give such incentives is
to commit to a contract that leaves the manager indifferent about which
54
RICK ANTLE AND JOHN FELLINGHAM
partition is realized; i.e., to commit to a contract that calls for a cutoff of
0.70547 if the first partition is realized and 0.7589 if the second is realized. This makes the manager's expected slack 0.146109 regardless of the
partition.
These cutoffs reveal the owner's use of restricted production and
slack in providing information incentives. The cutoff of 0.70547 in the
owner's dispreferred partition is strictly below the cutoff of 3 that
would be used without regard to information incentives. The cutoff of
2
that would be used in the owner's pre0.7589 exceeds the cutoff of
ferred partition if information incentives were not an issue. Thus, the
owner offers the manager additional slack and imposes additional production constraints to provide information incentives.
The principal is better off committing to the contract with information incentives than allowing the manager to choose his preferred partition. This conclusion follows from observing that the owner's expected
profits are j5 under the manager's preferred partition with no information incentives, 0.310517 under the manager's preferred partition with
information incentives, and 0.32486 under the owner's preferred partition with information incentives.
EXAMPLE 4. Suppose one of two partitions will be realized, either the
manager's most preferred partition: lM = {[0, I), [I, 3), [ , 7), (7,
1
[
),
], ... } or a partition that the owner prefers: rgo = {[?0, b) [,
1. The owner prefers nlo to flM because flo
[2, 3), [3, 7), (7, 51 ....
subdivides the lowest cost interval. Here, the most efficient way to make
the manager indifferent is to ignore all information if tIM is produced
and set a cutoff of
30 . In iro, the optimum
is to follow the case where
information incentives are not at issue and set cutoffs equal to the upper
limit of each interval. Thus, production always occurs with ro. The manager's expected slack in both flM and rO is 4. The owner is better off
committing to such a scheme if the information alternatives are flM for
sure or nlo with a probability greater than 0.5769, depending on the manager's actions. Under this structure, the owner's expected profits are 3.
These examples demonstrate several points. First, additional distortions in production or extra slack are introduced to provide information
incentives. Additional restrictions of production necessarily reduce social efficiency and have as their aim only a distributive effect. Both these
distortions are exhibited in example 3, whereas example 4 has only restricted production; i.e., the partition the owner is trying to avoid induces full production in the absence of commitment. Any alteration of
contract in such a case necessarily reduces social
the no-commitment
efficiency.
Second, the examples illustrate the role of a commitment to ignore
information if it is not produced by a desired partition. This is particularly vivid in example 4, where all information produced by IM is
INFORMATION
SYSTEMS IN RESOURCE ALLOCATION
55
ignored. The typical theoretical explanation of the role of committing
to ignore information is to provide incentives for communication.
Here
we show it can also provide disincentives for the production of information, if it is not the owner's preferred information.
Third, the provision of incentives requires differentiating the consequences to the manager under the various partitions. It may then appear that the information choice has been delegated to the manager,
who is in turn held responsible for the information. The usual explanation of why managers select the information system is private information (Demski, Patell, and Wolfson [1984]). Our model has no private
information at the point of information selection. Rather, we assume
that efficient production of information gives the manager some opportunity to influence it, and it is costly to insulate against such influence.
7. Conclusion
This paper has examined some issues arising from the ability of managers to influence the information in an organization in order to escape
its distributive effects. We gave necessary and sufficient conditions for the
owner's and manager's preferences over a public cost-reporting system
to be in conflict when costs are uniformly distributed and cost information partitions contain equal length elements. We described the owner's
and manager's most preferred public cost-reporting information systems
when costs are uniformly distributed. The potential for and nature of the
conflict of interest is clear from these results. Managers want to make
public cost information that accurately distinguishes highest costs but
pools low costs. This allows maximum possibility for extracting slack,
while curtailing as much as possible lost production. Owners want information that is more uniform over possible costs to facilitate capturing
slack from the manager in low-cost states.
Limiting production to socially suboptimal amounts is the owner's tool
for controlling the manager's slack consumption.
If the manager can
costlessly implement any information system, he will choose one with socially efficient production and one which allows him to capture as much
of the rents on cost information as possible (Proposition 2). The owner's
optimal strategy obtains a more favorable distribution for him while also
implementing socially optimal production. The owner's preferred information system gives all the rents, both from the firm's underlying technology and from the cost information, to the owner (Proposition 3).
Between these extremes, our analysis shows how socially suboptimal production can be used to affect distribution.
The distributive and productive effects of information interact, and
additional distortions can be created by information-influencing
activities. This was the focus of the analysis of moral hazard in information
acts that influence information systems can
production. Unobservable
RICK ANTLE AND JOHN FELLINGHAM
56
lead to incentive
cost information.
schemes
which commit
to ignore
otherwise
valuable
APPENDIX A
Several lemmas
lemmas all assume
LEMMA 1. Within
hurdle rate chosen
are helpful in proving Propositions
2 and 3. The
costs are uniformly distributed on [0, 1].
any element of a partition (ci, cs+,11 the optimal
by the owner is: min{'(1+ci),
ci,1}.
CH
Proof. The owner chooses a hurdle cost,
cH,
to maximize
f
(1 -
CH) dc =
Ci
(1 - cH)(cH- ci). The first-order condition on cH yields cH = 2(1 + ci)
This equation is valid when CH is interior. Otherwise, cH = ci+i.
LEMMA 2. In an optimal partition
all elements except the highest,
(can, 1], have the following property: ci < (1 + ci -). The statement is
true whether the partition is optimal for the owner or the manager.
Proof. The lemma means there is full production in all elements of
the partition except the last. Suppose the statement is not true, and
there are two adjacent elements of a partition without full production.
Then the manager's expected slack in those two elements of the par- c+1] 2. The
of
tition
is: I[i(1 + c.) - C.]2 + [9(I + C
derivative
the expected slack with respect to ci+l is '(-1 + c-+,) < 0. So expected
slack can be increased by decreasing c-+I to I(I + ci).
Notice the proof was for the case when the hurdle rate in the higher
partition element is interior. If the hurdle rate is on the boundary of
the higher partition element, it is easy to show the derivative of the
expected slack with respect to c,+1 is negative. Therefore, an interior
hurdle rate in the lower partition element is suboptimal. This logic
covers the case in which there is only one interior partition element
without full production.
The proof proceeds in the same way for the owner's partition. When
there are two adjacent elements without full production, the expected
residual is:
[9(1
+ cC-)-
Differentiating:
cj[1
a
+ C-)] [+(1
+
E(slack)
=-
-
+ C-+)c-+,)
< 0.
C-+,] [
-
(
C.+
The owner is made bet-
I + I
ter off by decreasing ci+1 to (1 + Ci).
LEMMA 3. The optimal partition for the manager will have at most
one c- - 9slack can be increased by moving
Proof. Suppose c1 < C
9. Expected
c1 to halfway between c2 and 1. Expected slack below c2 under the old
slack below
-1c + I(C2 - C,)2 =
Ic2
partition is ?2
2 - cl(2 - cl). Expected
SYSTEMS IN RESOURCE ALLOCATION
INFORMATION
57
c1(c2 - c1). Plus the manager
c2 under the new partition is 2c2 > 2c
+ 1) 2.
gets some extra slack at the high end: -(c2
Proof of Proposition 2. Using Lemma 2, the expected slack in the first
is E(Slack) =
optimal
partition
two elements
of the manager's
1 +
- c1)2. The
to c1 is:
with respect
partial derivative
d3ESlk = 2c, - c2. This partial derivative
a3c1
is an affine function
From Lemma 2 the bounda(The left-hand boundary
So we only have to check the boundaries.
ries on c1 for a given c2 are: 2c2 - 1 < ?,
is from the inequality c2 < (1 + c1)12.)
Plugging in the boundaries
gives two cases:
Case 1: c1
= 2-
of cl.
: 2.
for expected
into the expression
Then E(Slack)
=
+ 4-
--
Case 2: c1 = 2c2 - 1. Then E (Slack) =
slack
5C2 -
From Lemmas 2 and 3 we only need to check the
slack is
43. Some algebra reveals Case 1 expected
expected slack. Define g(c2) as the expected slack
expected
slack in Case 2: g(c2) = -2c2 + 5c2-
3c2 + 1.
two cases for 2
greater than Case 2
in Case 1 minus the
;
g(2)
=
g(3)
=
0;
> 0, g'(4)
slack in Case 1, c1 =2
< 0, and g"(c2) < 0. So expected
9'(2)
is always greater than Case 2 for all relevant c2. (For c2 = 2 and 3, the
two cases represent the same partition.) Therefore, the manager's optimal partition must have c1 =
3
Since c1
(halfway to
l = , logic identical to the foregoing yields c2 =
In
limit
the
and
so
forth.
the
C3
=
7,
one),
manager's expected slack is:
E(Slack)
=
-1
2 ((1/l1))
The
+ 1(1)2
2(1)2
amount
=
+ 1(1)2
approaches
produced
1
of 1 -
(
...
+
+
(1) 2 +
(4) 3
+
1-
f cdc
full production
with gains
to
residual
to the owner is
Proof of Proposition 3. Using Lemma 2, the expected
owner of an m element partition is:
residual for the
production
-
2
So the expected
2.
0
_
G
=
3-
E(n(m))
+
.
.+
=
c1(I
- cl)
+
+ * * * +(ci-
c-_.)(1
(Cm
i) (1
Cm
cl)(
(c2-
- ci)
-Cen
) +
-c2)
+ (c-+1
(Ci
-+ll)
+
c2)(1-
(c3-
- c-)(l
-
( 1-
ci+0
-)+1)
c3)
58
RICK ANTLE AND JOHN FELLINGHAM
Differentiating
with respect to c1, ci, and Cm respectively, and setting
equal to zero yields: c2 = 2c1; cI =
+I + ci-1); and cm- Cml =
of the optimal partition.
2(I - Cm), which is an equivalent representation
The owner's expected residual is:
I
1
I-
I
I
1-
)miMm+M+
1
m(m+ 1)
2
(m+ 1)2
2 )+
I
+
(1-m)
m+
ml+
1
)
m
2(m+ 1)
The manager's expected slack is Im(1/(m
ber of elements in the partition.
+ 1))2,
where m is the num-
REFERENCES
ANTLE, R., AND G. EPPEN. "Capital Rationing
and Organizational
Slack in Capital Budget1985): 163-74.
ATKINSON, A.; R. BANKER; R. KAPLAN; AND S. YOUNG. ManagementAccounting.Englewood Cliffs,
N.J.: Prentice-Hall,
1995.
DATAR, S., AND M. GUPTA.'Aggregation,
Specification
and Measurement Errors in Product
Costing." The Accounting Review (October 1994): 567-92.
DEMSKI, J.; J. PATELL; AND M. WOLFSON. "Decentralized
Choice of Monitoring Systems." The
Accounting Review (January 1984): 16-34.
ing." Management Science (February
FARLEE, M.; J. FELLINGHANM;
AND R. YOUNG.
"Properties of Economic Income in a Private Infor-
mation Setting." Working paper, Ohio State University, 1995.
MAHER, M., AND M. MARAIS. "Process-Oriented
Activity-Based Costing." Working paper, University of California at Davis, 1994.
MILGROM,
P. "Employment Contracts, Influence Activities, and Organization Design." Journal of Political Economy (February 1988): 42-60.
MILGROM, P., AND J. ROBERTS. 'An Economic Approach to Influence
Activities in Organizations." American Journal of Sociology (Supplement
1988): 154-79.
. Economics, Organization, and Management. Englewood
Cliffs, N.J.: Prentice-Hall,
1992.