Using different Budgeting Procedures to Coordinate Principal/Agent-Relationships
Christian Hofmann
∗University of Hanover, Germany
Abstract
Budgeting mechanisms assist the directors of a firm to restrict managerial discretion and, therefore, to mitigate the firm’s agency problems. By using flexible budgets, the director allows the manager to efficiently adapt his actions to changing economic conditions. Al- ternatively, rigid budgets result in a more extensive restriction of the manager’s actions.
Although rigid budgets reduce the manager’s flexibility to react to changing economic conditions and, hence, result in worse production decisions, they restrict the manager’s action space and, thus, are easier to implement. Therefore, depending on informational and production-related conditions, rigid budgets may well outperform flexible budgets.
In this paper, we analyze a moral hazard problem resulting from a combined hid- den action and hidden information situation. The agency problem is formulated with the assumptions of the LEN-model. Communication is not considered, i.e. we analyze authoritative budgeting procedures. For several budgeting procedures we determine sec- ond best compensation schemes, show the conditions where flexible or rigid budgets are efficient, and determine the incremental benefits of resource-oriented budgets.
Key words: moral hazard, LEN-model, resource-oriented budgets, incentive schemes JEL-Classification: D24, D82, M40
∗Prof. Dr. Christian Hofmann, Chair for Managerial Accounting, University of Hanover, K¨onigsworther Platz 1, 30167 Hanover, Germany. hofmann@controlling.uni-hannover.de
Helpful comments by the editor, two anonymous reviewers, Peter O. Christensen, Gerald A. Feltham, Michael Krapp, Heike Schenk-Mathes, and workshop participants at the University of British Columbia, University of Cemnitz, University of Mannheim, and University of Munich are gratefully acknowledged.
First Draft: February 10, 1999; Current Draft: June 4, 2002 forthcoming: Schmalenbach Business Review
Using different Budgeting Procedures to Coordinate Principal-Agent Relationships
1 Introduction
In this paper we consider the use of budgeting mechanisms for incentive purposes. The analysis is based on the observation that budgets restrict the manager’s action space.
From an incentive point of view this may result in lower agency costs. Especially, we focus on the use ofresource-oriented budgetswhere the director of a firm allocates physical resources like machinery, tools, or personell to the manager. Despite the extensive use of resource-oriented budgets in practice, agency theory mostly focuses on target-oriented budgets, where the budget serves as a target in the incentive scheme. The purpose of the paper is to identify tradeoffs between observed budgeting practices, and to understand the consequences of the budgeting procedures w.r.t. managerial decision making and the expected result to the firm.
Two research questions are of interest when considering resource-oriented budgets.
The first addresses the type of budget used, i.e. the degree to which the manager’s action space is restricted through flexible or rigid budgets. The second question refers to the incremental benefits of reducing the manager’s action space by means of resource-oriented budgets. The analysis shows that even for ex ante uncertain economic conditions flexible budgets are not always efficient. Rather, the economic conditions must be sufficiently different in order to justify the use of flexible budgets. We find that flexible budgets are not efficient in case of a small informational advantage of the manager, and when considering the management of a product in rather uncertain environmental conditions.
Regarding the incremental benefits, we find resource-oriented budgets to be of relevance especially when the manager has substantial pre-decision information.
In section 2 we describe the budgeting process and it’s impact on the agency-problem.
Section 3 presents the problem considered and solves it for an exclusive application of incentive schemes. Next, the different budgeting mechanisms are formulated and solved for in section 4. Section 5 shows the conditions for efficiently applying rigid and flexible budgets, and the incremental benefits from extending incentive schemes with resource- oriented budgets. Section 6 summarizes the findings, presents empirical implications of the analysis, and gives some conclusions.
2 General Framework of applying Resource-oriented Budgets
2.1 Impact of Budgets on the Agency-Problem
Agency-problems within firms follow from divergent preferences and information asym- metry2. An example refers to the relation between the director of a firm and the work averse manager of a cost center, whose decisions are unobservable to the director.3 In addition to incentive contracts, the director may restrict the manager’s action space by rationing certain resources available to him. We argue that reducing managerial action space by means of resource-oriented budgets can be useful in disciplining managers and, thus, may result in lower agency costs4.
Physical and monetary budgets are common techniques for restricting the action space and examples for resource-oriented budgets. Physical budgets refer to personell, machines, software, etc., while monetary budgets are often used for decentralized investment pro- cesses, where a certain amount of money is allocated to the manager. The fundamental difference, however, is that the ”rights allocated through ... physical budgets are less complete and therefore more constraining than are decision rights allocated by grant of monetary budgets.”5 Therefore, physical budgets are more effective in mitigating the firm’s agency problems.6
By using the physical or monetary resources the manager is expected tominimize the operating costs of his cost center. In addition, the director may prescribe specific results (performance standards) that are expected from the manager.7 If e.g. the manager is responsible for the maintenance of the firm’s machinery, the director expects a specific availability of the machinery, determines the necessary specialized workers, the appro- priate tools, and equipment available for the repair process, and allocates them to the manager. Further examples refer to maximizing the yield of a process while guaranteeing a specific product quality, and to minimize operating costs while performing well defined elements of a consulting job. Due to the limited capabilities of personell and tools, i.e. the non-complete rights of physical budgets, the director limits the manager’s decisions that
2SeeGrossman/Hart (1983).
3The subsequent results can easily be transferred to profit or revenue centers.
4SeeZhang (1997, p. 738).
5Jensen/Meckling (1992, p. 266).
6When budgets are included in incentive schemes, the ”term budget refers to a target level of sales, costs, or profits.” Magee (1986, p. 286)Suchtarget-oriented budgets, however, merely refine the incentive scheme and do not restrict the agent’s action space.
7See e.g. theOverhead-Value-Analysis(Neuman (1975)) and theZero-Base-Budgeting(Meyer-Piening (1990)).
are consistent with the performance standard. Hence, the standards’ role is to implicitly restrict managerial action space. In addition, the standards can be used to coordinate the prescribed results of the firm’s different responsibility centers. If we assume that any deviation leads to a dramatic coordination failure, the directors will be highly interested in the standards being realized.8
The restriction of the action space comes at a cost when it also limits the manager’s ability to adapt his decisions to changing environmental conditions. This is especially of relevance when the manager, e.g. while preparing the maintenance activities, privately observes information relevant for reducing the operating costs. Then, a restrictive resource allocation through rigid budgets may prevent an efficient cost reduction by the manager.
In contrast, flexible budgets allow diverse reactions to changing economic conditions.
Therefore, the fundamentaltradeoff considered subsequently refers to the two-sided influ- ence of the manager’s action space on the firm’s agency costs and the potentially state dependent decisions by the manager.
2.2 Characterization of the Budgeting Process
The budgeting process under study can be described as follows: First of all, the director (principal) allocates resourcesR to the manager (agent), and asks him to supply effort a in order to achieve a (nonfinancial) performance standardy∗while minimizing the center’s operating costs. The target y∗ is coordinated with the targets of further responsibility centers. In order to simplify the analysis we assume that due to a dramatic coordination failure, y 6= y∗ results in a tremendous loss to the principal; i.e. the expected return is E[π(y6=y∗, a)] = −∞,∀a. Furthermore, the principal’s expected gross result is supposed to increase with the agent’s effort level, i.e. E[π(y∗, a2)] > E[π(y∗, a1)] for a2 > a1. To summarize, the principal’s expected gross result E[π(y, a)] depends on the outcome of the predetermined standard y∗ (availability of the machinery) and the unobservable managerial effort a (operating cost reduction).
Referring to the production of y and the minimization of operating costs, we assume two different technologies to exist. We suppose the agent’s effort to jointly influence the outcome of y and the expected operating costs. In general, the production of y depends on the allocated resourcesR and the agent’s effort a, i.e.
y=g(R, a). (1)
8Further examples for extreme consequences of a coordination failure refer to interdependent processes requiring well defined results like the relation of a material’s loading capacity and its use in technical facilities, the compatibility of certain substances in chemical processes, and the combination of different software procedures.
Assuming a deterministic production function g, the manager can always meet the pre- specified standards y∗ with certainty.9 Because of the constraining nature of physical budgets we assume that for a given endowment of resources the desired outcome y∗ can only be produced for discrete effort levelsai. Therefore, by allocating resources R to the agent and choosing a standard y∗ the principal implicitly prescribes the potential effort levels of the agent.
Example. The resources R consist of a monetary budget of 20 u (units) and two workers A and B.y∗ is described by two propertiesP1 and P2. The agent can assign the workers to two different tasks 1 and 2, resulting in a specific outcome of the standard’s properties while partly consuming the monetary budget. The workers’ capabilities w.r.t.
the properties P1 and P2 depend on the tasks they are assigned to:
worker\ task 1 2
A 100% of P1 @ 10 u 50% ofP2 @ 8 u B 50% ofP1 @ 8 u 100% ofP2 @ 10 u
Each worker can only be assigned to one task. If worker A is assigned to task 1 he provides 100% of P1 and spends 10 u of the monetary budget. The standard y∗ is achieved only if both properties are at 100%. The following table describes the relevant alternatives for assigning workers to tasks.
task 1 2 deficit of the remaining managerial
\ performance standard monetary effort
alternative P1 P2 budget
I A B 0 0 0 u a= 0
II B A 50% 50% 4 u a= 1
Alternative I shows the solution where the two workers completely fulfill the perfor- mance standard. If the workers do not provide the complete properties ofy∗ (alternative II), the agent has to step in and has to supply an effort level that makes up for the dif- ference. We normalize the agent’s effort such that for alternative II the necessary level is a(50% of P1 and 50% ofP2) = 1.10 Since the agent’s effort also requires the monetary budget (travelling expenses, necessary tools, etc.),ais restricted by the remaining budget.
We assume the characteristics of the resources to be such that the remaining monetary
9Moreover, a deterministic function is necessary in order to avoid the dramatic coordination failure in case ofy6=y∗.
10More specifically, for each property the agent must supply a normalized effort of .5. If the agent’s disutility follows from the total effort spent, we can sum up to the total efforta= 1.
budget (4 u) is just sufficient for the manager to supply the missing parts of the target (a= 1).
For diminishing marginal returns of a w.r.t. y the agent must always assign the workers to specific tasks. Moreover, assigning both workers to a single task is not a feasible solution, since the remaining monetary budget (20 u) is not sufficient for the then necessary effort (a = 1). Therefore, in order to achieve the standard y∗, the agent must choose between the two alternatives I and II. These we, interpret that he either just coordinates and directs the available resources (a = 0), or that he additionally supplies his expertise, partly carries out certain tasks by himself and re-assigns the workers to the tasks (a= 1). Thus, the setting corresponds with theJensen/Meckling (1992)’sstatement regarding the non-complete rights of physical budgets.
To summarize, the allocation of resources R and the specification of a performance standard y∗ implicitly determine a set of discrete effort levels aRB ={0,1}. By changing the workers’ capabilities the principal may vary the set of effort levels that are consistent with y∗. For a worker B0 with capabilities 40% of P1 @ 7 u in task 1 and everything else equivalent, the set of effort levels changes to aRB = {0,1.1}. Here, the remaining monetary budget (5 u) is just sufficient in order to supply the necessary effort level (a= 1.1). Discrete sets with more than one positive effort level can be obtained, e.g., by allocating 3 (part-time) workers with specific capabilities to the agent.
The described budgeting process shows one typical complaint of budgeting mecha- nisms, i.e. managers are merely using their resources to just meet minimum requirements (a= 0)11. For the described setting, the principal’s expected return can be increased by combining resource-oriented budgets with incentive schemes which motivate the agent to choose an appropriate effort level within his action space (a= 1). In general, a may well depend on private signals ξ observed before choosing the effort. Because of the predeci- sion information, the principal may be tempted to use a direct revelation mechanism to learn the agent’s information. In the paper, however, we considerauthoritative budgeting procedures, i.e. we assume communication to be prohibitively costly. This may follow either from the technical nature of the agent’s private information12 or when considering responsibility centers in foreign countries. Therefore, the principal is not able to use the agent’s superior information when deciding about the resources that are to be allocated.
Moreover, due to the different nature of the elements of π, we suppose that any informa- tion privately observed by the agent does not influence the realization of the prescribed target.
Observable variables useful for contracting include the outcome y, the resources R
11See e.g. Albach (1967, p. 352);Fieten (1977, p. 77).
12See e.g. Melumad et al. (1992, p. 477).
allocated to the agent, and the elements of the principal’s total return π(y, a)≡π˜A(a) + πB(y(R, a))−c(R). For the sake of simplicity we assume the firm’s accounting system to be able to eliminate the result πB(y) of providing y, and the resource costs c(R) from the total return. In total, the two signals y(R, a) and ˜πA(a) can be used as (noisy) measures of the agent’s effort. Since the allocated resources aim at restricting the agent’s provision of y∗, we suppose R to not influence the stochastic production function ˜πA. In order to simplify the analysis and to focus on the incentive related effects of resource- oriented budgets, we additionally assume the resource costsc(R) to be independent of the budgeting mechanism under study, i.e. independent of the allocated resources13. Thus, we focus on the incentive related effects of resource-oriented budgets, i.e. the benefits of reducing the agent’s action space.
Fundamentally, the described setting represents a single task principal/agent-relation (a) with multiple performance measures (˜πA, y). Therefore, alternatives to using budget- ing mechanisms exist. Specifically, the refers to incentive schemes without any restrictions of the action space. In section 3.2 we present the principal’s problem when solely using incentive schemes and compare its result with the results of the budgeting procedures in order to determine the incremental benefits of restricting action space by means of resource-oriented budgets.
The restricting nature of the budgeting mechanism under study highly depends on the availability of workers with specific capabilities. Subsequently, we assume full flexi- bility w.r.t. the available resources, i.e. the principal can implicitly determine any set of discrete effort levels by appropriately allocating resourcesR and prescribing performance standardsy∗. In general, the diversity of available resources is an empirical question. For a less than full flexibility, however, the subsequent analysis provides a benchmark regarding the maximum benefits of restricting managerial action space by means of resource-oriented budgets. Because of the full flexibility assumption, comparing different budgeting proce- dures reduces to comparing different sets of effort levels.
2.3 Literature Review
There are at least three streams of relevant literature. The first is the analysis of the risk reduction/effort motivation problem in a principal/agent-relation with multiple perfor- mance measures14 andagent pre-decision information15. Extending the existing literature we suppose one of the available signals, i.e. the prescribed target y∗, to be based on a deterministic production function with discontinuous jumps in the technology. A further
13Budget-dependent resource costsc(R) are easily integrated into the analysis.
14See e.g. Holmstr¨om (1979), Banker/Datar (1989).
15See e.g. Demski/Sappington (1984).
extension is that the literature on budgeting mechanisms usually focuses on the use of a single performance measure where the budgets serve as targets in the incentive schemes16. The second relevant stream of literature deals with the firm’s resource allocation.
Harris et al. (1982) and Antle/Eppen (1985) determine conditions where rationing of resources by means of rigid budgets isex anteoptimal. Unlike our model, they assume that the manager has preferences for the allocated resources, e.g. because he can substitute the resources for the labor he is expected to provide. The non-existing preference for the allocated resources supposed in our paper is also a major difference w.r.t. the literature regarding the firm’s capital budgeting process, e.g. Harris/Raviv (1996) and Bernardo et al. (2000).
A paper related to ours isZhang (1997), which analyzes the use of predetermined rigid budgets in a capital budgeting framework. Zhang shows that financial policies such as a high hurdle rate or capital rationing can be helpful in disciplining managers. However, he focuses on the capital rationing’s role in enhancing the competition of multiple managers for capital. In our paper, rationing is used to restrict the effort choice of a single manager.
Furthermore,Zhang (1997)supposes the budget size to be exogenously given whereas we endogenize the decision regarding the size of the budget.
The third stream of literature focuses on the delegation of decision rights to agents.
In general, restricting the agent’s action space through flexible or rigid resource-oriented budgets is related to the question of whether or not to delegate certain decision rights to an agent17. The fundamental difference, however, is that non-delegated decisions must be performed by someone else, e.g. another agent, while we restrict the delegated actions available to the agent.
3 Problem description and benchmark solution
3.1 The Problem
We analyze an agency problem resulting from a combined hidden action and hidden information-situation as depicted in figure 1. Initially, principal and agent sign a con- tract specifying an incentive scheme s(·), the resourcesR allocated to the agent, and the standard y∗. Before choosing his effort the agent privately observes a signal ξ ∈ {l, h}
perfectly informing him about his productivity δ. The productivity shows the agent’s influence on the principal’s return, i.e. the greater δ the more valuable the agent is to the principal. When signing the contract the productivity is unknown both to the agent
16See e.g. Demski/Feltham (1978), Penno (1984, 1990), Kirby et al. (1991).
17See e.g. Holmstr¨om (1984), Demski/Sappington (1987), Melumad et al. (1995), Marino/Matsusaka (2000).
Figure 1: Sequence of events
-
Principal &
Agent sign contract [s(·), R, y∗]
Agent receives signal ξ about δ
Agent supplies
effort a
OutputπA, y realized Agent receives s(πA, y)
and to the principal. Then, they only know that the productivity might be either high (δh) or low (δl). The probability for the high (low) productivity is φh (φl). The difference
∆≡δh−δl shows the agent’s informational advantage.
After observing the signal, the agent chooses his effort a ∈ XaB which the principal cannot observe. Furthermore, we suppose that the agent may quit the firm after learning his productivity. Due to the agent’s fundamental value to the principal (πB(y∗)−c(R)>
0), however, she always wants to contract with the agent. Then, for both environmental conditions she guarantees the agent his reservation utility18. Finally, the outcomes πA and y are realized and the agent receives his compensation.
The agency-problem is formulated with the assumptions of the LEN-model19, i.e. there exists linearity both in the return ˜πAand in the incentive scheme: ˜πA =δa+˜². We assume the error term ˜² to be normally distributed with mean zero and variance σ2. The noise in measuring the results of the agent’s activities may follow from the stochastic and firm- specific influence of the product market or some shortcomings of the firm’s accounting system. The (partly) linear incentive scheme is
s(˜πA, y) =
νπ˜A+f if y=y∗
−p if y6=y∗ (2)
Because of the deterministic production function g, for a sufficient penalty p a rational agent will always provide the pre-specified standard y∗.20 Thus, in equilibrium we can restrict the analysis to the linear parts of the incentive scheme, i.e. s(˜πA) =νπ˜A+f, with f the fixed salary and ν the proportional share.
We assume the agent to be risk averse. His preferences are described by an exponential
18The situation of post-contractual information with the ability to quit is equivalent to the situation of pre-contractual information. See e.g. Melumad (1989). We assume that the decision to breach the contract cannot be contracted upon. First, it seems to be an empirical question of whether or not courts will enforce such a contract and require the agent to pay damages. Second, the ”assumption that managers cannot be required to implement plans they know will impose losses on them is more consistent with the autonomy that divisional managers have in decentralized organizations.” Kanodia (1993, p.
177).
19See e.g. Holmstrom/Milgrom (1987), Spremann (1987), Wagenhofer/Ewert (1993).
20Whilepis sufficient to motivate the agent to providey∗, we assume the penalties to be exogenously restricted in order to rule out the Mirrlees problem.
utility function: UA(·) =−exp{−r(s(˜πA)−βa2)} with r the coefficient of absolute risk aversion. The agent’s disutility of effort is convex in the effort level a, and the parameter β >0 is used to value the disutility of effort in monetary terms.
With the assumptions outlined above, in equilibrium the agent’s utility can be repre- sented by its certainty equivalent as:
CE(s(˜πA, y =y∗), a) = δνa+f−βa2 −r
2ν2σ2 (3)
The first three terms show the expected compensation minus the disutility of effort. The last term represents the agent’s risk premium, which increases with increasing risk aver- sion, proportional share, and variance. Finally, we assume the principal to be risk neutral.
Given that the agent choosesa such that y=y∗, she is only interested in maximizing the remaining expected net result, i.e. the expected difference between the outcome ˜πA and the compensation paid to the agent: maxν,f(1−ν)E[˜πA]−f.
Based on the agent’s pre-decision information we can differentiate three types of bud- geting mechanims (table 1). First, the principal allocates resources R and prescribes a performance standard y∗ such that the agent has the set XaF B ≡ {0, aF Bl , aF Bh } in order to achieve y=y∗. Here, the incentive scheme has to motivate the agent to appropriately choose aF Bl for ξ =l and aF Bh for ξ = h. Due to the state dependent effort this scheme may be addressed as a flexible budget.
Table 1: State-dependent activities of flexible and rigid budgets
Types of budget l h
Flexible budget (FB) aF Bl aF Bh Rigid budget with rationing (RB-R) aRBl aRBl Rigid budget with slack (RB-S) 0 aRBh
Alternatively, the resources can restrict the feasible set of effort choices to XaRB ≡ {0, aRB}. Then, the principal uses rigid budgets. First, she can ration the resources available to the agent such that the agent does not increase his effort level when he observes ξ = h as compared to ξ = l. Following Antle/Eppen (1985), we address this under-allocation of resources in case of ξ = h as a rigid budget with rationing. Unlike their rationing scheme, however, the under-allocation of resources does not lead to a zero output. Rather, it prevents the agent from choosing a larger effort level forξ =h. Second, resources and incentive scheme may motivate the agent to supply a positive effortaRBh only forξ=h. Then, forξ=l the agent only coordinates the available resources and does not supply any (additional) effort (a= 0). Since the agent has an excess of resources over the
minimum required in case ofξ =l, arigid budget with slack results. This matches Antle and Eppen’s (1985) definition of organizational slack. Furthermore,RB-S is comparable to a high hurdle rate as a capital budgeting rule where only investment projects which are in the high state are accepted21.
With the sequence of events depicted in figure 1 the principal chooses in advance between a flexible or a rigid budget. Moreover, comparable to Zhang (1997) the prin- cipal determines the existence of a rationing or slack solution. With the high hurdle rate in Antle/Eppen (1985), however, either organizational slack or rationing can occur ex post, depending on the information observed by the agent. The major differences of our paper’s assumptions as compared to Antle/Eppen (1985) and Zhang (1997) are that the allocated resources determine a deterministic production function, the performance standard restricts the agent’s effort choice to a discrete set, and that the principal in- centivizes the agent by using an incentive scheme with multiple performance measures without communication.
3.2 Benchmark Solution
As a benchmark solution we consider the situation where the principal does not restrict the agent’s action space by allocating a physical budget. Instead, she allocates a monetary budget at costc(R) and expects the agent to purchase the resources necessary to achieve y = y∗. We assume that the agent has to spend the budget completely, and that he is not able to consume any slack. The benefit to the agent from purchasing the resources by himself, however, is that his action space is not restricted to specific effort levels. In order to motivate the agent to supply a positive effort level, the principal specifies an incentive scheme as described in the previous section. Because of the technical nature of the agent’s private information, a more elaborate incentive scheme with message (and, hence, state) dependent fixed salary and proportional share is not possible.
LetPZbe the principal’s problem when she exclusively uses incentive schemes. Then, we have PZ:
ν,f,amaxlah
E[UP] = (1−ν)X
i
φiδiai−f (4)
s.t.
PCi νδiai+f −βa2i − r
2ν2σ2 ≥sA ∀i (5)
ICi ai = argmax
a
½
νδia+f −βa2− r
2ν2σ2 |a∈XaZ
¾
∀i (6) For all states, the principal considers incentive (IC) as well as participation (PC) con- straints. The participation constraints ensure that the agent’s certainty equivalent is at
21SeeZhang (1997).
Table 2: Incentive scheme, effort levels, and expected result to the principal when solely using incentive schemes
Proportional share Fixed salary νZ = E[δ2]
2E[δ2]−δl2+ 2rβσ2 fZ =sA+ E[δ2]2(2rβσ2−δl2) 4β(2E[δ2]−δl2+ 2rβσ2)2 Effort in low productivity state Effort in high productivity state aZl = δl
2β E[δ2]
2E[δ2]−δl2+ 2rβσ2 aZh = δh
2β E[δ2]
2E[δ2]−δl2+ 2rβσ2 Result to the principal
E[UPZ] = E[δ2]2
4β(2E[δ2]−δl2+ 2rβσ2)−sA
least equal to the certainty equivalentsA of his reservation utility. Therefore, he accepts the contract and does not quit after observing ξ. Following the incentive constraints (6), the agent chooses his effort a so as to maximize his certainty equivalent. Thereby, he considers the observed productivityδl orδh. Since the resources do not limit the agent’s action space he may choose any effort level of the setXaZ :={a∈ R | a≥0}. The princi- pal maximizes the expected net return after compensating the agent, thereby anticipating the agent’s reaction (al and ah) to the offered contract.
Finding 1 summarizes the main characteristics of PZ22, table 2 shows its closed form solutions.23 There, E[δ2] =φδ2h+ (1−φ)δl2 is the expected value of the squared produc- tivities.
Finding 1 (i) The agent receives a strictly positive rent if he observes the high produc- tivity. (ii) The effort level of both situations is below the first best effort level. (iii) The ratio of the effort levels equals the ratio of the productivities.
The principal chooses the compensation contract such that the participation con- straints are fulfilled for any productivity. Since the agent’s certainty equivalent increases with δ, she chooses f such that he just receives his reservation utility in case of ξ = l and a rent in case of ξ = h. Furthermore, because of the uncertainty w.r.t. δ she uses the expected value of the squared productivities E[δ2] when determining ν and f.
The agent chooses his effort such that his marginal benefits equal his marginal costs:
2aiβ = νδi, i ∈ {l, h}. Due to the state independent share ν, ah > al follows for δh > δl.
22All proofs are in the appendix.
23For ease of presentation of the results we useφh=φand, thus,φl= 1−φ.
Finally, the agent’s rent partly follows from his unrestricted action space. The principal, thus, can reduce the rent by restricting the agent’s action space by means of resource- oriented budgets.
4 Characteristics of Optimal Resource-oriented Budgeting Mechanisms
4.1 Incentive Schemes and Flexible Budgets
With flexible budgets the set of actions compatible with y∗ is XaF B := {0, al, ah}. In order to obtain a flexible budget the principal has to allocate resources and prescribe a performance standard such that the implicitly prescribed effort levels are positive (ai >
0, i ∈ {l, h}) and unequal (ah 6= al). Furthermore, the incentive scheme motivates the agent to supply a high effort ah if he observes ξ = h, and a low effort al if he observes ξ=l.
Let PFB be the principal’s problem when she uses flexible budgets. Then, we have PFB:
ν,f,amaxl,ah
E[UP] = (1−ν)X
i
φiδia(i)−f (7)
s.t.
PCi νδia(i) +f−βa(i)2− r
2ν2σ2 ≥sA ∀i (8)
ICi νδia(i)−βa(i)2 ≥νδia−βa2 ∀i, a∈XaF B∧a 6=a(i) (9)
a(l) =al, a(h) = ah (10)
Objective function and participation constraints are the same as in PZ24. Due to the restricted action space, only two alternative acitivities are considered in the incentive constraints. Incentive constraints (9) and (10) guarantee that the agent is always at least as good off if he chooses an activitya(i) = ai corresponding to the observed productivity δi as if he chooses an alternative activity a. Since fixed salary and risk premium are independent of the effort choice, only the expected proportional share and the disutility of effort remain.
In order to solvePFBwe apply a two step approach. In the first step we determine the optimal incentive scheme, given two arbitrary activities. The second step then determines the optimal activities, given the optimal incentive scheme. Finally, the two effort levels
24PFBresembles theGrossman/Hart (1983)formulation of the agency problem. Here, it is specified with the assumptions of the LEN-model (cf. Kleine (1996)) and extended for the hidden information situation.
Table 3: Incentive scheme, effort levels, and expected result to the principal for flexible budgets Proportional share
νF B = φ((1−φ)(δl+δh)2−δh∆) φ(4δh2−φ(δl+δh)2) + 2rβσ2 Effort in low productivity state aF Bl = ∆E[δ](φδh2+rβσ2) +φδlδh2
β(φ(4δh2−φ(δl+δh)2) + 2rβσ2) Effort in high productivity state
aF Bh = φδh(δh(2δh+ ∆E[δ])−∆E[δ])) β(φ(4δh2−φ(δl+δh)2) + 2rβσ2) Result to the principal
E[UPF B] = 2φδh2(E[δ2]−φδhδl) + ∆E[δ]2rβσ2 2β(φ(4δ2h−φ(δl+δh)2) + 2rβσ2) −sA
al and ah determine the resources to be allocated to the agent. Results are presented in table 3. There, ∆E[δ] =φδh−(1−φ)δl. Finding 2 summarizes the main results regarding the incentive scheme and the applicability of flexible budgets.
Finding 2 (i) The agent receives a strictly positive rent if he observes the high productiv- ity, and (ii) the incentive compatibility constraint is binding in the high productivity state.
(iii) Flexible budgets are feasible only for φˆl < φ <φˆh. A high risk aversion, a high disu- tility of effort and a high variance reduce the economic conditions where flexible budgets are feasible. Even for a risk neutral agent there exist conditions where the principal will not use flexible budgets.
Again, the agent’s rent is based on the fact that the principal has to guarantee the reservation utility for all productivities. Furthermore, the share parameterν and the two positive effort levels are chosen such that the agent is indifferent between choosing aF Bh and aF Bl in case of ξ = h. When observing ξ = l, however, the agent does not receive a rent and he is indifferent between choosing aF Bl and not supplying any effort.
In general, FB shows a separating equilibrium, i.e. the agent is expected to react differently depending on the observed productivity. Part (iii), however, suggests that the feasibility of flexible budgets, i.e. the existence of a separating equilibrium, is restricted to certain economic conditions. They follow from the general conditions for the existence of flexible budgets, i.e. that effort levels must be positive and not identical25. Finding
25In order to separate them from the conditions following the endogenous decision of whether to use
2 suggests that a low risk aversion, a low disutility of effort, and a low variance support the feasibility of flexible budgets. The limited feasibility of flexible budgets even for a risk neutral agent shows the influence of the private information regarding the produc- tivity: For φ≤φˆl and limr→0 the principal tries to establish a separating equilibrium by prescribing a non-positive effort level aF Bl . Since non-positive effort levels are ruled out, flexible budgets are not feasible for these conditions.
4.2 Incentive Schemes and Rigid Budgets
With rigid budgets the principal allocates resourcesRto the agent such that the standard y∗ can only be achieved if the agent chooses an activity a∈XaRB ={0, aRB}. Depending on the incentive scheme, the principal either motivates the agent to choose the same activity for both productivities (RB-R), or to supply effort only if he observes the high productivity (RB-S).
Rigid budgets with rationing. LetPRB-Rbe the principal’s problem when she uses rigid budgets with rationing. PRB-R follows from PFB with the set of activities XaRB and
a(l) =al, a(h) = al (100)
With PRB-R the principal chooses the incentive scheme such that the agent always prefers to supply an identical positive effort al instead of a = 0. Finding 3 summarizes the main characteristics of rigid budgets with rationing. Table 4 shows the closed form solutions for PRB-R; E[δ] =Piφiδi is the expected productivity.
Finding 3 (i) The agent receives a strictly positive rent if he observes the high produc- tivity. (ii) The incentive compatibility constraint is binding in the low productivity state.
(iii) Rigid budgets with rationing are feasible for all relevant economic conditions.
When using rigid budgets with rationing the principal establishes a pooling equilib- rium, i.e. to motivate the agent to choose an identical effort level for all productivities.
Hence, the compensation scheme critically depends on the less favorable productivity.
This explains the rent for ξ = h. Furthermore, the compensation scheme and the effort level aRBl are chosen such that the agent is indifferent between supplying aRBl and not supplying any effort at all. Finally, a pooling equilibrium with a positive effort level can always be established. Due to their unlimited feasibility, the principal may use RB-Rin situations where flexible budgets are not feasible.
flexible or rigid budgets, we refer to them as feasibility conditions. Since the optimization ofPFBw.r.t.
ai, i∈ {l, h}, indicates the optimality of a separating equilibrium, however, the conditions also follow an economic calculus.
Table 4: Incentive scheme, effort level, and expected result to the principal for rigid budgets with rationing
Proportional share Fixed salary νlRB = δlE[δ]
2δlE[δ] +rβσ2 flRB =sA+ r 2
"
δlE[δ]σ 2δlE[δ] +rβσ2
#2
Effort in both productivity states Result to the principal aRBl = δl2E[δ]
β(2δlE[δ] +rβσ2) E[UPRB−R] = δl2E[δ]2
2β(2δlE[δ] +rβσ2)−sA
Table 5: Incentive scheme, effort level, and expected result to the principal for rigid budgets with slack
Proportional share Fixed salary
νhRB = φδh2
2φδh2+rβσ2 fhRB =sA+ r 2
"
φδ2hσ 2φδh2+rβσ2
#2
Effort in high productivity situation Result to the principal aRBh = φδ3h
β(2φδh2+rβσ2) E[UPRB−S] = φ2δh4
2β(2φδh2 +rβσ2) −sA
Rigid budgets with slack. LetPRB-Sbe the principal’s problem when she uses rigid budgets with slack, i.e. the agent supplies effort only if he observes the high productivity.
PRB-S follows from PFBwith the set of activities XaRB and
a(l) = 0, a(h) = ah (1000)
A separating equilibrium is established through the incentive constraints and constraint (10”), i.e. the agent prefers to supply no effort in case of ξ =l and to supply a positive effort level in case of ξ =h. Finding 4 summarizes the main characteristics ofRB-S; its closed form solution is presented in table 5.
Finding 4 (i) For both productivities the agent receives his reservation utility. (ii) The incentive compatibility constraint is binding for the high productivity state but not binding for the low productivity state. (iii) Rigid budgets with slack are feasible for all relevant economic conditions.
When using rigid budgets with slack the principal establishes a separating equilibrium with a single positive effort level. Therefore, she chooses the effort level aRBh and the
proportional share such that the agent is indifferent between supplying either aRBh or a = 0 in case of ξ = h. As a consequence, the two participation constraints become identical and the agent does not receive a rent.26
Since the agent only receives his reservation utility, RB-S is less costly to implement than RB-R. However, an activity is omitted in RB-S in case of the low productivity, therefore reducing the principal’s expected result. This is especially of relevance if the probability for a low productivity is high. Therefore, different conditions for an efficient use of the rigid budgets exist.
5 Efficiency of Flexible and Rigid Budgets
5.1 Conditions for Applying the Different Types of Budgets
Following the solutions outlined above, the three budgets yield different expected results to the principal. Comparing the results shows conditions for their efficient application.
First, an example is used in order to illustrate the nature of the problem.
Example A. We consider a principal/agenct-relationship with the agent’s risk and effort aversion of r = β = 1, a variance of σ2 = 1250, and productivities of δl = 40 and δh = 80. The certainty equivalent of the reservation utility is assumed to besA= 0. Figure 2 shows the expected result to the principal for the three budgets and when she exclusively uses incentive schemes. The figure indicates that FB yields the highest expected result within the interval [ ˆφl,φˆh], with ˆφl = 0.1358 and ˆφh = 0.5830. Here, the conditions for a feasible application ofFBare also conditions for its efficient use. Forφ ≤φˆl the rationing schemeRB-Ryields a feasible solution with the highest expected return to the principal.
And, forφ ≥ φˆh the slack scheme RB-S provides the best feasible solution. Proposition 1 provides a general result regarding the conditions for efficiently using flexible or rigid budgets.
Proposition 1 .
(i) Rigid budgets with slack are preferred by the principal if φ∈ {φ≥max{φˆh,φˆRB−RRB−S}}, where φˆRB−RRB−S ≡δl2/(δ2h−δhδl+δl2).
(ii) Rigid budgets with rationing are preferred by the principal if
φ ∈ {φ ≤ max{φˆl,φˆF BRB−R} ∨φ ≤ {φˆRB−RRB−S|φ ≥ φˆh}}, where φˆF BRB−R solves E[UPRB−R] = E[UPF B].
(iii) Flexible budgets are preferred by the principal and are feasible if φ∈ {max{φˆl,φˆF BRB−S} ≤φ≤φˆh}.
26Unlike the solution to the high hurdle rate inZhang (1997), however, a message dependent incentive scheme and capital allocation is not necessary in order to reduce the agent’s rent to zero.
Figure 2: Expected result to the principal for the three budgets and when solely using an incentive scheme
0.0 0.2 0.4 0.6 0.8 1.0
0 500 1000 1500
..........................................................................................................................................
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............................................................................................................................................
.........................................................
. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .
. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .
. .. .. .. .
E[UPRB−R] E[UPRB−S] E[UPF B]
E[UPZ]
φˆl φˆRB−RRB−S φˆh φ→
↑ E[UP]
RB-R¾ -¾ FB -¾ RB-S -
Following Proposition 1, the conditions for an efficient application of the budgets can be described by using the probability φ for the high productivity. Therefore, rigid budgets with slack are efficient for high probabilities, rigid budgets with rationing are efficient for low probabilities, and, finally, flexible budgets are efficient for intermediate probabilities. Figure 3 illustrates the combined influence of the probability φ and the productivity difference ∆ on the optimal budgeting mechanism. The conditions follow from the feasibility of flexible budgets ( ˆφl,φˆh), and when comparing the expected return to the principal ( ˆφF BRB−R,φˆRB−RRB−S). Rigid budgetsRB-R with rationing are optimal either if the probability φ for the high productivity is low or if the difference between the productivities is small. Rigid budgetsRB-Swith slack are optimal either if the probability φ is high or for a large difference ∆. In order to use flexible budgets FB, the economic conditions must therefore be sufficiently different. Dominating conditions e.g. due to extreme probabilities or productivity differences, however, result in the principal using a rigid budget.
Zhang (1997) determines conditions for applying rigid budgets that are comparable to the conditions outlined in Proposition 1. Based on his Finding 4, a high hurdle rate is optimal for a low project profitability, i.e. when the cost of rejecting a project in ξ =l is low. Similar to the high hurdle rate, with RB-S the principal foregoes to induce an activity for ξ = l. This seems to be reasonable when the probability of ξ = l is rather low. In addition,RB-S reduces the agent’s rent to zero. For the other budgets, however, the agent receives a rent for ξ=h, whose amount increases withδh. Therefore, applying
