Slack and participative budgeting – always an evil?
Michael Kopel (University of Graz)
Christian Riegler (Vienna University of Economics and Business)
November 2014
Abstract:
Participative budgeting is widely used in corporate practice despite empirical research finds only
mixed evidence of its benefits. This may be due to neglected drivers in the theoretical grounding of
related research. So far analytical models focus on the benefits and costs of participative budgeting
within a firm. They find that participative budgeting may improve the knowledge of a superior or
increase the motivation of subordinates. However, this often comes at the costs of padding budgets
and slack building by subordinates. Most studies find that slack only drives the costs of participating
budgeting decreasing its benefits. By additionally considering market effects caused by participative
budgeting, we find that slack may also be beneficial for a firm. In an analytical model, we characterize
the basic trade-off between slack building and the decisions of market participants outside the firm.
The total effect may be positive or negative. Therefore, focusing only on aspects of budgeting within
a firm may miss an important effect of participative budgeting. It seems fruitful to consider this effect
in future empirical research.
1. Introduction
Budgets are one of the most widely used management accounting tools all over the world. We can
find extensive discussions of budgeting techniques and problems in almost every management accounting textbook.1 Research also documents a wide use in corporate practice in medium and large
firms and a high perceived usefulness.2 The high usefulness is also a result of the multiple functions
of budgeting, ranging from planning and controlling annual operations, communicating information,
coordinating activities, motivating managers and evaluating their performance. It is obvious that
these functions face increasing importance in decentralized large companies, where managers of
different hierarchical layers may have more decision making authority.
It has a long tradition in the budgeting literature to discuss whether the participation of managers in
the process of preparing a budget is beneficial for the firm. In the past, this important question was
often addressed based on different research traditions.3 Psychology based research focuses on motivation and behavior. It is argued that involvement in the budgeting process may increase job satisfaction and morale. This leads to greater commitment and acceptance of goals fixed in the budget. As a
consequence, performance of managers and of the company may increase. Empirical research addressing these aspects finds mixed evidence. Several studies find a significant positive relationship of
participation and performance, others observe no relationship and some even find a negative association.4
The role of asymmetric information and its impact on firm profit was especially addressed in economic based research. The question if and how the better information of the subordinate manager
should be used in the budgeting process was addressed in a series of papers in the 1980s and 1990s.
These studies focus on the game, in which managers try to bias communicated information. By padding the budget and building budgetary slack the subordinate manager communicates underestimated revenues or overestimated costs to the superior. This results in more easily achievable targets and
in inefficient resource consumption. Participation in the budgeting process has therefore the advantage of improving the knowledge of the superior, which he may use for planning and controlling
activities on the firm level. As a result, the process may also provide incentives for the subordinate to
work harder. However, participation comes at the costs of slack diminishing the benefits of this
budgeting regime compared to authoritative top down budgeting. As a consequence, participation in
the budgeting process may be beneficial or not.
A common view of slack in the budgeting literature is that slack is not beneficial for the firm. Slack
leads to biased information causing inefficient decisions based on this information like biased resource allocation, biased targets for subordinates or inefficient effort choices and resource consumption. Participation per se could be beneficial. However, slack building behavior of the subordinate
limits its benefits. To make better use of the beneficial aspects, firms try to find mechanisms to decrease the amount of slack.5 Related literature finds that benefits and costs of using budgets and the
optimal design of the budgeting process is highly context specific. The optimal solution depends on
the importance of the (sometimes conflicting) functions of budgeting as well as on the characteristics
1
See e.g. Drury (2012), Bhimani/Horngren/Datar/Foster (2011) or Atkinson/Kaplan/Matsumura/Young (2007).
See e.g. Shastri/Stout (2008).
3
See for a survey Covaleski/Evans/Luft/Shields (2007).
4
See Maiga/Nilsson/Jacobs (2014), p. 6.
5
See Atkinson/Kaplan/Matsumura/Young (2007), p. 490.
2
2
of the situation analyzed. The advantage from using budgeting as a mechanism itself and the best
way how to design the mechanism may differ from setting to setting. Thus, it is not surprising that
empirical research also observes mixed results when searching for evidence for the findings of analytical research.
The mixed results also motivate our following analysis. Due to the complexity of budgeting it does
not seem possible to develop a closed theory considering all functions and characteristics of the participative budgeting setting. Therefore, it is important to discuss aspects, which have been neglected
so far in the related literature. This may be helpful to further explain why participative budgeting is
widely used in corporate practice. We also want to emphasize the danger of misleading findings if
the focus of an analysis is set too narrow. Our aim is to add an additional piece to the budgeting puzzle.
We address the question if slack is always only a disadvantage or if slack could also be beneficial for a
firm increasing the value of participative budgeting. This is contrary to the common view of the
budgeting literature. To do this we see participative budgeting as being part of the culture and leadership style of a company. Especially for large firms, corporate culture is often well known also outside the firm. Some firms are known for a participative, employee oriented culture whereas others
are known for being authoritative. As culture does not change rapidly, a firm shows a strong sustainable commitment of being participative or authoritative. This is also reflected in the way the budgeting process is designed. When other market participants observe the commitment, this may also
have an impact on their decisions, whenever the decisions of the firms are in some way interrelated.
For an economic analysis, we model such a setting. We analyze the strategic impact of the choice
between two alternative designs of the budgeting process (top down versus participative) on the
market behavior of firms. The interrelated decisions of firms on the market are captured by the pricing decision of a supplier. He delivers a critical resource for the production process of the firm choosing the budgeting mechanism. The decentralized firm consists of two divisions, both requiring the
critical input resource for the production in their respective unit. Based on the budgeting process,
the cost budget for production for each division is fixed. The design of the budgeting process impacts
the cost budget of each division, but also the pricing decision of the supplier. Participative budgeting
may be beneficial despite slack building and increasing real production costs of the firm, because of
its strategic effect on the input market. Central headquarters can derive a threshold for the preferred
budgeting design based on its expected production costs (building on its ex ante expectation without
getting information of a better informed divisional manager). We find that c.p. headquarters prefers
participative budgeting if the ex ante expected production costs are in an intermediate range. If expected production costs are low or high, top down budgeting is preferred.
Our contribution to literature is to show that slack is not always only a cost for participative budgeting. Slack may even increase its benefits in some settings. This finding adds to the literature searching
for contingencies driving the benefits of the design of the budgeting process. It also highlights that
models focusing only on the effects of the budgeting process within the firm may come at the risk of
missing important effects on the market behavior. As a consequence, recommendations may also be
misleading. The analysis offers also room for empirical research. The setting is (as in most of the
models analyzing budgeting issues) very specific. However, the important drivers of the results are
(to some extent) observable outside the firm, which makes an empirical investigation possible.
3
The paper proceeds as follows. The next section discusses related literature. Section 3 provides the
model setup, analysis and presents the findings. Section 4 concludes.
2. Related Literature
Very recently, participative budgeting again gains increasing interest in analytical management accounting research. Heinle/Ross/Saouma (2014) compares top down and participative budgeting in a
different setting from ours. They assume that either the principal (top down budgeting) or the agent
(manager, bottom up budgeting) receives and communicates private information. In each of the two
budgeting mechanisms the better informed player has an incentive to misreport. For participative
budgeting, the manager has an incentive to bias the report pessimistically to allow for reducing effort
building slack. For top down budgeting, the principal has an incentive to bias the report optimistically
to motivate the manager to exert higher effort. The authors find that the level of information asymmetry drives the choice of the preferred budgeting mechanism. There is a switch from top down
budgeting to participative budgeting as the amount of private information increases. In this setting
slack is a cost negatively affecting the benefits of participative budgeting. However, slack is also a
commitment device of the principal to signal truthful reporting when top down budgeting is implemented. Our analysis differs from Heinle/Ross/Saouma (2014) as we do not only consider budgeting
as a communication tool within the firm. Budgeting may also serve to convey information to market
participants outside the firm. In this context, slack may not only have a negative impact on the superiority of participative budgeting for the principal. To the contrary, it may also increase its benefits.
Weiskirchner-Merten (2014) provides an analysis for a budgeting setting with one principal and two
agents (managers). The divisions of the managers are interdependent and jointly generate the firm’s
profit. For both divisions, cost budgets for production have to be determined either based on top
down or participative budgeting. Weiskirchner-Merten finds that if the profit potential is low, top
down budgeting is preferred. As the profit potential increases participative budgeting becomes more
favorable. The level of cooperation between the two divisions and the effectiveness of the principal’s
coordination of the two divisions also has an impact on the choice of the preferred budgeting regime.
Differing from her analysis we also consider budgeting as a tool to convey information to other market participants. In this regard, slack does not necessarily decrease the benefits of participative
budgeting and may even be advantageous. In our setting we find that top down budgeting is preferred for low expected ex ante production costs (which could be seen as high profit potential). This
is contrary to the findings of Weiskirchner-Merten and highlights the importance of considering different contextual factors and settings to get a more complete picture of the drivers of the benefits of
participative budgeting.
In the 1980s and 1990s, several analytical papers addressed the role of communication and target
setting on the effort choice of an agent.6 The findings emphasize that in most cases the principal has
to offer rents (i.e. slack) to the agent to induce truthful reporting. This is also in line with the findings
of the revelation principle. Again, slack has only a negative impact on the benefits of participative
budgeting. This is true for some functions of budgeting discussed in the introduction. However, it is
also possible to think of settings where it is not in the best interest of the principal to become in6
See e.g. Demski/Feltham (1978), Christensen (1982) or Baiman/Evans III (1983).
4
formed truthfully by the agent, although participative budgeting is implemented. By this, the principal may credibly commit to a behavior that an informed principal would never show. This may have
an impact on the decisions of market participants outside the firm. The total effect may be beneficial
for the principal, even if slack induces real costs and decreases the real profit of the firm.7 The economic forces driving the result are comparable to the findings of Sappington/Weisman (2005) that
increasing the cost of an upstream product may disadvantage downstream rivals. It is fruitful to consider their basic idea developed for the setting of a vertically-integrated producer for the budgeting
context as well.
The model also relates to the strategic use of transfer pricing on input markets analyzed by Arya and
Mittendorf (2010). Using transfer prices above marginal costs can have an impact on the pricing decision of a supplier of an input resource for the firm. An increase in the transfer price may induce the
supplier to lower the price for the input to stimulate demand for his resource. Depending on the
characteristics of the firm, this may be a profitable strategy for the firm. Contrary to these models we
focus on the design and choice of the budgeting regime. The corporate culture of a firm (authoritative or participative) is reflected in the design of its budgeting process. Additionally, corporate culture is often well known (observable) by other market participants. Thus, we can expect comparable
economic forces to be in place. However, in order to represent the budgeting process, the basic
model has to be altered significantly, especially by adding a stage representing the communication
between principal and divisional managers and the choice of the budgeting regime. On the one hand,
this provides a significant extension of this model class. On the other hand, this enables us to gain
new insights into the context of budgeting.
By this we want to contribute to the puzzle of mixed empirical results with respect to questions of
participative budgeting.8 By modeling aspects not included in analytical research in the past we extend the theory. The findings can also be investigated by empirical research. Divisions of different
relative profitability, who have to rely on a common input resource provided by a supplier with high
market power, represent important drivers of the results derived. This information is (to some extent) also observable for empirical researchers outside the firm.
3. The Model
We consider a principal, who employs two managers each running one of the two separate divisions
of the firm. We assume that the principal and the managers are risk-neutral. Both divisions serve two
separate monopolistic output markets. The demands for the respective product of each division are
described by pi=ai – xi, i=1,2. The demand functions are common knowledge.
An interdependence of the two divisions arises, because both of them require the same type of input
resource for their production process. The input comes from a single supplier from outside the firm.
There is no alternative source offering the resource needed. The firm buys the quantity needed in
one single order. So the price of the resource depends on the quantity ordered by both divisions. For
7
E.g. thinking of strategic transfer pricing, delegation of decisions and fixing transfer prices above marginal
costs may soften competition and also have an impact on other market participants. But here, only the costs
driving the delegated decision of a manager are biased, not the real costs of production within the firm. See
e.g. Göx (2000).
8
See for an overview Heinle/Ross/Saouma (2014), p. 1026f.
5
simplicity, we assume that each unit of the final products requires one unit of the input resource. The
supplier sets the price q for the resource to maximize his profit. For simplicity, we normalize the production costs of the supplier to zero.
To produce one output unit causes costs ci, i=1,2, in each division. The production costs of division 1
are stochastic and uniformly distributed in the interval [ c1 ,c1 ] . The distribution is assumed to be
common knowledge. The production costs c2 are deterministic and known by all players. The production costs ci include all manufacturing costs of one output unit except the costs of the input resource
delivered by the supplier. So the total product costs per unit are ci+q.
Each divisional manager receives a cost budget for production. The budget is fixed at the beginning
of the period and is specified per unit. The budgeting process may be either designed top down or
participative. When implementing top down budgeting, the principal only uses his ex ante knowledge
of the production costs without asking the managers to report. Therefore, the principal fixes the cost
budget based on his expectation of the stochastic costs in division 1, that is E(c1), and his knowledge
of the costs of division 2, c2.
When implementing participative budgeting, the principal asks the divisional managers to report and
fixes the cost budgets based on their respective cost reports ĉi ( ci ) . To introduce asymmetric information, we assume that the manager of division 1 may acquire costless additional information and
observes the true costs c1. This information is personal to manager 1. Neither manager 2 nor the
principal may acquire the information ex ante. The following illustrates this idea: Given his expertise,
manager 1 can thoroughly analyze the production process of division 1 generating the personal information. Manager 2 has no access to this information, because he has no detailed knowledge of
division 1 and its production site. The principal cannot acquire the information due to a lack of technical expertise to analyze the production facility.
Also ex post, the true costs of division 1 are not observable by the principal and bymanager 2. Manager 1 may consume resources not needed for production on the job. It is not possible to separate
real costs of production and slack consumed when observing actual production costs. This represents
the general idea of slack in literature.9 Manager 1 has an incentive to overstate costs, to build slack
and to consume slack privately. As true costs are never observable by all other players, there is no
risk of ex post detection. The consumption of slack increases the utility of the manager. We assume
that the amount of slack equals the utility arising from consuming slack.
To build slack, the manager has to overstate real costs observed and to bias the cost report to the
principal. We assume that the biasing behavior follows the linear function ĉ1( c1 ) = b ⋅ c1 ,10 with b >
1. If the report is unbiased, then b=1. If the manager reports truthfully, he receives no slack and his
corresponding utility is zero. This represents the lower bound of a report of a rational manager.
Whenever b>1, the manager overstates real costs. He builds slack and his utility is positive. The objective of manager 1 is assumed to be maximizing slack.
9
See e.g. Schiff/Lewin (1970).
Linear biasing functions are widely accepted in the literature. See e.g. Ewert/Wagenhofer (2012), 11ff, for
important arguments in favour of this assumption. A linear function, which additionally considers a fixed term,
e.g. ĉ1 ( c1 ) = β + b ⋅ c1 , would not change the qualitative results of the analysis.
10
6
Following this objective, manager 1 fixes b in a way that given his observation of the true costs c1 the
difference between the biased and unbiased cost budget is maximized. Hereby, manager 1 has also
to consider his production choice of output. As the demand function is common knowledge, the
quantity x1 has to be in line with the reported costs. Otherwise, the biased cost report is revealed.
Additionally, the manager has also to consider the impact of his decision on the price q of the input
resource set by the supplier. So division manager 1 maximizes slack s by maximizing the following
expression with respect to b:
s = cˆ1( b,c1 ) ⋅ x1( q( cˆ1( b,c1 )),cˆ1( b,c1 )) − c1 ⋅ x1( q( cˆ1( b,c1 )),cˆ1( b,c1 ))
It is common knowledge that the reporting strategy of the manager is linear in b. However, the manager’s choice of b itself is assumed to be not observable. The manager observes the true costs c1 before making the report. So he can use this information when fixing the optimal bias level b to maximize slack. To simplify the analysis, we assume that the costs of division 2 are deterministic. Its manager has no opportunity of building up slack by biasing reports and ĉ2 ( c2 ) = c2 .
The principal faces the typical benefits and costs of participative budgeting described in the literature:11 The budget may build on the better information of managers involved in the budgeting process. Though, this comes at the costs of a possible biased information and slack building behavior.
Hence, the principal has to decide whether to use top down budgeting not making use of the information of the better informed managers or implementing participative budgeting. Here, the principal
runs the risk of bearing the costs of slack. The budgeting literature sees slack as the major obstacle of
using participative budgeting.
The time line of events of the setting analyzed is as follows:
t=1:
The principal decides whether to use top down or participative budgeting.
t=2:
If top down budgeting is used: the principal fixes the cost budgets per unit for each division based on
his expectation of the costs.
If participative budgeting is implemented: The manager of division 1 observes the true production
costs c1 and reports costs per unit of ĉ1( c1 ) . Manager 2 reports costs ĉ2 ( c2 ) = c2 . The principal
provides a cost budget based on these reports.
t=3:
The supplier fixes the price q for the input resource.
t=4:
If top down budgeting is used: The principal fixes production quantity and prices for both divisions.
If participative budgeting is implemented: The divisional managers fix production quantities and prices for their respective product.
The products are sold and profits realize for both budgeting regimes.
11
See e.g. Atkinson/Kaplan/Matsumura/Young (2007), p. 489f.
7
The problem to find the most beneficial budgeting regime for the principal has to be solved by backward induction. The solution concept is SPNE. For convenience, we separate the analysis of the
budgeting regimes to give a better illustration of each case. At the end, we compare the expected
profits of each regime and argue which one is more beneficial for the principal.
Top down budgeting:
At the final stage (t=4) the principal fixes production quantities of both divisions to maximize total
expected firm profit π, which is the sum of the expected divisional profits π1 and π2. This decision is
based on the expected production costs of division 1, E(c1) and contingent upon the price of the input resource to be set by the supplier at stage t=3. As the distribution of c1 is common knowledge,
the supplier sets the price for the resource to be delivered to the firm based on E(c1) and the reaction
functions of stage 4 (quantity decisions of the principal). Stage 2 has only to be considered in the
participative budgeting setting. So we proceed to stage 1. Given the price of the input resource, the
equilibrium output quantities and corresponding expected profits can be calculated if top down
budgeting is used.
Observation 1:
If the principal implements top down budgeting, the equilibrium output quantities are12
•
•
1
*
x1*,TD ( qTD
) = ⋅ ( 3a1 − a2 − 3E( c1 ) + c2 ) for division 1 and
8
1
*
x*2 ,TD ( qTD
) = ⋅ ( 3a2 − a1 − 3c2 + E( c1 )) for division 2.
8
The supplier fixes the price for the input resource to be delivered to the firm with
•
*
qTD
=
1
⋅ ( a1 + a2 − E( c1 ) − c2 ) .
4
The firm expects to earn a profit of
•
*
*
*
*
*
*
π TD
( x1*,TD ( qTD
),x*2 ,TD ( qTD
),qTD
) = x1*,TD ( qTD
)2 + x*2 ,TD ( qTD
)2 ,
where the first term in the sum is the expected profit provided by division 1 and the second
term the expected profit earned by division 2.13
Observation 1 describes the benchmark solution for the principal. It states the expected profit of the
firm achievable without participation of the divisional managers in the budgeting process. Participa-
12
The index “*” characterizes the equilibrium solution, the index TD the top down budgeting regime.
It is highlighted that this is the expected profit of the principal at stage 1. To improve readability, the operator E(.) is suppressed here and later on.
13
8
tive budgeting is therefore only beneficial for the principal if the expected profit is at least as high as
when top down budgeting is used.
Participative Budgeting:
Compared to top down budgeting, we have to consider additionally stage t=2 of the time line. Now
the principal asks the managers for reports. Manager 1 observes the true costs c1 of producing one
unit of output x1 in division 1 before reporting. He uses this information for preparing the cost report
ĉ1( c1 ) . Given the cost information, he decides whether and to what extent to overstate the true
costs in the report. This is reflected by his objective of maximizing slack when choosing the bias level
b. Contrary to the top down budgeting setting, the divisional managers make the production quantity
decision at stage 4.
Again the equilibrium solution is derived by backward induction. At the last stage, the divisional
managers make their output quantity decisions conditional upon the price of the input resource set
by the supplier at stage 3 and upon the cost reports ĉ1 and ĉ2 made by the managers at stage 2.
Given the reaction functions of stage 4, the supplier fixes the price for the input resource at stage 3
conditional depending on the cost reports ĉ1 and ĉ2 of stage 2. Given the reaction functions of stage
3 and 4 the managers chose the cost reports at stage 2. As the true costs of division 2 are common
knowledge, we simplify the following notation by setting ĉ2 =c2. Manager 1 privately observes the
true costs c1 and selects the bias level b to maximize slack. Based on b he reports costs ĉ1 = b ⋅ c1 .
Given all decisions of stages 2 to 4, the equilibrium quantities, equilibrium price of the input factor,
the equilibrium bias level and the resulting expected profit for the principal can be derived. The resulting equilibrium solution for the participative budgeting mechanism is described in observation 2.
Observation 2:
If the principal implements participative budgeting the equilibrium output quantities are14
•
•
1
⋅ ( 3a1 − a2 − 3c1 + c2 ) in division 1 and
16
1
x*2 ,PB ( q*PB ( cˆ1* )) = ⋅ ( 17 a2 − 3a1 − 17c2 + 3c1 ) in division 2.
48
x1*,PB ( q*PB ( cˆ1* )) =
The supplier charges an equilibrium price for the input resource of
•
q*PB ( cˆ1* ) =
1
⋅ ( 3a1 + 7 a2 − 3c1 − 7c2 ) .
24
The slack maximizing bias for the manager and the resulting reported costs in equilibrium are
•
14
b* ( c1 ) =
3a1 − a2 + 3c1 + c2
1
and ĉ1* ( b* ,c1 ) = ⋅ ( 3a1 − a2 + 3c1 + c2 ) .
6
6c1
The index “PB” characterizes the participative budgeting regime.
9
The resulting expected profit of the firm is
•
π *PB ( x1*,PB ( q*PB ( cˆ1* ),x*2 ,PB ( q*PB ( cˆ1* )) = x1*,PB ( q*PB ( cˆ1* ))2 + x*2 ,PB ( q*PB ( cˆ1* ))2 ,
where the first term in the sum is the expected profit provided by division 1 and the second
term the expected profit earned by division 2.15
A closer look on the characteristics of b*(c1) at stage 2 shows the following:
For every feasible solution the manager overstates true costs, that is b*(c1)>1 is true for all x1,PB >0.
1
3
the function b*(c1) shows that b*(c1)=1 if x1,PB =0 and b*(c1)>1 if x1,PB >0. So the manager always
For x1,PB >0 to be true, the condition c1 < ( 3a1 − a2 + c2 ) must hold. Inserting the condition into
overstates the true costs in his cost report ĉ1 if production in division 1 is profitable and output is
nonnegative.
Inspection of the first derivative of b*(c1) with respect to c1 shows that b*(c1) is a concave function.
b*(c1) is decreasing in c1 if x1,PB >0. This demonstrates that the lower the true costs of production are
the more the manager overstates the reported costs. The resulting cost report ĉ1 is linear increasing
in the costs c1: b* ( c1 ) ⋅ c1 =
1
⋅ ( 3a1 − a2 + 3c1 + c2 ) .
6
The following graphs illustrate these findings based on a numerical example (for a1=110, a2=170 and
c2=50). Given this parameter setting, x1 is positive if c1<70.
Exhibit 1: Optimal equilibrium reporting bias for varying c1
15
It is highlighted that this is the expected profit of the principal at stage 1. To improve readability, the operator E(.) is suppressed here and later on.
10
Exhibit 1 shows that b* is larger than 1 and decreasing in c1. The optimal reporting bias of the manager reaches 1 (truthful reporting) as the production quantity x1 of his division becomes zero.
Exhibit 2 shows that given that manager 1 follows his optimal biasing strategy the resulting costs
reported to the principal are linear increasing in c1.
Exhibit 2: Costs reported based on the optimal equilibrium reporting bias for varying c1
Choice of budgeting regime
At stage 1 the principal has to decide whether to implement the top down or the participative budgeting regime. At this stage the principal has no other information about c1 than the ex ante expected
costs per unit E(c1). Only this cost information is common knowledge, whereas the knowledge of the
true costs c1 is private information of manager 1. Additionally, the information of the reporting strategy is common knowledge and the (unobservable) optimal bias level b*(c1) based on this strategy
* *
leads to a linear biased cost function ĉ1 ( b ,c1 ) . The principal can make use of this knowledge and
*
*
derive the corresponding expected biased cost report ĉ1 ( E( c1 )) = b ( E( c1 )) ⋅ E( c1 ) . Based on this
information, the principal is able to compare expected profits of both regimes. He prefers participative budgeting if
*
*
*
*
π *PB ( x1*,PB ( q*PB ( cˆ1* ( E( c1 )))),x*2 ,PB ( q*PB ( cˆ1* ( E( c1 )))) > π TD
( x1*,TD ( qTD
),x*2 ,TD ( qTD
),qTD
)
and vice versa.
Proposition 1
Expected profit of participative budgeting exceeds expected profit of top down budgeting if the following condition holds:
11
1
1
⋅ ( 45a1 − 31a2 + 31c2 ) ≤ E( c1 ) ≤ ( 3a1 − a2 + c2 ) 16
45
3
Otherwise the principal prefers top down budgeting. Proposition 1 states that the principal prefers
bottom up budgeting if the expected production costs E(c1) are in an intermediate range. For low and
high expected production costs, the principal prefers top down budgeting.
The total difference of expected profits between participative budgeting and top down budgeting is
given by:
*
π *PB − π TD
=−
1
⋅ [( 45 ⋅ ( a1 − E( c1 )) − 31 ⋅ ( a2 − c2 )) ⋅ ( 3 ⋅ (( a1 − E( c1 )) − ( a2 − c2 ))] .
1152
This difference is positive if the two multipliers in the brackets have different signs. This is only the
case if E(c1) is between the bounds stated in proposition 1. If E(c1) is smaller than a1 −
31
⋅ ( a2 − c2 ) ,
45
then the first and the second multiplier in brackets are negative. As there is a negative sign at the
beginning of the term, the entire difference is negative. If E(c1) is larger than a1 −
31
⋅ ( a2 − c2 ) , but
45
1
3
smaller than a1 − ⋅ ( a2 − c2 ) , then the first term in brackets is positive, the second negative. In
total, due to the negative sign at the beginning, the difference is positive. If E(c1) is larger than
1
a1 − ⋅ ( a2 − c2 ) , both terms in brackets become positive and the total difference becomes nega3
tive. Thus, the difference in expected profits is only positive, whenever E(c1) is between the bounds
shown in proposition 1. In this case, participative budgeting is more beneficial than top down budgeting.
The economic intuition of this finding is as follows: To switch from top town to participative budgeting, the profitability of the market, in which division 2 operates, must reach a minimum level represented by the lower bound. The lower bound can be rewritten as
31
( a2 − c2 ) > ( a1 − E( c1 )) . The
45
benefit of participative budgeting is to increase product costs in division 1 to influence the output of
division 2. Inspection of the equilibrium output functions stated in observation 2 shows that increasing costs of product 1 lead to decreasing output of product 1, but also to an increasing output of
product 2. This effect is only beneficial for the principal if the relative profitability of product market
2 compared to product market 1 is large enough. However, there is also a floor on inflating the costs
of product 1. If the relative profitability of product market 1 gets too small [i.e.
a2 − c2 > 3( a1 − E( c1 )) ], then it is not profitable to produce product 1 anymore. In this case, the
shift in production quantities stops and there is no further benefit of increasing the product costs of
division 1. This defines the upper bound stated in proposition 1. The selling price of the input resource is a major driving force of the trade-off described above. This is discussed later.
Exhibit 3 highlights the finding of proposition 1. It shows that for low values of E(c1), top town budgeting is preferred. Reaching the lower bound the decision of the principal switches to participative
16
The lower bound is smaller than the upper bound if c2<a2. This is always true.
12
budgeting. Reaching the upper bound the decision switches again and the principal prefers top down
budgeting again. Given the same parameter setting as above (a1=110, a2=170 and c2=50), proposition
1 predicts that participative budgeting is preferred if 27,33 < E(c1) < 70. The following graph illustrates this finding: Varying E(c1) shows that participative budgeting leads to a higher expected firm
profit only if E(c1) ∈ [27,33 , 70].
Exhibit 3: Illustration of expected profit differences in equilibrium for varying E(c1)
In equilibrium the profit for the with participative budgeting is higher compared to top down budgeting despite the manager builds slack. Remind that the slack increases the real costs of the firm. Exhibit 4 illustrates that the manager builds and consumes slack in the range of E(c1), where participative
budgeting is more profitable than top down budgeting.
Exhibit 4: Slack of manager in equlibrium
13
The important driver for the relative advantage of participative budgeting is the impact of slack on
the sourcing costs q. Slack increases real production costs of the firm, decreases the supply of x1 and
the expected profit of division 1. Slack has therefore negative consequences on the expected firm
profit. Nevertheless, slack has also a beneficial effect due to the common sourcing of the input factor
needed for both products. Increasing costs for producing one unit of product 1 decreases demand for
the input resource provided by the supplier. As a consequence, the supplier asks for a lower price to
increase demand. Product 1 as well as product 2 benefit from this discount. Product costs decrease
and product quantities increase. The reaction functions of stage 3 and 4 document these effects: The
first order condition of the profit function of the supplier πS,PB with respect to the price of the input
resource qPB shows that q decreases if the reported costs increase. The output reaction functions of
stage 4 show that a decrease of the price of the input resource causes an increase of the output
quantities of product 1 as well as product 2. As argued above, while the total effect on the expected
profit of division 1 is negative, it is positive on the profit of division 2. As a result, the impact on total
expected firm profit may therefore be negative or positive depending on the value of E(c1).
Exhibit 5 (based on the same parameter setting as given above) shows this impact of participative
budgeting on the equilibrium price of the input resource. The supplier charges a lower price whenever participative budgeting is used for a given E(c1).
Exhibit 5: Equilibrium prices of supplier for varying E(c1)
To make use of the strategic effect the commitment of the principal to stick to the cost report is important. The principal has to offer a cost budget based on the cost report of the manager. Although
the principal knows that the manager overstates the production costs, the expected profit of the firm
sticking to the cost report is higher (given that the expected product costs are within the range stated in proposition 1). A revelation mechanism to learn the true costs would destroy the effect on the
price setting behavior of the seller of the input resource. It is also important to delegate the production decision to the manager, because he has no incentive to deviate from the optimal output decision based on his reported costs. The overall participation - on the one hand in the budgeting process
and on the other hand in the delegation of decisions - guarantees the strategic effect. As participa14
tion is required in different stages, it could be also seen as a participative culture of the firm which is
also observable by outside market participants.
4. Conclusion
The paper shows that slack is not always a negative aspect of participative budgeting. The common
view in the literature is that participative budgeting may be useful for the principal to elicit information from better informed managers. Participative budgeting may also increase the motivation of
the managers involved. However, these positive effects come at the costs that the better informed
managers have incentives to bias their reports and to build slack. Depending on the setting, either
the benefits or the costs overweigh. That is why both types of budgeting mechanisms, top down as
well as bottom up, are observed in corporate practice. But for empirical research, it is difficult to
capture the benefits of participative budgeting. Regarding whether participative budgeting is beneficial the findings are mixed. Shields and Shields (1998) suppose that the mixed results may be caused
by incomplete theoretical models describing the benefits of participative budgeting.
Budgeting has to serve many different objectives and is used in varying settings in corporate practice.
Therefore, it does not seem possible to integrate all important aspects in one integrative model. To
our view, it is therefore fruitful to add aspects so far neglected in literature, especially in analytical
research. We do this by adding market effects outside the firm. This does not only add one driver
which has been neglected so far in the literature, but also broadens the view of the existing literature. The existing models only focus on the effects of budgeting inside a firm and do not consider
possible effects on other market participants outside the firm. We find that an analysis neglecting the
market impact of budgeting may miss important effects and may derive misleading recommendations with respect to which mechanism should be preferred.
We show that the commitment to participative budgeting may have an impact on prices of the input
market. Despite participative budgeting induces the manager to overstate the costs reported in the
budgeting process (i.e. to build and consume slack), participative budgeting may be beneficial for a
firm, because of its possible decreasing effect on the price for an input resource. This may be true
even if slack causes higher real costs for the firm.
There is evidence that firms allow for slack in corporate practice. For Dutch listed companies De
With/Dijkman (2008) finds that a large fraction of the firms analyzed allows for slack sometimes (and
a small fraction of firms even regularly). This happens despite the observation that management
would be able to detect slack in many cases.17
The setting analyzed in the paper could also be addressed by empirical research. Important characteristics of the setting are the type of input market, the reputation of a firm being authoritative or
participative, and a differing relative profitability of the divisions. This information is accessible to
some extent from outside the firm (and at least accessible to the same extent as other aspects of
budgeting within the firm).
17
See De With/Dijkman (2008), p. 32.
15
Appendix
Proof of Observation 1:
At stage 4 the principal makes the output decision in order to maximize expected overall profit:
π TD = π 1,TD + π 2 ,TD = ( p1,TD − E( c1 ) − qTD ) ⋅ x1,TD ( qTD ) + ( p2 ,TD − c2 − qTD ) ⋅ x2 ,TD ( qTD )
Calculating the first derivatives of πTD with respect to x1,TD and x2,TD, setting both derivatives equal to
zero and solving for x1,TD and x2,TD leads to:
1
x1,TD ( qTD ) = ( a1 − E( c1 ) − qTD )
2
1
x2 ,TD ( qTD ) = ( a2 − c2 − qTD )
2
At stage 3 the supplier fixes the price for the input resource to maximize profit πS. Inserting the reaction functions of stage 4 leads to
π S ,TD = qTD ⋅ ( x1,TD ( qTD ) + x2 ,TD ( qTD ))
Setting the first derivative of πS with respect to qTD equal to zero and solving for qTD characterizes the
*
profit maximizing price of the input resource qTD :
1
*
qTD
= ( a1 + a2 − E( c1 ) − c2 )
4
*
Inserting qTD into the functions derived at stage 4 gives the profit maximizing output quantities
1
*
x1*,TD ( qTD
) = ( 3a1 − a2 − 3E( c1 ) + c2 )
8
1
*
x*2 ,TD ( qTD
) = ( 3a2 − a1 − 3c2 + E( c1 ))
8
Inserting the results into the profit function of the firm shows the expected profit of the firm if top
down budgeting is used:
*
*
*
*
π TD
( x1*,TD ( qTD
),x*2 ,TD ( qTD
),qTD
)=
1
1
( 3a1 − a2 − 3E( c1 ) + c2 )2 + ( 3a2 − a1 − 3c2 + E( c1 ))2 =
64
64
*
*
= x1*,TD ( qTD
)2 + x*2 ,TD ( qTD
)2
q.e.d.
16
Proof of Observation 2:
At stage 4 the divisional managers make the output quantity decisions in order to maximize divisional
profit
π1,PB = ( p1,PB − cˆ1 − qPB ( cˆ1 )) ⋅ x1,PB ( qPB ( cˆ1 ))
π 2 ,PB = p2 ,PB − c2 − qPB ( cˆ1 )) ⋅ x2 ,PB ( qPB ( cˆ1 ))
The first order conditions of π1,PB and π2,PB with respect to x1,PB and x2,PB lead to:
1
x1,PB ( qPB ( cˆ1 )) = ( a1 − cˆ1 − qPB ( cˆ1 ))
2
1
x2 ,PB ( qPB ( cˆ1 )) = ( a2 − c2 − qPB ( cˆ1 ))
2
At stage 3 the pricing decision of the supplier maximizes his profit
π S ,PB = qPB ( cˆ1 ) ⋅ ( x1,PB ( qPB ( cˆ1 )) + x2 ,PB ( qPB ( cˆ1 )))
The first order condition shows the following result:
1
qPB ( cˆ1 ) = ( a1 + a2 − cˆ1 − c2 )
4
At stage 2 the manager of division 1 observes the true production costs c1 and chooses the cost report ĉ1 = b ⋅ c1 to maximize his slack s. s is the difference between the costs provided by the cost
budget of the principal given the production at reported costs and true costs. Because the demand
function at stage 4 is common knowledge, manager 1 has to make a quantity decision which is in line
with this demand function. Otherwise not truthful reporting would be revealed. Given this restriction, fixing the bias level has to be based on the corresponding biased output quantity:
s = cˆ1 ⋅ x1,PB ( qPB ( cˆ1 )) − c1 ⋅ x1,PB ( qPB ( cˆ1 ))
Inserting ĉ1 = b ⋅ c1 , calculating the first derivative of s with respect to b, setting the derivative equal
to zero and solving for b gives the optimal bias level b*(c1) of manager 1:
b* ( c1 ) =
3a1 − a2 + 3c1 + c2
6c1
and the slack maximizing cost report of manager 1: ĉ1* = b* ( c1 ) ⋅ c1 =
1
( 3a1 − a2 + 3c1 + c2 )
6
Note that manager 1 observes true costs before reporting. The costs reported are not only reported
to the principal but also revealed to the supplier when the sourcing decision is made (stage 3). There
is no incentive for the manager to reveal true costs at a later stage, because this would decrease his
slack.
17
Inserting the equilibrium solution of stage 2 into the reaction function of the supplier at stage 3 gives
the profit maximizing price of the input resource for the supplier:
q*PB ( cˆ1* ) =
1
( 3a1 + 7 a2 − 3c1 − 7c2 )
24
Inserting the equilibrium outcomes of stage 2 and stage 3 into the reaction functions of stage 4
shows the output chosen by the managers:
x1*,PB ( q*PB ( cˆ1* )) =
1
( 3a1 − a2 − 3c1 + c2 )
16
x*2 ,PB ( q*PB ( cˆ1* )) =
1
( 17 a2 − 3a1 + 3c1 − 17c2 )
48
Inserting the equilibrium outcomes into the divisional profit functions shows the resulting divisional
profits and overall firm profit:
π1*,PB =
1
( 3a1 − a2 − 3c1 + c2 )2 = x1*,PB ( q*PB ( cˆ1* ))2
256
π *2 ,PB =
1
( 17 a2 − 3a1 + 3c1 − 17c2 )2 = x*2 ,PB ( q*PB ( cˆ1* ))2
2304
π *PB = x1*,PB ( q*PB ( cˆ1* ))2 + x*2 ,PB ( q*PB ( cˆ1* ))2
q.e.d.
Proof of Proposition 1:
At stage 1 the principal has only information about the expected production costs in division 1, E(c1),
and he knows the equilibrium biasing strategy of manager 1. So the principal can derive the corresponding cost report for E(c1), that is ĉ1* ( E( c1 )) = b* ( E( c1 )) ⋅ E( c1 ) =
1
( 3a1 − a2 + 3E( c1 ) + c2 ) .
6
*
*
Inserting ĉ1 ( E( c1 )) into the profit function π PB leads to
π *PB ( c1 = E( c1 )) =
1
1
( 3a1 − a2 − 3E( c1 ) + c2 )2 +
( 17 a2 − 3a1 + 3E( c1 ) − 17c2 )2
256
2304
*
*
Setting π PB ( c1 = E( c1 )) = π TD and solving for E(c1) gives two results:
E( c1 ) =
1
1
⋅ ( 45a1 − 31a2 + 31c2 ) and E( c1 ) = ( 3a1 − a2 + c2 )
45
3
18
Inspection shows that
1
1
⋅ ( 45a1 − 31a2 + 31c2 ) < ( 3a1 − a2 + c2 ) if c2 < a2, which is always true.
45
3
Inspection of profits show that participative budgeting leads to a higher expected profit than top
down budgeting if E(c1) is in the range of the two bounds.
q.e.d.
19
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