Joint liability among bank borrowers

Abstract

A common feature of financial intermediaries is that the welfare of one borrower is adversely affected by the poor performance of other borrowers. That is, there exists a degree of joint liability among the borrowers of a financial intermediary. This paper provides an explanation for this observation. It demonstrates that in Krasa and Villamil's [14] formalization of a financial intermediary as a delegated monitor, intermediation with joint liability between borrowers Pareto dominates intermediation without joint liability. Copyright Springer-Verlag Berlin/Heidelberg 2004

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DOI: 10.1007/s00199-003-0381-4
Economic Theory 23, 383–394 (2004)
Joint liability among bank borrowers?
Philip Bond
NorthwesternUniversity,KelloggSchoolofManagement,DepartmentofFinance,2001SheridanRoad,
Evanston, IL 60208-2001, USA (e-mail: p-bond@northwestern.edu)
Received: September 4, 2002; revised version: March 21, 2003
Summary. Acommonfeatureoffinancialintermediariesisthatthewelfareofone
borrowerisadverselyaffectedbythepoorperformanceofotherborrowers.Thatis,
there exists a degree of joint liability among the borrowers of a financial intermedi-
ary. This paper provides an explanation for this observation. It demonstrates that in
Krasa and Villamil’s [14] formalization of a financial intermediary as a delegated
monitor, intermediation with joint liability between borrowers Pareto dominates
intermediation without joint liability.
Keywords and Phrases: Financial intermediation, Banks, Conglomerates, Dele-
gated monitoring, Joint liability, Credit crunch.
JEL Classification Numbers: D8, E5, G2, G3.
1 Introduction
Acommonviewoffinancialintermediariesisthattheyserveasdelegatedmonitors.
That is, instead of all providers of capital having to monitor an investment project,
this task is delegated to a single intermediary. This view of intermediation has been
formalizedbyDiamond[3],Williamson[20],KrasaandVillamil[14],andHellwig
[8]. The main finding of these papers is that intermediation performs better than
directinvestmentwhenevertheintermediaryisabletoholdasufficientlydiversified
investment portfolio. However, these papers have had relatively little to say about
more detailed properties of financial intermediaries. The object of this short paper
is to demonstrate that a similar framework to that used in these previous papers
?IamparticularlyindebtedtoDouglasDiamondandRobertTownsendfortheiradviceonthispaper.
I thank an anonymous referee for helpful comments.

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384P. Bond
can also explain the existence of joint liability between the borrowers of a financial
intermediary.
Empirically, the borrowers of a financial intermediary are often (at least par-
tially) jointly liable. By this I mean that the welfare of each borrower is adversely
affected by the poor performance of other borrowers. In some cases this joint lia-
bility aspect of borrowing is made explicit, as in the case of the use of joint liability
lendinggroupsbymicrocreditorganizationssuchastheGrameenBank.1However,
therearemanyothercasesinwhichborrowersareaffectedbythepoorperformance
of other borrowers, even though this may not be explicitly described as joint lia-
bility. For instance, a voluminous literature (see especially Hubbard et al. [10])
has demonstrated that a bank borrower’s access to future credit depends on the
overall performance of the bank, and thus on the performance of the bank’s other
borrowers. Likewise, conglomerates resemble financial intermediaries in many di-
mensions, and the amount invested by a conglomerate division has been found to
depend on the conglomerate’s overall performance (see, e.g., Lamont [15]). Fi-
nally, one can also think of a firm’s workers as being the entrepreneurs and the
firm manager being a delegated monitor (i.e. intermediary). Poor performance by
co-workers clearly raises the probability of job displacement arising from firm clo-
sure, and a wage reduction of the order of 25% has been documented following
job-displacement – see, e.g., Jacobson et al. [11] or Kletzer [13]. In each of these
cases, the welfare of an intermediary “borrower” is adversely affected by the per-
formance of others – that is, joint liability exists in the sense defined above. There
is nothing inevitable about any of these arrangements – in principle at least, the
payoff of the intermediary’s investors could be reduced by an amount sufficient to
shield the intermediary’s borrowers (or divisions or workers) from risk.
Thispaperwillshowthatthejointliabilityofintermediaryborrowersarisesnat-
urally in models of a financial intermediary as a delegated monitor – in particular,
that of Krasa and Villamil [14] (henceforth KV). The main intuition is straightfor-
ward. Delegation of monitoring is valuable in this model because it is assumed that
multiple investors are required to fund each borrower.2Consider now the situation
faced by an intermediary whose income is too low to pay the face value of investor
claims. He has two main options. On the one hand, he can default on the investor
claims, with all the investors monitoring to check that default is really necessary
(this is the only option allowed by Diamond [3] and by KV). On the other hand,
he can go to the subset of borrowers who still have resources, and request a higher
payment — that is, impose some form of joint liability. This second option entails
theborrowersmonitoringthebanktomakesuretheseextrafundsarereallyneeded.
But by the very assumption that drives intermediation in the first place – namely
that there are more investors than entrepreneurs — this second option is cheaper in
1See Morduch [16] and Ghatak and Guinnane [5] for recent surveys of microcredit.
2Empirically, this assumption would appear to be reasonable, at least for the case of bank loans to
small businesses. Kennickell et al. [12] report that the 1995 median US household bank balance was
$2,100.Ontheotherhand,themedianloansizereportedinthe1993NationalSurveyofSmallBusiness
Finance (NSSBF) is $50,000.

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Joint liability among bank borrowers385
termsofaggregateexpendituresonmonitoring.3Sinceintroducingadegreeofjoint
liability among borrowers reduces total monitoring costs, it is possible to make all
parties better off: the payments to the investors can be reduced, since they monitor
less, while the expected payment made by the borrowers can be reduced (i.e. the
interest rate lowered), since in aggregate the intermediary and investors monitor
less.
Related literature
To the best of my knowledge this is the first paper to seek to explain why borrowers
of a financial intermediary are adversely affected by the poor performance of other
borrowers. Perhaps most closely related is Winton’s [21] argument that the coexis-
tence of several seniority classes among debt-holders can be explained as a means
ofminimizingexpectedmonitoringcosts.Relatedinspiritareacoupleofpapersby
Hellwig [6, 7] that consider banks as a mechanism for economy-wide risk-sharing
and ask why deposit contracts are non-contingent with respect to aggregate shocks
such as interest-rate changes. The current paper also views banks as mechanisms
forrisk-sharing,butasksinsteadwhyitisthatincertainstatesalltheriskisborneby
intermediaryborrowers,whileintermediarylendersmaybeleftunaffected.Finally,
there is also a recent literature on why troubled banks cannot easily raise further
funds to avoid reducing credit – see, e.g., Holmstr¨ om and Tirole [9], Stein [17],
Bolton and Freixas [1] and Webb [19]. This paper departs fundamentally from this
literature by not assuming that deposit claims are both non-contingent and senior
toallotherclaimsonthebank.Instead,thesefeatures,togetherwithintermediation
itself, emerge endogenously from the basic frictions of the model.
2 Results
We will examine the same economy as that considered by KV (and follow their
notational conventions as much as possible). Agents i = 1,...,I are risk neutral
entrepreneursandagentsj = 1,...,J = yI areriskneutralinvestors,wherey ≥ 2
is an integer. Each entrepreneur i possesses a technology that transforms y units
of an input into θiunits of output, where θiis a random variable described below.
Each investor possesses a single unit of the input good. Thus y investors are needed
to “fund” each entrepreneur.
3This argument will apply in any model in which the deadweight cost of default is an increasing
function of the number of agents defaulted on. Note that one model that does not have this property is
Diamond’s [3] formalization of an intermediary as a delegated monitor. There, the intermediary would
in fact be indifferent between the two options described in the text – the deadweight loss incurred is a
function only of the shortfall in funds.

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386P. Bond
Therandomvariablesθiareindependentandidentically4distributedonaprob-
ability space (Ω,A,P), with a distribution function F and a density function f
with respect to the Lebesgue measure. Let ω ∈ Ω denote the state.
The realization of each entrepreneur’s technology is assumed to be initially pri-
vate information. However, any investor j can learn the realization by monitoring
the entrepreneur, at a non-pecuniary effort cost c. As in KV, only investors who
monitor acquire this information. To allow for intermediation, KV also allow in-
vestorstomonitoramonitoringagent—i.e.aninvestorwhoactsasanintermediary
and monitors the entrepreneurs. The cost of this second level of monitoring is c∗
KVconsidertwo-sidedcontractsofthefollowingform.Oneoftheinvestors(m
say) acts as an intermediary and has a contract (R(·),S) with each entrepreneur,
meaning that an entrepreneur with income realization w pays the intermediary
R(w) and is monitored if and only if w ∈ S. The contract (R(·),S) is required
to satisfy feasibility (that is, R(w) ≤ w) and incentive compatibility (that is, R(·)
is constant5over Sc, with R(Sc) ≥ R(w) for any w ∈ S). Let Gi(R(·);ω)
denote the intermediary’s income in state ω from entrepreneur i. Likewise, define
GI(R(·);ω) ≡ (1/I)?I
Below we will be interested in the set of entrepreneurs who are not monitored
in a state ω. We will refer to these entrepreneurs as being successful, and denote
the set by
A(R(·);ω) ≡ {i ∈ I : R(θi(ω)) = R(Sc)} .
Also,letC (R(·);ω)denotethetotalmonitoringcostsincurredbytheintermediary
in state ω,
C (R(·);ω) ≡ (I − |A(R(·);ω)|)c .
Theintermediarymalsohasacontract(R∗(·),S∗)witheachoftheremainingJ−1
investors, meaning that when the intermediary has an average income w∗from the
entrepreneurcontracts(i.e.w∗= GI(R(·);ω)),hetransfers(I/(J − 1))R∗(w∗)
to each investor, and is monitored by each investor if w∗∈ S∗. Feasibility and
incentive compatibility are analogous to above.
Each investor requires an expected return of r, in return for providing the initial
funding. Thus the participation constraints for the investors and intermediary are
respectively
?
I
(w∗− R∗(w∗))dFI(R(·),w∗)−I
I.
i=1Gi(R(·);ω). Let FI(·) denote the density function
of GI(·).
IR∗(w∗)dFI(R(·),w∗)−(J−1)
?
In adopting this formulation, KV implicitly assume that only other investors can
monitor the intermediary. We can relax this assumption by expanding the space
?
S∗c∗
IdFI(R(·),w∗) ≥ (J − 1)r (1)
?
S
cdF (R(·),w) ≥ r .
(2)
4In fact, it is not necessary to assume either that the random variables {θi: i = 1,...,I} are
independent or identically distributed. In particular, while independence helps in establishing that inter-
mediation dominates direct investment, it does not play any role in the result of this paper that adding
a degree of joint liability improves intermediation.
5Throughout, Scdenotes the complement of the set S.

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Joint liability among bank borrowers 387
of contractual possibilities to include intermediation with joint liability among
entrepreneurs. Joint liability will allow the intermediary to raise further funds from
the entrepreneurs in a contingent way.
The kind of joint liability arrangements that are feasible depend on exactly
what it is that monitoring the intermediary reveals. At one extreme, any agent
who monitors the intermediary may learn the full vector of transfers that he has
received from other agents. At the other extreme, monitoring may reveal only the
intermediary’s aggregate income and aggregate monitoring expenditures:6that is,
a monitoring agent is able to detect any income the intermediary attempts to hide,
withoutlearningtheexactsourcesofthisincome.Below,foreachoftheseextremes
we exhibit joint liability arrangements that are Pareto superior to any member of
the class of two-sided contracts considered by KV.7
Note that the aim of this paper is to demonstrate that intermediation with joint
liability is Pareto superior to intermediation without joint liability. The economy
considered is exactly that studied previously by KV, and the analysis is restricted to
exhibiting Pareto dominating arrangements. While solving for an optimal arrange-
ment in this environment does not appear tractable in general, Bond [2] is able to
characterize the optimal arrangement in the simplest variant of this economy – just
two entrepreneurs, each having a project with only two possible income realiza-
tions, and a large number of investors. Moreover, the analysis allows for investors
to belong to different seniority classes, a possibility that the current paper follows
KV in ignoring. It is found that even after allowing for different seniority classes,
forawiderangeofparametervaluesintermediationwithout jointliabilityisnot the
optimal arrangement. Instead, optimal arrangements feature multiple agents who
monitor multiple times and play a key role in absorbing aggregate income fluctu-
ations. Intermediation with joint liability is an example of such an arrangement.
Thus there is reason to believe that the results of the current paper are robust to
considering arbitrary contractual arrangements and seniority classes.
2.1 Monitoring reveals all transfers made to the intermediary
Given a two-sided contract ((R(·),S),(R∗(·),S∗)) of KV, we consider adding
joint liability as follows. If the vector of transfers received by the intermediary,
(Gi(R(·);ω))i∈I, falls in the set X∗⊂ ?I, then the intermediary invokes the
following joint liability arrangement:
1. Theintermediaryimposesanadditional“jointliability”contractonthesuccess-
fulentrepreneursA(R(·);ω).Denotetheadditionalcontractby?RX,X?.For
6Note that if monitoring reveals the transfer made by each individual entrepreneur the monitoring
activity of the intermediary can be inferred. Also, note that if monitoring revealed nothing about the
intermediary’s monitoring activity, then joint liability arrangements would be hard to sustain since they
entail increased monitoring activity by the intermediary in order to reduce monitoring by the investors.
7Ifgivenachoiceofwhichmonitoringtechnologytoemploy,undersomecircumstancesagentsmight
actually choose the second and less informative option: when monitoring the intermediary reveals the
transfer made by every entrepreneur, an entrepreneur’s competitors may acquire valuable information.
feasibility we require R(w) + RX(w) ≤ w, while for incentive compatibility