December 2015
Discussion Paper

No. 13The opinions expressed in this discussion paper are those of the author(s) and should not be
attributed to the Puey Ungphakorn Institute for Economic Research.

Observability and Endogenous Organizations∗
Weerachart T. Kilenthong
University of the Thai Chamber of Commerce
Gabriel A. Madeira
Universidade de São Paulo
December 8, 2015

Abstract
This paper establishes a relationship between the observability of common shocks
and optimal organizational design in a multiagent moral hazard environment. We consider two types of organizations, namely relative-performace and cooperative regimes,
and show that, with sufficient information regarding common shocks, a cooperative
organization can be optimal even if outputs are highly correlated. The model is thenembedded in a Walrasian general equilibrium model in which choices regarding organizations and investment in information on common shocks are jointly determined.
Numerical results reveal that both cooperative and relative-performance regimes cancoexist in equilibrium but only cooperative organizations invest in full observability ofcommon shocks. Changes in the cost of information and aggregate wealth can affectsubstantially the the types of organizations operating and the matching patterns of∗

We are thankful for helpful comments by Fernanda Estevan, Rafael Costa Lima, Ricardo Cavalcanti,

Marcos Nakaguma, Ned Prescott, Robert Townsend, the associate editor, two anonymous referees and participants at LAMES (Buenos Aires, 2009), SAET (Paris, 2013), and academic seminars at FEA-USP, FEARPUSP, PUC-RJ, FGV-RJ, FGV-SP. Tee Kilenthong would like to thank the University of the Thai Chamberof Commerce for the financial support. Gabriel Madeira gratefully acknowledges financial support from Fipe.
Tee Kilenthong’s email: tee@riped.utcc.ac.th. Gabriel Madeira’s email: gabriel.madeira@gmail.com.

1

heterogeneous agents in these organizations. General equilibrium effects are key indetermining how information costs impact the way production is organized.
JEL Classification Numbers: D23; D71; D85; O17.
Keywords: organizational design, observability, relative performance regime, groupregime, general equilibrium, value of information

1

Introduction

This paper examines how the observability of common production shocks that concurrently
affect multiple agents influences an optimal organization design. We consider an organizationas contractual arrangements between multiple individuals, who are engaged in production
subject to moral hazard, and an outsider/principal. Two alternative organizational regimes
are considered. In the first one, individuals act cooperatively, sharing information and taking
joint decisions subject to collective incentives. This type of organization represents teamwork or joint liability credit contracts, which encourage cooperation among agents, to takeadvantage of their capacity to interact and share information (e.g., Lazear and Shaw, 2007;
Ghatak and Guinnane, 1999). In the second regime, individuals compete in response to
individualistic incentives, possibly based on relative performance. This regime includes job
tournaments and relative-performance compensation schemes, which stimulate competition
among agents under comparative evaluation (e.g., Lazear and Rosen, 1981; Barlevy and Neal,2012).
We propose a framework that extends the standard multiagent moral hazard literature(e.g., Holmstrom and Milgrom, 1990; Ramakrishnan and Thakor, 1991; Itoh, 1993; Prescottand Townsend, 2002) to incorporate partial observability of common shocks. This literature
identifies output correlation as the key ingredient in determining an optimal organizational
regime. In our formulation, output correlation emerges as a consequence of the presenceof common shocks. This feature allows us to analyze the role of the (potentially costly)observability of common shocks. Although some small events may remain impossible toobserve at a reasonable cost, larger events, especially those that simultaneously affect multiple agents, are arguably observable at a certain cost. Examples include the measurement2

of weather conditions for index insurers, and the measurement of sector productivity by
sectoral consultants.
We show that the observability of common shocks is a key determinant of optimal organizational schemes. Cooperation has the advantage of allowing agents to make joint decisions
regarding mutually observable and enforceable actions that are unobserved by outsiders.
However, cooperating agents can collude in such a way that undermines incentives. Collusion will be particularly harmful if the common shocks are unobserved. This is because it
is difficult for an outsider to distinguish an adverse aggregate event from the coordinatedneglect of agents. By contrast, in a relative performance scheme, each individual’s output/performance is informative with respect to the common shocks that affect all agents.
Thus, unobserved common shocks provide an advantage for the relative performance compensation regime over the cooperation regime.
This paper shows that cooperation is optimal when the common shocks are perfectly observable, regardless of the correlation structure of outputs or the structure of common shocks.
This finding helps explain the empirical observation that cooperative arrangements are sometimes highly prevalent even when outputs are highly correlated (Ahlin and Townsend, 2007).
Indeed, according to our results, this pattern will be observed if the correlation of outputs
is driven by observable and contractible common events. Furthermore, our results indicatethat the emergence of cooperative behaviors can be a consequence of an improvement in
observability of common shocks. For a symmetric case in which individuals are ex ante identical, we can prove that a cooperative or group regime prevails when the common shocks are
perfectly observable. In another polar case in which all shocks are common and punishment
can be arbitrarily severe, relative performance will always dominate, regardless of the information structure. This result emphasizes the role of idiosyncratic shocks in group collective
arrangements.
We characterize optimal organizational regimes in two stages. First, we determine surplus
maximizing multiagent contracts as functions of outside options for each members and theamount of (costly) information regarding the common shocks. The resulting contracts areinterpreted as potential firms or organizations. Then, following Prescott and Townsend(2006), we formulate and solve the assignment problem of a continuum of individuals into3

these organizations. A solution to this assignment problem is Pareto efficient, and can bedecentralized as a Walrasian equilibrium.
Numerical solutions of general equilibria have been provided for several levels of risk
aversion and technologies, showing how organizations respond to changes in the cost of
information and wealth. In all of these specifications, when the cost of information aboutcommon shocks is sufficiently low, all firms invest in information and adopt cooperative
arrangements. With higher costs of information, some firms operate without investment in
information and relative performance arrangements can be observed. For a given cost of
information, wealth is also relevant to determine whether information is acquired or not.
Poor economies are less likely to purchase information, since investment in information
requires sacrifice of consumption. Economies with rich agents also have a low probability ofpurchasing information, since information about common shocks are an incentive tool, andrich agents typically make lower effort. So information is more likely to be purchased in anintermediary wealth range.
For some of the specifications computed, we present contractual details such as the levels of effort and heterogeneity of agents inside organization. Our results reveal a complex
interaction between wealth, inequality, effort, and information determining equilibrium allocations. Small changes in the cost of information or wealth can generate dramatic reshaping
in the contracts operating, and general equilibrium and matching effects are important forces
behind these abrupt changes.
Our numerical results reveal that distinct contractual arrangements can co-exist in equilibrium: some individuals will be assigned to cooperative/group contracts and others will
be assigned to relative performance contracts. This coexistence of diverse organizational
regimes is observed in the real world. Data from Indian villages reveal that although somelandowners have their land farmed by groups of individuals acting cooperatively, others divide their land into several plots and employ a single worker or family on each plot (e.g.,
Townsend and Mueller, 1998; Mueller et al., 2002). Ahlin and Townsend (2007) shows thatmany microcredit arrangements are one-per-credit contracts, but joint liability credit contracts have also been widely adopted in Thai villages. Some firms employ teamwork, whereas
others adopt individualistic incentive schemes (Lazear and Shaw, 2007).
4

Our examples also suggest that only cooperative organizations invest in full information
about common shocks. Since investment in information can be interpreted as accepting or
taking (insurance) contracts conditional on information regarding the common shocks, suchas rain insurances, this result suggests that index or weather insurance issuers should target
cooperative or group organizations as their main customers.
This paper belongs to a vast body of the literature on cooperative or competitive incentive
schemes. Lazear and Rosen (1981) and Barlevy and Neal (2012) showed that comparativecompensation may be a useful tool to create incentives when monitoring is costly or when
output measurement is subtle. Ray (2007) and Genicot and Ray (2003) presented examplesof the optimality of group organizations in an environment with complete information toaddress externalities and risk-sharing problems. Ghatak and Guinnane (1999) and Lazear
and Shaw (2007) argued that cooperation and teamwork can also be useful in addressing
asymmetric information problems. This literature focuses on establishing the optimality ofeither cooperation or competition in specific contexts. Our framework is sufficiently rich tocover cases in which either regime endogenously prevails as well as cases in which the two
regimes coexist.
The model also has novel empirical implications. A transition from relative-performance
to cooperative organizations should be observed if the cost of information becomes lessexpensive over time (possibly because of improvements in information technology). This implication is consistent with the evidence reported by Lazear and Shaw (2007), who showedthat teamwork has been increasingly adopted by large companies in recent decades. Further, one can interpret the observability of common shocks as useful knowledge about the
productive technology that commonly affects all individuals engaged in production. Our
results therefore imply that, when a new technology is adopted, incentives should initiallybe generated through competitive schemes, and cooperative schemes should subsequently be
adopted as the knowledge of the new technology improves.
This paper also relates to the risk-sharing literature. Although most empirical tests
rejected full risk sharing within villages (Deaton, 1992; Townsend, 1994; Jalan and Ravallion,1999), many studies showed that some groups of individuals can achieve a sufficiently highlevel of risk sharing (Grimard, 1997; Goldstein, 2000; Fafchamps and Gubert, 2007). Further,5

Chiappori et al. (2014) showed that some family networks and some villages in Thailand sharerisks perfectly, whereas others perform poorly. Through the lens of our model, differences in
the ability to share risks may partly result from the observability of information regarding
common shocks. That is, a group of households, who can share information better, could
potentially share risk more effectively by choosing a cooperative/group contract to serve theobjective, and vice versa.
The remainder of the paper is organized as follows. Section 2 describes the basic environment of the model, the informational structure, and the role of informational structure
in production. Section 3 formally presents the organizational regimes, and characterizes the
optimal arrangements for each regime. Section 4 formulates a Walrasian equilibrium modelwith endogenous organizational and informational regimes, and presents its numerical examples. Section 5 concludes the paper. Appendix A contains proofs.

2

The Model Economy

There are two physical commodities: a consumption good and a capital good. For the sakeof simplicity, we assume that consumption can have only finite (but possibly many) levels1 .
There is a continuum of risk-averse agents that are divided into I types, each of which isindexed by i = 1, 2, . . . , I. Each type i consists of an αi ∈ (0, 1) fraction of the population,Pand i αi = 1. Each agent type i is endowed with κi units of capital. Capital endowments
are the main source of heterogeneity among agents.
Each organization/firm has the same fixed number of workers. All workers of an organization encounter the same local state or the common shock, ω. The state space Ω is thefinite set of states of nature, and P r(ω) is the probability of state ω occurring, such that thefollowing equation holds:X

P r(ω) = 1

(1)

ω∈Ω

Agent i derives utility from consumption ci and effort ei , according to the utility functionu(ci , ei ). The utility function is assumed to be concave and to be strictly increasing in ci , and1

We can apply the limiting arguments used in Prescott and Townsend (1984) to establish results when

the commodity space is not finite.

6

decreasing in ei . Again, we assume that effort or action can take only finite (but possiblymany) values. An agent’s effort is private information; therefore, there is a moral hazard
problem. In addition, we assume that effort is exerted before the underlying state ω can beobserved. That is, effort cannot be assigned to be conditional on ω.
Each agent operates an identical production technology, f (q|e, k, ω), which indicates theprobability of obtaining output q (in units of the consumption good) , conditional on her
effort e, the amount of captal inside the organization k and the organization-specific production shock ω 2 . Again there are finite (but possibly many) feasible levels of output. The
production technology is random and thus satisfies the probability constraint:Xf (q|e, k, ω) = 1, ∀e, k, ω(2)qAgents can form a local organization whose members experience the same local underlying
state or the common shock. For expositional convenience, we assume that there are only
two agents in each firm, but the analysis can easily be extended to cases with any finite
number of agents per firm. Let q = (q1 , q2 ) and e = (e1 , e2 ) denote the realized outputs
and effort levels of firm members, respectively. Accordingly, we can write the ex ante andconditional joint distributions of the outputs of workers in a local organization as P r (q|e, k)
and P r (q|e, k, ω), respectively.
This paper assumes that the outputs of workers in a local organization are uncorrelated when conditional on the common shock ω but that they are correlated ex ante. This
assumption is summarized below:
Assumption 1. The joint distribution of outputs satisfies the following conditions:(i) outputs are independent, conditional on ω:
P r (qi , qj |ei , ej , k, ω) = f (qi |ei , k, ω)f (qj |ej , k, ω),(3)(ii) but not independent ex ante:
P r (qi , qj |ei , ej , k) =X

P r (ω) f (qi |ei , k, ω)f (qj |ej , k, ω)(4)ω

6= P r (qi |ei , k) P r (qi |ej , k)2

(5)Note that both k and ω are organization-specific variables, which affect simultaneously the production

functions of all workers assigned to an organization.

7

where P r (qi |ei , k) =P

ω P r (ω) f (qi |ei , k, ω).

Note that the joint distributions are well defined, i.e.,X

P r (q|e, k, ω) = 1, ∀e, k, ω

(6)

X

(7)

q

P r (q|e, k) = 1, ∀e, kq

The common shock ω is not necessarily distinctly observable, and therefore may not be
contractible. Nevertheless, agents may be able to distinctly identify an element of a partitionof the state space Ω. This partition characterizes an informational regime, which is defined
more precisely in the next section.

2.1

Informational Regimes

An informational regime z is a partition of Ω, and is denoted by Fz . Let a subset As ⊂ Ω
be a typical member of an informational regime z; i.e., As ∈ Fz . With abuse of notation, we
will refer to As as observed state s. For notational convenience, let Z denote the numberof distinguishable events that are non-empty subsets of Ω in Fz ; i.e., Fz = {A1 , . . . , AZ }.
T
Technically, a partition requires that ∪Zs=1 As = Ω and As As0 = ∅. For example, thecoarsest informational structure (containing the least amount of information regarding statesof nature) is Fz = {{ω1 , ω2 }}. Under this informational regime, we cannot distinguish theunderlying state from one another. By contrast, the finest information structure (in which
we can distinguish all underlying states of nature from one another) is Fz̄ = {{ω1 } , {ω2 }}.
For a given informational regime Fz , we can define a modified production function foreach subset As ∈ Fz (using Bayes’ rule) as follows:PP r(q|e, k, ω)P r(ω)
P r(q|e, k, s) = ω∈As
(8)
P r(As )P
where P r(As ) = ω∈As P r(ω) is the probability of having a common state in As . Note that
this joint production function satisfies the following probability condition
PX
X ω∈A P r(q|e, k, ω)P r(ω)
sP r(q|e, k, s) =P r(As )qq
PPω∈As P r(ω)
q P r(q|e, k, ω)== 1.
P r(As )8

An informational regime provides information that is relevant for local production. Suchinformation may include information regarding weather conditions or sectoral economic indicators. This type of information can be obtained at certain cost. More precisely, theinformational partition can be made finer by investing in information technology.
An informational regime Fz can be attained at a cost of Cz units of capital. That is,
the informational regime Fz for a local organization can be made available through an (exante) investment of Cz units of capital. This cost is assumed to be per unit of organizations
participating in the regime. The cost is assumed to be increasing in terms of the accuracyof the information. Thus, the information cost is higher when the informational regime isfiner.

3

Firms as Optimal Contracts: A Principal-Agent Formulation

Each individual is employed by a local organization or firm. Because workers are risk averse,they potentially benefit from risk-sharing contracts provided by the principal3 . The moral
hazard problem implies that optimal consumption depends on output in order to provide
incentives for an agent to exert costly effort. In addition, an organization in this model could
also mitigate the moral hazard problem by investing in an information technology that helps
identify the common shock.
We consider two organizational regimes, which are formally defined below; (i) a relative
performance regime and (ii) a group regime. Those are stylized regimes that are present
in the existing literature (e.g., Holmstrom and Milgrom, 1990; Ramakrishnan and Thakor,
1991; Itoh, 1993; Prescott and Townsend, 2002) that can be clearly interpreted as competitive(relative performance) versus cooperative (groups) contractual arrangements.
A firm is characterized by an organizational regime, an informational regime, capital,and promised utility levels for each position in the firm. More formally, the set of potential
3

In the general equilibrium formulation, principals will be modeled as competitive intermediaries.

9firms is defined by the following:
B = {b = (o, z, k, ū1 , ū2 )} ,(9)

where o is the organizational regime (relative performance or group), z is the informational
regime, k is the firm’s capital, and ūi is the promised utility level for an agent in position i
within the firm. Without loss of generality, we focus only on efficient firms. Specifically, eachfirm maximizes an expected surplus that is conditional on given incentives and technologicalconstraints. The set of efficient firms, B, will define the commodity space in the generalequilibrium model of Section 4, in which each individual will be (possibly randomly) assigned
to a position within the firm. Implicitly, this assumption includes choices of organizational
regimes and investment in information.

3.1

Relative Performance Firms

The relative performance regime features competition among agents as an incentive tool.
Workers do not share information regarding their effort levels, and each agent is rewarded
separately. If one agent performs poorly compared with the others, then she will be punished, but if she performs well compared with the others, then she will be rewarded. These
comparative compensation schemes are particularly useful when the output of one individual
is informative regarding the shocks that affect other individuals or the outputs are highly
correlated.
Formally, a relative performance contract π r (c, q, e, s) is the probability that a firm’s
workers will obtain consumption c = (c1 , c2 ), produce outputs q = (q1 , q2 ), provide effort
levels e = (e1 , e2 ), and the observed state is s (or As ). The subscript i = 1, 2 denotes the
position of a member of the firm, and the superscript r denotes the relative performance
regime. To be more precise, this contract is conditional on the capital input k, the informational regime z, and promised utility levels (ū1 , ū2 ), which are kept implicit for notational
convenience. Contract π r (c, q, e, s) implicitly encompasses two decisions: the distributionof recommended effort (P r(e)) and the distribution of consumption conditional on output,
effort, and the observed state, P r (c|q, e, k, s).
The timing of events is as follows. First, workers are randomly assigned to levels of
10

effort according to P r(e). After such efforts are undertaken, some state of nature ω ∈ As
is realized. This implies that state s is observed, and the outputs q are obtained withprobability P r(q|e, k, s).
The workers then obtain consumption goods according to P r (c|q, e, k, s), which potentially depends on the observed information set As . All of these probabilities are implicit in
the contract π r (c, q, e, s) = P r(e)P r(q|e, k, s)P r (c|q, e, k, s) P r(As ).
As a probability measure, a contract π r (c, q, e, s) must satisfy the following probability
constraint:X

π r (c, q, e, s) = 1, and π r (c, q, e, s) ≥ 0, ∀ (c, q, e, s)(10)c,q,e,sA feasible contract π r (c, q, e, s) must also be consistent with the production technology(8). The following mother nature constraint guarantees such consistency. For any vector ofP
effort levels e and any observed state s ∈ Fz , such that c,q π r (c, q, e, s) > 0, Bayes’ rule
implies the following:
P r
π (c, q̄, e, s)
Pc r= P r (q̄|e, k, s) , ∀q̄, e, s.
c,q π (c, q, e, s)
The mother nature constraints can be rewritten in the form of linear constraints: for a givenk,X

π r (c, q̄, e, s) = P r (q̄|e, k, s)X

π r (c, q, e, s) , ∀q̄, e, s.

(11)

c,q

c

A feasible contract must ensure that the utility level of a worker in position i is not lessthan the promised expected utility for that position, ūi . This participation constraint isdefined by the following:X

π r (c, q, e, s) u (ci , ei ) ≥ ūi , ∀i.

(12)c,q,e,sBecause efforts are privately observed, a feasible contract must be incentive compatible;that is, each worker must have incentives to undertake the recommended level of effort. The
incentive compatibility constraints can be formulated as follows:X
π r (c, q, ei , e−i , s) u(ci , ei ) ≥c,q,e−i ,sX

π r (c, q, ei , e−i , s)c,q,e−i ,s11

P r (q|ẽi , e−i , k, s)u(ci , ẽi ), ∀ ei , ẽi ,P r (q|ei , e−i , k, s)(13)

Effort level is determined before the state s is observed; thus, the assignment of effort
cannot be contingent on the observed state s. That is, for any vector of effort levels e,X

π r (c, q, e, s̄) = P r (As̄ )c,qX

π r (c, q, e, s) , ∀s̄ ∈ Fz

(14)

c,q,s

Note that we can show thatP

c,q,e πr(c, q, e, s̄) = P r (As̄ ) for all s̄ ∈ Fz using (10) and (14).

That is, the contract π r is consistent with the probability distribution over the observed
states in Fz .
A relative performance firm is an optimal contract π r (c, q, e, s) that solves the following
surplus maximization problem:
Program 1.
max
r
π

X

π r (c, q, e, s) (q1 + q2 − c1 − c2 )(15)

c,q,e,ssubject to constraints (10), (11), (12), (13), and (14).

3.2Group or Cooperative Firms

Another type of organizational scheme is a group or cooperative regime, under which decisions are made jointly by agents, who observe one another’s actions and are able to offer
side payments. Because the entire group can be punished for individual failures, each worker
has incentives to monitor and ensure that the others exert the desired amounts of effort.
However, the workers in a group firm can potentially collude/coordinate in (possibly low)
effort levels and make side payments to promote local Pareto improvements. The principal
anticipates this possibility and offers only collusion-proof contracts. The collusion-proof condition implies that the allocations of effort and consumption shares are optimal, given someinternal (within-group) Pareto weights. This type of contract in turn implies that there is
full risk sharing within groups, such that individual levels of consumption depend only on
the within-group Pareto weights and the aggregate consumption level. Thus, formally, agroup contract, π g (ca , µ, q, e, s), is the probability that the aggregate consumption is ca , its
members are assigned within-group Pareto weights µ = (µ1 , µ2 ), their realized outputs areq = (q1 , q2 ), their efforts are e = (e1 , e2 ), and the observed state is s.
12More formally, a group contract first involves the (possibly random) choice of withingroup Pareto weights, P r(µ), then the choice (also possibly random) of efforts, P r(e|µ),and finally aggregate consumption conditional on the within-group Pareto weights, outputs(following a random production function P r(q|e, k, s)), efforts, and the observed state s,
P r(ca |µ, q, e, s). The collusion-proof condition implies that when efforts e and consumption
levels c are recommended, it must be the case that, for a pair of weights µ1 and µ2 ,X

P r(ca |e, q, s)P r(q|e, k, s)X

ca ,q,sµi u(ci ) ≥iX

P r(ca |e, q, s)P r(q|e, k, s)

ca ,q,sXµi u(ci , ei )

(16)

i

for any e and any c and c, such that c1 + c2 = c1 + c2 = ca , where ca is the aggregate
consumption within the group. When the utility function is separable, i.e., u(ci , ei ) = ue(ci )−v(ei ), this condition implies that c solves the following within-group Pareto problem:
X

max
c

µi ũ(ci )

(17)

i

subject toX

ci = ca(18)iHenceforth, we assume that the utility function is separable, so the problem above is always
satisfied in groups. In effect, we can write c as a function of ca and µ ≡ (µ1 , µ2 ), i.e., c (ca , µ).
For notational purposes, we now write a group contract as a joint probability π g (ca , µ, q, e, s) =P r(µ)P r(e|µ)P r(q|e, k, s)P r(ca |q, e, s, µ)P r(As ). Hence, this contract is the probability
that a group of agents will obtain aggregate consumption ca , be assigned within-group
Pareto weights µ = (µ1 , µ2 ), produce outputs q = (q1 , q2 ), undertake the recommended
efforts e = (e1 , e2 ), and realize the observed state s.
The collusion-proof condition (16) can now be rewritten in the form of the following group
incentive constraints for each µ, e, ee:Xπ g (ca , µ, q, e, s)

ca ,q,sXµi u(ci (ca , µ), e) ≥i

X
ca ,q,sπ g (ca , µ, q, e, s)

P r(q|ee, k, s) X
µi u(ci (ca , µ), ee).
P r(q|e, k, s) i

13

(19)

Note that in (16), the within-group Pareto weights that are present in the risk sharing
condition (17) must be the same as those in the group incentive constraint (19). Additionally,note that in the group regime, there is a unique incentive constraint, which reflects that thedecisions are made jointly.
As a probability measure, a contract π g (ca , µ, q, e, s) must satisfy the following probability
constraint:X

π g (ca , µ, q, e, s) = 1, π g (ca , µ, q, e, s) ≥ 0, ∀(ca , µ, q, e, s).

(20)

ca ,µ,q,e,s

Again, π g (ca , µ, q, e, s) must be subject to mother nature constraints that guarantee thatrealized outputs are consistent with the productive technology:X

π g (ca , µ, q, e, s) = P r(q|e, k, s)caX

π g (ca , µ, q, e, s), ∀(µ, q, e, s).

(21)

ca ,q

The participation constraints for the group regime are as follows:X

π g (ca , q, e, s)u(ci (ca , µ), e) ≥ ui , i = 1, 2

(22)

ca ,µ,q,e,s

Finally, the distribution of effort must be independent of the information set As . Thus:X

π g (ca , µ, q, e, s) = P r(As )

ca ,q

X

π g (ca , µ, q, e, s), ∀(s, e, µ)(23)

ca ,q,sA group firm is an optimal contract that solves the following surplus maximization problem:
Program 2.
max
g
π

X

π g (ca , µ, q, e, s)(q1 + q2 − ca )ca ,µ,q,e,s

subject to constraints (19), (20), (21), (22), and (23).

14

(24)

3.3

Comparing Regimes: The Roles of Information, Wealth, andInequality

In this section, we present theoretical results comparing the surplus generated by groups versus relative performance organizations. In principle there might be costs related to adopting
one regime or the other4 . On the one hand, relative performance requires preventing side
payments and collusion among agents. On the other hand, groups require mutual observability of efforts. Imposing these conditions might be costly. However, our goal is to compare
cooperative versus competitive incentive schemes assuming that they are available, and weare agnostic about these costs.
We consider a symmetric case, in which the promised utility levels of both workers are
identical, i.e., ū1 = ū2 . In this case, we analytically demonstrate that for any relative
performance contract, there exists a group contract that generates a higher surplus when
the common shocks are perfectly observed. In other words, the optimal organizational regime
depends on the informational regime z. This argument is formally presented in Proposition
1 below.
Intuitively, the relative performance regime tends to dominate (generate a larger surplus)
when the correlation of outputs is high, and vice versa. However, when it is possible toobserve the common shock ω perfectly, the outputs are (ex post) uncorrelated across agents
conditional on ω, as in (3). Therefore, similar to Ramakrishnan and Thakor (1991) and
Itoh (1993), this study notes that the group regime will dominate when the local shocks are
perfectly observed because the (ex-post) correlation of outputs is zero in this case. A key
assumption is that the correlation of outputs results from local shocks only (Assumption 1).
Proposition 1. With additively separable utility and perfect observability of common shocks,
for any feasible surplus maximizing relative performance contract π r with ūi = ū for all i,there exists a feasible group contract π g with the same utility level for all agents that generates
a weakly larger surplus. Further, if for any pair effort/common shock (e, ω) the probabilityof each output level is positive, and π r has binding incentive constraints, the surplus under4

Madeira and Townsend (2008), for instance, assume that there is a cost related to adopting relative

performance.

15

π g is strictly higher than the surplus with π r .
A proof of Proposition 1 is provided in the appendix. A simple intuition for the two-agent
case is the following. Suppose there is full information about ω. For given efforts and ω, an
optimal relative performance contract will simply determine, for each individual, an amountof consumption conditional on his own output (regardless of the output of the other, since
outputs are independent given ω). A group with equal Pareto weights, would be able tosatisfy the incentive constraint with the following scheme. When outputs are equal among
agents, they receive the same consumption as in relative performance. When outputs aredifferent among individuals, both receive a certainty equivalent of a lottery that give each of
the relative performance consumptions with probability 0.5 5 . This step would save resources,
given risk aversion, thus increasing the total surplus 6 . Intuitively the advantage of groups
comes from the capacity of providing risk sharing in cases where outputs are different. Notethat in relative performance with binding incentive constraints, under some common state,consumption will be different among agents with different output levels (which happens withpositive probability given the assumption that the probability of each output level is positive
for any pair (e, ω)). So, risk sharing will generate strict resource savings. This argument
easily extends up to the case with more than two agents.
Proposition 2 below considers another extreme case, in which relative performance always dominates, regardless of the observability of common shocks. This case applies whenidiosyncratic shocks are absent and arbitrarily high punishment is allowed. The first condition states that an individual productive technology f (q|e, k, ω) has no idiosyncratic shocks
if, for any (q, e, k, ω) either f (q|e, k, ω) = 0 or f (q|e, k, ω) = 1. Thus, idiosyncratic shocks
will be absent if the distribution of outputs conditional on the common shock is always
degenerate. The second condition is that inf ci u(ci , ei ) is sufficiently negative for any ei .
5Under relative performance, one agent would consume c1 and the other would consume c2 . The lottery

mentioned gives each of these outcomes with probability 0.56Note that this consumption scheme would increase the payoff of lower effort for a given individual
acting independently (as in relative performance), since a contingency in which he is the only one with thelower output would now generate higher consumption. So this scheme would not be feasible under relative
performance16

Proposition 2. Suppose that f (q|e, k, ω) has no idiosyncratic shocks, and that an arbitrarily
high punishment is allowed, i.e., inf ci u(ci , ei ) is sufficiently negative for any ei . Then, for
any optimal group contract without full insurance and ūi = ū for all i , there exists a feasible
relative performance contract with the same utility level for all agents that generates a strictly
larger surplus.
A formal proof of Proposition 2 is provided in the appendix. The intuition behind thisresult is straightforward. With no idiosyncratic shocks, different outputs can only happen
when efforts are different. A very strong punishment when outputs are different would
easily motivate them to make the recommended level of effort, so that different output levels
would not be observed and full insurance would be possible (even if the effort recommended
is not the lowest one). Again, this result is valid regardless of the number of agents in eachorganization.
This proposition implies that a relative performance regime dominates a group regime,
regardless of the information structure, as long as idiosyncratic shocks are absent and punishment can be sufficiently harsh. This result emphasizes the role of idiosyncratic shocks
in group regimes. Note that the first-best optimal allocation can be achieved by either arelative performance regime or a group regime if the common shocks are perfectly observed.

4

General Equilibrium with Endogenous Organizationaland Informational Regimes

This section presents a general equilibrium model with endogenous organizational and informational regimes. To save some space, the welfare theorems and the existence theorem
are omitted but they are available in our working paper version Kilenthong and Madeira(2013). See also Prescott and Townsend (2006) for a similar general equilibrium model withendogenous organizational regimes.

17

4.1

Competitive Equilibrium

Let B be a finite set of all potential firms (optimal contracts with different organizational
regimes, informational regimes, capital inputs, and promised utility levels). A typical firm b
specifies an organizational form (either relative performance or group evaluation), informational regime z(b), capital input k(b), and the promised utility level ū(b, j) for a worker inthe j th position. In addition, each firm b is associated with an expected surplus S(b). Witha continuum of firms, the expected surplus of a firm is equal to the average surplus of firmsof the same type.
Denote the probability of an agent of type i working in position j in firm b by xi (b, j).
With a continuum of agents, xi (b, j) can also be interpreted as the fraction of agents assigned
to a bundle (b, j). With all choice objects gridded up as an approximation, the commodity
space L ⊂ Rn is assumed to be a finite-dimensional space in which n is the number of possible
bundles (b, j). Let xi denote an n dimensional vector or a lottery, each element of which isthe probability of being assigned to a given bundle (b, j), xi (b, j).
As a probability measure, a lottery xi must satisfy the following probability constraint:Xxi (b, j) = 1.

(25)

(b,j)

The consumption possibility set of an agent of type i is then defined by the following:




X
X i = xi ≥ 0 :xi (b, j) = 1
(26)


(b,j)

The linearity of the constraints ensures the convexity of the consumption possibility set X i .
The preferences of an agent of type i over X i are defined as follows:Xxi (b, j) ū (b, j)

(27)

(b,j)

Let P (b, j) be the price of a bundle (b, j) or the price of the j th position in firm b. Notethat the price of the capital good is 1 as it is the numeraire good. Each agent is infinitesimally small relative to the entire economy and takes all prices as given. The intermediaries
introduced below are assumed to act competitively.

18

Workers: Each agent type i, taking prices P (b, j) as given, chooses xi to maximize hisutility:
max
i
x

X

xi (b, j) ū (b, j)

(28)

(b,j)

subject to the probability constraintXxi (b, j) = 1,

(29)

P (b, j) xi (b, j) ≥ κi

(30)

(b,j)

and the budget constraintX(b,j)

The budget constraint (30) states that the agent sells her full endowment κi and uses theproceeds to buy lotteries xi .
Intermediaries: The primary role of an intermediary is to create firms by assigning/matching workers to firms and generating information about local underlying states
when necessary. With constant returns to scale, the profit of an intermediary is zero, andthe number of intermediaries becomes irrelevant. Therefore, without a loss of generality, we
assume that there is one representative intermediary who takes prices as given.
More formally, the intermediary creates y (b) ∈ R+ units of firms of type b, and mustfills both positions within the firm. Note that the intermediary can issue any non-negative
number of firms/positions; that is, the number of firms issued need not be between zero andone and is not a lottery. Let y ∈ L be the vector of the number of firms issued, each elementof which is the number of firms of each type b.
By creating a firm of type b, the intermediary must deliver the promised capital k(b),must pay the information cost of C(b), and must deliver potentially state-contingent transfers
conditional on outputs, consumption, and the observed state, i.e., T (b|q, c, s). Using thelaw of large numbers, the average transfers (per unit of firm) over all firms of type b isP
q,c,s T (b|q, c, s) = −S (b). Therefore, the intermediary must hold (buy/sell) −y(b)S (b)units of future contracts at the price PS .
The objective of the intermediary is to maximize its profit by choosing the number of19

firms y, taking prices P (b, j) and PS as given:
"
#
X
X
max
y (b)
P (b, j) − k(b) − C(b) + PS S (b) .
y

(31)

j

b

As in Prescott and Townsend (2006), the existence of an optimum in the intermediary’s
problem requires that for any bundle (b, j),X

P (b, j) ≤ k(b) + C(b) − PS S (b) ,

(32)

j

which holds with equality if y (b) > 0. HerePj P (b, j) is the revenue from the sale ofmemberships in firm b, and is the cost of creating firm b. This condition is in fact a necessary
and sufficient condition for the saddle-point problem (31).
Market Clearing: The market-clearing condition for capital inputs is as follows:Xy (b) [k(b) + C(b)] =

X

αi κi

(33)

i

b

The market-clearing conditions for lotteries are the following:X

αi xi (b, j) = y (b) , ∀b; j = 1, 2.

(34)

i

In addition, the market for future contracts clears, i.e.,Xy(b)S (b) ≥ 0.

(35)

b

Definition 1. A competitive equilibrium is a specification of allocations (x, y), and the priceof a position j in firm b, P (b, j), and the unit price of the future contract, PS , such that(i) for each i, xi ∈ X i solves (28), subject to (30), taking prices P (b, j) as given;(ii) for the intermediary, y ∈ L solves (31), taking prices P (b, j) and PS as given; and(iii) the markets for capital inputs, lotteries, and future contracts clear, i.e., (33), (34), and(35) hold.
As in Prescott and Townsend (2006), the economy here is a well defined convex economy.
Therefore, the first and second welfare theorems hold, and a competitive equilibrium exists
as in their model. For the sake of brevity, all theorems and their proofs are omitted. Readers
can see Kilenthong and Madeira (2013) and Prescott and Townsend (2006) for more details.
20

4.2

Pareto Optimal Allocations

We characterize the constrained optimum using the following Pareto program. Let λi ≥ 0
be the ex-ante (before organization assignment) Pareto weight on an agent type i7 . WithoutPa loss of generality, we can normalize the weights such that i λi = 1. A constrained Pareto
optimal allocation solves the following Pareto program.
Program 3.
max
i

X

(x ,y)

λi αi

i

X

xi (b, j) ū (b, j)

(36)

(b,j)

subject toXxi (b, j) = 1, ∀i,

(37)

(b,j)

X

αi xi (b, j) = y(b), ∀b; j = 1, 2,

(38)

X

(39)

i

X

y(b) [k(b) + C(b)] =αi κi ,ibX

y(b)S (b) = 0.

(40)

b

Note that the Pareto program includes all of the incentive constraints, which are embeddedin the grids of potential firms, through the surplus of each firm S (b).

4.3

Numerical Examples

This section presents numerical examples of competitive equilibria8 . We solved the model
for a large set of specifications, including different levels of risk aversion, wealth, inequality
and cost of information. Our results show that the relationship between availability of
7Note that λi represents ex-ante Pareto Weights, while µi represents ex-post inside-group Pareto weights.

As it is shown in Prescott and Townsend (2002), they are not necessarily the same. For instance, it is possiblethat agents with different Pareto weights are assigned to different groups, and in each of these groups they
have equal Pareto weights.
8
Technically, we solved Program 3, with 900 pairs of utility promises for each regime (groups with information, groups without information, relative performance with information, and relative performance
without information). Wealth inequality is measured by Pareto weights λ in all of the examples.

21

information and cooperation is robust to a large set of specifications. They also bring insights
into how wealth, inequality, effort, and information interact to generate general equilibrium
effects.
The numerical examples are based on the following model economy. There are two possible local underlying states, i.e., Ω = {1, 2}, each of which occurs with an equal probability,i.e., P r(ω = 1) = P r(ω = 2) = 0.5. Therefore, there are only two possible informational
regimes, Fz = {{1, 2}} (no information) and Fz̄ = {{1} , {2}} (full information).
Each agent derives her utility from the following utility functionu(c, e) =

e1−ρ
c1−ρ
−
,
1−ρ 1−ρ(41)

where c, e and ρ denote consumption, effort9 , and the relative risk aversion coefficient, respectively. Effort e can take only two values: el = 2.25 (low effort) and eh = 6.25 (higheffort). The relative risk aversion coefficient ρ can take on any positive number.
Output can take only two values: q l = 2 (low output) and q h = 20 (high output). The
production technology is assumed to be linearly additive in capital as follows.
f (q + k|e, ω, k) = f˜(q|e, ω).

(42)

In our benchmark technology, f˜(q|e, ω) is defined according to the probability distribution
in Table 1. We chose a specification that makes the value of information for incentives
clear. There is one state of the world in which effort is crucial, and another state in which
effort is irrelevant. Knowledge about the state is very useful to determine if outputs are
informative about efforts. In this benchmark specification, output correlation is 0.32 whenboth individuals make the same effort (either high or low).
There are two types of agents, i.e., i = 1, 2. Both types of agents have the same mass,i.e., α1 = α2 = 0.5. The key heterogeneity between agents lies in initial capital endowment
κi .
9Making the marginal utility of effort depend on ρ as above is convenient to study jointly different risk

aversions since it makes effort and consumption comparable, which brings the regime areas to similar wealthranges. Changes in the values of q h , q l , eh and el have no impact in the general profile of solutions, although
they change the wealth range where regimes are found.

22

Table 1: Distribution of output conditional on a local state, f (q|e, ω), for the benchmark
case.
ω=1

ω=2

eh

el

eh

el

f˜(q h |e, ω)

0.99

0.01

0.50

0.50

f˜(q l |e, ω)

0.01

0.99

0.50

0.50

In all specifications studied, all firms invest in information when its cost is zero, sincebetter information leads to more efficient contracts. This is true for all levels of risk aversion and wealth inequality, as shown in Figure 1a and 1b, which depict the probability ofacquisition of information as a function of it’s cost, for different risk aversions and inequality
levels. The figures show that the fraction of firms purchasing information is decreasing with
the information cost10 .

(a)

(b)

Figure 1: (a) Fraction of firms that invest in information when λ = (0.5, 0.5), aggregatePwealth i αi κi = −17. (b) Fraction of firms that invest in information when λ = (0.7, 0.3),
P
aggregate wealth i αi κi = −17.

For all specifications11 , only group firms are active in equilibrium when the cost of in10

There are some slightly upward sloping areas in some of these lines, possibly related to the fact that wehave a finite (although large) grid.
11
We performed a larger set of computation than those presented in this session. we computed the general23formation is zero. This result is true for both equal-wealth and unequal-wealth economies,
as shown in Figure 2a and 2b, respectively. As the cost of information increases, relative
performance regime starts to emerge. The probability of groups is normally decreasing withthe cost of information.
An important result that is found in all specifications studied, is that only group firms
acquire information about ω in equilibrium. This does not mean that this information is
not beneficial to the relative performance regime. In fact, information about the statesallow more state contingent contracts, which generally improves welfare. However, relative
performance firms never acquire information in the computational exercises. In equilibrium,
only three regimes exist: groups with information, groups without information, and relative
performance without information (hereafter simply called relative performance). This isrelated to the fact that, in our formulation, acquiring information is equivalent to acquiring
full information about common shocks.12
As shown in Figure 3, small changes in the cost of information can reshape the organization structure completely, both in terms of regime and matching of agent types. Generalequilibrium effects are crucial to determine how these dramatic changes occur. In the example presented in Figure 3a, only group firms with information are active when the information
cost is sufficiently low. As the cost of information approaches a certain value (slightly smaller
than 1) there is a sudden transition to another type of equilibrium in which the three types offirms, relative performance, group without information and group with information, coexist.
After this point, for a certain range of the cost of information, group firms with information
employs just one type of agents (type one, with high wealth), and relative performance firms
employ the other type of agents (type 2, with lower wealth), while group firms without information employs both types of agents. This matching pattern is presented in Figure 4a.
equilibrium for a grid of 20 values of λ, 40 values of wealth, 5 levels of risk aversion and 4 specifications of the
production function. In all of these specifications, when the cost of information is zero there is informationacquisition with probability one, and group firms are the adopters whenever information is acquired.
12
This result may not be true in general, especially when investment in partial information about common
shocks is possible. Partial information that bring small gains should be purchased by relative performanceorganizations if its cost is sufficiently low. However, in a region where relative performance dominates, if thisgain is sufficiently small, relative performance will be dominant, and, in this case, not invest in information.

24

(a)

(b)

Figure 2: (a) Fraction of firms that use group contracts when λ = (0.5, 0.5), aggregate wealthP i ii α κ = −17. (b) Fraction of firms that use group contracts when λ = (0.7, 0.3), aggregatePwealth i αi κi = −17.

Given this distribution of types, general equilibrium constraints require that the mass ofrelative performance firms equals the mass of group firms. As the cost approaches anothercritic value, roughly close to 1.5, another dramatic reorganization occurs. Groups with information disappear, and the market is split between relative performance firms and groupfirms without information. Importantly, now all firms, both relative performance and group
without information, employ same type of workers (group firms absorb wealthy agents andrelative performance firms take poor agents). That is, the matching structure completelychanges again. Note that the regime profile is similar for a higher risk aversion (ρ = 1.4), as
shown in Figure 3b,.
In order to understand the distribution of types across organizations, it is important toconsider the relationship between the efforts recommended to agents and the optimal organizational assignment. Groups without information are particularly efficient to manage agents
who make different efforts. In all the numerical exercises performed, groups without information are chosen in organizations where effort is unequal across agents. Figure 4b shows that,in the example just mentioned, groups without information have one agent exerting higheffort while the other exerts low effort. On the other hand, all agents in the other types of

25

(a)

(b)

Figure 3: (a) Fraction of firms in relative performance, group without information, andgroup without information regimes when λ = (0.7, 0.3), ρ = 0.8 and aggregate wealthP i ii α κ = −17. (b) Fraction of firms in relative performance, group without information,and group without information regimes when λ = (0.7, 0.3), ρ = 1.4 and aggregate wealthP i ii α κ = −17.

(a)

(b)

Figure 4: (a) Probability of having the same type of agents in a firm conditional each regimePwhen λ = (0.7, 0.3), ρ = 0.8 and aggregate wealth i αi κi = −17. (b) Probability of having
high effort in a firm (Probability will be one only if both of them exert high effort) conditionalP
each regime when λ = (0.7, 0.3), ρ = 0.8 and aggregate wealth i αi κi = −17.

26

firms exert high effort. Given that the optimal levels of effort are different within the group
without information firms, it can be convenient to employ different types of agents. This
helps to explain why groups without information employ different types of agents while others employ the same types. This profile also shows the benefit of the additional information
on enforcing high-effort contracts. As the information becomes sufficiently cheap (below 1),
agents move from group without information firms, where effort is sometimes low, to groupwith information firms, where efforts are always high.
Aggregate wealth also plays an important role on information acquisition and organizational designs. This is shown in Figures 5a and 6a, where we examine the organizational
profile across different levels of aggregate wealth for a particular level of the information
cost13 . With extremely low aggregate wealth, there is no information acquisition. This happens because information acquisition requires capital, which can also be used to produce
goods for consumption. With extremely low wealth, it is too costly to spend the limited
resources for information investment. This is true for both equal-wealth and unequal-wealtheconomies. As aggregate wealth grows, all firms start to acquire information. When theaggregate wealth is sufficiently large, firms start assign low effort to agents and information
becomes less valuable. For extremely high wealth levels, both agents make low effort, so therelative performance and group regimes are equivalent, since none of the incentive constraints
are binding. In this case there is full insurance. 14 (see Figure 5b and 6b).
A complex profile of regimes given wealth emerges when there is inequality among agents.
Figure 6a shows that the probability of information acquisition exhibits a double-peak pattern in the unequal-wealth economy when the relative risk aversion is high enough (aboveone). This is a consequence of general equilibrium effects. Let us consider the case withrelative risk aversion ρ = 1.4 and Pareto weights λ = (0.7, 0.3), described by Figure 7.
When wealth is extremely low, only the relative performance regime is active in equilibrium.
As wealth increases, groups with information emerge and coexist with relative performancefirms. Up to this point, all agents are assigned high effort. As wealth keeps increasing, some
13

Note that wealth is sometimes negative, which can be interpreted as debt. Identical profiles with non-negative wealth would be observed if we assumed there is a fixed cost in terms of capital for the firms to
produce14
In other words, consumption will be constant, regardless of output realizations

27

(a)

(b)

Figure 5: (a) Probability of information acquisition when λ = (0.5, 0.5), and cost of information C = 0.9. (b) Probability that relative performance and group regimes are equivalent
when λ = (0.5, 0.5), and cost of information C = 0.9.

(a)

(b)

Figure 6: (a) Probability of information acquisition when λ = (0.7, 0.3) and cost of information C = 0.9. (b) Probability that relative performance and group regimes are equivalent
when λ = (0.7, 0.3), and cost of information C = 0.9.

28

(a)

(b)

Figure 7: (a) Fraction of firms in relative performance, group without information, andgroup without information regimes when λ = (0.7, 0.3), ρ = 1.4 and cost of information
C = 0.9. (b) Probability of having high effort in a firm (Probability will be one only if bothof them exert high effort) conditional each regime when λ = (0.7, 0.3), ρ = 1.4 and cost of
information C = 0.9.

rich agents (type 1) will be assigned to group without information, where they exert low
effort and match with poor agents (type 2). At some point, this type of firms completely
dominates the entire economy. As this happens, group with information firms graduallydisappear. In fact, the unconditional probability of high effort is decreasing from this point
onward as shown in Figure 7b. As the optimal probability of high effort decreases, full insurance firms start to attract high Pareto weight members from groups without information. As
a result, some of the poor agents (type 2) that are released from groups without information
start matching with the same type to form groups with information, where both agents exerthigh effort. This generates a second peak in the fraction of groups with information. As
wealth keeps increasing, eventually all type 1 individuals will be employed in a full insuranceorganization. Type 2 individuals start to move to this type of organization. Eventually, allagents will be in the full insurance organization with both agents making low effort.
Figure 8 shows how organization and information investment decisions respond to different levels of output correlation. The production technologies used for these exercises are29

Table 2: Distribution of output conditional on a local state, f (q|e, ω) for the “high correlation”, “medium correlation”, and “low correlation” cases.
High correlation (0.36)

Medium correlation (0.26)

ω=1

ω=2

ω=1

eh

el

eh

el

eh

el

eh

f˜(q h |e, ω)

0.9

0.1

0.35

0.65

0.85

0.15

f˜(q l |e, ω)

0.1

0.9

0.65

0.35

0.15 0.85

(a)

ω=2

Low correlation (0.18)
ω=1

ω=2

el

eh

el

eh

el

0.4

0.6

0.8

0.2

0.45

0.55

0.6

0.4

0.2

0.8

0.55

0.45

(b)

Figure 8: (a) Fraction of firms that use group contracts when λ = (0.7, 0.3), ρ = 0.8,
P
aggregate wealth i αi κi = −25.6. (b) Fraction of firms that invest in information whenP
λ = (0.7, 0.3), ρ = 0.8, aggregate wealth i αi κi = −25.6.

30

presented in Table 2 15 . The results show that the downward sloping profiles of the fractionof groups and information acquisition are robust to changes in production technology. As
in Ramakrishnan and Thakor (1991) and Itoh (1993), when the cost of information is highenough, so there is no information acquisition, high correlation diminishes the probability ofgroups.
A striking feature of Figure 8 is that higher correlation does not necessarily causes more
information purchasing. Relative performance is used to deal with higher correlation and, infact higher correlation diminishes the fraction of firms purchasing information. This result
implies that the relationship between shocks, information and relative performance is subtle.
Increases in correlation can, simultaneously, lead to more adoption of relative performanceand less use of information.

5

Conclusion

This paper extends the multi-agent moral hazard model of Holmstrom and Milgrom (1990)
in two respects: (i) we add the costly observability of common shocks, and (ii) we embed
this structure in a Walrasian equilibrium model.
We present theoretical and numerical results showing that both relative-performance andcooperative/group regimes can be optimal, but information regarding common shocks yields
greater benefits for cooperative regimes. These results suggest that the emergence of cooperative behaviors may be related to technological advances (e.g., lower costs of acquiring
information). On the other hand, if information about common shocks is available, cooperation may be optimal even when outputs are highly correlated (contrast to Ramakrishnan
and Thakor, 1991; Itoh, 1993). For a symmetric case in which individuals are ex ante identical, we proved that cooperation or group regimes prevail when common shocks are perfectly
observable. In another polar case in which all shocks are common and punishment can be arbitrarily severe, relative performance regime always dominates, regardless of the information
15

In all of these production technologies, probabilities of high and low output conditional on effort (un-conditional on ω) are the same. The specifications depart from the benchmark case to make the effects ofcorrelation clearer

31

structure.
Our numerical exercises reveal that diverse organizational forms can coexist in equilibrium, but only groups obtain full information about common shocks. Both costs of information and the wealth of agents affect the set of organizations that are active in the economy.
For a given cost of information, investment on information is more likely for intermediarylevels of wealth. For these wealth levels, groups are likely to be dominant, while relative
performance may appear for lower wealth levels. For a given level of wealth, if the costof information is sufficiently low, only groups investing in information are observed. Withhigher costs of information, relative performance can be observed.
Examples show that general equilibrium effects can generate substantial reorganizationof production in response to small changes in wealth or the cost of information, affecting
both the set of organizational regimes operating and the assignment and matching patternsof heterogeneous agents given these regimes. A rich interplay among information, wealth,inequality and optimal effort levels is present in these transitions of regime configuration.
The current framework is compatible with a number of extensions. A dynamic version of
the model could be informative with respect to co-movements and transitions and could also
generate patterns of evolution in organizational forms, as agents learn about the environment
and the production process. In addition, the model can be adapted to admit different sizesof organizations/firms, so that it can be used to analyze the optimal size of organizations
and its interplay with the availability of information regarding common shocks.

References
Ahlin, C. and R. Townsend (2007). Selection into and across credit contracts: theory andfield research. Journal of Econometrics 136 (2), 665–698.
Barlevy, G. and D. Neal (2012). Pay for Percentile. American Economic Review 102 (5),1805–31.
Chiappori, P.-A., K. Samphantharak, S. Schulhofer-Wohl, and R. M. Townsend (2014). Heterogeneity and risk sharing in village economies. forthcoming in Quantitative Economics.

32

Deaton, A. (1992). Saving and income smoothing in cote d’ivoire. Journal of African
Economies 1 (1), 1–24.
Fafchamps, M. and F. Gubert (2007). The formation of risk sharing networks. Journal of
Development Economics 83 (2), 326–350.
Genicot, G. and D. Ray (2003). Group formation in risk-sharing arrangements. Review of
Economic Studies 70 (1), 87–113.
Ghatak, M. and T. Guinnane (1999). The economics of lending with joint liability theory
and practice. Journal of development economics 60 (1), 195–228.
Goldstein, M. (2000). Chop Time, No Friends: Risk and Intrahousehold Insurance in Southern Ghana.”. Manuscript, London School of Economics.
Grimard, F. (1997). Household consumption smoothing through ethnic ties: Evidence from
Cote dIvoire. Journal of Development Economics 53 (2), 391–422.
Holmstrom, B. and P. Milgrom (1990). Regulating Trade Among Agents. Journal of Institutional and Theoretical Economics: JITE 146, 85–105.
Itoh, H. (1993). Coalitions, incentives, and risk sharing. Journal of Economic Theory 60 (2),
410–427.
Jalan, J. and M. Ravallion (1999). Are the poor less well insured? Evidence on vulnerability
to income risk in rural China. Journal of Development Economics 58 (1), 61–81.
Kilenthong, W. T. and G. A. Madeira (2013). Observability and endogenous organizations.
RIPED Working Paper .
Lazear, E. and S. Rosen (1981). Rank-order tournaments as optimum labor contracts. The
Journal of Political Economy 89 (5), 841–864.
Lazear, E. and K. Shaw (2007). Personnel economics: The economist’s view of humanresources. The Journal of Economic Perspectives 21 (4), 91–114.

33

Madeira, G. and R. Townsend (2008). Endogenous groups and dynamic selection in mechanism design. Journal of Economic Theory 142 (1), 259–293.
Mueller, R., E. Prescott, and D. Sumner (2002). Hired hooves: Transactions in a south Indianvillage factor market. The Australian Journal of Agricultural and Resource Economics 46,
233–255.
Prescott, E. and R. Townsend (1984). General Competitive Analysis in an Economy with
Private Information. International Economic Review 25 (1), 1–20.
Prescott, E. and R. Townsend (2002). Collective organizations versus relative performance
contracts: Inequality, risk sharing, and moral hazard. Journal of Economic Theory 103 (2),282–310.
Prescott, E. and R. Townsend (2006). Firms as Clubs in Walrasian Markets with Private
Information. Journal of Political Economy 114 (4), 644–671.
Ramakrishnan, R. and A. Thakor (1991). Cooperation versus competition in agency. Journalof Law, Economics, and Organization 7 (2), 248–283.
Ray, D. (2007). A game-theoretic perspective on coalition formation. Oxford University
Press, USA.
Townsend, R. (1994). Risk and insurance in village india. Econometrica: Journal of the
Econometric Society, 539–591.
Townsend, R. and R. Mueller (1998). Mechanism design and village economies: From credit
to tenancy to cropping groups. Review of Economic Dynamics 1 (1), 119–172.

A

Proofs

Proof of Proposition 1. This proof is written for the general case in which there is a finite
number of firm members, N ≥ 2. Consider a relative performance contract π r with ū. Feasibility requires that π r satisfies conditions (10), (11), (12), (13), (14). Perfect observability
34

implies that one individual’s output is not informative with regard to the outputs of otherindividuals in the firm. Hence, an individual’s consumption ci will depend only on individual
output qi and on the underlying state ω. Given this information and the symmetry assumption, we can conclude that the optimal consumption for agent i under a relative performance
regime is cri = c (qi , ω).
We will now show that there is a feasible group contract π g that can generate a weakly
larger surplus. Symmetry, i.e., ūi = ū for all i, implies that there is no loss of generality
if we consider only a symmetric solution. That is, the within-group weights µi = N1 aresymmetric16 , where N is the number of firm members. This symmetric solution also implies symmetric consumption allocation, i.e., cgi = ca (q,ω), ∀i. For each relative performanceN
contract π r (c, q, e, s), we define a group contract π g (ca , µ, q, e, s) such thatuca (q, ω)
N


=

N
X
u (c (q` , ω))
`=1

N

(43)

and
g

π (ca , µ, q, e, ω) =
 π r (c, q, e, ω)

when condition (43) holds and µi = N1 ,

 0otherwise.

(44)

The concavity of the utility function implies that the aggregate consumption specified in
the group contract is no larger than the sum of the consumption allocations specified inP
the relative performance contract, i.e., ca (q, ω) ≤ N
i=1 c (qi , ω) which holds with equality ifnone of the incentive constraints is binding (so there is full insurance).
It is not difficult to show that the probability, mother nature, and consistency constraints,(10), (11), and (14), respectively, for the relative performance contract π r , imply that theprobability, mother nature, and consistency constraints, (20), (21), and (23), respectively, forthe group contract π g , hold. We now only need to show that the participation and incentive
constraints, (22) and (19), respectively, also hold under contract π g . The separability of theutility function implies that there is no loss of generality if we suppress the effort in theutility function for the participation constraints.
16

Without a loss of generality, an optimal group contract with different weights must randomize across µi ,and it will do so only if advantageous. Therefore, the proof is valid.

35

The participation constraints, (12), in case of the relative performance contract π r canbe rewritten as follows:
X

ūi ≤

π r (c, q, e, ω) u (cri )c,q,e,ω

=X XX
c,e,ω q−iπ r (c, q−i , qi , e, ω) u (c(qi , ω))

(45)

qi

The symmetry assumption implies the following:XXq−i

π r (c, q−i , qi , e, ω) u (c(qi , ω)) =

qi

XX
q−j

π r (c, q−j , qj , e, ω) u (c(qi , ω)) , ∀i, jqj

Thus, the following is implied:XXq−i

π r (c, q−i , qi , e, ω) u (c(qi , ω)) =N XX
X`=1 q−`

qi

=

=

N
XX
q

`=1

X

r

π r (c, q−` , q` , e, ω)q`π r (c, q−` , q` , e, ω)π (c, q, e, ω)qu (c(q` , ω))Nu (c(q` , ω))NNXu (c(q` , ω))N`=1

Substituting this equation into (45) yields the following:
ūi ≤

X

r

π (c, q, e, ω)NXu (c(q` , ω))NX
ca (q, ω)gπ (ca , µ, q, e, ω) u=
Nc ,µ,q,e,ω
c,q,e,ω

`=1aSubstituting (43) and (44) into the above inequality yields the participation constraint, (22),for the group contract π g :
ūi ≤

X



g

π (ca , µ, q, e, ω) u

ca ,µ,q,e,ω

ca (q, ω)NThis inequality proves that the candidate group contract, as defined by (43) and (44), satisfies
the participation constraint for the group contract, (22).
Now consider the incentive constraints (13) for the relative performance contract π r for36each ei , ẽi :X

π r (c, q, ei , e−i , ω) u(cri , ei ) ≥c,q,e−i ,ωX

π r (c, q, ei , e−i , s)c,q,e−i ,ω

P r (q|ẽi , e−i , ω) ru(ci , ẽi ).
P r (q|ei , e−i , s)Multiplying this constraint by N1 and summing over i yields the following:Xr

π (c, q, e, ω)NXu(c (qi , ω) , ei )c,q,e−i ,ω

N

i=1

X
c,q,e−i≥NP r (q|ẽi , e−i , s) X u(c (qi , ω) , ẽi )π (c, q, e, ω).
P r (q|ei , e−i , s) i=1
N,ωr

Substituting (43) and (44) into the above inequality yields the incentive constraint, (19), forthe group contract π g : for each ei , ẽi ,Xg

π (ca , µ, q, e, ω)

ca ,q,ω

X
i

X

µi u

c

a

N

, ei ≥π g (cA , µ, q, e, ω)

ca ,q,ωc
P r (q|ẽ, k, s) X
a
µi u
, ẽi
P r (q|e, k, s) i
NThis inequality proves that the candidate group contract, as defined by (43) and (44), satisfies
the incentive constraint for the group contract, (19).
In summary, the candidate group contract, as defined by (43) and (44), is a feasiblegroup contract that generates a weakly larger surplus. Further, if incentive constraints arebinding under π r , for some vector q, consumption is not equal among agents. This implies
P
that ca (q, ω) < N
i=1 c (qi , ω). Under the assumption that for any pair effort/common shock(e, ω) all output levels have positive probability, such q happens under π r with positive
probability. Therefore, π g generates a strictly larger surplus, with the same utility for all
agents.
Proof of Proposition 2. One of the difficulties with this proof is that the incentive compatibility constraints, (19), are not well defined when the denominator in each of these expressions,
P r(q|e, k, s) = 0, for some value of (q, e, k, s). That case is applicable when idiosyncratic
shocks are absent and efforts are identical among agents. This case requires a restatementof the incentive constraints.
37

For a level of output q that can be reached only out of equilibrium, i.e., P r(q|ei , e−i , s) =0, there is no loss of generality establishing corresponding consumption at the minimum level,c, i.e., P r(c|q, e) = 1, where c = (c, c) is the minimum level of consumption in the grid.
The incentive constraints for the relative performance regime can now be reformulated asfollows:X

π r (c, q, ei , e−i , s)u(ci , ei ) ≥c,q,e−i ,sX

Φ(c, q, ẽi , e, s) ∀ei , ẽi(46)c,q,e−i ,swhere P r(A )P r(e)P r(q|ẽ , e , s)u(c, ẽ ), when P r(q|e , e , s) = 0,
i
i −i
s
i −i
Φ(c, q, ẽi , e, s) = π r (c, q, e , e , s) P r(q|ẽi ,e−i ,s) u(c , ẽ ), otherwise.
i −i
i i
P r(q|ei ,e−i ,s)The proof now shows that a contract that solves Program 4 below, which is a relative
performance problem without the incentive constraints (46) and ūi = ū for all i, is also a
feasible relative performance contract (solves Program 1). In particular, we show that, asolution to Program 4 satisfies the incentive constraints (46) when idiosyncratic shocks areabsent, when arbitrarily high punishment is allowed, and when ūi = ū for all i.
Program 4.
max
r
π̄

X

π̄ r (c, q, e, s) (q1 + q2 − c1 − c2 )(47)

c,q,e,ssubject to constraints (10), (11), (14), andXπ̄ r (c, q, e, s) u (ci , ei ) ≥ ū ∀i.

(48)

c,q,e,sLet π̄ r (c, q, ē, s) be a solution to Program 4 such that effort levels are identical acrossagents, i.e., ē = (ē1 , . . . , ēN ) and ē1 = . . . = ēN = ē. If the minimal level of effort isadopted in the solution, then the incentive constraints would be trivially satisfied. If any
other level of effort ē is adopted with positive probability, then the incentive constraints
would be satisfied only because effort affects the distribution of output. Otherwise, theprincipal could recommend a lower effort level and lower consumption by holding utility
constant and increasing the surplus. As a result, there must be some state ω̄ such that for38

any ê < ē, E(q|ē, k, ω̄) > E(q|ê, k, ω̄). Given the absence of idiosyncratic shocks, it must
be the case that f (q̄|e, k, ω̄) = 1 and f (q̂|ê, k, ω̄) = 1 for some q̄ > q̂. Thus, if u(ĉi , ēi ) canbe set at a sufficiently negative level, then the incentive compatibility constraints (46) will
be satisfied. Note that since incentive constraints are not present in Program 4, any groupcontract delivering the same utility pair without full insurance will generate strictly lower
surplus.

39