Performance Aggregation and Decentralized Contracting *

Transcription

1 Performance ggregation and Decentralized Contracting * Gerald. Feltham University of ritish Columia Sauder School of usiness gfeltham@shaw.ca Christian Hofmann LMU Munich Munich School of Management hofmann@wl.lmu.de Raffi J. Indjejikian University of Michigan Ross School of usiness raffii@umich.edu Current version: ugust 014 * We are grateful to Francois Larmande, Florin Saac, and participants at the 014 Workshop on ccounting and Economics for for many helpful suggestions.

2 stract We examine how accounting and reporting practices that aggregate or disaggregate the contriutions of different economic agents influence the choice of organizational form. We consider a principal/multi-agent model where the principal either contracts with all parties directly or delegates part of the contracting authority to one of the agents. Delegating contracts promote etter risk-sharing and generate implicit incentives for the higher-level agent ut they also entail a loss of control in motivating the lower-level agent. However, when performance is aggregated, delegated contracting rights to a higher level agent render contracts more interdependent and create spillovers up and down the hierarchy. Spillovers alter oth agents ehaviors and potentially sway a principal s choice of organizational form. We demonstrate that accounting practices that aggregate the performance contriutions of different economic agents can complement organizational forms characterized y greater decentralization. In contrast, accounting practices that capture the performance contriutions of each agent separately tend to favor more centralized organizational forms. Our findings suggest that in settings where performance measurement systems are more aggregate, decentralization is more prevalent. Keywords: Delegation; Hierarchies; Incentives; Multi-agent contracting; Performance evaluation JEL-code: L, M1, M4

3 1. Introduction Corporate hierarchies and practices such as outsourcing and sucontracting are descried often as ways to organize and motivate work in settings where multiple economic agents jointly contriute to production (e.g., Williamson 1975, Jensen and Meckling 1976). t the same time, contracting theories suggest that organizational forms and structures affect and are affected y other organizational practices including how various parties are evaluated and compensated (e.g., Grossman and Hart 1986, Milgrom and Roerts 199). In this paper, we examine how accounting practices that report the performance of different economic agents in an aggregate or disaggregate fashion critically influence the choice of organizational form. For example, we find that accounting practices that aggregate the performance contriutions of different economic agents complement organizational forms characterized y greater decentralization or delegation. In contrast, we find that accounting practices that capture the performance of economic agents in a disaggregate fashion may e etter suited for more centralized organizations. To examine the relation etween organizational form and performance measurement practices, we consider a simple agency model where a risk-neutral owner engages two risk-averse agents (laeled and ) tasked with the production of joint output. When two or more agents are involved in joint production, one of the more important design considerations is whether the owner contracts with all parties directly or delegates part of the contracting authority to one of the agents. In this spirit, we refer to a centralized organization as one where the owner contracts with oth agents and a decentralized organization as one where the owner contracts with one agent (say gent ) and delegates to gent the authority to contract with the second agent (gent ). We compare the efficiency of these two organizational forms under two alternative assumptions aout how the two agents are evaluated. We refer to measurement practices that 1

4 capture the contriution of each agent separately as disaggregate accounting and practices that capture agents contriutions jointly as aggregate accounting. 1 s an illustrative example of our model, consider an owner (an individual or a company) involved in the completion of a large scale project. The owner can contract directly with multiple parties required to complete the project or she can hire a manager with responsiility to hire other workers as necessary. In the construction industry, for example, general contractors often do some construction work themselves ut, more typically, retain several sucontractors to perform most of the other tasks. Importantly, sucontractors are usually hired and compensated y general contractors without direct input from owners. Of course, elements of oth centralized and decentralized contracting arrangements are common in practice. Unit managers in divisionalized corporations, for instance, are evaluated usually y oth their immediate superiors as well as y more senior managers in the corporate hierarchy. Elements of oth aggregate and disaggregate accounting are also common in practice. In performance evaluation setting, measurement choices are guided in large part y the ease with which the performance of disparate agents can e measured separately. For instance, in production settings where output is easily divisile or produced in a series of discrete separale steps, the performance of workers in each step is, in principle, measurale. In divisionalized corporations, for example, measuring and reporting divisional income for two division managers separately may e just as convenient as reporting aggregate corporate income. In other settings, such separation is much more difficult. For example, in project construction settings, it may e very difficult to verifialy separate the contriution of a general contractor s organizational work 1 In particular, we assume disaggregate accounting implies that there is a single performance measure that reflects each agent s unique contriution to firm value. In contrast, aggregate accounting implies that the agents are evaluated on joint output only or on some other indicator of their joint production.

5 from the contriutions of sucontractors ecause many of the tasks are intertwined or overlap in time. For oth disaggregate and aggregate accounting, we illustrate how the two agents ehaviors under decentralized contracting compare with centralized contracting. We identify three distinct effects. First, we note that if gent is responsile for contracting with gent, then, y definition, gent s incentives cascade down from gent s incentives rather than reflect the principal s ojectives. Hence, decentralized contracting typically give rises to a control loss relative to centralized contracting ecause gent s incentives are not perfectly aligned with the principal s ojectives. Control losses are common in hierarchical organizations (Calvo and Wellisz 1978, Melumad et al. 1995, Williamson 1967) and manifest in our model as more muted incentives for gent. Second, we show that decentralized contracting motivates gent to provide more effort than under centralized contracting ecause decision rights over contracting enales gent to share some of his compensation risk with gent. In particular, gent reduces some of his compensation risk y asing gent s compensation partly on his own performance. Risk sharing with gent enales gent to ear more risk overall, which then manifests in our model as steeper incentives and higher effort for gent. Third, we show that decentralized contracting generates an implicit incentive for gent in the sense that his motivation to provide effort derives not only from his explicit contract with the principal ut also implicitly via his aility to contract with gent. Implicit incentives arise under decentralized contracting for two reasons. First, ecause gent s compensation is ased In construction settings, much of the work done y general contractors usually precedes the hiring of sucontractors, aleit there are some tasks that are simultaneous or even follow those of sucontractors. 3

6 partly on gent s performance, gent has an implicit incentive to decrease his effort in order to economize on paying gent. Second, ecause at the time of contract acceptance gent s eliefs aout his compensation are potentially influenced y gent s effort, gent has an implicit incentive to increase his effort in order to influence those eliefs. 3 When the latter incentive to increase effort is stronger (conversely, weaker) than the former incentive to decrease effort, we descrie the implicit incentive as eing favorale (conversely, unfavorale). Taken together, the comparison of decentralized and centralized contracting under disaggregate accounting generally revolves around a comparison of the aforementioned three effects, i.e., control loss, risk sharing and implicit incentives. Whereas the control loss effect favors centralized contracting, the risk sharing effect favors decentralized contracting. Hence, whether centralized or decentralized contracting is ultimately preferale for the principal depends on the extent to which the third effect, the implicit incentive, is favorale or unfavorale. For instance, for identical agents evaluated under disaggregate accounting, we show that decentralized contracting is more profitale than centralized contracting if the implicit incentive is not too unfavorale. Conversely, we find that centralized contracting is more profitale than decentralized contracting if the implicit incentive is sufficiently unfavorale. With aggregate accounting, where agents are evaluated jointly on their aggregate performance, the control loss, risk sharing and implicit incentive effects manifest jointly as well. Importantly however, contracts under a decentralized structure are more interdependent and incentives are intertwined as if oth agents are responsile for oth tasks. We refer to this effect 3 gent can influence gent s eliefs aout his future compensation if, for instance, gent performs at least some of his duties prior to hiring gent and gent has some awareness of gent s performance. In construction settings, for example, sucontractors such as electricians and plumers are likely cognizant of at least some of the project organization work done y the general contractor prior to accepting their employment. gent s implicit incentives to increase his effort in our setting is akin to the types of implicit incentives that arise in dynamic contexts where past performance often conditions future eliefs and contracts (e.g., Christensen et al. 013; rya and Mittendorf 011; utrey et al., 010; Feltham et al. 006; Christensen, et al. 003; Holmström 1999; Indjejikian and Nanda 1999; Gions and Murphy 199). 4

7 as incentive spillovers and note that they influence the ehavior of oth agents. In particular, we find that spillovers can sway the tradeoff for oth agents in a complementary way in the sense oth agents exert more effort under decentralized contracting than under centralized contracting. This contrasts with disaggregate accounting where delegating contracting rights to a higher-tier agent always dampens the performance of agents in lower tiers of the hierarchy (i.e., gent ). The idea that aggregate accounting generates spillovers under decentralized contracting raises the possiility that aggregate accounting practices complement decentralization more so than disaggregate accounting practices. To address this question, we compare the owner s profit with an aggregate performance measure to her profit with disaggregate measures assuming decentralized contracting prevails. In particular, we consider a setting where an aggregate measure is simply the sum of two constituent (and statistically independent) disaggregate measures so that, y construction, aggregation implies a loss of performance-relevant information. Despite this loss of information, we find that aggregate accounting may e more profitale than disaggregate accounting if the spillover effects are sufficiently consequential. The principal-agent literature in accounting and economics has considered the classic prolem of responsiility assignment in organizations from a variety of perspectives. The advantages and disadvantages of decentralized contracting, for instance, have een linked to the possiility of side contracting and collusive ehavior among agents (e.g., Tirole 1986, Laffont and Martimort 1998, Macho-Stadler and Perez-Castrillo 1998, aliga and Sjöström 1998, Feltham and Hofmann 007), to the presence of contracting imperfections including restrictions on communication (Melumad et al. 199, 1995, 1997), and to the possiility that agents efforts may e strategic complements (e.g., Jelovac and Macho-Stadler 00). Our model astracts away from most of these considerations. In particular, we feature a linear-exponential-normal (LEN) model without strategic complementarities or sustitutailities, 5

8 communication, collusion, or side contracting. 4 Perhaps the closest reference to our study is Hortala-Vallve and Villala (010). They also compare centralized and decentralized contracting in a LEN model ut they do not compare alternative performance measurement practices nor do they highlight the role of implicit incentives in assessing the efficiency of decentralized contracting. Despite the simplifications of our model, we show that contracting structure still matters. Moreover, we expect that the forces we highlight such as risk sharing, control loss, implicit incentives and effort spillovers likely prevail in more general models ecause these are precisely the kinds of effects attriuted to oserved practices such as outsourcing and sucontracting (e.g., Eccles 1981). Our results also give some insight aout the types of performance measurement practices that drive the use of (or are associated with) sucontracting and outsourcing versus the performance measurement practices of more vertically integrated organizations where typically contractual rights are concentrated at higher levels in the hierarchy. The remainder of the paper is organized as follows. Section presents the model as well as the timeline in oth a centralized and a decentralized contracting structure. Section 3 compares centralized and decentralized contracting structures assuming disaggregate accounting. Section 4 compares centralized and decentralized contracting structures assuming aggregate accounting. Section 5 illustrates the complementarity etween aggregate accounting and decentralized contracting. Section 6 concludes.. The Model We consider a single-period model where a risk-neutral principal hires two agents, agents and, to jointly produce output x. We assume the output can e expressed as 4 For example, under centralized contracting, we do not allow gent to offer a side-contract to gent. Similarly, under decentralized contracting, we do not allow the owner to offer a side-contract to gent. 6

9 xaa (1) where a i represents the activities of gent i=,, i is the marginal productivity of gent i s effort, and N (0, ) represents other factors unrelated to the efforts provided y the agents. We assume agents and are risk averse with identical preferences characterized y negative exponential utility functions with risk aversion coefficient r ; assuming different preferences with r r does not qualitatively affect our results. The agents provide costly effort to the tune of ½a i ut their efforts are not directly oservale or verifiale. 5 We assume that the agents compensation contracts, z and z are linear functions of verifiale measures of their performance. With aggregate accounting, we assume joint output x (or another metric of joint output) is the only verifiale performance measure. With disaggregate accounting, we assume there are two distinct measures; yi a i i i, i=, () where N (0, ) and and are uncorrelated. i i Finally, we assume that the agents compensation is set to ensure that they accept their contract and, without loss of generality, we set their reservation certainty equivalent to zero. The timeline of our model unfolds as follows: Stage 1: The principal chooses gent s contract z to maximize her expected net payoff, which is the difference etween her gross payoff, x, and the compensation of c, paid to gent. Stage : 5 We preclude the possiility of agent collusion and note that oth the agents marginal products (the s) and their effort disutilities (the ½a i s) are independent. lthough these are simplifications, they ensure that all possile interactions etween the two agents manifest through the focal features of our model, i.e., through the contracting structure and/or through the characteristics of the performance measures. 7

10 fter accepting the contract offered y the principal, gent chooses his effort a. Stage 3: The principal and oth agents oserve a signal of the form Ψ a where N(0, ) is potentially correlated with the performance measure(s) that will ultimately e realized for gent. In particular, we assume is correlated with in the aggregate accounting setting and in the disaggregate accounting setting. We assume Ψ is soft unverifiale information and thus cannot e explicitly contracted on. 6 Stage 4: This is the contracting stage for gent. ased on Ψ, gent accepts his contract z and chooses his effort a. Importantly, the principal chooses z under centralized contracting ut that choice is delegated to gent under decentralized contracting. We also preclude the possiility of side-contracting. That is, under centralized contracting gent cannot offer a sidecontract to gent. Similarly, under decentralized contracting, the principal cannot offer a sidecontract to gent. Stage 5: The performance measures are realized, the agents are compensated and the principal otains her payoff. The timeline outlined aove is the same for centralized and decentralized contracting except for Stage 4. In Stage 4, under centralized contracting the principal contracts with gent 6 Ψ is unverifiale in the sense that no outside authority responsile for enforcing a contract can oserve the signal directly. However, ecause Ψ is commonly oserved y all parties, one approach to rendering it verifiale is through a revelation mechanism where all parties truthfully reveal their information to an outside authority or a court of law. We preclude such mechanisms ecause, as Hermalin and Katz (1991) note, such a characterization of courts is not descriptive of practice. That said, we allow for the possiility that Ψ may e indirectly useful in structuring compensation arrangements. Indirect contracting ased on unverifiale information also manifests in dynamic settings where contracts are renegotiated ased on unverifiale information revealed at interim stages (e.g., Hermalin and Katz 1991; Christensen et al., 013). 8

11 whereas under decentralized contracting gent contracts with gent. The solution to the incentive prolem for oth decentralized and centralized structures is y ackward induction which we demonstrate in sections 3 and 4. In section 3, we compare the profitaility of centralized versus decentralized contracting structures assuming disaggregate accounting. In section 4, we compare the profitaility of centralized versus decentralized contracting assuming aggregate accounting. Finally in section 5 we compare aggregate accounting with disaggregate accounting, assuming a decentralized contracting structure and a particular aggregation rule. 3. Disaggregate Performance Measures and Organizational Form Our characterization of disaggregate performance measures is straightforward. Given yi a i i i, i=,, we write the agents compensation as c ( y, y ) f v y y, i,j=, with i j, (3) i i i i i j where f i is the fixed component of agent i s compensation, v i is the incentive rate for own performance y i, and i is the incentive rate for the performance of the other agent j. In addition, we assume that Ψ a is positively correlated with gent s performance measure y a. That is, Cov( y, ) 0. In what follows, we characterize the optimal contracts under centralized and decentralized structures separately and then compare the agents effort and the principal s expected net payoff under oth organizational forms. 3.1 Centralized contracting Under centralized contracting, the derivation of the agents efforts and the principal s expected profit is straightforward. We state the results in Lemma 1 elow and defer the details to the ppendix. 9

12 Lemma 1: In an organization characterized y disaggregate performance measures and centralized contracting, the agents efforts, their incentive contracts, and the principal s expected profit are: a DC DC i v i i, i=, (4) v DC i i i r i DC ; 0, i=, (5) i and 4 4 DC 1 r r. (6) s expected, Lemma 1 suggests that agents centralized contracts are separale ecause the performance of one agent is not informative aout the other agent s effort. The principal s expected net payoff in (6) provides a enchmark against which we compare the consequences of decentralized contracting in section Decentralized contracting With decentralized contracting, the principal chooses contract z ( f, v, ) ut delegates the choice of contract z ( f, v, ) to gent. Moreover, as we noted in section, all parties oserve a common signal, Ψ a, efore gent accepts his contract z from gent and efore his choice of a. This implies that gent s certainty equivalent from accepting gent s contract depends on the realization of Ψ and is given y r CE( Ψ, z; a, aˆ ) E( c Ψ; a, aˆ ) ½a Var( c Ψ; a, aˆ ) (7) where a ˆ represents gent s conjecture with respect to gent s action. Sustituting c and y into (7) and differentiating with respect to a yields gent s optimal choice of effort, a v, (8) 10

13 where the superscript refers to the comination of disaggregate information and decentralized contracting. To induce gent to accept contract z in Stage 4, gent offers a fixed salary that reflects the signal Ψ oserved in the prior stage. Setting (7) equal to zero and using (8), we write gent s incentive rationality constraint as 1 1 f ( ) Var( Ψ; ˆ ) E( Ψ; ˆ ) r y a r v y a v (9) where Var( y Ψ; aˆ ) 1. (10) and E( y Ψ; aˆ ) aˆ Ψ aˆ In Stage 4 then, gent chooses gent s contract z to maximize his certainty equivalent conditional on Ψ, r CE( z, z ; a, aˆ ) E( c c ; a, aˆ) ½a Var( c c ; a, aˆ) (11) suject to gent s IC and IR constraints given y (8) and (9) respectively. Given the expressions for c and c in (3) and sustituting the IC and IR constraints, the solution to gent s unconstrained maximization prolem yields gent s contract, v h and 1 v. where h r r (1) Two notale oservations emerge from (1). First, we note that gent s incentives ( v, ) cascade down from gent s incentives, ( v, ), rather than reflect the principal s ojectives. For instance, gent is compensated on y (i.e., v 0 ) if and only if gent is also compensated on y (i.e., 0 ). Second, gent is compensated on y (i.e., 0 ) despite the fact that y only captures gent s contriution to firm value. Setting 0 11

14 reflects gent s motivation to share risk with gent. For example, the coefficient ½ multiplying v in (1) reflects the fraction of total risk that is efficiently orne y gent. 7 In Stage, prior to the oservation of Ψ, gent chooses his effort a to maximize his certainty equivalent given y r CE( z, z, a, aˆ) E( c c; a, aˆ) ½a Var( c c; a, aˆ ) (13) which implies that: a v 1, (14) where is defined in (1). Expression (14) suggests that gent s motivation to perform his task derives from two sources; explicitly via his contract with the principal through the v term in (14) and implicitly via his relationship with gent through the 1 term in (14). Implicit incentives arise under decentralized contracting for two reasons. First, ecause gent s compensation is ased partly on y (i.e., through the y component in (3)), gent has an implicit incentive to decrease his effort in order to economize on paying gent. This is the term. Second, ecause at the time of contract acceptance gent s eliefs aout his compensation are potentially influenced y gent s effort, gent has an implicit incentive to increase his effort in order to influence those eliefs. 8 When the latter incentive to increase effort 7 We note that in a more general setting where r r, the coefficient multiplying which is the ratio of gent s risk tolerance to the sum of the risk tolerances of the two agents v in (1) is r / r r 8 gent s implicit incentives to increase his effort and therey influence gent s eliefs is similar to the types of implicit incentives that arise in dynamic contexts where past performance conditions future eliefs (e.g., Christensen et al. 013; Gions and Murphy 199).

15 is stronger (conversely, weaker) than the former incentive to decrease effort, we descrie the implicit incentive as eing favorale (conversely, unfavorale). In Stage 1, the principal chooses z ( f, v, ) to maximize her expected net payoff, E( x c ), suject to the two agents incentive compatiility constraints, (8) and (14), gent s individual rationality constraint that the certainty equivalent in (13) e greater than zero, and gent s choice of gent s incentive rates, (1). We have: Lemma : In an organization characterized y disaggregate performance measures and decentralized contracting, the agents efforts, their incentive contracts, and the principal s expected profit are: a v ( 1), a v (15a) v 1 1 ( 1) ( 1) r, / h 1h h r r (15) v h, 1 v where h r r, (15c) and ( 1) h 1 ( 1) r r r h 1 1 (15d) 3.3 Comparing Centralized and Decentralized Contracting To illustrate the advantages and disadvantages of decentralized contracting, we compare the agents efforts to their corresponding effort under centralized contracting. For gent, we have: a DC a r 1 ( (1 ) / 1 ). (16) r 13

16 r (1 )/ The ratio 1 1 ( 1) in (16) highlights two distinct effects that distinguish centralized and decentralized contracting for gent. The first effect is due to the risk orne y gent under decentralized contracting. This is represented y r which is less than the (1 ) / corresponding term under centralized contracting, given y r. We lael this effect a risksharing effect. Intuitively, decentralized contracting motivates gent to provide more effort in Stage ecause their joint oservation of Ψ later in Stage 3 enales him to share his y -related compensation risk with gent. Of course, if 1 so that the signal Ψ reveals y perfectly, then decentralized contracting does not offer risk sharing opportunities ecause once Ψ is oserved there is no y -related compensation risk left to e shared. Second, expression (16) illustrates that decentralized contracting generates an implicit incentive for gent as long as 1. We lael settings where 1 as favorale ecause they motivate an increase in effort, and conversely we lael settings where 1 as unfavorale ecause they motivate a decrease in effort. s noted earlier, implicit incentive arise in our model ecause gent s compensation is ased on gent s performance and ecause gent s eliefs aout his compensation are potentially influenced y gent s effort. From (16), we note that favorale implicit incentives reinforce the risk-sharing effect so that gent always provides more effort under delegated contracting than under centralized contracting. In contrast, unfavorale implicit incentives counteract the risk-sharing effect so that the comined effect is potentially amiguous. We have: Proposition 1. 14

17 With disaggregate performance measures, gent provides more effort under decentralized contracting than under centralized contracting if and only if his implicit incentives are not too unfavorale. In particular, a a DC if and only if (1 ) 1. (17) Proof: See ppendix. To illustrate the tradeoff underlying Proposition 1, consider a setting where y is a garled version of Ψ (e.g., y where N(0, ) is an independent noise term). It follows that decentralized contracting generates a risk sharing enefit ecause ( ) 1 ut does not generate implicit incentives ecause 1. Hence, the condition in Proposition 1 is easily met. Now consider a different setting where Ψ is a garled version of y (e.g., y where N(0, ) is an independent noise term). In this case 1 and it is easy to show that the unfavorale implicit incentives outweigh the risk sharing enefits of decentralized contracting. The comparison of gent s effort under centralized and decentralized contracting is more straightforward. We have: a DC a 0 where 3 3 1h r r h r h r r. (18) In contrast to gent, we note that gent s incentives are always more muted under 1 h decentralized contracting ecause of the additional risk premium term r. This reflects a control loss ecause delegated contracting implies that gent s incentives in essence cascade down from gent s incentives rather than reflect the principal s ojectives. 15 h

18 Taken together, the preceding discussion suggests that the principal s preference for a decentralized contracting structure reflects a tradeoff etween the potential enefits of a more productive gent (due to risk sharing and implicit incentives) and the control loss associated with a less productive gent. Clearly, a setting where gent s contriution to joint output is much more significant than gent s contriution favors decentralization. Conversely, a setting where gent s contriution is much more significant favors centralization. Of course, this would also suggest that the principal s choice of whom to anoint as gent versus gent matters. To ypass such concerns, we consider a standard setting with identically productive agents (i.e., ) and equally precise performance measures (i.e., ) so that the agents and are a priori interchangeale. This implies that Lemma can e rewritten as: DC in Lemma 1 and in DC 4 r (19a) and ( 1) ( 1) r r 3 6 r ( r ) (19) comparison of (19a) and (19) suggests the following proposition: Proposition. With disaggregate performance measures and identical agents, the principal prefers decentralized contracting if and only if agent s implicit incentives are not too unfavorale. In particular, DC if and only if ( 1 )( 1 k1) 1 (0) 1 where 0 k 1 is defined in the ppendix. 16

19 Proof: See ppendix. We note that the condition in favor of decentralized contracting in Proposition is stricter than the condition in Proposition 1 (ecause k1 0 ). This reflects the fact that the enefits of a more productive gent are partially offset y a less productive gent. Consider for instance the setting illustrated earlier for Proposition 1 where y is a garled version of Ψ and there are no implicit incentives (i.e., 1). Whereas 1 implies that decentralized contracting always generates risk-sharing enefits, these enefits must e sustantial enough to outweigh the control loss due to gent. For the example under consideration, we can show that the risk sharing enefits outweigh the control loss if and only if is not too large. Taken together, Propositions 1 and suggest that, with disaggregate measures, decentralized contracting is more profitale than centralized contracting if implicit incentives are not too unfavorale and/or risk-sharing enefits are sustantial. Conversely, we find that centralized contracting is more profitale than decentralized contracting if implicit incentives are sufficiently unfavorale and/or risk-sharing enefits are immaterial. 4. ggregate Performance Measures and Organizational Form In this section, we consider how an aggregate performance measure affects the tradeoff etween centralization and decentralization. This aggregate measure may e output x itself or some other indicator of the agents joint output. For example, in the construction setting cited earlier, the interrelated nature of the work performed y a general contractor and a sucontractor may make it more natural to measure their contriution jointly rather than separately. ssuming the aggregate performance measure is output x a a with ~ N (0, ), we write the agents compensation as c ( x) f vx, i=, (1) i i i 17

20 where f i is the fixed component of agent i s compensation and v i is the incentive rate on aggregate output. s in section 3, we assume that the principal and oth agents oserve an unverifiale signal Ψ a. In addition, we assume that Ψ is positively correlated with output xa a where Cov(, ) 0. x In what follows, we characterize the optimal contracts under centralized and decentralized structures, and compare the agents effort and the principal s expected net payoff under oth organizational forms. 4.1 Centralized and Decentralized contracting For centralized contracts ased on aggregate output x, the agents efforts, the compensation coefficients and the principal s profit mirror the corresponding constructs in Lemma 1 ut for the fact that gent s contract can now e conditioned on the oservation of Ψ. We state these without proof in the following Lemma: Lemma 3: In an organization characterized y aggregate performance measures and centralized contracting, the agents efforts, their incentive contracts and the principal s expected profit are: a C C i v i i ; i=, (a) v C r v C r (1 ) () and 4 4 C 1 1 r r, (c) (1 ) where the superscript C refers to aggregate information and centralized contracting. With decentralized contracting, the sequence of events and the derivations with an aggregate performance measure parallel our earlier analysis in Section 3. Hence for parsimony we do not repeat it here. We have: 18

21 Lemma 4: In an organization characterized y an aggregate performance measure and decentralized contracting, the agents efforts, their incentive contracts and the principal s expected profit are: and where D D D D D a v 1 v, a v (3a) v D D 1H 1 H H H r H 1 1H 1 H H H r H D D, v Hv (3), (3c) r 1 H r1 and the superscript D refers to the comination of aggregate information and decentralized contracting. In contrast to the disaggregate performance measurement in Lemma, the highlight of Lemma 4 is that performance aggregation and decentralized contracting renders the agents contracts more interdependent. That is, their incentives are intertwined in the sense that oth agents are evaluated as if they are responsile for oth tasks. This is an important consequence of performance aggregation coupled with decentralized contracts and does not arise in any other setting. In particular, we note that the productivity of gent,, affects gent s incentives and correspondingly affects gent s incentives despite the fact that oth output and the agents cost of effort are separale in the two agents efforts. 4. Comparing Centralized and Decentralized Contracting To illustrate the advantages and disadvantages of decentralized contracting with performance aggregation, we compare the agents efforts to their corresponding effort under centralized contracting. For gent, we have: 19

22 a 1 3 H 3 1 H ( 1) D C a 1 (1 )] r 1 H r [ H 1 H( 1) 1 H( 1) (4) and the corresponding expression for gent is: a 1 H ( 1) 3 1 H 3 D C a 1 H ( 1) 1 r H 1 r (1 ) 1 H r H H. (5) (1 ) where H r1 r1. The comparisons in (4) and (5) suggest that the risk-sharing and implicit incentive effects identified earlier in Section 3 for disaggregate measures continue to prevail with an aggregate measure. In particular, we note that the ratio r [ 1 H(1 )] 1 H ( 1) in the denominator of D a in (4) parallels a similar ratio in (16). Hence, decentralized contracting facilitates risk sharing and generates implicit incentives for gent as efore. 9 Similarly, (5) suggest that there is a control loss associated with motivating gent via a decentralized contract and this is reflected in the additional risk premium in the denominator of a. D These similarities notwithstanding, the comparisons in (4) and (5) highlight the unique impact of performance aggregation, namely interdependent contracts and intertwined incentives. In particular, we note that oth comparisons reflect an additional term which we refer to as incentive spillover effects to underscore the notion that the incentive spillover for gent depends on while the incentive spillover for gent depends on. While it is clear that 9 For instance, if 0, H 1 and the comparison in (4) mirrors exactly the comparison in the disaggregate case in Proposition 1. 0

23 these spillover effects sway the tradeoff for oth agents, it is particularly salient for gent. For instance, unlike Section 3 where decentralized contacting always dampens gent s effort, we find that decentralized contracting with an aggregate measure can enhance gent s effort if incentive spillovers outweigh the control loss effect. We have: Proposition 3. (i) With an aggregate performance measure, gent provides more effort under decentralized contracting than under centralized contracting if and only if gent s D C implicit incentives are not too unfavorale. In particular, a a if and only if 1 k where k 0 is defined in the ppendix. (6) (ii) With an aggregate performance measure, gent provides more effort under decentralized contracting than under centralized contracting if gent s incentive spillovers are not too small (i.e., is not too small) and gent s implicit incentives are not too favorale (i.e., / is not too large). Proof: See ppendix. Part (i) of Proposition 3 suggests that the risk sharing and implicit incentive effects for gent identified earlier (Section 3 and Proposition 1) are not sustantively affected y incentive spillovers due to performance aggregation. For instance, expression (4) shows that when gent s implicit incentives are favorale (or not too unfavorale), then the spillover effect reinforces gent s incentives to provide effort. Part (ii) of Proposition 3 is a unique consequence of performance aggregation. In particular, it suggests that the strength of gent s incentive spillovers depends critically on gent. Of course, if is small, then the incentive spillovers for gent are also small ecause gent s incentives necessarily cascade down from gent. Moreover, if gent s 1

24 implicit incentives are unusually strong then again the incentives that cascade down to gent are relatively weak. Hence, the incentive spillover effect is muted as well. Overall, Proposition 3 implies that if gent s implicit incentives are extreme (either too favorale or too unfavorale), then the incentives of the two agents will diverge under decentralized contracts so that one will provide more effort while the other will provide less effort than under centralized contracts. On the other hand, if gent s implicit incentives are modest (neither too favorale nor too unfavorale), then oth agents will likely provide more effort with decentralized contracts than with centralized contracts. To illustrate the principal s overall preference taking into account oth agents contriutions, we again consider a parsimonious setting with identical agents (i.e., ) so that the gents and are a priori interchangeale. This implies that: r r C (1 ) (7a) and D H H H r H r H (7) where H 1 r r 1. comparison of (7a) and (7) suggests the following proposition. Proposition 4. With aggregate performance measures and identical agents, the principal prefers decentralized contracting if and only if gent s implicit incentives are not too extreme. Proof: See ppendix. Our analysis in this section suggests that the use of aggregate performance measures in decentralized contracting environments gives rise to positive spillover effects. Moreover, Propositions 3 and 4 imply that spillover effects coupled with modest implicit incentives jointly

25 promote a preference for decentralized contracting. This suggests that aggregate performance measures potentially complement decentralized contracting practices, and perhaps more so than disaggregate measures. For instance, whereas with disaggregate measures gent always delivers lower profits with decentralized contacting than with centralized contracting, with an aggregate measure gent can potentially generate more profit with decentralized contracting than with centralized contracting (see Proposition 3). We address the potential for complementarity etween aggregate performance measures and decentralized contracting in the next section. 5. Complementarities etween ggregate Performance Measurement and Decentralized Contracting To investigate whether aggregate performance measures complement decentralized contracting more so than disaggregate measures, in this section we compare the principal s profit with an aggregate performance measure to her profit with disaggregate measures assuming decentralized contracting is the norm. Comparing a single aggregate measure to a pair of disaggregate measures requires a rule as to how to comine two measures into one or a formula as to how to separate an aggregate measure into two disaggregate ones. For our model, we adopt a simple aggregation rule which specifies that the aggregate measure is the arithmetic sum of two disaggregate measures. In particular, we assume that the disaggregate measures are as specified in Section 3, i.e., y a and y a, and write the aggregate measure as Y y y. To further simplify the analysis, we also assume identical agents (i.e., ) and comparale performance measures (i.e., ) so that the agents and are a priori interchangeale. This implies that Y ( a a ) with Var( Y ). Finally, as in 3

26 Section 3, we assume that the signal is correlated with agent s disaggregate report, Cov[ y ], so that, Cor [ Y, ] ½ and V ar[ Y ] ( ). If Y y y as descried aove, then evaluating agents performances ased on Y necessarily implies a loss of performance-relevant information, i.e., on an agent-y-agent comparison, the signal-to-noise ratio decreases. Hence, it is straightforward to show that, under centralized contracting, the principal always prefers disaggregate reporting, i.e., C DC. Our ojective is demonstrate that, despite the loss of performance-relevant information, aggregate accounting can complement decentralized contracting in the sense that D. From (19), we have an expression for for identical agents: ( 1) ( 1) r r 3 6 r ( r ). (8) D We also have an expression for in (7) which, under the simplifying assumptions of this section, translates to: D H H H r H r H, (9) where H r r. We have: Proposition 5. With decentralized contracting and identical agents, the principal prefers an aggregate performance measure if and only if gent s implicit incentives are not too extreme. Proof: See ppendix. In general, aggregation coarsens performance-relevant information and suggests a preference for disaggregate information. Yet, Proposition 5 suggests that, under decentralized 4

27 contracting, there is a countervailing effect. s we noted earlier in Section 4, positive spillover effects due to aggregation coupled with the implicit incentives that arise in decentralized contracting potentially motivate oth agents to e more productive. If the joint effects of the positive spillovers and implicit incentives are sufficiently pronounced, then a single aggregate performance measure may e more profitale than a pair of disaggregate measures. 6. Conclusion We examine whether accounting practices that measure the performance of different economic agents either jointly or separately influence the decision to delegate contracting rights in an organization. In particular, we compare the profitaility of a centralized structure where all contracts are centrally determined to a decentralized structure where individuals in higher tiers of a hierarchy set the contracts for others. For oth disaggregate and aggregate performance measures, we identify circumstances under which a decentralized contracting structure is etter than a centralized structure and vice versa. Decentralized contracting, for instance, improves risk sharing among agents in a hierarchy ut also implies a loss of control. Decentralized contracting also implies that higher-tier agents (i.e., those responsile for contracting) face implicit incentives that derive from their own contracting authority rather than from their relationship with the principal. Implicit incentive of higher-tier can e eneficial or detrimental to an owner depending on the nature of information that governs the agency relationship. With aggregate performance measures, where agents are evaluated jointly on their aggregate performance, contracts under a decentralized structure are more interdependent and incentives spill over as if oth agents are responsile for oth tasks. The implication is that, under some circumstances, incentives for higher-tier agents can complement or reinforce the incentives for lower-tier agents. Indeed, we find that if the spillover effects are sufficiently complementary, 5

28 then aggregate performance measures may e etter than disaggregate measures despite the coarseness usually associated with aggregation. Finally, we note that our results provide some insight aout the types of performance measurement systems we oserve in practice. For instance, we expect economic arrangements where most activities are organized inside the firm (e.g., vertically integrated firms) are also settings where more detailed or disaggregate accounting practices prevail. In contrast, we expect organizations that rely more heavily on suppliers and contractors eyond the oundary of the firm to employ less detailed or more aggregate accounting practices. 6

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32 ppendix Proofs Proof of Lemma 1 We solve for the optimal contract under centralized contracting and disaggregate reporting using ackwards induction. Under centralized contracting, gent s certainty equivalent from accepting the principal s contract in Stage 4 is characterized y r CE( ; z, a, aˆ) E( c Ψ; a, aˆ) ½a Var( c Ψ; a, aˆ ), (1) where z ( f, v, ), c is defined in (3) and a ˆ represents gent s conjecture with respect to gent s action. Sustituting () and (3) and differentiating with respect to a provides gent s optimal choice of effort, a DC DC v, () where the superscript DC refers to the comination of disaggregate information and centralized contracting. 10 In Stage 4, the principal chooses z ( f, v, ) to maximize her expected net payoff, ( a c), suject to gent s incentive compatiility constraint in () and the individual rationality constraint that the gent s certainty equivalent in (1) e greater than his reservation certainty equivalent of zero. Sustituting the IC and IR constraints and solving for the unconstrained maximization prolem in terms of v and yields: DC v r ; DC 0. (3) In turn, gent s certainty equivalent from accepting the principal s contract in Stage 1 is characterized y 10 We note that agent i s action choice is independent of the other agent s action choice. Hence, any pair of linear contracts induces a unique dominant strategy in the sugame played y the agents (Holmstrom and Milgrom 1990). 30