Stockholm School of Economics

Master’s Thesis in Finance

Credit Rationing in Microfinance

Abstract

This paper argues that borrowers who are considered to be too risky are excluded from microfinance
markets due to credit rationing. Insufficient institutional frameworks imply moral hazard which in turn
causes the rationing of credit. Focusing on outreach and pricing issues, it is shown here how the outreach
of microfinance depends on capital costs and subsidization. Capital costs worsen credit rationing and the
extent to which subsidies mitigate the effects of credit rationing on outreach is typically limited. Market
structure has no direct effects on credit rationing but affects the availability of credit through client-
maximizing cross-subsidization. Consequently, attempts to improve the outreach of microfinance through
subsidization and changes in market structure are believed to have little effect. Instead, it is advocated that
institutional changes reduce moral hazard and thus credit rationing.

Starting from a simplistic base case scenario, a model is developed covering both capital costs and
subsidies. The model distinguishes between profit- and client-maximizing MFIs and alternates between
monopolistic and competitive settings.

Authors Presentation
Katarina Kahlmann, 19236 November 14th, 2005
Fredrik Odeen, 18895 Room 343

Tutor Discussants
Professor Peter Englund Anders Danielsson, 19313
Mikael Salenstedt, 19597
 Acknowledgements

First of all, we would like to thank our tutor Peter Englund for guidance and advice. We also thank João
Fonseca at the Microfinance Market Exchange and Jonathan Morduch at NYU Wagner School for
sharing their insights. Acknowledgement should also be given to Axel Svedbom and Samuel Jones for
their valuable comments. Finally, we thank students at Lund Institute of Technology for useful comments
on the Arccotan function presented in appendix D.
1 Introduction 1
2 Background 2
2.1 Definition of microfinance 2
2.2 Some characteristics of credit markets in developing countries 2
2.2.1 Legal system in developing countries 2
2.2.2 The function of the legal system in rural credit markets 3
2.2.3 Collateral 4
2.2.4 Predatory interest rates 4
2.3 Description of credit institutions in developing countries 5
2.3.1 Formal banks and financial markets 5
2.3.2 Microfinance institutions 6
2.3.3 Moneylenders 6
2.4 Microfinance institutions 7
2.4.1 The microfinance market 7
2.4.2 Enforcement methods 8
2.4.3 MFI objectives 9
2.4.4 Self-sufficiency and subsidization 10

3 Theory of credit rationing 10

3.1 Credit rationing 10
3.2 Adverse selection 12
3.3 Moral hazard 12
3.4 Other research 13
4 Model 14
4.1 Definitions and assumptions 14
4.1.1 Credit rationing 14
4.1.2 Repossessable asset 16
4.1.3 The outcome of the projects 16
4.1.4 Constraints 18
4.1.5 Types of borrowers and institutions 18
4.2 Base case 19
4.2.1 Without credit rationing 19
4.2.2 Introducing credit rationing 19
4.2.3 Monopoly 19
4.2.4 Client-maximization 22
4.2.5 Introducing competition 22
4.3 Introducing a cost of capital 23
4.3.1 Monopoly 24
4.3.2 Competition 25
4.4 Subsidies 26
4.4.1 Monopoly 27
4.4.2 Competition 27
4.5 Effects on the critical level of risk 31
4.5.1 Market structure 31
4.5.2 Cost of capital and subsidies 31
4.5.3
βi as collateral 33
5 Outcomes and implications 34
6 Microfinance in Vietnam 36
6.1 The rural financial sector in Vietnam 37
6.2 Credit rationing on the Vietnamese microfinance market 38
6.3 Moral hazard in Vietnam 39
6.4 Desired legal and institutional reforms 40
6.5 Correlation between interest rate and borrower risk 41
7 Conclusion 42
8 References and readings 43
8.1 References 43
8.2 Readings 45
9 Appendices 46
9.1 Appendix A 46
9.2 Appendix B 48
9.3 Appendix C 48
9.4 Appendix D 50
Credit Rationing in Microfinance Stockholm School of Economics

1 Introduction

Many poor people do not have access to formal credit markets. This exclusion is detrimental for
development since it prohibits entrepreneurs to start small businesses that contribute to the economic
development. 1 The problem arises because financial institutions cannot profitably lend money to very
poor people. One of the objectives of so-called MicroFinance Institutions (MFIs) is to increase outreach
of formal credit markets to include these clients. New techniques such as group lending, dynamic
incentives and subsidies allow the MFIs to access many of these clients.2

This paper examines a mechanism limiting the outreach of MFIs. Risk is costly in credit markets where
players are risk averse. In competition, the increased cost from higher risk is normally compensated by a
high price (interest rate) until equilibrium is achieved, where supply equals demand. 3 Credit rationing
affects credit markets in a way that makes high prices unsustainable. The concept was introduced in some
form as early as 1965 by Freimer and Gordon and comprehensively by Stiglitz and Weiss in 1981.
Understanding the effects of credit rationing is important when developing methods to increase the
outreach of formal credit markets.4

In recent years, MFIs have faced increasing pressure from the academic world and donors to become
profitable, or at least self-sufficient. At the same time, the number of MFIs and the funds available to
them have increased dramatically. In other words, the impact of capital costs and subsidization in
microfinance markets are of great interest to both scholars and practitioners. By building a model where
credit rationing is isolated from other mechanisms in the market, we will look at how these changes can be
expected to affect the interest rates and outreach of MFIs with respect to credit rationing.

• This paper examines credit rationing in microfinance markets, focusing on outreach and
pricing issues.

Due to both a lack of data and a paucity of research within the field of credit rationing in microfinance
markets, we have chosen to develop a formal model rather than to conduct a quantitative analysis. To
ensure the reader’s understanding of the microfinance setting and the theory behind the concepts used in
our model, we first describe the environment in which MFIs operate and then outline the relevant theory.
Thereafter, we develop our model step by step, starting with a description of a monopoly with no capital
costs. Following this, we increase the number of players and introduce capital costs and subsidies. Finally,

1 Morduch, 1999.
2 See Ray, 1998.
3 See for example Bodie et al., 2004.
4 See Morduch, 1999; Greenbaum, 1995.

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we interpret the outcomes and implications of the model and relate the results to empirical findings by
describing an indicative example.

2 Background

This section describes the environment in which MFIs operate. First, microfinance is defined. Second,
some important characteristics of credit markets in developing countries are outlined. Third, the actors in
these markets are introduced. Finally, we focus on MFIs and describe their objectives and financing.

2.1 Definition of microfinance

We define microfinance as loans to entrepreneurs too poor to have access to the traditional credit market.5
These loans are facilitated either through subsidies or novel lending techniques. The purpose is to enable
poor people to generate a sustainable income for themselves and growth for the economy through
funding of entrepreneurial activity.

2.2 Some characteristics of credit markets in developing countries

Below, we identify some of the most important characteristics of credit markets in developing countries.

2.2.1 Legal system in developing countries

Recent corporate governance literature emphasizes the importance of how the legal systems determine
differences in the availability of external finance (equity and credit) between countries.6 Some observers
argue that this relationship is especially important for developing countries. In such regions, the
availability of external finance, particularly in the form of credit, has important effects on the economy in
general.7

When looking at legal systems, it is important to investigate how efficient laws and regulations are de jure,
in theory, as well as how efficient they are de facto, when they are implemented by the courts of law and
when corruption is taken into account. One must also bear in mind who has access to the courts of law
and who pays for trial costs. These factors determine how efficient the legal institutions will be in
protecting creditors from expropriation and other moral hazard effects. LaPorta et al. (1998) show that
countries of the same legal origin, e.g. common law or civil law, often have strong similarities in the
efficiency of the judicial system, the enforcement quality and the quality of the accounting standards.
Generally, common law countries such as the UK and the US have strong protection of creditors and
outside investors, while civil law countries lack such protection. LaPorta et al. (2000) argue that strong
protection of creditors and outside investors allow broad and deep capital markets to develop.

5 In other papers it is common to include different types of savings and insurance in the definition of microfinance.
6 Hart, 1995; LaPorta et al., 1998, 2000; Coffee, 2000.
7 Berglöf and von Thadden, 1999.

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Developing countries that are former colonies often belong to the same legal origin as the former
colonizer, e.g. former British colonies have common law systems. While it is beyond the scope of this
paper to examine, we would expect the effects of credit rationing to be more pronounced in civil law
origin developing countries.8

2.2.2 The function of the legal system in rural credit markets

The legal system and courts of law generally play a small role in helping to enforce contracts in rural credit
markets or indeed in most developing markets. Whereas they are the principal way of enforcing contracts
in developed countries, courts of law and other legal institutions often lack the ability to intervene
between lenders and borrowers in developing countries. 9 This is similar to international debt markets
where there is also often a lack of an authority that can intervene between lenders and borrowers. In fact,
many observers such as Ghosh et al. (2002) believe that rural credit markets are very similar to
international debt markets, where lenders tend to supervise and collect debts more actively rather than
depend on seizing collateral with the help of courts of law.

In international credit markets, one of the main incentives of borrowers to abide by contracts is the threat
of not being able to borrow money in the future.10 Therefore, in the same way as analysts closely follow
companies and rate their bonds in international markets, lenders in rural markets tend to have close
relations with the borrowers and supervise their ability to repay the loans. However, since there are few
means of forcing borrowers to repay loans, monitoring has a limited role to play. Even if the lender knows
that the borrower has the assets to repay the loan, he may not be able to enforce the contract. Instead,
screening is very important, partly to determine who will be able to repay the loan and partly to determine
who would have the right incentives to actually do it.11

Hence, in such circumstances there are of two different types of default. In developed countries default is
normally involuntary. If the project fails, there is not enough money to repay the loan. 12 In case of
voluntary default on the other hand, the borrower chooses to default either by not investing the borrowed
money in the project in the first place, or by keeping the returns from the project. Due to the enforcement
problems mentioned above, microfinance markets are characterized by a high probability of voluntary
defaults. If a project results in either a low or a high outcome, involuntary default implies that the lender
will at worst get the lower payoff, and at best get the face value of the loan. Voluntary default on the
contrary, usually results in the lender not receiving any repayment at all.13

8 For a more detailed argumentation of the above, see Ghosh et al., 1999.
9 Ghosh et al., 2002.
10 Banerjee et al., 1993.
11 Ghosh et al., 2002.
12 See Ray, 1998 for relation to MFI markets.
13 Ghosh et al., 1999.

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2.2.3 Collateral
One of the basic ways for lenders to protect themselves in case a borrower defaults is by using collateral.
A house loan is the typical example where the property is the collateral. If the borrower defaults on his
loan, the lender repossesses the building. This is commonly referred to as internal collateral, what the loan
finances works as collateral. Initial endowments are another common form of collateral. For example, the
house of an entrepreneur can be used as collateral for loans invested in different ventures, e.g. the start-up
of a small business.14 The external collateral, i.e. the borrower’s initial endowment, works as collateral.
Evidence indicates that a large part of small enterprise start-ups are funded this way in developed
countries.15

As discussed in the previous section, developing markets and especially rural areas are often characterized
by a lack of legal systems and property rights for the poor, which makes repossessing of collateral non-
viable. De Soto (2000) argues that this is the reason why poor countries are lagging behind rich countries
and that granting property rights to people living in slum areas could solve poverty. By allowing them to
raise capital to fund entrepreneurial activity, they may themselves create the economic opportunities
needed to support development. Once property rights and a functioning legal system with sufficient
enforcement are in place, collateral will allow most people to borrow at least some amount of money from
traditional banks. MFIs have a role in markets where these conditions are not fulfilled or where the
population is so poor that the amount they can borrow is not sufficient to fund entrepreneurial activity.16

When external collateral is not a viable alternative because of isufficient legal systems, internal collateral
still provides a viable, if not complete, alternative. Internal collateral is easy to identify and property rights
of physical assets that have been bought from formal enterprises are easily established since there will be
receipts and other documentation. In addition, the lender may monitor the use and location of the good.17

2.2.4 Predatory interest rates

The interest rates charged by different institutions in developing countries vary widely as the risk profiles
of customers are very different.18 Formal institutions such as banks that lend against collateral can charge
low interest rates as loans are relatively secure and there are legal institutions to enforce lending contracts.
Moneylenders acting on informal credit markets on the other hand charge very high rates, sometimes as
high as 10 percent per month (314 percent p.a.). 19 One of the motivations for MFIs has been that
moneylenders were thought to abuse borrowers by charging predatory rates.20 However, it has recently
been indicated that formal lenders, to be profitable, would also have to charge very high rates to cover the

14 See Banerjee et al., 1993.

15 See De Soto, 2000.
16 See Fischer, 2000.
17 De Soto, 2000.
18 Ray, 1998.
19 The Global Development Research Center, 2005. See section 2.3.3 for description of moneylenders.
20 Reserve Bank of India 1954, cited in Bell, 1990 p. 297.

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costs of informational asymmetries and the default risk of borrowers, if they were to act in the same
market as moneylenders. 21 This will be illustrated more closely in the indicative example in section 6.

As argued above, lending money to the poor is problematic since the lack of legal institutions increases
costs. The poorer and riskier their clients are, the higher cost institutions have for monitoring, supervising
and collecting debt. Loans from moneylenders are also often used for different purposes than money
borrowed from the formal sector.22 Often the need for borrowing money arises when an unforeseen event
occurs, e.g. when a relative falls ill. To be able to efficiently give credit in such a situation, the lender needs
to have local knowledge of the borrower’s situation. Therefore, the lender needs to establish a personal
relationship with clients. Local moneylenders who live out in the villages seem to be good at this, and the
conditions of the loans they offer are suited for these kinds of situations even though the costs of
monitoring and debt collection are much higher than for other types of loans.23

The above has lead many observers to believe that the high interest rates charged by moneylenders are not
as severe a problem as previously believed. After all, borrowers voluntarily agree to pay these rates.24
Indeed, some MFIs have realised this and lend money to local moneylenders in order for them to re-lend
at higher rates.25 The benefit from bringing these informal lenders into a formal market would be to lower
their cost of capital by increasing the availability of credit and perhaps more importantly, improve the legal
protection of lenders and borrowers.26

2.3 Description of credit institutions in developing countries

The credit market in developing countries can be divided into the following three groups of lending
institutions.

2.3.1 Formal banks and financial markets

Formal lending institutions in developing countries are similar or identical to lending institutions and
banks in developed countries. They operate in urban areas and have the affluent part of the population
and larger companies as customers. Often they have local branches in the rural areas and try to reach new
customers by lending money to smaller companies and farmers. Successful clients of MFIs become
customers of these institutions when they have come out of poverty.27

21 Ghosh et al., 1999.

22 Morduch, 1999.
23 Armendáriz de Aghion et al., 2000.
24 Woller, 2002.
25
Perry, 2002.
26 Floro and Ray, 1997 and Bose, 1996.
27 Ghosh et al., 1999.

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• Typical loan conditions are characterised by collateral, interest payments and lump sum
amortizations at maturity.28

2.3.2 Microfinance institutions

The majority of MFIs are subsidized, either by governments or by NGOs (non-governmental
organizations). They have a social goal set by the subsidizers to provide cheap credit to poor people that
lack the collateral to get normal bank loans.29 MFIs operate among poor people both in urban and rural
areas, but have traditionally been most prominent in rural markets with agricultural clients.30 They mainly
finance different types of small enterprises and start-ups, e.g. a mobile phone for a woman in a rural
village which she can rent to other villagers and thus improve the communications of the whole village
while making a living for herself.

• Typical loan conditions are characterized by lack of collateral, group lending, forced savings,
regular payment schedules, threats of non-refinancing and direct monitoring. 31 These
characteristics and other aspects of MFIs will be further explored below.

2.3.3 Moneylenders
Moneylenders are the traditional informal lenders that charge very high interest rates and lend small sums
of money for short periods. They are often accused of charging excessive rates and of using
unconventional (and often illegal) ways of securing repayment.32

• Typical loan conditions are characterized by rapid loan approval, flexible terms, repayment
periods measured in days or weeks and lump-sum payments.33

28 Ray, 1998.
29 The Global Development Research Center, 2005.
30 Morduch, 1999.
31 Ray, 1998.
32 Ghosh et al., 1999.
33 Ray, 1998.

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Figure 2.1 Average interest rates by different institutions in developing countries.

In figure 2.1 we show a highly simplified discontinuous representation of average interest rates by
different institutions in developing countries. The high interest rates charged by MFIs and especially
moneylenders may be explained partly by an increase in the risk of the borrowers and partly by increases
in the cost of monitoring and enforcement, x, due to asymmetric information and lack of regulatory
institutions.34

2.4 Microfinance institutions

From the above argumentation, it is not obvious that subsidized MFIs will always do a better job than
moneylenders at lending money to the extremely poor. However, moneylenders may lack the scale and
scope to lend money to individuals who wish to start and build enterprises. This is where MFIs have
found their purpose in the late 20th and early 21st century.35 The institutions lend money in larger sums and
over longer periods than moneylenders.36 Compared to traditional banks, specific enforcement methods
allow MFIs to lend profitably to borrowers unable to pose collaterals. Compared to formal credit
institutions, MFIs reach poor individuals more effectively.37

2.4.1 The microfinance market

Globally, one billion people live of less than 1 USD per day and about 500 million households are
believed to be in need of microfinance.38 Only around 30 million households were reported to have access
to sustainable microfinance services in 2002. Hence, assuming that each household consists of about five

34 See Ray, 1998.

35 Brau et al., 2004.
36 Charitonenko et al., 2002.
37 Fischer, 2000.
38 The Global Development Research Center, 2005.

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people, some 150 million people have access to microfinance. 39 Estimates of the excess demand are
considerably higher. Although there were about 10,000 MFIs worldwide in 2001 of which 70 percent
operated in developing countries, they only reached about 4 percent of the potential market. 40
Notwithstanding the excess demand for microfinance, the number of MFIs has increased substantially
during the past two decades. Over the past five years, the number of customers that use microfinance has
grown between 25 and 30 percent annually.41

The microfinance market is segmented, ranging from very small programmes lending to only a few
borrowers to large institutions with millions of clients. The top five MFIs in the world reach almost half
the market. The most prominent of these large MFIs, the Grameen Bank in Bangladesh, is a widely
imitated MFI lending 30 million USD a month to 1.8 million borrowers.42

In addition to the lending described above, an increasing number of MFIs provide saving services to the
poor.43 Such services are important both as a safety net for the poor and as a source of funding that does
not rely on external sources. 44 Hence, many MFIs, notably in Africa, use the savings of clients as a
principal source of loan funds.45 The saving services are, however, outside the scope of this paper.

2.4.2 Enforcement methods

Due to insufficient legal systems and lack of collateral, MFIs rely on non-collateral enforcement methods
to give borrowers an incentive to repay the loans. Below, we outline some of the most common methods.

Group lending is a widely used enforcement mechanism. A well-known version of group lending is the
Grameen bank model, where borrowers sort themselves into groups of five. Two of these group members
receive loans. The process continues and the borrowers take turns to get loans as long as performance is
satisfactory. If one member defaults, all five are barred from borrowing in the future. The creation of joint
liability induces subtle sanctions to help discipline borrowers through peer pressure rather than direct
actions of the MFIs. The borrowers risk social isolation, restrictions on inputs necessary for business or,
in some rather extreme cases, physical force.46

39 Microcredit Summit Report 2002.

40 2001 World Bank Statistics.
41 The total number of people with access to microfinance schemes rose from 7.6 million in 1997 to 26.8 million in

2001 (The Global Development Research Center, 2005).

42 2001 World Bank Statistics; The Global Development Research Center, 2005.
43 See Demirgüç-Kunt et al., 2002; Hoggarth et al., 2005; Kane, 2000.
44 According to the Microcredit Summit, approximately 10 percent of the USD 21.6 billion needed to provide

microfinance to 100 million of the world's poorest families could be raised from borrower’s savings alone (The
Global Development Research Center, 2005).
45 Microcredit Summit Report 2002.
46 Armendáriz de Aghion et al., 2000.

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However, group lending can be costly. The group members exert a lot of time and effort attending group
meetings and monitoring group members. Moreover, borrowers with growing businesses are hindered by
the loans being restricted to what the entire group can guarantee. In addition, the borrowers can collude
against the bank and agree to default. The costly implementation of group lending implies that MFIs
employing group lending rarely cover their costs.47

Consequently, other types of enforcement methods, such as individual “lender-borrower” contracts based
on dynamic initiatives, increase in popularity. In case of non-refinancing threats, the lenders will not
refinance the borrowers who default. In addition, the MFIs may enhance the effect through promises to
increase the size of the loans over time to good customers. Moreover, regular repayment schedules, where
the borrower starts repaying the loan almost immediately, have proven to increase the repayment ratio.48

2.4.3 MFI objectives

Academics as well as practitioners disagree amongst themselves on which are the optimal objectives and
methods of MFIs. Different groups emphasize social welfare and financial efficiency respectively. These
objectives are somewhat mutually exclusive since there is a trade-off between outreach, impact and
sustainability in microfinance lending.49

Outreach is defined as the effort of MFIs to extend loans to a wider audience (breadth of outreach), and
especially to poor people (depth of outreach). Impact, on the other hand, refers to whether microfinance
really helps the borrowers, i.e. raises the incomes and welfare of the poor. The third term, sustainability,
implies full cost recovery at worst and profitability considering the cost of capital at best. A sustainable
MFI is not dependent on subsidies from governments or donors.50

There seems to be a trend towards an increased focus on sustainability among MFIs. A few decades ago,
profits from lending to poor people were controversial, and profit-maximizing lenders were considered to
be predatory. However, too much dependence on donors and government seem to jeopardize future
funding and soft budget constraints may reduce the efficiency of the MFIs. Today profits are believed to
attract private investments to the sector, thereby improving sustainability and access to credit of the
institutions. Hence, the number of profit-maximizing MFIs is increasing at a steady pace.51

Nevertheless, there are practitioners, as well as academics, who oppose the current development. They
believe that too much emphasis on cost recovery only implies that MFIs refrain from lending to the very

47 Morduch, 1999.
48 Ibid.
49 Conning, 1999.
50 Morduch, 1999.
51 Ibid.

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poorest. Moreover, advocates claim that a profit-maximizing approach diverts attention and efforts from
the social and political objectives of lending to the poorest and most vulnerable.52

2.4.4 Self-sufficiency and subsidization

As mentioned above, sustainability is often defined in terms of self-sufficiency, i.e. the MFI’s ability to
cover its costs. However, there are two different kinds of self-sufficiency. Operational self-sufficiency
refers to the extent to which the MFIs cover their operational expenses. On the other hand, to be
financially self-sufficient, the MFIs must cover financial expenses as well.53

MFIs reach self-sufficiency by cutting their costs and by increasing their revenue. Asian MFIs often
achieve a high level of profitability due to low costs, whereas MFIs in the other regions such as Eastern
Europe, Latin America and Africa, face higher costs and generally reach self-sufficiency through a
combination of higher income and increased productivity.54

Many MFIs claiming to be self-sufficient rely on subsidies. The term subsidy is defined as a financial
resource received by an MFI at below market prices. Hence, it includes all types of donations.55 A majority
of the MFIs are subsidized in some way, either by governments or donors. However, due to the trends
mentioned above, unsubsidized MFIs increase in numbers. 56 Therefore, we believe that assessing the
effects of subsidization of MFIs is of great relevance.

3 Theory of credit rationing

Having described the microfinance market, we now turn to the relevant theory. First, we explain credit
rationing referring to the logic of adverse selection and moral hazard.57 Second, we briefly cover previous
research on credit rationing and microfinance respectively.

3.1 Credit rationing

Credit markets rarely follow the law of supply and demand.58 If they did, agents unable to borrow money
at the market rate would be able to do so by paying a higher price, i.e. interest rate. However, that is not
the case in many credit markets.59

52 Hulme, 2000.
53 Conning, 1999.
54 MBB, 2002.
55 Woller et al., 1999.
56 Morduch, 1999.
57 It is important to note that there are many different definitions of credit rationing. We try to capture the most

basic function and therefore our definition is slightly different and simplified compared to previous definitions e.g.
Stiglitz and Weiss, 1981; Keeton, 1979; Freimer and Gordon, 1965.
58 Ghosh et al., 1999.
59 Brau et al., 2004.

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Let us assume that the lender’s pay-off from a certain borrower is increasing in risk. The riskier the project
is, the higher interest rate the borrower will be prepared to pay. Hence, at high interest rates, only
borrowers investing in very risky projects are prepared to borrow money. Thus, the interest rate a player is
prepared to pay reveals his risk class. Due to adverse selection described below, only riskier players will
want to borrow at very high interest rates. Banks will suspect borrowers willing to pay high interest rates
of being very risky. Moreover, the interest rate charged affects the risk of the borrower. As stated in
section 3.3, a high interest rate adds to the burden of repayment, which has moral hazard implications on
the incentives of the borrower. For these reasons, banks often choose to ration their credit.60

Figure 3.1 Due to credit rationing, the optimal interest rate is above the equilibrium interest rate. Thus, the market-
clearing interest rate is not necessarily profit-maximizing.61

As illustrated in figure 3.1, the relationship between the interest rate charged and the expected return to
the bank is a concave function with an optimal interest rate, r*, after which the return to the bank starts to
decrease. The risk of default increases disproportionately among the borrowers willing to accept worsened
loan conditions. Because of this profit maximizing solution, demand and supply will not always clear the

60 Greenbaum et al., 1995.

61 Ibid.

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market. The level of the profit maximizing interest rate depends on the risk of the borrowers, the cost of
capital for the bank and the supply of credit.62

3.2 Adverse selection

When lending money, banks try to determine the risk level of the projects so as to charge the appropriate
interest rates. This can be done by various screening methods and by looking at past history of the
borrower. While these methods can be highly sophisticated, they are never completely accurate. For a
group of borrowers offered the same interest rates based on the risk assessment, the actual risk level
always varies between individual projects.63

Assume that banks observe the average risk level within a group, but that borrowers are better informed
than banks on the risk level of each individual project.64 The projects with higher risk level than the group
average will then be subsidized by the projects with lower risk. The borrowers with low risk projects are
likely to choose not to borrow or go to another bank because they pay too high a price. This implies an
increase in the average risk level of the group. Realising this, the bank will charge a higher interest rate.
Once again the borrowers with risk levels below the average will drop out and in the end the only
borrowers that are prepared to pay the banks interest rate will be the most risky borrowers.65

This leads to a reluctance among banks to lend at high interest rates as this will only attract very risky
projects. These high risk projects run a considerable risk of failing and the borrower of defaulting on the
loan. The banks profitability will be reduced and, under certain circumstances, completely eroded.
However, in addition to causing these involuntary defaults, increased interest rate can have other negative
effects on the banks profitability.66 For example, it may cause voluntary defaults as we will see below.

3.3 Moral hazard

Even when a borrower has accepted a loan at an interest rate, the interest rate level may still be
troublesome to the bank. If the interest rate is high, borrowers incentives to cheat the bank increases.
They can do this in two main ways, either by choosing riskier projects or by stopping exerting effort on
the project.67

Because of the option-like features of a debt-financed project, the borrower only receives the upside of
the outcome, which means that he always has incentives to increase the risk level of his projects.68 If the
interest rate is high, the borrower’s upside is smaller and the incentives to increase the risk level are larger.
In addition, if it is hard for the bank to verify what project the borrower is actually undertaking, the

62 Greenbaum et al., 1995.

63 Stiglitz and Weiss, 1981.
64 For an opposing view, see for example Manove et al. forthcoming.
65 Greenbaum et al., 1995.
66 Stiglitz and Weiss, 1981.
67 Greenbaum et al., 1995.
68 See appendix A.

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Credit Rationing in Microfinance Stockholm School of Economics

potential downside of changing project is smaller for the borrower.69 The increased risk means that the
loan becomes less profitable for the bank. At some level, the bank will make a loss from lending to the
borrower.70

The borrower may also choose not to undertake the project at all. If he believes the interest rate is so high
that his upside is smaller than his best alternative, i.e. going back to doing what he did before the project,
he may simply stop working on it. The borrower may realize this when he has worked for a while and start
observing the outcomes of his project. If the profit is not high enough and if the borrower cannot
increase the potential upside by changing the nature of the project, he may simply abandon the project.
The bank will then lose everything apart from what they can repossess from the project, i.e. investments
and inventories given that there is no collateral.71

The above implies that banks are reluctant to lend at high rates even if the borrowers initially are willing to
accept the interest rate.

3.4 Other research

From the above we conclude that credit rationing is based on both adverse selection and moral hazard. In
this section we present relevant fields of research. We first turn to the credit rationing literature and
present an article where microfinance is not mentioned. Thereafter, we describe a microfinance article
disregarding credit rationing.72

Stiglitz and Weiss (1981) present a model based on the option-like characteristics of loan contracts
presented in appendix A, implying that lenders are more risk averse than borrowers since the former face
all the down-side risk, whereas the latter capture the upside. However, the model was created to describe
credit markets where lenders are not aware of borrower characteristics. In microfinance markets on the
other hand, information on the characteristics of borrowers and projects is often available to lenders due
to the structure of the societies.73 Nevertheless, the ability to observe borrowers activities is limited and
costly. Hence, whereas adverse selection is less of a problem in microfinance markets, the moral hazard
issue is prominent. Unlike Stiglitz and Weiss’ model our model therefore only deals with the latter.

A large part of the microfinance literature is not compatible with the theories on credit rationing
presented above. Wydick and McIntosh (2002) investigate microfinance markets in different scenarios,
such as monopoly, competition and subsidization. They present a model similar to the model developed in
this paper, identifying the effects of new entrants in a monopolistic microfinance market. The outcomes

69 Some observers argue that it is actually easier for banks to verify this in rural markets where the institutions are
closer to their clients, see Ray, 1998, p. 537.
70 Greenbaum et al., 1995.
71 Stiglitz and Weiss, 1981.
72 For a general overview of the microfinance literature see Brau et al., 2004.
73 Ghosh et al., 1999.

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Credit Rationing in Microfinance Stockholm School of Economics

of both models concern outreach and interest rate. However, their model is different from ours in several
important aspects.

A crucial assumption in Wydick and McIntosh’s model is that the probability of default of an investment
depends on the initial endowment and the loan size. In other words, a wealthy borrower is more likely to
repay the loan than a poor borrower, everything else being the same. Accordingly, the size of the loan will
not increase the probability of repayment. However, modelling credit markets for poor people, we find it
inappropriate to put too much emphasis on initial endowments. The clients of MFIs are typically very
poor, and in case there are any initial endowments at all, weak legal systems complicate the expropriation
of collaterals in case of default. Therefore, we believe that the assumptions about initial endowments and
loan size weaken the applicability of the theory. Nevertheless, to not lose some of the advantages of
Wydick and McIntosh’s model, our model can easily be adjusted to allow for external collateral.

Most importantly, we will include the phenomena of credit rationing, disregarded by Wydick and
McIntosh. In addition, the MFIs in Wydick and McIntosh’s model compete with moneylenders, whereas
we believe that moneylenders and MFIs act in different markets.74

4 Model

Below, we develop a model to examine the effects of market structure, MFI objectives and subsidization
on the actions of lenders under credit rationing. Since we isolate the credit rationing mechanism from
other factors, our results are not directly applicable to reality, but rather indications of how credit rationing
can be expected to contribute to other effects. The environment in which we develop our model is that of
a developing country, and the lending institutions are MFIs.

We start by defining the framework and stating our assumptions. Thereafter, we model a base case
scenario, which we later extend to include cost of capital and subsidies. Each case is applied to both a
monopolistic and a competitive setting respectively. Finally, we examine some extensions of the model
that deal with collaterals.

4.1 Definitions and assumptions

4.1.1 Credit rationing

We define credit rationing as the phenomena that some borrowers will not get to borrow regardless of
what interest rate they are prepared to pay, as outlined in section 3.1. To isolate the effects of credit
rationing, we assume that projects only have one outcome, successful. The outcome of individual i is

74 The exclusion of moneylenders from our model is based on Armendáriz de Aghion and Morduch, 2000.

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Credit Rationing in Microfinance Stockholm School of Economics

denoted β i . However, borrowers may choose not to exert effort if they feel that their upside is too low.75
The bank then receives β i from individual i.76 The higher interest rate the bank is charging the lower is
the upside for the borrower. Thus the probability that borrower i will default voluntarily is a function of
the interest rate
θ i = θ i (ri ) ,
where θi is the probability of default associated with an interest rate ri charged from individual i.77 The
constraints on θ i (ri ) are that the probability of default must always be above zero but below one

0 < θ i (ri ) < 1 .

For these values of θ i (ri ) the relationship between probability of default and interest rate must be
positive

θ i′ (ri ) > 0
and given that
βi < 1
ri > 0
θi (ri ) < 1
we must have that the derivative of the MFI revenue (ReviMFI) as a function of the interest rate is

∂ Re viMFI
=0
∂ri
for credit rationing to exist.

In appendix D we develop a function of θ i (ri ) which is consistent for a wider range of constraint
assumptions than the function we will be using below. However, for the purposes of this paper we limit
our investigations to a simpler function. We assume that there is a linear relationship between ri and θi as
follows,
θ i = εri Formula 4.A

where ε can be interpreted as the average propensity for borrowers to default. This propensity is
dependent upon how the institutional framework and especially the legal framework affect the incentives
for moral hazard and adverse selection. As noted in section 2.2, it is well documented that many
developing countries have severe deficiencies in their legal framework. This means that the issues raised in
section 3.3 concerning moral hazard are relevant to the model. Improved institutional framework will
reduce ε which will increase the outreach of MFIs. We assume however, that ε is exogenously given and
focus on the effects of credit rationing on microfinance.

75 This follows the argumentation in section 2.2.2.

76 See section 4.1.2 for further description of β i
77 In this paper, we only consider real interest rates.

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Credit Rationing in Microfinance Stockholm School of Economics

4.1.2 Repossessable asset

In our model, we allow for voluntary default as discussed in section 2.2.2. However, we assume that the
MFI can repossess the share of the loan, β i , that has been invested in physical assets such as machinery
and inventory. In doing this we follow the argumentation in 2.2.1-3 that internal collateral is a more viable
alternative than external collateral in developing markets where there are deficiencies in the legal system.
Anyhow, the concept of the repossessable assets can also be broadened to represent other factors such as
external collateral, initial endowment or poverty level without compromising the dynamics of the model.

The repossessable asset β i is observable to MFIs because of their screening activities. Hence, adverse
selection is not included in the model. Monitoring of borrowers is futile because the lack of legal
institutions means that there are no means of repossessing anything beyond β i . This causes the MFIs to

discriminate between borrowers based only on the observed β i of the potential projects.

It is worth noting that since lenders choose between borrowers based on the reposssessable assets our
model captures the effects on the breadth of outreach and not depth of outreach as described in section
2.4.3. If we substitute repossessable assets with poverty level we would capture depth of outreach instead.

4.1.3 The outcome of the projects

We assume that each borrower undertakes one specific project, i.e. they cannot choose what project to
undertake. Further, we assume that each project requires an investment of one unit. Each project has an
outcome of β i which is the successful state when the project has been undertaken. Each project also has
an outcome when the borrower chooses not to exert effort, β i , i.e. the repossessable asset according to
the above discussion. As described above, this can be interpreted as the amount invested in fixed
investments or inventories that the MFI can repossess in case of default. By common sense we

understand that β i > (1 + ri ) or else the bank would never lend neither would the borrower borrow.

Further, β i <1 must hold since otherwise there is no risk to the bank.78

This gives that the expected revenue per unit lent by an institution is
Rev iMFI = (1− θ i )(1+ ri ) + θi β i .79
Inserting the probability of default function from section 4.1.1 we get
Rev iMFI = 1+ ri − εri − εri2 + εri β i Formula 4.B

78This holds true in our base case when there are no capital costs.
79We define ReviMFI as the expected revenue of the MFI from lending to individual i. Throughout the entire paper we
refer to the expected revenue when we discuss the revenue of the MFI.

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Credit Rationing in Microfinance Stockholm School of Economics

The profit constraint on an institution states that, assuming no cost of capital, the expected revenue per
unit lent cannot be lower than one.

Re viMFI ≥ 1
1 + ri − εri − εri 2 + εri β i ≥ 1
1
β i ≥ 1 + ri −
ε
This means that the highest interest rate an MFI can charge without violating the profit constraint is
1
ri = −1+ β i . Formula 4.C
ε
The right-hand side of this equation must be positive for the expression to be meaningful.

Hence, the interest rate will fall in the region

1
0 < ri ≤ −1 + βi
ε
visualized in figure 4.1. The graph illustrates the lender’s revenue at different interest rates.

Figure 4.1 The lender revenue curve shows that the lenders maximize their revenue at r*.

There is a revenue maximizing interest rate, ri*, for each project.

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Credit Rationing in Microfinance Stockholm School of Economics

4.1.4 Constraints
To sum up the restrictions mentioned above, we must set two constraints for the MFI. Firstly, a profit
constraint implies that the MFI cannot consume its capital base by making losses in the long run. Thus,

Re viMFI ≥ 1 for all individuals.

Secondly, there is a non-negativity constraint on the interest rate. In fact, we will assume that the interest
rate is positive, ri > 0 . If we allow the interest rate to be zero, the MFIs will be able to lend to all
borrowers. To be able to explain important elements of our model such as cross-subsidization already in
the base case, we assume that the interest rate is positive. In later sections, where we introduce cost of
capital and subsidies to make the model more applicable to reality, the assumption of ri > 0 becomes
superfluous. The capital cost implies that the MFIs must charge an even higher interest rate.

The interest rate constraint is also related to the profit constraint since the lender would certainly make a
loss from charging a negative interest rate, i.e. giving money away.

4.1.5 Types of borrowers and institutions

As described above, the downside risk of each project is captured by β i . The lower β i , the riskier the
project is for the MFI to finance. Based on moral hazard as defined in section 3.3, the riskiest borrowers
(the borrowers with the lowest β i ) will not get to borrow because of credit rationing. Charging the risky
borrowers an interest rate corresponding to their risk level would increase the risk of default in accordance
with formula 4.A. When the interest rate is higher than in formula 4.C, the default risk is so high that the
project is no longer profitable for the MFI to finance at any interest rate. Hence, borrowers with projects
with less than a certain level of repossessable assets will not get to borrow.

As β i becomes lower, the interest rate approaches zero.80 By observing when the optimal interest rate

approaches zero, we identify at what level of risk, i.e. at what β i , credit rationing is critical.

∂ Re viMFI
= 1 − ε (1 − β i ) .
∂ri r =0

The expression must be non-negative for the MFI not to make a loss from lending to the borrower.
Consequently, the following must hold
1
β i > 1− .
ε

80 This negative relation between interest rate and risk only holds when there is no cost of capital. We introduce such

costs in section 4.3.

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Credit Rationing in Microfinance Stockholm School of Economics

1
On the other hand, β i ≤ 1− implies that the optimal interest rate charged by a monopolist is negative.
ε
Our negativity constraint from 4.1.4 does not allow for such an interest rate. Hence, credit will be rationed
1
and projects with a β i ≤ 1− will not get to borrow. These projects are referred to as unprofitable.81
ε
1
Projects with β i > 1− are referred to as profitable. A profit-maximizing MFI will only lend to profitable
ε
borrowers, whereas a client-maximizing MFI will try to maximize its total number of clients.

To separate unprofitable borrowers from profitable borrowers, we introduce β ∗ to denote the lowest

level of repossessable asset that the profit-maximizing lender will accept. In other words, the lender makes
a profit of zero from lending to a borrower with a β i of β ∗ . Hence, the profit constraint is binding for

the marginal borrower, i.e. the riskiest player in the group of profitable players.

4.2 Base case

4.2.1 Without credit rationing

If ε equals zero a higher interest rate does not increase the probability of default. In this case there is
neither credit rationing nor any probability of default on average. A monopolist would charge an interest
rate of or in excess of the return on the project and leave no profits for the borrower. Two or more
lenders engaging in Bertrand competition would compete for customers by decreasing the interest rate
until it reached zero and all profits would be left to the borrower.82 However, our model is not applicable
when ε equals zero since ε appears in the denominator, e.g. in formula 4.C.

4.2.2 Introducing credit rationing

We now turn to the case of a positive average propensity for borrowers to default (ε>0), to see what
happens when the interest rate affects the probability of default in accordance with the theory of credit
rationing, presented in our theoretical section. For credit rationing to be an issue in the first scenario of
our model, we must further limit ε to ε>1. This is because if ε is less than one the MFI can lend
profitably to all borrowers with β i >0, i.e. are all borrowers.83

4.2.3 Monopoly
In many developing countries there is only one single institution providing microfinance. The borrowers
will thus face a monopoly market. A profit-maximizing monopolist will obviously only lend to profitable

81 The borrower is unprofitable to the lender but as stated in section 4.1.3, all projects are profitable to the
borrowers.
82 See section 4.2.5 for definition of Bertrand competition.
83 See appendix B for formal proof.

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Credit Rationing in Microfinance Stockholm School of Economics

borrowers and set the interest rate to maximize its profits. Optimizing the interest rate in the revenue
formula 4.B for a monopolist institution, we get

∂ Re viMFI
= 1 − ε − 2εri + ε β i
∂ri
MFI ∂ Re viMFI
Max Re v i =0
∂ri
11 
ri* =  −1 + βi 
2ε 
1 1 
Comparing with the profit constraint introduced in section 4.1.2, we see that ri* =  −1+ β i  will
2 ε 
1
always be lower than ri* = −1+ β i . Hence, a monopolist will choose an interest rate
ε
1 1 
ri* =  −1+ β i  . The revenue is given by
2 ε 

1ε 1 
22
( 2

2ε
)
Rev iMFI (ri* )=  1+ β i − 2β i + + β i + 1

The formula is visualized below.

Figure 4.2 The MFI makes a loss below 1. The lender revenue curves of the less risky borrowers (higher β i ) are
above the curves of the risky borrowers.

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Credit Rationing in Microfinance Stockholm School of Economics

Figure 4.3 The MFI will not lend to borrowers with a βi < β∗ .

Figure 4.3 shows that the MFI revenue equals one (profit equals zero) at a β ∗ of 1/3 for ε=1.5. The

model is not applicable for values to the left of β ∗ , since they are based on a negative interest rate. Hence,

due to moral hazard which implies credit rationing, a profit-maximizing monopolist will only lend to
borrowers with a β i ≥ β ∗ .

In case of success, the profitable borrowers will get a profit of β i less the face value of the loan (principal

plus interest rate), β i − (1 + ri ) . The interest rate is not as high as it would be without credit rationing. In
case of default, the borrower will not make any profit nor loss, since they do not face any downside risk
(see section) on option theory). Consequently, the borrower’s pay-off is

Re vi = (β i − (1 + ri ) )(1 − θ i ) .
B

The borrower’s profit is above zero but decreasing in the interest rate as long as β i > (1 + ri ) .

The interest rate charged from profitable borrowers decreases in the risk level of the borrowers. In other
words,

• in monopoly, credit rationing causes a negative correlation between interest rate and risk.

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Credit Rationing in Microfinance Stockholm School of Economics

4.2.4 Client-maximization
In similarity to a profit-maximizing monopolist, a client-maximizing monopolist will try to maximize its
profits from lending to profitable borrowers. The surplus obtained from lending to the profitable
borrowers is used to subsidize lending to a group of unprofitable borrowers and thereby increase the
number of clients in the MFI’s portfolio.84 To maximize the number of unprofitable borrowers to lend to
before the profit constraint becomes binding, the MFI will choose to lend to the least unprofitable
borrowers. The borrowers with the lowest β i will still not have access to the credit market.

The client-maximizing monopolist will use the profit incurred from lending to profitable borrowers with a
1 1 
β i ≥ β ∗ at ri* =  −1+ β i  to cross-subsidize lending to unprofitable borrowers with a β i < β ∗ .
2 ε 

4.2.5 Introducing competition

We now expand the model to include competition between MFIs. Let us assume that there are at least two
MFIs involved in Bertrand competition for projects, i.e. they compete in prices (interest rates). 85 The
MFIs will only compete for the profitable borrowers, since the profit-maximizing MFI is not interested in
the unprofitable borrowers. The MFIs underbid each other to capture projects until they have eroded any
profits they could have made in the absence of competition. In other words, the revenue will approach
one.

As shown in figure 4.1, the MFI revenue is one at both ends of the curve. However, the reasons behind
the absence of profit are different in the two cases. The first interest rate identified above, ri=0, is the
approximate result of two MFIs competing, in other words the interest rate we were looking for. The
other interest rate leaves the MFI with a profit of zero but is a result of non-meaningful behaviour where
the MFIs overbid instead of underbid each other.

Consequently, both MFIs will undercut each other until the interest rate approaches zero.86 Continued
undercutting would then imply losses for the MFIs. Since neither of the MFIs will make any profit, the
client-maximizing MFI cannot cross-subsidize. Thus, it will not be able to lend to unprofitable borrowers.

84 See Wydick and McIntosh, 2002.

85
Since we assume that MFIs compete in prices and not in quantity, we base our model on Bertrand competition as
opposed to e.g. Cournot competition. Bertrand competition is a model of price competition between duopoly firms
where each firm charges the price that would be charged under perfect competition, i.e. the marginal cost, and makes
zero profits. For the model to hold, the firms cannot cooperate and must have the same marginal cost (which has to
be constant). The basic version of the model only allows for two firms competing. However, the outcome will be the
same in an extended version with more firms. In fact, the model holds for the extreme case of perfect competition.
Goods should be homogenous and demand must be linear. The firms compete in price, and choose their respective
prices simultaneously. When the price is set, the firms supply the quantity demanded. Consumers buy everything
from the cheaper firm. If the price is equal, the consumers buy half at each. In financial markets firms typically set
prices, i.e. interest rates, as opposed to quantities. Hence, such markets are often characterized by Bertrand
competition.
86 In section 4.1.4 we introduced the constraint r >0.
i

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Credit Rationing in Microfinance Stockholm School of Economics

Hence, the MFIs will act the same way in competition regardless of whether they are client- or profit-
maximizing. They will both lend to a share of the profitable borrowers and make zero profit.

• Outreach is lower in competition than in the case of a client-maximizing monopolist.

The profitable borrowers are better off than in monopoly since they now face a much lower interest rate.
In case of success, they will get a profit of β i minus the face value of the loan (principal plus interest rate),

β i − (1 + ri ) . Since the interest rate is approaching zero, the profit of a profitable borrower in case of

success will approach β i − 1 . Consequently, the borrower’s profit will be

Re vi = (β i − 1)(1 − θ i ) .
B

The group of unprofitable borrowers that got to borrow because of the cross-subsidization in section
4.2.4 is now worse off, not having access to credit.

4.3 Introducing a cost of capital

An interest rate approaching zero as in the previous section, is far from reality. We have so far assumed
that there are neither fixed costs nor costs of capital. Therefore, the competing MFIs could set their
interest rates close to zero. In reality, MFIs face a cost of capital, which we call c.87 Consequently, the
revenue formula is

Re viMFI = (1 − θ i )(1 + ri − c) + θ i ( β i − c)
= 1 + ri − εri − εri 2 + εri β i − c

Accordingly, the reasoning on graph 4.2 in section 4.2.3 is no longer accurate. We must now add the cost
of capital to the level at which the MFI previously made a profit of zero without capital costs. Now, the
MFI will make a loss below the zero-profit line at (1+c).

87 The argumentation on cost of capital is also valid for other costs (administration etc).

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Credit Rationing in Microfinance Stockholm School of Economics

1+ c

Figure 4.4 The lender makes a loss below the higher zero-profit line.

4.3.1 Monopoly
The cost of capital does not affect the profit-maximization of the monopolist since the first order
condition is the same. Following the same procedure as in the base case, we maximize revenue to find the
optimal interest rate. Hence, the interest rate charged by the monopolist is negatively correlated to risk
regardless of whether we include a cost of capital or not. However, the MFI profit will be slightly lower,
implying less cross-subsidization if the MFI is client-maximizing.

The profitable borrowers are in general unaffected by the cost of capital, and credit will still be rationed.
However, the MFI can no longer charge a zero interest rate from the marginal borrower, since it has to
compensate for the cost of capital. Because of credit rationing, increasing the interest rate charged from
the marginal borrower would not increase the MFI revenue. Consequently, the MFI will not lend to
borrowers for which the bank revenue curves never reach the horizontal line at (1+c) in figure 4.4. Hence,
borrowers which used to belong to the group of profitable borrowers but for which the lender revenue
curves have maximums between one and (1+c), will now be considered unprofitable, i.e. have too low β i
to get to borrow.88 Hence,

• increased capital costs cause β ∗ to increase and credit to be more rationed.

A profit-maximizing MFI will be worse off because of the decrease in profits caused by the capital cost.
Likewise, a client-maximizing MFI will be worse off since it cannot lend to as many borrowers as in the

88 See section 4.5 for further discussion on the effects of the risk level.

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Credit Rationing in Microfinance Stockholm School of Economics

case of no capital costs due to the increased β ∗ as well as the decreased profits used for cross-

subsidization.

4.3.2 Competition
The interest rates charged by competitors are affected by the cost of capital. The competitors will still
undercut each other until they do not make any profit. However, as figure 4.5 illustrates, the level at which
the MFI makes zero profit is higher with capital costs. Since the lender will make a loss charging interest
rates resulting in revenues of less than (1+c), he can no longer choose an interest rate of zero. The zero-
profit condition of Bertrand competition implies that the lender will charge the interest rates at which the
curve of each borrower cuts the zero-profit line.89 As shown in figure 4.5, the lender will now charge
different interest rates from each borrower.

1+ c

Figure 4.5 With higher capital costs, the MFI charges higher interest rate from riskier borrowers with lower lender
revenue curves. The lower βi of the borrower the higher the interest rate charged and for sufficiently low βi the

borrower does not get to borrow.

Moreover, we notice that the more risky a borrower is, the higher interest rate he will have to pay. The
lender revenue curves of the less risky borrowers cut the zero-profit line further to the left than those of

89
As in section 4.2.5, we assume that the competitors will undercut each other’s interest rate until they do not make
any profits.

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Credit Rationing in Microfinance Stockholm School of Economics

the risky borrowers.90 In section 4.2.3 we saw that credit rationing implies that a monopolist charges a
higher interest rate from less risky borrowers. Hence, isolating for credit rationing,

• the interest rate charged by the bank is negatively correlated to risk in monopoly, but
positively correlated to risk if we introduce competition and a cost of capital.

The latter correlation is in line with traditional financial theory on risk and interest rates.

The zero-profit condition implies that the MFIs will charge the following interest rate
Re viMFI = 1 + ri − εri − εri 2 + εri β i − c = 1
1  c
ri 2 −  − 1 + β i ri − = 0
ε  ε
2
1  1 
 −1 + βi   − 1 + βi 
ri =  ε ±  ε  −c
 2  4 ε
 
 
In line with the reasoning in section 4.2.5, the lower of the two solutions gives the relevant interest rate.
The profitable borrowers are worse off than without capital costs since they now face a higher interest
rate. Since the borrower still does not face any downside risk, his profit will be

Re viB = (1 − θ i )(β i − (1 + c) ) .

The unprofitable borrowers will still not get to borrow, just as in competition without capital costs.
Moreover, profit-maximizing MFIs will be as worse off as they would be in case of competition without
capital costs, making a zero-profit. Client-maximizing MFIs will be worse off since they cannot lend to as
many borrowers.

4.4 Subsidies
In the previous section we saw that the number of borrowers that get to borrow and the lowest interest
rate the MFIs are able to charge without making losses are dependent on the cost of capital. This result
has important implications on subsidization of MFIs. Donors and governments often subsidize MFIs by
providing funds at a low cost of capital. Since such subsidization simply implies a lower cost of capital, it
is covered by the previous section. However, the effects of lump-sum subsidies are not as straight-forward.

90
As described in section 4.2.5, the revenue curves cut the zero-profit curve twice, at a high and a low interest rate.
We refer to the lower and relevant interest rate, i.e. the cut-off point further to the left.

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Credit Rationing in Microfinance Stockholm School of Economics

The analysis on the effects of a non-targeted subsidy is analogous to the analysis on the cost of capital. We
therefore apply the reasoning used in the previous section on cost of capital to the case of non-targeted
subsidization. The MFI revenue formula can be generalized into
Rev iMFIsub = (1− θ i )(1+ ri − c) + θ i (β i − c) + G /n ,
where cost of capital (c) and a non-targeted lump-sum subsidy (G) affect the scenario in similar ways,
except for the costs being subtracted and the subsidy added to the MFI revenue. The MFI lends to a
number of n borrowers.

4.4.1 Monopoly
As shown in section 4.3.1, the interest rate charged by a monopolist is not affected by the cost of capital,
nor by other costs or subsidies. Hence, if a monopolist is profit-maximizing, the borrowers will not be
affected by the subsidy. The interest rate will be the same as in the base case. Only profitable borrowers
will get to borrow and the entire subsidy will end up in the hands of the MFI, increasing the total profit by
G. However, a profit-maximizing MFI is not likely to receive a non-targeted subsidy that can be used for
whatever purpose the MFI desires. Therefore, we will not investigate the case of non-targeted subsidies to
profit-maximizing MFIs any further.

On the other hand, if the MFI is client-maximizing, the subsidy will be used to provide credit to a larger
number of unprofitable borrowers in addition to those who get to borrow due to the cross-subsidization.
Accordingly, the client-maximizing MFI will be better off since the number of borrowers has increased.
Likewise, some unprofitable borrowers are better off. The interest rate is still unaffected since the MFI
first maximizes the profit received from the profitable borrowers. Consequently, the situation of the
profitable borrowers is unchanged. Hence,

• when there is only a client-maximizing monopolist, the only effect of a non-targeted

subsidy is an increase in the breadth of outreach.

4.4.2 Competition
Introducing subsidies to the competitive setting, we start by allowing only for one subsidized MFI. We
then identify the outcomes in a market where two MFIs are subsidized. Finally, we consider targeted
subsidies.

A. One subsidized MFI

Let us assume that there are two MFIs of which one is subsidized. Consequently, the subsidized MFI will
always be able to undercut the unsubsidized MFI. To maximize its profit doing so, the subsidized MFI
will charge the interest rate leaving the MFI with a zero profit in case of no subsidies, i.e. the interest rate
charged by the unsubsidized MFI, reduced by an arbitrarily small amount, δ. Thereby the subsidized MFI

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Credit Rationing in Microfinance Stockholm School of Economics

captures all the profitable borrowers. Since δ is very small, the interest rate change as well as the
subsequent change in the probability of default is negligible. Consequently, the effects of credit rationing
are similar to the effects in the case of no subsidies, implying an unchanged β ∗ .

A client-maximizing MFI will use the arbitrarily small amount δ times the number of profitable borrowers
n, A = δ × n , to undercut the competitor and capture all the profitable borrowers. The MFI will then use
the remainder of the subsidy, G-A, which is practically the entire subsidy, to fund lending to unprofitable
borrowers. Obviously, the subsidy makes the client-maximizing MFI better off since the number of clients
is increased.

We conclude that the unsubsidized MFI will not be able to lend profitably to any borrowers, since the
subsidized MFI captures all the profitable clients by accepting a minor loss. Therefore,

• an unsubsidized MFI will be driven out of the market or alternatively prevented from
entering the market, due to the existence of a client-maximizing MFI with a non-targeted
subsidy.

B. Two subsidized MFIs

To describe the outcome of two subsidized MFIs, we first return to the cost of capital scenario. If there is
a cost of capital but no subsidies, the MFIs will charge the interest rates where the lender revenue curves
cut the zero-profit curve in figure 4.5.

Now imagine that there are two subsidized client-maximizing MFIs. Accordingly, they will both be able to
lower the interest rate. Further, imagine that one MFI undercuts its competitor by a very small amount δ
lending to a specific borrower, as when there was only one subsidized MFI. However, this time the
competitor will respond by lowering his interest rate as well. The MFIs will follow the same procedure for
all borrowers until there is no subsidy left, i.e. until G − δ × n = 0 . At that point, each borrower will be
indifferent to what MFI to borrow from since they both offer the same interest rate.91

The intuition behind the above is based on a trade-off between interest rate and the number of clients.92 If
we add the subsidies received by each MFI and divide the total amount Ga+Gb by the number of
profitable borrowers n each MFI lends to,
Ga + Gb
α=
na + nb

91 The interest rate charged will still depend on the borrower’s risk. Riskier borrowers will face higher interest rates.
92 See Wydick and McIntosh, 2002.

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we get an average subsidy per profitable borrower, α. Both MFIs subsidizing each loan with an amount of
α is a Nash equilibrium. As explained above, both MFIs will make zero profits in competition and set δ
and the number of borrowers n so that G = δ × n .

If one of the MFIs would like to lower the interest rate offered to some borrowers to undercut the
competitor, it would have to increase the interest rate to other borrowers because of the zero-profit
condition. Any gain from lowering the interest rate offered to one group of borrowers would be
outweighed by the loss from increasing the interest rate offered to another group of borrowers. In fact,
the gain would be more than offset since the cost of undercutting per borrower is higher for the new
group of borrowers than for the initial set of borrowers. Hence, the MFI will be able to lend to fewer
borrowers trying to undercut the competitor. Therefore, given the choices of the opponent, neither of the
MFIs can choose an alternative that will make them better off.

We conclude that both MFIs will use the same amount to subsidize each borrower, i.e. the total subsidy
divided by the number borrowers that the MFI lends to. Hence, the zero-profit line shifts downward,
implying that the MFIs will be able to undercut each other until they reach the zero-profit line shown in
figure 4.6.

Revenue

Figure 4.6 The effects of a subsidy are the reverse from those of cost of capital. The zero-profit line falls and the
interest rates charged by competitors are lower.

Thus, the MFIs will use the same amount to subsidize lending to each borrower, regardless of the size of
their subsidies. The effects of two MFIs receiving lump-sum subsidies are similar to those of per borrower
subsidies. In other words,

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Credit Rationing in Microfinance Stockholm School of Economics

• subsidies function as cost of capital reductions.

However, for the above to hold true and for the MFIs to charge the same interest rate given the borrower
risk class, the size of their subsidies must affect the number of client they lend to, n.
Ga Gb
α= =
na nb
Ga n a
=
Gb n b
Hence, the share of the total amount of borrowers each MFI gets to lend to, na/nb, is equal to the relative
size of the subsidies. The MFIs are indifferent to which of the profitable borrowers they get to lend to,
and which are captured by the competitor.

Since the MFIs will both use their entire subsidies to fund the undercutting there will be no cross-
subsidization and no subsidy left to fund lending to unprofitable borrowers. Therefore, unprofitable
borrowers will be worse off and

• in competition, breadth of outreach will be lower when two client-maximizing MFIs

receive non-targeted subsidies, compared to when only one client-maximizing MFI get a
non-targeted subsidy.

Competition reduces the MFI profit to zero as well as implies that the entire subsidies will be used to fund
lending to profitable borrowers. The client-maximizing MFIs will be just as bad off as in the case of
competition without subsidies, only lending to a share of the profitable borrowers and not to any
unprofitable borrowers.

C. Targeted subsidies

So far we have only considered non-targeted subsidies, i.e. subsidies that can be used in whatever way the
MFI wishes. If we on the contrary introduce a subsidy that is targeted, e.g. that can only be used to fund
lending to a certain group of borrowers such as very poor and risky people, the scenario changes
considerably.

Let us assume that there are one unsubsidized and one subsidized MFI as in section 4.4.2 A, but that the
subsidy is targeted to be used only for lending to people that otherwise would not get to borrow, i.e.
unprofitable borrowers. Since the subsidy cannot be used to fund borrowing to profitable borrowers, the
revenue from lending to such borrowers will then be the same as without subsidies. Hence, given that they
face the same cost of capital, both MFIs will have to stop the undercutting at the interest rate leaving the

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MFI with a zero profit in case of no subsidies. Consequently, they will both only lend to profitable
borrowers, making a zero profit. Hence, cross-subsidization is not possible.

However, as opposed to in the previous section, some of the unprofitable borrowers will still get to
borrow. The entire subsidy will be used to lend to as many unprofitable borrowers as possible, given that
the MFI is client-maximizing.

A client-maximizing MFI will be worse off than in monopoly with a subsidy, but better off than in
competition with or without a non-targeted subsidy. β ∗ is unchanged and the profitable borrowers will

face the same interest rate as in the case of competition without subsidies, whereas some of the
unprofitable borrowers are better off. However, fewer of the unprofitable borrowers get to borrow
compared to the case of a subsidized, client-maximizing monopolist. The outcome of the competitive
scenario when only one client maximizing MFI receives a non-targeted subsidy, is similar to the outcome
of a targeted subsidy. In the former case, G-A was used to fund lending to unprofitable borrowers, A
being arbitrarily small. In the latter case, the entire subsidy G will be used to fund such lending.

4.5 Effects on the critical level of risk

4.5.1 Market structure

To examine how β ∗ , separating unprofitable borrowers from profitable borrowers, is affected by the

market structure, we consider the lending decision of the MFIs. We showed in sections 4.2.3 and 4.2.5
how MFIs will set their interest rates in monopoly and competition respectively. However, these
procedures only concern the decision of what interest rate to charge from a specific individual. Regardless
of market structure, the MFI will choose to lend to any borrower for which the profit constraint is
fulfilled. Hence, the profit constraint is binding for the marginal borrower, i.e. the riskiest player in the
group of profitable players.

Therefore, β ∗ depends on the profit constraint and not on the monopoly profit maximization. In other

words, β ∗ will be the same in monopoly as in competition. Hence, disregarding cross-subsidization,

• the effects of credit rationing on breadth of outreach is not affected by market structure.

4.5.2 Cost of capital and subsidies

Turning our attention to the effects of capital costs and subsidization on β ∗ , we note from the previous

section that the profit constraint is binding for the critical borrower, i.e. the riskiest borrower in the group

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of profitable borrowers. From the interest rate in the case of competition and cost of capital,
2
1  1 
 −1 + βi   −1 + βi 
ri =  ε − ε  −c ,
 2  4 ε
 
 
we conclude that an increase in the cost of capital raises the interest rate to cover the higher costs.

Subsidies, on the other hand, have the opposite effect. Figure 4.7 shows that the capital cost shifts the
lender profit curve downwards. The interest rate charged by the monopolist for a specific borrower is
unchanged, but the cut-off point, i.e. the interest rate at which the lender makes a zero profit, is further to
the right. Once again, we see that the increased cost of capital has caused the competitive interest rate to
rise. The lowest interest rate charged by the monopolist also increases in the cost of capital. Therefore, β ∗

changes.

Figure 4.7 The cost of capital shifts the lender profit curve down-wards.

An increase in interest rate implies an increase in the probability of default. Hence, due to credit rationing,
the riskiest borrowers in what used to be the profitable group will not be profitable any longer. Increasing

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the interest rate charged by the marginal borrower is not viable. Instead, to increase the interest rate, the
MFI must raise the risk requirements, i.e. β ∗ .

To solve for the β i for which the lender profit constraint is binding, we turn to the revenue formula in

section 4.3.2. Solving for β i we get

c 1
βi = − + 1 + ri .
εri ε
1
We derive the above formula with aspect to capital costs and get β i′ = .
εri

The derivative is positive as long as the cost of capital is above zero. Hence, β ∗ increases in capital costs.

The interest rate at which the profit constraint is binding is higher due to the increased cost of capital.
Consequently,

• increased costs of capital or decreased subsidies raise β ∗ .

In other words, the riskiest borrowers in the group of profitable borrowers will now be classified as
unprofitable. Increased subsidies imply a lower β ∗ , i.e. a riskier marginal borrower.

In section 4.5.1, we learnt that β ∗ is not affected by the number of players in the market (i.e. monopoly or

competition). We therefore conclude that the above is valid in monopoly as well as in competition.

4.5.3
β i as collateral
If we relax our assumption that the MFI can only repossess assets financed by the loan, we may include
collateral in the model. By adding the amount of collateral per unit borrowed to β i , the collateral raises
the lowest amount the lender will be repaid, given that repossession of collateral is a viable alternative in
the legal setting.

The collateral implies a larger downside for the borrower in case of default. The downside raises the
incentives of the borrower to exert effort to make the project successful, which is captured in the model
through the interest rate function. Looking at the previous sections, we see that
*
ri = f ( β i ) .

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Credit Rationing in Microfinance Stockholm School of Economics

In monopoly the optimal interest rate is positively correlated to the level of repossessable assets. This
means that when β i increases due to collateral, the optimal interest rate also increases. This is completely
logical if we consider that our model only captures the credit rationing effects. Less overall risk in a
project means that credit rationing becomes less severe and thus the interest charged will be higher. Hence,

• in monopoly, borrowers face a higher interest rate if they post collateral due to credit
rationing.

Therefore, there are no incentives for borrowers to post collateral in this framework.

When there are competition and cost of capital on the other hand, the optimal interest rate is negatively
related to the level of repossessable assets. Accordingly,

• in competition, borrowers face lower interest rates if they post collateral.

Thus, when there is a well-functioning competitive market which ensures that borrowers do not get
expropriated by the MFIs, there will be incentives for individuals to pose collaterals and there are better
possibilities to reduce credit rationing.

5 Outcomes and implications

This paper outlines how credit rationing affects the relation between interest rate and risk of default in a
microfinance setting. In our model we isolated credit rationing from other factors that also affect the
choices of MFIs. To understand what happens in reality, all effects must be combined. It is beyond the
scope of this paper to combine all the factors, in light of which the following argumentation has to be
viewed.

Credit rationing implies that there are some borrowers that are too risky to lend to, regardless of how
much they are willing to pay. The most important results of the model concern the outreach of the MFIs
and the relation between the interest rate and the risk level of the borrower.

Our model shows that in a monopolistic market, the riskiest borrowers that have access to credit face a
lower interest rate than less risky borrowers. 93 When the model is expanded to deal with competitive
markets and capital costs, high risk projects have to pay higher interest rates than low risk projects.

93
This is not specific to our linear model, but holds true in most credit rationing models, see for example Stiglitz and
Weiss, 1981.

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However, there are still projects that receive no financing at all, no matter how much interest they are
prepared to pay.

The effects of credit rationing on breadth of outreach are not affected by market structure directly.
However, outreach is not as strongly affected by credit rationing in the presence of a client-maximizing
monopolist as when there is only a profit-maximizing monopolist. In a monopoly with only one client-
maximizing MFI, some of the unprofitable borrowers will get to borrow, whereas if there is only one
profit-maximizing MFI, credit rationing will have full effect and only profitable borrowers will have access
to credit. In fact, outreach is lower in competition than in monopoly with only a client-maximizing
monopolist.

Since an increase in the cost of capital raises the interest rate to cover for the higher costs, capital costs
cause β ∗ to increase and credit to be more rationed. When subsidies are introduced they function as cost

of capital reductions. Moreover, credit rationing is less palpable if a client-maximizing MFI is subsidized,
since the subsidy will then to some extent be used to subsidize lending to unprofitable borrowers. Non-
targeted subsidies will not make a profit-maximizing MFI lend to unprofitable borrowers. Thus,
subsidizing a profit-maximizing MFI will not reduce credit rationing unless the subsidy is targeted, i.e. can
only be used for lending to unprofitable borrowers.

If a client-maximizing MFI in a competitive market receives a non-targeted subsidy, unsubsidized MFIs

will be driven out the market. Allowing for two client-maximizing MFIs to receive non-targeted subsidies,
both institutions will be able to use the subsidy to undercut the competitor. Consequently, the subsidy will
not fund lending to unprofitable borrowers. Outreach will be lower compared to when only one MFI gets
a non-targeted subsidy.

The increased interest rate in the case of collateral described in section 4.5.3 is yet another implication of
credit rationing. Putting up collateral may be considered beneficial to most borrowers. The collateral
implies a lower risk for the bank reflected in a lower interest rate. However, as we showed above, credit
rationing effects make it less beneficial for lenders to put up collateral when borrowing from a
monopolistic MFI.

One of the most interesting aspects of our model is the relationship between the objectives of MFIs and
the nature of the subsidies. Non-targeted subsidies to profit-maximizing MFIs will only end up in the
hands of the MFIs and not benefit the borrowers. Hence, to benefit borrowers, non-targeted subsidies
should only be given to client-maximizing MFIs. Targeted subsidies will benefit unprofitable borrowers if
given to profit-maximizing as well as client-maximizing MFIs. Which is the most appropriate method of
subsidization depends on which actor can most efficiently determine where the credit is most needed.

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Credit Rationing in Microfinance Stockholm School of Economics

In case of profit-maximizing MFIs and targeted subsidies, the positive incentives created by profit-
maximization are expected to improve the execution of microfinance. On the other hand, there are
inefficiencies in that the donor of the subsidy has to decide how to target the subsidy. A common way to
do this is to limit the subsidy to borrowers under a certain wealth level. This restriction is likely to be a
rough and rather inaccurate way of identifying who needs the subsidies. Borrowers can be tempted to
appear poorer than they really are to get subsidized loans and MFIs may accept this to get borrowers with
lower default ratios and thereby increase their profits.

Nevertheless, client-maximizing MFIs with non-targeted subsidies are also problematic. Most likely, the
closer the allocators of subsidies are to the borrowers, the more efficient and informed the decision.
However, the absence of profit-maximization implies that many incentives to make efficient choices in
execution are missing. One of the most obvious deficiencies is that it is very hard or impossible to tell
whether client-maximizing MFIs make losses because their execution is bad or because they are lending to
the people who need it the most.

6 Microfinance in Vietnam

The possibility to assess the appropriateness of theoretical models such as the one presented in this paper
is typically limited.94 In the absence of large unbiased samples, it is not possible to isolate the effects of
credit rationing within the industry. Lately, efforts have been made to create more substantial databases.
These databases show that microfinance markets most often are competitive and that MFIs are almost
always subsidized. 95 At the moment however, the databases are based on voluntary participation and
reporting of statistics. Consequently, the MFIs contributing data are mainly the more successful ones that
have nothing to hide, meaning that the databases are severely biased.

Due to the lack of accountable data on microfinance markets, we present an indicative example to
illustrate the outcomes of our model. For this purpose, we have chosen the rural financial sector of
Vietnam.

Vietnam is one of the fastest growing economies in the world, partly due to the development efforts
within the financial market. In ten years, between 1993 and 2002, poverty was heavily reduced.96 However,
the country still being very poor, the financial sector shows many of the characteristics typical for credit
markets in developing countries mentioned in section 2. The legal system is insufficient causing a large

94 Jonathan Morduch, personal communication 2005.

95 See appendix C for description of the Mix Market database.
96 ARCM, 2005.

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extent of moral hazard. Being a former French colony, Vietnam has a civil law system.97 A large part of
the population is too poor to be able to pose any collateral. The Vietnamese MFIs are free to set their
own interest rates, unlike in some countries where the institutions are heavily regulated.98 We therefore
find Vietnam to be an appropriate country to apply to our model.

Even though there are MFIs that target the urban sector, we limit this example to the rural sector. We first
describe the market and identify which institutions to refer to as MFIs. Thereafter, we focus on the
concepts dealt with in our model and describe credit rationing and moral hazard on the Vietnamese
microfinance market. Finally, we comment on the correlation between interest rate and risk.

6.1 The rural financial sector in Vietnam

According to the Vietnam 1997-98 Living Standards Survey, 50 percent of the Vietnamese households are
in debt.99 Only considering rural households, the figure is even higher (54 percent). The loans can be
divided into two groups, the informal financial sector and the formal/semi-formal financial sector.100

Loans (%) Average loan size (1000 VND101)

Informal financial sector 51 1,752
Moneylender 9.8 2,141
Relatives 24.2 1,861
Ho/Hui 16.8 1,366
Formal/semi-formal financial sector 49 3,209
Private banks and cooperatives 2.2 2,230
Government banks 40.0 3,512
Government programmes and others 7.7 1,547
Total 100 2,480

Table 6.1 Rural household loans and average loan sizes in rural Vietnam 1997-98.102

Even though the Vietnamese microfinance market is segmented, separating MFIs from other financial
institutions is not a straight forward process. Microfinance schemes are defined as all small-scale formal
and quasi-formal financial lending to rural households, directly or through groups. The formal sector
consists of financial institutions recognized as credit organizations by law.103 The government bank, the

97 AusAID, 2000.
98 GSO, 2000.
99 Ibid.
100 ARCM, 2005.
101 1 USD ~ 15,746 VND (2004).
102 GSO, 2000.
103 Note that formal financial institution are defined differently from in section 2.3, where we seperated formal banks

from MFIs. Here, MFIs fall in the group of formal or semi-formal institutions.

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Vietnam Bank of Agriculture (VBARD), dominates the formal sector, lending to 38 percent of the rural
households in Vietnam. The bank lends to poor people, but only if they are credit-worthy, i.e. if the bank
can repossess collaterals.104 The Vietnam Bank for the Poor (VBP) lends to the poor people that do not
get to borrow from VBARD. However, many of these loans are once-off loans and the maximum loan
limit was 2.5 million VND.105 The semi-formal sector presented in table 6.1 includes cooperatives and
programmes such as group lending initiatives, joint-stock banks and foreign NGO schemes.106

The pool of borrowers consists of a group that can borrow from the VBARD and a group that cannot.107
Financial institutions lending to the latter group are often labelled MFIs, which includes private banks and
cooperatives, government programmes and the VBP. Since our model does not include collateral, it is not
applicable on the VBARD.108

The MFIs are in general client-maximizing, even though there are tendencies towards an increased focus
on sustainability. All the MFIs in the rural financial market in Vietnam are more or less subsidized.
Moreover, the subsidies given to NGOs are often targeted to be used only for lending to people below a
certain level of poverty. The VBP activities are targeted in the same way.109

The informal financial sector consists of moneylenders, borrowing from relatives and Ho/Hui110, local
rotating savings and credit associations.111

6.2 Credit rationing on the Vietnamese microfinance market

There is a great excess demand on the Vietnamese rural credit market, implying that the outreach of the
MFIs is limited. Only about 50 percent of the 12 million households in rural Vietnam have access to
microfinance.112 Since demand outstrips supply, poor households tend to be pushed into market segments
where they have no formal sector lending options. The main reason why formal institutions do not lend to
poor people is because they are considered to be too risky.113 However, the interest rates charged by MFIs
are not very high. The formal institutions seem to be reluctant to increase their interest rates to
compensate for high risk, indicating that there is credit rationing on the Vietnamese credit market.114 In
other words, ε of our model seems to be large. If the MFIs increased their interest rate, the probability of
default would increase so much that the revenue would fall.

104 McCarty, 2001.

105 GSO, 2000.
106 ARCM, 2005.
107 Economist Intelligence Unit, 1999.
108 McCarty, 2001.
109 Ibid.
110 Traditional Vietnamese rotating savings and credit associations (ROSCAs) are called Ho in the North and Hui in

the South. Some of them are created for special purposes such as weddings, funerals or New Year’s celebrations.
111 ARCM, 2005.
112 There are 15 million households in Vietnam. About 80 percent of these are rural.
113 GSO, 2000.
114 Economist Intelligence Unit, 1999.

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We conclude that a large group of poor people in rural Vietnam does not have access to credit from
formal institutions because they are considered to be too risky. In our model, we defined the measure for
risk β i as the share of the loan invested in physical assets that the lender can repossess. Applying that
definition to the Vietnamese financial market, we need to consider what the loans are used for. Table 6.2
shows the reasons for taking out microfinance loans in rural Vietnam stated by households in the Vietnam
Living Standard Survey 1997-98 mentioned above.

Reasons for taking out loans Share of households with

loans outstanding (%)

Production or construction 66.3

Buy or build a house 10.3
Buy consumer durables 2.9
General consumption and food
before harvest 3.3
Others 17.2

Total 100

Table 6.2 Reasons for taking out microfinance loans in rural Vietnam.115

We see that a majority of the borrowers obtaining loans states that they will invest the money in
production. The second largest group of borrowers uses the loan to finance buying or building of houses.
In both cases, the lender is likely to retain some value (e.g. the house) in case of default. Hence, β i is
substantial. On the other hand, very few loans are given for consumption. In such cases there is rarely any
value for the bank to reclaim. Hence, β i equals zero or approximately zero. Notably, poor people often
apply for loans to finance consumption.116 The above indicates that the poor people excluded from the
rural credit market are those who apply for loans to finance consumption, i.e. have lower β i .

Consequently, the group excluded from the credit market can be ascribed a β i below the critical risk level

of our model, β ∗ .

6.3 Moral hazard in Vietnam

Having identified indications of credit rationing, we now turn to the underlying reasons described in the
theory section. Our model is based on moral hazard. An increased interest rate implies reduced incentives
to repay the loan since the borrower now avoids a higher cost by defaulting. As mentioned above, the
Vietnamese legal system is insufficient.117 Since the semi-formal sector falls outside the existing law on
credit institutions, there is still no comprehensive legal framework covering microfinance activities in

115 GSO, 2000.

116 Ray, 1998.
117 Havers et al., 2000.

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Vietnam.118 Consequently, since monitoring and enforcement are limited, the MFIs are reluctant to lend to
poor individuals applying for loans to finance consumption. In other words, moral hazard, implying a
substantial ε is likely to cause credit rationing in rural Vietnam.

To see how moral hazard and enforcement affect the interest rate charged by financial institutions in
Vietnam, we compare the formal and semi-formal institutions to informal lenders.

Figure 6.1 Monthly interest rates charged by different types of financial institutions in rural Vietnam.119

Figure 6.1 shows the monthly interest rates charged by the different types of institution in 1997-98.120 The
lenders charging the highest interest rate, moneylenders, are renowned for their efficient and sometimes
dubious enforcement methods. Formal financial institutions on the other hand, face severe moral hazard
problems in the Vietnamese rural credit markets due to the limited possibilities to enforce repayment. In
fact, as mentioned above, formal institutions sometimes cooperate with informal players to mitigate the
moral hazard problem.121 Hence, the interest rates in figure 6.1 seem to be negatively correlated to the
extent to which the lender is exposed to moral hazard. The institutions exposed to moral hazard cannot
charge high interest rates since that would increase the probability of default to such an extent that their
revenue would fall. On the other hand, moneylenders can lend profitably charging interest rates at which a
formal institution would make a loss.

6.4 Desired legal and institutional reforms

The above reasoning indicates a need for legal and institutional reforms within the Vietnamese
microfinance sector. A survey made by the British Department of International Development (DFID) in
1998 shows that a majority of the managers of 78 Vietnamese MFIs desires legal reform. Specified legal
frameworks for different types of MFIs and improved supervision and transparency are some of the
desirable changes identified.122 Such reforms would improve the informational flow of the credit market
and reduce problems of moral hazard and adverse selection. Hence, the reforms could remedy the very
causes of credit rationing by reducing moral hazard, i.e. lowering ε.

118 ARCM, 2005.

119 McCarty, 2001.
120 Ibid.
121 GSO, 2000.
122 DFID, 1998.

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In fact, there has been a move towards an improved legal framework in Vietnam since 1996. 123 For
example, commercial banks now have greater flexibility in deciding on loan guarantee requirements.
Moreover, the registration possibilities for non-credit institutions with banking activities and the legal
framework for credit cooperatives are improved. Consequently, there has been an overall increase in
interest rates in Vietnam.124 This might imply a reduction of credit rationing. There are indications that the
formal and semi-formal sectors have crowded out the informal sector, implying that moral hazard is less
of a problem due to the reforms. Data from the 1992-93 Vietnam Living Standards Survey shows that
private money lenders provided 33 percent of loan funds in rural areas, whereas government banks had a
23 percent market share. In the 1997-98 Vietnam Living Standards Survey the corresponding figures were
10 percent and 40 percent respectively.125

6.5 Correlation between interest rate and borrower risk

Finally, we focus on the correlation between interest rate and the risk level of the borrower. In section
4.3.2 we showed that in a competitive market with subsidized MFIs, such as the Vietnamese rural credit
market, there is a positive correlation between interest rate and risk. However, from figure 6.1 we see that
government programmes charge the lowest interest rate of all. Considering that such institutions lend to at
least as many poor and risky clients as the private banks and cooperatives, we suspect that there is no
strong positive correlation between interest rate and risk. Moreover, the MFIs often charge the same
interest rate to customers of different wealth and risk class. 126 Hence, there are no indications of the
positive correlation between interest rate and risk predicted by section 4.3 of our model.

To summarize our analysis of the rural credit market in Vietnam, formal and semi-formal institutions
facing moral hazard problems charge substantially lower interest rates than informal institutions with more
effective enforcement methods. Moreover, we recognize that a large group of poor people is excluded
from the formal and semi-formal credit markets since they are considered to be too risky. Hence, outreach
is obviously limited. However, whereas there are marked effects of credit rationing on outreach, we find
little support for the interest rate implications predicted by our model. The interest rate seems to depend
on other factors.

123 Dao Van Hung, 1999; Havers et al., 2000.

124 McCarty, 2001.
125 GSO, 2000.
126 ARCM, 2005.

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7 Conclusion

In this paper, we examined how credit rationing affects microfinance markets in developing countries. We
developed a model where credit rationing is isolated from other effects. The focus is upon the outreach of
MFIs and the relation between the interest rate and the risk level of the borrower.

In monopoly, we find a negative correlation between the risk level of the borrower and the interest rate
charged by the MFI due to credit rationing. In competition, the negative correlation between interest rate
and risk level caused by credit rationing identified in monopoly is outweighed because of the zero-profit
condition. The interest rate will no longer decrease but rather increase in the level of risk, given that cost
of capital is included.

Subsidies mitigate the rationing of credit if a monopolist is client-maximizing. To improve the outreach,
the MFI will use the profit made from lending to profitable borrowers to cross-subsidize lending to
unprofitable borrowers. However, in competitive markets, subsidies will not improve the outreach of
MFIs to the same extent. In such markets, there will be no cross-subsidization since the subsidies are used
to undercut the competitor. Hence, in competitive markets, credit rationing will limit the outreach of
microfinance even if there are subsidies.

Evidence from microfinance data bases as well as our indicative example suggest that microfinance
markets often are characterized by substantial competition between subsidized MFIs. The analysis of the
rural credit market in Vietnam shows that institutions facing moral hazard problems are reluctant to
charge high interest rates. Hence, borrowers who are considered to be too risky are excluded from the
formal credit market.

In summary, credit is rationed and cross-subsidization is limited in microfinance markets. Given the
observed level of competition and subsidization in such markets, there are limitations to the extent to
which subsidies can mitigate the effects of credit rationing on outreach. To reduce the negative impacts of
credit rationing in microfinance markets, the underlying causes must be altered. Improving the
institutional framework in general and the legal framework in particular would reduce moral hazard and
consequently credit rationing. In light of the findings revealed in our model, it would be profitable to
further investigate the impacts of such institutional changes.

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Credit Rationing in Microfinance Stockholm School of Economics

8 References and readings

8.1 References
Armendáriz de Aghion, B. and Morduch, J., 2000. “Microfinance Beyond Group Lending”. Economics of.
Transition, 8, 401–420.

Asia Resource Centre for Microfinance (ARCM), 2005. Vietnam - Microfinance Country Profile. Available at
www.bwtp.org.

AusAID, The Australian Gorvernment Overseas Aid Program, 2000. Vietnam Legal and Judicial Development.
Working Paper 3. April 2000.

Banerjee, A. V. and Newman A. F., 1993. ”Occupational Choice and the Process of Development”. The
Journal of Political Economy, 101:2, 274-298.

Becht, M., Bolton, P. and Röell, A., 2002. Corporate Governance and Control. ECGI Working Paper Series in
Finance No. 02/2002.

Berglöf, E. and von Thadden, E.-L., 2000. ”The Changing Corporate Governance Paradigm: Implications
for Transition in Developing Countries”, in Plescovic, K. and Stiglitz, J. E. (eds.) 2000, World Development
Conference, The World Bank.

Bell, C., 1990. “Interactions between Institutional and Informal Credit Agencies in Rural India”. World
Bank Economic Review, 4:3, 297-328.

Bodie, Z., Kane, A. and Marcus, A. J., 2004. Essentials on Investments. New York: McGraw-Hill.

Bose, A., 1996. “Subcontracting, Industrialisation and Labouring Conditions in India – an Appraisal”.
Indian Journal of Labour Economics, 39:1.

Brau, J. C. and Woller, G., 2004. “Microfinance Institutions: A Comprehensive Review of the Existing
Literature and an Outline for Future Financial Research”. Journal of Entrepreneurial Finance and Business
Ventures, 9, 1-26.

Charitonenko, S. and de Silva, D., 2002. Commercialization of Microfinance, Sri Lanka. Asian Development
Bank, Manilla, Philippines.

Coffee, J. C., 2000. Convergence and Its Critics: What are the Preconditions to the Separation of Ownership and Control?
Center for Law and Economic Studies, Working Paper No. 179, Columbia Law School.

Conning, J., 1999. “Outreach, Sustainability and Leverage in Monitored and Peer-Monitored Lending”.
Journal of Development Economics, 60:1, 51-77.

Dao Van Hung, 1999. Outreach Diagnostic Report: Improving Low-income Household Access to Formal Financial
Services in Vietnam. February.

Demirgüç-Kunt, A. and Detragiache, E., 2002. “Does Deposit Insurance Increase Banking System
Stability? – An Empirical Investigation”. Journal of Monetary Economics, 49:7, 1373–1406.

De Soto, H., 2000. The Mystery of Capital: Why Capitalism Triumph in the West and Fails Everywhere Else. New
York: Basic Books.

DFID, 1998. Microfinance: Banking on the Poor. DFID, Enterprise Development Group.

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Credit Rationing in Microfinance Stockholm School of Economics

Economist Intelligence Unit, 1999. Country Profile: Vietnam. The Economist Intelligence Unit, London,
United Kingdom.

Ekstrand, T. and Tofighian, N., 2004. Guidelines for Creating Efficient Credit Programs for the Poor. A field study
on rural credit programs in the Philippines. Minor Field Study, Series No. 89.

Fischer, K. P., 2000. A Market Approach to Microfinance: A Deserving Research Agenda. Working Paper,
CREFA, Laval University.

Floro, M. S. and Ray, D., 1997. “Vertical Links between Formal and Informal Financial Institutions”.
Review of Development Economics, 1:1, 34-56.

Freimer, M. and Gordon, M. J., 1965. “Why Bankers Ration Credit”. Quarterly Journal of Economics, 79, 397-
416.

General Statistics Office (GSO), 2000. Viet Nam Living Standards Survey 1997-1998. Hanoi: Statistical
Publishing House.

Ghosh, P., Mookherjee, D. and Ray, D, 1999. “Credit Rationing in Developing Countries:
An Overview of the Theory”, in Mookherjee, D., and Ray, D. (eds). A Reader in Development
Economics. London: Blackwell.

Ghosh, A., Gulde, A. and Wolf, H., 2002. Exchange Rate Regimes: Classifications and Consequences. Cambridge:
MIT Press.

Greenbaum, S. and Thakor, A., 1995. Contemporary Financial Intermediation. Fort Worth: Dryden Press.

Hart, O., 1995. Firms, Contracts, and Financial Structure. Oxford: Oxford University Press.

Havers, M. and Moyart, M. 2000. Legal Framework for Microfinance in Vietnam Visit Report. Report to DIFID,
Hanoi, December.

Hoff, K and Stiglitz, J. E., 2001. “Modern Economic Theory and Development”, in Meier, G. M. and
Stiglitz, J. E. (eds.). Frontiers of Development Economics: The Future in Perspective. New York: Oxford University
Press.

Hoggarth, G., Jackson, P. and Nier, E., 2005. “Banking Crises and the Design of Safety Nets”. Journal of
Banking and Finance, January 2005, 29:1, 143-159.

Hulme, D., 2000. ”Impact assessment Methodologies for Microfinance: Theory, Experience and Better
Practice”. World Development, 28:1, 79-98.

Kane, E. J., 2000. Designing Financial Safety Nets to Fit Country Circumstances, The World Bank.

Keeton, W. R., 1979. Equilibrium Credit Rationing. New York: Garland Press.

Kyei, A., 1995. Deposit protection arrangements: A survey. IMF Working Paper No. 134.

LaPorta, R., de Silanes, F. L., Schleifner, A. and Vishny, R. W., 1998. “Law and Finance”. Journal of Political
Economy, 106, 1113-1155.

LaPorta, R., de Silanes, F. L., Schleifner, A. and Vishny, R. W., 2000. “Investor Protection and Corporate
Governance”. Journal of Financial Economics, 58, 3-27.

Manove, M., Padilla, A. J. and Pagano, M. Collateral vs. project screening: a model of lazy banks, Forthcoming:
Rand Journal of Economics.

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Credit Rationing in Microfinance Stockholm School of Economics

MBB, 2005. The MicroBanking Bulletin. 10. March 2005.

McCarty, A., 2001. Microfinance in Vietnam: A survey of Schemes and Issues. DFID.

Morduch, J., 1999. ”The Microfinance Promise”. Journal of Economic Literature, 37, 1569-1614.

Perry, D., 2002. “Microcredit and Women Moneylenders: The Shifting Terrain of Credit in Rural Senegal”.
Human Organization, 61, 30-40.

Ray, D., 1998. Development Economics. New Jersey: Princeton.

Stiglitz, J. E. and Weiss, A., 1981. ”Credit Rationing in Markets with Imperfect Information”. The American
Economic Review, 71:3, 393-410.

The Global Development Research Center, 2005. Data Snapshots on Microfinance – The Virtual Library on
Microcredit. Available at www.gdrc.org

The Microcredit Summit. Microcredit Summit Report 2002. Available at www.microcreditsummit.org

The World Bank, 2000. Vietnam 2010: Entering the 21st Century: Vietnam Development Report 2001. The World
Bank, Hanoi.

The World Bank. 2001 World Bank Statistics, 2001. Available at www.worldbank.org

Woller, G. M., Dunford, C. and Woodworth, W., 1999. ”Where to Microfinance?” International Journal of
Economic Development. 1:1, 29-64.

Woller, G. M., 2002. “From Market Failure to Marketing Failure: Market-Orientation as the Key to Deep
Outreach in Microfinance”. Journal of International Development, 14, 305-324.

Wydick, B. and McIntosh, C., 2002. Competition and Microfinance. Working Paper, University of California at
Berkeley.

8.2 Readings
De Luna-Martinez, J., 2000. Management and Resolution of Banking Crises: Lessons from the Republic of Korea and
Mexico. World Bank Discussion Paper No. 413.

Mathison, S., 2003. Microfinance and Disaster Management. The Foundation for Development Cooperation.

Mishkin, F. S., 1996. Understanding financial crises: A developing country perspective. NBER Working Paper No.
5600.

Nagarajan, G., 1998. Microfinance in the Wake of Natural Disasters: Challenges and Opportunities, available at
http://www.gdrc.org/icm/icm-documents.html.

Pantoja, E., 2002. Microfinance and Disaster Risk Management. Provention Consortium.

Steindl, F. and Weinrobe, M. D., 1983. “Natural Hazards and Deposit Behavior at Financial Institutions :
A Note.” Journal of Banking and Finance, 7:1, 111-118.

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Credit Rationing in Microfinance Stockholm School of Economics

9 Appendices

9.1 Appendix A

Option-like characteristics of loan contracts

The interest rate may function as a screening device for banks to distinguish between good and bad
projects.127 Lending institutions can rarely identify projects with different risk but the same mean return, R.
This means that the potential projects are sorted into a number of groups with similar return profiles and
are offered the same interest rate, r, on a loan of size V.

Figure A.1 The density functions of a low risk and a high risk project.

As shown in figure A.1 both projects have the same mean expected return, but differ in variance. The
bank owns the rights to the cash flows below the principal and the interest, V(1+r). As can be seen in the
graph, the risk of the return R being smaller than V(1+r), i.e. the loan being in default, is greater for the
borrower with the highest variance. The borrowers get nothing if the default. The borrower with the
highest variance gets the largest profit in case of success. Hence, for a given interest rate, the bank prefers
projects with low risk and borrowers prefer projects with high risk. In other words, the risk profiles of
lenders and equity holders respectively are determined by the option-like mechanisms of loan contracts.

The lender’s position can be described as if he owned the assets in the project and had issued a call option
to the entrepreneur/owner, i.e. there is an upward limit to his pay-off.

127 The section is based on Becht et al., 2002 and Bodie et al., 2004.

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Figure A.2 The lender holds a put option.

The borrower on the other hand, has a call option, i.e. there is a down-ward limit to his pay-off. In other
words, the borrower does not face any downward-risk.

Figure A.3 The borrower holds a call option.

Since the pay-off function of the borrower is convex, his pay-off is increasing in risk. The riskier the
project is, the higher interest rate he will be prepared to pay. Hence, at high interest rates, only borrowers
investing in very risky projects are prepared to borrow money. Thus, the interest rate a player is prepared
to pay reveals his risk class.

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9.2 Appendix B

ε must be larger than one

In section 4.2.2 we argue that ε needs to be larger than one based on the calculations presented below. We
start in the revenue formula presented in section 4.1.3 and derive an expression for the optimal interest
rate at given levels of β i and ε.
Rev iMFI = 1+ ri − εri − εr 2i +εri β i
∂ Rev iMFI
= 1− ε − 2εri + εβ i
∂ri
∂ Rev iMFI
=0
∂ri
* 1 1 
ri =  −1+ β i 
2 ε 
This is the interest where the MFI maximizes its revenue. We stated that the MFI will try to capture as
many profitable customers as possible but always maintain an interest rate above zero. In the base case of
our model the marginal borrower is charged an interest rate of zero. Consequently, the interest rate and
the critical level of β i given ε is then
ri* = 0
1
βi * = 1 −
ε
We also know from the definition of β i that
0 < βi < 1
Thus
1
1 < 1−
ε
ε >1

If β ∗ is zero, everybody will have access to the credit market. Hence, β ∗ must be larger than zero for
there to be credit rationing. In other words, since we want our model to deal with credit rationing, we
assume that ε is larger than one.

9.3 Appendix C

The Mix Market

Despite the limited possibilities to assess our model, we here present data from one of the most
recognized databases, the Mix Market (MBB, 2005). The database aims at improving the microfinance
infrastructure, offering data sourcing, benchmarking and monitoring tools. The objectives are to help
increase standardized reporting among MFIs, improve and stimulate MFI performance and transparency
and boost public and private investment in microfinance. To reach these goals, the Mix Market
standardizes financial reporting across the entire industry, provides a leading benchmarking service and
offers a reliable open information marketplace to facilitate the exchange of quality data. The Mix Market
database is considered a relatively reliable source of information, often referred to in the most prominent
literature within the field.128

The data presented in the table below is based on the 10th edition of the MicroBanking Bulletin.129 The
MFIs contributing with information were invited based on length, quality and depth of previously

128 Morduch, 1999; Ghosh et al., 2002.

129 MBB, 2005.

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Credit Rationing in Microfinance Stockholm School of Economics

reported data. The 60 MFIs participating in the survey are of different size and have different objectives.
Some have non-profit status, i.e. client-maximizing in our model, whereas others are profit-maximizing.
The data spans all across the globe. Even though the MFIs are chosen to represent different parts of the
industry, the criteria on previously reported data stated above implies a bias of the data set. Established,
well-functioning MFIs are overrepresented in the sample. Hence, the statistical accuracy is questionable
since the sample is far from random.

To relate our model to the real world microfinance market, we describe the risk of different types of MFI
portfolios as well as profitability and sustainability documented in the MBB.

Return on Assets (%)

2002 2001 2000 1999
For Profit 1,7 0,4 0,4 -1,5
Not for Profit 3,2 2,9 -1,0 -4,4

Financial Self-sufficiency (%)

2002 2001 2000 1999
For Profit 111 105 103 99
Not for Profit 121 118 103 97

Portfolio at Risk >30 days (%)

2002 2001 2000 1999
For Profit 4,2 4,8 5,4 7,9
Not for Profit 2,9 2,5 3,5 3,4

Average Loan Balance per

Borrower (USD)
2002 2001 2000 1999
For Profit 630 640 634 767
Not for Profit 276 317 277 270

Table C.1 Profitability, sustainability, risk proxies and loan sizes for the MFIs in the sample.130

Firstly, the profit-maximizing MFIs in the data set have riskier portfolios than the non-profit MFIs.131
Hence, at first glance, the data set seems to contradict a basic characteristic of our framework. Based on
credit rationing, our model predicts that MFIs cannot lend profitably to very risky borrowers. The
empirical evidence however, implies that the credit rationing might not be as outstanding as we have
assumed. Political factors such as interest rate restrictions on client-maximizing institutions have opposing
effects to credit rationing. We would therefore need to isolate for such effects. However, such isolation is
not feasible due to the lack of data.

Secondly, the implications of competition between MFIs predicted by our model seem to be supported by
the empirical evidence. The returns on assets 132 presented in the table shows that neither the profit-
maximizing, nor the client-maximizing MFIs make substantial profits on average. However, there are
several possible explanations for the absence of profit in the industry.

130 MBB, 2005.

131
Based on Portfolio at Risk > 30 Days = Outstanding balance, loans overdue > 30 Days / Adjusted Gross Loan
Portfolio.
132
Return on Assets = Adjusted Net Operating Income, net of taxes / Adjusted Average Total Assets. The values
are adjusted for inflation, subsidization and loan loss provision.

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Credit Rationing in Microfinance Stockholm School of Economics

Thirdly, the MFIs in the sample seem to be self-sufficient133 on average. However, the surprisingly high
self-sufficiency documented might be caused by the doubtful reporting mentioned above rather than true
sustainability. For example, subsidized MFIs tend to subtract the subsidies from the cost of capital instead
of reporting them separately. Even though the MBB tries to adjust for subsidies, the figures presented
above are likely to be slightly exaggerated.134 Most MFIs are subsidized in some way and the subsidies are
in general non-targeted. Instead of targeting the subsidies, donors choose which MFIs to subsidize
according to the objectives of the MFIs.

Finally, the average loan size 135 is used as an estimate of how poor the borrowers are. 136 Hence, in
accordance with the cross-subsidization element of our model, the empirics show that client-maximizing
(non-profit) MFIs tend to lend money to poorer people than profit-maximizing MFIs.

To conclude, microfinance markets seem to be characterized by substantial competition and subsidization.

9.4 Appendix D

One relationship between probability of default and interest rate which offers many attractive features is
an arctan function, f(ri). We want the function to fulfil the following criteria; f’(ri)>0 and f’’(ri)>0 for ri<a and
f’’(ri)<0 for ri>a. This has the attractive feature that the probability of default can be modelled to always
stay between 0 and 1 and that the marginal effect of higher interest is increasing at low interest rates but
decreasing as probability approaches 1.

The inclusion of an intercept, c, also has many attractive features since it indicates that the borrower has
some level of incentives to take the money as soon as he receives it and run. It should be noted that this is
somewhat inconsistent with our concept of β i however.

One function that fulfils the above criteria is an arccotangent function

θ ( ri ) = g(1 − arc cot( h( ri − a)) + c )
where a is the inflexion point where the marginal effect of increased interest rate becomes lower than one,
c is the intercept and g<1 and h>1 are constants that ensures that the probability of default never
becomes larger than one. The resulting relationship is illustrated in figure D.1.

133
Financial self-sufficiency = Adjusted Financial Revenue / Adjusted (Financial Expense + Net Loan Loss
Provision Expense + Operating Expense). The values are adjusted for inflation, subsidization and loan loss
provision.
134 See Murdoch, 1999.
135
Average Loan Balance per Borrower = Adjusted Gross Loan Portfolio / Adjusted Number of Active Borrowers.
The values are adjusted for inflation, subsidization and loan loss provision.
136 Jonathan Morduch, personal communication 2005.

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Credit Rationing in Microfinance Stockholm School of Economics

Figure D.1 θ ( ri ) as an Arccotan function.

51