Developing a Risk Group Predictive Model for Korean Students Falling into Bad Debt*

Transcription

1 Asian Economic Journal 2018, Vol. 32 No. 1, Developing a Risk Group Predictive Model for Korean Students Falling into Bad Debt* Jun-Tae Han, Jae-Seok Choi, Myeon-Jung Kim and Jina Jeong Received 3 December 2015; Accepted 27 December 2017 Using direct loan data for 2012 to 2014 from the Korea Student Aid Foundation, we develop a risk group predictive model for borrowers defaulting on their loans. We used a logistic regression model and the Cox proportional hazards model to develop the risk predictive model. We verified the validity of the models using a receiver operating characteristic curve and a validation dataset. The present study shows that area under the receiver operating characteristic curves is similar for the models and that the major influencing factors for defaulting on their loans are household income, whether a national grant was received, age, whether more than two accounts are overdue, field of study and the monthly repayment amount. The risk group predictive model in this study will be the basis for more efficient management of direct student loans. Keywords: Cox proportional hazards model, direct student loan, regression model. logistic JEL classification codes: I20, I22, I23. doi: /asej I. Introduction The Korea Student Aid Foundation (KOSAF) student loan program is designed to support Korean students studying in Korean institutions. KOSAF s student loan program is divided into three main categories: income contingent loans (ICL), direct loans and loans for rural students. Income contingent loans are for students from low-income families that may be used for tuition and qualifying education-related costs. ICL are not subject to credit approval. The income contingent repayment system gives students the flexibility of choosing repayment options that best suit their personal circumstances. Direct loans are for students from families of any income level that may be applied towards tuition and qualifying education-related costs. Borrowers *Han: Department of Student Aid Policy Research, Korea Student Aid Foundation, 125 Sinam-ro, Dong-gu, Daegu 41200, Korea. Choi (corresponding author): Department of Student Loan Repayment, Korea Student Aid Foundation, 125 Sinam-ro, Dong-gu, Daegu 41200, Korea. jasonchoi75@gmail.com. Kim: Department of Student Loan Management, Korea Student Aid Foundation, 125 Sinam-ro, Dong-gu, Daegu 41200, Korea. Jeong: Department of Student Aid Policy Research, Korea Student Aid Foundation, 125 Sinam-ro, Dong-gu, Daegu 41200, Korea East Asian Economic Association and John Wiley & Sons Australia, Ltd

2 ASIAN ECONOMIC JOURNAL 4 may be eligible for interest relief. Direct loans are subject to credit approval. The standard repayment system offers a borrower a grace period, followed by a repayment period of up to 10 years. Loans for rural students are non-interest loans for students whose parents or guardians reside at a permanent rural address, specifically in an agriculture and fisheries community area, and for students who have made a living in agriculture and fisheries for over a specified period of time. Loans may be applied towards tuition and qualifying school fees. The annual supply of KOSAF loans (for tuition and living expenses) increased from US$1.04billion in 2009 to US$3.03billion in 2014 and the number of borrowers increased from approximately 348,000 in 2009 to 967,000 in However, the value of overdue direct loans increased from US$34 million in 2009 to US$271 million in 2014 and the delinquency rate increased consistently, from 3.4 percent in 2009 to 6.1 percent in The increase in the amount of overdue direct loans is due to the increase in the number of students who have borrowed as well as the increase in default because of lack of wages and low salaries. Student loan defaults and long overdue repayments have become major concerns for KOSAF, and the development of appropriate management processes for student loans is critical. To meet the demand for more efficient loan management, a high-risk group predictive model is built in this study based on various data of borrowers. Many models have previously been developed to address the issue of credit risk; however, few studies have looked at developing a high-risk group predictive model for Korean college or graduate students. The objective of our study is to develop a risk group predictive model for Korean students falling into bad debt after taking out direct loans. The aim of developing the model is to determine the major risk factors for students defaulting on their loans. This study will be the basis for forming appropriate management processes to prevent loan default. The paper is organized as follows. Section II provides a brief review of previous studies. Section III describes the data. Section IV outlines the methods of the study. Section V presents the results and an evaluation of the predictive models. Finally, Section VI concludes the paper and provides some recommendations for future work. II. Previous Studies II.1 Methodological studies A variety of statistical techniques have been applied to credit scoring and credit risk assessment over the past two decades. For example, papers by Rosenberg and Gleidt (1994) and Hand and Henley (1997) are concerned with detecting and reducing loan defaults and serious delinquencies. Desai et al. (1996) analyze

3 MODEL FOR KOREAN STUDENTS BAD LOANS 5 the usefulness of neural networks and traditional techniques, such as discriminant analysis and logistic regression, in building credit scoring models for credit unions. Zurada (2007) examines and compares the effectiveness of three decision tree algorithms (χ 2, entropy reduction and Gini reduction) to predict whether a consumer will default or pay off a loan. Stepanova (2002) examines three extensions of Cox s proportional hazards model applied to personal loan data. Wekesa (2012) also applies the proportional hazards survival model in predicting credit risk. Madan (2014) shows that the monitoring model can display credit default swap quotes that are increasing concave in the default probability and decreasing convex in the recovery. Im et al. (2012) study a modification of the proportional hazards survival model that includes a time-dependency mechanism for capturing temporal phenomena, and develop a maximum likelihood algorithm for fitting the model. Cao et al. (2009) propose a basic method for estimating the probability of default, which is performed using three different methods: the Cox proportional hazards model, a generalized linear model and nonparametric kernel estimation. Zhou and Wang (2012) propose an improved random forest algorithm which allocates weights to decision trees in the forest. West (2000) investigates the credit scoring accuracy of five neural network architectures and compares them to traditional statistical methods. Thomas (2000) surveys the techniques for forecasting the financial risk of lending to consumers and discusses the need to incorporate economic conditions into the scoring systems. II.2 Empirical studies Chang and Liao (2014) consider the nature and role of banks soft information in the context of loan default using a proprietary database from one of the largest state-owned commercial banks in China. It is concluded that soft information has a more significant economic effect on the incidence of default among firms that are more likely to manipulate their earnings. Herr and Burt (2005) investigate the risk factors for student loan defaults for borrowers who had attended the University of Texas at Austin and commenced repayments between 1996 and The results show that student program completion, persistence and success were strong predictors of student loan default, as were race and ethnicity, gender, and the school of enrollment at UT Austin. These results emphasize the role of student success and graduation in eventual loan repayment. Interventions that focus on student persistence and academic success were seen as the primary actions needed to help prevent student loan default. Chen and Wu (2014) estimate sectoral and macroeconomic frailty factors and their effects on default intensity using data for Japanese firms from 1992 to The study shows that common sources of unobserved default risk among firms in a similar business exist relative to observed firm-specific and macroeconomic variables that are thought to contain important information for default probability.

4 ASIAN ECONOMIC JOURNAL 6 The results suggest that there are important channels of default risk covariations associated with different corporate sectors. The results of the empirical study show that defaults of Japanese firms are less sensitive to stock market performance and that the sensitivity of default to observed covariates varies by sector. Fitzpatrick and Mues (2016) evaluate the performance of several modeling approaches for determining future mortgage default status. Boosted regression trees, random forests, penalized linear and semi-parametric logistic regression models are applied to four portfolios covering 300,000 Irish owner occupier mortgages. The results of the empirical study show that a boosted regression tree performed significantly better than logistic regression. Fitzpatrick and Mues suggest that tree-based methods and semi-parametric generalized additive models could be more widely used in credit risk applications, particularly in exploratory modeling where it is not known ex-ante which predictors are important. III. Data Description We develop risk predictive models for falling into bad debt by using direct loan data for 2012 to 2014 from the KOSAF. The key explanatory variables used for our analysis are household income level (class), whether a national grant has been received, whether more than two accounts are overdue and field of study. The household income class variable is divided into four categories based on KOSAF s assessment (Table 1). The field of study variable is divided into seven categories: humanities social sciences, education, engineering, natural sciences, medical science and pharmacy, and art and physical education (Table 1). The statistical analyses control for the primary socio-demographic characteristics assessed at the time of providing the loan, such as sex, age and marital status, Table 1 Data description in the analysis Variable Dependent variable Sex Age Marital status Household income National grant Overdue account School foundation Location Field of study Monthly repayment Definition Loan defaulter or person of bad credit standing (1: Yes, 0: No) Male, female 20, 21 23, 24 26, 27 30, 31 Married, not married Class 3, Class 4 5, Class 8 10, etc. No, yes 1, 2 National, private Metropolitan, local Humanities, social sciences, education, engineering, natural sciences, medical science and pharmacy, and art and physical education Amount of loans/(loan period Grace period)

5 MODEL FOR KOREAN STUDENTS BAD LOANS 7 in addition to the school foundation (i.e. whether the school is a national or private institution), school location and monthly repayment amount (Table 1). To ensure the clarity of our analysis, we consider a loan in the default stage if the principal is unpaid by the due date. Therefore, our definition of a person with a bad loan is someone with bad credit standing or who is a loan defaulter. The categories and descriptive statistics (proportions and means) relating to each variable in this study can be found in Table 2. People who were unmarried and went to a private school comprised the majority of both groups. The biggest proportion of the good loan group were between the ages of 21 and 23 (34.7 percent), while the biggest proportion of the bad loan group were under 20 (31.3 percent). Those in household income classes 8 10 comprise the biggest proportion of the good loan group (63.4 percent). The largest proportion in the bad loan group are from classes 8 10 (39.9 percent), followed by those in classes 1 3 (24.8 percent). Table 2 also provides a breakdown of the proportion in both groups depending on whether they receive national grants or they have more than two overdue accounts. Those in the good loan group were much more likely to have received national grants (39.0 percent) than those in the bad loan group (26.6 percent). In addition, those in the good loan group were much more likely to have fewer than two overdue accounts (64.6 percent) than those in the bad loan group (57.0 percent). The biggest proportion of the good loan group were from social sciences fields (24.9 percent), followed by engineering (24.8 percent). In comparison, among the bad loan group, 27 percent of borrowers came from fields classified as social sciences, while 20.2 percent of borrowers were from the engineering field. The average monthly repayment for direct loans by those in the good loan group was US$105.9, while that by bad loan group was US$ IV. Description of Methods This study examines and compares the effectiveness of two methods (logistic regression and the Cox proportional hazards model) to predict whether borrowers will default on their loans. We divided the dataset into a training set and a validation set. The training set contained 127,432 cases (60 percent), including 125,291 good loans and 2141 bad loans. The validation set comprised 85,040 cases (40 percent), including 83,560 good loans and 1480 bad loans. We built the models on the training set and tested the validity of the models on the validation set. In this study, we employ a logistic regression 1 model and 1 In the dataset, the borrowers who defaulted are represented by a 1 in the dependent variable. The borrowers who did not default are represented by a 0 in the dependent variable. Let p be the probability of a borrower falling into bad debt, which is denoted as follows: 1 P logistic ðbadþ= 1+expð zþ, (1) where z = β 0 + P κ i =1 β ix i. z is the function of k independent variables (x), called predictors, and β i are the coefficient estimates from the logistic regression model.

6 ASIAN ECONOMIC JOURNAL 8 Table 2 Descriptive characteristics for the variables in the analysis Good Bad N % N % χ 2 Total Sex Male Female Age ** Marital status Married ** Not married Household income Class ** Class Class etc National grant No ** Yes Overdue account ** School foundation National ** Private Location Metropolitan ** Local Field of study Humanities ** Social sciences Education Engineering Natural sciences Medical science and Pharmacy Arts and physical education Mean Standard deviation Mean Standard deviation T Monthly repayment $105.9 $115.3 $111.5 $ ** Notes: *p < 0.05, **p < 0.01

7 MODEL FOR KOREAN STUDENTS BAD LOANS 9 the Cox proportional hazards model 2 to develop a risk predictive model for falling into bad debt. Statistical analyses were performed using SAS version 9.2. Logistic regression is a powerful statistical method of modeling a binomial outcome with one or more explanatory variables. Logistic regression provides a quantified value for the strength of the association adjusting for other variables (removes confounding effects). The exponentials of coefficients correspond to odds ratios for the given factor. The main advantage of logistic regression is the ease of interpretation through use of odds ratios. In addition, the logistic regression model is simple and universal. Survival models relate the time that passes before some event occurs to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. In general, if proportional hazards models are used, a Cox proportional hazards model is used. The real advantage of Cox proportional hazards models is that you can apply survival models regardless of the distribution. An additional strength of Cox proportional hazards models is that they can include censored and truncated data. This analysis is special in that it originates from the education economy in Korea. The data show nine factors as strongly influencing bad student loans: age, marital status, household income, whether a national grant was received, whether more than two accounts are overdue, whether attending a national or private school, location, field of study and monthly repayment amount. The results provide KOSAF with powerful information about the possibility of lowering their overall loan default rate and preventing individual loan defaults. The results can be helpful for KOSAF setting up the default rate management plan for student loans and the Korean Government establishing the student aid policy. V. Results and Evaluation of the Predictive Models Table 3 provides the parameter estimates of the risk prediction models for falling into bad debt. The logistic regression estimates provided reveal that students between the ages of 24 and 26 are significantly less likely to default on loans than are those aged under 20 (p < 0.01). The parameter estimate for household income reveals that those in classes 4 7 and 8 10 are significantly less likely to default on loans than those with household income that is categorized as class 3 2 We used the Cox proportional hazards model to develop a risk predictive model for bad loans. The probability of falling into bad debt within 3 years (1 095 days) was estimated as follows: P Cox (Bad) =1 S(t) exp [f(x)], (2) where f(x) =β 1 x 1 + β 2 x 2 + β 3 x β k x k. In the above equation, x 1,, x k are the values of independent variables and β 1,, β k are the coefficient estimates from the Cox proportional hazards model. Baseline survival analysis probability at time t (t = days), S(t), is estimated when all independent variables are at their mean values.

8 ASIAN ECONOMIC JOURNAL 10 Table 3 The risk prediction models Logistic Cox ^β OR ^β HR Intercept ** Sex (reference: female) Male Age (reference: 20) ** ** ** Marital status (reference: not married) Married Household income (reference: Class 3) Class ** Class ** ** etc National grant (reference: Yes) No ** ** Overdue account (reference: 1) ** ** School foundation (reference: national) Private Location (reference: metropolitan) Local ** ** Field of study (reference: humanities) Social sciences Education Engineering Natural sciences Medical science and pharmacy ** ** Arts and physical education Monthly repayment 1.21E-06** E-07** Notes: *p < 0.05, **p < HR, hazard ratio; OR, odds ratio and below (p < 0.01). Likewise, those in medical science and pharmacy are significantly less likely to default on loans than those in humanities (p < 0.01). The estimates from the logistic model reveal that non-beneficiaries of national grants are more likely to default on direct loans than those who have received national grants (p < 0.01). Interestingly, borrowers who have more than two overdue accounts are more likely to default on direct loans than those who have fewer than two loans (p < 0.01). The Cox proportional hazards model estimates provided show that those aged and are significantly less likely to default on loans than those aged under 20 (p < 0.01). The parameter estimate for household income reveals that those in classes 8 10 are significantly less likely to default on loans than are

9 MODEL FOR KOREAN STUDENTS BAD LOANS 11 those with household incomes in classes 1 3 (p < 0.01). Moreover, those studying in the fields of medical science and pharmacy are significantly less likely to default on their loans than are those in humanities (p < 0.01). The estimates from the Cox proportional hazards model reveal that non-beneficiaries of national grants are more likely to default on direct loans than are those who have received national grants (p < 0.01). In addition, borrowers who have more than two overdue accounts are more likely to default on direct loans than those who have fewer than two loans (p < 0.01). Both models show that the borrowers at local universities are more likely to default on direct loans than those at metropolitan universities (p < 0.01). We tested the validity of our models with a validation dataset. Data for borrowers were used in the validation analysis. The performances of the models were evaluated with respect to discrimination using the receiver operating characteristic (ROC) curve. The ROC charts are graphical displays that give the global measure of the predictive accuracy of the models (Figures 1 and 2). They display the sensitivity against 1-specificity of a classifier for a range of cut-offs. Sensitivity is a measure of accuracy for predicting events that is equal to the true positive divided by the total actual positive. 1-specificity is a measure of accuracy for predicting non-events that is equal to the true negative divided by the total actual negative. The performance quality of the models is demonstrated by the degree to which the ROC curves push upward and to the left. The area under the curves can provide a quantitative performance measure. The area will range from 0.5, for a worthless model, to 1, for a perfect classifier. Figure 1 1 Receiver operating characteristic curve for the predictive model (train data) 0.8 Sensitivity Cox: Approximate area under curve = Logistic: Approximate area under curve = Specificity

10 ASIAN ECONOMIC JOURNAL 12 Figure 2 1 Receiver operating characteristic curve for the predictive model (validation data) 0.8 Sensitivity Cox: Approximate area under curve = Logistic: Approximate area under curve = Specificity The shapes of the ROC curves indicate that the predictive power of the two models (the logistic model and the Cox proportional hazards model) for predicting bad and good loans is reasonably good (Figures 1 and 2). The difference between the logistic regression model and the Cox proportional hazards model was tested using all the datasets available. The performance of the area under the ROC was similar between the logistic regression model and the Cox proportional hazards model (see Table 4). VI. Summary and Conclusions A total of 212,472 individuals who took out direct loans from the KOSAF between 2012 and 2014 were included in this study. We performed stratified sampling and allocated 60 percent of borrowers ( ) to the training set and 40 percent of borrowers (85 040) to the validation set. We have developed a risk group predictive model for Korean students defaulting on direct student loan payments. We employ a logistic regression model and the Cox proportional hazards model to develop a risk predictive model. Table 4 Area under receiver operating characteristic curve Model Train data Validation data Logistic regression model Cox proportional hazards model

11 MODEL FOR KOREAN STUDENTS BAD LOANS 13 The models were similar in area under ROC and the major influencing factors for borrowers defaulting on their loans are household income class, whether a national grant was received, age, whether more than two accounts were overdue, field of study and monthly repayment amount. Sex and marital status were not significantly related to the risk of falling into bad debt. In particular, both models showed that national grants had the greatest effect on falling into bad debt. In addition, the household income class at the time of loan supply is also one of the main factors affecting Korean student loan defaults. The present study has some limitations. First, we could not include students asset holdings in our model because the KOSAF did not collect asset holding data. However, we have developed the risk group predictive model including household income class. Second, the KOSAF did not know all students household income. In these cases, we classified the income class as etc.. Despite these limitations, the present study has been able to develop a robust risk group predictive model for predicting whether Korean students will default on their loans. Finally, the risk group predictive model in this study will be the basis for more efficient management of direct student loans. Further research should focus on utilizing various models (e.g. decision tree and neural network models) to improve the performance of the area under the ROC analysis. References Cao, R., J. M. Vilar and A. Devia, 2009, Modelling consumer credit risk via survival analysis. Sort, 33, pp Chen, P. and C. Wu, 2014, Default prediction with dynamic sectoral and macroeconomic frailties. Journal of Banking & Finance, 40, pp Chang, C., G. Liao, X. Yu and Z. Ni, 2014, Information from relationship lending: Evidence from loan defaults in China. Journal of Money, Credit and Bank, 46, pp Desai, V. S., J. N. Crook and G. A. Overstreet, Jr, 1996, A comparison of neural networks and linear scoring models in the credit union environment. European Journal of Operational Research, 95, pp Fitzpatrick, T. and C. Mues, 2016, An empirical comparison of classification algorithms for mortgage default prediction: Evidence from a distressed mortgage market. European Journal of Operational Research, 249, pp Hand, D. and W. Henley, 1997, Statistical classification method in consumer scoring: A review. Journal of the Royal Statistical Society, Series A (Statistics in society), 160, pp Herr, E. and L. Burt, 2005, Predicting student loan default for the University of Texas at Austin. Journal of Student Financial Aid, 2, pp Im, J. K., D. W. Apley, C. Qi and X. Shan, 2012, A time-dependent proportional hazards survival model for credit risk analysis. The Journal of Operations Research Society, 63, pp Madan, D. B., 2014, Modeling and monitoring risk acceptability in markets: The case of the credit default swap market. Journal of Banking & Finance, 47, pp Rosenberg, E. and A. Gleidt, 1994, Quantitative methods in credit management: A survey. Operations Research, 42, pp Thomas, L. C., 2000, A survey of credit and behavioural scoring: Forecasting financial risk of lending to consumers. International Journal of Forecasting, 16, pp

12 ASIAN ECONOMIC JOURNAL 14 Stepanova, M. and L. C. Thomas, 2002, Survival analysis methods for personal loan data. Operations Research, 50, pp West, D., 2000, Neural network credit scoring models. Computers and Operations Research, 27, pp Wekesa, O. A., M. Samuel and M. Peter, 2012, Modelling credit risk for personal loans using product-limit estimator. International Journal of Financial Research, 3, pp Zhou, L. and H. Wang, 2012, Loan default prediction on large imbalanced data using random forests. TELKOMNIKA Indonesian Journal of Electrical Engineering, 10, pp Zurada, J., 2007, Rule induction methods for credit scoring. The Review of Business Information Systems, 11, pp