A Theory of Participative Budgeting

THE ACCOUNTING REVIEW American Accounting AssociationVol. 89, No. 3 DOI: 10.2308/accr-506862014pp. 1025–1050

A Theory of Participative Budgeting

Mirko S. Heinle

University of Pennsylvania

Nicholas Ross

TinyCo

Richard E. Saouma

Microsoft

ABSTRACT: This paper complements the ongoing empirical discussion surrounding

participative budgeting by comparing its economic merits relative to a top-down

budgeting alternative. In both budgeting regimes, private information is communicated

vertically between a principal and a manager. We show that top-down budgeting incurs

fewer agency costs than bottom-up budgeting whenever the level of information

asymmetry is relatively low. Although the choice between top-down and bottom-up

budgeting ultimately determines who receives private information within the firm, we find

that both the principal and manager’s preferences over the allocation of private

information remain qualitatively similar across the two budgeting paradigms. Specifically,

while the principal always prefers either minimal or maximal private information, the

manager prefers an interim or maximal level of private information regardless of who is

privately informed. Last, we use our model to address empirical inconsistencies relating

the firm’s choice of budgeting process, the resulting budgetary slack, and performance.

Keywords: participative budgeting; top-down budgeting; bottom-up budgeting; decen-tralization; budgetary slack; rents.

I. INTRODUCTION

Akey element of any firm’s organizational design is the structure of information flows

between different levels of hierarchy. By governing ‘‘coordination and communication

among subunits within the company,’’ budgeting processes formalize how information is

used and shared within firms (Horngren, Datar, and Rajan 2012, 185). Consistent with recent trends

toward organizational decentralization (Rajan and Wulf 2006; Roberts 2004), surveys report that

firms are increasingly turning to participative, or so-called ‘‘bottom-up,’’ budgeting processes (Stout

First and foremost we thank John Harry Evans III for his support in improving the paper. We further thank twoanonymous referees as well as workshop participants at the 2012 AAA Annual Meeting and at the Workshop onAccounting and Economics and seminar participants at Columbia University; Tuck School of Business, DartmouthCollege; and Foster School of Business, University of Washington.

Editor’s note: Accepted by John Harry Evans III.

Submitted: July 2011Accepted: December 2013

Published Online: December 2013

1025

and Shastri 2008). In contrast to top-down approaches, participative budgeting processes rely on

managerial reporting, thereby empowering managers to influence their day-to-day activities and

performance targets. One of the main criticisms of participative budgeting processes is that

managers may benefit from strategically misreporting private information. To prevent managers

from ‘‘padding their budgets,’’ Baiman and Evans (1983) establish that effective participative

budgeting contracts must provide managers with informational rents, i.e., with additional

compensation to incentivize truthful reporting.

In contrast, top-down or authoritative budgeting processes eliminate a manager’s option to

game his compensation by transferring all decision rights to the firm’s central office or principal.

Common wisdom and accounting textbooks suggest that authoritative budgeting is largely

inefficient because the manager’s information goes unused. However, we find that even holding the

level of private information constant between top-down and bottom-up budgeting, the latter may

nonetheless prove optimal. In our model, the principal receives all interim private information under

top-down budgeting, whereas the manager receives the identical information under bottom-up

budgeting. Top-down budgeting eliminates the manager’s incentive to game his compensation by

endowing the principal with all private information. However, the manager may still collect rents so

as to incentivize the principal to report truthfully. In this paper we show how the level of private

information available in the firm—which we term the firm’s information environment—affects the

relative merits of top-down versus bottom-up budgeting.

Empirical work connecting the use of participative budgeting processes to firm performance,

slack, and asymmetric information has largely provided mixed evidence.1 For example, J. Shields

and M. Shields (1998, 50) state that ‘‘studies have reported [. . .] that participative budgeting has

linear positive, linear negative, ordinal and disordinal interaction (with other independent or

moderating variables), and no effect on motivation and performance.’’ Similarly, while Merchant

(1985) and Young (1985) conclude that participatory budgeting increases the amount of slack in

financial budgets, Dunk (1993) suggests that participation can reduce slack.

In their review of the literature, Shields and Young (1993) suggest that the mixed evidence

could be the result of ignoring path dependencies among information asymmetry, the use of

participatory budgeting, and budget-based incentives or budgetary emphasis. Similarly, Shields and

Shields (1998) propose that the conflicting empirical results may be due to ‘‘a lack of general or

integrative models.’’ We provide such an integrative model that explicitly examines the effects of

the firm’s information environment on its choice of budgeting process and subsequent incentives.

Specifically, in Stage 1 of our two-stage model, the principal chooses between a participative and a

top-down budgeting process. In Stage 2, private information is shared between the principal and

manager via the chosen budgeting process, production targets are established, the manager provides

productive effort, and payoffs are realized.

Textbooks argue that the advantages of bottom-up budgeting include the ability for managers to

impound their localized information in setting goals and that managers’ involvement in the budgeting

process increases their motivation to reach the specified goals (Braun, Tietz, and Harrison 2009, 477).

Top-down budgeting, on the other hand, enables firms to use the information gleaned from one

department in negotiating with other departments and to choose targets that are consistent with the

firm’s long-term strategy. We show that either budgeting process can be the firm’s preferred choice,

even holding constant the amount of available information between the two budgeting regimes, the

manager’s motivation, and the firm’s coordination initiatives. Instead, we identify the costs that arise

from the budgeting process purely as a result of information asymmetries, namely, the informational

1 Surveys of the literature can be found in Shields and Young (1993), Shields and Shields (1998) and Brown,Evans, and Moser (2009).

1026 Heinle, Ross, and Saouma

The Accounting ReviewMay 2014

rents (budgetary slack) necessary to induce honest reporting. To capture the value of communication

in organizations, we assume that the firm’s productivity is unknown in Stage 1, but that at the

beginning of Stage 2, either the principal or manager receives relevant, interim private information

about the manager’s productivity.2 Inherent with her choice of budgeting process, the principal

chooses who receives information and how the information is used in setting goals. We assume that

under bottom-up budgeting, the manager receives and communicates private information, whereas

under top-down budgeting, the principal receives and communicates private information. For

example, a manager’s information may pertain to segment demand or lower-level employee quality,

whereas a principal’s information may pertain to industry or firm-level demand shocks. To compare

between the two budgeting processes, we hold the quality of information received constant across

both systems. Once the budgeting report is made, the manager decides how much effort to exert based

on his updated productivity beliefs. When the principal holds an informational advantage, she benefits

from misreporting excessively optimistic information, since this leads the manager to exert high effort

in expectation of earning high compensation. A similar intuition explains the manager’s interest in

misreporting excessively pessimistic information when he himself is privately informed, as he can

reduce his effort and still expect high compensation.3

As noted above, Baiman and Evans (1983) point out that to prevent misreporting in a

bottom-up system, the principal must provide the manager with information rents when he reports

favorable information. However, the literature has largely ignored the fact that to prevent

misreporting in a top-down system, the principal must forgo profits when she reports favorable

information. In both budgeting processes, the principal has two budgetary levers to induce truthful

reporting: fixed payments from the manager’s division and variable payments contingent on

divisional cash flows. While fixed payments directly alter the incentives for honest reporting,

variable payments have an additional indirect effect by distorting the manager’s effort choice. To

ensure honest reporting, the optimal budget in a bottom-up regime distorts the manager’s effort

incentives when he reports unfavorable information, whereas the optimal top-down budget distorts

the manager’s effort incentives when the principal reports favorable information. In other words,

when the informed party communicates information that coincides with their preferred (strategic)

report, the manager’s effort incentives are optimally reduced below first-best.

We find that the total surplus shared between the manager and the principal is maximized under

bottom-up budgeting. However, the principal’s surplus is maximized under top-down budgeting

when the amount of private information is relatively low.4 Because the principal ultimately chooses

which budgetary system to put in place, we predict a switch from top-down to bottom-up budgeting

as the amount of private information increases. Because the different regimes provide very different

incentives, our model predicts a non-monotonic relation between budget-based incentives and

information asymmetry, consistent with Shields and Young (1993).

That the principal’s preferences (and therefore the firm’s performance) vary with the level of

asymmetric information is a result of two fundamental effects. First, effort distortions are more

costly under top-down budgeting than under bottom-up budgeting, because the former occurs when

productivity is greatest. Second, under bottom-up budgeting, the principal suffers from a control

2 While we assume that the principal and manager cannot both receive private information, we discuss settingswith bilateral private information in Section V.

3 We refer to the manager as ‘‘misreporting excessively pessimistic information’’ and the principal as‘‘misreporting excessively optimistic information’’ to indicate when, independent of the actual informationcontent, the manager reports his information as unfavorable whereas the principal reports her information asfavorable, respectively.

4 The ‘‘amount of private information’’ and the ‘‘level of information asymmetry’’ both refer to the informativenessof the private information. In our model, multiple less precise signals are equivalent to one more precise signalwhen both sets induce the same posterior beliefs.

A Theory of Participative Budgeting 1027


loss because the manager controls both the reporting and productive effort decisions.5 Top-down

budgeting avoids this control loss and the associated agency costs by separating the production and

reporting roles, with the principal issuing the report and the agent choosing the productive effort.

When choosing the budgeting process, the principal trades-off the costs of the necessary effort

distortions with the control loss. The cost of the effort distortion increases relative to the control loss

as the amount of private information increases, such that the principal prefers top-down budgeting

for lower levels of private information, but shifts to bottom-up budgeting as the private information

becomes more informative.

Our modeling of both budgeting processes is rooted in the associated economics literature on

screening. Bottom-up budgeting shares many common features with the adverse-selection model

first introduced by Baron and Myerson (1982) in which a regulator contractually screens the firm’s

private information. Top-down budgeting is similar to the informed principal problem found in

Maskin and Tirole (1990).6 However, the economics literature typically assumes that the allocation

of information, for example through the budgeting process, is entirely exogenous. One notable

exception is Eso and Szentes (2003) where the principal cannot decipher the favorableness of

information, but must nonetheless decide how much information to share with the manager at the

outset, and how much to reveal after the manager’s interim report. Our work differs because our

principal and manager are equally adept at interpreting information; therefore, the principal can

control the allocation of information ex ante and, in the top-down regime, she can strategically

misreport information ex post.A second stream of related literature investigates the design of information systems. This

literature examines preferences over the level of information available but holds constant the

allocation of information (Antle and Fellingham 1995; Christensen 1982). We extend this literature

in the following two ways. First, we characterize the principal’s choice of the information allocation

or budgeting process for any level of available information. Second, based on the chosen budgeting

process, we analyze the principal’s and manager’s preferences over the level of information

available. Surprisingly, we find that both parties’ preferences are qualitatively similar regardless of

who receives private information. We show that in both budgeting frameworks, the principal’s

(manager’s) utility is U-shaped (single peaked) over the total level of private information.

When the principal receives the private signal, both she and the manager are subject to agency

problems, akin to the dual moral-hazard problem with asymmetrically informed players. Arya,

Glover, and Sivaramakrishnan (1997) consider such a setting and allow the principal to condition

her efforts on her privately observed interim signal. The authors identify conditions under which

additional information aggravates the principal’s commitment problem, indicative of a non--

monotonic preference for private information. In our setting, we find that even in the absence of a

second moral-hazard problem, the principal will exhibit a similar, non-monotonic preference for

additional private information.

Importantly, our model addresses the extant empirical and experimental literature on

budgeting. Much of the prior research on participative budgeting has analyzed the consequences

of participative budgeting in terms of performance (Brownell 1982; Frucot and Shearon 1991),

budgetary slack (Dunk 1993; Fisher, Maines, Peffer, and Sprinkle 2002), and budget emphasis

(Young 1985). As described earlier, the different empirical studies have identified positive,

negative, or non-existent effects of participative budgeting on performance, motivation, and

budgetary slack. We offer a possible explanation for the mixed empirical results by isolating the

5 Similar to Melumad, Mookherjee, and Reichelstein (1997), we use the term ‘‘control loss’’ in reference to themanager’s ability to exploit his private information in choosing effort in conjunction with his report in thebottom-up framework.

6 An excellent survey of the screening literature can be found in Riley (2001).



roles of a firm’s information environment and the firm’s choice of budgeting process on the

outcomes of the firm’s budgeting choice. Specifically, we find that the firm’s information

environment is a monotonic driver of the choice of budgeting process, but a non-monotonic driver

of the firm’s performance, motivation, and budgetary slack. Therefore, the relation between a firm’s

choice of budgeting process and the outcomes is also non-monotonic.

We present the model below in Section II. Section III first characterizes the optimal contracts

under top-down and bottom-up budgeting, and Section IV then analyzes the relative attributes of

each regime. Section V introduces a numerical example and Section VI concludes following a

discussion of the results.

II. MODEL

We model a principal (she), who employs a manager (he) at time t¼ 1 to manage a division of

the principal’s firm until time t ¼ 5. We assume that both players are risk-neutral and that the

manager retains—and therefore maximizes—his division’s profits. At time t¼ 4 the manager exerts

unobservable effort, e, at a personal cost of ½Te2: The manager’s efforts contribute to the

probability that his division generates high cash flows, p; rather than low cash flows,�p; at t ¼ 5.

Cash flows are contractible and received directly by the manager’s division. Out of the realized cash

flows the manager makes payments to the principal at t¼ 5 such that his compensation is given by

divisional profits that equal the realized cash flows minus any payments to the principal. Cash

flows, p; are random with an expected value of p ¼ ehpþ ð1� ehÞ�p; where eh 2 [0,1] is the

probability of attaining high cash flows and h is a measure of the manager’s productivity.7 At the

time of contracting, t ¼ 1, the manager’s productivity is known to be either high, hH, with

probability p, where 0 , p , 1, or low, hL, with probability 1 � p. We denote the expected

productivity as h:At time t¼ 1 the principal proposes a set of two budgets to the manager. After the manager is

hired, at time t ¼ 2, interim information concerning the manager’s true productivity becomes

available in the form of a signal, h 2 fhL; hHg that is ‘‘soft’’ in the sense that it cannot be verified by

anyone other than the recipient. Budgets are finalized at time t ¼ 3, when either the manager

(bottom-up budgeting) or principal (top-down budgeting) reports his/her private information, which

is hL or hH: The budget report is then mapped to one of the budgets from the set proposed at time t¼1. By filing a report, the informed party communicates his/her information to the uninformed party.8

The firm’s budgeting process therefore defines both the underlying information system and the

responsibilities of the principal and the manager. We assume that the principal publicly chooses the

firm’s organizational structure at time t¼0. This choice if reflected in the set of budgets proposed at

t¼ 1. Figure 1 depicts the timing of events in our model.

Note that in this context budgets would convey no information were the specific budget chosen

prior to the arrival of information. This is particularly relevant in models with risk-neutral managers

because, depending on wealth constraints, the first-best solution could often be obtained by the

principal ‘‘selling the firm’’ to the manager. For budgeting to convey relevant information, the

budget must therefore be chosen at t¼ 3, i.e., after private information is received, but before the

manager selects his effort.9

7 Rather than imposing an upper limit on the probability of attaining high cash flows, we instead assume that themanager’s cost of effort parameter, T, is sufficiently large to prevent e � 1=h from ever being optimal.

8 We refer to the privately observed information as a ‘‘signal’’ and to the communication of that signal as a‘‘report’’ or the ‘‘choice of a budget.’’

9 We later discuss our rationale for excluding ex ante contracting and the limitations of this approach.



The signal received at t¼ 2 provides incremental information regarding whether the manager’s

true productivity is hL or hH: Following Rajan and Saouma (2006), we parameterize private

information such that:

Pr½hijhj� ¼aþ ð1� aÞPr½hi� i ¼ jð1� aÞ Pr½hi� i 6¼ j

8a 2 ð0; 1Þ and i; j 2 H; Lf g: ð1Þ�

From (1), the signal realization is itself the ex post expected productivity, as

E½hjhi� ¼ ahi þ ð1� aÞh ¼ hi:10 Since high productivity is preferred, we refer to hH as favorable

information and hL as unfavorable information. The exogenous parameter a measures the

correlation between the true productivity, h, and the signal, h: One may interpret a as the quality or

quantity of information conveyed by the signal, or more generally, a can be thought of as the

‘‘informativeness’’ of the signal. Since the signal is only observed by the informed party, a also

captures the degree of information asymmetry. As a ! 1, our setting approaches the perfectly

informed paradigm found in the adverse-selection and informed principal literatures, while as a!0, all members of the firm become symmetrically uninformed, regardless of any privately observed

information. For our parameterization to be properly specified, the ex ante expected productivity at t, 2 must be independent of future information for all values of a, E½E½hjhj�� ¼ E½h�: Therefore, we

must assume that the signal and the true productivity share the same underlying distribution, such

that Pr½hH� ¼ Pr½hH� ¼ p and Pr½hL� ¼ Pr½hL� ¼ 1� p: Consequently, the informativeness

parameter a, measures the correlation between the privately observed signal h and the manager’s

realized productivity h.

The manager’s cost of effort T, the probabilities of both high effort productivity and a favorable

signal Pr½hH� ¼ Pr½hH� ¼ p, and a, the level of information conveyed by h, are all determined

exogenously, and commonly known at time t¼ 0. The bargaining power is distributed between the

principal and manager such that at t ¼ 1, the principal makes a take-it-or-leave-it offer to the

manager that specifies the firm’s budgeting process, the manager’s responsibilities, and a set of two

budgets, one that corresponds to hL and the other to hH: The budgets are chosen by the informed

party during the budgeting process at t ¼ 3 and outline the payments required of the manager’s

division. In both the top-down and bottom-up setting, the initial menu serves as a commitment

device that disciplines the informed party to reveal their information truthfully by limiting the

opportunities to profit from misrepresentation.11

Because the manager’s division receives all cash inflows at t ¼ 5, the principal’s payoffs are

entirely determined by the payments specified by the final budget. We assume that the budget can

FIGURE 1Timeline of Events

10 We thank an anonymous referee for suggesting this notation, which carries no loss of generality.11 Under top-down budgeting, the principal could alternatively offer a single contract after becoming informed and

all results would remain unchanged.



include both a fixed payment and a payment that depends on realized divisional cash flows.

Specifically, from the proposed set of two budget pairs at t ¼ 1, f(aL,bL),(aH,bH)g, the informed

party selects one budget pair (ai,bi ), such that at t ¼ 5 the manager’s division must provide a

payment of ai þ bi p to the principal. Because only bi p depends on the divisional cash flows, we

label ai the fixed payment and bi p the variable payment.

The specification of ai and bi in our model is consistent with multiple interpretations, including

overhead cost allocation, burden/tax rates, and linear profit-sharing schemes. First, textbooks on

budgeting commonly discuss the allocation of a firm’s overhead costs to its divisions.12 In this

context, the direct payments can be interpreted as the allocated overhead costs, where ai is a fixed

allocation of overhead costs and bi is the overhead allocation rate applied to the division’s

revenues.13 Second, in decentralized organizations it is common for headquarters to apply a burden

rate or ‘‘tax rate’’ to the divisions’ revenues. For example, business schools frequently transfer a

percentage of their collected tuition to central campus. Third, one can interpret our direct payment

scheme as a linear-sharing rule applied to the divisional cash flows. In this setting, divisional profits

are the (1 � bi ) share of divisional cash flows that are retained within the division, net of the

corporate overhead charge ai. For ease of exposition, we will refer to budget pairs (ai,bi ) as fixed

and variable payments.

The Revelation Principle allows us to restrict attention to contract menus that specify two

contracts per budgeting process such that contract i is selected if and only if hi is reported with i 2fH, Lg. The menu of contracts must satisfy incentive compatibility constraints to prevent

misreporting. We assume that the principal must honor the terms she offered at t¼ 1 throughout the

duration of the contract. In contrast, the manager can leave the firm at any time before receiving

divisional cash flows, in which case the game ends.14

As a benchmark, we first establish the first-best solution, where the manager’s effort is

contractible and the signal h is privately observed.

Lemma 1: When the manager’s effort is contractible, the principal is indifferent between top-

down and bottom-up budgeting. Under both regimes, the principal instructs the

manager to exert first-best effort eFBi ¼ hi

T ðp� �pÞ and pays him a wage of

h2

i

2T ðp�

�pÞ2 if he takes the specified effort following a report hi 2 hH; hL

n o: The

principal’s expected profits are increasing and convex in signal informativeness, a,

whereas the manager always earns his reservation utility.

The optimal first-best effort eFBi ¼ hi

T ðp� �pÞ is derived from the principal’s first order

condition. Intuitively, higher effort increases the probability of receiving p instead of�p at an

expected rate of hi and a cost of T. The manager’s first-best salary equals the manager’s cost of

effort such that the manager is indifferent between accepting and not accepting the contract. The

benchmark setting of Lemma 1 highlights the importance of the underlying moral-hazard problem

because without hidden effort, both the principal and manager are indifferent over the choice of

budgeting regimes. When effort is contractible, the principal claims all divisional cash flows and the

manager will nonetheless accept to work since the principal can pay the manager as a function of

12 For example, Horngren et al. (2012, Chap. 15) discuss the allocation of support department costs, common costs,and revenues from bundled products.

13 This corresponds to the notion in accounting textbooks that, for example, common costs may be allocated to thefirm’s divisions based on budgeted numbers (ai ) and actual numbers (bip )

14 In particular, the principal must be able commit to how the budget report is used before private information isreported. For a discussion on budgeting in the absence of commitment, see Arya et al. (1997). We thank ananonymous referee for pointing out that the tensions we discuss in our model also arise if the signal is privatelyreceived at time t ¼ 0 followed by reporting at t ¼ 1.



his effort. Because the manager is always reimbursed for his exact cost of effort, regardless of his

productivity, he is indifferent between the two signal realizations concerning his productivity, and

he therefore has no incentive to misreport under bottom-up budgeting. The same intuition holds for

the principal in a top-down budgeting process, which implies that the principal obtains the same

optimal payoffs in both settings.

Lemma 1 shows that the principal’s profits increase in a. In line with the terminology first

proposed in Demski and Feltham (1976), a controls the level of decision-facilitating information

provided in the signal. To simplify the intuition used later, it is important to understand why

first-best profits are increasing and convex in a. Assuming the manager chooses his first-best effort,

as a increases, expected productivity in the favorable state increases and that in the unfavorable

state decreases. Therefore, even if the manager does not adjust his efforts in the two states, expected

profits increase linearly with a, since higher (lower) effort is matched with even higher (lower)

productivity. However, the manager complements the changing productivities by further raising his

effort in the favorable state and lessening it in the unfavorable state, thus profits increase convexly

with a as in Figure 2. That the manager’s effort increases in the favorable state and decreases in the

unfavorable state can be seen from Lemma 1, as eFBH ¼

p�pT ðhþ að1� pÞðhH � hLÞÞ and

eFBL ¼

p�pT ðh� apðhH � hLÞÞ, and both hH� hL and p�

�p are positive.

III. HIDDEN EFFORT

In this section, we analyze the choice of the budgeting process when the manager’s efforts are

hidden and therefore non-contractible. We define a budgeting equilibrium with hidden effort as an

outcome where:

(1) the informed party maximizes its utility by truthfully communicating his/her interim signal;

(2) the uninformed party correctly infers the informed party’s information from the latter’s

communication;

(3) the manager always selects his expected utility-maximizing effort;

(4) the manager’s interim expected utility at t ¼ 3 is non-negative; and

(5) the uninformed party is free to choose any contract from the t ¼ 0 menu if the informed

party fails to do so at t¼ 2.

The Revelation Principle guarantees that the first equilibrium requirement is without loss of

generality. Conditions (2)–(4) imply that both the principal and manager are rational, while

FIGURE 2First-Best Expected Cash Flows



condition (5) specifies the necessary off-equilibrium beliefs required to uphold any equilibrium

with communication.

Top-Down Budgeting

We first consider the case where the principal obtains interim productivity information in

accordance with the top-down budgeting paradigm described earlier. The principal chooses

budgeting parameters ai and bi, with i 2 fH, Lg to solve:

maxai;bi

p�aH þ eHhHbHpþ ð1� eHhHÞbH�

p�þ ð1� pÞ

�aL þ eLhLbLpþ ð1� eLhLÞbL�

p�

subject to:

eHhHbHpþ ð1� eHhHÞbH�pþ aH � eLhHbLpþ ð1� eLhHÞbL�

pþ aL ðTT:PHÞeLhLbLpþ ð1� eLhLÞbL�

pþ aL � eHhLbHpþ ð1� eHhLÞbH�pþ aH ðTT:PLÞ

eihið1� biÞpþ ð1� eihiÞð1� biÞ�p� ai �1

2Te2

i � 0 i 2 H; Lf g ðIRÞ

ei 2 argmaxe ehið1� biÞpþ ð1� ehiÞð1� biÞ�p� ai �1

2Te2 i 2 H; Lf g ðICÞ

0 � bi � 1; i 2 H; Lf g

The principal’s objective function represents the firm’s expected profits. With probability p,

high productivity occurs and expected profits are given by the sum of the deterministic fixed

payment, aH, and the expected variable payment, eHhHbHpþ ð1� eHhHÞbH�p: With probability 1�

p, expected profits are the sum of aL and eLhLbLpþ ð1� eLhLÞbL�p: This shows that the probability

of high cash flows is given by eHhH in the good state and eLhL in the bad state.

The two truth-telling constraints, (TT.PH) and (TT.PL), ensure that the principal always

reports her observed signal truthfully, given the realized signals hH and hL; respectively. The two

individual rationality constraints in expression (IR) guarantee that the manager prefers the

contract to his reservation utility of zero at time t¼ 2. The two constraints (IC) characterize the

manager’s optimal effort given the realized signals hH and hL: Finally, while bi � 0 ensures that

the manager does not receive all cash flows and an additional direct payment from the principal,

bi � 1 ensures that the manager will never transfer more cash flows than he receives. Solving

(IC), the manager puts forth effort ei ¼ 1=Tð1� biÞhiðp��pÞ in response to a report of hi:

Compared with the benchmark setting of Lemma 1, top-down budgeting with moral-hazard

induces the manager to distort his effort below first-best, eFBi ; whenever he makes direct variable

payments (bi . 0) to the principal.

In a top-down regime, at t¼ 3 the budgeting process requires that the principal make a report,

h; that determines which of the two sets of direct payment pairs applies. Because the preceding

expression for the manager’s second-best effort shows that the manager’s effort is increasing in the

reported signal, the principal has a potential incentive to exaggerate the favorableness of her

information by reporting hH to the manager. This exaggeration could lead a manager who fails to

anticipate the principal’s reporting incentives to mistakenly exert high effort in return for relatively

low expected compensation. However, Proposition 1 shows that the optimal budget induces the

principal to report truthfully by tying her payoff to realized cash flows whenever she reports

favorable news.

Proposition 1: Under top-down budgeting the optimal budget parameters are as follows:



(i ) When the principal reports an unfavorable signal, hH; bL¼ 0 and aL ¼�pþ 1

2eLhLðp�

�pÞ;

(ii ) When the principal reports a favorable signal, hL:

a: bH ¼hHðhH � hLÞ � hL

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2hHðhH � hLÞ

q

h2

H � 2hHhL

aH ¼ ð1� bHÞ �pþ 1

2eH hHðp�

�pÞ

� � for 1 � 2hL2hL � hH

h2

H

b: bH ¼1

2

aH ¼ ð1� bHÞ �pþ 1

2eHhHðp�

�pÞ 2hL

2hL � hH

h2

H

0B@

1CA

0B@

1CA

for 1 . 2hL2hL � hH

h2

H

:

Proposition 1 establishes that when the principal reports unfavorable news, hL; the optimal

budget includes only a direct fixed payment, leaving the manager’s effort incentives free of

distortion and inducing him to exert the first-best level of effort, eFBL : In this scenario, the principal

collects the entire first-best surplus. If the same direct payment scheme were used following a

favorable report, the principal would always report hH; irrespective of the realized signal. To make

truth-telling sequentially rational, the optimal budget must instead distort the manager’s effort

incentives following a favorable report.

The key to reporting incentives is that if the principal reports hH upon observing hL, she could

potentially mislead the manager into believing that his productivity is greater than what her actual

signal predicts. To make truthful reporting in the principal’s interest requires dampening the

principal’s payoff when she reports favorable information and, per Proposition 1, there are two

optimal procedures to do so. The first method involves reducing the fixed payments aH and

simultaneously raising bH to leave the manager with a constant expected profit of 0. The principal’s

payoff from reporting favorable news decreases, because while the manager’s expected profits

remain constant, raising bH causes the manager to distort his effort away from first-best and

therefore reduces the surplus generated. The second method holds constant bH and simply reduces

aH, which directly transfers surplus from the principal to the manager. As we explain next, in

equilibrium the principal uses both methods.

The more informative the principal’s signal, the greater her payoff to misreporting and, hence,

the greater the required distortions to keep her honest. When the principal has no private

information (a ! 0), the problem reduces to the standard moral-hazard problem without adverse

selection. Specifically, since the signal is uninformative, the principal offers the same budget for the

two reports. Since there are no further contracting frictions, the principal provides first-best effort

incentives by setting bH ¼ bL ¼ 0 and reimburses the manager for the cost of effort by setting

aH ¼ aL ¼�pþ 1

2eLhðp�

�pÞ as a! 0. When the principal’s private signal is not very informative,

she gains relatively little from misreporting her private information. Therefore, when a is relatively

small, it suffices to distort the manager’s effort choice by relatively small amounts, which in turn

destroys relatively little surplus. By doing so, the principal avoids paying the manager rents since

both of the manager’s individual rationality constraints and the principal’s truth-telling constraint,

(TT.PL), are binding.

As the signal becomes more informative, the principal’s payoff to misreporting rises, as do the

effort distortions required to satisfying her truth-telling constraint, (TT.PL), and simultaneously

retain all surplus generated. However, when the signal is informative, effort distortions destroy

large quantities of surplus, as noted above. Therefore, when the signal is sufficiently informative,



the optimal budgets ensure that the principal reports truthfully by allowing the manager to retain

informational rents rather than by further distorting his effort. To be precise, the manager’s

individual rationality constraint, (IRH), no longer binds when the signal is sufficiently informative;

i.e., when principal’s payoff to misreporting is sufficiently high, though the principal’s truth-telling

constraint, (TT.PL), continues to bind. The threshold at which the optimal contract switched from

inducing further effort distortions to paying direct informational rents is expressed as a condition on

2hL2hL�hH

h2

H

; which decreases monotonically in signal informativeness, a.

Bottom-Up Budgeting

In a participative, bottom-up budgeting process, lower-level managers are involved in setting

profit targets and the associated direct payments. We model bottom-up budgeting by endowing the

manager exclusively with private information at t¼ 2, and requiring him to report on his signal to

the principal in the budgeting process at t ¼ 3. The prior section showed how the principal could

benefit from misreporting unfavorable information as favorable. The contrary is true when the

manager reports to the principal under participative budgeting. By erroneously reporting favorable

information as unfavorable, the manager causes the principal to undervalue the expected divisional

cash flows and consequently reduce the direct payment requests made of the manager’s division.

Similar to the principal’s problem under top-down budgeting, the optimal bottom-up budget must

limit the manager’s payoff to misreporting. Let ei, j denote the manager’s optimal effort when he

observes hi; but reports hj for fi, jg 2 fH, Lg, and set ei,i [ ei. Accordingly, the principal’s

maximization problem is given by:

maxai;bi

p�aH þ eHhHbHpþ ð1� eHhHÞbH�

p�þ ð1� pÞ

�aL þ eLhLbLpþ ð1� eLhLÞbL�

p�

subject to:

��pþ eHhHðp�

�pÞ�ð1� bHÞ � aH �

1

2Te2

H

��

�pþ eH;LhHðp�

�pÞ�ð1� bLÞ � aL �

1

2Te2

H;L ðTT:MHÞ�

�pþ eLhLðp�

�pÞ�ð1� bLÞ � aL �

1

2Te2

L

��

�pþ eL;HhLðp�

�pÞ�ð1� bHÞ � aH �

1

2Te2

L;H ðTT:MLÞ�

�pþ eihiðp�

�pÞ�ð1� biÞ � ai �

1

2Te2

i � 0; i 2 H; Lf g ðIRÞ

ei 2 argmaxe ehið1� biÞpþ ð1� ehiÞð1� biÞ�p� ai �1

2Te2; i 2 H; Lf g ðICÞ

0 � bi � 1; i 2 H; Lf g:

As before, the principal maximizes her expected profits and the constraints (IR) and (IC)

ensure that the manager does not leave the firm before t ¼ 5 and that he chooses his effort to

maximize his expected utility at t¼ 4. Since the (IC) constraint is identical to top-down budgeting,

the manager optimally chooses ei ¼ 1=Tð1� biÞhiðp��pÞ. Similar to the principal’s truth-telling

constraints in the top-down regime, under bottom-up budgeting, (TT.MH) and (TT.ML) ensure that

the manager truthfully reports his private information h during the budgeting process. Under top-

down budgeting, the informed principal’s only responsibility after observing private information is



to communicate the information to the manager. Under bottom-up budgeting, the informed manager

communicates his private information to the principal and chooses a productive effort. Therefore,

unlike the top-down setting, with bottom-up budgeting the informed party can coordinate his/her

report with the realized private signal. As first discussed in the hierarchy literature (Melumad et al.

1997), the principal thus suffers a ‘‘control loss’’ when reporting duties are delegated downward. In

equilibrium, the principal rationally anticipates the manager’s strategic reporting and discourages

strategic reporting, albeit at a cost.

Proposition 2: Under bottom-up budgeting the optimal budget parameters are as follows:

(i ) When the manager reports an unfavorable signal, bL ¼pðh

2

H�h2

LÞh

2

Lþpðh2

H�2h2

LÞand aL ¼ ð1� bLÞð�pþ½hLðp�

�pÞeLÞ;

(ii ) When the manager reports a favorable signal, bH ¼ 0 and aH ¼ aL þ bL�pþ ½hHð1�

ð1� bLÞ2Þðp� �pÞeH.

As noted in the introduction, the bottom-up setting and results follow the standard adverse-

selection problem introduced by Baron and Myerson (1982). Similar to the top-down contract

menu, the optimal participative budgeting scheme provides first-best production incentives

whenever the informed party reports his/her least preferred news. Specifically, the principal avoids

inefficient variable payments and relies solely on fixed payments to extract surplus when the

manager reports favorable information. However, if the principal would offer a similar contract

following an unfavorable report, then the manager could increase his payoff by misreporting

favorable information as unfavorable. In response, to reduce the manager’s misreporting payoff, the

principal requires the manager to make both a fixed and a variable payment when the manager

reports unfavorable information. The optimal budget ‘‘taxes’’ divisional cash flows by requiring a

transfer to the principal that is only as large as is necessary to satisfy the manager’s truth-telling

constraint, (TT.MH). This causes the optimal contract to impose the greatest effort distortions when

such inefficiencies are least costly.15 Therefore, unlike the optimal top-down contract, the optimal

participative budgeting contract always responds to additional information asymmetry with

additional effort distortions. The two paradigms also differ in their payoffs to the principal and

manager, which we explore in the next section.

IV. SECOND-BEST RESULTS

The choice of budgeting process significantly impacts the firm’s production schedules, slack,

and performance. Each regime poses a unique reporting problem: under top-down budgeting the

principal has an incentive to misreport unfavorable information, while under bottom-up budgeting

the manager has an incentive to misreport favorable information. To counter these incentives, the

optimal budgets under top-down and bottom-up budgeting distort the manager’s effort incentives in

the productive and unproductive states, respectively. The following proposition compares the total

surplus of the two budgeting paradigms.

Proposition 3: Total expected surplus is always greatest in bottom-up systems.

Bottom-up budgeting maximizes total surplus because the surplus lost to inefficient effort is

tied to productivity. When the stakes are greatest, i.e., when a favorable signal is observed,

inefficient effort destroys the greatest value. Accordingly, effort distortions in the top-down

budgeting regime are more destructive than those in a participative budgeting framework. While

15 This corresponds to the ‘‘no distortion at the top’’ result found in the standard adverse-selection and monopoly-pricing paradigms (see Varian 1992).



Proposition 3 analyzes total surplus, the principal chooses a budget system based on her own

expected payoff at t¼5, which equals the total surplus net of agency costs. Therefore, to predict the

prevalence of each budgeting practice, we analyze the principal’s expected payoff.

Proposition 4: The principal only prefers bottom-up budgeting when the privately observed

signal is sufficiently informative.

As a increases, so that the private signal becomes increasingly informative, the expected

productivity with a favorable signal increases, and that with an unfavorable signal decreases.

Accordingly, the cost of inefficient effort under top-down budgeting increases with the level of

private information, whereas the same cost under bottom-up budgeting decreases with private

information. Conversely, as the signal less informative (as a! 0) the principal’s payoff in the two

regimes converges to one another. Although these facts suggest that the principal will always favor

participative budgeting, Proposition 4 establishes that there are exceptions. The intuition behind

Proposition 4 rests with the different responsibilities assigned to the informed party across the two

regimes. The optimal bottom-up budgets recognize that the manager can strategically control his

payoff from misreporting via unobservable effort following his report. In other words, the principal

suffers a control loss since she is unable to coordinate effort and reporting with top-down

budgeting, though the manager can do so under bottom-up budgeting. This causes there to be fewer

opportunities to benefit from misreporting under top-down budgeting because the principal cannot

influence her payoffs after the budgeting process at t ¼ 3. The control loss associated with

participative budgeting is costly, because it raises the rents required to discourage managerial

misreporting. Independent of signal informativeness, participative budgeting may always prove

optimal in sufficiently restrictive settings. For example, Antle and Eppen (1985) rule out all fixed

payments for reasons of managerial limited liability, in which case our model predicts top-down

budgeting will always be dominated, as shown in Lemma 2.

Lemma 2: If the manager is protected by limited liability, then the principal always prefers

bottom-up budgeting.

Lemma 2 implies that Proposition 4 hinges on the principal’s ability to use direct fixed

payments. The use of variable payments is sub-optimal because it distorts the manager’s efforts

away from the efficient first-best levels identified in Lemma 1. While Lemma 2 provides an extreme

setting in which our analysis no longer applies, our results continue to hold in settings where the

manager can accommodate some liability. Specifically, if the manager can shoulder liability up to M. 0 such that a þ bp . �M must hold, then top-down budgeting again dominates participative

budgeting in the presence of relatively little asymmetric information. However, our setting does not

speak to settings where the manager has unlimited, ex ante liability. To understand why, note that if

the manager has sufficient initial wealth, then the principal could effectively sell the division to the

manager at an up-front direct fixed payment equal to the expected first-best profit. The agency

literature generally rules out such contracts based on the argument that the manager or, in this case,

the division, may not have sufficient ex ante funds to pay the principal. However, if the division can

sustain only limited ex post losses, then it is straightforward to show that the principal may prefer

top-down budgeting to the no budgeting alternative whereby the firm is sold to the division at the

limited, maximum price.

To further validate the intuition behind Proposition 4, we next verify that the manager’s rents

and the principal’s payoffs are qualitatively similar across the two regimes.

Proposition 5: Using the optimal budgets, the manager’s rents and the principal’s expected

utility are single peaked and U-shaped, respectively, over signal informative-

ness in both budgetary regimes.



Proposition 5 shows that informational rents are not necessarily monotone with respect to

information asymmetry. Even more surprisingly, the manager’s information rents are single peaked

over the level of information asymmetry, regardless of who observes the asymmetric information.

This non-monotonic relationship between rents and information asymmetry reflects the fact that the

manager’s rents always mirror the informed party’s payoff to misreporting. We measure

information asymmetry as the informed party’s informational advantage. As information

asymmetry increases, the expected productivity in the favorable state rises, while that in the

unfavorable state declines. When the principal falsely reports hH in the top-down paradigm, she

induces the manager to exert eH, and she credits his department for the cost of effort. As the signal

becomes more informative, the marginal return to excessive effort in the unproductive state ðe .

eFBL Þ; decreases linearly with a yet the associated credit grows convexly. Combined, the principal’s

payoff to misreporting, and consequently the manager’s rents, eventually decrease in signal

informativeness under top-down budgeting. A similar tension is behind the manager’s single

peaked rents in the participative budgeting regime. In particular, the control loss discussed above

allows the manager to misreport his signal, and nonetheless exert the efficient level of effort.

However, recall that the two efficient effort levels diverge as signal informativeness increases

(Lemma 1). By falsely reporting hL; the manager will exert less effort than the productive state

warrants. As a ! 1, the manager wishes to increase his effort in the favorable state yet by

misreporting hL; he instead choses a level of effort that decreases as a ! 1. Therefore, the

manager’s payoff to misreporting, and consequently his rents, must (again) decrease as a ! 1.

A natural extension to Proposition 5 would characterize when the principal prefers that neither

she nor the manager receive any private information (a ¼ 0), as opposed to the informed party

receiving perfect information (a¼ 1). Since the answer depends on the value of a set of exogenous

parameters, it is helpful to first define environmental uncertainty.

Definition: An information setting C with support (hH, hL) features more environmental

uncertainty than a setting C0 with support ðh 0H; h

0LÞ provided both share the same

unconditional mean, h ¼ h0; and hL , h 0

L , h 0H , hH:

In our setting, the environmental uncertainty ranking is equivalent to second-order stochastic

dominance. In fact, one can characterize the entire set of information settings admitting an

environmental uncertainty ranking by:

hHðkÞ ¼ hH þ kðhH � hÞhLðkÞ ¼ hL � kðh� hLÞ

k 2 0;hL

h� hL

0@

1A;

where h ¼ phH þ ð1� pÞhL; as before. The parameter k varies the support—and consequently the

variance—of the two alternative productivities while leaving the (unconditional) mean constant.

The upper bound on k ensures that the productivity support remains well defined (strictly positive).

Varying k has the same effect on the conditional expectations hH and hL as does varying the

informational content of the signal, h; via a. The intuition is fairly straightforward; the

informational advantage gleaned from the private signal depends both on the informational content

of the signal itself and the initial uncertainty that is (at least partly) resolved with the signal.

Observation 1: Varying environmental uncertainty while holding fixed the level of private

information is equivalent to holding fixed environmental uncertainty and

varying the level of private information received.

We now return to characterizing the principal’s informational preferences. Recall that the

principal’s preferences were convex over the level of private information, a in both the top-down

and bottom-up settings. However, her preferences must differ across the two regimes, as



Proposition 4 found that she only prefers bottom-up budgeting when the level of information

asymmetry is high.

Corollary 1: The principal prefers that the signal h confer all available information (a ¼ 1)

rather than no information (a ¼ 0), provided the environmental uncertainty is

sufficiently large.

Put differently, Corollary 1 finds the principal favors perfect information over no information

only when the environmental uncertainty is sufficiently large. This result follows from Lemma 1,

which shows that profits are convex in environmental uncertainty. Therefore, as environmental

uncertainty increases, the value of information increases, leading to Corollary 1.

In line with both Shields and Young (1983) and Shields and Shields (1998), our model

distinguishes between the antecedents and the consequences of participative budgeting. In

particular, we assume that the informational setting dictates the optimal budgeting process, and the

budgeting process forms the basis for the types of contracts employed, their limitations, and

consequences. Our results thus far primarily speak to differences between firms within individual

industries, as private information resolved a fixed level of uncertainty. However, we can use our

environmental uncertainty framework to also address cross-sectional analyses involving varying

levels of environmental uncertainty.

It is important to note that changes in the level of information asymmetry and the

environmental uncertainty affect the division’s capacity to generate profits in a similar way.

Although the unconditional expected productivity remains constant as a or k vary, Lemma 1 and

Figure 2 showed that with a fixed mean h; as the conditional expectations hH and hL diverge, the

additional profits in the favorable state dominates the lowered profits in the unfavorable state.

Therefore ceteris paribus, our model predicts a positive correlation between firm profits (principal’s

payoff ) and the use of participative budgeting.

Corollary 2: The use of participative budgeting and an increased firm performance are, ceterisparibus, both associated with elevated levels of information asymmetry and/or

environmental uncertainty.

Merchant (1981) finds evidence in support of Corollary 2, as he identifies a significant

correlation between lower-level managers’ influence on budget plans, and performance. The most

direct test of our hypothesized correlation between information asymmetry and participative

budgeting can be found in Merchant (1984) who reports a significant (positive) correlation between

functional differentiation and individual participation in the determination of budgets. Our

interpretation of functional differentiation as a proxy for informational asymmetry relies implicitly

on the notion that the greater the number of business activities, the lower the likelihood that

managers or principals are informed on the full set of business activities. Note however, that the

causality between participatory budgeting and firm performance is the reverse of common wisdom.

It is not participative budgeting that increases firm performance; instead, circumstances that allow

for higher performance induce firms to use participative budgeting.

The most commonly studied consequence or artifact of the budgeting process is budgetary

slack. Young (1985) defines budgetary slack as ‘‘the amount by which a subordinate understates his

productive capability when given a chance to select a work standard against which his performance

will be evaluated.’’ Young’s (1985) definition of budgetary slack is best captured in our model by

the manager’s informational rents. Specifically, in the bottom-up framework, when the manager

announces high productivity, he collects rents that are equivalent to what he would have earned had

he understated productivity. Top-down budgeting also provides rents whenever high productivity is

reported, the level of which again relates to productivity in the less favorable state. In an

experimental setting, Young (1985) rejects the null hypothesis correlating private information and



budgetary slack in the presence of participative budgeting. Although Proposition 4 predicts that the

use participative budgeting alone signals elevated levels of information asymmetry, Proposition 5

posits that regardless of the budgeting regime employed, budgetary slack is single peaked in the

level of asymmetric information communicated or uncertainty resolved via the budgeting process.

Corollary 3: In either the top-down or bottom-up regime, budgetary slack is single peaked

over the level of asymmetric information.

Corollary 3 follows directly from Proposition 5. Here, our results suggest a potential increase in

budgetary slack following the implementation of participative budgeting as long as both the ex anteand ex post levels of information asymmetry are relatively small. However, because rents were

found to eventually decrease over signal informativeness, our model also predicts decreased

budgetary slack in response to increased levels of information asymmetry where both the beginning

and ending levels are relatively high. Simply put, Young (1985) rejects a monotone relation

between slack and information asymmetry under bottom-up budgeting, whereas our model predicts

a unimodal relation, regardless of the budgeting mode.

V. NUMERICAL EXAMPLE

This section provides a numerical example to illustrate the economic forces in our model. In

what follows, we set the probability of high productivity, p, to p¼ 0.6, the cost of effort T to T¼ 1,

the low and high cash-flow states to�p ¼ 1 and p ¼ 2, and finally, we set the low and high

productivities respectively to hL ¼ 1 and hH ¼ 2.

The intuition behind Proposition 4 can be seen from Figures 3 and 4. The figures plot the

first-best efforts and the second-best efforts under top-down and bottom-up budgeting following an

FIGURE 3Manager’s Effort Following the Unfavorable Signal as Signal Informativeness Varies



unfavorable signal in Figure 3 and a favorable signal in Figure 4. Figure 3 shows that the manager’s

second-best effort following the unfavorable signal, h ¼ hL, is identical to the first-best effort under

top-down budgeting. However, Figure 3 also shows that only the manager’s second-best effort

under bottom-up budgeting is distorted away from the first-best effort. Further, the extent of the

distortion increases with a, the level of private information. Note that in all settings, the probability

of a low productivity realization following an unfavorable signal increases with signal

informativeness. Therefore, barring agency frictions, the first-best response to a more precise,

unfavorable signal is to reduce the effort demanded from the manager. This explains why the

first-best effort level, and consequently the top-down effort level, in Figure 3 decreases with the

level of private information. To understand why the bottom-up effort is also decreasing, recall that

that the regime incentivizes truthful reporting using downward effort distortions and that the

optimal downward distortions increase with the level of private information a, therefore while the

bottom-up regime places multiple tensions on eL, they all tend downward with a in unison.

Figure 4 shows that the opposite is true following a favorable report. In this situation, the

manager’s second-best effort is distorted under bottom-up and the extent of the distortion increases

as a increases. Because the favorable signal is indicative of high-productivity, distortions away

from first-best prove particularly costly in the top-down setting for high levels of private

information. Similar to above, note that the probability of a high productivity following a favorable

signal always increases with signal informativeness, therefore the optimal response to a more

precise favorable signal (absent agency frictions) is to raise the effort demanded from the manager.

The preceding intuition explains why both the bottom-up and first-best effort increases in Figure 4.

However to understand the behavior of top-down effort in Figure 4, recall that the optimal

top-down contract incentivizes truthful reporting by distorting the manager’s effort downward when

FIGURE 4Manager’s Effort Following the Favorable Signal as Signal Informativeness Varies



the signal is relatively uninformative. In Figure 4, the manager’s effort is initially decreasing with

signal precision, because the rate at which the principal must distort the manager’s effort downward

initially outpaces the rate at which the optimal effort increases over a. As predicted by Proposition

1, the principal eventually satisfies her truth-telling constraint in the top-down setting by

relinquishing rents to the manager rather than further distorting his effort, causing the manager’s

effort in Figure 4 to eventually follow in the direction of the efficient, first-best effort level and

increase with informativeness for a . 0.32.

Finally, Figure 5 shows that under top-down budgeting, the principal retains all the generated

surplus for low levels of private information, leaving the manager without rents. When a increases

further, however, the principal has to share the surplus and thereby increase the manager’s utility, as

described in the discussion of the manager’s second-best effort under top-down in Figure 4. On the

other hand, under bottom-up, while the manager earns rents for all levels of private information,

these rents only increase for low values of a and decrease thereafter. The reason for the manager’s

rents to decrease as his private information increases lies again in the second-best effort incentives.

As discussed in Rajan and Saouma (2006), the manager’s informational rents under bottom-up

follow from his payoff to misreporting high productivity as being low. When signal informativeness

is very high, the expected cash flows following an unfavorable report are very low compared to a

favorable report. This causes the agent’s incentive to misrepresent to decrease and allows the

principal to reduce the necessary rents paid to the agent.

Taken together, Figures 3, 4, and 5 illustrate why it is optimal to employ a top-down regime for

low levels of private information but to use bottom-up budgeting for higher levels of private

information. In practice, our findings suggest that budgets are set by senior management when the

information being transmitted is relatively limited, but that lower-level managers will be called

FIGURE 5Manager’s Rents as Signal Informativeness Varies



upon to collect and communicate private information in environments in which they possess more

extensive private information.

VI. CONCLUSION

This paper models the principal’s choice between top-down and bottom-up budget systems.

What differentiates the two settings is the allocation and flow of interim information. In a bottom-up

system, the manager receives interim information and has an incentive to misreport favorable

information as unfavorable, whereas in top-down systems, the principal receives the information

and has an incentive to misreport unfavorable information as favorable. Under bottom-up

budgeting, the budget must provide the manager with informational rents to elicit truthful reporting.

To ensure truthful reporting in the top-down budgeting regime, the budgets must limit the

principal’s payoff upon reporting favorable news, which means she must either destroy surplus,

share surplus with the manager via rents, or both.

We find that the total surplus is always maximized with bottom-up budgeting, because the

optimal bottom-up contract always sustains truth-telling with less surplus destruction than the

optimal top-down contract. However, the principal will still prefer top-down budgeting for smaller

levels of information asymmetry. We develop predictions on the effect of the budgeting regime and

the informational structure on budgetary slack and firm performance. Informally, we can also

address budgetary emphasis for which the most obvious proxy is the extent to which the manager’s

division is rewarded for attaining the budgeted cash flows, 1 � b. The smaller the b facing the

manager’s division, the more his divisional profits—and ultimately, his compensation—rely on

meeting the budgeted target. Here we predict that budget emphasis decreases with information

asymmetry and environmental uncertainty and that it is smaller under top-down budgeting for low

levels of information asymmetry (treating the budgeting regime as given). Budgetary slack is found

to be single peaked over information asymmetry under either regime, and since the first-best-profits

are convex in a, performance increases with environmental uncertainty.

It is important to note that in our model the sole purpose of budgeting is to communicate

private information. If the interim productivity information is publicly available, then there is no

role for budgeting in our model. Furthermore, we acknowledge that in practice, many actual

budgeting regimes are likely to be a mixture of top-down and bottom-up budgeting. In this regard,

our results can be interpreted as comparing different weights on the manager’s versus the

principal’s involvement in the budgeting process. A mixture of both regimes would require that

both principal and manager receive private information. To the extent that either the principal or the

manager are charged with reporting independent information, we suspect that our qualitative results

will remain largely unchanged. However, if the principal’s and manager’s private information

overlap, then the resulting equilibrium will critically depend on off-equilibrium beliefs. To model

overlapping, non-contractible information reporting, one must first settle on a set of reasonable

punishments if one party reports information that conflicts with that of the other.

Another issue for future research is to extend the present analysis to include unobservable,

costly information acquisition. In this framework, the principal would either face a dual

moral-hazard signaling problem, or a screening problem with two moral-hazard tasks. Earlier

research in economics has considered a similar setting where the manager’s private information

relies on his unobservable efforts. Lewis and Sappington (1997) find that ‘‘extreme reward

structures’’ can satisfy both the moral-hazard and consequential adverse-selection problems. We

suspect that the addition of unobservable, costly information acquisition would add similar agency

costs across the two budgeting modes, in which case our primary contribution tying information to

the choice of budgeting regime would persist.



In closing, we note that our model ignores the many behavioral tensions that undoubtedly

contribute to the firm’s choice of budgeting mode. We hope that by presenting an economic

perspective on participative budgeting, future researchers can better delineate how altering

perspectives conflict with ours, and ultimately test which of the two perspectives can best explain

the observed instances of bottom-up versus top-down budgeting.

REFERENCES

Antle, R., and G. Eppen. 1985. Capital rationing and organizational slack in capital budgeting.

Management Science 31 (2): 163–174.

Antle, R., and J. Fellingham. 1995. Information rents and preferences among information systems in a

model of resource allocation. Journal of Accounting Research 33 (Supplement): 41–58.

Arya, A., J. C. Glover, and K. Sivaramakrishnan. 1997. The interaction between decision and control

problems and the value of information. The Accounting Review 72 (October): 561–574.

Baiman, S., and J. H. Evans III. 1983. Pre-decision information and participative management control

systems. Journal of Accounting Research 21 (Autumn): 371–395.

Baron, D. P., and R. B. Myerson. 1982. Regulating a monopolist with unknown costs. Econometrica 50

(July): 911–930.

Braun, K., W. M. Tietz, and W. T. Harrison. 2009. Managerial Accounting. 2nd edition. Englewood Cliffs,

NJ: Prentice Hall.

Brown, J. L., J. H. Evans III, and D. V. Moser. 2009. Agency theory and participative budgeting

experiments. Journal of Management Accounting Research 21: 317–345.

Brownell, P. 1982. A field study examination of budgetary participation and locus of control. TheAccounting Review 57 (October): 766–777.

Christensen, J. 1982. The determination of performance standards and participation. Journal of AccountingResearch 20 (Autumn): 589–603.

Demski, J. S., and G. A. Feltham. 1976. Cost Determination: A Conceptual Approach. Ames, IA: Iowa

State University Press.

Dunk, A. S. 1993. The effect of budget emphasis and information asymmetry on the relation between

budgetary participation and slack. The Accounting Review 68 (April): 400–410.

Eigenwillig, A. 2007. On multiple roots in Descartes’ Rule and their distance to roots of higher derivatives.

Journal of Computational and Applied Mathematics 200 (March): 226–230.

Eso, P., and B. Szentes. 2003. The One Who Controls the Information Appropriates Its Rents. Evanston, IL:

Northwestern University, Center for Mathematical Studies.

Fisher, J. G., L. A. Maines, S. A. Peffer, and G. B. Sprinkle. 2002. Using budgets for performance

evaluation: Effects of resource allocation and horizontal information asymmetry on budget proposals,

budget slack, and performance. The Accounting Review 77 (October): 847–865.

Frucot, V., and W. T. Shearon. 1991. Budgetary participation, locus of control, and Mexican managerial

performance and job satisfaction. The Accounting Review 66 (January): 80–99.

Horngren, C. T., S. M. Datar, and M. V. Rajan. 2012. Cost Accounting: A Managerial Emphasis.

Englewood Cliffs, NJ: Prentice Hall.

Lewis, T. R., and D. E. M. Sappington. 1997. Information management in incentive problems. The Journalof Political Economy 105 (August): 796–821.

Maskin, E., and J. Tirole. 1990. The principal-agent relationship with an informed principal: The case of

private values. Econometrica 58 (March): 379–409.

Melumad, N., D. Mookherjee, and S. Reichelstein. 1997. Contract complexity, incentives, and the value of

delegation. Journal of Economics and Management Strategy 6 (Spring): 257–289.

Merchant, K. A. 1981. The design of the corporate budgeting system: Influences on managerial behavior

and performance. The Accounting Review 56 (October): 813–829.

Merchant, K. A. 1984. Influences on departmental budgeting: An empirical examination of a contingency

model. Accounting, Organizations and Society 9:291–307.

Merchant, K. A. 1985. Control in Business Organizations. Marshfield, MA: Pitman.



dx.doi.org/10.1287/mnsc.31.2.163

dx.doi.org/10.2307/2491373

dx.doi.org/10.2307/2490780

dx.doi.org/10.2307/1912769

dx.doi.org/10.2308/jmar.2009.21.1.317

dx.doi.org/10.2307/2490887

dx.doi.org/10.2307/2490887

dx.doi.org/10.1016/j.cam.2005.12.016

dx.doi.org/10.2308/accr.2002.77.4.847

dx.doi.org/10.1086/262094

dx.doi.org/10.1086/262094

dx.doi.org/10.2307/2938208

dx.doi.org/10.1162/105864097567101

dx.doi.org/10.1016/0361-3682(84)90013-8

Rajan, M. V., and R. Saouma. 2006. Optimal information asymmetry. The Accounting Review 81 (May):

677–712.

Rajan, R. G., and J. Wulf. 2006. The flattening firm: Evidence from panel data on the changing nature of

corporate hierarchies. The Review of Economics and Statistics 88 (November): 759–773.

Riley, J. G. 2001. Silver signals: Twenty-five years of screening and signaling. Journal of EconomicLiterature 39 (June): 432–478.

Roberts, J. 2004. The Modern Firm: Organizational Design for Performance and Growth. New York, NY:

Oxford University Press.

Shields, J. F., and M. D. Shields. 1998. Antecedents of participative budgeting. Accounting, Organizationsand Society 23 (January): 49–76.

Shields, M. D., and S. M. Young. 1993. Antecedents and consequences of participative budgeting:

Evidence on the effects of asymmetrical information. Journal of Management Accounting Research5:265–280.

Stout, D., and K. Shastri. 2008. Budgeting: Perspectives from the real world. Management AccountingQuarterly, IMA (Fall): 18–25.

Varian, H. 1992. Microeconomic Analysis 3e. New York, NY: W.W. Norton & Company.

Young, S. M. 1985. Participative budgeting: The effects of risk aversion and asymmetric information on

budgetary slack. Journal of Accounting Research 23 (Autumn): 829–842.

APPENDIX A

Lemma 1

The principal’s expected payoff is given by:

p�

eHhHpþ ð1� eHhHÞ�p�þ ð1� pÞ

�eLhLpþ ð1� eLhLÞ

�p�� C;

where C denotes the manager’s compensation. Since the principal can dictate an effort choice, the

only condition that C must satisfy is the manager’s participation constraint. The manager’s expected

utility from accepting the contract is given by C� 12

Te2i ; i 2 fH,Lg. We scale the outside

opportunity to zero such that the principal optimally selects C ¼ 12

Te2i : Substituting C into the

principal’s expected utility and solving the first-order conditions with respect to eL and eH yields the

efforts and wage reported in Lemma 1. The principal’s value function V thus becomes (substituting

in C*, eFBL ; eFB

H ; and hi ¼ ahi þ ð1� aÞh):

V ¼�pþ p

1

2T

�hþ að1� pÞðhH � hLÞ

�2

ðp��pÞ2 þ ð1� pÞ 1

2T

�h� apðhH � hLÞ

�2

ðp��pÞ2:

Since V is quadratic in a and ]V]a ¼ 1

T ð1� pÞpðhH � hLÞ2ðp��pÞ2a . 0; first-best profits are both

increasing and convex over a.

Proposition 1

The principal’s maximization problem is presented in the ‘‘Top-Down Budgeting’’ subsection

in Section III. We will ignore constraint (TT.PH) and later demonstrate that the solution to this

reduced program also solves the program above. Ignoring (TT.PH), the manager’s individual

rationality constraint (IRL) must bind at the optimal solution, otherwise the principal could increase

her expected utility by raising aL. Additionally, it is straightforward to show that (TT.PL) must bind

at the optimal solution since the principal can increase aH. However, increasing aH can lead to a

violation of (IRH), which is not possible in equilibrium. To see this, we first examine the reduced

program under the assumption that constraint (IRH) binds, and later under the assumption that it



dx.doi.org/10.2308/accr.2006.81.3.677

dx.doi.org/10.1257/jel.39.2.432

dx.doi.org/10.1257/jel.39.2.432

dx.doi.org/10.1016/S0361-3682(97)00014-7

dx.doi.org/10.1016/S0361-3682(97)00014-7

dx.doi.org/10.2307/2490840

does not. Denoting k ¼ hH

hL� 1; we find that the two programs yield the same value whenever

k ¼ffiffiffi5p� 1: Moreover, for k �

ffiffiffi5p� 1 all constraints are satisfied and the principal’s payoff

between the two programs is greatest when (IRH) binds, and for k .ffiffiffi5p� 1 all constraints are

satisfied and the principal’s payoff between the two programs is greatest when (IRH) does not bind.

Combined, the optimal solution is given as denoted in the proposition.

For the remainder of this appendix, we restrict our proofs to the case where k .ffiffiffi5p� 1; the

techniques are identical for the k �ffiffiffi5p� 1 case; details are available from the authors upon request.

Proposition 2

The principal’s maximization problem is presented in the ‘‘Bottom-Up Budgeting’’ subsection

in Section III. Standard arguments from the adverse-selection literature allow us to conclude that

constraint (TT.MH) and constraint (IRL) are always binding. Substituting these two binding

constraints into the principal’s objective function and maximizing over the two burden-rates bH and

bL yields the provided result. The candidate solution satisfies all the principal’s constraints,

allowing us to conclude that the proposed solution is in fact optimal.

Proposition 3

We measure total surplus, S, as the sum of both the principal and manager’s utility:

S ¼ p eHHhHpþ ð1� eHH hHÞp�e2

HH

2T

� �þ ð1� pÞ eLLhLpþ ð1� eLLhLÞp�

e2LL

2T

� �:

Indicating Bottom-Up (Top-Down) with a BU (TD) subscript, we have:

Sbu � Std ¼ ðp��pÞ2p

p2h6

H � 2ph4

Hh2

L þ�

1þ 4ð1� pÞp�h

2

Hh4

L � 4ð1� pÞph6

L

8T�h

2

L þ pðh2

H � 2h2

LÞ�2

:

The only term that varies in sign is the numerator, which we divide by h6

L to obtain p2k6� 2pk4

þ (1 þ 4(1 � p)p)k2 � 4(1 � p)p. This numerator has at most two roots in p, which are given by2�2k2þk4 6 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�3k2þ3k4�k6p

4�4k2þk6 . Since 1 � 3k2 þ 3k4 � k6 ¼ 0 at k ¼ 1 and is decreasing for all

k . 0 ð ddkð1� 3k2 þ 3k4 � k6Þ ¼ �6kðk � 1Þ2ðk þ 1Þ2Þ, there are no real roots to the numerator of

Sbu� Std in p and, hence, the difference never alternates in sign. Moreover, because the numerator is

trivially positive when p ¼ 0, the difference Sbu� Std must be positive.

Proposition 4

As before, let Pi for i 2 fbu,tdg denote the principal’s payoffs under the bottom-up and top-

down regimes, respectively. The difference in payoff can be written as:

Pbu �Ptd ¼ ðp��pÞ2pðhH � hLÞ

�hHh2

L þ pðh3

H þ 2h2

HhL � 2h3

LÞ4T�h

2

Lð1� pÞ þ pðh2

H � h2

LÞ� :

Note that the sign of the difference is determined by the sign of the numerator. Again,

substituting k ¼ hH

hL� 1 allows us to write the numerator as�kþ p(k3þ 2k2� 2), which is positive

provided that p . kk3þ2k2�2

. However, kk3þ2k2�2

is equal to 1 when k ¼ 1, and the fraction

asymptotically decreases to 0 as k! ‘, therefore given any probability p, there exists a k*(p) such

that Pbu (k) � Ptd (k) � 0 if and only if k � k*(p).



Proposition 5

Bottom Up

The manager’s rents can be expressed as the weighted average of his individual rationality

constraints:

rbu ¼ p eHhHð1� bHÞðp� �pÞ þ ð1� bHÞ�p� aH �

1

2Te2

H

� �

þ ð1� pÞ eLhLð1� bLÞðp� �pÞ þ ð1� bLÞ�p� aL �

1

2Te2

L

� �:

The second term above equals zero because (IRL) was shown to bind in the proof to

Proposition 2. Using the optimal contract from Proposition 2, the manager’s rents are given by:

rbu ¼ pðp�

�pÞ2ð1� pÞ2h4

Lðh2

H � h2

LÞ

2T�h

2

Lð1� pÞ þ pðh2

H � h2

LÞ�2:

Since ]rbu

]a ja¼0 ¼ pðp�

�pÞ2ðhH�hLÞh

T . 0, the manager’s rents are increasing in informativeness

when the signal is entirely uninformative. More generally, we have:

]rbu

]a¼

pðp��pÞ2ð1� pÞ2h3

LðhH � hLÞ

T�ð1� pÞh2

L þ pðh2

H � h2

LÞ�3

mðaÞ; where

mðaÞ ¼ hHh3

L � phLðhHh2

L þ h3

H � h3

LÞ þ p2ðh3

HhL � 2h4

H þ 3h2

Hh2

L � 2h4

LÞ:

We next establish that the rents are unimodal. To this end, we note that the coefficient of m(a) is

positive. We will show that m(a) alternates in sign at most once, by demonstrating that it admits at most

a single root in the interval a 2 (0,1). To facilitate the exposition, we use the notation hH¼ jhL, with j .

1 for the remainder of this proof. To proceed, note that since m(a) is a 4th order polynomial in a, if the

polynomial m(a) has an arbitrary number of roots over a 2 (0,1), the Mobius transformation, ~mðaÞ¼ ð1þ aÞ4m 1

1þa

� �will have exactly the same number of roots in the interval a 2 (0,‘) (see

Eigenwillig [2007] for details). We search for positive roots to the function ~mðaÞ by studying the

coefficients of a, because if m(a) has y positive roots, then the ordered coefficients of m(a) will have

exactly yþ 2g sign variations for an arbitrary positive integer, g. We can write m(a) as:

~mðaÞ ¼ a4h4

Lc4 þ a3h4

Lð1� pþ jpÞc3 þ a2h4

Lð1� pþ jpÞ2c2 þ ah4

Lð1� pþ jpÞc1 þ h4

Lc0;

where:

c4 ¼ ð1� pÞð1� pþ jpÞ4

c3 ¼ ðj � 1Þ�ð1� pÞ2 � 2p

�þ 4ð1� pÞ

c2 ¼ 1� 2j2p2 � j2pþ 5jp2 � 2jpþ j � 3p2 þ pc1 ¼ 1� 7j3p3 � j3pþ 9j2p2 � 3j2pþ 6jp2 � 3jpþ 3j � 8p2 þ 3pc0 ¼ jð1� pÞ � 2j4p2 � j3pð1� pÞ þ 3j2p2 � 2p2 þ p

The sign of the coefficients of as are determined by the signs of cs. With the exception of c4,

which is always non-negative, each cs can be positive or negative. An examination of the roots to c0

to c3 reveals that each has at most one root in p. When p¼ 0, all cs except c0 are positive, therefore

m(a) has a unique root in a. When p¼ 1, all cs except c4 are negative, therefore m(a) again has a



unique root in a. More generally, m(a) will admit a unique root for all 0 , p , 1 provided that

ci � 0� ci�1 � 0 for i . 1, which we prove next. Let pi denote the single root to the coefficient ci

in the interval 0 , p , 1:

p3 ¼2j �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3� 2j þ 3j2

pj � 1

p2 ¼1� 2j � j2 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13� 12j � 10j2 þ 12j3 þ j4

p2ðj � 1Þð2j � 3Þ

p1 ¼3� 3j � 3j2 � j3 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi41þ 54j � 117j2 � 68j3 þ 99j4 þ 6j5 þ j6

p2ðj � 1Þð7j2 � 2j � 8Þ

p0 ¼j3 þ j � 1�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 6j þ j2 � 14j3 � 2j4 þ 8j5 þ j6

p2ðj � 1Þð2þ 2j � j2 � 2j3Þ :

We note that all roots above are equal to 1 when j¼ 1, and p0 � p1 � p2 � p3 for j . 1; thus

ci � 0� pi � p� pi�1 � p� ci�1 � 0 for i ¼ 1,2,3 as was to be shown.

Turning to the principal’s payoffs under bottom up budgeting:

Pbu ¼

�ph

2

H þ ð1� pÞh2

L

�2

� ph2

Hh2

L

2T�h

2

L þ pðh2

H � 2h2

LÞ� ðp�

�pÞ2 þ

�p

Hence:

]Pbu

]a¼�ðp�

�pÞ2ðhH � hLÞð1� pÞp

T�h

2

L þ pðh2

H � 2h2

LÞ�2

nðaÞ; where

nðaÞ ¼ pðhH � hLÞðh2

H � h2

LÞ�

2h2

L þ pðhH � hLÞðhH þ 2hLÞ�� ð1� pÞh5

L:

We first note that ]Pbu=]aja¼0 , 0; implying that the principal’s payoff is decreasing when the

manager’s informational advantage is negligible. To complete the proof, we must show that the

principal’s payoff is either always decreasing, or eventually increasing; i.e., ]Pbu=]a will change

sign at most once over the interval a 2 (0,1). Because the coefficient of n(a) is strictly negative, it is

sufficient to show that n(a) has at most one single root over a 2 (0,1). The number of roots

belonging to n(a) over a 2 (0,1) is identical to the number of roots belonging to ~nðaÞ ¼ ð1þ aÞ5

n 11þa

� �over a 2 (0,‘), the Mobius transform of n(a). As before, we use hH¼ jhL, with j . 1 and

proceed by analyzing the as coefficients of n(a) that we denote Cs below:

C5 ¼ h5Lð1� pÞ

�1þ ðj � 1Þp

�5

, 0

C4 ¼ 5h5Lð1� pÞ

�1þ ðj � 1Þp

�4

, 0

C3 ¼ 2h5L

�1þ ðj � 1Þp

�3

5��

7þ 2ðj � 2Þj�

ph i

C2 ¼ 2h5L

�1þ ðj � 1Þp

�2

5��

10þ j�

jðj þ 3Þ � 9��

p� 3ðj � 1Þ3p2h i

C1 ¼ h5L 5� p

�18� 17j þ 4j3 þ ðj � 1Þ

�20þ 3j

�� 7þ jð3j � 1Þ

��pþ ðj � 1Þ4ð7þ 5jÞp2

�h i

C0 ¼ h5L 1� p� ðj � 1Þðj2 � 1Þp

�2þ ðj � 1Þð2þ jÞp

�h i



The sign of Ci for i , 4 is determined by the expression in the bracketed terms. As p! 0, all

coefficients are positive, implying that ]Pbu=]a has no roots over a 2 (0,1), in which case the

principal’s payoff is uniformly decreasing over a 2 (0,1). As p ! 1, all Ci for i , 4 are negative,

implying that there is a unique root over a 2 (0,1). To sign the coefficients for p 2 (0,1), we search

for roots to each coefficient in the interval p 2 (0,1) by explicitly solving for such roots. Let Pi

denote the root of Ci, then we have:

P3 ¼5

7� 4j þ 2j2

P2 ¼10ðj � 1Þ � j

�1þ jð3þ jÞ

�þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi40� 39j2 þ 26j3 � 9j4 þ 6j5 þ j6

p6ðj � 1Þ3

P1 ¼12ðj � 1Þ � 4j3 � 1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi29þ 4jð2þ 6j � 14j2 þ j3 þ 4j5Þ

p2ðj � 1Þ3ð5j þ 7Þ

P0 ¼2

1þ 2ðj � 1Þðj2 � 1Þ þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 4j3ðj � 1Þðj2 � 1Þ

p

When j¼ 1, the roots are all equal to 1, for all j .1, the roots are ordered P0 � P1 � P2 � P3,

therefore Cs � 0� p � Ps � p . Ps�1� Cs�1 � 0; i.e., the ordered coefficients of n(a) change

sign at most once over a . 0, which implies that n(a) has at most one positive root over the same

interval. Accordingly, n(a) has at most a single root over a 2 (0,1), implying that the principal’s

payoff is either always decreasing, or initially decreasing and eventually increasing.

Top Down

In the top-down regime, the principal’s payoffs are convex in a since:

]2PTD

]a2¼ðj � 1Þ2ðp�

�pÞ2pð1þ pÞ

2Th2

L . 0:

The manager’s rents are single peaked, though they may not be convex since:

]rTD

]a¼ �p

ðp��pÞ2ðhH � hLÞ

4T

�a�� 1þ pð4þ pÞ

�ðhH � hLÞ � ð2þ pÞh

�:

Provided that hH , 4hL, the manager’s rents are increasing throughout the entire range of

signal informativeness, a 2 (0,1). Alternatively, if hH � 4hL, then the manager’s rents are increasing

for 0 , a , ~aðp; hL; hHÞ, 1 and decreasing for 0 , ~aðp; hL; hHÞ, a , 1:



Observation 1

For an arbitrary function, F, we have:

dF

dk¼ ]F

]hH

]hH

]kþ ]F

]hL

]hL

]k

¼ ]F

]hH

ðhH � hÞ þ ]F

]hL

ðhL � hÞ

¼ ]F

]hH

]hH

]aþ ]F

]hL

]hL

]a¼ dF

da:

Therefore, mean preserving spreads attained via k will induce the same effect as raising the

level of private information, a, conveyed with the signal, hi.



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