Why the Poor can Gain

From Increased Interest Rates

in Grameen Bank.by

Magnus Hatlebakk*

Department of Economics, University of BergenFosswinckelsgate 6, 5007 Bergen, Norway

e-mail: magnus.hatlebakk@econ.uib.no

Abstract:We believe that group-lending institutions have incentives to include members outside thetarget-group of poor households. This implies a methodological problem that is rarely takeninto account in empirical studies. We apply a general household survey, and find someevidence of non-poor households within the Grameen Bank of Nepal. A self-selectionmechanism is proposed, where the interest rate is set above the bank rate to exclude wealthyhouseholds, and the interest rate is further increased to exclude middle-wealth households.Furthermore, we demonstrate that only the poor will make productive investments, and theseinvestments will be delayed due to financial investments.

Keywords: Group-lending, targeting, class-formationJEL classifications: D52, I38, O16, Q14

* I would like to thank the Chairman of Eastern Grameen Bikash Bank of Nepal, Prafulla K. Kafle, Executive

Director, L. Prakash Sitaula, all the helpful staff at the area and branch offices of Grameen Bank, and alsothose members I met, who had to listen to my stupid questions. Many thanks go to my field-assistant NandaRaj Rai. Thanks also go to Jan Erik Askildsen and Gaute Torsvik for valuable discussions and comments. Theresearch has been supported by the Norwegian Research Council.

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1. Introduction

We discuss the design of group-lending institutions, like the well known Grameen Bank.

Group-lending or micro-credit has become a very popular policy instrument. There are two

reasons for this. First, group-lending can reduce the information problems facing traditional

banks. Second, group-lending can satisfy the credit demand from poor households that can

otherwise only get expensive loans in the informal credit market. The first reason is

extensively analyzed in the literature, with a focus on the joint-liability aspect of group

lending1. As described in the reviews by Ghatak and Guinnane (1999) and Morduch (1999a),

group-lending systems can deal with three types of information problems, that is adverse

selection, moral hazard and auditing2. Besley and Coate (1995) discuss enforcement of

repayment, which is another problem that can be dealt with through joint-liability3. In line

with this literature, we believe that a group-lending institution is a good mechanism to

enforce repayments and select and monitor borrowers. However, we are not sure that a group-

lending institution is a sufficient mechanism to exclusively target the poor.

To focus on targeting, we apply a model where the selection of profitable projects and borro-

wers is not a problem, i.e. we assume that individual profits are deterministic and common

knowledge within the local community. The local program-staff might be a part of this com-

munity. The community will have strong incentives to select borrowers with profitable

projects, but they have only weak incentives to select borrowers from the target-group. We

1 Rai and Sjöström (2000) point out that "cross reporting" will often be more efficient than joint-liability in

solving information problems, and they find empirical support for this kind of revelation mechanism withinGrameen Bank.

2 For the literature see Armendariz de Aghion and Gollier (2000), Ghatak (1999), Van Tassel (1999) and Varian(1990) for adverse selection, Banerjee, Besley and Guinnane (1994), Conning (1996) and Stiglitz (1990) formoral hazard, and Rashid and Townsend (1994) for both cases.

3 As is well known, the repayment rate of Grameen Bank loan is very high, i.e. 96.7% in the Grameen Bank ofBangladesh according to Hossain (1988). Sharma and Zeller (1997) characterize the repayment performance inmore detail. Our impression from fieldwork, is that households with repayment problems will typically leavethe groups, as described in Karim and Osada (1998).

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suggest a self-selection mechanism that is similar to adverse selection screening models, but

where the principal's objective is poverty reduction instead of profit maximization. Since we

are not concerned with profit maximization, we need only one instrument to screen the

borrowers4.

In section 3 we introduce the interest rate of the group-lending institution as a screening

mechanism, that is, we suggest that the interest rate should be higher than the interest rate in

commercial banks. So the paper contributes to the discussion on interest rates in group-

lending institutions. For example, the World Bank sponsored Consultative Group to Assist

the Poorest argues that group-lending institutions should be financial sustainable, and the

poor are able to pay high interest rates, see Rosenberg (1996). Conning (1999) also supports

sustainability. He argues that the costs of lending to the poor are high, and the interest rate

should cover these costs. Morduch (2000) is critical to this position, and argues that

subsidized credit programs may be an efficient way to target the poor, as compared to

alternative programs. For a detailed study of subsidies in Grameen Bank, see Morduch

(1999b).

Our argument is in line with the position that the poor are able to pay high interest rates, but

we suggest that the interest rate is applied as a screening mechanism to target the poor, and

not necessarily to make the institution sustainable. The screening mechanism is based upon

less expensive credit options for the non-poor5. Similar results exist in the literature on

workfare programs that are designed to target the poor for direct transfers. Within that

literature, Besley and Coate (1992) suggest work requirements, while Basu (1981) suggests a

4 A profit-maximizing principal, would need an additional instrument to subtract consumer surplus. Our mecha-

nism might lead to positive profit, which may be of use for the local community, e.g. in financing local publicgoods.

5 An alternative to our selection mechanism is a revelation mechanism where members truthfully report thewealth of the other members. This is suggested by Rai (1999), who proposes a mechanism where the richmembers get a fine if they are detected, and the poor receive a reward if they tell on rich cheaters.

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low wage as a self-selection mechanism to target the poor. In addition to the screening

mechanism, the present paper identifies the effects of a credit program on households'

intertemporal allocation of consumption and production. The extension makes sense, since

credit by definition allows intertemporal allocation, and this in turn affects individual welfare.

Although we apply the interest rate as a screening mechanism, we are aware that group-

lending institutions are complex, and we also believe that the complex design elements are

necessary in explaining the relative success of the programs. Jain (1996) argues that the

repeated weekly center meetings in the Grameen Bank contribute to making it a cultural habit

to follow the rules of the bank. In a cross-section study of different programs, Hulme and

Mosley (1996), p. 56, also find that the loan-collection method is important, in addition to the

proportion of female borrowers, and the fact that there is a savings element in the program6.

The weekly meetings can also be a targeting mechanism, in case the cost of attending the

meetings is higher for the non-poor, due to social norms or higher alternative cost of labor. In

addition, the benefits may differ between the groups, for example if the bank organizes

educational programs, where the marginal benefits might be higher for the less educated and

usually poorer people7. Finally, the groups might have some external effects such as

stimulating entrepreneurship and self-consciousness among women.

We introduce a group-lending program, like Grameen Bank, into a model of the rural credit

market. In the present paper, interest rates and credit constraints are exogenous, but they are

in line with an equilibrium model8. We model both formal and informal commercial credit in

addition to the group-lending institution. By suppressing the equilibrium effects we allow for

6 Rahman (1999) describes how the cost for the male household-head of not repaying the GB loan becomes

higher when his wife has to represent the household.7 In addition the response to these benefits may differ between groups due to different social norms, e.g. when it

comes to female education.

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a more complex model of household behavior. We first present a model where households'

long term consumption and productive capital are determined by their initial wealth and time-

preference rate9. Then we introduce a credit program. We argue that some categories of

households will not be allowed as members due to previous myopic behavior, where they

have applied credit for consumption instead of production. Among the remaining non-target

households the demand for program loans will decrease as the interest rate increases, while

the target households will in the short run always demand program loans.

We assume that less demand from non-target households allows more target households

within the program. The enrollment of target households will thus increase as the demand

from non-target households decrease. As long as the interest rate is below a critical value, all

target households will immediately be able to leave a poverty trap if they receive a program

loan. For those target households that are enrolled in the program, savings will decrease as

the interest rate increases, and consequently they will need more time to make their optimal

investments. This is the only negative consequence for the poor of a high program interest

rate.

In addition to the screening mechanism, the model identifies intertemporal effects that might

be surprising for organizers of credit programs. Households from the target group are not

likely, and should not be encouraged, to make immediate productive investments. They

should rather be allowed to replace expensive informal loans. Furthermore, any non-target

household will actually have a higher long-term consumption if they are forced to leave the

program. Although this would be against their myopic interests, a paternalistic program board

8 The equilibrium model needs to explain a real informal interest rate above the formal rate and also credit ratio-

ning. At the same time the model needs to allow for more than one lender. Our model in Hatlebakk (2000) hasthese characteristics.

9 This is a model of class formation. The model is different from the model of class formation in Eswaran andKotwal (1989), where wealth is exogenous.

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might still consider it to be a welfare improvement (at least if the program board care about

the next generation that will inherit a larger wealth).

The Grameen Bank has always charged an interest rate within the range of the commercial

bank rate. This implies that we are not able to test all predictions of the theoretical model. For

an interest rate at the level of the formal interest rate, the model predicts that a certain

proportion of Grameen Bank members are non-poor. This hypothesis is discussed in section

4, referring to previous empirical studies and analyses we have done of data from the Nepal

Living Standard Survey. Whether an increase in the interest rate will improve targeting is

another issue that we are not able to investigate. This would require social experiments,

where Grameen Bank had to charge higher interest rates in selected villages.

A related empirical question that we do not study, is the effect of credit programs on income

and health indicators. In such analyses sample selection should be considered. The selection

of households to the Grameen Bank is not, and should not be, random. Households with

profitable projects are more likely selected, and any empirical analysis should control for the

selection bias. A notable study of this kind is Pitt and Khandker (1998).

Since the present paper relies on a field study of the Grameen Bank of Eastern Nepal, we also

refer to Nepal in the theoretical part of the paper. However, the analysis is relevant for

Bangladesh where Grameen Bank is very influential, and for other poor rural economies

where group-lending institutions exist or will be established.

In section 2 we model the households' equilibrium behavior and the resulting class structure

of the rural economy. In section 3 we present Grameen Bank (GB) and study the effect for the

different categories of households, of introducing such a credit program in the model from

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section 2. The results include that the number of poor borrowers in GB will increase in the

interest rate. In section 4 we present some empirical support for the prediction that non-poor

households will be members of GB at the present (low) interest rate. We also discuss the

empirical literature on targeting within GB. Section 5 summarizes.

2. Model

Households maximize intertemporal utility U =u(ct )

(1 + δ)tt =1

∞

∑ , subject to the intertemporal

budget I0 +ct + I t

(1 + r)tt =1

∞

∑ = A 0 +yt

(1+ r) tt =1

∞

∑ , where yt = F(Kt) and K t = K0 + Iss= 0

t −1

∑ , and subject

to a subsistence constraint ct ≥ c , and borrowing and lending constraints A ≤ Abt ≤ 0 ≤ Alt ≤

A , where Abt + Alt = At = (At-1 + yt-1 - ct-1 - It-1)(1 + r). The K is productive capital, which

includes land and other durable inputs, such as oxen, carts, irrigation pumps etc. Variable

inputs are reflected in the production function10. We solve for the first order-conditions in the

appendix, where also the notation is specified in more detail. For any time interval where the

subsistence and credit constraints are not binding, the first order conditions are F'(K*) = r, for

the production decision, and u' (ct)u' (ct −1)

= (1+ δ)(1 + r)

for the separable consumption decision.

The first-order conditions imply an immediate adjustment of productive capital to K*, and a

gradual change in consumption over time. Any arbitrage will also be done immediately. After

the initial adjustments, the households will have a decreasing consumption path if the time-

preference rate is characterized by δ > r, and an increasing path if δ < r. As consumption

decreases or increases, the households will eventually have to borrow or lend, and due to the

10 The F(Kt) function may be interpreted as a profit function in a model where we allow markets for variable

inputs. However, here we suppress variable inputs.

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infinite horizon a credit constraint will finally bind. This might already happen during the

initial adjustments of capital.

When the credit constraints bind, both productive capital and consumption will gradually

change over time according to u' (ct)

u' (ct −1)=

1 + δ1+ F ' (K t)

. Households will consume from their

productive capital if δ > F'(K), and invest in productive capital if δ < F'(K). This will conti-

nue until F'(K) = δ . Production and consumption will then be constant for all remaining

periods11. The long term consumption level is determined by the long term productive capital,

and the previous borrowing and lending behavior. So a household with δ > r, will have the

permanent consumption c = F(K) + rA , while a household with δ < r, will have the

permanent consumption c = F(K) + r A .

There are two types of credit, and arbitrage will be available for some households.

Households may borrow or lend in the informal credit market at the interest rate ri, and some

households may borrow in the formal market at the interest rate rf < ri. Both interest rates are

exogenous. Only households with sufficient collateral will have formal loans. In the informal

market borrowers can have a maximal loan of A i and lenders can lend at a maximum of A .

In the formal market borrowers can have a maximal loan of A f . We find it reasonable that the

interest rate and the borrowing constraint are exogenous for the local branch of a formal bank.

To focus on individual behavior, we do not apply an equilibrium model for the informal

credit market. However, the characteristics of the market are in line with the outcome of an

equilibrium model, such as Hatlebakk (2000). We may still imagine that the interest rate and

11A similar result exist for growth models. In a closed economy with perfect credit markets as described by neo-

classical growth models, an endogenous interest rate r will adjust such that we also for the separable case willhave F'(Kd*) = δ , i.e. the modified golden rule. Note that this result is due to an equilibrium mechanism at theaggregate level, while we model individual behavior.

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even the credit constraints will change with exogenous shocks, such as the introduction of a

credit program. However, equilibrium effects are not modeled in the present paper.

As described above, long term consumption depends on the individual time-preference rate

and the interest rates. Since there are two separate interest rates, there are three relevant

ranges for the time-preference rates. We simplify by specifying a uniform time-preference

rate for each range, and denote the time-preference rates as, δ1 > ri > δ3 > rf > δ5 . The

respective long term levels of productive capital are identified by the first-order condition

F'(Kj) = δ j, with j = 1, 3, 5.

So any household with δ3 will end up with K3. Recall that collateral is needed for formal

loans. To focus on the critical initial capital, we assume that only households with capital

larger than K3 have sufficient collateral for formal loans.

We have already identified the long term consumption levels as c = F(K) + rA for

households with δ > r, and c = F(K) + r A for household with δ < r. Applying these results,

we can specify the long term consumption for four different categories of households (subject

to a non-binding subsistence constraint):

ˆ c 1 = F(K1) + A iri,

c3 = F(K3) + A ri + A f rf,

c4 = F(K3) + A ri,

c5 = F(K5) + A ri.

Note the notation ˆ c 1 (which is not c1) and the missing category 2. The missing consumption

9

levels c1 and c2 will be introduced below when we add a subsistence constraint. Also note that

all households have adjusted the productive capital to their time-preference rate, and the net-

borrowers have permanent interest payments, while the net-lenders have permanent interest

incomes.

We name the categories according to the subscripts for consumption, and we have ˆ c 1 > c3 >

c4 > c5. Due to the fact δ1 > δ3 > δ5 , we also have K1 < K3 < K5. All households of

categories 3 and 4 will have the long term capital K3, but consumption is smaller for category

3 than for category 4. This is because category 3 is allowed formal loans due to a high initial

wealth. However, category 3 is better off in terms of discounted life time utility, due to larger

initial consumption.

We will now add the subsistence constraint. This implies that the category of households that

otherwise consume ˆ c 1 will now consume c2 = c , while some households from category 4 will

have a consumption level c1 ≤ c . In principle also some households from category 5 might

consume c1, but we find this less likely. To simplify the presentation, we assume that house-

holds of category 5 will have initial capital larger than K3, which implies that they will

consume c5.

In an infinite horizon model, a voluntary decreasing consumption path implies that the subsis-

tence constraint will eventually bind. We do not believe that any household will voluntarily

choose malnutrition, and we interpret c as the upper bound of malnutrition. We assume that

the subsistence constraint binds for any level of δ1 ≥ ri, which means that ˆ c 1 < c even if δ1 =

ri, and we have F(K2) + A iri < c . The subsistence constraint thus binds, while the credit

constraint does not bind. Consequently households with the time preference rate δ1 and

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sufficient initial capital will have the long term consumption, c2 = F(K2) + Ab ri = c , where

Ab > A i, and we name the households as category 2.

Next, we identify the critical initial wealth ˆ A that is necessary to the sustain c . The critical

wealth is determined by F(K2) - (K2 - ˆ A ) ri = c . Furthermore, we assume that all households

are allowed sufficient informal loans to finance K2, and the poorest households are allowed

exactly A i. So any household with initial wealth A0 + K0 < ˆ A will have ˆ A - K2 = Ab ≥ A0 +

K0 - K2 ≥ A i , where only one of the inequalities will be strict. Households with initial wealth

below ˆ A , will thus have the initial consumption c1 = F(K2) - (K2 - A0 - K0) ri ≤ c , which can

be permanently sustained. Recall that c is the smallest voluntary consumption level, and it is

also the upper bound for malnutrition. Consequently households with insufficient initial

capital are malnourished. We might expect these households to be willing to save to increase

their future consumption. However, that would require consumption below c1. In the present

paper we assume that the initially malnourished households are not able to save, and they will

rather permanently consume at the initial level c1 ≤ c . We will now discuss this assumption

in more detail.

The assumption implies a low-consumption debt trap for category 1 that is in line with

Bhaduri (1973). We will first emphasize the empirical support for a debt trap. For example in

South-Asia, we find very high informal interest rates and permanent and widespread

malnutrition. Basu (1997) discusses the robustness of Bhaduri's model. Basu seems to agree

with the empirical support for a low-consumption trap, but he emphasizes the need for a

plausible explanation for why the poor are not able to save. Although we have avoided the

issue by assumption, we would like to justify the assumption.

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Basu argues that the poverty trap might be due to a strategic game between the poor and the

lender, who might also be a landlord. Any marginal savings by the poor can be counteracted

by a (marginal) change in credit, land or labor contracts. If this happens repeatedly, the poor

may learn that savings will not work, and they will rather consume the available income. This

kind of strategic game can justify our assumption of no savings among the poor. However,

we will rather argue directly for the assumption. We will argue that in a specific sense, we

cannot expect the poor to be far-sighted. This type of argument is mentioned (but not

approved) by Basu (1997).

In the model we have implicitly allowed two separate subsistence levels. The level c is the

smallest voluntary consumption. However, we allow households to survive below this level,

although they are malnourished. This implies a more basic subsistence level below c , which

is the level of survival. In formulating a consistent relation between these two subsistence

levels we have three options.

1) The two levels are equal, which implies that some households voluntarily reduce their con-

sumption to the edge of survival. 2) All households behave according to the intertemporal

model of consumption, but households with initial wealth below ˆ A will apply the lower

subsistence level. In that case, some of the households will be far-sighted and they will leave

the poverty trap, while others will reduce their consumption to the edge of survival. For

explanations 1) and 2), all permanently poor households will have income and consumption

at the edge of survival. In our opinion this is not a realistic outcome, and we rather apply a

third explanation. 3) We allow the two subsistence levels to be lower and upper bounds for a

range of subsistence, where households are malnourished to different degrees. All households

with an initial consumption within this range will have neutral savings behavior. They are

neither myopic nor far-sighted. They rather apply the simplest rule of behavior, which is to

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consume the available net income.

Whatever explanation is reasonable, a permanent low-consumption trap seems to exist. The

trap is not likely to exist in a model where the poor can save. Applying the assumption of no

savings for the poor, we can summarize the long term consumption levels for the five catego-

ries of households. The consumption levels are functions of time-preference rates and initial

capital, as categorized in Table 1. Recall that A f is a negative number.

Table 1 about here.

1: Debt bonded malnourished farmers: c1 = F(K2) - (K2 - A0 - K0) · ri ≤ c .

2: Myopic subsistence farmers: c2 = F(K2) + Ab ri = c .

3: Previously wealthy farmers: c3 = F(K3) + A ri + A f rf.

4: Middle wealth farmers: c4 = F(K3) + A ri.

5: High wealth farmers: c5 = F(K5) + A ri.

Note that in the long run, only category 3 will have formal loans. For transitional periods of

investments category 5 can have formal loans. In the informal market, category 1 and 2 are

borrowers, while the others are lenders. In the next section, we argue that the members and

the local staff of credit programs are likely to exclude categories 2 and 3 due to previous

myopic behavior. We then argue that the central office of the program may apply the interest

rate of the credit program as a self-selection mechanism. By increasing the interest rate,

category 5 households will not demand loans from the program. For an even higher interest

13

rate, some category 4 households will not demand loans, and more households from the target

group of category 1 will be allowed as members.

In our opinion the basic model in this section covers important stylized facts for poor rural

economies, specifically in South-Asia. 1) We have a model where some informal borrowers

are in a poverty trap. 2) Some of the informal lenders are relatively poor, due to a relatively

low productive capital and permanent formal loans. 3) Credit rationing implies that income

from the informal credit market will be limited, but positive. 4) Binding credit constraints

also imply non-separability between production and consumption decisions. Consequently,

households will allocate resources from consumption to production according to their time-

preference rates. 5) In the long run, that is after any investments, productive capital and

consumption are constant. This may also explains low activity in the land market. Note that

for households of categories 3 to 5, the productive capital is determined by the time-

preference rates, while for households of category 1 and 2, the productive capital is adjusted

to the informal interest rate.

3. Introducing Grameen Bank

In this section we discuss the effects of introducing a credit program like Grameen Bank

(GB) into the economy described in section 2. First we present the main characteristics of GB

and our specification of these characteristics within the model. For more detailed

presentations of the Grameen Bank of Nepal, see Grameen Bank of Nepal (1993), Sharma

(1996) and Smedsdal (2000).

In GB a group of five women are jointly liable for their loans, and consequently for

suggesting new members, whom also have to be approved by the local bank staff. In the

14

model we assume that borrowers who have revealed myopic behavior, in the form of

consumption of productive capital or loans, will not be allowed as group members. This

implies that categories 2 and 3 will not be included.

GB has an explicit goal of allowing only low wealth households as borrowers. In the model

we will assume that only category 1 is eligible according to this criterion. In Nepal the

eligibility criterion is formulated as an upper limit on land holdings of one bigha (0.68 ha).

However, as we will verify in section 4, GB does not strictly apply this rule. This is not

surprising, since a likely prerequisite for support and trust of a new member is that the

member is involved in repeated local social and economic interactions. In the local economy

it may be profitable both for other group members and for the local staff to interact with the

more powerful and wealthy households. These incentives are in conflict with the targets for

GB. We do not need to specify the magnitude of the conflicting effects, we only assume that

the local staff will allow a certain proportion of non-target applicants as members. Also note

that GB has a target of raising loans for productive investments in contrast to consumption

loans. Note that being a permanent GB borrower indicates myopic non-productive behavior.

If the loan is financing productive capital, then the resulting income can be applied to repay

the GB loan.

GB has an upper limit on individual loans A g , which at the time of our fieldwork was

Nepalese rupees (NR) 15 000 (approximately $ 220). We also assume that GB is rationed by

e.g. the central bank, such that the aggregate amount of credit is fixed. The installment rules

for GB are such that A g is repaid during one year (50 weeks) of weekly installments,

followed by the option of receiving a new loan of the same size. Households with permanent

and maximal GB loans, will have a stream of annual loans of NR 15 000, and a stream of

installments of NR 330 every week. These weekly installments are equivalent to weekly

15

installments on a savings scheme with a 10% interest rate, which is in line with the actual

savings rate in the commercial banks. Since the installments are evenly distributed over the

year, the 10% rate is (almost) the same as a 20% annual interest rate, which is in line with

the borrowing rate in the commercial banks. Also note that the repeated annual loans are

equivalent to a permanent loan of the same size, as long as the borrower is able to maintain

the cash-flow. To make GB loans comparable to the informal loans, and also to bank loans,

we study the equivalent permanent GB loan having an annual interest rate rg.

Note that the equivalence holds only when households have a cash-flow in line with the loan,

i.e. when households have a large annual expenditure, and weekly incomes. In a previous

version of the paper we discussed whether this characteristic of the GB institution will

exclude households that do not have such cash-flows. However, we did not find any empirical

support for this hypothesis12. As we will see, GB borrowers will become informal lenders,

and consequently they can adjust their cash-flow in the informal credit market. Whenever

they receive a new GB loan, they can lend to the informal market conditional on repayment

during the following year. Consequently, the cash-flow of GB loans will not necessarily

exclude borrowers, and we find it satisfactory to assume that the equivalence holds.

Now we are prepared to identify the households that will become borrowers if a credit

program like Grameen Bank is introduced into the economy described in section 2. In Lemma

1 we identify the categories of households that will demand GB loans at different interest

rates. In Proposition 1, categories 2 and 3 are excluded due to previously myopic behavior.

Next, we assume that the GB interest rate rg will only vary within the same range as the time-

preference rate δ3 , that is between the formal and the informal interest rates. Consequently

there will be no demand from category 5. We allow the time-preference rates to vary within

12We looked for a correlation between land holdings and type of project reported in the files of Grameen Bank.

16

the same range, and in Corollary 1 we specify the long run consumption for categories 1 and

4. By comparing these consumption levels to the pre-program levels from section 2, we can

identify the effects of the credit program.

For Lemma 1 we will assume that any transitional loan can be covered by commercial banks,

i.e. they will be smaller than A f . We also assume that if households of a certain category are

indifferent between GB and formal loans, then some of the households will have GB loans. In

the proofs we refer to the model in section 2, and we use the term utility maximization when

households behave according to the first order condition for intertemporal consumption, and

the term profit maximization when they select the smallest interest rate.

Lemma 1.

a) At rg ≥ ri only households of category 2 will demand GB loans.

b) At ri > rg > rf households of category 5 will not demand GB loans.

c) At rg ≤ rf some households from categories 5 will demand transitional GB loans, and all

households in categories 1 - 4 will demand permanent GB loans.

Proof: a) By assumption category 1 are not able to have additional loans. Among the others,

only households of category 2 will have δ > rg, and consequently by utility maximization no

others will have positive demand. b) By profit maximization category 5 prefer bank loans. By

utility maximization they will only have transitional loans. By assumption transitional loans

are smaller than the credit limit in the banks. c) By profit maximization GB loans are weakly

preferred to formal loans, and consequently households with δ < rg will weakly prefer to

have transitional loans from GB. In case of equal interest rates, some households will by

assumption have GB loans. By utility maximization any household having δ > rg will have

permanent demand for GB loans. ||

17

Next, we apply the assumption that GB groups will not allow members who have revealed

myopic behavior, which we define as the households that have had loans without investing in

productive capital, i.e. categories 2 and 3. Also recall the reasonable assumption that GB will

allow a certain proportion of non-target applicants as members. The assumption is due to the

social and economic relations between the local staff and members of the credit program.

With these assumptions, Lemma 1 implies Proposition 1.

Proposition 1.

a) At rg ≥ ri there will be no borrowers in GB.

b) At ri > rg > rf only households from categories 1 and 4 will be borrowers in GB.

c) At rg ≤ rf some households of all categories except 2 and 3, will be borrowers in GB.

Proof: a) By Lemma 1 there is only demand from households in category 2. By assumption

these households are not allowed as members. b) By Lemma 1 households from category 5

are excluded. Category 2 and 3 are excluded by assumption. c) By Lemma 1 households from

all categories will have demand. Category 2 and 3 are excluded by assumption. ||

Proposition 1 describes the realistic situation that GB will exclude households that have

revealed myopic behavior, while they will not necessarily exclude the wealthy households.

We emphasize this result in Remark 1.

Remark 1.

Some non-target households will have GB loans, whenever the interest rate is at or below the

formal interest rate.

18

This is a rather obvious result, which still does not seem to be considered by policy makers.

Subsidized interest rates, i.e. where rg < rf, are common in credit programs throughout the

world. In Nepal the two interest rates are approximately equal.

Remark 1 is a main result of the present paper, due to the practical implications for the design

of credit programs. The remark implies that credit programs like Grameen Bank should not

charge interest rates below the formal bank rate. Now, we will add an even stronger result.

We will argue that the program interest rate should be higher than the formal bank rate. This

is to exclude non-target households that have low reservation rates.

We study the implications of credit programs that charge an interest rate between the formal

and the informal interest rates. From Proposition 1 we know that only households from

category 1 and 4 are potential borrowers. Within category 1, we may have households that

turn into myopic category 2 borrowers, due to a time-preference rate in the range of δ1 . When

they receive a GB loan they reduce their informal loan to the level of Ab, and they

permanently consume c . Since they do not make any additional investments, they are

detected as myopic households, and they will have to leave the program. They are

consequently a small group within the program, which we will not take into account. We

focus on households from categories 1 and 4, and we allow heterogeneous time-preference

rates between the formal and the informal interest rates. We apply the notation K3 to denote

the optimal productive capital for any household having time-preference rates in this interval,

but K3 will vary according to the individual time-preference rates.

Recall that category 1, i.e. households with A0 + K0 ≤ ˆ A , have the permanent consumption c1

= F(K2) - (K2 - A0 - K0) ri ≤ c . If these households receive GB loans, they will cash in an

19

arbitrage profit. In case they are still below c , they will have the permanent consumption c1g

= F(K2) - (K2 - A0 - K0) · ri + A g (rg - ri), where the last part is the arbitrage profit. Note that

c1g is decreasing in rg, since A g is a negative number. Applying c1

g , we will in Corollary 1

identify the long term consumption for categories 1 and 4 in case they receive GB loans.

Corollary 1.

Suppose ri > rg > rf , and ri > δ > rf , then from Proposition 1 only category 1 and 4 will be

borrowers in GB, and they will have the long term consumption:

a) Households with c1g ≤ c , will consume c1

g .

b) Households with c1g > c and δ > rg will consume c3

g = F(K 3 )+ A ⋅ ri − A g ⋅ rg .

c) Households with c1g > c and δ < rg will consume c4 = F(K 3 )+ A ⋅ ri .

Sketch of a proof: a) By assumption. b) The household behavior is parallel to category 3 in

section 2, with GB loans replacing formal loans. c) The household behavior is parallel to

category 4 in section 2. ||

If we suppose that a group-lending program like Grameen Bank behave according to Remark

1, which means to set the program interest rate above the bank rate, then Corollary 1

summarizes the effects of the lending program for the potential borrowers identified in

Proposition 1. The effects are summarized in Table 2.

Table 2 about here.

20

Recall that c1g is decreasing in rg. This means that there is a critical upper bound r g for the

program interest rate, where the poorest household will be able to permanently consume c .

Recall that the poorest household is allowed exactly A i in the informal market. The critical

value r g can thus be identified from c1g = F(K2) + A i· ri + A g (r g - ri) = c . Also recall that we

have F(K2) + Ab ri = c , where Ab is the informal loan for the household that consume exactly

at the subsistence level. We thus have r g A g = (Ab - A i + A g ) ri. If GB allows the poorest

household to exactly replace the informal loan, then the critical value is defined by r g =

Abri/A g . In that case the poorest household will have program interest payments that equal

the pre-program informal interest payments for the wealthiest household of category 1. If GB

only allows smaller loans, then r g will be even smaller to compensate for the smaller

arbitrage profit. If GB would like the category of still trapped households in Table 2 to be

empty, then the program board has to choose rg ≤ r g .

Suppose that rg < r g , then all target households will leave the poverty trap, whenever they

receive a GB loan. They will first repay the informal loan, then become informal lenders

themselves, and finally invest in productive capital. The GB borrowing constraint is likely to

bind before all investments are done. When the constraint binds, the target households will

invest from own savings until the productive capital is at the optimal level. The most far-

sighted target households (with δ < rg) will repay the GB loan during the periods of

investment, while the others will become permanent GB members.

During the investment phase, the target households are likely to start out with the maximal

savings of c1g - c . They thus consume c , and are no longer malnourished. Eventually, con-

sumption will increase and they end up with respectively c4 (the far-sighted households) and

21

c3g (the myopic households). Note that the initial savings are smaller the higher is rg. The

optimal investment phase will thus be longer the higher is rg.

The non-target households will not apply the GB loan for productive investments, since they

initially have an optimal level of productive capital. They will only take GB loans for short

term consumption purposes. They will become permanent GB borrowers, and their long term

consumption will be smaller than it was before they received the GB loan. In this sense the

credit program implies myopic behavior.

The number of non-target households that will apply for GB loans, is decreasing in rg, while

all target households will apply for GB loans. We have assumed that GB will allow a certain

fraction of non-target applicants as members. As the number of non-target applicants

decreases, we thus suppose that the number of non-target members will decrease, and

consequently fewer target households are crowded out. We now summarize the main results

in Remark 2.

Remark 2.

a) Only category 1 will make productive investments, and they will not invest immediately.

b) Category 4 borrowers will use the GB loan for consumption.

c) Some (myopic) borrowers are permanent members, and are crowding out target

households.

d) The myopic members will become better off in the long run if they are forced to leave.

e) The number of permanent members is decreasing with rg.

f) The number of target members is increasing with rg.

Recall that GB has the goals of providing credit for the poor and only for productive invest-

22

ments. Our analysis indicates (Remark 2a) that there is no conflict between the goals, but GB

cannot expect immediate effects in terms of productive investments. This is because the target

households will first repay their informal loans.

Non-target households are likely to be at a long term stable consumption level even before

the GB program is established. In case any of these households become GB members, they

will have loans only for consumption (Remark 2b). They will, together with target

households having δ > rg, borrow the maximal amount from GB, and they will prefer not to

repay the loan. This implies that an increasing number of permanent borrowers is crowding

out target households from GB (Remark 2c). If the GB board is able to target the poor, then

the permanent borrowers have to leave the program. If this happens, then the households will

have the burden of reduced consumption for some periods, but the long term consumption

will be higher (Remark 2d). Due to heterogeneous time-preference rates, the number of

permanent borrowers is decreasing with rg (Remark 2e), and consequently fewer target

households are crowded out (Remark 2f).

If GB has a goal of providing credit for the poverty trapped households, as defined by the

malnourished households of category 1, then the program interest rate should first of all be

higher than the formal bank rate. Furthermore, the higher is rg the faster will the target house-

holds be enrolled in the program, and the fewer permanent borrowers will be allowed. Appa-

rently this is a counter-intuitive result. One might object that the poor cannot benefit from a

higher interest rate. Within the model, the losses for the poor are of two kinds. First, for rg >

r g , some of the enrolled target households are not able to leave the poverty trap. Second, the

higher is rg, the longer will it take until the target households have been able to make their

optimal investments.

23

If the GB program board intends to make any target member able to escape from

malnutrition, then rg should not be higher than r g . The enrollment of target households will

actually increase for rg above this level, but the board may prefer that their members are able

to leave the poverty trap, and thus choose rg below r g . If the board chooses rg marginally

below r g , then all target members will in the long run be able to make their optimal

investments. If the program board chooses an even smaller rg, then the enrollment of target

members will decrease, but those target households that are enrolled will have a shorter

investment phase.

Although the program board is faced with a theoretical trade off, in the real world they will

not have the necessary information to select an optimal interest rate, that is, they will not

know the exact value of r g and the distribution of the time-preference rates. We would

believe that the GB program board is reluctant to an increase in the interest rate. The present

analysis indicates that the program board should put more weight on the counter-intuitive

result that a higher interest rate will make it easier to target the poor. Due to the lack of

empirical evidence, the best practical advice might be to experiment with the interest rate.

Today, the GB borrowers of Nepal pay the weekly amount of NR 110 if they have a loan of

NR 5000. The program board might as an experiment consider to vary additional weekly

payments over geographical regions. As an example, the additional weekly payments for a

loan of NR 5000 might vary from 1 to 5 rupees, which is equivalent to additional 2% - 10%

on the annual interest rate.

A lesson from the present analysis is that Grameen Bank should have as a main goal to

replace expensive informal loans. The financial investments in the informal credit market

imply that productive investments are delayed. Furthermore, since the poor have the highest

24

reservation rates, targeting becomes easier the higher is the program interest rate.

Some readers may object to this result, due to the burden for households that are already

enrolled in Grameen Bank. However, note that these households have been able to leave the

poverty trap where they were malnourished, or they are myopic middle wealth households

that will actually be better off in the long run, if they are forced to leave the program.

4. Empirical evidence of non-target members

The focus of the present paper is on the Grameen Bank (GB) of Nepal (and Bangladesh). The

GB interest rate has been within the range of the formal interest rate. This implies that we can

only test the theoretical prediction formulated in Remark 1 and not the predictions formulated

in Remark 2 in section 3. According to Remark 1, some non-target households will have GB

loans as long as the program interest rate is the same as the formal interest rate.

If GB actually have non-target households as members, then we know that these households

demand GB loans at the present interest rate, and the local branch offices of GB allow them

as members. This in turn implies that the present administrative targeting procedure is not

perfect. Alternative mechanisms can either affect the incentives for the local staff to select the

poor, or affect the demand from the non-target households, as described in section 3. Note

that any empirical evidence of non-target households in GB will not prove that the suggested

mechanism in section 3 will work. But the evidence will support the need for alternative

mechanisms.

Data collection on targeting within GB is a difficult issue, since only households with land

below a certain eligibility criterion are supposed to be members. If non-poor households are

25

allowed as members, then we should not expect the households themselves or the local bank

staff to reveal the true land holdings in public. Rahman (1999) describes a similar

discrepancy between the public and hidden rhetoric within Grameen Bank, when it comes to

targeting of women. For this topic also see Goetz and Gupta (1996).

Staff members may allow non-target households as members, since their repayments might

be considered as more reliable. As described in Yaron (1994), promotions and bonuses within

Grameen Bank depend on the profit of the branch. The staff may also have private incentives

from economic and social relations with non-poor households, which means that they find it

difficult to reject applications from the non-poor households.

In the present section we will argue that some influential studies of Grameen Bank do not

take into account the methodological problem that borrowers and staff members have

incentives to disguise the true land holdings of the non-poor. On the contrary, the

investigators directly revealed their contact and interest in Grameen Bank. As an alternative,

we suggest the use of general household surveys that are collected for different purposes. In

such studies, Grameen Bank will be only one of many sources of credit, and questions on

borrowing activities will only be a part of the study. At the end of the section we will present

an example of how household surveys can be applied. We will also report from a study that

circumvents the data problem, i.e. Amin, Rai and Topa (1999). They collected data on land

holdings before the credit programs were fully established. Before we report these two

studies, we will present two influential studies of Grameen Bank, and we will present our

own experiences from a field work in Eastern Nepal.

Hossain (1988) is a main reference for empirical investigations into the ability of the

Grameen Bank of Bangladesh to select households from the target group. In the presentation

26

of his methodology the incentive to misreport land holdings is not discussed. Hossain selected

the sample villages with help from Grameen Bank and only members of Grameen Bank are

reported to be interviewed in the survey. Some questions were also related to the Grameen

Bank, i.e. questions on occupation before and after the respondents joined the Bank. The land

holdings were reported by the households during the interviews. All these methodological

elements imply that respondents were likely to believe that the field-staff represented the

Grameen Bank, and we would expect misreports of land holdings. In our opinion one should

not rely on this study in discussing the ability of Grameen Bank to target the poor. However,

this is done in influential reviews of the performance of Grameen Bank, such as Rahman and

Islam (1993) in Wahid (1993) and Hulme and Mosley (1996).

Pitt and Khandker (1998) do not study targeting. They study a related question, i.e. the impact

of Grameen Bank on success indicators such as average expenditures in the village. We

include the study, because the survey illustrates the methodological problem in question. The

household survey was conducted by the World Bank and the Bangladesh Institute for

Development Studies. Details on the survey design can be found in Khandker (1998) and Pitt

and Khandker (1996). Households were categorized into three groups, i.e. non-eligible non-

members, eligible members and eligible non-members. The fourth category of non-eligible

members was by definition not included in the study. This means that any non-eligible

members, which is our concern, had to be classified into one of the other categories.

At first glance it seems like the fourth category is identified ex-post in their study. In a

survey, 17% of the members actually reported more land than the eligibility criterion.

However, Pitt (1999) documents that these households actually have low quality land, and

they might have been accepted by the bank according to a quality adjusted eligibility

criterion. So it seems like the staff members apply the (quality adjusted) eligibility criterion,

27

even when this, at first glance, seems not to be the case. However, this does not prove that

households report their true land holdings and land values.

Our hypothesis, that Grameen Bank borrowers and staff do not reveal the true land holdings

for the non-poor, is based on observations that we made during visits to branch offices of the

Grameen Bank of Nepal. During some few interviews with borrowers we were able to

disguise our interest in the Grameen Bank. These interviews turned out as very different from

the few interviews we did, where the connection to the bank was obvious. We stayed 1-2 days

at six different branch offices, and the informal conversations with the bank staff did also

contribute to the hypothesis. The purpose of the visits was to translate household and loan

information from the files of the bank, including information on land holdings. However,

during the translations from Nepali, we realized that some of the recorded land was actually

not the borrowers property, but rented, sharecropped or mortgaged land13. So the

approximately 10% who reported more land than the eligibility criterion is not perfectly

reliable. As argued by Pitt (1999) these records may even be due to low quality land.

To evaluate our hypothesis we will first refer the only proper study we know of targeting wit-

hin Grameen Bank. Amin, Rai and Topa (1999) apply a technique that avoid the methodolo-

gical problem discussed above. They sampled 129 households from two villages in

Bangladesh with respectively 395 and 398 households. Due to lack of data, the samples were

reduced to 112 and 117, including 38 members of Grameen type credit programs. The

households were interviewed every month for a full year in 1991/1992, covering

consumption, income and land holdings. At that time only a few respondents had loans from

the credit programs. A new survey was conducted in 1995, with many of the respondents

having loans from the credit programs at that time. Consequently this is a unique study that

28

circumvents the methodological problem, since membership status is collected from the latest

survey, while consumption, income and land ownership data is from the first survey. Village

A in the study had more agricultural activities than village B, and hence village A is likely to

be more in line with rural Nepal. From Table 4 in their paper we find that non-members in

village A have only non-significant and marginally higher income (16% for the mean) and

consumption (5% for the mean) than members of the credit programs. In village B the

differences are significant and large (respectively 50% for income and 58% for consumption).

This reliable study indicates that at least for poor economies, Grameen Bank is not able to

target the poor.

Finally, we will illustrate how a living standard survey can reveal independent information on

land holdings among Grameen Bank type borrowers. We apply the Nepal Living Standard

Survey (NLSS) conducted by the Central Bureau of Statistics (1996a) in Nepal during

1995/1996. A stratified random sample of 3373 households from all over Nepal were

interviewed, with 2657 households from rural Nepal. The NLSS survey was very extensive,

with a questionnaire of 70 pages asking questions related to almost every part of the

respondents' life. Consequently, the respondents had no reason to believe that the information

on Grameen Bank was of special interest, which was also true for the Central Bureau of

Statistics (CBS).

Among the rural respondents, 1676 reported borrowing activities, with 28 households repor-

ting GB type loans. Among these, 25 are from the central and eastern regions of Nepal. The

three other GB members are outliers both in terms of land holdings (which are above

average) and literally (in terms of geography). We do not include them in the reported

descriptive statistics. The 25 borrowers are located in 14 villages in the central and eastern

13This information is included as a warning for others who would like to apply the information from the files of

29

part of terai and the nearby hills14. The total number of respondents in these villages is 168.

Consequently, we have a dataset of 168 households from 14 villages, where 15% of the

respondents have GB type loans. All respondents report land value, while 157 report land

holdings, including 23 GB borrowers.

In Table 3 we report the descriptive statistics for the samples of borrowers and non-

borrowers. Land holdings are measured in bigha and land value in Nepalese rupees (NR). We

report the proportion having more land than the eligibility criterion for terai of 1 bigha = 0.68

ha of land15. Using bigha as a determinant of land value in a linear regression for the 157

respondents, we identify NR 138 000 as the monetary equivalent to the eligibility criterion.

No borrowers have land value between NR 125 000 and NR 300 000, and we also report the

proportions having land value above NR 300 000. In addition we report the proportions

having no land, the medians, and means.

We use sampling weights provided by CBS, which reflect the respondents' probability of

being selected. We apply the STATA (1999) survey commands to estimate standard errors,

with villages as clusters and hills and terai as two strata16. The standard errors for proportions

are calculated as the means of the corresponding dichotomous variable. This approximation is

not necessarily true for small samples. As a consistency check, we have estimated standard

errors without taking into account clusters and strata, and compared these standard errors to

Grameen Bank.

14Terai is the lowlands along the Indian border. The two regions cover the land from Chitwan to the Indianborder in east, one day travel by bus.

15In the hills the criterion is 10 ropani = 0.51 ha, but since the majority of the households live in terai we applyone bigha as the cutoff. Conversions from bigha into ropani (including sub-units) and into hectare are accor-ding to Central Bureau of Statistics (1996b).

16In the survey commands all observations within a cluster collapse to one observation, which usually increasesthe variance. The variance is calculated separately for every strata, which usually decreases the variance, andthen the weighted sum is calculated. The number of clusters minus the number of strata is applied as thedegrees of freedom in the t-statistics for the confidence intervals and the F-statistics for the Wald test used tocompare means and proportions. In our data the total effect of taking clusters and strata into account is onlymarginal for some proportions and increases the confidence intervals for others.

30

the exact standard errors calculated from the binomial distribution. The discrepancies are

minor. We thus regard the normal approximation applied in the survey commands as

satisfying, although the sample of borrowers is small and the frequencies from the binomial

distribution cannot be considered to be normal distributed17.

For the reported means, the small sample biases as compared to the normal distribution, seem

to be so large that we will not report confidence intervals. However, we log-transform land

holdings and land value, and estimate the means and confidence intervals for the transformed

variables, which are approximately normal distributed. Then we re-transform the means and

the upper and lower ends of the confidence intervals using the exponential-function, and

report these values. The transformed means are the geometric means18.

In cases where the confidence intervals are reported, we have tested for significant

differences between the two samples, without finding any difference. This was to be expected

due to the small sample size of borrowers. The small sample size implies that we may

conduct a type II error, when we conclude that the two sub-samples have similar land

distributions. However, this conclusion is in line with the less developed village in the study

17We have conducted simple tests for normality, where we let the full rural (unweighted) sample represent the

distribution of individual land holdings. We randomly draw 100 and 300 sub-samples, with every sub-samplehaving the same size. This is done for sample sizes from 16 (0.6% of the rural sample) to 213 (8% of the ruralsample). For every sub-sample we calculate the binomial frequencies corresponding to the proportionsreported in the table, and we also calculate the means and the means for the log-transformed variables for landholdings and land value. For every sample-size, we thus have a sample with 100 observations and another with300 observations, where the observations are frequencies or means. Finally we test whether the samples arenormal distributed using normality tests available in the STATA software (Shapiro-Francia, Skewness/Kurtosis and Shapiro-Wilk tests). We conclude that the normal distribution can be rejected at the sample-sizefor GB borrowers. This seems to be due to the relatively large proportions having either very large landholdings or zero land, which in turn is reflected in the means and frequencies since some of these observationsare included in the randomized sub-samples. An exception is the proportion reporting higher land value thaneligible, which seems to approximate the normal distribution.

18We calculate the geometric means "by hand" in stead of using the "means" command in STATA, to be able touse survey commands in calculating the confidence intervals for the log-transformed variables. As analternative to log-transformations, we have considered to exclude the highest values from the sample.However, the log-transformations seem to be better approximations to the normal distribution. Note that logsare not defined for zero, so the reported geometric means are calculated for the households having positiveland holdings.

31

by Amin, Rai and Topa (1999), where borrowers and non-borrowers have about the same

income and consumption levels.

Table 3 about here.

We will now emphasize the main result from the descriptive statistics. The probability

weights did not matter for that result. We have a random sample of 25 borrowers from

Grameen Bank type credit programs. Among the 25 respondents, four have land value above

NR 300 000. For any reasonable measurement error, these households are not eligible for

loans. The standard error for the proportion 4/25 (16%) can be exactly calculated from the

binomial distribution as 2 21 /125 = 0.0733, leading to a 95% confidence interval for the

proportion of [1.6, 30.4], which is close to the parallel interval for the weighted proportion in

Table 3. So even though the sample is small, we have sufficient information to conclude that

a certain proportion of Grameen Bank borrowers are non-eligible. The proportion is

significantly different from zero and smaller than 1/3.

We conclude that the descriptive statistics support the prediction from the theoretical model

that the Grameen Bank will have non-eligible members. In addition, we will emphasize that

the proposed screening mechanism may even work for eligible households. Note that the

proportion of landless households is large even among non-borrowers. These households

might be in the line for Grameen Bank loans, and can in principle replace borrowers that own

some land.

32

5. Main results

We believe that group-lending institutions have incentives to include members outside the

target-group of poor households. If this is true, then the non-target members will have incen-

tives not to report their true land holdings. We have solved this data problem by using a

general household survey, where questions on borrowing activities are from a small subset of

the questionnaire. We find that non-poor households have loans from the Grameen Bank of

Nepal and refer to similar results from Bangladesh.

We argue that a self-selection mechanism is an alternative to staff interviews and group

formation in selecting poor households. We demonstrate that the program interest rate should

be set higher than the interest rate in the commercial banks to exclude wealthy households.

We also demonstrate that a further increase in the interest rate will increase the number of

poor members as compared to middle-wealth members in Grameen Bank. There is a critical

upper bound for the interest rate, defined by a subsistence constraint. An interest rate below

the critical rate, will allow all target households to leave a poverty trap. The smaller is the

program interest rate, the fewer target households will thus be allowed in the program, but

they will be able to save more.

Furthermore, we demonstrate that only the poor will use the loan for productive purposes, and

these investments will not be made immediately. In the long run, Grameen Bank will only

have permanent members that will not apply the loans for production. At that time, Grameen

Bank may prefer to close down.

33

Appendix

In this appendix we derive the first order conditions for the households' optimization

problem, from section 2.

Households maximize utility U =u(ct )

(1 + δ)tt =1

∞

∑ , where u' > 0, u'' < 0, and u is the instantaneous

utility as a function of the period t consumption level ct. Utility is maximized subject to the

intertemporal budget I0 +ct + I t

(1 + r)tt =1

∞

∑ = A 0 +yt

(1+ r) tt =1

∞

∑ , with yt = F(Kt), where the production

function is characterized by F' > 0, F'' < 0, the productive capital K t = K0 + Iss= 0

t −1

∑ , where I is

investment, and subject to a subsistence constraint ct ≥ c , and borrowing and lending const-

raints A ≤ Abt ≤ 0 ≤ Alt ≤ A , with Abt + Alt = At = (At-1 + yt-1 - ct-1 - It-1)(1 + r), where Abt is

total borrowing at time t and Alt is total lending.

First, consider the case where only the budget is binding. Then the Lagrangian becomes

L = u(ct)

(1 + δ) tt =1

∞

∑ - µ I0 +ct + I t

(1+ r)tt =1

∞

∑ − A0 −F K 0 + Is

s= 0

t−1

∑

(1+ r) t

t =1

∞

∑

.

Since there is no credit constraint, K can be adjusted immediately, which means that in

optimum It = 0 for t > 0, leading to the budget I0 +ct

(1 + r)tt =1

∞

∑ = A 0 +F(K0 + I0 )

(1 + r)tt =1

∞

∑ , and

consequently the first order condition for I0 is F ' K 0 + I0( )

(1+ r)tt =1

∞

∑ =1, which is equivalent to

34

F'(K0 + I0) = F'(K1) = F'(K*) = r. For consumption we have the first order condition

u' (ct)u' (cs )

= (1 + δ)(1 + r)

t− s

, as described in Deaton (1992), which implies that the household will

end up with positive financial capital if r > δ .

Second, consider the case where the subsistence constraint binds, i.e. ct = c . The subsistence

constraint will either bind for all t ≤ u, or all t ≥ v, where u and v are critical periods. For

some households, u = 1 or v = 1, i.e. the constraint is binding only for the first period, or for

all periods. In the present model some myopic households are likely to have a decreasing con-

sumption path, which eventually implies a binding subsistence constraint. Since the

households are not credit constrained they will select the first-best I0 = K* - K0, which we can

insert in their intertemporal budget. We also insert the binding consumption constraint,

leading to

I0 +ct

(1 + r)tt =1

u−1

∑ +c

(1 + r)tt =u

∞

∑ = A 0 +F(K*)(1 + r)t

t =1

∞

∑ = A 0 +F(K*)

r,

and consequently we have the Lagrangian,

L = u(ct)

(1 + δ) tt =1

∞

∑ - µct

(1+ r)tt =1

u −1

∑ +c

(1+ r)tt =u

∞

∑ − (A 0 − I0 ) −F(K*)

r

,

leading to the first order conditions for consumption during the unconstrained periods,

u' (ct)u' (cs )

=(1 + δ)(1 + r)

t− s

. The subsistence constrained budget implies that every ct is smaller than

in the unconstrained case, since the household has to maintain c in the constrained periods.

35

In the extreme case, the subsistence constraint is binding for all periods. Then we have the

constrained budget, c = (A 0 + K0 − K*) ⋅ r + F(K*). Note that this can only happen by

coincidence, that is, for a certain initial wealth A0 + K0 = ˆ A . We generalize the model, by

assuming that all households having A0 + K0 ≤ ˆ A , will have a constant consumption

c1 = (A 0 + K 0 − K*) ⋅ r + F(K*) ≤ c . We can interpret any c1 ≤ c as representing malnutrition.

Third, consider the case where a credit constraint binds. We allow for both borrowing A and

lending A constraints, and both constraints may bind in the case of a time- preference rate in-

between the two interest rates. For periods where the credit constraints bind, the household

will have the permanent annual credit income, A · ri + A · rf, where ri is the lending and rf is

the borrowing rate. Since reallocation of consumption to the credit market is no longer an

option, we replace the intertemporal budget by the per period budget ct = A · ri + A · rf +

F K0 + Iss =0

t −1

∑

- It. From this we see that the sequence of ct is fully determined by the

sequence of It. We can identify the first order conditions for It-1 and It by inserting the per

periods budgets into the utility function, leading to

∂U∂It

=u' (cu )F ' (Ku )

(1 + δ)uu= t +1

∞

∑

−u' (ct )

(1 + δ)t = 0 ,

∂U∂I t −1

= u' (cu )F ' (Ku )(1 +δ)u

u= t

∞

∑

− u' (ct −1)(1 +δ)t −1 = 0 .

We can insert from these first order conditions into the equality,

u' (cu )F ' (K u)(1 + δ)u =

u' (ct)F ' (K t)(1 + δ)t +

u' (cu )F ' (Ku )(1 + δ)u

u= t +1

∞

∑u= t

∞

∑ ,

36

leading to

u' (ct −1)(1 + δ)t −1 = u' (ct )

(1 + δ)t + u' (ct )F ' (Kt)(1 + δ) t ,

which implies the first-order condition,

u' (ct)u' (ct −1)

=1 + δ

1+ F ' (K t)=

1+ δ1+ F ' (K t −1 + It −1)

=1+ δ

1 + F ' (Kt −1 + A ⋅ r + F(Kt −1) − ct−1 ).

This condition can be interpreted as a combination of the first order conditions for

consumption and production for the unconstrained case. During a period of growth, the

marginal return to productive capital F'(K) replaces the marginal return to financial capital r,

leading to u' (ct)

u' (ct −1)=

1 + δ1+ F ' (K t)

. When the period of growth is over we have F'(K) = δ , or

F'(K)/δ = 1, where the first order-condition is satisfied only for constant consumption. The

condition says that the infinitely discounted present value of the marginal return to productive

capital equals the marginal cost, which in turn is the marginal (unit) reduction in present

consumption.

37

Table 1. Classification of households (long term consumption in parentheses).Time- preference rates

Initial wealthδ1 > ri

(myopic)

ri > δ3 > rf

(relatively farsighted)

rf > δ5

(farsighted)K0+A0≤ ˆ A (below subsistence)

Trappedinformalborrowers (c1).

Trapped informalborrowers (c1).

ˆ A <K0+A0≤K3

(medium wealth)Informalborrowers (c2).

Informallenders (c4).

K0+A0> K3

(sufficient collateral)Informal lenders,formal borrowers (c3).

Informallenders (c5).

38

Table 2. Classification of GB borrowers (long term consumption in parentheses).Long run program effect

Pre-programc1

g ≤ c c1g > c

rg > δ > rf

c1g > c

ri > δ > rg

Target group(category 1)

Still trapped (c1g ). Leave trap (c3

g ).Permanent in GB.

Leave trap (c4).Leave GB.

Non-target group(category 4)

Permanent in GB (c3g ). No demand (c4).

39

Table 3. Descriptive statistics.Borrowers Non-borrowers Borrowers Non-borrowersLand (bigha) Land (bigha) Value (NR) Value (NR)

% with zero land 26.3% (6.7-46.0)

32.8%(15.7 - 50.0)

Median 0.56 0.4 53 000 60 000

Mean 1.08 1.38 112 200 171 300

Geometric mean 1.00(0.57 - 1.78)

1.00(0.74 - 1.35

93 000(63 800 - 135 400)

130 000(85 200 - 198 300)

% with > 1 bigha 36.1%(6.8 - 65.5)

32.0%(18.4 - 45.5)

% with > NR 138 000 16.4%(1.6 - 31.3)

31.9%(18.1 - 45.7)

% with > NR 300 000 16.4%(1.6 - 31.3)

13.2%(4.3 - 22.1)

Sample sizes* N = 23 N = 134 N = 25 N = 14395% confidence intervals in parentheses.* The sample sizes are respectively 16, 18, 88 and 97 for the geometric means.

40

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