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APPENDIX 2.1

In the model of Ghatak and Guinnane (1999), it is assumed that borrowers are

risk-neutral and that they are of two types, safe (a) and risky (b). Given a project undertaken by a

borrower of type i, output now takes two values Y iH and 0, with the probability of high output

being pi, i = a, b. It is assumed pa > pb. If the lender does not know the type of a borrower and

standard screening instruments like collateral cannot be used, the lender will offer loans with the

same nominal interest to all borrowers. In this situation, safe borrowers will cross-subsidize risky

borrowers because safe borrowers succeed more often (even as both repay the same amount when

they succeed). The presence of enough risky borrowers, however, can raise the equilibrium

interest rate high enough so that safe borrowers leave the market. Alternatively, safe borrowers

may continue to subsidize some undeserving risky projects.

Assuming borrowers know each other’s types, a joint-liability contract can

improve efficiency. With a joint liability credit contract, a borrower must repay the amount r if

her project yields a high return. She must also pay an extra amount c if the project of her partner

yields a low return. Thus, the expected payoff of a borrower of type i when her partner is of type

j in a joint-liability arrangement is the following:

EUij (r, c) = pi pj ( YH – r ) + pi ( 1 – pj ) ( YH – r – c ) (A2.1.1)

In general, all borrowers would prefer a safe partner. But the safer a borrower is,

the more she would want to have a safe partner. Consequently, safe borrowers would tend to

group together. In theory, a risky borrower could pay a safe borrower so that the latter would

agree to become her partner. The calculations below, however, indicate that this payment would

have to be larger than that which the risky borrower would be willing to make. In this regard,

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given Equation (2.1), note that the net expected return of a risky borrower when she has a safe

partner is the following:

EUba (r, c) – EUbb (r, c) = pb ( pa – pb ) c (A2.1.2)

At the same time, the net expected loss of a safe borrower when she has a risky partner is the

following:

EUaa (r, c) – EUab (r, c) = pa ( pa – pb ) c (A2.1.3)

If c > 0 and given pa > pb, then the latter expression ( = the compensation a safe borrower would

require for making a risky borrower her partner) is greater than the former ( = the amount the

risky borrower would be willing to pay). All the foregoing, therefore, implies that safe borrowers

will end up grouping together, and risky borrowers by default will do the same.

Given the assortative matching result described above, a lender can screen

borrowers by offering two contracts. If the first contract has high joint liability and a low interest

rate while the second has low joint liability with a high interest rate, then safe borrowers will

choose the former while risky borrowers will prefer the latter. Consequently, repayment rates

and efficiency improve as joint-liability contracts are able to take advantage of a useful resource

untapped by conventional individual-liability contracts: the information borrowers have of each

other.

To show how joint liability addresses the moral hazard problem, Ghatak and

Guinnane (1999) assume that borrowers are risk-neutral as before, but this time the actions of the

borrower determine the probability of project success. In this regard, borrowers choose a specific

level of effort p ( 0 ≤ p ≤ 1 ) which imposes on them a disutility cost equal to (1/ 2) γ p2 (with γ >

0). As a result of the effort level choice of the borrower—a choice which is assumed to be

unobservable to the lender—output takes on two values: it is YH with probability p and 0

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otherwise. Given the foregoing, social surplus p YH – (1/ 2) γ p2 is maximized if p = p* = YH /

γ. With regard to the latter, it is assumed that:

YH < γ (A2.1.4)

to ensure an interior solution. Under these circumstances, if the lender had perfect information, it

could specify that all borrowers choose level of effort p = p* and consequently charge an interest

rate r = ρ / p*. Given asymmetric information, however, with the choice of p subject to moral

hazard, an individual borrower will choose p so as to maximize her individual gain. Given a

particular interest rate r, she will solve the following maximization problem as shown below:

Max p ( r ) = Max { p ( YH – r ) – (1/ 2) γ p2 } = pi ( r ) = ( YH – r ) / γ (A2.1.5) p p

Given the above, we have p* = pi ( 0 ) > pi ( r ) for r > 0, and the higher the interest rate, the

lower is pi. In other words, the interest rate is like a tax on success, and the higher is the interest

rate, the lower is the resulting level of effort of the borrower.

The zero-profit condition of the lender is the following:

p r = ρ (A2.1.6)

Substituting pi ( r ) = ( YH – r ) / γ into the above, we obtain:

γ ( pi ) 2 – YH pi + ρ = 0 (A2.1.7)

Solving for pi and assuming that the equilibrium with the higher value of pi is chosen (since the

lender is indifferent while the borrower is strictly better off), we have:

pi = { YH + [ (YH )2 – 4 ρ γ ]1/2 } / 2 γ (A2.1.8)

With joint liability, a borrower once again pays the amount c when the project of

her partner fails. Given that her partner chooses the action p’, the borrower maximizes her

individual payoff by solving the following maximization problem:

Max { p ( YH – r ) – c p ( 1 – p’ ) – (1/ 2) γ p2 } (A2.1.9) p

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Given the above, the best response function of each borrower, pg1 (r), is the following:

pg1 = [ ( YH – r – c ) / γ ] + [ ( c / γ ) p’ ] (A2.1.10)

If borrowers who are partners make decisions about project choice non-cooperatively, then we

obtain the following symmetric Nash equilibrium:

pg1 = p’ = ( YH – r – c ) / ( γ – c ) (A2.1.11)

The zero-profit condition of the lender under joint liability is the following:

r p + c p ( 1 – p ) = ρ (A2.1.12)

Inserting the value of r in Equation (A2.1.11) into Equation (A2.1.12), we obtain the following:

γ ( pg1 ) 2 – YH pg1 + ρ = 0 (A2.1.13)

Equation (2.13) is identical to Equation (2.7) and thus implies that the equilibrium

project choice of a borrower in a non-cooperative group liability situation is the same as the

choice of a borrower under individual lending: joint liability by itself does not seem to alleviate

the moral hazard problem. This result, however, arises because it is assumed that each borrower

does not consider how her actions affect the choice of action of her partner. If, on the other hand,

we assume that borrowers decide on project choice in a cooperative manner—with each borrower

now fully internalizing the effect of her actions on the choice of action of her partner—the

maximization problem of an individual borrower is the following:

Max { p ( YH – r ) – c p ( 1 – p ) – (1/ 2) γ p2 } (A2.1.14) p

The solution to the above maximization problem, pg2 ( r, c ), is the following:

pg2 = ( YH – r – c ) / ( γ – 2c ) (A2.1.15)

Substituting pg2 for pg1 in Equation (A2.1.11) and then inserting the value of r in the transformed

equation into Equation (2.15), we obtain the following:

( γ – c ) ( pg2 ) 2 – YH pg2 + ρ = 0 (A2.1.16)

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Solving for pg2 above as before, we have:

pg2 = { YH + [ (YH )2 – 4 ρ ( γ – c ) ]1/2 } / 2 ( γ – c ) (A2.1.17)

Given that γ > YH by Equation (2.4) and the fact that a borrower cannot be asked to pay more

than what her project yields, it must be true that γ > c. Consequently, for 0 ≤ c ≤ γ, we have:

pg2 > pi (A2.1.18)

The above tells us that the equilibrium value of p, and therefore the repayment rate, is higher

under joint-liability group lending when borrowers decide on p cooperatively, as compared to its

value under individual-liability lending

The discussion of joint liability above has thus far assumed that borrowers can

contract on p among themselves. As part of this assumption, it is understood that borrowers can

observe the actions of one another perfectly and without cost, as well enforce agreements among

themselves. In an extension of the model as elaborated on above, Ghatak and Guinnane show

that, even when monitoring is costly, joint liability lending can still improve repayment rates

through peer monitoring. This requires, however, that monitoring costs are not too high and/ or

that associated social sanctions are effective enough.

In the final theoretical section of their research, Ghatak and Guinnane (1999)

discuss the problem of enforcement—when the project of a borrower is successful but she still

refuses to repay. The latter does not result from informational asymmetries but arises rather from

the limited ability of the lender to impose sanctions on a delinquent borrower. In this context,

joint liability lending has two opposing effects on repayment rates. On one hand, group lending

allows a borrower whose project has realized very high returns to repay the loan of a partner

whose project has failed. On the other hand, a borrower who is only moderately successful may

decide to default on her own repayment because of the burden of having to repay the loan of her

partner. It is argued that the net effect of these two movements is positive as long as social ties

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among borrowers are sufficiently strong. This is because borrowers who willfully default would

receive sanctions from both the lender and the community. In other words, with sufficient social

capital, the repayment rate would be higher under group lending compared to what it would be

under individual lending.

The following simple model illustrates this point. We assume that borrowers are

risk-averse and that the only departure from first-best happens when borrowers default even when

they are capable of repaying. The punishment that the lender imposes on a delinquent borrower

is to never lend to her again. In the context of individual lending, if the project of a borrower

produces output Y ≥ r (i.e. the borrower is capable of repaying her loan), she will repay only if

the benefit she derives from the additional income as a result of defaulting ( = the interest cost) is

less than B, the present value of the net benefit to the borrower of having continued access to

credit from the lender. In notational form, the borrower will repay if:

u (Y) − u (Y − r) ≤ B (A2.1.19)

The above implies that, for a given r, there will be some critical Y (r) such that the borrower will

repay only if Y ≥ Y (r). As project returns get smaller (i.e. Y gets lower), there is an increasing

motivation for a borrower not to repay. This is because repayment gets more costly as the

marginal utility of income increases.

Under joint-liability group lending, a borrower is considered to be in default if her

partner does not repay. Under these circumstances, that borrower will choose to repay her loan

and that of her defaulting partner (assuming she has income Y with Y ≥ 2r) if:

u (Y) − u (Y − 2r) ≤ B (A2.1.20)

Once again there is a critical level of income Y (2r) such that if Y ≥ Y (2r), then the borrower

will repay her own liability and that of her partner. It is to be noted, moreover, that Y (2 r) > Y

(r). This is because paying off two debt obligations (that of the borrower and her partner) is more

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burdensome for the borrower than just paying of her own debt obligation, and thus income would

need to be higher for her to decide to do this.

If we assume for simplicity that Y (r) > 2r and that two borrowers bound together

by a joint liability repay if each has an income Y > Y (r), then the following two distinct cases

emerge with group lending contracts: (1) One borrower is unable or unwilling to repay [has

income Y1 with Y1 ≤ Y (r) ] while the other is willing to repay both her own obligation and that

of her partner (has income Y2 with Y2 ≥ Y (2r). In this case, repayment rates are higher under

group lending than they are under individual lending. (2) One borrower is again unable or

unwilling to repay [ Y1 ≤ Y (r) ] while the other is willing to repay her own debt but not her debt

and that of her partner together [ Y (r) < Y < Y (2r) ]. In this case, as far as repayment rates are

concerned, individual lending outperforms group lending. Whether case 1 or 2 is more likely to

occur depends on the probability distribution of output. Whichever case is more prevalent,

however, social sanctions would alter significantly decisions made by borrowers in such a joint

liability setting. Social sanctions would reduce the payoff stream of borrowers who default

intentionally [those with Y such that r < Y < Y (r) ] and those who are willing to repay their own

loan but not that of their partner also [ those with Y such that Y (r) < Y < Y (2r) ]. In such a

context, it is argued, repayment rates would definitely be higher with group lending contracts.

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APPENDIX 2.2

In the model of Armendariz and Morduch (2000), the focus is on the individual

debt contract between a MFI and a borrower, with the assumption that the MFI has all the

bargaining power. A simple two-period model is considered in which a loan of size D is

extended by the MFI to the borrower at the beginning of each period. The borrower uses the loan

extended for the period to invest in a project which yields a total return π with a probability p,

and a total return of zero with probability (1 − p). Initially, p is assumed to be exogenous,

meaning there is no moral hazard problem with regard to the effort exerted by the borrower in

undertaking the project. The moral hazard problem is only in the repayment stage at which point

the client can “take the money and run” after returns on investment have been realized (also

referred to as the ex post moral hazard problem).

To prevent borrowers from doing the above, the MFI can threaten to not extend a

new loan in case of default, in which case it is assumed that the borrower will be unable to

finance a second-period investment. Given the foregoing, the sequence of events is the

following: In period t = 1, the borrower is given a loan of size D and this is invested by the

borrower to gain a first-period investment return. She then makes a decision on whether or not

she will default on her first-period debt obligation. In period t = 2, the MFI decides on whether

or not to extend a new loan to the borrower. If a new loan is extended, this is invested by the

borrower to generate a second-period return.

If projects are sure to succeed (that is, assuming p = 1), the total net pay-off of the

borrower if she defaults is the following:

π + δ v π (A2.2.1)

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where δ is the discount factor and v is the probability of the borrower being given a new loan by

the MFI (0 ≤ v ≤ 1). On the other hand, the total net pay-off of the borrower if she decides to

repay is the following

π − R + δ π (A2.2.2)

where R is the debt obligation of the borrower. The repayment R is deducted from the first-

period return π, after which the MFI automatically grants a second-period loan (that is, we set

v = 1) to the borrower to reward her for her good conduct. For both Equation (2.21) and (2.22), it

is assumed that the borrower defaults with certainty on her second-period debt obligation, after

she realizes her second-period return. This is because the bank, in the present limited horizon

model, can no longer reward the borrower with a new loan if she repays during the second period.

Comparing the two prospective total net pay-offs, the borrower will decide to

repay the MFI in the first period if:

π + δ v π ≤ π − R + δ π (A2.2.3)

The above is referred to as the incentive compatibility constraint and it specifies that the MFI

must ensure that the pay-off of the borrower is at least as large when she repays as when she

defaults. It is binding not only when p = 1 but for any value of p. Moreover, if the MFI credibly

carries out the threat to not finance a second-period loan in case of first-period default, v = 0 in

Equations (2.21) and (2.23). This in turn implies, based on Equation (2.23), that the maximum

interest rate that the bank can charge the borrower is R = δ π. In other words, the value δ π is the

opportunity cost of the borrower in not repaying her first-period obligation, and she cannot be

asked to repay more than this.

The MFI maximizes R subject to: (1) the incentive compatibility constraint as

defined by Equation (2.21); and (2) the individual rationality constraint of the borrower as

defined by the following equation:

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p ( π − R + δ π ) ≥ 0 (A2.2.4)

This latter constraint means that it must be profitable for a non-delinquent borrower to secure

loans over the two periods from the MFI—her total net pay-off must be positive.

The optimal solution for the MFI is to always carry out the threat of not extending

new loans to delinquent borrowers (i.e. to set v = 0) and to set R = δ π. Alternatively, it may opt

to share surpluses (by setting R < δ π) in accordance with its social objectives.

In order to lessen the probability of default, an MFI can impose collateral

requirements in the case of individual lending programs or induce social sanctions in the case of

group lending programs. Both can be introduced into the model and represented by the

additional sanctions variable W. Given W and assuming once again that the MFI follows the

optimal strategy of setting v = 0, the incentive compatibility constraint of the borrower is the

following:

π − W ≤ π − R + δ π (A2.2.5)

which simplifies to

− W ≤ − R + δ π (A2.2.6)

The latter in turn implies that the optimal R of the MFI, R*, is the following:

R* = δ π + W (A2.2.7)

It is assumed that R* is less than π because limited liability means that the borrower cannot be

forced to repay the MFI more than the value of her investment. When there are no additional

sanctions (W = 0), R* would be equal to δ π. On the other hand, additional sanctions (W > 0)

would allow the MFI to charge a higher R* without inducing a higher probability of borrower

default.

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The variable W can be re-interpreted as representing not sanctions but positive

inducements for repayment. If the MFI, for example, establishes a reputation of extending

progressively larger loans to borrowers who pay their obligations, Equation (2.21) becomes the

following:

π ≤ π − R + δ π2 (A2.2.8)

where π2 > π. Under these circumstances, we have:

R* = δ π2 = δ π + δ ( π2 − π ) (A2.2.9)

In the last equation, we can set W = δ ( π2 − π ) and the variable W would now represent the net

present value of future loans of increasing size over and above the net present value of loans that

remain constant at the initial size.

Apart from representing sanctions or incentives to repayment, the variable W can

also be used as a proxy for the probability of a borrower being re-financed by a rival lender. In

this regard, we assume that the borrower can secure a second loan from another lender with

probability v2. As a result, the incentive compatibility constraint (assuming as before that v = 0)

becomes the following:

π + δ v2 π ≤ π − R + δ π (A2.2.10)

According to this last equation, as the likelihood v2 of a borrower being refinanced by a second

lender increases, the incentive to repay the first lender decreases, and as a consequence, the

maximum repayment R that can be extracted by the first lender goes down as well.

Thus far, the model of Armendariz and Morduch (2000) has focused on incentives

to repay loans after projects have been undertaken successfully. This framework, however, can

be extended to cases in which the probability of success is endogenous. We introduce the latter

by assuming that the borrower can choose the level of p. In doing so, we get the following

sequence of events: The MFI first proposes a debt contract to the borrower, with a specified

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repayment schedule R. The borrower then makes her effort choice, which is modeled as

choosing a particular level of p. Returns are then realized from projects that are undertaken and

repayments are made. The borrower, of course, can still choose to default on her debt obligation.

If she does, she is not able to secure a second-period loan with probability (1 − v) and has to bear

the additional social sanction W.

The non-monetary cost of effort for the borrower is assumed to be the following:

c (p) = k ( p2 / 2 ) (A2.2.11)

where k is a fixed cost factor and the increasing marginal cost of effort is captured by quadratic

form of the cost function. The borrower chooses p so as to solve the following maximization

problem:

Max p ( π − R + δ π ) + ( 1 − p ) ( δ v π − W ) − c ( p ) (A2.2.12) p

The first-order condition for maximization of the above is:

π − R + ( 1 − v ) δ π + W = p k (A2.2.13)

The equilibrium probability p* corresponding to the equilibrium level of effort of the borrower is

thus the following:

p* = [ π − R + ( 1 − v ) δ π + W ] / k (A2.2.14)

Based on this last equation, it can be inferred that p* is: (1) decreasing as the debt obligation R of

the borrower increases; (2) increasing as the social sanction W increases; and (3) decreasing as

the probability of gaining access to a second-period loan increases.

Anticipating the equilibrium effort response of the borrower as described above,

the MFI will choose ex ante to set v = 0 (to not extend a new loan to a borrower who defaults)

and offer a repayment schedule R that will maximize its expected repayment revenue. In

accordance with the latter, the MFI will solve the following maximization problem:

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Max p (R) R = [ ( π − R + δ π + W ) / k ] R (A2.2.15) R

subject to R ≤ π. The first-order condition for maximization of the above is:

π − R + δ π + W = R (A2.2.16)

which yields the following optimal repayment schedule:

R* = [ ( 1 + δ ) π + W ] / 2 (A2.2.17)

with the assumption that R* < π. The last equation indicates that R* is an increasing function of

social sanctions W, project returns π and the discount factor δ.

As a final theoretical discussion, Armendariz and Morduch (1999) analyze what

was—at the time they wrote—one of the least remarked upon but most unusual features of

microfinance credit contracts. This was the requirement that repayments must start almost

immediately after disbursement of a loan and then proceed regularly thereafter. In the Grameen-

style MFIs surveyed by the authors, the repayment schedule for a year-long loan was determined

by summing up the total principal and interest due, dividing by 50, and then beginning weekly

collections a couple of weeks after loan disbursement. Such a system of weekly repayments

meant that these MFIs were in effect lending partly against streams of household income realized

outside of projects financed by their loans.

The desirability of regular repayment schedules from the point of view of MFIs is

modeled by the Armendariz and Morduch (2000) as follows. It is assumed that households, after

the purchase of household necessities, have disposable income X every week. This amount is

generated from “outside” sources and does not come from the household enterprise that is

financed by the MFI. This income, moreover, is diverted into miscellaneous consumption

expenses and decays at a discount factor d per week. It is assumed that the mentioned expenses

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do not provide the household any utility—an assumption, however, that can be released with

affecting the main argument.

Assuming that a loan has a one-year duration, the MFI must determine the number

of installments in a year ( = n ) by which the loan is to be repaid. Given that T = the length of a

period separating successive loan repayments (in terms of number of weeks), then n = 52 / T.

The loan may be paid in a one-time installment, for example, in which n = 1 and T = 52.

Alternatively, it may be paid monthly (n = 12, T = 52 / 12) or weekly (n = 52, T = 1). The total

of all the principal and interest payments made by the borrower to the MFI is denoted by L, while

the transaction costs per installment payment—which is assumed to be borne wholly by the

borrower—is denoted by γ. Assuming that the preferences of the borrower with respect to

income are linear and that the optimal loan size is not bigger than that which can be supported by

outside revenues of the borrower, the MFI chooses the value of T that will maximize the size of

L. This maximization problem is the following:

Max L = { ( d + d2 + d3 + … + dT ) ( 52 X / T ) − ( 52 γ / T) } (A2.2.18) T

Based on the maximization problem above, what is the optimal value of T for the

MFI? If d is close to one and γ is large, the optimal T will tend toward 52. However, as is more

likely with poorer households, if d is low (because income gets channeled to miscellaneous

expenses and mechanisms to enforce financial discipline are relatively limited) and γ is also low

(because the opportunity cost, for example, of time is relatively low), then the optimal T will tend

toward 1. This result is reinforced by the fact that micro-enterprises funded by MFIs (such as

those engaged in petty trading) usually generate a flow of revenue on a daily or weekly basis,

making frequent collections desirable given the lack of satisfactory savings facilities.

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As demonstrated in theoretical terms above, regular repayment schedules make the

largest amount of household income available for repayment to MFIs. It is also argued,

moreover, that they help screen out undisciplined borrowers, as well as provide MFIs with a

regular flow of information on borrowers. Finally, various authors have noted that regular

repayment schedules make microfinance credit contracts resemble arrangements for saving.

They provide a substitute for imperfect savings vehicles. By committing to make small, regular

payments to an MFI, borrowers are able to access a usefully large amount of money, in a way not

different from what would happen through a regular saving plan.

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APPENDIX 2.3

In the model of Vogelgesang (2003), the borrower obtains a loan of size L and has

non-business income V and wealth W. The borrower invests L and V into her business and the

latter yields a return equal to g (V + L, A) when successful. In the preceding function, A

represents the idiosyncratic characteristics that determine productivity and g is assumed to be

increasing in all arguments with decreasing returns in the first argument. Business output is

defined further by a binary variable π whose value is one if the business is successful and zero

otherwise. It is assumed that the borrower has to repay the total loan amount plus interest at the

end of the period, and thus the total repayment is equal to (1 + r) L where r is the interest rate.

Alternatively, the borrower has to pay a penalty P if the loan is not paid on time. This penalty

consists of higher interest rates if the borrower pays late or of collateral seizure if eventually no

payment is made at all. Furthermore, repeat loans from the same lender can only be secured by

the borrower if she has paid back the first loan on time. Otherwise, a new loan is not granted by

the lender and the borrower can be penalized with a bad credit record.

The future benefits from timely repayment are denoted by B. the factors that

determine the magnitude of B are assumed to include the following: (1) the degree of availability

of credit records, denoted by δ, (2) the extent of competition among MFIs, denoted by ζ, (3) the

borrower’s possession of idiosyncratic characteristics that increase her access to alternative

borrowing possibilities, denoted by R, and (4) the degree of leverage of the business of the

borrower, denoted by λ. A greater availability of credit records increases the barriers to obtaining

a future loan after default and is thus assumed to increase B. On the other hand, greater MFI

competition (which increases the supply of loans and the possibility of a borrower obtaining a

loan from another lender after default) is assumed to decrease B. Likewise, greater possession of

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favorable idiosyncratic characteristics (associated with gender, business sector and location) is

also assumed to decrease B. Finally, greater leverage of the business of the borrower—as well as

a bigger loan size L—increases the borrower’s need for a subsequent loan to maintain the scale of

her business and thus increases B.

For simplicity of notation, all relevant values in the analysis that follows are

denoted in terms of second period utility and there is no discounting. Total utility of the

borrower with repayment, UR, and with default, UD, are specified, respectively, by the following

equations:

UR = v { W + π g [V + L, A] – (1 + r) L } (A2.3.1)

+ B ( W, R, δ, ζ, λ, L )

UD = v { W + π g [V + L, A] – P } (A2.3.2)

Based on the Equations (2.39) and (2.40) above, the following variables used in the analysis are

defined:

vSR = v { W + π g [V + L, A] – (1 + r) L } (A2.3.3)

vFR = v { W – (1 + r) L } (A2.3.4)

vSD = v { W + π g [V + L, A] – P } (A2.3.5)

vFD = ( W – P ) (A2.3.6)

B* = B* ( W, V, P, r, L, A ) = vSD – vSR (A2.3.7)

B^ = B^ ( W, P, r, L ) = vFD – vFR (A2.3.8)

As defined in the equations above, vSR is the total utility of the borrower excluding

B when her business is successful ( π = 1 ) and she repays. vFR is the total utility of the borrower

excluding B when her business fails ( π = 0 ) and she repays. vSD is the total utility of the

borrower when her business is successful ( π = 1 ) and she defaults. vFD is the total utility of the

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borrower when her business fails ( π = 1 ) and she defaults. B* is the gain in total utility of the

borrower as a result of not paying her loan when her business succeeds, with her loss of future

benefits B not being taken into consideration. Finally, B^ is the gain in total utility of the

borrower as a result of not paying her loan when her business fails, with her loss of future

benefits B not being taken into consideration. It is to be noted that both B^ and B* are positive

because it is assumed (based on the actual practice of MFIs) that (1 + r) L > P. Furthermore, B^

> B* given the standard assumption that the utility of the borrower increases with income but at a

decreasing rate.

Based on all of the foregoing, borrowers can be divided into three client groups

based on their optimal repayment behavior. The latter is derived by comparing the borrower’s

total utility with repayment to her total utility with default, including now in the comparison how

the borrower would or would not enjoy future benefits B in the respective scenarios. The first

group of clients is constituted by those whose optimal policy is always to repay (whether their

business succeeds or fails) because for them the value of future benefits B is big enough such that

B ≥ B^ > B*. The second group of clients is constituted by those whose optimal policy is to

repay if their business succeeds and to default if it fails. For this second group, B^ > B ≥ B*.

With the last group of clients, the optimal policy is never to repay because B > B* ≥ B.

Who are the borrowers who are more likely to repay? First, borrowers who derive

greater future benefits B are more likely to repay. Secondly, borrowers with lower B^ (= smaller

gains from not repaying when their business fails) are more likely to repay after a business

failure. Third, borrowers with lower B* (= smaller gains from not repaying when their business

succeeds) are more likely to repay when their business is successful. Finally, borrowers with

higher W, V, A and π are more likely to have incomes that are sufficiently large to repay.

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Based on the model, therefore, individual borrower characteristics would affect

repayment as follows. Higher borrower productivity increases the likelihood of repayment.

Higher borrower nonbusiness income and/ or wealth have the same effect. On the other hand,

better alternative borrowing possibilities decreases the probability of repayment. With respect to

loan terms, low interest rates and high penalties increase the likelihood of repayment. Finally,

the environment also significantly influences repayment. The availability of credit records

increases the probability of repayment and so does a positive economic environment. More

competition among MFIs and the consequent greater supply of loans in the market decreases the

likelihood of repayment.

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APPENDIX 2.4

In the model of Gonzalez (2008), each household is assumed to live for only two

periods. In each period, it has a maximum endowment of labor emax. It also has an initial

endowment of productive assets (capital) a0 with no depreciation. Assets can be accumulated or

they can be liquidated to be transformed into consumption. The price of assets in period one is L1

while its price in period two is L2 with L1 < L2 < 1.

In each period t, net output yt is a stochastic function such that:

zt Y ( kt , et ) with probability p (A2.4.1)

yt = { } for t = 1, 2 0 wih probability (1 – p)

In the specification above, the first component zt is a non-tradable factor input consisting of the

entrepreneur’s skill or ability in production, which is assumed to be unevenly distributed in the

population. The second component represents a production function with two inputs, capital k t

and labor et with Yk > 0, Ykk < 0, Ye > 0 and Yee < 0. The second component, moreover, is

assumed to be zero when the project fails with a probability (1 – p).

Households can store output produced in period one to be used as capital and later

consumed in period two. As such, household consumption in each period c t is specified by the

following equation:

ct = yt – pt – ( at – at -1 ) Lt (A2.4.2)

where ct is consumption, pt is debt service payments, ( at – at -1 ) is asset accumulation (savings),

with all variables being end of period totals. Equation (2.48) represents the budget constraint that

must be satisfied in every period. It is assumed, moreover, that there is a minimum level of

consumption cMin > 0 below which the household does not survive.

The household maximizes expected utility W specified as:

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W = E0 [ U1 + β U2 ] (A2.4.3)

where β is the discount factor with 0 < β < 1. β is equal to 1 / (1 + ρ ) where ρ is the rate of time

preference. U is a utility function with Uc > 0, Ucc < 0, Ue > 0 and Uee < 0. Et is the expectations

operator conditional on the information/ expectations available to the individual at time t. For

simplicity, it is assumed that output yt is not equal to zero and the expectations operator is

removed and Equations (2.47) and (2.49) respectively become:

yt = zt Y ( kt , et ) (A2.4.4)

W = [ U1 + β U2 ] (A2.4.5)

It is assumed that each household does not have sufficient resources to take full

advantage of its investment opportunities and thus borrowing is welfare-improving.

Furthermore, each borrower establishes a credit relationship with only one lender and all funds

accessed from borrowing are used to purchase capital at the beginning of each period. Debt

matures in one period and the repayment function is the following:

dt = ( 1 + rt ) bt (A2.4.6)

where dt is the total debt service obligation at the end of the period, rt is the interest rate and bt is

the amount borrowed for the period with bt { 0∈ , Bt ]. Bt is the maximum loan size available to

the household in each period. B1 can be based on characteristics of the borrower household (that

are associated with its repayment capacity) so that for period one we have the following:

B1 = B1 (a0 , emax, z1) (A2.4.7)

The maximum loan size in period two is a function of the maximum loan size and

the repayment performance of the household in period one:

B2 = B2 ( B1, T) (A2.4.8)

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where T ∈ { D or Default, R or Repayment }. When default—defined as any situation where

pt < bt —occurs in period one, the household is denied access to a loan in period two. In other

words, we have:

B2 ( B1, D ) = 0 (A2.4.9)

for any value of B1. Under the preceding full repayment assumption, the household will choose

p1 = d1 if it decides to pay and p1 = 0 if it decides not to pay its debt in period one.

The household has an incentive to repay its loan in period one because this is

required in order to access a welfare-enhancing loan in period two. There is no such incentive for

loan repayment in period two, however, because the model assumes that the household lives for

only two periods. Consequently, default is always observed in the second period. Furthermore, a

no bequest condition is assumed (the household does not pass on wealth to a future generation)

and thus a2 = 0.

Apart from assets acquired through loaned funds, the household owns assets which

are available for production in each period. Consequently, capital kt is the following:

kt = bt + at - 1 (A2.4.10)

The household maximizes its intertemporal utility by choosing the optimal

amounts of effort, consumption, savings and borrowing/ capital in periods one and two. The

optimization problem of the household is given by the following:

Max W = [ U1 ( c1 , e1 ) + β U2 ( c2 , e2)] (A2.4.11) c1, c2, e1, e2, k1, a1

where Uc > 0, Ucc < 0, Ue > 0, Uee < 0, Yk > 0, Ykk < 0, Ye > 0 and Yee < 0, 0 < β < 1 and β

= 1 / (1 + ρ )

subject to:

a0 ≥ 0 (A2.4.12)

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et ≤ emax (A2.4.13)

ct ≥ cMin (A2.4.14)

ct = yt – pt – ( at – at -1 ) Lt (A2.4.15)

yt = zt Y ( kt , et ) (A2.4.16)

kt = bt + at - 1 (A2.4.17)

dt = ( 1 + rt ) bt (A2.4.18)

a1 ≥ 0 (maximum asset drawdown in period one condition) (A2.4.19)

a2 = 0 (no bequest motive condition) (A2.4.20)

0 ≤ b1 ≤ B1 (a0 , emax, z1) (A2.4.21)

b2 = B2 ( B1, T) with B2 ( B1, D) = 0 if default (A2.4.22)

and B2 ( B1, R) > B1 if repayment

W ≥ W0 = sup W ( b1 = b2 = 0 ) (A2.4.23)

If full repayment of debt in period one is assumed and with some substitutions, the

following Kuhn-Tucker Lagrangian associated with the household optimization problem is

obtained:

Γ = [ U1 ( c1 , e1 ) + β U2 ( c2 , e2)] (A2.4.24)

+ λ1 { z1 Y ( k1 , e1 ) – ( a1 – a0 ) L1 – c1 – ( 1 + r1 ) ( k1 – a0 ) }

+ λ2 { z2 Y ( a1 + b2 , e2 ) + a1 L2 – c2 }

– μ (e1) ( e1 – emax ) – μ (e2) ( e2 – emax )

+ μ (c1) ( c1 – cMin ) + μ (c2) ( c2 – cMin )

– μ (B1) ( b1 – B1) + μ (b1) b1 + μ (a1) a1

The first-order conditions (FOCs) for the intertemporal maximization of utility with loan

repayment are derived from the equation above and are the following:

∂ Γ/ ∂ c1 = ∂ U1 (c1 ,e1) / ∂ c1 – λ1 + μ (c1) = 0 (A2.4.25)

∂ Γ/ ∂ c2 = ∂ U2 (c2 ,e2) / ∂ c2 – λ2 + μ (c2) = 0 (A2.4.26)

∂ Γ/ ∂ e1 = ∂ U1 (c1 ,e1) / ∂ e1 + λ1 z1 [ ∂ Y (k1, e1) / ∂ e1 ] – μ (e1) = 0 (A2.4.27)

∂ Γ/ ∂ e2 = ∂ U2 (c2 ,e2) / ∂ e2 + λ2 z2 [ ∂ Y (k2, e2) / ∂ e2 ] – μ (e2) = 0 (A2.4.28)

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∂ Γ/ ∂ k1 = λ1 [ z2 (∂ Y (k2, e2) / ∂ e2) – (1 + r1) ] – μ (B1) + μ (b1) = 0 (A2.4.29)

∂ Γ/ ∂ a1 = – λ1L1 + λ2 [ z2 (∂ Y (k2, e2) / ∂ k2) + L2] + μ (a1) = 0 (A2.4.30)

∂ Γ/ ∂ λ1 = { z1Y (k1 , e1) – (a1 – a0) L1 – c1 – (1 + r1 )(k1 – a0)} = 0 (A2.4.31)

∂ Γ/ ∂ λ2 = { z2 Y (a1 + b2 , e2) + a1 L2 – c2 } = 0 (A2.4.32)

μ (e1) (e1 – emax) = 0 , μ (e2) (e2 – emax) = 0 (A2.4.33)

μ (c1) (c1 – cMin) = 0 , μ (c2) (c2 – cMin) = 0 (A2.4.34)

μ (B1) (b1 – B1) = 0 , μ (b1) b1 = 0 (A2.4.35)

μ (e1) , μ (e2) , μ (c1) , μ (c2) , μ (B1) , μ (b1) ≥ 0 (A2.4.36)

( e1 – emax ) ≤ 0 , ( e2 – emax ) ≤ 0 (A2.4.37)

( c1 – cMin ) ≥ 0 , ( c2 – cMin ) ≥ 0 (A2.4.38)

( b1 – B1) ≤ 0 , b1 ≥ 0 , b2 = B2 (A2.4.39)

μ (a1) a1 = 0 (A2.4.40)

μ (a1) ≥ 0 , a1 ≥ 0 (A2.4.41)

It is assumed that a solution to the maximization problem exists and that this solution is the

following:

Ψ* = ( c1*, c2*, e1*, e2*, k1*, a1*) (A2.4.43)

The above solution defines the optimal levels of utility in period one and two, U1* and U2*,

respectively, as well as the maximum level of utility (value function) W*, with repayment.

If the household defaults on loan repayment in period one, it loses access to credit

in period two. The household can choose to do this even when it generates sufficient capacity to

repay its loan in period one. The household chooses to default when the maximum level of utility

of the household under default is greater than its maximum level of utility under repayment. In

the default scenario, the household decides on the optimal level of the decision variables,

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constrained by the fixed level of capital k1* set in the beginning of period one, with k1* equal to

the initial level of assets a0 plus the loan funds b1 obtained for period one. The Kuhn-Tucker

Lagrangian associated with the optimization problem of the household under default in the first

period is thus the following:

Γ = [ U1 ( c1 , e1 ) + β U2 ( c2 , e2)] (A2.4.44) k1 = k1*

+ λ1 { z1 Y ( k1*, e1 ) – ( a1 – a0 ) L1 – c1 }

+ λ2 { z2 Y ( a1 , e2 ) + a1 L2 – c2 }

– μ (e1) ( e1 – emax ) – μ (e2) ( e2 – emax )

+ μ (c1) ( c1 – cMin ) + μ (c2) ( c2 – cMin ) + μ (a1) a1

The FOCs for the intertemporal maximization of utility under default are derived from the

equation above. It is assumed that a solution to the maximization problem exists and that this

solution is the following:

ΨD = ( c1D, c2

D, e1D, e2

D, a1D ) (A2.4.45)

The above solution defines the optimal levels of utility in period one and two, U1D and U2

D,

respectively, as well as the maximum level of utility WD, under default.

The maximum value of the objective function for different levels of b1 given the

decision to repay the loan accessed in period one is the following:

WR (b1) = sup { U1 [ (z1 Y ( b1 + a0 , e1 ) – (a1 – a0) L1 – b1 (1 + r1) , e1 ] (A2.4.46) b1

≤ B1

+ β U2 [ (z1 Y (b2 + a1 , e2) + a1 L2 , e2 ] }

On the other hand, the maximum value of the objective function for different levels of b1 given

the decision to default on the loan accessed in period one is the following:

WD (b1) = sup { U1 [ (z1 Y (b1 + a0 , e1) – (a1 – a0) L1 , e1 ] (A2.4.47) b1

≤ B1

+ β U2 [ (z1 Y (a1 , e2) + a1 L2 , e2 ] }

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Let b1R

be the amount of assets purchased with the use of loaned funds by the household in period

one at which its maximum utility under repayment is equal to its maximum utility under default.

In other words, b1R is defined by the following equation:

WR ( b1R ) = WD ( b1

R ) (A2.4.48)

It is shown that b1R > 0 may not exist. Moreover, it is also be shown that when b1

R > 0, for any

b1' < b1R and b1'' > b1

R, respectively, we have:

WR (b1' ) > WD (b1' ) (A2.4.49)

WR (b1'' ) < WD (b1'' ) (A2.4.50)

The above equations imply the following: (1) For any loan b1' smaller than b1R, WR > WD and

the household repays its loan. (2) For any loan b1'' larger than b1R, WR < WD and the household

defaults on its loan obligation. The preceding points relate to the importance of an MFI being

able to correctly estimate the entrepreneurial ability of a borrower household, particularly in

terms of not over-estimating the capacity of the latter to use a particular amount of loaned funds

in a productive manner.

The analysis thus far has not modeled the impact of unexpected adverse shocks on

both the repayment capacity of the household and its decision to repay its loan, respectively.

Adverse economic shocks, however, can have a significant effect on household welfare. The

analysis that follows now takes this into account and models household repayment behavior with

the occurrence of an unexpected adverse shock in period one. In this regard, it is assumed that

the household experiences this shock early in period one, just after assets have been bought with

the loan. The latter investment is assumed to be irreversible (that is, the household cannot

disinvest and return the loaned funds to the lender). The shock reduces the level of z in the

production function of the household so its value after the shock, z1E, is lower than z1. It is

assumed further that, after the shock has occurred, there is no longer uncertainty about the

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production function of period one. In particular, the household becomes certain that the effective

level of output after the shock for period one equal to z1E YE ( k1*, e1* ) will be lower than the

previously planned level of output z1 Y ( k1*, e1* ), given the previously set optimal amount of

capital k1* and planned level of effort e1*.

The lower post-shock level of output makes the effective repayment capacity of

the household inadequate to meet its debt obligation. The latter situation is described by the

following equation:

(1 + r1) (k1* – a0) > ztE YE ( k1*, e1*) – c1* – (a1* – a0) L (A2.4.51)

Given the above, the household has only two options, either to default on the loan or to repay by

undertaking “costly actions.” There are three types of “costly actions” that the household can

engage in, all involving a modification of an initially planned level of (optimal) action in period

one: (1) reduce consumption, (2) increase effort and (3) reduce savings (sell assets). The first

two costly actions reduce the level of household utility in period one while the third action

reduces the level of household utility in period two. Furthermore, the shock may change the

production function of period two causing a reduction in the level of output of the household in

period two.

Let G1 represent the additional repayment capacity necessary for a household to

repay its loan after the occurrence of an adverse economic shock. The value of G1 is given by the

following equation:

G1 = ztE YE (k1*, e1*) – {c1* + (a1* – a0) L1 + (1 + r1) (k1* – a0)} < 0 (A2.4.52)

A larger negative value of G1 implies that the household must engage in greater magnitudes of

costly action in order to repay its loans. This would involve one or two or all of the following:

more reduction in consumption, a larger asset drawdown and greater increase in effort.

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If the household chooses to repay its loan after a shock, its new optimization

problem involves generating the additional repayment capacity it needs with a minimum loss of

utility. This is equivalent to the optimization problem in which the objective function is still the

one specified in Equation (2.57) and but the constraints now include the requirement that G1 = 0

with k1 = k1* and b1 = b1*. The Kuhn-Tucker Lagrangian associated with this optimization

problem is the following:

Γ = [ U1 ( c1 , e1 ) + β U2 ( c2 , e2)] (A2.4.53) k1 = k1*, G1 = 0

+ λ1 { z1E YE ( k1* , e1 ) – ( a1 – a0 ) L1 – c1 – ( 1 + rt ) ( k1* – a0 ) }

+ λ2 { z2 Y ( a1 + b2 , e2 ) + a1 L2 – c2 }

– μ (e1) ( e1 – emax ) – μ (e2) ( e2 – emax )

+ μ (c1) ( c1 – cMin ) + μ (c2) ( c2 – cMin ) + μ (a1) a1

The corresponding FOC for the intertemporal maximization of utility are derived from the

equation above. It is assumed that a solution to the maximization problem exists and that this

solution is the following:

ΨRS = ( c1RS, c2

RS, e1RS, e2

RS, a1RS ) (A2.4.54)

The above solution defines the optimal levels of utility in period one and two, U1RS and U2

RS,

respectively, as well as the maximum level of utility WRS, with repayment after an adverse

economic shock.

If the household defaults on its loan in period one, it loses access to credit in

period two. It will, however, avoid engaging in costly actions in period one. The Kuhn-Tucker

Lagrangian associated with the optimization problem of the household if it chooses to default on

its loan obligation after an adverse economic shock is the following:

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Γ = [ U1 ( c1 , e1 ) + β U2 ( c2 , e2)] (A2.4.55) k1 = k1*

+ λ1 { z1E YE ( k1* , e1 ) – ( a1 – a0 ) L1 – c1 }

+ λ2 { z2 Y ( k2 , e2 ) + a1 L2 – c2 }

– μ (e1) ( e1 – emax ) – μ (e2) ( e2 – emax )

+ μ (c1) ( c1 – cMin ) + μ (c2) ( c2 – cMin ) + μ (a1) a1

The corresponding FOC for the intertemporal maximization of utility are derived from the

equation above. It is assumed that a solution exists and that this solution is the following:

ΨDS = ( c1DS, c2

DS, e1DS, e2

DS, a1DS ) (A2.4.56)

The above solution defines the optimal levels of utility in period one and two, U1DS and U2

DS,

respectively, and the maximum level of utility WDS, with default after an adverse economic

shock.

The household will choose to repay its loan after a shock if WRS > WDS, and

conversely, will default after a shock if WDS > WRS.

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APPENDIX 2.5

Sharma and Zeller (1997) survey the group-based credit programs of three

Bangladeshi MFIs—the Association for Social Advancement (ASA), the Bangladesh Rural

Advancement Committee (BRAC), and the Rangpur Dinajpur Rural Service (RDRS). They

examine the factors that affect the repayment performance of 128 borrower groups belonging to

the said institutions. Their research uses the following repayment function:

DELIQ = f (LNSIZE, X, Z, M) (A2.5.1)

where DELIQ is equal to the delinquency rate defined as the proportion of the total loan amount

in arrears at the date when complete repayment was promised, LNSIZE is the loan size, X is a

vector of group characteristics, and M is a vector of lender characteristics. Z is a vector of

community characteristics. The function is specified such that

Lim DELIQ = 0 (A2.5.2) LNSIZE 0

It is argued that the preceding specification is a reasonable assumption. It,

moreover, implies that the effects of X, Z, M on the default rate are conditional on the loan size.

Consequently, when Equation (2) is a linear function, the repayment function interacts X, Z, M

with LNSIZE as follows:

DELIQi* = β1 (LNAMT) + (LNAMT) X β2 + (LNAMT) Z β3 (A2.5.3)

+ (LNAMT) M β2 + ei

where DELIQ* = 0 if DELIQi* ≤ 0 and DELIQi = DELIQi* if DELIQi* > 0. DELIQi* is

thus a latent variable that is observable only when it takes a positive value. Equation (A2.5.3) is

estimated by using the TOBIT maximum likelihood technique.

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Based on the results of the estimation, the factors that lower the borrowing group

delinquency rate include the following: (1) the mean level of land owned by the borrowing

group, (2) a higher group-wise mean dependency ratio, (3) a greater percentage of group

members who are female and (4) the fact that the borrowing group had formed itself on its own.

The factors that increase the borrowing group delinquency rate include the following: (1) an

increasing size of the loan to the group, (2) a greater proportion of members in the group that are

related to each other, (3) a greater proportion of group members reporting agricultural production

as the principal occupation, (4) a greater number of informal mutual self-help and insurance

groups in the village and (5) the presence of a food-for-work program in the village.

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APPENDIX 2.6

Gonzalez (2008) studies the over-indebtedness of borrower households in Bolivia

in the 1997-2001 period. The research defines “over-indebtedness" as occurring in the following

three situations: (1) when the borrower is not willing to repay the loan, even if she has the ability

to do so, and consequently, default occurs; (2) when the borrower has to undertake costly

“extraordinary” actions in order to repay the loan, beyond those anticipated at the time when

agreement for the transaction was completed, and (3) when the borrower is willing to repay the

loan, but does not have the ability to do so in full and when agreed, and consequently, arrears,

partial repayment or full default are observed.

1,282 lending relationships with formal lenders in the 1997-2001 period (and

involving 959 borrower households) are the focus of the research analysis. Each of the lending

relationships is classified into one of the following three mutually exclusive groups, according to

associated levels of arrears: (1) those with a perfect repayment record or 0 days of arrears for all

loans in the period, (2) those with arrears of less than 30 days at least once in the period, and (3)

those with arrears of 30 or more days at least once in the period. Furthermore, each lending

relationship is also classified into one of the following two groups, according to whether or not

the concerned borrower household had to engage in costly actions (involving the increase of

labor, the reduction consumption and/ or the sale of assets) in the process of repaying its loans:

(1) those with an active borrower household (which engaged in some costly actions at least once

in the period) and (2) those with an inactive borrower household (which did not engage in any

costly action). By putting together the two ways of classifying lending relationships explained

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above, the following six mutually exclusive categories of lending relationships are observed: (A)

those with 0 days of arrears and no costly actions, (B) those with 0 days of arrears and costly

actions, (C) those with less than 30 days of arrears and costly actions, (D) those with less than 30

days of arrears and no costly actions, (E) those with 30 or more days of arrears and costly actions,

and (F) those with 30 or more days of arrears and no costly actions. It is to be noted that the only

borrower households who are not over-indebted—according to the research definition of over-

indebtedness—are those involved in lending relationships of category (A).

Given all the foregoing, two sets of logistic regressions are performed. The first

set analyzes factors that are associated with the borrower household being over-indebted, in terms

of its being willing to repay but lacking sufficient capacity to do so without arrears and/ or

engaging in costly actions in repaying. The dependent variable in these regressions is a dummy

variable that is equal to 1 when the lending relationship belongs to either category (B), (C), (D) or

(E) and 0 when the lending relationship belongs to category (A), with lending relationships

belonging to category (F) excluded from the analysis. The second set of regressions analyzes

the factors associated with over-indebted borrower households having less willingness to engage

in costly actions in order to repay their loans and being less able to generate extraordinary

repayment capacity when they do. The dependent variable in these regressions is a dummy

variable that is equal to 1 when the lending relationship belongs to category (D) or (E) and 0

when the lending relationship belongs to category (B) or (C), with lending relationships

belonging to category (A) and (F) excluded from the analysis.

The independent variables for both sets of regressions are grouped into the

following four categories: (1) household experience of shocks, expectations and timing of

events; (2) lender and loan characteristics; (3) household experience with lenders and incentives

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to repay and (4) household repayment capacity. Table A2.6.1 below contains a description of the

independent variables that turned out to be significant in the regressions.

With reference to Table A2.6.1, the main significant results of the first set of

regressions are the following: (1) Being located in particular cities of the study increases the

probability of over-indebtedness (reflecting the effect of location-specific shocks as well as the

different degrees of competition among MFIs in different locations). (2) The borrower

household’s experience of an adverse shock increases the probability that it is over-indebted. (3)

An increase in the number of years in which a borrower household receives at least one new loan

from a particular lender decreases the probability that it is over-indebted. (4) An increase in the

number of years to maturity of the last loan provided by a particular lender increases the

probability of over-indebtedness but its effect is small. (5) The borrower household having an

outstanding loan with a commercial lender increases the probability that it is over-indebted. (6)

The only socio-economic variable associated with household repayment capacity that is

significantly related to over-indebtedness is the level of education of the main person in the

household, with an increase in the latter reducing the probability of over-indebtedness.

The main significant results of the second set of regressions are the following: (1)

The identity of the lender in a lending relationship is related to the probability that the concerned

borrower household belongs to the “lower quality” group of over-indebted households. Borrower

households in the “lower quality” group (as viewed from the financial management perspective

of the MFI) are less willing to engage in costly actions and/ or less able to generate extraordinary

repayment capacity when they do. Village banks (which are not assigned a dummy variable in

the regressions) had the lowest probability of having over-indebted households in the “lower

quality” group. Having a relationship with a group lender, individual lender and consumption

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lender, respectively, significantly increases, in ascending order, the probability that the over-

indebted household belongs to the “lower quality” group. (2) The location of the borrower

Table A2.6.1Description of Significant Independent VariablesUsed in the Empirical Models of Gonzalez (2008)

Household experience of shocks

Regional dummies

Shocks

Dummies for sector of main household economic

activity

Dummy variable = 1 if the borrower household is located in a particular city and 0 otherwise (NOTE: A dummy variable is assigned, respectively, for four of the five cities in which borrower households of the sample are located.)Dummy variable = 1 if the household experienced a shock and there was an outstanding formal loan during any year in the 1997-2001 period and 0 otherwiseDummy variable = 1 if the main economic activity in the 1997-2001 period belongs to a particular sector and 0 if the main economic activity was not stable or belonged to some other sector (NOTE: The three sectors assigned dummy variables are manufacturing, commerce and services, respectively.)

Lender and loan characteristics

Individual lender

Group lender

Consumption lender

Commercial lender

Loan term

Dummy = 1 if lending relationship is with one of the four MFIs without a banking license that operate on the basis of individual lending and 0 otherwiseDummy = 1 if lending relationship is with one of two regulated MFIs that operate on the basis of group lending and 0 otherwiseDummy = 1 if lending relationship is with a consumption lender and 0 otherwiseDummy = 1 if borrower household has an outstanding loan with a commercial lender in the 1997-2001 period (for purchase of goods at particular stores, like hardware stores, warehouses, etc.)The number of years to maturity of the last loan provided by a particular lender

Household experience with lenders

Cohort 1997 – cohort 2001

Years with new loans

Default first

Five dummy variables defined on the basis of the year that the household received its first formal loan in the 1997-2001 period.The total number of years in which the borrower received at least one new loan from a particular lender in the 1997-2001 periodDummy = 1 if the borrower household indicates that, if in trouble, they would repay the particular lender last and 0 otherwise

Household repayment capacity

Education main person Measure of the education of the household head or household member that generated the most household income

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Source of basic data: Gonzalez (2008)

household in particular cities of the study increases the probability that it belongs to the “lower

quality” group of over-indebted households.

APPENDIX 3.1

The following analysis of household decision-making when there is no economic

shock proceeds from the exposition of the Gonzalez (2008) model in Appendix 2.4 and Chapter

3. It is assumed in what follows that the optimal level of effort of each household under the four

different repayment/ default scenarios of the Gonzalez (2008) model are all close to the

maximum level of effort emax if not equal to it. Consequently, for each household, e1* is not

significantly different from e1D, so that the simplifying assumption can be made that:

e1* = e1D = e1** (A3.1.1)

Likewise, e2* is not significantly different from e2D, so that the simplifying assumption can be

made that:

e2* = e2D = e2** (A3.1.2)

Under the preceding assumptions, differences in the levels of consumption c1*, c2*, c1D and c2

D,

respectively, of the household become a function of its accessing a second period loan equal to b2

if it repays and its setting of the levels of a1* and a1D, respectively.

Let A be the change in the level of the capital stock from period one to two that

maximizes the utility of a household under repayment when there is no economic shock, such

that:

a1* – a0 = A (A3.1.3)

Given the above, if the household chooses to repay when there is no economic shock, its optimal

levels of consumption in period one and two, respectively, are the following:

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c1* = z1 Y ( b1* + a0 , e1** ) – A L1 – b1* ( 1 + r1 ) (A3.1.4)

c2* = z2 Y ( b2 + a0 + A, e2**) + (a0 + A) L2 (A3.1.5)

Consequently, the maximum level of intertemporal utility of the household, WR, when there is no

adverse economic shock and it repays its period one loan is:

WR = U1 [ c1* , e1** ] + β U2 [ c2* , e2** ] (A3.1.6)

where c1* and c2* are defined by Equations (A3.4) and (A3.5), respectively.

Consider that the household, in determining how to maximize its utility if it

chooses to default, contemplates a preliminary level of capital stock at the beginning of period

two equal to a1DA where:

a1DA – a0 = b2 + A (A3.1.7)

a1DA makes the total amount of productive capital in period two when the household defaults

equal to its optimal total amount when the household repays ( both are equal to [b 2 + a0 + A] ). If

the household sets a1 = a1DA, its levels of consumption in period one and two, respectively, would

be the following:

c1DA = z1 Y ( b1* + a0 , e1** ) – ( b2 + A) L1 (A3.1.8)

c2DA = z2 Y ( b2 + a0 + A, e2**) + (a0 + b2 + A) L2 (A3.1.9)

Let the level of intertemporal utility of the household when there is no adverse economic shock

and it defaults on its loan with its level of capital stock at the beginning of period two set at to

a1DA be equal to WDA where:

WDA = U1 [ c1DA , e1**] + β U2 [ c2

DA , e2**] (A3.1.10)

In choosing to repay or default, the household can compare WDA with WR— even

without yet determining a1D, its optimal level of capital stock at the beginning of period two if it

defaults, and WD, its maximum level of intertemporal utility when there is no adverse economic

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shock and it chooses to default. Given that WD ≥ WDA, if WDA > WR, or alternatively, if WDA

– WR > 0, the household chooses to default.

Let Vc1* ( k ) be the change in household utility as a result of adding k to the value

of c1* and Vc2* ( m ) be the change in household utility as a result of adding m to the value of

c2* such that

Vc1* ( k ) = U1 [ c1* + k , e1** ] − U1 [ c1* , e1** ] (A3.1.11)

Vc2* ( m ) = U2 [ c2* + m , e2** ] − U2 [ c2* , e2** ] (A3.1.12)

Based on the foregoing definitions and on Equations (A3.4) to (A3.6) and Equations (A3.8) to

(A3.10), we have the following:

WDA – WR = { U1 [ c1DA, e1**] + β U2 [ c2

DA, e2**] } (A3.1.13)

− { U1 [ c1*, e1**] + β U2 [ c2*, e2**] }

= U1 [ c1DA, e1**] − U1 [ c1*, e1**]

β { U2 [ c2DA, e2**] − U2 [ c2*, e2**] }

= U1 [ c1* + b1* (1 + r1) − b2 L1 , e1**] − U1 [ c1*, e1**]

+ β { U2 [ c2* + b2 L2 , e2**] − β U2 [ c2*, e2**] }

= Vc1* [ b1* (1 + r1) − b2 L1 ] + β Vc2* [ b2 L2 ]

The household chooses to default on its loan if:

WDA – WR = Vc1* [b1* (1 + r1) − b2 L1] + β Vc2* [ b2 L2] > 0 (A3.1.14)

Let B be the change in the level of the capital stock from period one to two that

maximizes the utility of a household under default when there is no economic shock, such that:

a1D – a0 = B (A3.1.15)

Given the above, if the household chooses to default when there is no economic shock, its

optimal levels of consumption in period one and two, respectively, are the following:

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c1D = z1 Y ( b1* + a0 , e1**) – B L1 (A3.1.16)

c2D = z2 Y ( a0 + B, e2**) + (a0 + B) L2 (A3.1.17)

Consequently, the maximum level of intertemporal utility of the household, WD, when there is

no adverse economic shock and it defaults on its period one loan is:

WD = U1 [ c1D , e1** ] + β U2 [ c2

D , e2** ] (A3.1.18)

where c1D and c2

D are defined by Equations (A3.16) and (A3.17), respectively.

Consider that the household, in determining how to maximize its utility if it

chooses to repay, contemplates a preliminary level of capital stock at the beginning of period two

equal to a1*A where:

a1*A – a0 = – b2 + B (A3.1.19)

a1*A makes the total amount of productive capital in period two when the household repays equal

to its optimal total amount when the household defaults ( both are equal to [a0 + B] ). If the

household sets a1 = a1*A, its levels of consumption in period one and two, respectively, would be

the following:

c1*A = z1 Y ( b1* + a0 , e1** ) – ( – b2 + B ) L1 – b1* ( 1 + r1 ) (A3.1.20)

c2*A = z2 Y ( a0 + B , e2** ) + ( a0 – b2 + B ) L2 (A3.1.21)

Let the level of intertemporal utility of the household when there is no adverse economic shock

and it repays its loan with its level of capital stock at the beginning of period two set at to a1*A be

equal to WRA where:

WRA = U1 [ c1*A , e1**] + β U2 [ c2*A , e2**] (A3.1.22)

In choosing to repay or default, the household can compare W*A with WD—even

without yet determining a1*, its optimal level of capital stock at the beginning of period two if it

repays, and WR, its maximum level of intertemporal utility when there is no adverse economic

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shock and it chooses to repay. Given that WRA ≤ WR, if WD < WRA, or alternatively, if WD

– WRA < 0, the household chooses to repay.

Let Vc1D ( p ) be the change in household utility as a result of subtracting p from

the value of c1D and Vc2D ( q ) be the change in household utility as a result of subtracting m

from the value of c2D such that:

Vc1D ( p ) = U1 [ c1D , e1** ] − U1 [ c1

D – p , e1** ] (A3.1.23)

Vc2D ( q ) = U2 [ c2D, e2** ] − U2 [ c2

D – q , e2** ] (A3.1.24)

Based on the foregoing definitions and on Equations (A3.16) to (A3.18) and Equations (A3.20)

to (A3.22), we have the following:

WD – WRA = { U1 [ c1D, e1**] + β U2 [ c2

D, e2**] } (A3.1.25)

− { U1 [ c1*A, e1**] + β U2 [ c2*A, e2**] }

= U1 [ c1D, e1**] − U1 [c1*A, e1**]

β { U2 [ c2D, e2**] − U2 [c2*A, e2**] }

= U1 [ c1D, e1**] − U1 [ c1

D − b1* (1 + r1) − b2 L1 , e1**]

+ β { U2 [ c2D , e2**] − U2 [ c2

D − b2 L2 , e2**] }

= Vc1D [ b1* (1 + r1) − b2 L1 ] + β Vc2D [ b2 L2 ]

The household chooses to repay its loan if:

WD – WRA = Vc1D [b1* (1 + r1) − b2 L1] + β Vc2D [ b2 L2] < 0 (A3.1.26)

Taken together, Equation (A3.14) and (A3.26) tell us that decision of the

household to repay or default on its loan—while being a function of the values of c1*, c2*, c1D and

c2D—can be determined theoretically by the value of the following parameters: b1*, r1, b2 , L1, β

and L2. In this regard, when b1* and r1 decrease in value, the decision to repay becomes more

likely. When the value of L1 decreases so that the value of k = L1 / L2 (with 0 < L1 < L2 ≤ 1)

121

decreases, repayment becomes more likely. When the value of β increases, repayment becomes

more likely. An increase in the value of b2 either increases or decreases the probability or

repayment, depending on the relative values k and β.

A theoretical scenario where all households repay their respective loan is possible

—no matter what the level of productivity z and asset endowment a0 of each particular household

may be. This happens when the values of b2 and L1 are high enough while the value of β is low

enough to make WD – WRA < 0 no matter what the value of c1D and c2

D are. Conversely, another

theoretical scenario where all households default on their respective loan is also possible—once

again, no matter what the level of productivity z and asset endowment a0 of each particular

household may be. This happens when the values of b2 and L1 are low enough while the value of

β is high enough to make WDA – WR > 0 no matter what the value of c1* and c2* are.

The first scenario would include the case of a household with very low

productivity, which—instead of choosing to default—pays off its period one loan and sells

relatively high-priced assets to augment its consumption in period one. It then uses its second

period loan to restore the level of its capital stock for period two. The second scenario would

include the case of a household with very high productivity, which—instead of choosing to repay

—defaults on its period one loan. It then uses the additional income generated by its first period

loan to buy low-priced assets to augment its capital stock, and hence, its income, in the second

period.

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APPENDIX 3.2 (A)

PROGRESS OUT OF POVERTY INDEX (PPI) SCORECARD

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APPENDIX 3.2 (B)

TABLE OF ESTIMATED POVERTY LIKELIHOODS

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ASSOCIATED WITH PPI SCORES

APPENDIX 3.3

According to Grameen Foundation (2014), there are currently more than 200

organizations worldwide that use Grameen Foundation’s Progress out of Poverty Index (PPI).

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These organizations—nonprofit organizations, for-profit businesses, investors, networks and

rating agencies, in countries across Africa, Asia, Latin America and the Middle East—work with

poor clients and communities in diverse ways, including providing financial services, providing

health care and conducting research that can benefit the wider anti-poverty community. For

them, the PPI is a statistically-sound yet simple tool used to measure poverty outreach, to assess

the performance of interventions among the poor and poorest and to track poverty levels over

time. There are now 46 country PPI scorecards that have been constructed, and if an expert-

based scorecard for China—constructed using an alternative methodology due to data restrictions

—is included, the PPI now covers countries that are home to 90 % of the world’s poorest people.

In the Philippines, as in many other countries, the PPI is associated primarily with

the microfinance industry. In this regard, Grameen Foundation (2011) describes how the Center

for Agriculture and Development (CARD) Bank is moving towards collecting the PPI score of

every one of its nearly 580,000 clients. CARD Bank in particular hopes to use the PPI to help

generate marketing strategies that promote micro-savings among its clients. Biggar (2009)

reports on how the Negros Women for Tomorrow Foundation (NWTF)—with its more than

70,000 clients spread across its 37 branches in the Visayas region—has increasingly used the PPI

to target new clients and to adjust its products to serve those clients more effectively.

As explained by Schreiner (2009), the Philippine PPI scorecard is based on data

from the 2004 Annual Poverty Indicators Survey (APIS) conducted by the National Statistics

Office (NSO). The 2002 APIS is also used for testing the accuracy of changes in poverty rates

from 2002 to 2004 estimated with the use of the scorecard.

Schreiner (2009) describes how the procedure for making the Philippine PPI

scorecard involved randomly dividing the 42,789 households sampled by the 2004 APIS into

three sub-samples, with every household designated to be part of either: (1) the construction sub-

126

sample (to be used for selecting poverty indicators and associated scores), (2) the calibration sub-

sample (to be used for associating scores with poverty likelihoods), and (3) the validation sub-

sample (to be used for testing scorecard accuracy with data not used in construction or

calibration). Table A3.3.1 below lists down the sample sizes of construction, calibration and

validation sub-samples, respectively, and associated poverty rates by sub-sample and poverty

line.

In the whole PPI scorecard construction process, it is household income (rather

than consumption) that is used as the basis for classifying the household as being below the

poverty line or not. Poverty rates, moreover, are calculated at the household-level, that is, each

household is counted as if it had only one person, regardless of true household size, so that all

households are counted equally. The Philippine PPI scorecard is “calibrated” to eight different

poverty lines. Sample and sub-sample poverty rates in reference to six of the eight poverty lines

are shown in the Table A3.3.1. Altogether, the eight poverty lines are the following: (1)

National, (2) Food, (3) USAID “extreme,” (4) USD 1.25/day 2005 PPP, (5) USD 2.50/day 2005

PPP, (6) USD 3.75/day 2005 PPP, (7) USD 5.00/day 2005 PPP and (8) USD 4.32/day 1993 PPP.

For the national and food poverty lines, respectively, the 2004 lines set by the National Statistics

Coordination Board (NSCB) based on the 2003 Family Income and Expenditures Survey (FIES)

were used.

The first phase of constructing the Philippine PPI scorecard began with 60

potential poverty indicators—covering the areas of family composition, education, housing and

Table A3.3.1

PPI scorecard construction based on 2004 APIS:Sample sizes of construction, calibration and validation sub-samples,

and household poverty rates by sub-sample and poverty line______________________________________________________________________________

127

% with income below designated poverty line

______________________________________________________________________________Source: Schreiner (2009)

ownership of durable goods—being screened with the use of the construction sub-sample.

Screening involved calculating for each poverty indicator an “uncertainty coefficient” that

measured how well it predicted poverty on its own (with reference to the national poverty line).

In this regard, Table A3.3.2 lists the poverty indicators with the highest “uncertainty

coefficients.” After the screening process, the scorecard itself was built using the national

poverty line and logit regression on the construction sub-sample. Poverty indicators were

selected based on both statistics and judgment. As outlined by Schreiner (2009), the steps

followed were the following: (1) Logit regression was used to build a scorecard for each

candidate indicator. (2) One of the one-indicator scorecards was chosen based on factors that

included improvement in accuracy, likelihood of acceptance by users, sensitivity to changes in

poverty status, variety among indicators and verifiability. (3) A series of two-indicator

scorecards were then built by adding a second candidate indicator to the one-indicator scorecard

that was previously chosen. (4) The

Table A3.3.2

PPI scorecard construction based on 2004 APIS:Poverty indicators with the highest uncertainty coefficients

128

based on use of construction sub-sample

Source: Schreiner (2009)

best two-indicator was then chosen, again based on statistics and judgment. (5) The preceding

steps were repeated until the scorecard had 10 indicators.

The second phase in the construction of the Philippine PPI scorecard used the

calibration sub-sample. In this phase, a given score was non-parametrically associated

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(“calibrated”) with a poverty likelihood by defining the latter as the share of households in the

calibration sub-sample which had the particular score while also having income below a given

poverty line. This method was used to “calibrate” scores with estimated poverty likelihoods for

all the poverty lines. Table A3.3.3 shows the end result of the whole “calibration process” in

terms of the distribution of household poverty likelihoods across income ranges demarcated by

poverty lines. Schreiner (2009) emphasizes how the use of judgment in the construction of the

Philippine PPI scorecard in no way compromises the objectivity of the poverty likelihoods that it

generates. This is because the “calibration” process ensures that the aforementioned poverty

likelihoods are derived from objective survey data and quantitative poverty lines.

The final phase in the construction of the Philippine PPI scorecard was concerned

with testing the accuracy of its estimated poverty rates. To do this, the scorecard was applied to

1,000 bootstrap samples of size n = 16,384 using the validation sub-sample. In each bootstrap

sample, differences in actual vis-à-vis estimated poverty rates across the various poverty lines

and for different sample sizes was calculated. With reference to the national poverty line,

Table A3.3.4 shows the average difference of estimated poverty rates from their respective true

values as these were recorded for different sample sizes with each bootstrap sample. The

associated confidence intervals of the estimated poverty rates for different sample sizes are also

shown.

An important question that can be raised with regard to the use of the Philippine

PPI scorecard in the present research is the following: Beyond the legitimacy it has earned from

its acceptance and wide use by numerous socially-oriented organizations like ASHI, is the

scorecard a valid measure of the poverty likelihood of ASHI borrower households? In this

regard,

Table A3.3.3

130

2004 poverty scorecard based on 2004 APIS:Distribution of household poverty likelihoods across income ranges demarcated by poverty lines based on the calibration sub-sample

______________________________________________________________________________

______________________________________________________________________________ Source: Schreiner (2009)

a central issue is whether the poverty likelihood estimates of ASHI borrower households

produced by scorecard are statistically “unbiased” (in the sense that in repeated samples from the

same population, the average estimate matches the true poverty likelihood). Schreiner (1990)

notes that as long as the scorecard is applied to the same population from which it was

constructed—so that the relationship between poverty indicators and the poverty situation does

not change—poverty likelihood estimates remain unbiased. But this is precisely the “problem”

that arises with the use of the Philippine PPI scorecard to estimate the poverty likelihood of ASHI

131

Table A3.3.4

Poverty scorecard based on 2004 APIS:Average difference from the true value and precision of differences

of bootstrapped estimates of poverty rates (with reference to the national poverty line)

for groups of households at a point in time by sample size

________________________________________________________Source: Schreiner (2009)

borrower households (as the present research does): it involves crucial changes in the

relationship between the poverty indicators and the poverty situation in terms of: (1) time and (2)

the population surveyed. In other words, while the Philippine PPI scorecard was constructed

based on data collected from the whole Philippine population in the year 2004, it is being used to

generate estimates for a small sub-group of the Philippine population (= ASHI borrower

households) in the year 2013.

The above “problem” is treated as a data limitation by the present research. It is

argued here that the PPI scores generated by ASHI and other socially-oriented MFIs—despite

their inherent limitations as pointed out above—remain a valid tool for estimating the poverty

likelihood of microfinance borrower households. In the present research, the use of PPI scores is

132

considered a valid empirical methodology for—at very the least—segmenting ASHI borrower

households into broad groups on the basis of differences in average poverty likelihood that are

statistically significant. In other words, PPI scores can be used to identify a “poorer” group of

ASHI borrower households (e.g. those with a PPI score of 24 or lower), whose members can be

considered to have a statistically significant greater average likelihood of being officially poor

when compared to ASHI borrower households belonging to a “more well-off” group (e.g. those

with a PPI score of 45 or more).

133

APPENDIX 3.4

DISTRIBUTION OF ASHI BORROWERS BY PPI SCORE, LOCATION AND MEMBERSHIP DURATION

(ASHI Borrowers Surveyed Between January and June 2011)

134

APPENDIX 3.5

Data-gathering Procedures

(A) 3-step process in choice of ASHI borrowers for inclusion in the research

sample of borrowers: First, data on the number of members in each of all the borrower centers

of a concerned branch was obtained from the ASHI branch manager, with the said borrower

centers classified by the branch manager into the following three mutually exclusive types of

“very good,” “problem,” and “crisis.” Second, particular borrower centers of each branch were

chosen for inclusion in the data-gathering process, based on (1) the total number of each of three

aforementioned types of centers in the branch, (2) prioritizing centers which had the most

borrower households with data available from the ASHI MIS database, and (3) including centers

of all the ASHI branch loan officers in the data-gathering process. Third, particular borrowers

from each of the chosen centers were selected based on the availability of their relevant

member’s assessment record as these were accessed from the files of the branch. Borrowers on

their first general loan cycle were chosen only if they received their first general loan by October

2013.

(B) 2-stage process with regard to collecting data on the repayment

performance of a borrower household: The first stage involved accessing the relevant

member’s assessment form from the records of the ASHI branch. In this way, information was

obtained on the repayment performance of a borrower household over a one-year period ending

on the month in the year 2012 or 2013 when its second to the last general loan matured or was

fully paid. The foregoing information was obtained only for borrower households that had

received at least two general loans in the years 2012-2013 and only for months in the

aforementioned one-year period when the borrower household had to make loan obligation

135

payments. The second stage involved interviewing the concerned ASHI loan officer. Through

the latter, information was obtained on the repayment performance of the concerned borrower

household over the period consisting of all the months in the six-month period from June to

November 2013 in which the borrower had to make loan obligation payments excluding all the

months already covered by the first stage.

(C) 2012-2013 repayment observation period of the borrower household: All

the months in which information on the repayment performance of a borrower household was

obtained as explained above constitutes the 2012-2013 repayment observation period of the said

borrower household.

(D) Division of the 2012-2013 repayment observation period of the borrower

household into segments: The 2012-2013 repayment observation period of the borrower

household is divided into segments (consisting of a one to six-month periods each) defined as

follows.

The first segment consists of all the months in the six-month period from June to

November 2013 in which the borrower had to make loan obligation payments. The first segment

excludes all months that are part of the second segment as the latter is defined below.

If the borrower has received at least two general loans in the 2012-2013 period, the

second segment is the six-month period that ends on the month when the second to the last

general loan of the borrower matured (i.e. was fully paid) and begins on the 5 th month before the

aforementioned month. If the borrower has received only one general loan, there is no second

segment.

136

There is a third segment only if there is a second segment. The third segment

consists of all the months in which the borrower had to make loan obligation payments in the six

month period immediately preceding the second segment.

(E) Calculation of the “group_particip” variable: For each borrower center of

the branch, data on borrower member attendance in center meetings was provided by the branch

manager. For the Rizal East branch (REB), data for the months of November 2013, May 2013

and November 2012 was provided. For the Rizal Southwest branch (RSW), data for the months

from September to October 2013 was provided. For the Rizal West branch (RWB), data for the

months of September, October and November 2013 was provided. The “group_particip” variable

is equal to the average value—over the months for which data was provided—of the “attendance

rating” given by ASHI branch managers to the respective borrower centers in their branch. As

computed by the branch managers, the borrower center “attendance rating” is equal to the

percentage value for a particular month of the ratio AA / AE. AA is “actual borrower attendance in

center meetings” computed by adding together the actual number of borrowers present in each

borrower center weekly meeting over a particular month. AE is “expected borrower attendance in

center meetings” and is equal to the total number of borrower members of the center multiplied

by the number of meetings held by the center in a particular month.

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APPENDIX 4

Table A4.1Logistic regression results for borrowers of three ASHI Rizal branches

(Results with use of the “rpcap_34” variable)

Explanatory variable Coefficient Std. Err. z P>z [95% Conf.Interval]

rpcap_34 .2523431 .3037911 0.83 0.406 -.3430765 .8477627lend_memyrs -.0734679 * .0441744 -1.66 0.096 -.1600482 .0131123luse_maxloan -.0001352 .0001411 -0.96 0.338 -.0004117 .0001413luse_minratio -.072566 .4702976 -0.15 0.877 -.9943324 .8492004shock_yagri -.2689482 .7686782 -0.35 0.726 -1.77553 1.237633

shock_yemploy .2051053 .5190063 0.40 0.693 -.8121284 1.222339shock_agri -1.142298 * .6023307 -1.90 0.058 -2.322844 .0382485

shock_retoth -.347866 .3193497 -1.09 0.276 -.9737799 .278048shock_ms -.4901079 .453583 -1.08 0.280 -1.379114 .3988984

group_particip -.0219163 ** .0098379 -2.23 0.026 -.0411982 -.0026345obs_months .111405 *** .0339946 3.28 0.001 .0447768 .1780332

cons -.2611304 1.076235 -0.24 0.808 -2.370512 1.848251

Number of obs. = 404, Dependent variable = repaydifrizal, Log likelihood = - 168.77369 LR chi2(12) = 28.64, Prob > chi2 = 0.0026, Pseudo R2 = 0.0782 *, ** and *** denote significance at the 10%, 5% and 1% level, respectively

Table A4.2Logistic regression results for borrowers of three ASHI Rizal branches

(Results with use of the “rpcap_29” variable)

Explanatory variable Coefficient Std. Err. z P>z [95% Conf.Interval]

rpcap_29 .4142346 .3565393 1.16 0.245 -.2845696 1.113039lend_memyrs -.0747183 * .0442394 -1.69 0.091 -.1614259 .0119893luse_maxloan -.0001403 .0001405 -1.00 0.318 -.0004157 .0001351luse_minratio -.0770574 .4698131 -0.16 0.870 -.9978742 .8437593shock_yagri -.2375406 .7739433 -0.31 0.759 -1.754442 1.279361

shock_yemploy .2118918 .5192421 0.41 0.683 0-.805804 1.229587shock_agri -1.191643 * .6093894 -1.96 0.051 -2.386024 .0027382

shock_retoth -.3561575 .3192553 -1.12 0.265 -.9818865 .2695714shock_ms -.5168958 .4552158 -1.14 0.256 -1.409102 .3753108

group_particip -.0226625 ** .0098903 -2.29 0.022 -.0420471 -.0032778obs_months .1139904 *** .0341808 3.33 0.001 .0469973 .1809835

_cons -.2048578 1.065022 -0.19 0.847 -2.292262 1.882546

Number of obs. = 404, Dependent variable = repaydifrizal, Log likelihood = - 168.46339 LR chi2(12) = 29.26, Prob > chi2 = 0.0021, Pseudo R2 = 0.0799 *, ** and *** denote significance at the 10%, 5% and 1% level, respectively

138

Table A4.3Summary statistics for data of borrowers of ASHI Rizal Southwest branch (RSW)

Variable No. of Obs Mean Std. Dev. Min. Max.

repaydif_rsw 167 .1736527 .3799498 0 1rpcap_ppi 167 41.98204 14.13382 9 75rpcap_39 167 .4850299 .5012789 0 1rpcap_34 167 .3113772 .4644493 0 1rpcap_29 167 .1976048 .3993899 0 1

lend_memyrs 167 4.994012 4.349902 1 16

luse_maxloan 167 1811.737 1057.089 417 5917luse_minratio 167 .6774251 .3777469 0 1shock_yagri 167 .0958084 .2952135 0 1

shock_yemploy 167 .0838323 .2779697 0 1shock_agri 167 .1796407 .3850425 0 1

shock_retoth 167 .3353293 .4735253 0 1shock_ms 167 .1916168 .3947568 0 1

group_particip 167 74.83832 10.93977 54 93obs_months 167 11.21557 4.899127 1 18

Table A4.4Logistic regression results for borrowers of ASHI Rizal Southwest Branch (RSW)

(Estimation using “rpcap_ppi” variable)

Explanatory variable Coefficient Std. Err. z P>z [95% Conf.Interval]

rpcap_ppi -.0617506 *** .0205368 -3.01 0.003 -.102002 -.0214992lend_memyrs -.0823039 .0659847 -1.25 0.212 -.2116316 .0470237luse_maxloan -.0006562 ** .000326 -2.01 0.044 -.0012952 -.0000172luse_minratio -.3543814 .7064962 -0.50 0.616 -1.739089 1.030326shock_yagri 8788217 1.238408 0.71 0.478 -1.548413 3.306057

shock_yemploy -1.20652 .9693794 -1.24 0.213 -3.106469 .6934282shock_agri -1.991295 * 1.10357 -1.80 0.071 -4.154253 .1716627

shock_retoth -.5987587 .5624062 -1.06 0.287 -1.701055 .5035373shock_ms .1405514 .6537812 0.21 0.830 -1.140836 1.421939

group_particip .0262755 .0209903 1.25 0.211 -.0148647 .0674157obs_months .1750937 *** .063314 2.77 0.006 .0510005 .2991869

_cons -.9079004 1.963299 -0.46 0.644 -4.755895 2.940094

Number of obs. = 167, Dependent variable = repaydifrsw, Log likelihood = - 64.741292 LR chi2(11) = 24.70, Prob > chi2 = 0.0101, Pseudo R2 = 0.1602 *, ** and *** denote significance at the 10%, 5% and 1% level, respectively

139

Table A4.5Logistic regression marginal effects for borrowers of ASHI Rizal Southwest Branch (RSW)

(Estimation using “rpcap_39” variable)

Explanatory variable dy/dx Std. Err. z P > z [95% Conf.Interval] Mean

value

rpcap_39 .1512351 *** .0541271 2.79 .005 .0451479 .2573223 .4850299lend_memyrs -.0092712 .0073654 -1.26 0.208 -.0237071 .0051646 4.994012luse_maxloan -.0000714 ** .000035 -2.04 0.042 -.0001401 -2.74e-06 1811.737luse_minratio -.0512947 .0787577 -0.65 0.515 -.205657 .1030675 .6774251shock_yagri .0729934 .1340436 0.54 0.586 -.1897273 .3357141 .0958084

shock_yemploy -.1186717 .1085803 -1.09 0.274 -.3314853 .0941418 .0838323shock_agri -.1984245 * .1151886 -1.72 0.085 -.4241899 .027341 .1796407

shock_retoth -.0660273 .063097 -1.05 0.295 -.1896952 .0576405 .3353293shock_ms .0010577 .0737423 0.01 0.989 -.1434746 .1455901 .1916168

group_particip .0034884 .0023303 1.50 0.134 -.0010789 .0080556 74.83832obs_months .0168907 *** .0065257 2.59 0.010 .0041006 .0296808 11.21557

*, ** and *** denote significance at the 10%, 5% and 1% level, respectively

Table A4.6Summary statistics for data of borrowers of ASHI Rizal East branch (REB)

Variable No. of Obs Mean Std. Dev. Min. Max.

repaydif_reb 131 .1145038 .3196445 0 1repay_ppi 131 42.54198 15.50943 13 82rpcap_39 131 .4427481 .4986182 0 1rpcap_34 131 .3282443 .4713768 0 1rpcap_29 131 .1832061 .3883204 0 1

lend_memyrs 131 4.687023 4.591102 1 20

luse_maxloan 131 2074.099 1460.374 813 9250luse_minratio 131 .6651145 .3585191 0 1shock_yagri 131 .221374 .4167655 0 1

shock_yemploy 131 .1832061 .3883204 0 1shock_agri 131 .2900763 .4555394 0 1

shock_retoth 131 .3740458 .485733 0 1shock_ms 131 .1526718 .3610515 0 1

group_particip 131 89.72519 8.522417 65 100obs_months 131 11.28244 5.226081 1 18

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Table A4.7Logistic regression results for borrowers of ASHI Rizal East Branch (REB)

(Estimation with use of the “rpcap_ppi” variable)

Explanatory variable Coefficient Std. Err. z P>z [95% Conf.Interval]

rpcap_ppi -.0181295 .0220442 -0.82 0.411 -.0613354 .0250763lend_memyrs -.1386463 .1124307 -1.23 0.218 -.3590065 .0817138luse_maxloan .0004032 .0002916 1.38 0.167 -.0001683 .0009747luse_minratio .3670393 1.107465 0.33 0.740 -1.803552 2.53763shock_yagri -.6712285 1.356741 -0.49 0.621 -3.330391 1.987934

shock_yemploy -.1149379 1.014926 -0.11 0.910 -2.104156 1.87428shock_agri -.7887043 * 1.444965 -0.55 0.585 -3.620785 2.043376

shock_retoth 1.125968 .8422808 1.34 0.181 -.524872 2.776808shock_ms -.0174146 1.256041 -0.01 0.989 -2.47921 2.44438

group_particip -.0842715 ** .0398484 -2.11 0.034 -.162373 -.0061699obs_months .1703742 * .0914913 1.86 0.063 -.0089454 .3496939

cons 3.005108 3.796636 0.79 0.429 -4.436162 10.44638

Number of obs. = 404, Dependent variable = repaydifrizal, Log likelihood = - 33.868755 LR chi2(11) = 25.49, Prob > chi2 = 0.0077, Pseudo R2 = 0.2734 *, ** and *** denote significance at the 10%, 5% and 1% level, respectively

Table A4.8Logistic regression results for borrowers of ASHI Rizal East Branch (REB)

(Estimation with use of the “rpcap_29” variable)

Explanatory variable Coefficient Std. Err. z P>z [95% Conf.Interval]

rpcap_29 1.83179 ** .8386123 2.18 0.029 .18814 3.47544lend_memyrs -.1777691 .1275171 -1.39 0.163 -.4276981 .0721598luse_maxloan .0005125 * .0003067 1.67 0.095 -.0000885 .0011136luse_minratio .1015673 1.161112 0.09 0.930 -2.17417 2.377305shock_yagri -.6653914 1.413899 -0.47 0.638 -3.436582 2.105799

shock_yemploy -.073344 1.017783 -0.07 0.943 -2.068163 1.921475shock_agri -1.055823 1.527549 -0.69 0.489 -4.049763 1.938117

shock_retoth 1.204669 .8769315 1.37 0.170 -.5140848 2.923423shock_ms -.6781252 1.465616 -0.46 0.644 -3.55068 2.194429

group_particip -.0997816 ** .0426585 -2.34 0.019 -.1833906 -.0161725obs_months .1656133 * .0970763 1.71 0.088 -.0246527 .3558793

_cons 3.28397 3.930856 0.84 0.403 -4.420366 10.98831

Number of obs. = 131, Dependent variable = repaydifreb, Log likelihood = - 31.684102 LR chi2(12) = 29.86, Prob > chi2 = 0.0017, Pseudo R2 = 0.3203 * and ** denote significance at the 10% and 5% level, respectively

141

Table A4.9Summary statistics for data of borrowers of ASHI Rizal West branch (RWB)

Variable No. of Obs Mean Std. Dev. Min. Max.

repaydif_rwb 106 .2264151 .420499 0 1repay_ppi 106 42.84906 16.93337 4 89rpcap_39 106 .4339623 .4979743 0 1rpcap_34 106 .3113208 .4652333 0 1rpcap_29 106 .1886792 .3931123 0 1

lend_memyrs 106 4.179245 3.161667 1 13

luse_maxloan 106 2249.208 1642.477 500 7894luse_minratio 106 .7398113 .3026297 0 1shock_yagri 106 0 0 0 0

shock_yemploy 106 .0471698 .2130091 0 1shock_agri 106 .0377358 .191462 0 1

shock_retoth 106 .5188679 .5020175 0 1shock_ms 106 .1037736 .3064154 0 1

group_particip 106 74.56604 17.92525 44 100obs_months 106 10.75472 6.266785 1 18

Table A4.10Logistic regression results for borrowers of ASHI Rizal West Branch (RWB)

Explanatory variable Coefficient Std. Err. z P>z [95% Conf.Interval]

rpcap_ppi .0169532 0.27 0.786 -.0286231 .0378324 0.27lend_memyrs .1075203 0.10 0.921 -.2000309 .2214411 0.10luse_maxloan .0002556 * -1.73 0.084 -.0009421 .0000598 -1.73luse_minratio 1.037623 -0.35 0.728 -2.394593 1.672813 -0.35

shock_yemploy 1.072727 1.60 0.109 -.3809274 3.824083 1.60shock_agri 1.342438 0.26 0.797 -2.28569 2.97657 0.26

shock_retoth .5666399 -1.38 0.167 -1.894347 .3268411 -1.38shock_ms 1.187151 -1.34 0.181 -3.914142 .7394026 -1.34

group_particip .0170929 * -1.90 0.057 -.0660598 .000943 -1.90obs_months .0591289 * 1.80 0.071 -.0093048 .2224763 1.80

cons 2.0725 0.63 0.532 -2.765378 5.358673 0.63

Number of obs. = 106, Dependent variable = repaydifrwb, Log likelihood = - 48.597805 LR chi2(10) = 16.20, Prob > chi2 = 0.0939, Pseudo R2 = 0.1429 * denotes significance at the 10% level

142