Moral hazard and reputational concerns in teams: Implications for organizational choice

,~ ElSEViER

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International Journal of

Industrial

International Journal of Industrial Organization 14 (1996) 297-315

Organization

Moral hazard and reputational concerns in teams" Implications for organizational choice Seonghoon Jeon Department of Economics, Sogang University, C.P.O.Box i142, Seoul, South Korea

Received 16 February 1994; accepted 9 January 1995

Abstract

I study how and to what extent market reputation controls moral hazard in the presence of joint production. I characterize the nature of free-riding and the dependence of an agent's reputational concerns on his partner's characteristics as well as his own. Using these results, I address two organizational issues: grouping agents in teams and sharing team output among agents. The main implications are the advantage of mixing young and old employees and the optimality of equal sharing in terms of market incentive provision. Keywords: Moral hazard; Reputation; Team; Organizational choice J E L classification: D83; L14; L23

1. Introduction

T h e incentive problems arising from imperfect information are now at the forefront of economic organization theory. The analysis of moral hazard has played a prominent role in this development. Moral hazard is, in its conventional sense, an agency problem in which agents do not expend as much effort on their tasks as the principal desires. This occurs in situations where the agents' choice of effort is their private information, and the principal's observation of their performance is confounded by uncertainties. T w o approaches have been taken to study moral hazard: the explicit contract approach and the implicit incentive approach. The explicit contract 016%7187/96/$15.00 (~ 1996 Elsevier Science B.V. All rights reserved SSD1 0167-7187(95)00482-3

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s. Jeon / Int. J. Ind. Organ. 14 (1996) 297-315

approach considers contingent contracts, based on all contingencies that are verifiable to a third party and therefore can be enforced in a court of law. Numerous papers have contributed to our understanding of the nature of such contracts (see the survey article by Hart and Holmstrom, 1987). The implicit incentive approach, on the other hand, relies on market forces to control moral hazard. The market mechanism implicitly provides incentives by paying wages as a function of perceived productivity. The idea that market reputation can solve agency problems was first suggested by Fama (1980), and was rigorously investigated by Holmstrom (1982b). Models in which incentives are affected by implicit, as well as explicit, mechanisms include Gibbons and Murphy (1992), and Meyer and Vickers (1994). I adopt the reputation model developed by Fama and Holmstrom to address the problem of moral hazard in teams. There are three ingredients in the model: time, incomplete information, and strategic action. First, reputation builds over time. Second, there must be some unknown characteristics of agents, like their abilities. Third, agents take some hidden action, such as their choice of effort. The key features in our context are as follows. In a dynamic model of teams with uncertainties about the agents' abilities, past team performance can be used to reassess their abilities and set future wages in a competitive labor market. The agents then try to influence the learning process by exerting effort; however, they cannot succeed in fooling the market in the rational expectations equilibrium. None the less, trapped in market expectations, they have to exert themselves to maintain their reputation.1 Moral hazard in teams has been studied in the context of optimal contract theory by Holmstrom (1982a), Demski and Sappington (1984), and M o o k h e r j e e (1984), among others. However, it has never been addressed from the perspective of the market incentive mechanism. I adopt the reputation model developed by Fama and Holmstrom to analyze the ramifications of joint production. In a simple dynamic multiple agency model with two periods and two agents, I obtain two features in teams: first, the incentive provided by reputational concerns in teams is weaker because of a free-rider problem; and second, an agent's reputational concerns are stronger if his own ability is less known, or if his partner's ability is better known. Using these results, I address two organizational issues: grouping agents in teams and sharing team output among agents.

1Fundenberg and Tirole (1986) coined the word 'signal-jamming' to describe the abstract nature of this reputation model, and showed its potential for broad applications by applying it to explain predation. The reputation model is now applied to the analyses of various incentive problems beyond the conventional moral hazard, as done by Holmstrom and Ricart i Costa (1986), Stein (1989), and Scharfstein and Stein (1990).

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299

G r o u p i n g is a new issue in the economic theory of organization. 2 To find appropriate methods of grouping agents in teams, the firm can exploit the d e p e n d e n c e of one's incentive upon one's partner's characteristics. In a simple overlapping-generation framework, I find that an inter-generational grouping, with both younger and older generations in teams, is more efficient than an intra-generational grouping with the same generation in teams. This result highlights a role of the older generation in teams in terms of providing greater incentives for the younger generation. In a more general set-up with two types of agents, namely less-known and betterknown, I compare two methods of grouping, heterogeneous vs. homogeneous. In this case, I identify two countervailing forces: the heterogeneous grouping provides greater total incentives for the two types of agents than the homogeneous one, while the homogeneous grouping aligns the two types' of incentives better than the heterogeneous one. Hence, the result is not definite, and depends upon which effect is dominant. For the issue of team sharing, i.e. how to distribute the total product of a team among its members, I show the optimality of equal sharing within a specific class of team sharing arrangements. This suggests one explanation for why groups often ignore obvious differences in members' attributes, and share equally instead. The efficiency gains of equal sharing comes from aligning two agents' market incentives. The paper is organized as follows. Section 2 constructs a simple twop e r i o d - t w o - a g e n t model, and analyzes how and to what extent the agents, who are concerned about reputation in a competitive labor market, exert effort in equilibrium. Section 3, based on the identified equilibrium, deals with grouping and team sharing. Section 4 discusses other issues related to team organizations, and concludes with some remarks on a future agenda.

2. Moral hazard and reputational concerns in teams 2.1. M o d e l

Two agents, who may be either workers or managers, work together for a firm during two periods. They supply inputs in the following simple team production technology, which is linear and time-invariant. That is, team outputs in period 1 and 2, denoted by y and y*, respectively, are:

2Meyer (1994) also studies the issue of how to group employees in teams. However, in that model, incentive issues are suppressed, and the focus is purely on learning. Also, the questions about task assignment posed there are somewhat different from those posed here.

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s. Jeon / Int. J. Ind. Organ. 14 (1996) 2 9 7 - 3 1 5 y = a l + l.~1+ a2 + l.~ + e ;

y* = a *1 + / x 1 + a 2* +/.h + e * .

(1)

a; and ai* represent agent i's effort in period 1 and 2, respectively, while/x; denotes agent i's ability, which is assumed not to change over time. T e a m production technology is separable with respect to the two agents' inputs. This assumption is mainly for analytical tractability, but also for focusing on organizational problems due to imperfect information rather than nonseparable technology. 3 E and e* are r a n d o m shocks in periods 1 and 2, respectively. I assume that they have an identical normal distribution with m e a n zero and variance cr z, and that they are independent of each other, and independent of agents' abilities. Our notational convention of attaching superscript * to period 2 variables is to avoid confusion between agent and time indexes. A g e n t i's choices of effort, a; and a~*, are private as in conventional moral hazard models. Agents' abilities, /~1 and P-2, are unknown, and all parties hold a c o m m o n prior distribution over (/x~,/xz): (/~t,/~2)--BN(ml,

m2, S~, $22,0),

(2)

where BN abbreviates 'bivariate normal', rni and s; 2 represent mean and variance, respectively, and 0 is the value of covariance. That is, at the beginning of period 1, every one believes that /~; is drawn from a normal distribution with m e a n m i and variance s; 2, and that /x~ and ~2 are independent. The information about /x is symmetric to all parties, and hence, we do not encounter the problem of adverse selection. 4 At the end of each period, joint output is observed by the agents, the firm, and other m a r k e t participants. H o w e v e r , the agents' contribution to team output cannot be identified individually, which is one of the essential characteristics of the t e a m model. I assume that the agents are risk-neutral and effort-averse, and that they have the same utility function: u i ( w i, a i, w i• , ai * ) = w i - c ( a i ) + w * - c ( a * )

c(0) = c'(0) = 0 , where

wi

c' > 0 ,

c"> 0,

,

i = 1, 2 ,

(3)

and w;* represent agent i's wage in periods 1 and 2, respectively.

3 On the other hand, Alchian and Demsetz (1972) emphasize non-separability of team production in their discussions of factors determining organizational forms. 4The assumption of symmetric information is to avoid the complicated issue of adverse selection (see Laffont and Tirole, 1988; Ma, 1991). Instead we may assume that agents, even with private information, have no means to signal it convincingly, and that firms cannot offer a menu of contracts to screen the types of agents.

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Notice that the cost of effort, c(.), is specified in monetary terms. For simplicity, I disregard discounting; this does not materially affect the results. The function c(. ) has the usual properties of cost functions; it is increasing and convex. Firms are risk-neutral. They pay wages in advance of the realization of output in each period. That is, even if the team output y is observable, firms do not use payment schemes that are contingent on the current team output. This may be justified by the assumption that the team output is not verifiable to a third party, e.g. the courts, making contingent contracts unenforceable. Admittedly, the assumption of non-verifiability could be a strong assumption in many applications.5 In Section 4, I provide some brief remarks on relaxing it in line with Gibbons and Murphy (1992). Lastly, competition in the market for the agents' services is assumed to be perfect. We may envisage that there are two firms competing for the agents' services in Bertrand fashion; they bid the wages up to the point of zero expected profits. 2.2. B a y e s i a n learning in t e a m s

Although the team output aggregates the two agents' contribution, it contains valuable information for updating each agent's ability Ixi. Hence, it affects the agents' market values. In this subsection, I solve the Bayesian inference problem of updating beliefs about the agents' abilities (IXI,IX2), given the aggregate team performance. This clears the way for an analysis of market equilibrium. The following lemma characterizes the posterior distribution of agents' abilities (IX1,Jlz2), given the output observation y and the anticipated level of agent i's effort (denoted di). I define: z ~-y - d I - d

2.

L e m m a 1. With ( 1 ) a n d ( 2 ) , the p o s t e r i o r distribution o f (IX1 ,P-e) g i v e n z is a bivariate n o r m a l distribution with *

*2

*2

(Ix,, I X e g / z - - B N ( m I , m e , s I , s 2 , r * ) ,

(4)

where . mi =

( s 2 + ~ r ) 2m i

+ s 2i (z - m i )

2 2 2 s I + s 2 + o"

'

(5)

Baker, Jensen and M u r p h y (1988) notice that the explicit pay-for-performance contracts s e l d o m account for an important part of a worker's compensation, and they list the viable economic explanations as a challenge to economists.

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$2($2 + 0"2)

S7 2 -

2

2

r*

2,

--s~s~ -

S 1 q- $2 -'~ 0-

2

2

2.

(6)

S 1 -'~S 2 q-O"

We expect that the posterior distribution is bivariate normal, given the bivariate normal prior distribution, since the normal distribution belongs to the conjugate family. Lemma 1 is derived by applying the Bayes rule and checking its conformity to the bivariate normal distribution. The learning process implied by Lemma 1 is intuitive. The posterior mean m i* in (5) is a weighted average of i's own prior mean, m i and a residual, (z - mj), which is the part of team output that is imputed as i's ability: m* = (1 - oti)m i + oli(z

-

-

mi) ,

where ai=--- 2 2 $1+$2+0-2

•

(7)

Notice the weight attached to the residual or the coefficient of z in the updating formula, ai, depends on all variances. We see later that this coefficient is of particular importance since it captures the incentive that the market provides for agent i. Posterior variance s *e is smaller than prior variance s~. That is, by observing team performance, even though it is an aggregate datum, people learn more about individual abilities. Though we start with a zero covariance in the prior distribution, we end up with a negative covariance in the posterior distribution. It is somewhat digressing, but interesting, to see if we can infer individual abilities with certainty, provided we have an infinite number of observations of team output. I can show that even though s ~ 2 gets smaller with the accumulation of data, it converges to a non-zero value, and the correlation coefficient, which is r / s I s 2 , converges to - 1 (see Jeon, 1991). The sum, /x1 + / z 2, becomes known certainly, but individual abilities do not become completely known even in the limit. 2.3. Equilibrium

I now analyze the market equilibrium. The equilibrium notion is that of perfect Bayesian equilibria, which is the weakest refinement of subgame perfect equilibria that meets sequential rationality and Bayesian inference. 6 Perfect competition in the labor market ensures that wages are set equal to the expected contribution of each agent. That is, 6 For the more precise definition of perfect Bayesian equilibria, refer to Fudenberg and Tirole (1991). Incidentally, the market equilibrium in our model is unique, therefore, any further refinements are unnecessary.

S. Jeon / Int. J. Ind. Organ. 14 (1996) 2 9 7 - 3 1 5 w i* = d *

I~'i ~ ai ~- m i ,

+rn* ,

i=1,2

303

,

w h e r e ti, and d~* are the anticipated levels of i's effort in periods 1 and 2, and m i and mi* are the prior and the posterior m e a n s of agent i's ability, respectively. E x p e c t a t i o n s a b o u t the agents' choices of effort are selffulfilling in equilibrium, and posterior m e a n s are given by the Bayesian u p d a t i n g formulas in L e m m a 1. N o w consider the agents' optimal choice of effort. Table 1 summarizes the s e q u e n c e of decisions and information revelation. Since wages are not c o n t i n g e n t on t e a m o u t p u t in period 2, and are d e t e r m i n e d before its realization, there is no reason why the agents should exert effort in period 2. T h u s , in equilibrium, they set a i* = 0, and the m a r k e t anticipates this and pays t h e m just rn~* in the second period. 7 While effort is zero in period 2, incentives in period 1 are different. E f f o r t in p e r i o d 1 does not affect wages in period 1, since w i are already d e t e r m i n e d before a~ are chosen. H o w e v e r , the first period effort has an effect on the s e c o n d period wage wi* t h r o u g h its effect on m i * . In equilibrium, the agent balances the marginal cost of exerting effort, c ' (a~), with the marginal benefit of boosting the next period wage. T h e marginal benefit is a~ as defined in (7): Ow*

~m7

0z

Oa i

Oz

Oa i

°ti"

W i t h m a r k e t expectations a b o u t the agent's choice of effort fixed at a certain level, di, ai affects z o n e - f o r - o n e , and z affects m~ * by a~. T h e conditions for m a r k e t equilibrium are s u m m a r i z e d as follows: w i=a i+m

i,

w*=m

(8)

i ,

Table 1 The sequence of decisions and information. Period 1 Period 2

Firms offer Agents privately choose People publicly observe Firms offer Agents privately choose People publicly observe

Wi ~ a i + Fn i ai

y =a 1 +/zl +a 2 +/x 2 +e w~*= ~i* + m~*

a~

y * - - a ~ * + ~ + a 2.+/x2+~*

Note: Period 2 has the same structure as period 1, except that the distribution of /x's is

updated, based on public observation y. 7 Let me remark on the seemingly degenerate nature of the agents' choice of effort in period 2. It does not literally mean that the agents do not exert any effort. If they enjoy exerting effort up to a certain level without any reputation incentives, then zero should be interpreted as that level. Of course, we could have assumed a U-shaped cost function c(. ) instead.

S. Jeon /lnt. J. Ind. Organ. 14 (1996) 297-315

304

c'(ai)

a i* = 0 ,

= oli,

i=1,2

(9)

In this equilibrium, market wages are determined by rational expectations of the agents' choice of effort and Bayesian updating of their abilities, while the agents' choices of effort are determined by equalizing marginal cost and marginal benefit in period 1. Recall that agents do not exert any effort in period 2. Since a i is positive, the equilibrium choice of a i is positive. I call a i agent i's reputation coefficient since it captures the incentive due to his concerns about reputation in the labor market. We can reinterpret the reputation coefficient in terms of the so-called signal-to-noise ratio. That is, what is crucial in determining reputation incentives in teams is the ratio of the variance of the 'signal' (the uncertain ability of an agent, the signal of which we try to extract from data) to the variance of the 'effective noise' (which consists of the sum of the other agent's uncertain ability and the exogenous shock ~). If we denote the ratio by /3i, the reputation coefficient is a simple increasing function of /3i as follows: 2

Oti - 1 "q- J~i

,

where J~i ~ S2 _]_ 0 2 "

(10)

Thus, agent i's reputational concerns are stronger if his ability is less known, if his partner's ability is better known, and if the team production environment is more certain. Notice that mean abilities do not affect reputational concerns whatsoever. This is a feature special to the normal distribution. However, the importance of the signal-to-noise ratio in determining reputation incentives is intuitive enough to expect that for other distributions, the effects of mean abilities on reputation incentives may come through their effects on variances, and that the result analogous to (10) may hold true. We note two features in teams, which are implied by the presence of 'additional noise' in the signal-to-noise ratio. One is the habitual free-rider problem; incentives in the team situation are weaker than if each agent worked independently, with output subject to the same exogenous shock as in the team setting. Uncertainty about the teammate's ability reduces the weight placed by the market on team output in updating its beliefs about each agent's ability, and through this route reduces incentives. Another is the dependence of an agent's reputation incentive on his partner's characteristics as well as on his own. This suggests the importance of organizational design, such as grouping, in providing adequate incentives.8 8 If variances of agents' abilities were endogenous variables, we could exploit such dependence to improve organizational efficiency. For instance, ignoring information about some agent's ability, which results in greater uncertainty, might provide more adequate incentives for the two agents.

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305

I apply the equilibrium results of the two-agent-two-period model in the following comparative organizational exercises. Before doing that, let me briefly explore extending the results to the model with more agents and periods. For the case of N agents and 2 periods, we can easily extend the 2 2 2 2 Bayesian updating rule to get a i = s i / ( s I + s 2 + ... + s N + 0-2). Hence, the interpretation of the signal-to-noise ratio analogous to (10) applies with the stronger flee-rider problem as expected. On the other hand, with 2 agents and T periods, we can show that agent i's effort at t ( = 1, ..., T ) , a / t ) , affects the market inference of his expected ability some later time at r ( = t ÷ 1, ..., T), rni(~-), and hence, his market wage at that time, by S ~ / [ ( T - 1)s 2I + (~- - 1)s 22 + 0.2].9 Therefore, agent i's reputation coefficient at t is given by: T

2

c,i(t) = ~]

si

r = t + l (T -- 1)$21 + (T -- 1)$22 + 0 . 2 '

where i = 1 , 2

and t = l .... , T .

where i = 1, 2, and t = 1, ..., T. Besides these basic features, we can confirm the general idea that reputation effects get diluted over time. It requires a horrendous amount of work to formally extend the results to the general case with N agents and T periods simultaneously, but we can make an educated guess about them from the above discussions.

3. Organizational choice 3.1. E f f i c i e n c y criterion

The efficiency of a particular form of organization can be measured by the social surplus that it produces. In our framework, the social surplus is defined by y - c(a 0 - c(a2) + y * - c ( a l ) - c(a2 ). It is well defined because the cost function c ( . ) is specified in monetary terms. As an objective function to be maximized, it is equivalent to a l - c ( a l ) + a 2 - c ( a 2 ) . The second period terms are washed out because agents' choice of effort in period 2 is degenerate in our reputation framework. For the schemes considered in the following, I derive the associated reputation coefficients, which determine the equilibrium levels of effort through equilibrium condition (9). Inverting the marginal condition: a, = k ( a i )

[¢:~c'(ai) = a,],

(11)

and defining: 9See Jeon (1991) for the relevant rule of Bayesian updating with multiple observations.

S. Jeon / Int. J. Ind. Organ. 14 (1996) 297-315

306

f (ai) =- k(ai) - c(k(ai)) ,

(12)

the function f ( a i ) measures the net gains from agent i's effort induced by % Now, the objective function is transformed into f(oq) + f ( a 2 ) . This serves as the basic standard for the welfare comparisons below. The shape of f ( . ) is important for some later results. Its first and second derivatives are obtained from (11) and (12) as follows: 1

f"=

1 c"

c"

(1

-

-

Oli)cO3 .

Notice that the curvature of function f ( . ) depends on the third derivative of cost function c(. ). A sufficient condition for the concavity of function f ( - ) is that: c"' > 0

[~f"<0].

(13)

I assume this in the following comparisons. This seemingly technical assumption has a behavioral interpretation: the marginal response of effort to the reputation coefficient decreases as effort increases. In other words, c " > 0 if and only if

d {da,'~ da i \-d-~i~i / < O. Suppose that two schemes A and B are being compared. I define:

Definition. Scheme A is more efficient than scheme B if and only if

:(A) + i ( A ) > Recall that the f ( . ) function is the same for each agent, because their cost functions are the same and their marginal products of effort are the same. On the other hand, the reputational coefficients can differ across agents, because the prior variances on their abilities can differ. The efficiency criterion embodied in the above definition is stronger than that of Pareto superiority. For this we need f ( a A ) > f ( a B i ) , i.e. a/a >a/B, i = 1,2. However, if we allow a transfer payment between agents 1 and 2, it can then be interpreted in terms of Pareto superiority.

3.2. Grouping In this subsection, I compare two methods of grouping four agents into two teams. Two agents are type h, the prior variance of whose abilities is Sh E, and the other two agents are type l with s~ < s~. Each team has the same

S. Jeon / Int. J. Ind. Organ. 14 (1996) 2 9 7 - 3 1 5

307

production technology (1). The first method of grouping matches h - l in both team production units, while the second one matches h - h in one team production unit and l - l in the other. There are two possible ways of analyzing this grouping issue: namely, a comparison of inter-generational vs. intra-generational grouping and that of heterogeneous vs. homogeneous grouping. 3.2.1. Inter-generational vs. intra-generational grouping First, I assume that all agents start their careers with the same variance 2 s h , and derive differential variances endogenously. I will do this by introducing a simple overlapping generations model. Let each agent live for two periods, young and old, while the firm continues forever. 1° The evolutionary process is based on the following scenario: when the firm begins its business, it employs just two young agents, and, in the next period, it matches two newly hired young agents with the old agents to form two teams, and so on. The variance of an old agent is smaller than the prior variance of a young agent because of first-period learning. In equilibrium, only young agents exert effort. Thus, the comparison between an inter-generational ( h - l; h - l-= A) and an intra-generational (h - h; l - l =- B) grouping only concerns young agents' incentives. From (7), we have the reputation coefficients of the young agents as follows: 2

Ot~(t)= 2

Sh

S h + s t ( t ) 2 + 0 -2 ,

B O~h--

2

Sh 2

2S h -4- 0-

2,

(14)

where Sl(t) 2 is the variance of the old agents' abilities when the firm continues to adopt the inter-generational grouping for t periods; it changes over time. Given the overlapping-generation framework, we can establish the following result. Proposition 1. A n inter-generational grouping, with both younger and older generations in teams, is more efficient than an intra-generational grouping with the same generation in teams. Moreover, the efficiency gains from inter-generational grouping increase over time. Proof. Applying (6) recursively, we can describe the evolution of the variances of the old agents' abilities in the case of inter-generational grouping as follows: ~oCremer (1986) also deals with incentives of agents with finite lives in ongoing organizations within the framework of overlapping games. Its main finding is that younger generations can have cooperative incentives, even if the one-period game has a prisoners' dilemma structure.

308

S. Jeon / Int. J. Ind. Organ. 14 (1996) 297-315 2

st(l) 2 -

2

Sh(S h -[- 0 -2) 2 2 02,

Sh + S h +

1)2 + 02) st(t) 2 =

2

2,

t=2,3,...

s h ~- st(t -- 1) 2 + o"

T h e r e f o r e , its stationary value, such that s t ( t -2

--0-

2

1) 2 = st(t) 2 = s -2t , is:

A 2 2"~ 1/2 --~- ( 0 - 4 - ~ - o t O " Shl

st=

2

F r o m these formulae, we can easily see that s~ > st(l) 2 > . . . > st(t) e > . . . > -2 s t . This implies: O/hB ~ O~ a(1)

< .."

(

Z

ah(t)<

... (

-A O~h .

Q.E.D. At first glance, this proposition reads like well-known wisdom. H o w e v e r , such folk wisdom, if any exists, is likely to be based on the presumption that with the young and the old mixed in a group, it is easier and faster to transfer knowledge and experience to the young. I do not intend to argue against this, but rather to c o m p l e m e n t it. According to Proposition 1, the old have an additional value as partners for the young; since their abilities are better known, team output is m o r e useful for updating the abilities of the young. Hence, the young are m o r e concerned about their reputation and w o r k harder. 1~ Moreover, in the inter-generational grouping, the information about old agents' abilities improves as time goes on. Even if old agents are gone in the next period, they enable the ongoing firm to m a k e sharper inferences about the agents, who are currently young, but are old in the next period. In this way, old agents in the inter-generational grouping contribute to the accumulation of 'organization capital' in the sense of Prescott and Visscher (1980). ~2 On the other hand, such accumulation of information cannot be expected from the intra-generational grouping. 3.2.2. Heterogeneous

vs. h o m o g e n e o u s

grouping

A n o t h e r way of addressing the grouping issue is to take the structure of the agents' variances as given e x o g e n o u s l y . That is, I do not address why some agents start their career with high variance and others with low

" Incidentally, the proposition suggests coupling junior and senior researchers in a coauthorship. 12They conceive information as an asset to the firm, for it affects the production possibility set, and hence, call it organization capital. They also address how information of employee characteristics is accumulated, but the determining factor in their model is the rate of firm growth, not organizational structure.

S. J e o n

/ I n t . J. I n d . O r g a n .

14 ( 1 9 9 6 ) 2 9 7 - 3 1 5

309

variance, taking it as given (e.g. some are newly trained while others have experience in related industries). I term the comparison as a heterogeneous (h - l; h - l -~ A ' ) vs. homogeneous (h - h; l - l --- B') grouping. The comparison involves incentives for both types of agents to exert effort in period 1. Let a/A' denote the reputation coefficient of the agent of type i in grouping A' and correspondingly, let a ~" be the coefficient for grouping B' (i = h, l). Notice that two coefficients are sufficient to characterize the four agents' reputational concerns, since there are two agents of each type. Applying (7), we have A' Ol h - -

2 Sh 2 2 S h _}_Sl ..}_ 0 . 2 ,

A' Ol l - -

2

B' Ol h - -

2

Sh 2

2s h +

2 SI 2 2 2 , S h . ~ S I nL O-

0.2 ~

B' Ol l - -

SI 2--~-----'~ "

(15)

2s l + o-

Simple algebra shows that: A' A' B' B' ~ h - - Ol l ~ Ol h - - Og l "~

A'

)

B'

'

These inequalities show two countervailing effects on the relative efficiency between heterogeneous and homogeneous groupings. In both methods, type h has stronger incentives than type I. However, the difference is smaller in the case of grouping B' than in the case of grouping A'. That is, the homogeneous grouping aligns the two types' incentives more closely, which I call an a l i g n m e n t effect. To see its meaning, suppose that total incentives are the same, i.e. a ~' h + a A' = a~' + a~'. Then, the concavity assumption in (13) implies that f ( a ~ ' ) + f ( a ~ ' ) > f ( a A') + f ( a ' ~ ' ) . Hence, the alignment effect favors the homogeneous grouping. However, total incentives are not the same. In fact, the heterogeneous grouping increases the sum of two types' incentive coefficients, which I call a total i n c e n t i v e effect. This favors the heterogeneous grouping. The intuition for the inequalities a ~' < a ~' < a hB' < a A. h , which underlie the alignment effect, is rather easily obtained from the interpretation of reputation coefficients in terms of the signal-to-noise ratio in (10); as the ratio increases, the reputation coefficient increases. The above inequalities 2 2 2 2 / are clear from the fact that/3 z' = s t / ( s h + = s t/(s, + (S2 + O2), and [3 A' h = S h2/ ( S , 2 + O"2) (and hence, that/3i a'
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positive effect of the former on type-h's incentive against the negative effect of the latter on type-l's incentive. The clue for reaching the net effect is the 2 That is, the absolute magnitude of the fact that O2ai/Os~Os 2 < 0 when s~ = sj. effect on one's incentive of the change in the variance of the partner's ability increases with the variance of one's own ability. Hence, the positive effect dominates the negative one. In general, the comparison between a heterogeneous grouping and a homogeneous grouping is not obvious. However, for some configurations of S h2, s 2, and tr 2, we can determine the relative sizes of the total incentive A' 2 2 A" 2~t" 2 effect and the alignment effect. As or--* O, a h ~ Sh / (Sh + S~), a t ---~St /~Sh + S2), ol h"' ---~1/2, and ol~ ~ 1/2. Thus, the total incentive effect is neutral between A' and B', while the alignment effect operates in favor of B'. Hence, the homogeneous grouping is preferred to the heterogeneous one, for all cost functions c such that f is strictly concave• This result is easily interpreted. In the limit as the exogenous noise disappears, the total A' A' B'_~_ B' incentive becomes the same, i.e. ol h +of t =of h olt = 1, because the signal-to-noise ratio that determines the total incentive (the ratio of the variance of/z~ + ~ to the variance of e) becomes infinite for any grouping method. 2 2 ' B' 2 2 S h / ( S h + Or2), ol A " ' ~ 0 , Ol h " ' ) S h / On the other hand, as st---~0, ol A' h (2s] + or2), and ol~'---~0. Hence, the heterogeneous grouping is preferred, no matter what the sign of c'. In this case, as the prior variance of type-l's ability goes to zero, their incentives become degenerate in whatever type of team they are placed, and hence the performance comparison is reduced to a comparison of the incentives of type-h agents• As we know from the previous subsection, type-h agents have stronger incentives in heterogeneous teams than in homogeneous teams.

3.3. T e a m sharing arrangement

When individual wages are determined according to (8) in Section 2, each worker is a bargaining unit, and the firm evaluates his ability and effort, and pays him separately. I call this the scheme of individual market wages. However, in the team environment, we can conceive of an alternative scheme, the team sharing arrangement, where the team as a whole is a bargaining unit, receives a total payment for team output, and then splits this between its members according to a pre-set rule. The objective here is to identify team sharing arrangements that improve upon individual market wages in terms of reputational incentives• The team as a bargaining unit will receive team wages: w r = d I + d 2 + T* m ~ + m 2 1 n•p e r l o d" l , andw = a-*I + a-*2 + m l * + m 2* in period 2. I consider the following specific class of team payments:

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S. Jeon / Int. J. Ind. Organ. 14 (1996) 297-315 WTi = aTi + 8i(m 1 ÷ m2),

*

-T*

w/z = a i

÷ 8i(m I ÷ m ~ ) ,

i = 1, 2

(16)

where 81 + 62 = 1. A characteristic feature of this rule is that the team divides the part of team wages corresponding to the team's expected ability, which is m I + m 2 in period 1, and m r + m 2 in period 2, into each agent's share according to preset proportions, (81,82). I assume that the members commit to the division rule which is agreed upon initially. That is, individuals who work in a team in period 1 remain together, without complaining about the pre-set rule, in period 2. This commitment assumption is restrictive, but important for the implementation of team sharing arrangements since after the realization of y in period 1, a conflict of interest arises among the members regarding the choice between an individual market wage and a team payment. T* T As in Section 2, in equilibrium, a i 0 (i = 1, 2), while a i in period 1 is determined, through marginal condition (9), by the reputation coefficient: =

T _ Owri * O(ml + m ~ ) Oz s~ + s~ a i -- Oa~ = 8i OZ Oai -- 8iS12 ÷ $29 + 2 "

(17)

Comparing a i in (7) and a f above shows that the scheme of individual 2 2 2 market wages corresponds to the special case of 8 i = s i / ( s ~ +s2). The following proposition shows the optimality of equal sharing: Proposition 2. Within the class o f team sharing arrangements o f (16), the equal sharing arrangement with 81 = 62 = I / 2 is the most efficient. Moreover, the difference between efficiency under equal sharing and efficiency under individual m a r k e t wages grows larger, the greater the difference between s~ and s t. Proof. Given (17), for any choice of (61,62), total incentives under (16) are

the same as those under the scheme of individual market wages: a ~ + a ~ = a t + a 2. The reputation coefficients of the two agents under equal sharing T are the same: ar~ = a 2 = (al + a2)/2. On the other hand, as the discrepancy 2 2 between s I and s 2 increases, the discrepancy between a 1 and a 2 also increases. The results in Proposition 2 are straightforward implications of the concavity assumption of (13). Q.E.D. Notice that equal sharing in (16) applies only to the part of team wages corresponding to the team's expected ability. However, equal sharing, in the literal sense, is realized by the equilibrium choice of the same level of efforts. We commonly observe equal sharing in groups, even when the participants contribute unequal amounts. For example, scholars usually get

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equal credit for joint work, and law partners often share profits equally. 13 Proposition 2 suggests one explanation for why groups often adopt equal division rules, disregarding the difference in members' attributes. The gains come from aligning incentives; even though equal sharing cannot change the sum of two agents' reputation coefficients, it results in reducing the gap, and hence, increasing the sum of net gains from two agents' efforts. Therefore, paradoxically, in our framework, more gains are realized from equal sharing when a greater difference exists in the prior variances of their abilities. 14 On the other hand, the equal sharing arrangement is equivalent to individual market wages when the agents are identical.

4. Conclusions The most direct way of improving efficiency in team organizations is to introduce organizational designs that alleviate the free-rider problem. From the perspective of market incentive provision, we can show the advantage of separating out individual performances or introducing individual monitoring; it comes from sharpening the process of learning about the agents' unknown abilities, and making them more concerned about their reputation in the market. With individual information available, a relative performance evaluation that links one's pay with the other's performance becomes necessary. The contract literature explain it in terms of correct incentive provision (e.g. Holmstrom, 1982a; Nalebuff and Stiglitz, 1983). However, within our framework, the basis of peer group reference is purely due to learning; yet, it does have an incentive effect. A n o t h e r important issue in team organizations is cooperation. 15 If agents cooperate in making effort choices, they are concerned about the team's reputation rather than each individual's reputation, and thus, the free-rider problem is resolved. The efficiency-enhancing effect of cooperation is also noted in the contract literature, but with a different focus on risk-sharing (e.g. Holmstrom and Milgrom, 1990; Itoh, 1993; Macho-Stadler and PerezCastrillo, 1993). With the introduction of cooperation, it may be the case that observing only team performances, rather than separating out individual performances, induces stronger market incentives. With only 13According to Farrell and Scotchmer (1988), equal sharing is adopted by most two- or three-person law firms, which account for 2/3 of all firms. 14However, it should be emphasized that this is in contrast to cooperation, under which individuals do internalize the total effect on the team of their efforts. The class of sharing arrangements considered does not result in such internalization. Total incentives for the team are the same, but simply divided differently among the two individuals as 6, varies. 1~See Tirole (1992) for general issues of side contracting in an organization, including the detrimental case of collusion.

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team output observable, cooperation results in internalization of positive externalities. This outcome may dominate that when individual outputs are observable, because in the latter case, the market's updating results in the agents' wages being independent, so there are no externalities, and therefore no gains from cooperation. More formal discussions could be made on the above ideas (see Jeon, 1991). But in the paper, I focused on other possibilities of improving organizational efficiency rather than dealing with the free-rider problem directly. The examples was grouping agents into teams, and sharing team output among agents in an appropriate manner. The underlying ideas are the following: grouping should exploit the fact that one's reputational concerns depend on the partner's characteristics as well as one's own; team sharing arrangements can align members' incentives better than individual market wages, even though they may not improve total incentives. T h e r e are several interesting directions towards which this work can be further developed. First, we may consider how the main results change when team performance is contractable. For example, we can extend Gibbons and Murphy (1992) to deal with the optimal design of short-term (i.e. one-period) contracts in a setting where agents are in the market for two or more periods, and are concerned about reputation. There arises an interesting question in regard to team situations: how does the optimal explicil incentive coefficient depend on the prior variances of an agent's own ability and of his partner's ability? In order to answer the question adequately, we have to take into account two factors which are likely to affect the nature of the optimal contract: the countervailing effect of implicit market incentives on explicit incentive coefficients, and the effect of changes in variances of abilities on the total risk to which individuals are exposed. Second, the learning model of team production can be adapted to deal with some interesting issues in the internal labor market, for example, the firm's policy of promotion, its task assignment, and the use of job rotation. It seems important to include multi-attribute characteristics in such extensions. For this purpose, the team model is valuable because learning about two agents each with a single attribute is essentially the same as learning about a single agent with two attributes. Of course, if we introduce incentive issues as well, incentives will not be the same in general; incentives will be the same if in the two-agent case the agents cooperate and internalize the externalities, but will not be the same if they do not. Lastly, there may be non-labor applications of this model. For example, workers here can be interpreted as divisions or firms who provide goods and services of unknown quality to the market. Two divisions or firms may combine into a firm or a multiproduct firm. The ramifications of these extensions and variations await future work.

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Acknowledgements T h i s p a p e r is b a s e d o n the first essay in m y d o c t o r a l thesis at Yale U n i v e r s i t y . I a m grateful for helpful c o m m e n t s f r o m N a n c y Lutz, D a v i d P e a r c e , R a a j Sah, Joe T r a c y , a n d a n o n y m o u s referees. I a m especially i n d e b t e d to B e n g t H o l m s t r o m , whose suggestions have i m p r o v e d this p a p e r . O f c o u r s e , I a m r e s p o n s i b l e for all r e m a i n i n g errors.

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