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The PDEA model is used for analysing the financial performance of MFIs, by looking at two inputs (interest expense and operating expense) and two outputs (interest income and operating income). The rationale for use of this particular model, as a tool for assessing financial sustainability dimension of the MFIs’ performance, has already been

discussed in Chapter 5. Here, we would like to elaborate how the application of appropriate trade-offs can help in incorporation of additional relevant information to the standard DEA models. For the PDEA model, we were able to finalize trade-off

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relationships between three variables i.e. interest expense, interest income, and operating income. These trade-offs are explained next.

Trade-off 1: Interest expense and interest income

Judgement: For each additional million of interest expense, an increase of 1.5 million in interest income is technologically possible, without requiring any additional resources63.

Explanation: An alternative explanation of this trade-off is that in order to increase the interest income by 1.5 million, no more than an increase of 1 million in the interest expense is required. This first trade-off relationship has been represented through a simple judgement that proposes simultaneous changes to the values of one input (interest expense) and one output (interest income); while the remaining two variables of the PDEA model remain unchanged. From the perspective of enhancing profitability, increased expense is an extra cost that should be incurred only if it is possible to earn something over and above the cost incurred. Moreover, increased interest expenses generally represent additional funds available, for provision of micro credits and related services to the clients. These additional funds are thus expected to generate more loans, leading to earning of additional income for the MFIs.

Now, we will explain how we arrived at the values for the proposed trade-off between the interest expense and interest income variables. For getting an initial estimate for the value of the proposed trade-off; we investigated the relevant interest rates, applicable to the borrowing and lending of the MFIs in our sample. It was observed that the microfinance industry in Pakistan was having access to cheap funds from PPAF and other resources. On the other hand, these MFIs were charging comparatively higher

63 _{For information on relevant units of measurements used for different input and output variables, refer to} Chapter 5, section 5.8.4.

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interest rates on amounts lent64, as is the common practice in most microfinance industries. As a further test for estimating an appropriate value for the proposed trade- off, we reviewed our data set and calculated the ratio of interest income to interest expenses. It was observed that the average value for this ratio was 3.63.

These observations led us to believe that the selected MFIs can increase their interest income by more than three times the value of the interest expenses incurred. Therefore, we initially proposed a ratio of 1: 3, between interest expense and interest income. These proposed values were then communicated to different respondents for their feedback. Many of the MFIs considered the increase of 3 million in interest income, resulting from a 1 million increase in interest expense, feasible. However, there were some MFIs, which considered the proposed increase to be somewhat high. Therefore, considering the fact that the any trade-off relationship is required to be acceptable for all MFIs, we then proposed an increase of either 2 or 1.5 or 1 million in interest income. We were finally able to get a consensus that with an additional 1 million of interest expense, it would be possible to increase the interest income by 1.5 million.

Translating Trade-off 1 into equivalent weight restriction

As discussed earlier, existing DEA software do not support incorporation of required modifications, resulting from the proposed trade-off relationships, in the envelopment form of the DEA model. However, if we translate the proposed trade-offs into equivalent weight restrictions, we can use any standard DEA software for calculation of efficiency scores. Therefore, the next step in the application of the trade-off approach required us to translate the proposed trade-off into corresponding weight restriction, which could then be incorporated into the multiplier DEA model, as an additional constraint. The general form of the output oriented multiplier DEA model is presented

64 _{The subsidized interest rates available to the selected MFIs, ranged from 5 to 8 %. While the interest} charged on loans by MFIs (constituting interest income for these institutions) was around 33% on average.

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in Chapter 3, Model 3.12. As we are using homogeneous weight restrictions; therefore, for the PDEA model, we consider the following generally used form of the homogenous weight restrictions:

a1u1 + a2u2 – b1v1 – b2v2 ≤ 0 (6.5.1)

In the above equation, a1 anda2 are the coefficients for the weights u1 and u2 attached to

the two outputs (interest income and operating income). While b1 and b2 are the

coefficients for the weights v1 and v2 that are attached to the two inputs (interest expense

and operating expense). Each of the four coefficients a1, a2, b1,and b2 can be either

zero, positive or negative. Moreover, if at least one of the coefficients a1,a2, and one of

the coefficients b1, b2 are equal to some non- zero values, then the corresponding weight

restriction would be called a linked weight restriction; because it would be linking input and output weights. Using these notations, the proposed trade-off can be expressed as follows:

(a1,a2) = (1.5, 0); (b1,b2) = (1, 0) (6.5.2)

For incorporating this trade-off into the dual multiplier model, we need to translate the above formulation into an equivalent weight restriction, which can be written in the form:

1.5 u1 – 1 v1 ≤ 0 (6.5.3)

According to this constraint, an increase of one million in interest expenses is adequate for increasing the interest income by 1.5 million, provided that nothing else changes.

Trade-off 2: Interest expense, interest income and operating income

Judgement:For each extra million of interest expense, an increase of 1.5 million in interest income and an increase of 0.2 million in operating income is technologically possible, without requiring any additional resources.

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A basic assumption for Trade-off 1 is that an increase in the interest expense will only affect the interest income, while no other variable would be affected. In other words, the proposed trade-off will not result in a change in either the operating expense or the operating income, which are the two remaining variables for the PDEA model. We need to explain here that this assumption may or may not hold true in different situations. For example, if we are looking at it purely from the outreach perspective, then ideally, all the available funds should be used only for creating loan portfolio. This would mean that there would not be any substantial increase in the operating income with increase in the amount of the increased interest expense. Conversely, from a profitability perspective, augmentation of MFIs’ earnings from various sources, in addition to those related to the issuance of micro-credits, is not an uncommon practice. Therefore, to adequately capture the profitability dimension of MFIs’ performance, it was considered

necessary to incorporate additional information about this aspect of MFIs’ operations. The next trade-off thus required us to estimate an increase in operating income that could result from an increase in the interest expense. We were able to get consensus from all the MFIs that an increase of 0.2 million in their operating income was feasible from an increase of 1 million in interest expense.

An added complexity in this trade-off was that while the Trade-off 1 could be applied, without considering a change in any of the other variables; Trade-off 2 would be complete only if a change in the interest expense was related to subsequent changes in, both the interest income and operating income. In other words, increasing just the operating income, when interest expense increased, was not considered feasible. The underlying logic is that MFIs tend to use the available funds mainly for microfinancing purposes in view of their basic mission of providing micro financing services. At the same time, there is also some operating income that is normally generated from

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loanable funds, in routine. Considering this fact about the production technology of MFIs, we thus came up with the above quoted judgment for Trade-off 2. Next, we explain how this judgment can be expressed as a homogeneous weight restriction.

Translating Trade-off 2 into Weight Restrictions

Using the notations specified for Trade-off 1 in equation (6.5.1), the Trade-off 2 can be expresses as follows:

(a1,a2) = (1.5, 0.2); (b1,b2) = (1, 0) (6.5.4)

The weight restriction that follows from the above expression can be stated as: 1.5 u1 + 0.2 u2 – 1 v1 ≤ 0 (6.5.5)

We can observe from the above equation that when we are using this trade-off, we no longer need to apply Trade-off 1 individually, as it is already a part of the more complex Trade-off 2.

Trade-off 3: Interest expense and interest income

Judgement: For each 1 million less of interest expense, a decrease of 10 million in interest income is technologically possible, provided nothing else changes.

Explanation: This trade-off is based on the logic that a decrease in interest expense generally implies lesser amount of loanable funds available; which would in turn mean smaller loan portfolio, as well as lesser income65. For arriving at some reasonable estimates for the values of this trade-off, we needed to consider the fact that the larger a proposed decrease in one of the outputs, resulting from a unit decrease in one of the inputs; more intuitively appealing it would seem to various MFIs. This, in turn, increased chances of its acceptability by more MFIs. Therefore, we proposed that a decrease in interest expense by 1 was sufficient to decrease the interest income by 10. We originally proposed a decrease of 12 million in interest income from a decrease of I

65 _{Note that availability of the loanable funds at lesser interest rate, or the use of retained earnings as} loanable funds, can also lead to having lesser interest expense. However, in such cases, there would be no subsequent decrease in the amount of loanable funds or interest income.

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million in interest expense. This value was obtained by calculating the ratio of the interest income to interest expense and choosing the highest value. However, after consultation with the selected MFI, this value was decreased to 10 million.

Translating Trade-off 3 into Weight Restrictions

Once again, using the notations specified for Trade-off 1 in equation (6.5.1), the above value judgment can be expressed as the following trade-off:

(a1,a2)= (-10, 0); (b1,b2) = (-1, 0) (6.5.6)

The above formulation can then be translated into a weight restriction of the following form:

–10 u1 – (–1) v1 ≤ 0, or – 10 u1 + 1 v1 ≤ 0 (6.5.7)

Note that if Trade-off 1 and Trade-off 3 are applied simultaneously, these will result in forming a range for the ratio of the two weights. To explain it in mathematical notation form, we consider the two weight restrictions representing the proposed trade-off relationship once again. We know that the weight restriction relating to Trade-off 1 was expressed as follows:

1.5 u1 – 1 v1 ≤ 0

From this weight restriction, it follows that: 1.5 u1 ≤ 1 v1

The weight restriction representing Trade-off 3 was written as: - 10 u1 + 1 v1 ≤ 0

From this second weight restriction, it follows that: 1 v1 ≤ 10 u1

Combining these two expressions, we get: 1.5 u1 ≤ 1 v1 ≤ 10 u1, or

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