humanOrg Working Papers
Série Organisations
Positive vs Negative Incentives for Loan
Repayment in Microfinance : a Game Theory
Approach
Thomas Brihaye, Julie De Pril, Marc Labie
& Anaïs Périlleux
humanOrg Working Paper : 2014/05
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POSITIVE VS NEGATIVE INCENTIVES FOR LOAN REPAYMENT
IN MICROFINANCE: A GAME THEORY APPROACH
THOMAS BRIHAYE1 , JULIE DE PRIL2,∗ , MARC LABIE3 , AND ANAÏS PÉRILLEUX4
1
UMONS-complexys, Belgium – [email protected]
UMONS-CERMi-complexys, Belgium – [email protected]
3
UMONS-CERMi-humanOrg, Belgium – [email protected]
4
UCL-CIRTES-IRES-CERMi, Belgium – [email protected]
2
Key words: microfinance, incentives, game theory.
JEL: C7, G21, O16.
Abstract. Over the last 30 years or so, microfinance – the provision of financial services to people previously
excluded from formal financial institutions – has developed tremendously. However, looking at financial
intermediation at world level, there is still a large unmet demand, and innovations remain needed in order
to face the mismatch existing between financial supply and demand. In most of the methodologies used so
far in microfinance, negative incentives are predominant. This paper tries to understand whether or not the
microfinance industry could benefit from focusing more on positive incentives. More precisely, it compares
two different incentives – a positive one as a bonus and a negative one as a sanction – to encourage loan
repayments. In order to do so, we model, via game theory, the interactions between a borrower and a
microfinance institution in the case where the bonus scheme or the sanction scheme is implemented. Our
game model shows that clients are more likely to repay their loans (on time) in the positive incentive scheme
than in the negative one, therefore questioning the predominance of negative incentives in the industry.
1. Introduction
Four decades ago, economists started to confront the concept of informal economy, which led them to study
informal markets, including informal financial markets. Looking at older practices inherited from informal
markets and from previous, rather old institutions (like cooperatives), some actors designed new ways of
attending the financial needs of excluded populations through what is now known as microfinance institutions
(MFIs). A huge variety of schemes and institutions was established all around the world: village banking,
cooperatives, NGOs, non banking financial institutions, and even made-up banks were created in order to
deliver microfinance services. Asia got the biggest share (by number of clients), Africa got most of the huge
cooperatives networks, and Latin America focused on NGO-born commercial microfinance.
From these multiple innovations, some standard practices progressively emerged in microfinance to become
what we now call “mainstream microfinance”. Mainstream microfinance is most of all a question of methodologies applied in order to deliver financial services to financially excluded people. It is made of various common
procedures/rules that make sure that potential microfinance clients are correctly selected, correctly attended,
and that they do respect their commitments (for instance in reimbursing their loans). By applying these
rules and procedures, MFIs now serve over 200 million people around the world (Global Microcredit Summit,
2014)1. At the same time, the number of people who could benefit from higher financial inclusion is estimated
somewhere between 500 million and 2,5 billion people: there is still a long way to go.
∗ Corresponding
author. Address: University of Mons, 20, Place du Parc, 7000, Mons, Belgium.
1 www.globalmicrocreditsummit2011.org/ (visited in December 2012 and February 2013). In 2011, the number of served
clients exceeded 200 million, but in 2012, after a crisis incurred by an important part of the microfinance industry in India, a
decrease of the number of clients has been observed for the first time since many years (the number of clients fell below 200
million) to bounce back to 204 million by the end of 2013.
1
In this paper, we first analyze the features of mainstream microfinance and establish the predominance of
“negative incentives” in present methodologies. To a certain extent, one could think that this is not different
from mainstream finance and banking. However, the difference comes from the bases of the banking contracts
that are being made: in classical banking, loans are attributed first and foremost based on standardized
information (like audited accounts) and on collateral and guarantees that can easily be seized by the bank
should the client not repay his/her loan. Of course relying on collateral is a practice existing in microfinance,
but the key issues are the relationship with customers and the attribution of loans based first and foremost
on the analysis of the profile of the customer as perceived by the credit officer. This means that psychological
relationships do play a higher role. In this context, we discuss to which extent a higher use of “positive
incentives” may actually help stimulating further more mainstream microfinance. Cadena and Schoar (2011)
evaluated the effectiveness of three positive incentives to encourage timely repayments in Uganda. They
found in particular that, compared to the control group, customers who faced positive incentives had a higher
probability (8% more) of repaying all their installments on time. Moreover, on average, their arrears per
month were 2 days shorter. Besides, Peysakhovich (2014) studied different kinds of commitment contracts: he
compared “carrot” contracts (rewards for good behavior) with “stick” contracts (fines for bad behavior) and
showed that, from a welfare point of view, decision-makers strictly prefer to use carrots instead of sticks. In
our case, we use game theory to model and investigate loan repayments in microfinance through two different
mechanisms: the MFI grants a bonus for on-time repayments (positive incentive), or the MFI imposes a
sanction for late repayments (negative incentive). The results we obtain seem coherent with previous findings:
our model shows that positive incentives are a more effective way to encourage on-time repayments than
negative incentives. More attention could therefore be dedicated to positive incentives and to the conditions
in which they should be provided.
The rest of this paper is organized as follows. Section 2 provides an overview of what is mainstream
microfinance and of what it has achieved so far through negative incentives; Section 3 discusses negative and
positive incentives in microfinance; Section 4 reviews incentives modeled in microfinance literature; Section 5
presents and studies our model; finally Section 6 sums up the results we obtained from the model and provides
some concluding remarks.
2. Mainstream Microfinance: an Overview
Some people are denied access to banks and other financial services, not because they do not represent a
potential market, but rather because they are “unbankable” based on the criteria on which traditional banking
relies (Armendáriz & Morduch, 2010; Armendáriz & Labie, 2011).
Combining the research of economists and socio-anthropologists, we can attribute this exclusion to three
fundamental reasons. The first reason is sociological “misalignments” (Beck & Demirgüç-Kunt, 2008): poor
people and bank employees do not belong to the same “world” and have a hard time communicating and
interacting with each other. It is not just a question of “the bad banker” against “the gentle poor”, but rather
a question of each being a “stranger” for the other, in the way they speak, in the way they dress, and most
of all in the way they deal with financial and administrative work, the bankers’ “jargon” being meaningless to
most. All this results in a situation where traditional bank employees often tend to view “poor people” as a
waste of time and energy and as a source of unnecessary troubles. On their side, “poor people” are also quite
reluctant to work with employees of traditional banks (Bertrand et al., 2004): the appearance of their office,
the way they dress and talk, the fact that they always seem in too much a hurry to clarify the doubts and
questions the poor may have. . . All this is considered rather suspicious by the poor.
A second reason why regular banks and poor customers often part ways is linked to transaction costs (Beck
& Demirgüç-Kunt, 2008; Johnston & Morduch, 2008). Regular banks usually do not attend to the poorest
people because of the small amounts they usually need. Indeed, attending to people is, to a large extent, a
“fixed cost” (f.i. the amount of employee time needed to attend a 100 USD loan is not so different from that
needed to attend a 1,000 USD loan.); so, relatively speaking, granting small loans is much more expensive for
the bank than granting larger loans (but of course this is not a purely linear function as there are obviously
some thresholds in this relation). Therefore, financing “relatively poor customers” is rather less attractive.
However, for the customers themselves, the option of going to a bank may also be considered too expensive
compared to “informal markets providers” (roscas, moneylenders,. . . ), not so much because of the interest
rates (that are almost always much higher on informal markets) but because of the transaction costs they have
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to bear in order to have access to a loan. As an example, imagine a poor customer who needs a 100 USD loan.
In order to get access to this loan, she will typically need to go to the bank three times (to have information,
to apply for the loan with the relevant paperworks, and to collect the money when the loan is granted). She
may also have to spend a day collecting the paperwork needed to open a file at the bank. In addition, each
time, in order to adapt to institutions opening hours, she may have to give up work opportunities. When you
add up traveling costs, administrative costs of all types and loss of incomes (due to the time needed), there
are cases where continuing with informal financial providers may be perfectly rational from a pure economic
point of view, particularly for poor customers usually asking smaller amounts.
The last, but maybe most important reason explaining why banks and excluded customers have a hard
time working together concerns the asymmetries of information (Besley, 1994; Guinnane, 2001). In order to
assess customers, banks usually base their decisions on credit history, on business plans (or past accounts),
and on written documentation and figures that help them have a good overview of the business they intend
to finance, while asking for some rather standardized types of guarantees or collaterals. Financially excluded
customers are usually unable to provide any of these, and traditional banks therefore feel that they are facing
a classical moral hazard/adverse selection problem that logically translates into the disappearance of this
segment (Stiglitz and Weiss, 1981).
Considering those three reasons together, the formal financial (auto) exclusion of many customers from
traditional banking becomes rather understandable (if not logical), even if – economically and socially speaking
– it may of course not be pareto optimal. This explains why the microfinance industry has developped
innovations at three levels: products, guarantees, and most of all procedures.
In terms of products, the innovation is mainly in designing simple products (easy to understand by MFIs
employees and by customers) that could somehow match the clients’ needs (Armendáriz & Labie, 2011).
In terms of guarantees, the innovations are much more diverse, ranging from “solidarity group” (resulting
in peer pressure from the other members of the group in order to make sure that everyone will fulfill their
commitments) (Al-Azzam et al., 2012), to “personal collateral” (from someone saying that he/she would pay if
the client were not assuming his/her duties), and to “consumer products put as collateral”. These guarantees
are clearly much more flexible than what is usually practiced in traditional banking (Bhole & Ogden, 2010;
Giné et al., 2010).
In terms of procedures, the key issue is the establishment of a close relationship between the client and
the credit officer (Conning, 1999). It starts with the analysis of the demand (usually on the client’s premises)
and continues with the credit officer visiting regularly to check if everything is going well (most credit officers
spend part of their working day “on the field”, in the neighborhood where they work). This of course allows
for what is sometimes called “decentralized credit” in the sense that MFI branches are in the neighborhood of
their customers and that credit officers (who are chosen and trained in order to match “the standards of their
customers” and therefore avoid the “stranger effect” previously mentioned) visit customers at home, therefore
resulting normally into lower transaction costs for the customers. Besides, loans are usually adapted to the
customer’s needs, allowing for fast disbursement and a frequent repayment calendar that matches the cash flow
cycle of the financed activities. This regular repayment scheme has a role of both enforcement and control. Jain
and Mansuri (2003) attempted to design the optimality of an installment contract in microfinance. However,
Field and Pande (2008) conducted a randomized study to analyze the impact of repayment frequency on
default in a MFI in Kolkata (India) and found that the repayment schedule does not affect borrowers’ defaults
significantly.
If the customer repays his/her loan well, he/she is then granted the “right” to a higher loan: this is called
“progressive lending” (Egli, 2004). If the customer does not repay well, he/she is not granted any new loan,
and a lot of pressure is put on him/her by the credit officer (who will call and come by often, until the debt is
repaid) as well as by the community (the village chief, the solidarity group, the collateral, etc.). Depending on
the context, this may ultimately translate into social stigmatization, e.g. with people excluded from villages,
or posters denouncing non-repayment glued to the customers’ house. The progressive lending dimension can
be divided in two different incentives: first, there is the non-refinancing threat (cut of credit access); second, if
the client reimburses on time, there is the promise of future loans at better conditions. Indeed, MFIs’ clients
generally have access to bigger loans with more flexibility over time. Due to this second aspect, Vogelgesang
(2003) stresses that incentives to repay are exponential: clients do not want to loose the better position that
they have acquired over time.
3
Based on all the “innovations” we just mentioned, when we try to sum up the reasons why microfinance has
been quite successful, we can choose from two different perspectives. For some, microfinance is a wonderful
way to finance excluded people by providing them with financial services they need through adequate products,
procedures, and guarantees mechanisms. For others, microfinance is only an innovation in the sense that it
has been able to identify key features (different to a large extent from traditional banking) that allow to put
enough pressure on customers before, during, and after a loan is given to them, so that, on average, they
tend to reimburse well, therefore ultimately resulting into the creation of a new “niche” for financial markets.
These two perspectives are somehow complementary. But we have to recognize that, thinking it over, we can
see most of these characteristics at least partly as means of pressure, therefore making microfinance closer to
traditional banking than most would expect. In a way, the stick (pressure) is therefore predominant compared
to the carrot (adaptation of the product). In Table 1, we summarized most of the abovementioned features
from the point of view of the customer, categorizing them into four categories: “responding to sociological
misalignments”, “responding to economic rationale”, “creating motivation”, “putting pressure”.
Table 1. The perceptions that MFI customers have of mainstream microfinance features.
Justification
Responses to
Responses to
sociological
economic
misalignments
rationale
Products
Cashflow-based
Simple
Small amounts
Guarantees
Solidarity group (and autoselection)
Collateral (people)
Collateral (goods that the client
value)
Procedures
Decentralized services (geographically and culturally)
Non-refinancing threat
Progressive lending (bigger loans
over time)
Credit officer follow-up
Social stigmatization
×
×
×
Logic of Action
Creating
Putting
motivation
pressure
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
Source: authors’ presentation.
Microfinance has succeeded (to some extent) because it has been able to develop a business model that
addresses the traditional shortcomings of classical financial intermediation thanks to a methodology largely
inspired from informal markets practices. Its success relies on three fundamental items: screening its customers well (through social pressure – group forming, collateral search,. . . ), offering them simple products
that reasonably match their needs but in a very standardized way, and, last but not least, being able to come
up with a huge diversity of social pressure means that guarantees that most people will indeed repay their
loans. Thanks to these elements, an industry was born, and it has since experienced a tremendous growth.
According to the Microcredit Campaign, in December 2010, the microfinance sector included 3,652 microfinance institutions serving more than two hundred millions clients (205,314,502). Even if a small decrease has
been observed in 2012 (see footnote 1), undoubtedly, a lot has been accomplished. But at the same time, there
are more and more debates about the microfinance industry. First, because the expected results of the industry
were originally largely overstated by some and, therefore, when rigorous analysis became available (notably
4
through Randomized Control Tests), it became clear that microfinance is much more of a consumer smoothing
and shock resisting mechanism than it is a true assets building one (Karlan & Zinman, 2011; Duvendack et
al., 2011; Banerjee et al., 2013). Using Amartya Sen’s approach, one could say that, by increasing the potential choices of excluded people, microfinance improves their situation but without really getting them out of
poverty (Sen, 1999). So, the largely shared point of view of many authors today seem to be that microfinance
certainly has a role to play in fighting poverty (after all, having a fair access to good financial services remains
a challenge for most of the world population), but it is by no means a magic bullet. The second reason is
that microfinance started with a wonderful promise, which has proved right on some occasions but has been
neglected on many other, i.e. the development of a double bottom line industry that would simultaneously
be able to reach reasonable financial objectives while achieving social goals. This feature is probably what
has made microfinance so attractive to the international community: microfinance can do good and still make
some money that will allow for its own development. Of all the MFIs institutions that have developed around
the world, some “world-class institutions” have clearly shown that this is possible. But, at the same time,
many have failed to do so, and in many cases, commercial priorities have taken over social ones, therefore
resulting in what is commonly called “a mission drift” in the literature, even if this concept may deserve a
deeper discussion as shown by some authors (Armendáriz & Szafarz, 2011). The third reason why there are
more debates about microfinance is due to (anecdotal) evidence that, in some cases, the pressure put by MFIs
is so strong and well-structured that indeed microfinance customers do repay their loans but only by getting
other debts from other sources (family, informal markets, etc.), sometimes resulting in even more problematic situations in terms of their well-being (Fouillet et al., 2007). As an example of this, some studies have
shown that the concept of over-indebtedness itself should be reconsidered, as “estimations of it through loan
delinquency” may actually underestimate it quite largely (Schicks, 2013a). In this paper, we focus on this last
element and try to see to which extent microfinance development could be maintained or even improved by
putting more emphasis on positive incentives rather than on negatives one (as illustrated in Table 1). Indeed,
so far standardized microfinance is clearly dominating the field. However, some recent works show that a
higher level of flexibility is possible and could certainly benefit to microfinance customers (Laureti, 2014),
therefore opening the way for further discussion on how to better balance positive and negative incentives in
order to improve product design in microfinance. The next section of this paper focuses on this issue.
3. Positive vs Negative Incentives
We suggest defining negative incentives as “threats of sanction” and positive incentives as “promises of bonus”.
In some cases, both may co-exist. For instance, having decentralized services very close to the customers can
be seen as a promise of being considered as a real customer, able to develop a true dialogue with his/her
financial institution and benefiting besides from some direct advices when the credit officer comes around.
However, the very same set of procedures can be perceived as a means of “social control” in order to make sure
that the micro-entrepreneur is indeed well screened, that he/she does what he/she is supposed to do with the
money, and that he/she is putting all the necessary attention to its use in order to guarantee the repayment.
In other cases, the situation is clearer: the promise of a higher loan in case of good repayment of the previous
one is a positive incentive, whereas the threat of not being granted another loan in case of bad repayment in
clearly a negative incentive.
So far, negative incentives seem to be predominant in microfinance. If we consider the three phases of a
loan: before, during, and after, the only time where positive incentives do play a key role is at the end of
the process (notably through the promise of another, larger loan being granted). Before and during the loan
repayment, negative incentives are predominant. Before, through the screening resulting from the guarantees
being asked. Indeed, if those guarantees are usually more flexible than what is current banking practice, they
nevertheless work mainly as a selection process (much more than as a true hedging mechanism): the people
who are “bad risks” will not be able to join a “solidarity group” and may have a hard time finding someone
willing to act as “collateral” to assume his/her debts should he/she not repay. The same goes for selection
through “village chief types of authorities”: outsiders will not get the “buena vista” that gives access to the
village bank mechanism. The situation is the same with “consumer goods” that are taken as collateral. When
stickers are put on fridges or television sets as “put into guarantees for this or that MFI”, the idea is not so
much that if the client does not repay, the MFI will be able to get its money back by selling this appliance. In
fact, in most cases, it will not be able to do so, either because legally taking it will be extremely difficult, or
5
because selling it will almost be impossible; or if it is possible, the amount collected generally will not cover the
overall cost of the loan and of the collecting procedure. The real motivation for the MFI to put those stickers
and take those appliances as collateral is totally different: it is intended to remind the client constantly that if
he/she does not pay, he will loose something he/she cares for. This is clearly a negative incentive, “a threat of
sanction”. During the repayment of the loan, when payment may be late, the “automatic and fast” reaction
in microfinance will be to put pressure, either through the credit officer (who clearly threatens to seize the
collateral and to deny further access to credit if this one is not repaid) or through the collateral themselves
when they are individuals (as a group or not).
So most of the mainstream microfinance methodology is based on negative incentives. But not all of it (as
we have already seen). Indeed, there are some examples where creative, positive incentives have generated
excellent results in term of financial intermediation. As an example, more and more attention is devoted to
studying to which extent a higher flexibility and a better response to customers wishes in product design could
improve microfinance supply (Hamp & Laureti, 2011).
A very famous example comes from Indonesia, i.e. Bank Rakyat Indonesia: it has a very interesting
practice in terms of “charging for its loans”. Indeed, BRI has set up a lending methodology that includes
rebates: borrowers received one quarter of interest payment back if they repay their loans on time and reach
a perfect repayment records over a period of six month. As mentioned by Churchill when comparing different
institutions: “Of the five institutions, BRI’s unit system has the most obvious repayment incentive. The units
actually reimburse clients a portion of the interest that they have already paid. The prompt payment incentive
is built into the repayment schedule. When clients repay their installments on or before their repayment date for
six consecutive months, they are repaid 25 percent of their interest payments for that period. If one repayment
in the six month period is missed or is late, the client forfeits her prompt payment incentive to the bank as a
late payment penalty.
For example, a client who receives a $1,064 loan for one year with monthly installments makes repayments
of $110. After six months of timely repayments, BRI transfers $32 into the client’s saving account. Since most
of BRI’s loan terms are 12 or 24 months, which is long by microlending standards, this serves as an important
short-term repayment motivation. While the next loan may be a year or more away, the repayment incentive
provides a more immediate goal. It is estimated that approximatively 90 percent of the KUPEDES borrowers are
eligible for the incentive in most months, which suggests that it is an effective repayment incentive.” (Churchill,
1999, p.65).
Another interesting example is given by Green Bank in the Philippines for the case of savings. Indeed, for
savings, motivation is known to be based on a few key features, security and availability (for the reason it is
for) being the most important ones: the reason to save in an institution is to have the money in a place where it
will not be that easy to divert it from its original destination. At home, this may turn out to be more difficult
due to “temptations” and “family and friends pressure and demands”. Having understood this, “Green Bank
officials decided that it made sense to offer a commitment savings product. They allow clients to select a
savings goal, either by setting a goal amount or a savings goal date, but restrict their rights to withdraw
their funds until they have reached their pre-specified goal or date” (Ashraf et al., 2010). Another even better
example of how products with attractive (positive) features may meet their market is to be found in the case of
“prize-linked accounts” that provide customers with rights to take part to random prize drawings, based most
of the time on the amount they keep on their accounts. In South Africa, the First National Bank did create
such an account in order to provide a product that may be more popular for low-income people. By doing
so, it was just applying a recipe that has largely been used all around the world, since its first appearance, in
1694 in Britain, as shown by Cole et al. (2008).
Based on the presentation of those challenging examples, a particularly relevant question for the industry is
to know which kind of incentives – positive or negative – used in the methodology it applies to its customers
would be more effective in terms of loan repayment. For positive incentives to get more attention from
mainstream microfinance, they have to reach similar (or better) results than present microfinance practices
at a similar or lower cost. Therefore, a good understanding of what conditions are required for a positive
incentive to be more effective is fundamental if we wish to include them more in microfinance practices. This
issue seems especially important in this period, as microfinance is experimenting more and more cases of
excessive pressures on borrowers for repayment (Schicks, 2013b). In the next sections, we try to contribute to
this objective by reviewing incentives modeled in the microfinance literature (Section 4), and by presenting a
model that helps us identify the potential of positive incentives in microfinance (Section 5).
6
4. Incentives and Model – a Game Theory Approach
Many authors have analyzed clients’ default behaviors and have modeled the incentives schemes used by MFIs
to ensure good repayment. The first models focused on groups lending. Among others, Stiglitz (1990), Ghatak
and Guinnane (1999), and Townsend (2003) modeled the mechanisms at work in the credit group methodology,
which enables to solve moral hazard and adverse selection. Besley (1994) designed a similar model but for small
microfinance cooperatives. All these authors show how group-lending and joint liability create incentives for
the borrowers to select each other (screening process) and monitor each other’s activities. The social pressures
at work within these groups have been strongly underlined by Besley and Coate (1995).
With Grameen II and the increasing use of individual lending in microfinance, some authors started to model
the repayment incentives at work for individual loans. In this type of loans, peer pressure and mutual monitoring do not work anymore. Consequently new types of incentives were created to enforce individual repayment.
The most common type seems to be “non-refinancing threats”. To analyze this specific incentive, Armendáriz
and Morduch (2000) designed, for economies in transition, a two-period model showing the importance for
MFIs to carry out non-refinancing threats. Vogelgesang (2003) created a two-period model, which includes
non-refinancing threats as well as other types of punishments in order to analyze repayment incentives in a
Peruvian MFI. Latter, Tedeschi (2006) questioned the necessity and social impact of non-refinancing threats.
He designed a model with an endogenized default penalty and showed that, in certain cases, the punishment
does not need to be the cut of credit access for the client’s whole life. The period of punishment should be
long enough to avoid any strategic default, but short enough to not over-punish borrowers who default due to
a negative external shock. To design this modelization, Tedeschi used a two-phase structure, in the presence
of default uncertainty.
More recently, Bond and Rai (2009) modeled how the repetitive game between borrowers and an MFI can
be affected by borrowers’ expectation of collective defaults and the resulting destruction of future loans access.
They explain that MFIs tend to respond to the risk of “borrower run” by making their loans more profitable
and/or reducing the repayments required on their loans. Other authors stress that the non-refunding threat is
credible only if the MFI makes no profit to renegotiate the loans or if it has a possibility to pre-commit itself,
a role that the supervising institutions could play (Vogelgesang, 2003).
Apart from the “non-refinancing threat”, other repayment incentives exist and have been modelized such
as the regular repayment schedules or the collateral substitutes (Morduch, 1999). Indeed, Jaina and Mansuri
(2003) designed a model of an optimal installment schedule. Armendáriz and Morduch (2000) created a
simple model that captures all type of negative sanctions (such as loss of reputation, exclusion from the village
community, etc.) through a variable representing additional costs if default. There is also an increasing
literature on incentive at the credit officer (CO) level (Aubert et al., 2009). Models study which kind of
incentives should be put on COs’ salaries to increase clients’ repayment while avoiding mission drift. Finally,
authors, such as Van Tassel (2004), analyzed how incentives for borrowers to repay a loan can be influenced
by household bargaining problems. However, none of these authors investigate the effect of a positive versus
a negative incentive on borrowers’ effort to repay. In this paper, we compare the following two mechanisms:
the MFI grants a bonus for on-time repayments (positive incentive), and the MFI imposes a sanction for late
repayments (negative incentive). At first sight, one might think that these two mechanisms are equivalent,
but, thanks to game theory, we model the fundamental difference between the two and show that clients are
more likely to repay on time in the first case than in the second.
5. Model
In this section, we compare theoretically positive and negative incentives. To this aim, we use a two-player
game to model a situation where a MFI 2 interacts with a potential borrower (whom we call client): the MFI
can grant him/her a loan, or not; if the MFI does so, then the client uses the money for a project and can repay
his/her loan on time, repay it late, or not repay it. In order to compare positive and negative incentives, we
consider three variants of this game: the first variant is the basic one (no bonus or sanction), in the second one,
the client is granted a bonus when repaying on time, and in the last one, the client is imposed a sanction when
repaying late. For each variant, we study optimal strategies for the MFI and the client. Then, we compare the
2We consider MFIs that only provide loans.
7
different conditions for the client to repay on time or late, or not repay in the three variants. This way, we
deduce which kind of incentive is more effective to encourage (on-time) repayments. Note that these incentives
can only affect strategic defaults.
Like Armendáriz and Morduch (2000), we consider a two-period model: the relation between the MFI and
the client ends after at most two consecutive loans (and they both know that).3 Though this is obviously
an oversimplistic assumption, the model enables to show the effectiveness of the incentives in the first loan
period. In the three variants of the model, we also assume that the MFI automatically grants another loan if
the previous one has been repaid (on time or late). Moreover, we include the progressive lending methodology
that is generally used in microfinance: the client will be granted a larger loan if he/she repays the previous
one on time and a similar loan if he/she repays it late. This induces a sort of intrinsic positive incentive for
repaying on time, but it is quite different from the bonus in the sense that it occurs at the next loan period or
may not occur (if the client does not ask for a new loan), whereas the bonus is directly granted at the end of
the current loan.
Figure 1 represents this situation as an extensive-form game. It models the temporal structure of all the
possible interactions between two players: the MFI (which makes choices at square nodes labelled M1 , M2 ,
M3 , and M4 ) and the client (who makes choices at circle nodes labelled C1 , C2 , C3 , and C4 ). The letters
on the arrows linking the nodes symbolize the possible choices that the MFI and the client have. The story
is as follows: the MFI plays first at node M1 and chooses to grant a Loan (action L) or to grant No Loan
(action NL). If the MFI chooses to grant a loan, then the client chooses4 (at node C1 ) to Repay his/her loan
on Time (action TR), to Repay it Late (action LR) or Not to Repay it (action NR).5 If the client repays
his/her loan (on time or late), then the MFI automatically grants a new loan (action L at nodes M2 and M3 ).
Then, the client can repay this new loan on time, repay it late, or not repay it (actions TR, LR, or NR at
nodes C2 and C3 ). If the client does not repay his/her first loan, then the MFI can choose to grant a new
loan or not (actions L or NL at node M4 ). If the MFI grants a new loan, then the client can repay it on time,
repay it late, or not repay it (actions TR, LR, or NR at node C4 ).
M1
L
NL
C1
TR
M3
L
1
2
M4
L
C2
LR
NR
LR
M2
TR
11
L
C3
NR
TR
3
4
LR
NL
C4
NR
5
TR
6
7
LR
8
10
NR
9
Figure 1. Two-period model.
The shaded nodes, which we call “cases”, represent the end of the relationship between the MFI and the
client and correspond to different possible final situations (eleven different situations in this two-period model:
shaded nodes 1 to 11). Depending on the considered case, the MFI and the client get a certain amount, which
3Considering a one-period model is not interesting since the client will not repay his/her loan; except in the bonus scheme, if
the bonus is unreasonably high.
4When we use the word “chooses”, it should be understood as a priori potential paths or possibilities. Of course, in real life,
some clients may be in a situation where they cannot repay a loan while others – committing strategic default – choose not to
repay. Our model consider all options without preconceptions on the issue of the game.
5We will keep these notations in the rest of the paper.
8
we call payoff (term commonly used in game theory, but often named utility in microfinance). For example,
if the MFI grants no loan, their payoffs are both zero. Quite naturally, we assume that both players, the
MFI and the client, want to maximize their own payoff (they always prefer a higher to a lower payoff) and
consequently act accordingly.
If the client repays a loan late, we must distinguish, in the model, the payoffs in this case from those in the
case where he/she repays the loan on time. In fact, if the client repays the loan late, he/she somehow gets a
late repayment gain, and the MFI has a late repayment cost. In order to determine the payoffs in all cases, we
introduce some notations in Table 2. Remark that we do not fix a priori a maximal value for the bonus or the
sanction, because we do not want to restrict our model precisely on the key point we study. Nevertheless, we
show further that the bonus or the sanction does not have to be high for the client to repay on time. Besides,
the gain for late repayment is influenced by the fact that the client’s default can be considered strategic or
not.
Table 2. Notations.
A1
A2
λI
λI Ai
(1 + λI )Ai
λP Ai
αm
αc
B
S
the amount borrowed by the client for the first loan, and also the amount borrowed by the client
for the second loan if the first loan has not been repaid on time (A1 > 0).
the amount borrowed by the client for the second loan if the first loan has been repaid on time
(A2 > A1 ).
the interest rate (0 < λI < 1).
the interests to repay for the borrowed amount Ai , i = 1, 2 (λI Ai > 0).
the total amount to repay by the client for the borrowed amount Ai , i = 1, 2 ((1 + λI )Ai > 0).
the gross income of the client’s project for the borrowed amount Ai , i = 1, 2 (λP ≥ 0).
the late repayment cost for the MFI (0 < αm < (1 + λI )A1 ).
the late repayment gain for the client (0 < αc < (1 + λI )A1 ).
the bonus offered by the MFI when the client repays the loan on time (positive incentive) (B > 0).
the sanction demanded by the MFI when the client repays the loan late (negative incentive) (S > 0).
We study three variants of the two-period model of Figure 1: the basic variant, denoted by M0 ; the variant
where the MFI uses a positive incentive as a bonus B, denoted by MB ; and finally, the variant where the MFI
uses a negative incentive as a sanction S, denoted by MS . Notice that we could have considered the variant
where both a positive and a negative incentive are used. However, we prefer to discuss them separately in
order to stress the differences.
According to the notations of Table 2, in the basic variant, if the MFI grants the client a loan A1 and the
client repays it on time, then the MFI gets the interests
λ I A1 ,
while the client gets his/her project income minus the amount he/she repays, i.e.
λP A1 − (1 + λI )A1 .
If the MFI grants the client a loan A1 and the client repays it late, then the MFI gets the interests minus the
late repayment cost, i.e.
λI A1 − αm ,
while the client gets λP A1 − (1 + λI )A1 plus the late repayment gain, i.e.
λP A1 − (1 + λI )A1 + αc .
As already mentioned, the value of the late repayment gain αc for the client depends on the strategic dimension
of the default. Indeed, if the default is not strategic – meaning that the client’s project has not yet generated
the cash flows needed to repay the loan – then αc can potentially be very high: waiting some days or weeks
could be enough to obtain the cash flows to reimburse the loan. But, if the default is strategic, αc will depend
on the level of returns that can be obtained in the meantime through alternative uses.
9
If the MFI grants the client a loan A1 and the client does not repay it, then the MFI loses the borrowed
amount, i.e. gets
−A1 , 6
while the client gets his/her project income
λ P A1 .
If the MFI does not grant a loan to the client, then they both get 0.
In the case where the MFI uses a positive incentive and gives a bonus B to the client when he/she repays
on time, then the MFI gets
λ I A1 − B
and the client gets
λP A1 − (1 + λI )A1 + B.
On the other hand, if the MFI uses a negative incentive and requires a sanction S to the client when he/she
repays late, then the MFI gets
λI A1 − αm + S
and the client gets
λP A1 − (1 + λI )A1 + αc − S
in this case.
We have described the possible payoffs of the MFI and the client after the first loan. In order to give their
payoffs after the (possible) second loan, we use a discount factor 0 < δ < 1 to model the fact that the money
we get tomorrow has less value than the money we have today. If one gets a certain amount x1 (resp. x2 ) after
the first period (resp. second period) of loan, then we say that one gets x1 + δx2 (since x2 will be received
later than x1 ). For example, case 1, corresponding to the shaded node 1 of Figure 1, represents the situation
where the MFI grants the client two loans that he/she both repays on time. In the basic variant, this implies
that the MFI gets
λI A1 + δλI A2
and the client
λP A1 − (1 + λI )A1
δ(λP A2 − (1 + λI )A2 ),
+
where A2 > A1 (progressive lending). In the same way, case 2, corresponding to the shaded node 2, refers to
the case where the MFI grants two loans to the client, and he/she repays the first on time, but repays the
second late. Then, in the basic variant, the MFI gets
λ I A1
+
δ(λI A2 − αm )
λP A1 − (1 + λI )A1
+
δ(λP A2 − (1 + λI )A2 + αc ),
and the client gets
where A2 > A1 . All payoffs for the MFI and the client in the basic variant, the variant with a positive incentive
and the variant with a negative incentive are listed in Tables 3, 4 and 5, respectively.
In order to study the three different variants, we apply backward induction 7 on each game to obtain the
possible subgame perfect equilibria. This process starts at the end of the game (nodes C2 , C3 and C4 ) and
goes back up to the top (node M1 ) in order to determine optimal strategies for the players. The idea is that
at each step, the player in question chooses the action(s) that maximizes his/her payoff, given the reasonable
choices made by him/her or the other player on the previous steps.
In the sequel, we first analyze each variant of the model separately, and then we compare them with each
other.
Basic variant M0 : backward induction.
Table 3 lists the payoffs of the MFI and the client for all cases in the basic variant of the model.
6We have made the conservative choice of only considering the loss of capital in this case; an alternative would have been to
also include the interests. However, this would not have modified the results of the model analysis.
7See, for example, Osborne and Rubinstein, 1994.
10
Table 3. Payoffs in the basic variant M0 (2 periods).
M0
Cases
MFI
Client
1
2
3
4
5
6
7
8
9
10
11
λI A1 + δλI A2
λI A1 + δ(λI A2 − αm )
λI A1 + δ(−A2 )
λI A1 − αm + δλI A1
λI A1 − αm + δ(λI A1 − αm )
λI A1 − αm + δ(−A1 )
−A1 + δλI A1
−A1 + δ(λI A1 − αm )
−A1 + δ(−A1 )
−A1
0
λP A1 − (1 + λI )A1 + δ(λP A2 − (1 + λI )A2 )
λP A1 − (1 + λI )A1 + δ(λP A2 − (1 + λI )A2 + αc )
λP A1 − (1 + λI )A1 + δλP A2
λP A1 − (1 + λI )A1 + αc + δ(λP A1 − (1 + λI )A1 )
λP A1 −(1+λI )A1 +αc +δ(λP A1 −(1+λI )A1 +αc )
λP A1 − (1 + λI )A1 + αc + δλP A1
λP A1 + δ(λP A1 − (1 + λI )A1 )
λP A1 + δ(λP A1 − (1 + λI )A1 + αc )
λP A1 + δλP A1
λP A1
0
We first consider node C2 (see Figure 1). While comparing the client’s payoffs in cases 1, 2, and 3 (see
Table 3), the client prefers his/her payoff in case 3 since
−(1 + λI )A2 < 0
and
αc < (1 + λI )A2 .
Then, he/she chooses action NR in node C2 , that is, he/she does not repay his/her second loan. With the
same reasoning, the client also chooses action NR in nodes C3 and C4 .8 Therefore, cases 1-2-4-5-7-8 are not
plausible from the client’s point of view. Then, we go back up and we consider node M4 .9 The MFI compares
its payoffs in cases 9 (according to the previous rational choice of the client) and 10. As δ(−A1 ) < 0, case 9
is not plausible from the MFI’s point of view, i.e. the MFI chooses action NL in node M4 (the MFI does not
grant a second loan). Consequently, the client compares his/her payoffs in cases 3, 6, and 10 in order to make
a choice in node C1 . According to the values of the variables, we consider three possible situations:
• Situation 1: the client’s payoff is greater in case 10 than in cases 3 and 6, i.e. it is greater when he/she
does not repay his/her first loan than when he/she repays it late or on time. Formally, it happens when
λP A1 − (1 + λI )A1 + δλP A2 < λP A1
and λP A1 − (1 + λI )A1 + αc + δλP A1 < λP A1 ,
which means that
δλP A2 < (1 + λI )A1
and αc < (1 + λI )A1 − δλP A1
(1)
(the return of the second loan and the late repayment gain αc are too low). Then the client prefers not
to repay his/her first loan (action NR in node C1 ). Then, the MFI chooses not to grant the first loan
(action NL in node M1 ) since −A1 < 0 (see the MFI’s payoffs in cases 10 and 11). Consequently, the
outcome of the equilibrium given by backward induction is case 11: no contract – no loan provided.
• Situation 2: the client’s payoff is greater in case 6 than in cases 3 and 10, i.e. it is greater when
he/she repays his/her first loan late than when he/she does not repay it or repays it on time. Formally,
it happens when
αc + δλP A1 > δλP A2
and
− (1 + λI )A1 + αc + δλP A1 > 0,
which means that
αc > δ(λP A2 − λP A1 )
and αc > (1 + λI )A1 − δλP A1
(2)
(the late repayment gain αc is high enough). Then the client chooses to repay his/her first loan late
(action LR in node C1 ). The MFI thus compares its payoffs in cases 6 and 11. If
λI A1 − αm − δA1 > 0, which means that λI A1 > αm + δA1
8This is understandable since the client knows that his/her relation with the MFI ends after the second loan, so he/she has
no reason to repay it.
9Note that there is no need to consider nodes M and M since the MFI automatically grants a new loan if the first one has
2
3
been repaid (the MFI has no action to choose in these nodes).
11
(the interest rate is high enough), then the MFI accepts to grant the first loan (action L in node M1 ),
and case 6 is the outcome of an equilibrium. Otherwise, the MFI refuses to grant the first loan
(action NL in node M1 ), and we end up with case 11.
• Situation 3: the client’s payoff is greater in case 3 than in cases 6 and 10, i.e. it is greater when
he/she repays his/her first loan on time than when he/she does not repay it or repays it late. Formally,
it happens when
δλP A2 > αc + δλP A1
− (1 + λI )A1 + δλP A2 > 0,
and
i.e.
δ(λP A2 − λP A1 ) > αc and δλP A2 > (1 + λI )A1
(3)
(the return of the second loan is high enough). The first condition means that the gain for the client
to get a larger second loan is higher than the late repayment gain (the increase of the second loan
compensates for the late repayment gain). In other words, the progressive lending incentive is high
enough to motivate the client to repay on time. According to the two conditions above, the client
chooses to repay his/her first loan on time (action TR in node C1 ). The MFI thus compares its
payoffs in nodes 3 and 11. If
λI A1 − δA2 > 0, which means that λI A1 > δA2
(the interest rate is high enough), then the MFI accepts to grant the first loan (action L in node M1 ),
and case 3 is the outcome of an equilibrium. Otherwise, the MFI refuses to grant the first loan
(action NL in node M1 ), which leads to case 11.
To summarize, in the two-period basic variant, the client will have a relatively low incentive to repay his/her
first loan on time: the increase of the second loan should be high enough to motivate the client to repay on
time. However, since the MFI knows that the client will not repay his/her second loan, it will be reluctant to
allocate a larger loan in the second period. More generally, we can stress that if the client knows when his/her
relationship with the MFI ends, then there are chances that he/she does not assume his/her final commitment.
A good example of this is when a MFI cannot secure liquidity and is therefore not able to provide future loans
to its clients. In that case, it has been observed that even good clients will tend to default on their present
loan (Bond and Rai, 2009; Austin et al., 1998).
Variant MB with a positive incentive: backward induction.
Table 4 lists the payoffs of the MFI and the client for all cases in the variant of the model where a bonus is
given by the MFI when the client repays on time.
Table 4. Payoffs in variant MB (2 periods/positive incentive).
MB
Cases
MFI
Client
1
2
3
4
5
6
7
8
9
10
11
λI A1 − B + δ(λI A2 − B)
λI A1 − B + δ(λI A2 − αm )
λI A1 − B + δ(−A2 )
λI A1 − αm + δ(λI A1 − B)
λI A1 − αm + δ(λI A1 − αm )
λI A1 − αm + δ(−A1 )
−A1 + δ(λI A1 − B)
−A1 + δ(λI A1 − αm )
−A1 + δ(−A1 )
−A1
0
λP A1 − (1 + λI )A1 + B + δ(λP A2 − (1 + λI )A2 + B)
λP A1 −(1+λI )A1 +B +δ(λP A2 −(1+λI )A2 +αc )
λP A1 − (1 + λI )A1 + B + δλP A2
λP A1 −(1+λI )A1 +αc +δ(λP A1 −(1+λI )A1 +B)
λP A1 −(1+λI )A1 +αc +δ(λP A1 −(1+λI )A1 +αc )
λP A1 − (1 + λI )A1 + αc + δλP A1
λP A1 + δ(λP A1 − (1 + λI )A1 + B)
λP A1 + δ(λP A1 − (1 + λI )A1 + αc )
λP A1 + δλP A1
λP A1
0
According to the same arguments as in the basic variant, the client always prefers not to repay his/her
second loan, i.e. chooses action NR in nodes C2 , C3 , and C4 (see the client’s payoffs in cases 1,. . . ,9 in
Table 4). In node M4 , the MFI does not grant a second loan as the client will not reimburse it, i.e. the MFI
12
chooses action NL (case 9 is not possible). In node C1 , the client then compares his/her payoffs for cases 3, 6,
and 10. According to the values of the variables, we consider the three possible situations:
• Situation 1: the client’s payoff is greater in case 10 than in cases 3 and 6, i.e. it is greater when he/she
does not repay his/her first loan than when he/she repays it late or on time. Formally, it happens when
λP A1 − (1 + λI )A1 + B + δλP A2 < λP A1
and λP A1 − (1 + λI )A1 + αc + δλP A1 < λP A1 ,
which means that
B < (1 + λI )A1 − δλP A2
and αc < (1 + λI )A1 − δλP A1
(4)
(the bonus B and the late repayment gain αc are too low). Then the client prefers not to repay
his/her first loan (action NR in node C1 ). It follows that the MFI chooses not to grant the first loan
(action NL in node M1 ) since −A1 < 0 (see the MFI’s payoffs in cases 10 and 11). Consequently, the
outcome of the equilibrium is case 11: no contract – no loan provided.
• Situation 2: the client’s payoff is greater in case 6 than in cases 3 and 10, i.e. it is greater when
he/she repays his/her first loan late than when he/she does not repay it or repays it on time. Formally,
it happens when
αc + δλP A1 > B + δλP A2
− (1 + λI )A1 + αc + δλP A1 > 0,
and
which means that
αc > B + δ(λP A2 − λP A1 )
and αc > (1 + λI )A1 − δλP A1
(5)
(the late repayment gain αc is high enough). Then the client chooses to repay his/her first loan late
(action LR in node C1 ). The MFI thus compares its payoffs in cases 6 and 11. If
λI A1 − αm − δA1 > 0, which means that λI A1 > αm + δA1
(the interest rate is high enough), then the MFI accepts to grant the first loan (action L in node M1 ),
and case 6 is the outcome of an equilibrium. Otherwise, the MFI refuses to grant the first loan
(action NL in node M1 ), and we end up with case 11.
• Situation 3: the client’s payoff is greater in case 3 than in cases 6 and 10, i.e. it is greater when
he/she repays his/her first loan on time than when he/she does not repay it or repays it late. Formally,
it happens when
B + δλP A2 > αc + δλP A1
− (1 + λI )A1 + B + δλP A2 > 0,
and
which means that
B > αc + δ(λP A1 − λP A2 )
and B > (1 + λI )A1 − δλP A2
(6)
(the bonus B is high enough). Then the client chooses to repay his/her first loan on time (action TR
in node C1 ). The MFI thus compares its payoffs in cases 3 and 11. If
λI A1 − B − δA2 > 0, which means that λI A1 > B + δA2
(the interest rate is high enough), then the MFI accepts to grant the first loan (action L in node M1 ),
and case 3 is the outcome of an equilibrium. Otherwise, the MFI refuses to grant the first loan
(action NL in node M1 ), which leads to case 11.
In summary, when the MFI gives a bonus high enough, it increases the incentive for the client to repay
his/her first loan on time. The equilibrium with case 3 as outcome is more likely to occur in this variant than
in the basic one. Indeed, we obtain this equilibrium if
B > αc + δ(λP A1 − λP A2 )
and B > (1 + λI )A1 − δλP A2 .
10
This result is not difficult to reach if the second loan has a good return (such as the return of the first loan
when the client is able to repay his/her loan) and if the discount factor is not too low. It means that the client
gives a relatively high value to the future:
(1 + λI )A1 ≈ δλP A2 .
10Notice that δ(λ A − λ A ) < 0 as A > A .
2
1
P 1
P 2
13
However, in a model with only two periods, the interest rate has to be high enough to motivate the MFI
to lend to the client. Indeed, the MFI knows that the client will not repay the second loan. Consequently,
the interest rate obtained on the first loan has to compensate for the losses supported on the second loan.
Situation 3 shows that:
λI A1 > B + δA2
for the MFI to agree to provide the loans. This condition is very strong if the discount factor is high.
So, the bonus does not need to be high to motivate the client to repay the first loan on time (if the second
loan has a good return and if the discount factor is not too low), but the high interest rate needed for the MFI
to agree to lend to the client can prevent the lending relationship to occur.
Variant MS with a negative incentive: backward induction.
Table 5 lists the payoffs of the MFI and the client for all cases in the variant of the model where a sanction is
imposed by the MFI when the client repays late.
Table 5. Payoffs in variant MS (2 periods/negative incentive).
MS
Cases
MFI
Client
1
2
3
4
5
λI A1 + δλI A2
λI A1 + δ(λI A2 − αm + S)
λI A1 + δ(−A2 )
λI A1 − αm + S + δλI A1
λI A1 − αm + S + δ(λI A1 − αm + S)
6
7
8
9
10
11
λI A1 − αm + S + δ(−A1 )
−A1 + δλI A1
−A1 + δ(λI A1 − αm + S)
−A1 + δ(−A1 )
−A1
0
λP A1 − (1 + λI )A1 + δ(λP A2 − (1 + λI )A2 )
λP A1 − (1 + λI )A1 + δ(λP A2 − (1 + λI )A2 + αc − S)
λP A1 − (1 + λI )A1 + δλP A2
λP A1 − (1 + λI )A1 + αc − S + δ(λP A1 − (1 + λI )A1 )
λP A1 − (1 + λI )A1 + αc − S + δ(λP A1 − (1 +
λI )A1 + αc − S)
λP A1 − (1 + λI )A1 + αc − S + δλP A1
λP A1 + δ(λP A1 − (1 + λI )A1 )
λP A1 + δ(λP A1 − (1 + λI )A1 + αc − S)
λP A1 + δλP A1
λP A1
0
According to the same arguments as in the basic variant, the client always prefers not to repay his/her
second loan, i.e. chooses action NR in nodes C2 , C3 , and C4 (see the client’s payoffs in cases 1,. . . ,9 in
Table 5). This implies that in node M4 , the MFI prefers not to grant a second loan (action NL), since when
looking at its payoffs in cases 9 and 10, we have that
−A1 > −A1 + δ(−A1 ).
The client then compares his/her payoffs in cases 3, 6, and 10. Like for the variant with a positive incentive,
we consider the three possible situations according to the values of the variables:
• Situation 1: the client’s payoff is greater in case 10 than in cases 3 and 6, i.e. it is greater when he/she
does not repay his/her first loan than when he/she repays it late or on time. Formally, it happens when
λP A1 − (1 + λI )A1 + δλP A2 < λP A1
and λP A1 − (1 + λI )A1 + αc − S + δλP A1 < λP A1 ,
which means that
δλP A2 < (1 + λI )A1
and αc < (1 + λI )A1 + S − δλP A1
(7)
(the discounted gross income of the project and the late repayment gain αc are too low). Then the
client prefers not to repay his/her first loan (action NR in node C1 ). It follows that the MFI chooses
not to grant the first loan (action NL in node M1 ) since −A1 < 0 (see the MFI’s payoffs in cases 10
and 11). Consequently, the outcome of the equilibrium is case 11: no contract.
14
• Situation 2: the client’s payoff is greater in case 6 than in cases 3 and 10, i.e. it is greater when
he/she repays his/her first loan late than when he/she does not repay it or repays it on time. Formally,
it happens when
αc − S + δλP A1 > δλP A2
− (1 + λI )A1 + αc − S + δλP A1 > 0,
and
which means that
αc > S + δ(λP A2 − λP A1 )
and αc > (1 + λI )A1 + S − δλP A1
(8)
(the late repayment gain αc is high enough). Then the client chooses to repay his/her first loan late
(action LR in node C1 ). According to this choice, the MFI thus compares its payoffs in cases 6 and 11.
If
λI A1 − αm + S − δA1 > 0, which means that λI A1 > αm − S + δA1
(the interest rate is high enough), then the MFI accepts to grant the first loan (action L in node M1 ),
and case 6 is the outcome of an equilibrium. Otherwise, we end up with case 11: the MFI refuses to
grant the first loan (action NL in node M1 ).
• Situation 3: the client’s payoff is greater in case 3 than in cases 6 and 10, i.e. it is greater when
he/she repays his/her first loan on time than when he/she does not repay it or repays it late. Formally,
it happens when
δλP A2 > αc − S + δλP A1
and
− (1 + λI )A1 + δλP A2 > 0,
which means that
S > αc + δ(λP A1 − λP A2 )
and δλP A2 > (1 + λI )A1
(9)
(the sanction S and the discounted gross income of the project are high enough). Then the client
chooses to repay his/her first loan on time (action TR in node C1 ). The MFI thus compares its
payoffs in cases 3 and 11. If
λI A1 − δA2 > 0, which means that λI A1 > δA2
(the interest rate is high enough), then the MFI accepts to grant the first loan (action L in node M1 ),
and case 3 is the outcome of an equilibrium. Otherwise, the MFI refuses to grant the first loan
(action NL in node M1 ), which leads to case 11.
In summary, when the MFI applies a sanction, the client is more motivated to repay his/her first loan on
time. As in the variant with a positive incentive, the equilibrium with case 3 as outcome is more likely to
occur in this variant than in the basic one. Indeed, we obtain this equilibrium if
S > αc + δ(λP A1 − λP A2 )
and δλP A2 > (1 + λI )A1 .
As in the positive incentive variant, this result is not difficult to reach if the second loan has a good return
and if the discount factor is not too low. In this case, the interest rate does not need to be as high as in the
positive incentive variant to motivate the MFI to lend to the client, here it suffices that
λI A1 > δA2 .
Comparison between the variants M0 , MB , and MS .
Let us now proceed to a more systematic comparison between the variants M0 , MB , and MS from the point
of view of repayment of the first loan.
(1) The client chooses not to repay his/her first loan if,
• in variant M0 : (1 + λI )A1 − δλP A2 > 0 and (1 + λI )A1 − δλP A1 > αc (see Equation (1));
• in variant MB : (1 + λI )A1 − δλP A2 > B and (1 + λI )A1 − δλP A1 > αc (see Equation (4));
• in variant MS : (1 + λI )A1 − δλP A2 > 0 and (1 + λI )A1 − δλP A1 + S > αc (see Equation (7)).
15
When comparing the conditions in the three variants, we observe that the conditions in variant MB
imply the conditions in variant M0 , and the conditions in variant M0 imply the conditions in variant MS (as B, S > 0).11 This means that the client is more likely not to repay his/her first loan in the
variant with a sanction incentive (variant MS ) than in the basic variant (variant M0 ), and the client
is more likely not to repay his/her first loan in the basic variant (variant M0 ) than in the variant with
a bonus incentive (variant MB ).
(2) The client chooses to repay his/her first loan late if,
• in variant M0 : δ(λP A2 − λP A1 ) < αc and (1 + λI )A1 − δλP A1 < αc (see Equation (2));
• in variant MB : B + δ(λP A2 − λP A1 ) < αc and (1 + λI )A1 − δλP A1 < αc (see Equation (5));
• in variant MS : S + δ(λP A2 − λP A1 ) < αc and (1 + λI )A1 − δλP A1 + S < αc (see Equation (8)).
When comparing the second condition in the the variants MB and MS , we observe that the second
condition in variant MS implies the second condition in variant MB . This means that, if the first
condition holds in both variants, then the client is more likely to repay his/her first loan late in a
bonus scheme (variant MB ) than in a sanction one (variant MS ).
Moreover, the two conditions in variant MB (or in variant MS ) imply the two conditions in variant M0 . Thus, the client is more likely to repay his/her first loan late in the basic variant (variant M0 )
than in the other variants with bonus or sanction (variants MB and MS ).
(3) The client chooses to repay his/her first loan on time if,
• in variant M0 : αc + δ(λP A1 − λP A2 ) < 0 and (1 + λI )A1 − δλP A2 < 0 (see Equation (3));
• in variant MB : αc + δ(λP A1 − λP A2 ) < B and (1 + λI )A1 − δλP A2 < B (see Equation (6));
• in variant MS : αc + δ(λP A1 − λP A2 ) < S and (1 + λI )A1 − δλP A2 < 0 (see Equation (9)).
When comparing the second condition in the three variants, we observe that the second condition in
variant MS implies the second condition in variant MB .12 This means that, if B, S > αc + δ(λP A1 −
λP A2 ), the client is more likely to repay his/her first loan on time with a bonus (variant MB ) than
with a sanction (variant MS ).
Moreover, the two conditions in variant M0 imply the two conditions in variant MB (or in variant MS ). Thus, the client is more likely to repay his/her first loan on time in the variants with bonus
or sanction (variants MB and MS ) than in the basic variant (variant M0 ).
6. Concluding Remarks
Over the past forty years, the microfinance sector has experienced a huge expansion. It has achieved some
major successes but also went through some critical crises. A key ingredient for microfinance to work is the
repayment incentive schemes. Indeed, in order to lend small loans to poor people who cannot bring traditional
guarantees or collaterals, implementing adequate incentives for them to repay is crucial.
After having developed the group-lending methodology, the tendency is now to favor individual loans. So
far, most of the methodologies applied have been based on standardization and social pressure. They are
mainly relying on an extensive use of negative incentives such as extra-fees for late payment, threats of no
refinancing, or social stigmatization. The use of all these has certainly allowed for a certain level of development
of the industry. However, it is now time to have a closer look at those practices in order to establish if a higher
use of positive incentives could not do any better. This paper is a step in this direction, investigating the effect
of a positive versus a negative incentive on borrowers’ efforts to repay, and showing theoretically that MFI’s
clients tend to repay their loans better if they are faced with a positive incentive.
More precisely, let us summarize the main results of our model analysis. As one would have thought,
our model shows that incentives (bonus or sanction) contribute to on-time repayments (see point (3) of the
comparison between the three variants in the previous section). Note that the non-repayment of a second
loan by the client is completely due to the finite horizon of the model. In reality, MFIs build long-term
11In each situation where the client does not repay his/her first loan in variant M , then the client does not repay it either
B
in the same situation in variant MS .
12In each situation where the client repays his/her first loan on time in variant M , then the client also repays it on time in
S
the same situation in variant MB .
16
relationships with their clients, and neither the client nor the institution knows when the lending relationship
will end. Nevertheless, the model displays some interesting differences between the bonus and sanction schemes
for the first loan period.
All together, the main interesting result is the following one. When comparing bonus with sanction, it
appears that in some situations13, the client will not repay his/her first loan in the sanction scheme but will
repay it (on time or late) in the same situations in the bonus scheme. Moreover, in each situation where
the client does not repay his/her first loan in the bonus scheme, then he/she does not repay it either in the
same situation in the sanction scheme (see point (1) above). Consequently, with a bonus scheme, the client
has a lower propensity for strategic default: the positive incentive induces more repayments than the negative
incentive, regardless of the amount of the sanction or the bonus (B, S > 0).
The model also establishes that, if the bonus and sanction satisfy: B, S > αc +δ(λP A1 −λP A2 ) (see point (3)
above), then the client is more likely to repay his/her first loan on time when the MFI uses a bonus for ontime repayments (positive incentive) than when it uses a sanction for late repayments (negative incentive). In
other words, the bonus is a more effective strategy compared to the sanction in order to encourage on-time
repayments in this case. Indeed, if a bonus is used, the client still has an incentive to reimburse even for
projects with lower internal return. Note that asking B > αc + δ(λP A1 − λP A2 ), that is, asking for the
bonus to be greater than the late repayment gain plus the difference between the gross incomes of the client’s
first project and the second one multiplied by the discount factor, does not seem unreasonable since the first
borrowed amount is strictly lower than the second one (A1 < A2 , and so δ(λP A1 − λP A2 ) < 0).
It is important to stress that we study the effectiveness of the bonus and sanction schemes only in terms of
loan repayments, but we did not take into account the operational costs generated by their implementation.
There should be a trade-off between the cost of the strategy to implement and the reduction of default.
In terms of costs, the bonus scheme is only interesting for the MFI if the extra costs it generates are
compensated by better repayments, reducing eventually loans losses and administrative cost linked with the
follow-up of non-performing loans. Therefore, for a given MFI, a conclusion that could derive from this is
that interest rate should be defined taking these costs into consideration. When the MFI is in a monopoly
situation or in a situation that is more frequent in microfinance, where competition is not taking place through
prices, the MFI may consider an increase of its interest rates in such a way that, for customers who are
paying on time, the bonus more than offsets this increase thanks to the extra-amount that would be perceived
from non-performing customers (who would pay the new higher interest rate without receiving the bonus).
Alternatively, another more frequent case could materialize: when operational efficiency is being improved in
a given MFI, it could decide not to translate it into lower interest rates but rather use the additional margin
to pay for the establishment of the bonus scheme, resulting – based on our model – in higher repayments, and
in the long run, on a better relationship between the MFI and its customers.
There are several interesting directions for further research. We have considered two specific kinds of
incentives: a bonus for on-time repayments and a sanction for late repayments, but other types of incentives
could be studied and compared. More important even, some work should be done in order to identify the
optimal combinations of positive and negative incentives. Last but not least, validating our findings through
empirical tests – for instance, through randomized control trials – should be considered in future research.
Acknowledgements. The authors thank Ariane Szafarz, Marek Hudon, and the participants in the Third
European Research Conference on Microfinance (Kristiansand, June 2013), the 5th International Conference on
Institutional and Technological Environment for Microfinance (Casablanca, March 2014) and the CERMi Research Day (Mons, April 2014) for valuable comments. Julie De Pril is a F.R.S.-FNRS postdoctoral researcher.
Anaı̈s Périlleux is the beneficiary of a post-doctoral grant from the AXA Research Fund.
13It is the case when (1 + λ )A − δλ A > 0 and (1 + λ )A − δλ A + S > α , but (1 + λ )A − δλ A < α .
c
c
1
1
1
I
P 2
I
P 1
I
P 1
17
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19
Derniers humanOrg Working Papers parus :
2014/05
2014/04
2014/03
2014/02
2014/01
2013/02
2013/01
Positive vs negative incentives for loan repayment in microfinance : a game theory approach
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La gouvernance dans les entreprises familiales : le cas du BEL20 (Jonathan Bauweraerts &
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Flexible Products in Microfinance: Overcoming the Demand-Supply Mismatch (Marc Labie,
Carolina Laureti & Ariane Szafarz)
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Crises microfinancières et responsabilité des IMFs : proposition d’un cadre d’analyse (Marc
Labie & Bert D’Espallier)
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