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The raw data for four MFIs from different countries located at South America and Sub-Sa- haran Africa have been extracted from administrative loan books gathered by Micro Finanza Rating, which is a private and independent international rating agency specialized in micro- finance. It contains two MFI types, with three NGOs (CACIL Honduras, INSOTEC Ecuador, and FINCA Peru) and one cooperative (MICROCRED Madagascar). All loan books were compiled by the MFIs and submitted to Micro Finanza Rating between 2010 and 2011. As the percent- ages of missing values are very low, the impact brought by missing values is marginal. Hence, a simple listwise deletion approach is applied here. On the other hand, the occurrence of outliers in the data used for this papers is limited. With no signs of correlated outliers, sim- ple winsorizing and trimming (Wainer, 1976) are adopted. All the observations of loan amount under (or above) a 5% (95%) percentile are replaced by the limits. The data of age, time to maturity, arrearage, and the length of delayed repayment are trimmed in the same way with different percentiles (see footnotes of Table 3.1). In order to represent the actual population proportions of different countries (UN World Population Prospects, 2010), the raw data is also processed by weighted random selection. In the end, our sample consists of 32,673 clients. Ecuador, Honduras, Madagascar, and Peru, take up 21%, 11%, 28.4% and 39.6% in the sample respectively.

It should be mentioned that the analysis in this study is based on clients with approved loans only. The standard loan approval processes applied by the MFIs are unknown, and no gener- alisations can be made for a random sample of all microfinance applications. The issue of ob- taining the default risk profile of rejected applicants is called reject inference. In general, ab- solute reliable reject inference cannot be achieved (Hand and Henley, 1993). Besides, the ef- fect of sample election problem in credit portfolios depends on the rejection rate and be- comes influential only when the rejection rate is extremely high (Crook and Banasik, 2004). Therefore, the models developed in this study are applied to the borrowers who have been approved by the four MFIs in our sample, and the problem of rejection inference has been assumed to be negligible.

There is no universally accepted approach to choose the explanatory variables for credit scoring (Dinh & Kleimeier, 2007). The explanatory variable choice in the case study pre- sented in this paper is based on prior studies and expert advice from the microlender staff. All explanatory variables used in this study can be classified into two categories: 1. socio-de- mographic characteristics (marital status, gender, age, and education level); and 2. loan pur- pose (consumption, buy a fixed asset, agriculture, commerce, manufacture, service, and fi- nancing). The control variables include two categories as well: 1. loan status (loan amount and time to maturity); and 2. MFIs.

This is an unusually short list; most scorecards for microfinance institutions would also use the income, occupation, and the number of dependents; ownership of a phone, house, or car; and measures of the size and financial strength of the business. Therefore, the research in this paper is conservative and mainly focusing on the variables stated in the hypotheses. If a scorecard with these characteristics works, then a scorecard with a full complement of characteristics on the borrowers would work even better.

For the dependent variable of loan default or delinquency, authors often need to create their own proxies when the rating agency requires a specific variable or the required data is not directly available. For example, Schreiner (2004) defines a bad customer to be 15 days late on the repayment, Vogelgesang (2003) characterizes default loans by an average of 10 days overdue per payment, while some other authors like Van Gool et al. (2012) focus on late repayment that indicated by an average two days late on the installments. As results, the findings in these studies become incomparable, and their practical implementations are limited.

In order to standardize the measurement of loan default, there are three variables used in this paper: 1. the current amount of arrears; 2. the number of days of delayed repayment; 3 Portfolio at Risk (PaR), which is calculated by dividing the outstanding loan amount with ar- rears over a particular period (e.g., PaR30 denotes Portfolio at Risk over a 30-day period), plus all restructured loans, by the outstanding gross portfolio as of a certain date.

However, occasional late payment of a few days does not constitute a problem to MFIs, and our rigorous definition may lead to overestimation of default risk. To solve the issue, a sepa- rate regression analysis is necessary to capture the intensity of loan default. Therefore, the Two-Part Model and the Double-Hurdle Model (which will be discussed in the next section) should be applied in this case.

Table 3.1summaries the mean, standard deviation, minimum, maximum, and quartiles, for all variables in our sample. We see that the average outstanding loan amount is $970 and the average time to maturity is 317 days. Meanwhile, these two numbers rise to $1360 and 457 days respectively in the subsample of clients with non-zero arrears. It indicates strong associations between the outstanding loan amount, time to maturity, and the probability of default. Comparing the medians and means, we also see that the outstanding loan amount is heavily skewed to the right. 25% of our clients borrowed less than $232 and 50% of them borrowed less than $580. These statistics well describe the primary mission of microfinance – providing small loans and saving facilities to those who are excluded from commercial fi- nancial services.

As far as the repayment variables are concerned, the dummy of late payment equals 0.07 on average, which means that 7% of clients are delinquent or have defaulted. For these clients specifically, the arrearage is $238, and the length of delayed repayment is 230 days on aver- age. By measuring the delinquency loans based on the standardized schedule RC-N, the de- linquency rate of the subsample1_{including CACIL and FINCA is 2.65% in 2010.}

For socio-demographic variables, we see that 52% clients are married and 14% of them are cohabiting with their partners. The rest of them are either single, divorced, or widowed. The statistics show that the probability of loan default might associate with marriage and single status to some extent. The proportion of married clients for the defaulted group is 7% lower than that for the normal group, and the proportion of single clients for the defaulted group are 12% higher than that for the normal group. On average, 65% of clients in MFIs are women. The 75th percentile in the distribution of female clients is 1.0. What is more, the cli- ents in our sample are 39 years old on average. 12% of clients are completely illiterate, and 56% of them have completed secondary or tertiary education.

For loan purposes variable, 56% of outstanding loans are invested in commercial activities. The second and the third biggest sectors are agriculture and service, which take up 16% and 13% of loans respectively. The proportion of investment in commerce for the defaulted group is 10% lower than that for the normal group. Hence, there might be a potential associ- ation between loan purpose and the probability of default as well.

Table 3.2shows the correlation matrix of ten different loan default indicators and all explan- atory variables. As can be seen from the table, the selection of loan default indicator has a

1_{Unable to calculate the default rate for the hold sample as INSOTEC and MICROCRED have not rec-} orded the length of delayed repayment in their administrative loan books.

substantial influence on the correlation coefficients of all variables. For example, the relation between age and the probability of default is found to be significant and negative in columns (1) to (5) and (7), but it becomes insignificant in the other columns. We can see that the co- efficients of some variables have opposite signs in different panels (PaR30 vs Delayed Repay- ment), such as cohabitation. These statistics bear out the former supposition that even a slight modification of the measurement of loan default may lead to completely different conclusions. The loopholes in definition make the MFIs extremely difficult to establish a reli- able credit scoring model, in which the significances of explanatory variables are irrelevant to the risk preferences of microlenders.

As the measurement of loan default is standardized in this study, we focus on the results presented in column (1) and (6) only. As can be seen from column (1), there is a negative correlation between marriage and PaR30 (-0.07), indicating that married borrowers have better repayment rates (H1). The correlation between both age and education and the PaR30 are also negative (H2, H4). Loan purposes variables indicate that lending to clients en- gaged in agriculture occurs in significant lower PaR30 than lending to clients engaged in con- sumption, purchasing a fixed asset, and commercial activities (H5). Additionally, no signifi- cant relationship between gender and PaR30 is found (H3).

On the contrary, column (6) tells a completely different story. The length of being in delin- quent is irrelevant to both marriage and age (H1, H2), while it positively associates with co- habitating and single clients. Unexpected positive relations have been found between edu- cation levels and the length of being in delinquent (H4). In terms of loan purposes, the corre- lations between the length of delayed repayment and both agriculture and commerce have changed signs (H5), which is unexpected as well. Both abnormal results will be discussed in detail in the empirical results section.