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Bank and Nonbank Financial Intermediation 2493
The current paper is clearly closely related to previous work on conglomer-
ates, trade credit, and banking. In Section V, I discuss representative contri-
butions to the study of each of these three institutions. Formally, the model
developed is most closely related to the strand of the financial intermediation
literature that has accounted for intermediation as a form of delegated mon-
itoring. Diamond (1984), Williamson (1986), Krasa and Villamil (1992a), and
Hellwig (2000) all fall within this class. As discussed in detail in Section III,
the current paper differs in that it establishes the viability of intermediation
without assuming that the probability of intermediary default is arbitrarily low.
Aside from being of some interest in its own right, this property of the model
is important because it allows us to address questions of the allocation of risk
and the identity of the intermediary.
8
The model employed is essentially a multiagent generalization of Townsend’s
(1979) costly state verification model. That is, an agent’s output is private in-
formation unless a verification cost is incurred to disclose it to another agent.
Krasa and Villamil (1992a) use a multiagent model of this sort to demonstrate
that intermediation will emerge whenever the probability of intermediary de-
fault is close enough to zero, or equivalently whenever the degree of diversifi-
cation possible is sufficiently high. However, because intermediary default is
essentially nonexistent in this case, questions (I) to (IV) are hard to address.
As discussed in Section III, the need to let the probability of default approach
zero stems from assuming that all intermediary investors hold the same type
of claim. In contrast, this paper uses Winton’s (1995a) analysis of optimal se-
niority in a costly state verification setting to demonstrate that changes in an
intermediary’s income process that lead to second-order stochastic dominance
will reduce the costs of monitoring the intermediary. This result is then enough
to show that even with only two projects in the economy (i.e., very limited di-
versification and no way to eliminate intermediary default risk), the benefits
of intermediation outweigh the costs. The default-prone intermediary can then
be analyzed to study the consequences of different institutional responses to
questions (I) to (IV).
The paper is organized as follows. Section I specifies the economic environ-
ment to be analyzed. Section II replicates Winton’s (1995a) results on seniority
8
Cerasi and Daltung (2000) and Krasa and Villamil (1992b) present models of intermediaries
as delegated monitors in which perfect diversification is not possible. Both papers assume that
the per-depositor costs of monitoring a bank are increasing in bank size, and so there is a size at
which the increase in diversification provided by a larger bank is outweighed by the increase in
monitoring costs. That is, there is an optimal bank size, and at that size there is a positive risk
of failure. However, in order to establish the viability of intermediation, both papers must assume
that the optimal bank size is large enough and that the corresponding probability of bank failure
is close enough to zero. Moreover, both papers concentrate on the size of the bank; in contrast, the
current paper explores the determinants of other properties of the financial intermediary. Finally,
also related is the work of Winton (1995b). He establishes that with free entry into banking, there
exist equilibria in which multiple banks exist, and each is of finite size with a positive probability of
default. Again, the focus of the current paper is on the distinct issues of which agents intermediate,
and whether or not entrepreneurs absorb intermediary risk.
2494 TheJournal of Finance
in the context of the current model, and derives the result that second-order
stochastic dominance is associated with a lowering of monitoring costs. Sec-
tion III establishes the existence of financial intermediaries when only partial
diversification is possible. Section IV establishes results concerning the opti-
mal form of intermediation, which Section V then applies to derive predictions
concerning conglomerates, banks, and trade credit arrangements. Section VI
concludes.
I. The Model
A. The Agents
To keep the model as transparent as possible, we consider an economy with
just two projects, where these projects represent the only sources of uncertainty.
The projects 1 and 2 are run by entrepreneurs 1 and 2, respectively. We will
typically use h to represent a generic project/entrepreneur. Each of projects
h = 1, 2 has a probability q
h
≥ 1/2of“succeeding” and returning an amount
H > 0, and a probability 1 − q
h
of “failing” and returning L ∈ [0, H).
9
We write
ω
h
for the random variable corresponding to the output of project h, and ¯ω
h
for its mean. The outcomes of the two projects are potentially correlated. The
entrepreneurs have no income outside of the project returns.
In addition to the two entrepreneurs, there are 2n investors, with typical
member i.Atotal of n investors are needed to provide financing for each of the
two entrepreneurs’ projects. As compensation for financing the entrepreneurs,
each investor requires an expected payoff of ρ
n
≡ ρ/n—that is, ρ
n
is the product
of the funds provided by each investor, 1/n, and the market interest rate, ρ.
Investors have no income other than what the entrepreneurs transfer to them
(ω
i
= 0 for all investors i).
We write I for the set of the 2n investors, and K = I ∪{1, 2} for the set of all
agents in the economy, with j, k generic agents. We make the following assump-
tions throughout:
ASSUMPTION 1 (Both projects profitable): Both projects are profitable in the ab-
sence of any financing frictions, that is, for h = 1, 2, ¯ω
h
>ρ.
ASSUMPTION 2 (Both projects essential): Some portion of the output from the
high payoff of both entrepreneurs is needed in order to provide a payoff of ρ
n
to
each of the 2n investors, that is, 2ρ>max{ ¯ω
1
+ L,¯ω
2
+ L}.
The realization of each entrepreneur’s payoff ω
h
is privately observed by that
entrepreneur. However, each entrepreneur h can disclose the realization of ω
h
to any second individual k ∈ K\{h} at an effort cost c. Additionally, any agent k
can disclose to any other agent j information he has previously acquired from
the entrepreneurs 1 and 2. The cost of these “disclosures of disclosures” is also
9
The assumption that q
h
≥ 1/2isnot essential, but simplifies the analysis.
Bank and Nonbank Financial Intermediation 2495
c.
10
Thus, the basic information structure is that of a generalized costly state
verification model. In addition to disclosing endowment realizations, agents
can also disclose information acquired from prior disclosures.
11
All agents are risk neutral over nonnegative amounts of consumption x, and
over nonnegative effort exertion e. That is, preferences are given by u(x, e) =
x − e. Note that it is this limited liability constraint on consumption that makes
the risk allocation problem nontrivial.
B. Timing and Contracts
There are three dates, labeled s = 0, 1, 2. The timing is as follows:
s = 0: Agents write contracts t (see below). The entrepreneur payoffs ω
1
, ω
2
are realized (after the contracts have been written).
s = 1: Each entrepreneur h = 1, 2 can disclose his project realization to any
subset of other agents. Following the disclosure of this information,
transfers are made as contractually specified.
s = 2: Each agent j ∈ K can disclose to any subset of other agents the dis-
closures he received at date 1. Following these disclosures, further
transfers are made, again as contractually specified.
All contracts are bilateral, and specify payments as follows. At each of dates
1 and 2, the transfer made between agent j and agent k can depend only on
information that both possess—that is, either on information that agent j has
disclosed to agent k,orvice versa. Thus the portion of the contract relating to
the date 1 payment from agent jtoagent k is just
t
1
jk

d
1
jk
, d
1
kj

, (1)
where d
1
jk
is the disclosure made by agent j to agent k at date 1. Similarly, at
date 2 the transfer to be made from agent j to agent k is specified by
t
2
jk

d
1
jk
, d
1
kj
, d
2
jk
, d
2
kj

. (2)
We obviously impose that at both dates s = 1, 2,
t
s
jk
=−t
s
kj
. (3)
10
It would obviously be straightforward to generalize the analysis to the case in which the cost
of disclosing disclosures differed from c. The implications of the analysis would be qualitatively
unaffected.
11
As in Townsend (1979), the verification cost is borne by the agent disclosing the information.
Note that with two rounds of information sharing, it is easier to think of the verification decision as
being made by the verified agent rather than by the verifying agent. Doing so avoids the complexity
of modeling the degree to which a date 2 verification policy can depend on information possessed
by the verifying agent. It is for this reason that we will refer to “disclosure” in place of “verification”
throughout.
2496 TheJournal of Finance
If agent j does not disclose to agent k at date s,wewrite d
s
jk
=∅.Atdate 1,
only the two entrepreneurs 1, 2 have anything to disclose—so d
1
jk
=∅if j ∈ I,
while d
1
hk
∈{∅, ω
h
} for h = 1, 2. At date 2, disclosures are made as to the vector of
disclosures received at date 1. Thus d
2
jk
∈{∅,(d
1
1j
, d
1
2j
)}.
12
Notationally, to capture
the possibility of an entrepreneur disclosing his own endowment at date 2, we
write d
1
hh
= ω
h
.
The set of bilateral contracts t ≡{t
s
jk
: s = 1, 2 and j, k ∈ K} defines a game in
which actions are disclosures. Each agent is restricted to choose from among
strategies that give him nonnegative consumption,
13
independent of other
agents’ strategies.
14
Any pure-strategy equilibrium of this game induces a map-
ping from the state space  to the transfers and disclosures:
δ
1
jk
:  →ℜ∪
{
∅
}
, (4)
δ
2
jk
:  →
(
ℜ∪
{
∅
}
)
2
∪
{
∅
}
, (5)
τ
s
jk
:  →ℜ. (6)
We will refer to any particular set of mappings (δ, τ) ≡{δ
s
jk
, τ
s
jk
: j, k ∈ K, s = 1, 2}
as an arrangement.Wesay that an arrangement (δ, τ)isincentive compatible
if the mappings {δ
s
jk
, τ
s
jk
: j, k ∈ K, s = 1, 2} arise as a pure-strategy equilibrium
given contracts t.
Let γ
j
(ω; δ, τ ) denote the total disclosure costs of agent j in state ω under an
arrangement (δ, τ), that is,
γ
j
(ω; δ, τ ) ≡ c

s=1,2

k∈K \
{
j
}
1
δ
s
jk
(
ω
)
=∅
(
ω
)
, (7)
where 1
δ
s
jk
=∅
(ω)isthe indicator function taking the value 1 whenever δ
s
jk
(ω) =∅
and 0 otherwise. Let y
s
j
(ω; δ, τ ) denote the resources of agent j at the end of
period s in state ω, that is,
y
s
j
(ω; δ, τ ) ≡ ω
j
+
s

˜s=1

k∈K \
{
j
}
τ
˜s
kj
(
ω
)
. (8)
So the utility u
j
(ω; δ, τ )ofagent j in state ω under arrangement (δ, τ )issimply
u
j
(ω; δ, τ ) ≡ y
2
j
(ω; δ, τ ) − γ
j
(ω; δ, τ ). (9)
12
Allowing an agent to disclose only one of the disclosures, for example, d
1
1j
and not d
1
2j
, would
have no qualitative effect on the results.
13
This restriction is the two-period generalization of the assumption in the costly state veri-
fication literature that an agent cannot report an income of ˜ω that leads to no verification, but
that triggers a required transfer in excess of his true income ω.That is, there is an implicit as-
sumption that there exists some central authority with enforcement capabilities that can punish
an agent enough to deter this kind of behavior. Note that this central authority is required to act
only out-of-equilibrium.
14
We restrict attention to contracts t that possess such strategies.
Bank and Nonbank Financial Intermediation 2497
Finally, let U
j
(δ, τ)bethe expected utility of agent j under arrangement (δ, τ ),
U
j
(δ, τ) ≡ E[u
j
(ω; δ, τ )]. (10)
In the analysis that follows, we will explore the properties of constrained effi-
cient incentive compatible arrangements. We are interested in arrangements
that maximize the entrepreneurs’ payoffs while delivering the market rate of
return to the investors, that is,
U
i
(δ, τ) ≥ ρ
n
for all i ∈ I. (I-IR)
The entrepreneur participation constraints are
U
h
(δ, τ) ≥ 0 for h = 1, 2. (E-IR)
Consider an arrangement (δ, τ) that satisfies both the investor (I-IR) and en-
trepreneur participation constraints (E-IR). We say that an arrangement (
ˆ
δ,ˆτ )
dominates (δ, τ)ifitgives (weakly) higher utility to both entrepreneurs and
satisfies the investor participation constraints (I-IR).
15
Moreover, we will say
that (
ˆ
δ,ˆτ ) strictly dominates (δ, τ)ifitdominates (δ, τ) and either strictly in-
creases the utility of one of the entrepreneurs, or weakly increases the utility
of all investors while strictly increasing the utility of at least one of them. An
arrangement is undominated whenever it is not strictly dominated.
C. Informational Insiders
The class of possible arrangements is very large. As we will see, a useful
property of the arrangements to keep track of is the number of agents who pool
information from multiple sources. Because of their privileged information, we
refer to such agents as (informational) insiders.Formally, given an arrangement
(δ, τ), we will say that an agent is an insider either if he receives disclosures from
at least two other agents, or if he is an entrepreneur and receives a disclosure
from one other agent. That is, agent j is an insider either if j ∈ I and ∃ω, ω
′
∈ ,
s, s
′
∈{1, 2} and k = l ∈ K\{j} such that δ
s
kj
(ω) =∅and δ
s
′
lj
(ω
′
) =∅;orifj ∈{1, 2}
and ∃ω ∈ , s ∈{1, 2} and k ∈ K\{ j} such that δ
s
kj
=∅. Any agent who is not an
insider is an outsider.
II. Disclosure to Multiple Investors
As in Diamond (1984), intermediation of financial arrangements in the cur-
rent setting lets an entrepreneur avoid disclosing to multiple agents (i.e., avoid
duplication in monitoring), but introduces the delegation problem of keeping
the intermediary honest. Diversification is the key to establishing that the
former effect dominates, and overall disclosure costs are lower under inter-
mediation. Previous research has focused on the advantages of almost perfect
15
Note that this definition of domination is implied by, but does not imply, Pareto domination.
2498 TheJournal of Finance
diversification (see the introduction): In this case the intermediary’s income-
per-investor is close to nonstochastic, so the intermediary is basically left with
no information to misrepresent. In contrast, intermediation in the current pa-
per depends on the benefits of a much less extreme form of diversification,
namely the shift from financing one project to financing both. As we will see,
the consequent reduction in the variance of the intermediary’s income allows for
the transformation of some of the more junior investor claims on the interme-
diary into more senior claims. Thus even a marginal increase in diversification
leads to a reduction in delegation costs, which is enough to establish the viabil-
ity of poorly diversified intermediaries.
Because the seniority structure of investor claims on the intermediary is
central to this argument, we start by analyzing the seniority structure that
arises when a single agent k discloses to some set J of outsider investors. This is
the extension of the costly state verification problem studied by Winton (1995a).
As is well known, with a single investor the optimal contract is debt-like, in the
sense of involving costly verification (here, disclosure) only over some lower
interval of the entrepreneur’s income realization (see Townsend (1979) and
Gale and Hellwig (1985)). Winton established that this property continues to
obtain with multiple investors. Moreover, he showed that the optimal contract
will feature multiple levels of seniority (in the sense that verification regions
of the investors can be ordered), and that when all agents in question are risk
neutral with limited liability, there will be as many seniority levels as there
are investors. In this section I first map some of Winton’s key results into the
framework of the current paper, and then apply these results to quantify the
size of each seniority class.
For the purposes of this paper, we need to be able to characterize the total
expected disclosure costs of one individual k disclosing to a subset of investors
J in the following two cases: (a) an entrepreneur disclosing directly to investors
J and (b) an “intermediary,” who could be either an investor or one of the en-
trepreneurs, and who receives transfers from the entrepreneurs and then in
turn discloses to investors J.For this characterization we need to isolate the
component of agent k’s income process that he either consumes (i.e., y
2
k
), or
transfers to the investors J (i.e.,

s=1,2

i∈J
τ
s
ki
). We denote this quantity by
T
k,J
(ω; δ, τ ),
T
k, J
(ω; δ, τ ) ≡ y
2
k
(ω; δ, τ ) +

s=1,2

i∈J
τ
s
ki
(
ω
)
. (11)
All income in the economy originates with one of the two entrepreneurs, h =
1, 2. As such, the disclosing agent k will in general have the most resources
available when both entrepreneurs succeed (state HH) and the least available
when both fail (state LL), with the one-success-one-failure states LH, HL falling
somewhere in between. All arrangements that we need to analyze in this paper
do in fact satisfy this resource ordering across states. Moreover, since we can
always change the naming of the two entrepreneurs, we can without loss assume
Bank and Nonbank Financial Intermediation 2499
that the resource mapping T
k,J
takes a higher value in state HL than LH.
Formally, for the remainder of this section we assume:
T
k, J
(
LL; δ, τ
)
≤ T
k, J
(
LH; δ, τ
)
≤ T
k, J
(
HL; δ, τ
)
≤ T
k, J
(
HH; δ, τ
)
. (12)
Whenever inequality (12) holds, it will be useful to refer to state LL as being
lower than state LH, which in turn we will refer to as lower than state HL,
which in turn is lower than state HH.
As is standard, we will say that the subarrangement between agent k and
the investors J is debt-like if agent k only discloses to each investor when his
available income (given here by the mapping T
k,J
) falls below some critical level,
and moreover does not disclose in any state in which the investor receives his
maximal transfer.
16
Formally, we have the following definition.
DEFINITION 1 (Debt-like): The subarrangement of (δ, τ) between agent k and in-
vestors J is said to be debt-like if for each i ∈ J the subset of states in which agent
k discloses to investor i is one of ∅, {LL}, {LL, LH}, {LL, LH, HL}, and moreover
agent k does not disclose to investor i in any state ω ∈ arg max
˜ω∈
(τ
1
ki
(˜ω) + τ
2
ki
(˜ω)).
When a subarrangement between agent k and investors J is debt-like, it is
natural to speak of an investor i ∈ J as being senior to a second investor j ∈ J if
investor i receives his maximal payment in strictly more states than investor j,
or equivalently, if investor i is disclosed to in strictly fewer states than investor
j. Given the resource ordering (12), the four possible seniority classes for the
investor J are as as follows. First, we have the most senior group N
∅
k,J
(δ, τ),
who agent k never discloses to. Second, we have the next most senior group
N
LL
k,J
(δ, τ), who agent k discloses to only in the fail–fail state LL. The next in
terms of seniority is the group N
LL,LH
k,J
(δ, τ), who agent k discloses to whenever
entrepreneur 1 fails (i.e., states LL and LH). Finally, the most junior group is
N
¬HH
k,J
(δ, τ), who agent k discloses to in all states other than the success–success
state HH.
17
What can we say about the size of these seniority classes? Agent k must be
transferring a constant amount to investors in the most senior class N
∅
k,J
, since
he never discloses to these investors. Moreover, the constant payments must be
at least ρ
n
, the amount investors demand in expectation. The expected resources
agent k possesses to make these constant payments is simply T
k,J
(LL). So there
can be at most [T
k,J
(LL)/ρ
n
] investors to whom agent k never discloses, where
for the remainder of the paper [x] will be used to denote the largest integer
weakly less than x.
18
16
It is common to speak of the constant maximal payment received in nondisclosure states as
the “face value” of debt.
17
Note that when the subarrangement between agent k and investors J is debt-like, there is
never any disclosure in states in which the resource mapping T
k,J
obtains its maximal value. So
agent k will never disclose to any member of J in state HH.
18
Observe that for any x, y, λ ∈ℜ
+
, the following hold: [x] ∈ (x − 1, x], [x] + [y] ≤ [x + y], [x − y] ≤
[x] − [y] ≤ [x − y + 1], and λ[x] ≤ [λx].
2500 TheJournal of Finance
For investors in the next seniority class N
LL
k,J
, the transfer from agent k must
be constant over the states LH, HL, and HH.Sothe aggregate transfer received
by members of the two most seniority classes N
∅
k,J
and N
LL
k,J
can be no more than
Pr
(
LL
)
T
k, J
(
LL
)
+ Pr
(
LH, HL, HH
)
T
k, J
(
LH
)
. (13)
This expression corresponds to the expected resources agent k has available
when he is restricted to access T
k,J
(LH)orless in all states other than the state
in which he discloses, LL.
Continuing in this manner implies that the size of the four seniority classes,
N
∅
k,J
, N
LL
k,J
(δ, τ), N
LL,LH
k,J
, and N
¬HH
k,J
, must satisfy the following three inequali-
ties:
19


N
∅
k, J


≤ min

|J|,

T
k, J
(LL)
ρ
n

(14)


N
∅
k, J
∪ N
LL
k, J


≤ min

|J|,

Pr(LL)T
k, J
(LL) + Pr(LH, HL, HH)T
k, J
(LH)
ρ
n

(15)


N
∅
k, J
∪ N
LL
k, J
∪ N
LL, HL
k, J


≤ min

|J|,

Pr(LL)T
k, J
(LL) + Pr(LH)T
k, J
(LH) + Pr(HL, HH)T
k, J
(HL)
ρ
n

.
(16)
Note for use below that the right-hand sides of the inequalities (14) through
(16) are of the form
min

|J|,

1
ρ
n
E
ω
[min{T
k, J
(ω), T
k, J
(ζ )}]

(17)
for ζ = LL, LH, HL respectively.
To give a corresponding lower bound for the size of the seniority classes we
need to know more about the relationship between the agent k and the investors
J.Tothis end, we define the following three additional properties that the
subarrangement between these agents may possess. The first two are straight-
forward.
DEFINITION 2 (Absolute priority): The subarrangement of (δ, τ ) between agent k
and investors J is said to feature absolute priority if it is debt-like, and whenever
agent k discloses to agents in one seniority class in some state ω then any agent
i ∈ J who belongs to a more junior seniority class receives a zero transfer in that
state, that is, τ
1
ki
(ω) + τ
2
ki
(ω) = 0.
19
Of course, |N
∅
k,J
∪ N
LL
k,J
∪ N
LL,HL
k,J
∪ N
¬HH
k,J
|=|J|.
Bank and Nonbank Financial Intermediation 2501
Absolute priority implies that an investor who is junior to another investor
receives no consumption (at least not from agent k) whenever the more senior
investor is disclosed to. In a similar vein, agent k is effectively junior to all the
investors J if he himself does not receive any consumption in states in which
he discloses:
DEFINITION 3 (Agent k junior): The subarrangement of (δ, τ) between agent k
and investors J is said to make agent k junior (to the investors J) if agent k has
zero consumption in any state ω ∈  in which he discloses to at least one of the
investors in J.
Our third property corresponds to Winton’s (1995a) Corollary 3, which states
that in a continuous state-space setting there are as many seniority classes as
investors. We term this property maximal use of seniority. Since in our discrete
state space there can be at most four seniority classes, this property will clearly
not hold in the same form here. Instead, we will say that maximal use of senior-
ity holds if in any state, agent k concentrates all his transfers to disclosees in J
to just one of these investors. Moreover, if this “preferred” investor is disclosed
to in several other states, he should be the preferred investor in these states
also. By maximizing the transfers to this preferred investor in disclosure states,
agent k can lower the transfer the preferred investor receives in nondisclosure
states, in turn potentially leading to an increase in the seniority of one of the
other investors. Finally, the participation constraints of all investors in j should
hold at equality—again, this frees up the resources to increase the seniority of
all investors as much as possible. Formally,
D
EFINITION 4 (Maximal use of seniority): The subarrangement of (δ, τ) between
agent k and investors J is said to make maximal use of seniority if the following
conditions hold:
(1) In any state ω, there is at most one investor in J to whom agent k discloses
and makes a strictly positive transfer.
(2) Suppose agent k discloses to an investor i ∈ Jinboth states ω and ω
′
,
where ω is lower than ω
′
. Then if the transfer from agent k to investor i is
strictly positive in state ω, it must be strictly positive in state ω
′
also. That
is, whenever state ω is lower than state ω
′
,
δ
2
ki
(ω
′
), δ
2
ki
(ω) =∅ and τ
1
ki
(ω) + τ
2
ki
(ω) > 0 ⇒ τ
1
ki
(ω
′
) + τ
2
ki
(ω
′
) > 0. (18)
(3) Each investor i ∈ J receives exactly ρ
n
in expectation.
Our first result is then essentially a generalization of Winton’s (1995a) anal-
ysis to a discrete state-space setting (although only for the case in which agents
are risk neutral with limited liability), and establishes that the three properties
just defined, plus debt-likeness, are optimal.
2502 TheJournal of Finance
PROPOSITION 1 (Basic properties): Let us suppose an incentive compatible ar-
rangement (δ, τ ) that satisfies the investor participation constraints (I-IR) and
involves an agent k disclosing to some set J of outsider investors, who themselves
never disclose. Then there exists an incentive compatible arrangement (
ˆ
δ,ˆτ ) that
dominates (δ, τ ) and in which the subarrangement between agent k and investors
Jisdebt-like, features absolutes priority, has agent k junior, and makes maximal
use of seniority. Moreover, no agent discloses to an agent under (
ˆ
δ,ˆτ ) to whom he
did not disclose under (δ, τ).
Proof: The proof is omitted, but is available upon request from the author. The
first part of the proof parallels that given in Winton (1995a); because attention
is restricted to the case of risk neutrality with limited liability, the final step
of establishing that the subarrangement is debt-like can be established more
directly. Q.E.D
In light of Proposition 1, we make the following additional definition.
D
EFINITION 5 (Optimal seniority): An incentive compatible arrangement (δ, τ )
is said to feature optimal seniority between an agent k and a set of outsider
investors J if the subarrangement between agent k and investors J is debt-
like, features absolutes priority, has agent k junior, and makes maximal use of
seniority.
This paper’s main results stem from considering how the expected disclosure
costs borne by some agent are affected by a change in the income process of
that agent. The remainder of this section is devoted to showing conditions un-
der which second-order stochastic dominance implies a reduction in expected
disclosure costs. The first step is to apply Proposition 1 to complete our charac-
terization of the size of the four seniority classes.
L
EMMA 1 (Number in each seniority class): Let us suppose an incentive com-
patible arrangement (δ, τ ) features optimal seniority between an agent k and a
set of outsider investors J, and that inequality (12) holds. Then each of the three
inequalities (14) to (16) holds at equality.
Proof: See the Appendix.
The characterization of the size of the seniority classes that is provided by
Lemma 1 is enough for us to establish the key result of this section, that is,
acharacterization of how disclosure costs change if we change the resource
mapping T
k,J
:  →ℜthat determines the combined consumption of agent k
and the total transfer to be made to outsider investors J.
Before proceeding to the formal result, consider the following simple numer-
ical example in which agent k is entrepreneur 1 and is disclosing to three of the
investors, J ={i
1
, i
2
, i
3
},say. Let the project success payoff be H = 120 and the
failure payoff be L = 0, with the probability of success equal to 2/3 and the two
projects being stochastically independent. Since agent k is entrepreneur 1, he