*3.2. Data Selection*

The performance and the selection of variables were inspired by the contributions in the microfinance industry (Gutiérrez-Nieto et al. 2009; Gyapong et al. 2021; Mersland et al. 2013; Schwarz et al. 2015; Wijesiri et al. 2015; Wijesiri and Meoli 2015), etc. The sample of 127 MFIs was selected from the World Bank financial database (Mix market) with annual periods 2008–2018. The specific variable "Female borrowers" is inspiring with the increase in clients annually in many countries. Table 2 discusses the MFIs list and the percentage of borrowers, investments, and equity in each type of MFIs.

**Table 2.** Financial funding of different microfinance institutions.


Source: Mix market 2019, World Bank's data catalog (%).

#### *3.3. Variable Selection*

Table 3 describes the explanation of dependent and independent variables for efficiency measurement with definitions. The selection of indicators is influenced by the previous works published in the articles where cross-country data have importance. The analysis is not based on specific country performance instead, it is cross-country productivity impaction.

**Table 3.** Selection and description of input/output variables for the first stage of analysis.


The financial revenue is an output variable to determine the financial performance of MFIs. The financial performance tends to raise if there are more dependents and good repayment rates irrespective in rural or urban regions, for this purpose the variable borrowers are used to determine the social outreach performance of MFI. (*Microfinance-Barometer-2019\_web-1*, n.d.) report specifies there is an incremental increase with women entrepreneurs annually for a decade so, women/female borrowers help to determine the social efficiency. The following Table 4 has numerical statistics of input and output variables along with the correlations between the variables are in Table 5.


**Table 4.** Mean and standard deviation of input/output variables.

**Table 5.** Correlations of input/output variables.


#### *3.4. Borrowing Rate*

Women workers in developing countries all through the world contribute their development in financial turn and microfinance helps to empower them and helps with making their commitment (Somavia 2007). According to the data, women clients are up to 73% on average. The average female borrowing rate is classified in Table 6, from the countries which are considered in the analysis. Ghana and Pakistan which have faith-based MFIs are dominating in the second position and Azerbaijan, Tanzania takes the last position in the female borrowing rate.

**Table 6.** Percentage of female borrowers in 25 countries.


Source: Mix Market 2019.

#### **4. Methodology**

Data envelopment analysis (DEA) is a non-parametric bootstrap approach that requires simple time-series data (with no financial gaps) to analyze the competence scores without any complex assumptions in any industry. Charnes et al. 1978 first developed the efficiency measuring model, later applied to identify the organizational performances in the banking sector (Wijesiri et al. 2015, 2017). Bootstrapping has the simple notion of repeated data generating process (DGP) and applying the original simulant to each outcome model (Wijesiri et al. 2015). The selection of appropriate input and output variables depends on the input-oriented and output-oriented methods. In this analysis, we restricted the nonparametric, output-orientated, and constant return to scale DEA approach to determine the production performances. The MFI identities are disclosed and are represented by the normal series from 1, 2, 3 ... ., 127 which act as the decision-making units to produce efficiency scores (Simar and Wilson 2010). We assume for the development of efficiencies from the decision-making units "p" (DMUs), it is necessary to select "m" different inputs and "n" output/s from the available dataset. Each DMU ("p") has one positive input and one positive output.

We assume:

$$\mathbf{x}\_{ij} \succeq \mathbf{0} \text{ for } i \text{ input} \tag{1}$$

$$y\_{kj} \ge 0 \text{ for } k \text{ output} \tag{2}$$

The virtual output to the virtual input to maximize the efficiency of each DMU (p) is formulated and should be less than or equal to zero.

$$\text{i.e.}\_{\prime} \max h\_o(u, v) = \frac{\sum\_{r} \mu\_r y\_{ro}}{\sum\_{i} \upsilon\_i \chi\_{io}} \le 1 \tag{3}$$

where *j* = 1, . . . , *n*; *urvi* ≥ 0 for all *i* and *r*.

The censored Tobit truncated random effect regression (as we have time-series data) was discussed to exhibit the relation between the measured dual efficiency scores (act as dependent variables) in the first stage of DEA analysis on the explanatory factors. Tobit model aids in determining the marginal changes on dependent variables by concerning lower and upper impediments. It represents the effect of an independent variable over the conditional variable. The regression provides the validation by considering the dual efficiencies and the overall empirical performance of the microfinance industry is obtained and controls different parameters. The linear regression is followed:

$$
\theta\_{(i,j,p)\*} = \beta\_0 + \beta\_1 var1 + \beta\_2 var2 + \varepsilon; \ i, j = 1, \dots, \dots, p \tag{4}
$$

$$
\theta\_{(i,j,p)\*} = \beta\_0 + \beta\_1 var1 + \varepsilon; \ i, j = 1, \dots, \dots, p \tag{5}
$$

$$\theta\_{(i,j,p)\*} = \beta\_0 + \beta\_1 var2 + \varepsilon; \ i, j = 1, \dots, \dots, p \tag{6}$$

where *i* represents the social efficiency score, *j* represents the financial efficiency score, the *β*0, *β*1, *β*<sup>2</sup> are the coefficients for the explanatory variables and *ε* is the statistical error term, where *p* represents the DMSs/MFIs (127). Equation (3) represents the social efficiency depending on all the three explanatory indicators. Whereas Equations (4)–(6) represent two explanatory indicators. The indicators imply the religious status, geographic region, and type of financial organization. The religious status, geographic position, and type of the institutions are imported as dummy variables and represent binary numbers. For instance, if religion is a faith, I considered it as 1 otherwise 0. The same with the location and type. We tabulate the results from the analysis in Table 6.

#### **5. Results**

#### *5.1. First Stage Non-Parametric Constant Rail Scale DEA Approach*

Table 7 reports the efficiency scores of 127 MFIs globally. The aggregate efficiency score of MFI in 10 years and the individual scores are calculated separately. It is observed that financial outreach is dominating with social outreach.

**Table 7.** The DEA social and financial efficiencies.



**Table 7.** *Cont.*

The efficiency scores, aggregate efficiency (*θa*), determined efficiency (*θ*) are bounded between 0 and 1. The MFIs with the efficiency scores of 1 are assumed developed or highly productive with high outreaches either socially or financially or both. Hence, we had clustered data with both religious and non-religious institutions, it is a bit challenging to spot the differences. The graphical representation of dual efficiency scores of faith and traditional institutions is exhibited in Figure 1.
