Joint liability Lending and Moneylender
Competition in Developing Credit Markets
Thomas Mosk
July 29, 2009
Abstract
This paper studies MFI moneylender competition in an adverse selection and moral hazard setting. It shows that a moneylender is not driven out of the market by a more efficient Microfinance Institution (MFI) with a joint liability lending technology when the cost of funds of the moneylen-der is not too high. In a market characterized by adverse selection, the moneylender captures safe borrowers because of their information advan-tage over the MFI. When borrowers experience a liquidity shock at an intermediate date, MFI moneylender competition could result in a wel-fare improvement. In this situation the MFI functions as an insurance mechanism against exogenous shocks by spreading the risk over the bor-rowers pool, while the moneylender screens which project is worthwhile to refinance and provides short term emergency finance. When the possi-bility of moral hazard exists, borrowers could get a cheaper joint liapossi-bility loan contract which allows them to lower their effort, which reduces their utility.
1
Introduction
One of the puzzles of rural credit markets is that ”formal and informal sectors
coexist, despite the fact that formal interest rates are substantially below those
charged in the informal sector” (Hoff and Stiglitz, 1990). People continue to
borrow from moneylenders, despite of their extremely high interest rates.
Im-perfect information is according to Hoff and Stiglitz the key to this puzzle. Local
moneylenders make use of local information which might explain why
compe-tition is so limited. An important trend in developing credit markets is the
emergence of the microfinance sector. With new lending technologies, such as
joint liability lending, Microfinance Institutions (MFIs) are able to reach poor
borrowers which were previously rationed from formal credit sources. Joint Li-ability technologies enable MFIs to lend small amounts to borrowers with a
weak balance sheet. These borrowers could get these loans when they organise
themselves in groups and carry joint liability for the repayment of the loan.1 A
series of papers show that joint liability lending could resolve information
prob-lems: joint liability affects group formation, influences the effort level of the
borrowers, helps to avoid costly audits and encourages borrowers to repay their
loan without enforcement (Ghatak, 2000; Stiglitz, 1990; Laffont and Rey, 2003;
Besley and Coate, 1995). Although joint liability lending reduces information
asymmetries and MFIs have a lower cost of funds, moneylenders remain to be
an important credit source in developing countries. For example, in Rwanda, 40 percent of the loans are provided by moneylenders, while only 22 percent
of the people surveyed had loans from the formal sector (Habyalimana, 2007).
The puzzle of Hoff and Stiglitz could therefore be rephrased in a more specific
one: What justifies the coexistence of moneylenders when they face MFI
com-petition? Or, how do moneylenders compete in the market for small business
loans when they face an MFI with a social mission offering joint liability loans
1A general joint liability contract specifies a.) an amount of individual liability which has
to small entrepreneurs?
Competition between formal and informal lenders in developing credit
mar-ket has been studied theoretically in models where informal lenders are direct competitors with the formal sector (Bose, 1998; Jain, 1999; Varghese, 2005). In
all these models, the informal lender holds a monitoring or screening advantage
over formal lenders. However, the existing literature suffers from one major
drawback: all models assume that the formal sector could not observe the
bor-rower characteristics and actions. With this assumption the authors neglect the
development of new lending technologies in developing credit markets. In the
standard models, the information advantage of the informal lender explains why
moneylenders could set high interest rates. However, with joint liability lending
technologies, MFIs could reach borrowers with a lack of collateral, which are
normally unable to obtain loans in the formal credit market. The literature on joint liability lending has a similar deficiency. All models which explain the
suc-cess of the joint liability contract do not take into account that an MFI could
face an informed moneylender as competitor. This is strange, because
mon-eylenders are omnipresent in developing credit markets and they often serve the
same pool of borrowers as the MFI.
This paper aims to study MFI moneylender competition. We are interested
how competition affects: 1. the portfolio composition of the MFI and the
mon-eylender 2. the term structure of the loans and 3. the choice of effort of the
borrowers. With regard to the joint liability contract we are interested to which
extend the contract could solve the problems of adverse selection and moral hazard when the MFI faces competition from a fully informed but inefficient
moneylender. To answers these questions we add a fully informed moneylender
to the standard adverse selection model of Ghatak (2000) and the moral hazard
model of Ghatak and Guinnane (1999). We assume that the MFI has lower cost
of funds than the moneylender. This is because MFIs have better access to
cap-ital markets. In both models, the moneylender has complete information about
the borrowers characteristics. Moneylenders have this information advantage
of the same kinship. Our paper contributes to the existing microfinance
litera-ture on several fronts. Firstly, it shows that the use of joint liability contract is
limited when MFIs face competition from a moneylender. This is a new finding in the literature on the properties of joint liability contracts. Secondly, it links
the literature on joint liability contracts with the literature on informal credit.
Thirdly, it introduces a new linkage between the formal and informal sector
which explains why the informal sector specialises in short term loans and show
that this linkage could be welfare improving.
Section two discusses the answers and gaps in the literature. In section three
we describe our baseline model which is based on Ghatak (2000) but included
an inefficient but perfectly informed moneylender. In section four we show that
a moneylender is not driven out of the market by a more efficient Microfinance
Institution (MFI) with a joint liability lending technology when the cost of funds of the moneylender is not too high. If the cost difference between the
MFI and the moneylender are not too large, the moneylender could offer a
better interest rate for the safe borrowers. As a result the MFI attracts only
the risky borrowers. We expect to observe empirically that the MFIs have a
larger share of risky borrowers and borrowers without payment history in their
portfolio when they face competition from a moneylender. Section five extends
the model of section three by introducing a liquidity shock at an intermediate
date. It shows a new linkage between MFIs and moneylenders in which the
MFI and moneylender partly finance the liquidity shock. The MFI insures
the borrowers against the exogenous shock, while the moneylender screens the projects worthwhile to refinance and provides short term emergency loan to safe
projects. The extension provides a simple model for the maturity structure of
debt in developing countries. This is consistent with the empirical observation
that moneylenders usually provide short term loans (Moll et al., 2000). To
determine the effect of competition on the effort choice of the borrowers we take
the moral hazard model of Ghatak and Guinnane (1999) in section six. We show
that in a developing credit market subject to moral hazard, borrowers turn to
not too high. From the MFI they get a cheaper joint liability loan contract, but
this contract allows them to lower their effort, which reduces their probability
2
Answers and Gaps in the Literature
In this section we look at the existing literature to get initial answers on the
research question how MFI moneylender competition affects the portfolio
com-position, the term structure of the loans and the effort choice of the borrowers.
We examine the structure of the rural credit market and discuss the
differ-ent lenders who operate in this market. Thereafter, we focus on the question
how competition in the rural credit market affects the portfolio composition of
lenders. Then, we examine the literature on the term structure of corporate
debt and the effects of competition on effort choice. Finally, we point out the
gaps in the existing literature.
The Structure of Rural Credit Markets
Competition between moneylenders and MFIs is embedded in the structure of
a rural credit market. Before developing a model on competition we need to
know whether this market is homogeneous or a differentiated. The rural credit
market is segmented on both the supply and demand side. On the supply side
it is possible to distinguish four types of lenders; formal financial institutions,
semi-formal institutions (MFIs), private suppliers of credit (moneylenders) and
relatives and friends. Formal lenders such as development banks could use the
rule of law to enforce contracts. These banks focus on larger, well established
clients with collateral. MFIs belong to the group of semi-formal lenders which often have social objectives. Formal and semi-formal lenders have better access
to capital markets and therefore a lower cost of funds compared with informal
lenders. Informal lenders such as moneylenders operate in the neighbourhood
of their borrowers and could easily collect information on the creditworthiness
of borrowers and could enforce contracts through coercion and social pressure.
Moneylenders also often link their contracts with transactions in other markets
to reduce risk. Family and friends offer loans on a reciprocal basis and usually at
a zero interest rate (Moll et al., 2000). On the demand side, borrowers are
1989), on the wealth of borrowers by Binswanger and Sillers, (1983) and by the
farm size in a rural credit market (McReynolds et al. 1989). The differences in
the types of lenders and demands of the borrowers are reflected in the contracts. Considering only the size, term and interest rate of the loan is too limited to
describe the spectrum of contracts offered in a rural credit market. In addition,
access to credit is an important factor. Formal and semi-formal lenders often
have long administrative procedures and are not based in the same village as
the farmer. Since the informal lender often lives in the proximity of the farmer
he is better equipped to serve short term liquidity needs of farmers. This
differ-ence could explain why formal and semi-formal lender usually offer long-term
contracts for about 12 month and the contracts of informal lenders last usually
for 1 to 3 months. Furthermore, we can distinguish contracts in the type of
security, the use of the loan, the type of loan (individual or group), the form (cash or in kind), the borrowing cost and the relative borrowing cost (Adams,
1994). Despite of the differences in contracts, Moll et al. (2000) show that
mon-eylenders and MFIs have an overlap in the segments of the market which they
serve. The specific characteristics of the rural credit make it difficult to cover all
aspects of the competition between moneylenders and MFIs in one theoretical
model. The models below focus on differences between a moneylender and an
MFI in the cost of funds, the information about the borrowers and the type of
contract.
What if the moneylender operates in an environment without competition
from other lenders? Hoff and Stiglitz (1990) propose three theories on mon-eylenders. The first theory sees moneylenders as usurious monopolists which
set high interest rates to maximize their profits (Bhaduri 1973). In the second
view, high interest rates are a reflection of a perfectly competitive credit
mar-ket which take a high risk of default into account. High interest rates could
therefore genuinely reflect the cost of the moneylenders to acquire capital,
exe-cute their business, monitor their clients or a high default risk (Adams, 1984).2
2For example: lenders make zero profit when their expected return (by charging an interest
The third theoretic perspective focuses on the high degree of asymmetric
in-formation in developing credit markets, which could lead to moral hazard and
adverse selection. To overcome these information problems, informal lenders use screening and monitoring mechanisms. Often moneylenders rely on geography,
kinship and interlinkages with other markets to solve problems of information,
incentives and enforcement. With data from a broad survey in Pakistan, Aleem
(1990) shows that an important part of the moneylenders’ costs result from high
screening and enforcement costs. The third perspective does not necessarily
ex-clude the second one. It only sees monitoring and screening costs as the most
important source of costs. In our model, the moneylender maximizes its profits
and sets a monopolistic interest rate when he is the only supplier of credit in
a market. Furthermore, the moneylender has a higher cost of funds than the
MFI. We attribute this cost difference to the high screening and monitoring costs of a moneylender and his limited access to the capital market. Therefore,
our model is based on the monopolistic and asymmetric information view of the
moneylender.
The Effects of Competition on the Portfolio Composition of Lenders
What determines the portfolio composition of formal and informal lender when
they compete with each other? An important part of the literature which
an-swers this question focuses on the government policies in the 1980s in many
developing countries which tried to alleviate financial constraints in rural
mar-kets. Governments established development banks which ’on lended’ funds to local moneylenders or competed directly with informal lenders. It was hoped
that this cheap credit would lower the dependence of borrowers on moneylenders
or would provide a beneficial trickle-down effect of reducing the usurious interest
rates. However, a number of studies (Basu, 1994; Bell, 1990; Hoff and Stiglitz,
1990; Siamwalla et al., 1990) point out that these policies of cheap credit failed
to achieve its desired result. Rural moneylenders continue to dominate the
in-formal sector and the interest charged by them have been relatively unaffected.
As a reaction on these findings, theoretical models have been developed which study the effect of ’on lending’ from the formal sector to the informal sector and
direct competition between the formal and informal sector.
The effects of these policies has been studied by Hoff and Stiglitz (1997)
and Bose, (1998). Hoff and Stiglitz (1997) show that an injection of funds in
the Thai and Indian rural bank system did not lower the interest rates charged
by commercial and rural moneylenders. Hoff and Stiglitz explain this negative
impact by a change in borrowers incentives when the face a higher supply of
funds. This results in higher agency and enforcement costs. More competition
decreases the number of clients per moneylender, which raises marginal costs
and ultimately the interest rate. Borrowers have more opportunities to turn to another moneylender when they default, which weakens incentives to repay.
Finally, because of an increase in the number of lenders, moneylenders could
rely less on reputation-building as an enforcement device, which makes
enforce-ment more costly. According to Hoff and Stiglitz, implicit linkages between
the formal and informal sector by increasing the supply of funds results in a
deterioration of the quality of the loan portfolios. Bose (1998) shows that a
reduction of the interest rates in a market with heterogeneous borrowers could
adversely affect the mix of potential borrowers for the moneylender in the
in-formal sector. The introduction of cheap credit could lead to two contradictory
effects on the lender: it reduces the cost of funds, but also results in a higher rates of defaults or higher cost of recovering funds. They derive their results
within a model which incorporates convex enforcement costs and informational
asymmetry across lenders. A reduction of interest rates enables the informed
lender to expand selectively by adding only safe borrowers. This reduces the
quality of the loan portfolio of the uninformed lenders. The deteriorated loan
portfolio in Hoff and Stiglitz (1997)is caused by entry of new moneylenders. In
contrast, the number of moneylenders is fixed in Bose (1998). Lower interest
of informed and uninformed moneylenders.
Different from the previous models, another class of models considers
in-direct linkages between the formal and the informal sector. In these models, formal lenders take the presence of moneylenders into account to extract
lo-cal information. In the context of competition, these models give insight how
an MFI and moneylender could strategically interact. Jain (1999) develops a
model in which moneylenders have better information and could identify the
borrower’s type. Banks can extract the information about the borrowers type
from the moneylenders by underfinancing projects, which results in a separating
equilibrium. They know that only good borrowers have access to the informal
credit market and all borrowers require a critical amount of funds to start their
project. By underfinancing projects, they use the implicit knowledge that only
good borrowers resort to moneylenders for the rest of the funds. Bad borrowers will not mimic good ones since they cannot obtain money from moneylenders.
In the separating equilibrium, the bank thus only finances good borrowers. In
the pooling equilibrium the formal lender offers a loan to both inefficient risky
borrowers and efficient safe borrowers. Banks face a trade-off when choosing
be-tween a pooling or separating equilibrium. Information extraction comes with
a cost; co-financing is less efficient than the bank and this becomes more costly
when the informal sector is very inefficient. The profit maximizing solution will
only yield higher profits when the proportion of bad borrowers is high, the risk
of bad contracts is relative large and the cost differences between two sectors
are small. Varghese (2005) develops a model in which banks could not observe whether the incomes of borrower are low or high. Borrowers will always claim
that they realized a low income and therefore not repay their loans. Bank can
separate good and bad borrowers by only offering borrowers who repaid their
loan a loan in the second period. Alternatively, banks could set their interest
rates in such way that borrowers who realised a low income in the first period
could lend from moneylenders (who perfectly observe the realised income) to
The Maturity Structure of Debt
Moneylenders usually provide short term loans while MFIs sign loans with a
longer maturity (Moll et al., 2000). If small farmers face a liquidity shock on an intermediate date, which lender will provide the short term loan and why?
To find an answer we first look at the theory of corporate debt maturity. The
literature offers several leading theories on debt maturity structures, namely
agency costs (e.g. Myers, 1977), leverage (e.g. Leland and Toft, 1996),
matu-rity mismatching and signalling (Flannery, 1986 and Diamond, 1991). In many
of these models the maturity structure is endogenously chosen by the firm in
an environment with identical lenders. In Flannery (1986), for example, good
firms signal their quality with short term debt. We are interested in a slightly
question: could competition between MFI and moneylender determine the
ma-turity of the loans they offer to borrowers. More specifically, could competition explain why usually MFIs offer long term loans and moneylenders short term
loans? As far as we know there is no literature on the maturity structure of
debt in developing countries.
Competition and Effort
In an environment in which MFIs are not able to observe the effort level of
the entrepreneur, how does competition with a perfectly informed moneylender
affect the effort level of the borrower? Ghosh and Van Tassel (2008)
demon-strate in a two-period moral hazard model that subsidized MFIs could coexist
with a profit maximizing moneylender, without distorting the incentives of the borrowers. The borrowers could use their revenue of a successful project in the
first period as equity in the second period. Only when borrowers use equity
their effort level is high enough to yield a positive profit for the moneylender.
The MFI offers subsidized credit in the second period to unsuccessful first
pe-riod borrowers. This has no negative implications on the agent’s first pepe-riod
incentive to work hard. The reason for this is that the MFI outreach affects the
bargaining power of agents that obtain loans from the moneylender. The
credit is negated because the outreach of the MFI puts a downward pressure on
the interest rates of the moneylender. This restores the incentives to put effort
and apply for a loan from the moneylender in the second period. In the model of Ghosh and Van Tassel (2008) both MFI and moneylender have asymmetric
information about the effort level of the borrower. Furthermore, both lenders
offer an individual liability contract. We are interested in the question how the
type of contract (joint liability vs individual liability) affect the effort level of
a borrower and the choice for a particular lender. Our interest in this question
stems from the strong result in the microfinance literature that joint liability
lending could resolve ex ante moral hazard. In Laffont and Ray (2003),
borrow-ers observe each other’s effort level and exert more effort when they are jointly
responsible for the repayment. Similar results are obtained by Stiglitz (1990),
Varian (1990) and Itoh (1991).
Summary: What do we Know and What are the Gaps
In this part we shortly summarise the gaps in the literature we want to answer
in our research. We know that the credit market is a differentiated market.
Borrowers go to different types of lender such as moneylenders and MFIs. An
open question is how competition affects the choice of a borrow for a
particu-lar lender and consequently the portfolio of the lender. What could we learn
from the literature when analysing the effect of MFI moneylender competition
on the portfolio composition? Hoff and Stiglitz (1997) tell us that it worsens
asymmetric information problems because competition reduces the effectiveness of lenders to resolve these problems. Our models focus on differences in the cost
of funds, the information about the borrowers and the type of contract. We do
not endogenize screening and monitoring since we assume a perfectly informed
moneylender and an MFI which could only use a joint liability contract.
There-fore we do not expect similar results as in Hoff and Stiglitz (1997). A similarity
between our model and Bose (1998) is difference between informed and informed
lenders. However, in Bose (1998) competition is represented by a decrease in the
the contract of the MFI and the moneylender differs and we model competition
as the coexistence of both lenders on the market. Interest rates are best replies
on the actions of the other player. The models on the indirect linkages between the MFI and the moneylenders show that these could improve the loan portfolio
of the MFI model do not explicitly model the behaviour and portfolio
compo-sition of the moneylender. The moneylender is only a passive player while we
study the strategic interaction between the MFI and the moneylender. Another
question is how competition between lenders affects the maturities of the loans
which they offer. We want to answer whether competition between two lenders,
which offer different contracts and have a different information sets affect the
maturity of the contracts. Corporate finance theory focuses on the question
how firms choose their maturity structure and not how lender characteristics
affect the maturities of the contracts they offer. Finally, we are interested in the question how the choice of effort is affected by competition. We know that
a joint liability contract could resolve moral hazard problems, but we want to
know whether borrowers prefer this contract above a loan of the moneylender
3
The Model
This section describes the basic setting of the competition game between two
asymmetrically informed principles, the moneylender and the MFI, in presence
of adverse selection. The model is based on the standard Ghatak (2000) adverse
selection model. Under the same assumptions as Ghatak (2000) this model
in-troduces a less efficient, but fully informed profit maximizing moneylender.
Borrowers
A continuum of risk neutral borrowers on the interval [0, 1] consists of two
types: a fraction λ of the borrowers is risky (r) and has a probability of success
of p = pr, and a fraction (1−λ) of the borrowers is safe (s) and has a probability
of success of ps. An entrepreneur can borrow 1 dollar and invest in a project
that yields Xk with probability pk, k = [r, s] and zero with probability (1 − pk).
Assumption 1 0 ≤ pr< ps≤ 1 and Xr= Xs= X
We use first order stochastic dominance as definition of risk, as in De Meza and
Webb (1987). Assumption 1 implies that the expected return of safe borrowers
is higher than the expected return of risky borrowers psX > prX. In this paper
we use riskiness in a broader perspective than only the difference in probability
of success of the project. Safe borrowers are borrowers with a high ability and
willingness to repay their loan. Risky borrowers are borrowers without a
pay-ing record and the reputation of bepay-ing a creditworthy borrower. In developpay-ing credit markets reputation is of far greater importance than the riskiness of an
individual project. Borrowers get a reputation in the lending relationship with
a moneylender, but also within their peer group. The latter is important for
the MFI, because joint liability contracts induce endogenous group formation.
Borrowers do not have collateral which could be used as signalling device as
de-scribed in Bester (1985). The borrowers’s utility equals Uk(Rk, pk) = pk(X −Rk)
if he borrows and U0 if he does not borrow. This reservation utility represents
Information
An important assumption in the model is the assumption that the moneylen-der and MFI are asymmetrically informed about the borrowers types. The
moneylender can observe the risk characteristics of borrowers, while the MFI
cannot. It is common to assume that the MFI does not observe the borrower’s
type. Most theoretical model on microfinance introduce this information
asym-metry to explain the success of the joint liability contract. The assumption
that the moneylender perfectly observes the borrower’s type is stronger, but in
line with the literature on linkages between the formal and informal financial
sector. Fuentes (1996) presents a moral hazard model in which a formal lender
delegates the monitoring task to a local ’village agent’ such as a moneylender.
He justifies the assumption that the local agent is perfectly informed about the actions and abilities of the borrower in the following way:
”The village agent possesses an information advantage over the
fi-nancial institution in regard to the potential borrower’s risk
charac-teristics due, in large part, to his proximity to the applicant. For
instance, he would know the applicant farmer’s farm management
skills, his current asset holdings and, more than likely, the small,
farmer’s repayment performance on previous loans. [...] The agent’s
proximity may also give him a cost advantage in monitoring and
pursuing loan repayment”. Fuentes (1996), p192.
A similar assumption is made in the MFI moneylender linkage models of Jain
(1999) and Varghese (2005). We assume that both moneylender and the MFI
observe the returns of the project. Therefore, we rule out the costly verification
problem as considered by Townsend (1979). In addition, we assume that the
MFI and moneylender perfectly observe each other’s costs. The cost of funds of
The Moneylender and the MFI
In the whole paper we model the moneylender as a profit maximizing lender and
the MFI as an institution with a social objective which maximizes borrower’s utility. Although commercial MFIs exist, most of the MFIs have a NGO charter
which stresses its social objectives. Theoretical models on MFIs, such as Ghatak
(2000), also assume borrower’s utility maximizing MFIs. McIntosh and Wydick
(2002) study the effects of competition within the microfinance industry. We
assume that the MFI only provides business loans to small entrepreneurs and
does not provide consumer credit. We are interest in the competition between
borrowers’ utility maximizing MFIs and profit maximizing moneylenders. In
addition to the differences in information sets we make the following assumption
about the costs of funds:
Assumption 2 ρM L> ρM F I
The cost of funds of the moneylender are strictly higher than the cost of funds of
the MFI. MFIs have better access to capital markets and have therefore a lower
costs of funds. Another justification is the high monitoring and screening cost
of the moneylender which results in a higher cost of funds (Aleem, 1990). For
simplicity we do not consider capacity constraints in the availability of funds.
The difference in costs of funds creates an inefficiency in the model. If the
mon-eylender finances a positive share of the borrowers this reduces welfare, because
those borrowers are not financed by the most efficient lender.
Loan Contracts
The moneylender offers a single individual limited liability loan contract to its
borrowers and specifies a loan contract for each borrower’s type with an interest
rate of RM L
k , with k = r, s. When the MFI operates in the credit market, it
has asymmetric information about the borrowers quality. A wide applied
lend-ing technology by MFIs is joint liability lendlend-ing. When signlend-ing a joint liability
joint responsibility for the loan. We consider a contract specified for a group
consisting of two borrowers. When they form groups of two borrowers, they pay
a normal interest rate RM F I to the MFI when their project succeeds, but also have to pay an amount of joint liability CM F I when their project succeeds and
the project of their partner fails. Ghatak (2000) shows that this joint
liabil-ity contract results in assortative matching; risky borrowers form groups with
risky borrowers, and safe with safe. The intuition is simple; safe borrowers do
not want to be liable for the failures of risky borrows and prefer borrowers of
their own kind with a higher probability of success. For simplicity, we consider
a pooling joint liability contract in which the MFI sets an interest rate which
equals the amount of joint liability RM F I = CM F I. We only consider group loans for two borrowers which apply for a loan of the same size. The conditions
under which Ghatak(2000) proofs the assortative matching property (proposi-tion 1, Ghatak (2000)) hold in both sec(proposi-tion 4 and 5.3 We refer to the original
paper for a proof of this assortative matching property.
Returns on Investment
We make the following assumption on the returns on investment:
Assumption 3 X ≥ ρj+Up 0
k , k = r, s, j = M F I, M L
All projects are socially viable, independent of their source of finance.
3In Ghatak(2000) the utility of a group of two risk neutral safe borrowers is greater than
a mixed group if ps> prand CM F I> 0. This is sufficient to prove the assortative matching
4
MFI Moneylender Competition and Adverse
Selection
In this section we analyse MFI moneylender competition in the simple adverse
selection model described in section three. We want to answer the question
how MFI moneylender competition affects the portfolio composition of the MFI
and the moneylender. In addition to the assumptions described in section, we assume in the rest of the rest of the section:
Assumption 4 X ≥ 2ρM F I/[λ(p
r(2 − pr)) + (1 − λ)(ps(2 − ps))]
and
Assumption 5 U0< p2
k[ρM F I/[λ(pr(2 − pr)) + (1 − λ)(ps(2 − ps))]]
Assumptions 4 and 5 are are feasibility conditions for the joint liability contract.
Assumption 4 ensures that the return of a project is at least as high as the total
amount of individual and joint liability under which an MFI makes zero profits.
Assumption 5 ensures that both borrowers’ types participate in a joint liability
contract.
4.1
The Moneylender without MFI competition
In this section we show how a monopolistic moneylender sets his interest rate and
calculates the equilibrium interest rates when he does not face competition from
an MFI. We assume that the moneylender operates in a specific geographic area
without competition from other moneylenders. The monopolistic moneylender
could observe the risk characteristics of the borrowers and could discriminate
between safe and risky borrowers. The moneylender maximizes his profits , but
could only charge an interest rate which leaves each borrowers group with a
utility at least as high as their reservation utility. When a borrowers group
has to pay a higher interest rate, they would not start the project and instead enjoy their reservation utility. On the other hand, moneylenders only lend to a
funds. Therefore, a moneylender faces the following maximization problem: max RM k pkRM Lk − ρ M L, k = r, s (1) subject to: pkX − pkRkM L≥ U0, k = r, s (2) pkRM Lk − ρ M L≥ 0, k = r, s (3)
The moneylender maximizes his profits (1) subject to the participation
con-straint of borrower k (2) and his own borrower specific participation concon-straints
(3)
Lemma 1 Without competition from the MFI, the moneylender drives the
bor-rowers down to their reservation utility and sets the following interest rates:
RM Lk = X −
U0
pk
, k = r, s (4)
The participation constraint of each borrowers’ group (2) determines the
max-imum interest rate and binds in equilibrium. Both borrowers types only enjoy
their reservation utility Ukb= U0, k = r, s and the profits of the moneylender on each borrowers group equals ΠM Lk = pkX − U0− ρM L. The total social surplus
(S) is S = (λpr+ (1 − λ)ps)X − ρM L.
4.2
The MFI without Moneylender Competition
This section describes how an MFI sets a joint liability contract in a developing
credit market without moneylender competition. We specify an MFI as a small
microfinance organisation with an NGO-charter and a social mission to
pro-vide credit to the poor. We assume that the MFI maximizes borrowers’ utility
without making financial losses. Furthermore this section shows the optimal
contract and social surplus.
As described in section three, we consider a pooling joint liability contract with
in which the amount of individual liability equals the amount of joint liability
RM F I = CM F I. The MFI solves the following maximization problem: max
RM F IU
b= λ(p
subject to:
pkX − pk(2 − pk)RM F I ≥ U0, k = r, s (6)
λ(pr(2 − pr)RM F I) + (1 − λ)(ps(2 − ps)RM F I) ≥ ρM F I (7)
X ≥ RM F I+ CM F I = 2RM F I (8)
The total borrowers’ utility Ub consists of the expected utility of λ risky
bor-rowers and the expected utility of 1 − λ safe borbor-rowers. Since we assume
RM F I = CM F I, the expected payment of the borrower to the MFI pkRM F I−
pk(1 − pk)CM F I becomes pk(2 − pk)RM F I. Each borrowers’ group only borrows
when their expected revenue exceeds their reservation utility. The
participa-tion constraint (6) for each borrowers’ group should be satisfied. Although the
MFI wants to maximize the overall borrowers’ utility, he has to make at least
zero profits to run a sustainable business. This is represented by the zero-profit
constraint for the MFI (7).Furthermore, the amount of individual liability and
joint liability could not exceed the total revenue X when the project succeeds.
This result in the limited joint liability constraint (8). The amount of
individ-ual liability plus the amount of joint liability could not exceed the return of a
project. By assumption 4 this constraint is satisfied.
Lemma 2 Without moneylender competition, the MFI maximizes borrowers’
utility, makes zero profits and sets the following individual and joint liability rate: e RM F I = eCM F I= ρ M F I λ(pr(2 − pr)) + (1 − λ)(ps(2 − ps)) (9)
If the MFI wants to maximize borrowers’ utility, the zero-profit constraint (6)
binds in equilibrium. The MFI makes in total zero profits. However, it makes a
positive profit on safe borrowers since the zero-profit interest rate of the MFI for
only safe borrowers ispρM F I
s(2−ps which is less than (9), because ps(2 − ps) > pr(2 −
pr). In the same line of reasoning, the MFI makes a loss on risky borrowers.
The borrower’s utility is: Uk = pkX − pk(2 − pk)ρM F I/[λpr(2 − pr) + (1 −
λ)ps(2 − ps)], k = r, s. Safe borrowers still cross-subsidize risky borrowers. Both
the expected payment of the risky borrower is stricly lower than the expected
payment of the safe borrower. The profits of the MFI are ΠM F I= 0.
4.3
Competition between MFI and Moneylender
This section models competition between a moneylender and an MFI. It shows that moneylenders could capture good borrowers when cost difference between
the MFI and moneylender are small and for larger cost differences only when the
share of risky borrowers is high. The information advantage of the moneylenders
enables them to distinguish risky and safe borrowers and discriminate in interest
rate rates. The competition restricts to competition between moneylenders and
MFIs on the market for small business loans and does not focus on consumer
credit. In this model, moneylender and MFI set simultaneously their interest
rates and compete in a Bertrand fashion.
First, we analyse the behaviour of the moneylender. The moneylender faces
the same optimisation problem as in section 3.2.1, but now borrowers could also borrow from the MFI, which could result in a higher utility. Borrowers choose to
either enjoy their reservation utility U0or to borrow from the MFI, as alternative
for the moneylender. Therefore, the borrowers participation constraint changes
into
pkX − pkRM Lk ≥ max(pkX − pk(2 − pk)RM F I, U0), k = r, s (10)
Risky and safe borrowers only participate when the moneylender offers a higher
utility than either their reservation utility or the utility they could get from
the MFI. Borrowers are indifferent between the moneylender and the MFI when
the expected interest payment to the moneylender pkRM Lk equals the expected
payment to the MFI pk(2 − pk)RM F I or equivalently RM Lk = (2 − pk)RM F I.
The moneylender could capture the segment k = r, s of the borrowers
mar-ket by charging an interest rate of RM L
k = (2 − pk)RM F I − , where is
a value close to zero. The moneylender undercuts the MFI and borrowers
of type k goes to the moneylender, because their expected interest payment
pkRM Lk = pk[(2 − pk)RM F I− ] < pk[(2 − pk)RM F I. Undercutting is only
prof-itable for the moneylender when his expected interest revenue is higher than his
costs of funds. Therefore, the lowest interest rate which a moneylender could charge to borrowers type k is RM L
k = ρ M L/p
k. When the moneylender charges
his lowest interest rate and the expected payment to the moneylender is higher
or equal than the expected payment to the MFI pk[ρM L/pk] ≥ pk(2 − pk)RM F I,
the moneylenders does not want to undercut the MFI anymore. Therefore,
the moneylender only want to undercut if the following condition is satisfied:
ρM L < p
k(2 − pk)RM F I. This results in the following reaction function of
moneylender RFM L: RFM L(RM F Ik ) = RM L k = (2 − pk)RM F I− if pk(2 − pk)RM F I > ρM L ρM L/p k if pk(2 − pk)RM F I ≤ ρM L (11)
The moneylender only wants to undercut the MFI by when his costs of funds
are lower than the expected payments of borrower k to the MFI. Otherwise, he
only offers his lowest interest rate ρM Lk /pk.
Now we turn to the MFI. The MFI maximizes borrowers’ utility, but now faces a profit maximizing moneylender with perfect information about the
bor-rowers risk characteristics as competitor. As we derived in section 3.2.2, the
MFI maximizes borrower utility and set
e
RM F I = eCM F I= ρ
M F I
λ(pr(2 − pr)) + (1 − λ)(ps(2 − ps))
. (12)
The MFI could only makes zero profits when both safe and risky borrowers
participate, since safe borrowers cross subsidize risky borrowers. So, the MFI
only charges this rate when it could ensure the participation of safe borrowers.
When safe borrowers do not participate, the MFI sets an interest and joint
liability rate on which it makes zero profits if only risky borrowers are their
customers: b RM F I = bCM F I= ρ M F I (pr(2 − pr)) (13)
Safe borrowers are indifferent between borrowing from the MFI and borrowing
of the moneylender and the cost of funds of the MFI ρM L> ρM F I are not too high. By setting the minimum interest rate which a moneylender could offer to
a safe borrower ρM L/ps equal to the zero-profit interest rate of the MFI, this
defines the maximum level of the moneylender’s cost of funds at which it could
offer a cheaper contract to safe borrowers:
ρM L= psρ
M F I
λ(pr(2 − pr)) + (1 − λ)(ps(2 − ps))
. (14)
Proposition 1 When Moneylender and the MFI compete, the moneylender and
MFI set the following contracts:
RM L, (RM F I, CM F I) = ρM L/p k, ( eRM F I, eCM F I) if ρM L> ρM L (2 − pk)RM F I− , ( bRM F I, bCM F I) if ρM L≤ ρM L (15)
The MFI captures both risky and safe borrowers in the first case. In the second
case, the moneylender captures safe borrowers and the risky borrowers go to the
MFI.
Proof. When the cost of fund of the moneylender are lower than ρM L, the
MFI offers ( bRM F I, bCM F I). The MFI could not offer a pooling joint liability
contract on which it makes zero-profits. When the MFI offers such a contract,
the moneylender could offer a cheaper loan to safe borrowers. The moneylender
then will capture the whole market of safe borrowers, and the MFI will make
a loss on the pooling contract, since safe borrowers cross-subsidized risky
bor-rowers when participating. The MFI is forced to only serve risky borbor-rowers,
because moneylenders will always ask a lower rate when the MFI sets a pooling
contract to attract safe borrowers. The moneylender knows that the MFI could not attract safe borrowers and set its interest rate for safe borrowers slightly
lower than the contract which the MFI offers to risky borrowers and maximizes
its profits. If the cost of funds of the moneylender are higher than ρM L, the
MFI offers ( eRM F I, eCM F I).
This proposition shows that a joint liability contract only attracts both
the thresholds value ρM L. When this is not the case, the information ad-vantage helps the moneylender to capture the safe borrowers, while the risky
borrowers go to the MFI anyway. The moneylender keep the borrowers with a good reputation and offer them a better contract than the MFI.
Borrow-ers without reputation form groups and borrow from the MFI. In practice,
each moneylender has a capacity constraint. Therefore the extreme result
of the separation of the borrowers types between the moneylender and MFI
does only hold in theory. In practice, safe borrowers will also lend from the
MFI when the moneylender reaches its capacity constraint. When safe
bor-rowers are financed by moneylenders and risky by the MFI the total social
surplus is S = λ[prX − rhoM F I] + (1 − λ)[psX − ρM L], the MFI makes zero
profits ΠM F I = 0 , and the moneylender positive profits on safe borrowers ΠM L= (1−λ)[psρM F I/pr(2−pr)−ρM L]. The utility of risky borrowers is Ur=
prX − ρM F I. The utility of safe borrowers is Us= psX − psρMF I/pr(2 − pr).
When both risky and safe borrowers are financed by the MFI, the total social
surplus is S = (λpr+(1−λ)ps)X −ρM F I, which is higher than the previous case,
since ρM L > ρM F I. The MFI makes zero profits ΠM F I = 0. The borrower’s
utility is Uk = pkX − pk(2 − pk)ρM F I/[λpr(2 − pr) + (1 − λ)ps(2 − ps)], which
is higher for both risky and safe borrowers.
4.4
Conclusion MFI Moneylender Competition and
Ad-verse Selection
In this section we examined the effects of competition between an MFI and a
moneylender in an environment characterised by adverse selection. When the
cost of funds of the moneylender are below the threshold ρM L, the moneylender captures the safe borrowers while the MFI only finances the risky borrowers.
Compared with the benchmark case in section 4.2, MFI moneylender
competi-tion deteriorate the quality of the loan portfolio of the MFI. The joint liability
welfare is lower than the case in section 4.2 without moneylender because the
safe share of the borrowers is now financed by a less efficient lender. When the
cost of funds of the moneylender exceeds the threshold ρM L, both borrowers prefer the joint liability contract over the individual liability contract of the
moneylender. The social welfare equals the benchmark case in 4.2 because all
5
MFI Moneylender Competition and Liquidity
Shocks
This section extends the adverse selection model of the previous section by
intro-ducing an exogenous liquidity shock at an intermediate date. Liquidity shocks
are common in rural agricultural markets. An example of such a liquidity shock
is an insect plague. A farmer hit by a plague could either harvest his crops early or invest in pesticides. We assume that a borrower has no internal
finan-cial sources and relies on external lenders to refinance the liquidity shock. A
lender in a rural credit market, either a moneylender or an MFI, only refinances
the borrower if it pays-off to do so. In this section we show that a moneylender
without MFI competition sets a social optimum threshold for refinancing the
liquidity shock. To extract all the borrower’s surplus, the best thing what a
moneylender can do is to maximize the NPV of the project, just as a social
planner. Therefore he sets the same liquidation threshold as the social
opti-mum. Contrary to the moneylender, the MFI sets a threshold liquidation value
which might inefficiently liquidate safe borrowers or might inefficiently contin-ues risky firms. The optimal liquidation threshold is type dependent. Since the
MFI does not observe the borrower’s type he sets an average threshold, which
is the source of the inefficiency. MFI Moneylender competition could resolve
this problem. When an MFI and moneylender operate in the same market, a
moneylender could partly finance the liquidity shock. Since the moneylender
observes the borrower’s type, he could choose which liquidity shock is
prof-itable to refinance. The model shows that the moneylender only refinances safe
borrowers. By partly refinancing liquidity shocks, the MFI could now improve
the borrowers’ utility and resolve the two problems of inefficient liquidation of
safe borrowers and inefficient continuation of risky borrowers. This is a novel MFI moneylender linkage which shows that the presence of a monopolistic
mon-eylender result in a higher social welfare. The MFI functions as an insurance
pool, while the moneylender screens which project is worthwhile to refinance.
Since the MFI sets ex ante a threshold, it could incorporate this in its zero-profit
interest rate. All borrowers pay a slightly higher interest rate (an insurance pre-mium) which equals the expected value of the threshold liquidity shock financed
by the moneylender. Borrowers which are actually hit by a liquidity shock get
a loan from the moneylender for the remaining part and pay him interest rate.
The basic setting of the model has been described in section 3. Novel in this
model is the introduction of a liquidity shock. The magnitude of the liquidity
shock is learned at the intermediate date. There are only two possible values for
the liquidity shock: 0 with probability 1 − ξ and φ with probability ξ, ξ ∈ [0, 1].
To withstand a liquidity shock, the entrepreneur has to reinvest the amount φ.
If the entrepreneur does not reinvest φ, then the project is liquidated. Both
moneylender and MFI know ex ante the size of the potential liquidity shock φ. We assume that the realized value of φ is verifiable. The model is derived
from the ’two-shock case’ of Tirole(2006) and applied to our fixed-investment
adverse selection model described in section 3. The contracts of the moneylender
and MFI slightly change. The moneylenders offers (RM L k , φ
M L
k ) in section 5.1,
where (RM L
k is the interest rate which borrower k pays and φ M L
k the maximum
liquidity shock it wants to refinance. In section 5.3 the moneylender offers an
individual liability at an interest rate RM L
k . The MFI offers in section 5.2 and
5.3 the contract (RM F I, CM F I, φM F I), where RM F Iis the amount of individual liability, CM F I the amount of joint liability and φM F I) the maximum liquidity shock which an MFI wants to refinance. For simplicity we set the amount of joint liability equal to the amount of individual liability RM F I = CM F I. In addition
to the model described in section 3, we make the following extra assumptions:
Assumption 6 φ < psX/ρM L
Assumption 6 puts a restriction on the height of the liquidity shock. Liquidity
shocks higher than φ > psX/ρM Lare not interesting cases, because even for safe
exceeds the expected revenue.
Assumption 7 X ≥ (2 − ps)(1 + ξ(1 − λ)φ)ρM F Iθ−1+ U0/ps,
where θ ≡ [λ(1 − ξ)pr(2 − pr) + (1 − λ)ps(2 − ps)]. Assumption 6 is a
tech-nical assumption which selects projects which have enough surplus and allow
the moneylender to co-finance the liquidity shock. It ensure the feasibility of the
equilibrium described in proposition 2 of this section. We also assume that the
loans of an MFI is senior to a loan of the moneylender. When the MFI jointly
finances a loan with a moneylender, the borrowers firstly pay off their
liabili-ties (to secure future group loans) and then its liabililiabili-ties to the moneylender.
Firstly, we analyse the case in which the moneylender operates without MFI
competition. We show that the moneylender liquidates and continues projects
always in a social optimal way. Secondly, we discuss how the MFI deals with the liquidity shock. Since the MFI is not able to observe the borrowers type, it
could not make an optimal refinancing decision. This could result in an
ineffi-cient liquidation of safe project and ineffiineffi-cient continuation of risky projects. In
the third subjection we show how MFI moneylender competition could resolve
these two problems.
5.1
The Moneylender without MFI competition
The monopolistic moneylender provides individual liability loans to risky and
safe borrowers and decides, given the magnitude of the liquidity shock, whether
to refinance a borrower. The moneylender knows ex ante the height of the
liquidity shock φ. When the moneylender grants a loan to a borrower he has the following choices:
1. Grant a loan and refinance the liquidity shock φ of the borrower
2. Grant a loan and liquidate the project if the borrower will be hit by a
We introduce a dummy variable δ = [0, 1] for this choice, which takes the value
δ = 1 if the moneylender refinances the project and takes the value δ = 0 if
the moneylender liquidates the project . What is the maximum liquidity shock of borrower k = r, s which a moneylender wants to withhold? To answer this
question we maximize the following program:
max δk,RMkL (1 − (1 − δk)ξ)pkRM Lk − [δkξφ + 1]ρM L, (16) subject to: (1 − (1 − δk)ξ)pk[X − RM Lk ] ≥ U 0, k = r, s, (17) (1 − (1 − δk)ξ)pkRM Lk − [δkξφ + 1]ρM L≥ 0, k = r, s, (18)
In this maximization problem (17) is the borrowers participation constraint
and (18) the participation constraint of the moneylender. If δ = 0 and the moneylender does not refinance borrower k, only (1−(1−δk)ξ)pk of the projects
succeed, but the cost of finance of a project of borrower k is just ρM L. If δ = 1
and the moneylender does refinance borrower k, pk of the projects succeed
and the expected cost of financing and refinancing a project of borrower k is
[ξφ + 1]ρM L. The profit maximizing interest rate at which the moneylender
extracts all the surplus from borrower k equals:
RM Lk (δk) = X − U0/(1 − (1 − δk)ξ)pk, k = r, s. (19)
The participation constraint (17) of borrower k binds at this rate and depends
on δ. The moneylender will refinance the liquidity shock if his profits when refinancing exceeds his profits when he is not refinancing the shock:
pkRM Lk (δk= 1) − [ξφ + 1]ρM L≥ (1 − ξ)pkRM Lk (δk= 0) − ρM L (20)
The left-hand side of this equation represents the maximum profits in the case
the moneylender refinances the liquidity shock (δk= 1). The right-hand side of
the equation represents the maximum profits which a moneylender could attain
RM Lk (δk = 1) 6= RkM L(δk = 0). By substituting (19) into (20) and solving for φ
we derive the threshold liquidity shock:
e
φM Lk ≡ pkX/ρM L (21)
For any liquidity shock higher than this threshold it is more profitable to
liqui-date the firm instead of refinancing the liquidity shock. The intuition for this value is simple. If a moneylender already invested in a project and this project
experiences a liquidity shock, the moneylender maximally wants to reinvest the
amount of the expected return of the project. What is the maximum
liquid-ity shock which a moneylender wants to refinance? We derive the maximum
liquidity shock by plugging the profit maximizing interest rate (19) into the
participation constraint of the moneylender (18) and solving for φ which results
in:
φM LM AX,k = ξ−1[(pk/ρM L)[X − U0/pk] − 1] (22)
The overall maximum liquidity shock a moneylender wants to withhold depends
1.) on the trade-off between refinancing and non-refinancing and 2.) the
partic-ipation constraint of the moneylender. Therefore the maximum liquidity shock
which the moneylender wants to withhold is:
φM Lk = min(φ M L
M AX,k, eφM Lk ) (23)
Which of the two values is the lowest depends on the parameter values of the
model. When the probability of a liquidity shock ξ is high or when the
partici-pation constraint of the moneylender binds, the first expression determines the
maximum liquidity shock. When the probability of a shock is low and the
mon-eylenders participation constraint is non-binding, the expected return divided by
the moneylenders cost of funds determines the maximum liquidity shock which
the moneylender wants to withhold. In the rest of this subsection we assume that φM Lk,M AX > eφM L
k . This is true if X > [ξ−1U
0+ ξ−1ρM L]/(−(1 − ξ−1)p k),
which is a positive value since (1 − ξ−1) < 0, because ξ ∈ [0, 1].
Lemma 3 The maximum liquidity shock which a moneylenders wants to
Proof. A social planner maximizes the net present value of the project (NPV)
and has perfect information about the borrowers type. Suppose the cost of
capital equals ρM L. When the social planner refinances the liquidity shock, the NPV of borrowers’ type k = r, s becomes (1 − (1 − δk)ξ)pkX − [δkξφ + 1]ρM L.
The social planner does not refinances the project if the NPV is lower than
the reservation utility U0, which result in a maximum threshold φSP k,M AX =
ξ−1[(pk/ρM L)[X − U0/pk] − 1] = φ M L
k,M AX. The social planner only refinances
the liquidity shock if pkX − [ξφ + 1]ρM L≥ (1 − ξ)pkX − ρM L, which gives the
threshold value of eφSP
k ≡ pkX/ρM L= φM Lk
The result that monopolistic competition results in a social optimum is
counter-intuitive. Note that monopolistic competition is not optimal for the borrowers.
The monopolist extract their whole surplus up to U0. However, a monopolist which is perfectly informed and maximizes his profits is equivalent to maxi-mizing the Net Present Value of the project. Furthermore, independent of the
form of competition, eφ ≡ pkX/ρM Lis always the optimal threshold value. Both
profit maximizing lenders as well as borrowers’ utility maximizing lenders have
the value as optimum. If these lenders refinance larger liquidity shocks, their
refinancing costs exceed the expected return of a project, what leads to a loss
in profit and borrowers’ utility. Since the demand of the borrower depends
on their participation constraint, there is no downward sloping demand curve.
The downward sloping demand curve drives the welfare loss in the standard
monopolistic competition models. This welfare loss is absent in this model.
5.2
The MFI without moneylender competition
The objective of the MFI is to maximize borrowers’ utility. When signing a joint liability contract the MFI is aware that borrowers could be hit by a liquidity
shock and determines therefore ex ante the threshold value of the liquidity shock
which the MFI wants to refinance. An important assumption we make here is
that shocks are perfectly correlated across borrowers. So, if borrowers form
of the potential liquidity shock φ, the MFI could make two choices:
1. Grant a group loan to two borrowers and refinance the liquidity shock of
the borrowers
2. Grant a group loan to two borrowers and liquidate the projects if the borrowers will be hit by a liquidity shock
The MFI will only go for the last option if the liquidity shock is ’too high’.
But when is a liquidity shock too high? This could be determined with the
following maximization problem:
max δ,RM F I(1 − (1 − δ)ξ)[λpr[X − (2 − pr)R M F I] + (1 − λ)p s[X − (2 − ps)RM F I]] (24) subject to: (1 − (1 − δ)ξ)pk[X − (2 − pk)RM F I] ≥ U0, k = r, s, (25) (1 − (1 − δ)ξ)[λpr(2 − pr)RM F I+ (1 − λ)ps(2 − ps)RM F I] − (δξφ + 1)ρM F I ≥ 0, k = r, s, (26) X ≥ 2RM F I (27)
where δ ∈ [0, 1] is a dummy which equals 0 if the MFI does not refinances the
borrower k = r, s and equals 1 if the MFI does refinance the liquidity shock of
borrower k. In this maximization problem (25) is the borrowers participation
constraint and (26) the participation constraint of the moneylender. Constraint
(27) is the joint liability constraint of the borrower. The borrower could not pay
more interest and joint liability than his revenue X. The interest rate at which
the MFI makes zero-profits is obtained by making the participation constraint
of the MFI (26) binding:
RM F I(δ) = [δξφ + 1]ρM F I/(1 − (1 − δ)ξ)[λpr(2 − pr) + (1 − λ)ps(2 − ps)]. (28)
Note that the interest rate depends on the choice of δ. The MFI, which
utility with refinancing is higher than the borrowers’ utility without
refinanc-ing:
[λpr+ (1 − λ)ps]X − [λp(2 − pr) + (1−)ps(2 − ps)]RM F I(δ = 1) ≥
(1 − ξ)[λpr+ (1 − λ)ps]X −
(1 − ξ)[λpr(2 − pr) + (1−)ps(2 − ps)]RM F I(δ = 0) (29)
The left-hand side of this equation represents the borrowers’ utility if δ = 1 and
the right-hand side of this equation represents the borrowers’ utility if δ = 0.
By solving this equation for φ, we can show that the threshold liquidity shock
at which the MFI refinances the project is:
e
φM F I ≡ [λpr+ (1 − λ)ps]X/ρM F I (30)
For any liquidity shock higher than this threshold it is more profitable to liqui-date the firm instead of refinancing the liquidity shock. If an MFI refinances a
liquidity shock it wants at least an expected return as high as the reinvestment
e
φM F I. What is the maximum liquidity shock which a MFI wants to refinance?
The maximum liquidity shock which the MFI wants to withhold is determined
by the borrowers participation constraint (25). When plugging in the interest
rate at which the MFI makes zero-profits and solving for φ results in:
φM F IM AX = ξ−1[[λpr(2 − pr) + (1 − λ)ps(2 − ps)][[X − U0/pk]/(2 − pk)]/ρM F I− 1]
(31)
At this point both the participation constraint of borrower k (25) and the zero-profit constraint of the MFI (26) bind. The last constraint which should be
fulfilled is the joint liability constraint (27). This constraint says that the
in-dividual liability and joint liability rate together should not exceed the total
return of the borrower. This constraint determines the maximum interest and
joint liability rate RM F I = X/2. When plugging this rate in the zero-profit
constraint of the MFI (8) we get:
which is the liquidity shock at which the joint liability constraint bind.
Com-bining this with the maximum liquidity shock at which both the borrow and the
MFI make zero profits, the maximum liquidity shock a MFI wants to withhold is:
φ = min( eφM F I, φM F IM AX, φM F IJ LC) (33) The threshold level for withholding a liquidity shocks is determined by three
aspects: 1.) the trade-off between refinancing and non-refinancing ( eφM F I), 2.) the participation constraint of the borrower (φM F IM AX) and 3.) the return of the project which determines the maximum interest rate which an MFI could charge (φM F IJ LC). For the rest of the section we assume that the participation constraint of the borrowers and the joint liability constraint do not bind. Therefore the
refinancing threshold is eφM F I.
Lemma 4 For a liquidity shock φ ∈ (psX/ρM F I, prX/ρM F I), the optimal
re-financing decision of the MFI results in two inefficiencies: it liquidates either
safe borrowers too early or continues inefficient risky borrowers.
Proof. Recall that the maximum liquidity shock a social planner wants two
whithold in case of perfect information is φSPk = pkX/ρM F I for k = r, s. The
refinancing threshold takes always a value between the optimal threshold for safe
borrowers and the optimal threshold for risky borrowers φSPr = prX/ρM F I ≤
[λpr + (1 − λ)ps]X/ρM F I ≤ φ SP
s = psX/ρM F I. When the liquidity shock
is smaller or equal to this threshold level, it is ease to see that the MFI now
inefficiently continues risky projects. When the magnitude of the liquidity shock
exceeds the threshold level slightly, the MFI inefficiently liquidates safe projects. The MFI liquidates all projects, while it is efficient to refinance good projects up
to a liquidity shock of size psX/ρM F I. Here we assume that refinancing always
results in a positive NPV.
5.3
Competition between MFI and Moneylender
In this section we analyse the competition between the MFI and the
• date 0: The MFI offers a joint liability contract (RM F I, CM F I) and
de-termines the amount of the liquidity shock which it wants to refinance φM F I
• date 1: The liquidity shock φ occurs to ξ of the borrowers. Borrowers who could not finance their liquidity shock with φM F I go to the
moneylen-der for emergency finance. The moneylenmoneylen-der offers them (RM L k , φM Lk ).
Borrowers decide whether they want to obtain an emergency loan from
the moneylender. Borrowers which are able to reinvest φ continue their
project, other project are liquidated.
• date 2: Returns of the projects are realized.
When the liquidity shock is realized, the moneylender could now offer
emer-gency finance and finance the liquidity shock. When the moneylender offers an
emergency loan, he extract all the surplus, up to the reservation utility, from
the borrower. The moneylender could discriminate between risky and safe
bor-rowers and is willingly to give safe borbor-rowers more liquidity. The MFI could
anticipate on the presence of a moneylender by partly financing the liquidity
shock at such a level that the moneylender is only willing to refinance the safe
borrowers. This resolves the problem of inefficient continuation and liquidation
of risky an safe borrowers. In the previous two subsections the moneylender
and the MFI both insured the borrowers ex ante against idiosyncratic shocks. In the case of the MFI, the MFI charged a higher interest rate (compare for
example the interest rate in lemma 2 and (28)) to cover the expenses on the
liquidity shock. When the moneylender and MFI compete, the MFI functions
still as an insurance mechanism, because the cost of refinancing safe borrowers
is spread over all borrowers. The moneylender acts as a screening device, since
he only refinances safe borrowers hit by a liquidity shock. We show for which
parameters partly refinancing borrowers improves social welfare and borrowers’
We firstly analyse the behaviour of the moneylender after the realization of
the liquidity shock φ. We assume that the MFI partly finances the liquidity
shock with the amount 0 ≤ φM F I ≤ φ and determine the additional amount which the moneylender is willing to refinance. If the moneylender partly
refi-nances the liquidity shock he maximizes his profits according to the following
programme: max RM L k prRM Lr − φ M LρM L (34) subject to: pkX − pk[(2 − pk)RM F I+ RM L] ≥ U0, k = r, s (35) pkRM Lk − φM LρM L≥ 0, k = r, s, (36)
where φM L is the amount which the moneylender finances at the intermediate date, which is the difference between the magnitude of the liquidity shock and
the amount which MFI wants to finance φM L= φ − φM F I. The borrower’s par-ticipation constraint (35) tells that a borrower only participates if his expected return minus his expected payment to the MFI and his expected payment to the
moneylender exceeds his reservation utility. The moneylender extracts all the
surplus from the borrower. Constraint (35) binds and the profit maximizing
in-terest rate becomes:RM L
k = X − (2 − pk)RM F I− U0/pk. The maximum amount
which a moneylender wants to finance is obtained by plugging in the previously
determined interest in the participation constraint of the moneylender (36):
φM Lk = [pk(X − (2 − pk)RM F I− U0/pk)]/ρM L, k = r, s (37)
We assume in the rest of this section that the maximum liquidity shock which the moneylender wants to refinance is greater than zero φM Lk > 0.
Lemma 5 The moneylender is always willing to provide more liquidity to safe
borrowers than risky borrowers: φM Ls > φM Lr .
Proof. We have to show that φM Ls > φM Lr :[psps(X − RM F I) + ps(1 − ps)(X −
2RM F I)] > [p
rpr(X − RM F I) + pr(1 − pr)(X − 2RM F I)] Firstly note that X −
