MODELLING THE PROBABILITY OF CREDIT CARD DEFAULT IN BANKS.
Grace Mwonga – SCM214-9270/2015
Eileen Muga – SCM214-8876/2015
Thomas Mbashu – SCM222-0223/2016
Micheal Maina – SCM283-3636/2014
A research project submitted in the partial requirement for the awarding of a Bachelor of Science degree in Financial Engineering at the Jomo Kenyatta University of Agriculture and Technology under the Department of Actuarial Science and Statistics.
2020
DECLARATION
We declare that the work herein belongs to us and has not been presented for the award of any degree at any university.
Signed:……………………………………… Date:………………………….
Grace Mwonga – .SCM214-9270/2015
Signed:……………………………………… Date:………………………….
Eileen Muga – SCM214-8876/2015
Signed:……………………………………… Date:………………………….
Thomas Mbashu – SCM222-0223/2016
Signed:……………………………………… Date:………………………….
Micheal Maina – SCM283-3636/2014
This research project has been submitted for examination with my approval as the University Supervisor.
Signed:……………………………………… Date:………………………….
Dr. Charity Wamwea
ACKNOWLEGEMENTS
We would like to start by thanking our supervisor, Dr. Charity Wamwea, who has walked with us every step of the way and whose insightful advice has enabled us to make progress at every juncture of this research. We would also like to thank our parents whose support and encouragement gave us the morale to keep moving forward. Above all we would like to thank the Good God Almighty, who gave us the strength, wisdom, knowledge and understanding to be able to come this far in our research. All Glory and Honor be unto Him.
TABLE OF CONTENTS
1.1. BACKGROUND OF THE STUDY.. 5
1.2. STATEMENT OF THE PROBLEM… 7
1.4 JUSTIFICATION OF THE STUDY.. 9
CHAPTER TWO: LITERATURE REVIEW… 10
CHAPTER THREE: RESEARCH METHODOLOGY. 16
3.5 THE LOGISTIC REGRESSION EQUATION. 18
CHAPTER FOUR: RESEARCH FINDINGS. 22
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS. 32
1.1.BACKGROUND OF THE STUDY
A credit card is a financial instrument that allows the cardholder to obtain funds at interest from a financial institution at his or her own discretion, up to some limit. A credit card loan or credit card debt refers to the money one borrows when he or she uses his or her credit card. Credit card default is the failure to make credit card debt repayments by the due date for six months in a row.
The use or issuance of credit cards has been growing exponentially in the financial sector. The Federal Reserve Payments Study 2016 estimates that the credit card payment value in the US grew from $2.55 trillion in 2012 to $3.16 in 2015 at a rate of 7.4% per annum. Capgemini 2016 annual report noted that the trends in the US are observed worldwide. Such growth has catapulted credit cards to the leading noncash payment system.
Credit cards being an example of a revolving product has made modern banks take a different approach in credit risk mitigation unlike the one employed in traditional loan facilities. Unlike the traditional loans, with credit card loans the actual borrowing decision is solely at the discretion of the customer after receiving a fixed line of credit. Moreover, credit card loans do not require any collateral hence posing a greater risk to banks.
The study of credit card default has gained a lot of traction among researchers (Ausubel, 1991). Ausubel’s empirical study found that high profits and interest rates existed in the market despite their being a competitive structure with over 6,000 credit issuers in the US. It is rational for credit card holders to hold positive credit card balances despite the high interest rates due to the aspect of high liquidity presented by the credit cards hence saving consumers the opportunity cost of holding cash for payment (Brito & Hartley, 1995).
Despite the high interest rates charged on credit card loans, information problems on the part of credit card banks would ensure that no irrationality on the part of the consumers usage of credit cards (Mester, 1994). The phenomenon of high interest rates charged on credit card loans is further expounded to underscore the open-ended nature of credit cards and the high credit risk presented by credit card loans forced banks to charge such high interest rates. A strong positive correlation between credit card default and personal bankruptcy filings was a common finding by Ausubel, Domowitz, and Sartain. These findings clearly proved that credit card default posed a threat to the general state of the US economy and led to many researchers taking a keen interest in the credit card default issue.
The current research on credit card default provides vital information about the trends in the credit cards market but lack of detailed data has limited the understanding of consumer behavior and motivation in the use of cards and moreover in the understanding of credit card default, especially in developing countries. As such the study on credit cards default is gaining more momentum in developing countries such as Kenya.
The concept of credit cards is not a new phenomenon in Kenya having first been introduced in the country in 1967 by the Diners Club Africa. The franchise was later on taken over by the Royal Card. Currently all the major banks in Kenya including the Kenya Commercial Bank, the Equity Bank Kenya Ltd, the Barclays Bank of Kenya (which will rebrand to Absa Kenya in 2020), and the Co-operative bank of Kenya. The number of credit cards in Kenya as at May, 2016 was 221,050.
Kenya’s banking sector is very competitive and banks in the country are currently trying to have a competitive edge in the credit card service due to the improved technology experienced in the country.The low adoption of credit cards in Kenya is therefore a concern to the banks as they seek to grow their banking operations as they endeavor to also provide a maximum customer satisfaction. However, an increase in the usage of credit cards in the country will increase the number of people who default and therefore banks will suffer more negative consequences. As such banks have to stay adept with the ever evolving customer attributes in an effort to optimize their credit card service while also seeking a competitive edge in the financial sector.
In this study we will focus on significant customer attributes, namely, age, gender, and the level of income, that influence the ability to promptly pay the credit card loan and show their contributions towards the probability of credit card debt default. We are going to model the probability of credit card default in Kenya using the logistic regression model which is very efficient with categorical variables.
1.2.STATEMENT OF THE PROBLEM
Credit card debt is a matter of great concern to the lending banks since an increase in the credit card usage has led to an increase in credit card defaults. Credit card defaults end up becoming bad debts which are then written off by the lending banks hence affecting the banks net profit. However, there has been very scanty research of credit cards default in developing countries due to the slower growth of credit cards in such countries compared to the developed countries.
Credit card debts do not require customers to post collateral hence placing a greater credit risk on the lending bank. In 2017, the International Monetary Fund estimated the average inflation rate in Kenya to amount to 7.99 percent. Such high inflation rates has led to an increase in the cost of living coupled with the never ending cases of employee retrenchment in both public and private services for instance the recent staff layoffs at Telkom Kenya, East African Breweries, and East African Portland Cement. To this end consumer credit is steeply rising hence increasing the default rate since the level of income is either stagnating or taking a downward spiral for the worst. Hence, credit card loans have become more significant due to the need to maintain consumer consumption at the same level.
This has prompted the lending banks to carry out thorough risk analysis, both qualitative and quantitative, on the potential borrower so as to determine their ability to pay back their outstanding credit card loan. This may involve checking the financial history of the potential borrower on the Credit Reference Bureau Kenya, conducting an interview, or even confirming the source of their regular income. As such, the lending banks will be able to effectively model the probability of credit card debt default since default is only observed once the customer is unable to payback their outstanding credit card debt.
Locally, a series of studies concerning credit cards have been conducted but none of them has modelled the probability of credit card default in banks. This research attempts to fill the gap by proposing a model of the probability of credit card default in banks. Moreover, this study is guided by the research question: What is the probability of credit card default in commercial banks?
We will use the logistic regression model to model the probability of consumer credit card default. This is because we will use two discrete classes namely, default and no default hence the logistic regression model becomes more appropriate than the linear regression model.
1.3.OBJECTIVES
1.3.1Main objective
To model the probability of credit card default.
1.3.2Specific objectives
- To fit a Logistic Regression Model.
- To determine the significant variables for predicting credit card default.
- To estimate the probability of credit card default.
- To determine the predictive power of the fitted model.
1.4 JUSTIFICATION OF THE STUDY
This study will give the lending banks a clear understanding of the probability of credit card loan default based on different categorical variables such as the level of income hence the lending banks will be able to revert extreme trends of credit card loan default by putting in place appropriate and adequate measures. Moreover, this research is intended to inform the banks’ decision on the reasonable credit card limit that they should allow for each card holder. The model will enable banks to effectively monitor their loan portfolio risk, thus, mitigating credit risk.
The field of academia is always growing and as such this study will be a useful point of reference to researchers interested in credit cards as an area of study.
1.5.SCOPE
This study is carried on the model of the probability of credit card loan default. We have selected three variables which we intend on investigating their statistical significance. The variables are namely: education, age, gender, marriage, and credit limit.
2.1. INTRODUCTION
This chapter summarizes information from previous researched work in the same area of interest. The specific areas covered are theoretical review, empirical review, conceptual framework and lastly the summary of the literature review.
2.2. THEORETICAL REVIEW
2.2.1 Credit Risk Theory
In 1974, Merton introduced the credit risk theory also called structural theory which suggested the default events derive from a firm’s asset evolution modelled by a diffusion processes with constant parameters.
The Basel I accord of 1988 which was a set of regulatory requirements on banking institutions in the European Countries is in line with the credit risk theory. It came up as a way to mitigate risks faced by banks. At this time they only considered on credit risk. Banks had to maintain a minimum capital requirements of 8% of risk weighted assets. These regulations were the same throughout the countries.
2.2.2Gender and credit card default
In 2007, Abdul-Muhmin and Umar, noted that the tendency to default on credit card loans is significantly higher in males. However, recent studies note that the probability of credit card ownership in Saudi Arabia is higher among females hence the female demographic in Saudi Arabia is at a higher probability of default. An analysis on credit card misuse scores to determine the effects of demographic variables concluded that the mean credit card scores were essentially the same for men and women (Pirog & Robert, 2007). The above previous research suggests that research on gender differences is inconclusive.
2.2.3Age and credit card default
Age is one of the significant and socioeconomic characteristic in describing consumer credit card practices(Wickramasinghe & Gurugamage, 2009). The usage of credit cards based on age has led researchers to suggest both positive and curvilinear relationships. On the curvilinear relationship, evidence suggests that credit cards usage intensity is higher among the middle-aged than the lower- and old-aged demography (Abdul-Muhmin & Umar, 2007). Credit cards are very problematic to young adults(Joireman et al., 2010). The average college student in the US will graduate with more than $2,800 in credit card debt and up to one-fifth carry a credit card of $10,000 or more (Mae, 2005).
The correlation between age and credit card scores to is significant (Pirog & Robert, 2007). People aged under 35 are significantly more likely to become revolvers and the older one gets, the less likely they are to revolve(Hamilton & Khan, 2001). Hamilton and Khan conducted their research using Linear Discriminant Analysis and Logistic Regression on a sample of 27,681 bank credit card holders who had held and used their cards in the 14 month sample period to identify the characteristics of active card holders with the great propensity to revolve that is, pay interest (Hamilton & Khan, 2001).
2.2.4Level of income and credit card default
The significant shift of consumer debt from installment debt to credit card debt has made consumers’ debt burden to be more sensitive to changes in the level of income. The higher the consumers’ level of income, the greater their likelihood of paying their credit card bills in full. The lower the level of income or a decline in the consumers’ level of income leads to a greater likelihood of late repayments or minimum payments on their credit cards bills hence their debt burden increases leading to a very a high probability of credit card default.
Although credit cards allow consumers smooth consumption when their incomes fall, the cost of doing so is extremely high and may cause some debtors to enter a state of ongoing financial distress (White, 2007). Unpredictable expenses, such as illness, may lead people in to credit card debt. When people take on debt, credit card issuers react by doing at least one of the following: (1) charge penalties or fees; (2) increase interest rates; and (3) increase credit limits. Such actions increase the likelihood of credit card default. Trying to change consumers’ attitudes toward over-consumption does not necessarily solve the problem of credit card default because in most instances people are simply trying to exist in the prevailing tough economic conditions. Over-borrowing among a majority of credit card holders is due to lack of sufficient income (Scott, 2007).
A majority of credit card users have relatively high propensities to consume but limited monetary assets, otherwise, they would not continue to pay high interest rates on unpaid balances and even defaulting completely in the end (Stauffer, 2003). Recent studies show that the ownership and use of credit cards by low-income households has increased and credit card holders have become riskier. Credit card companies have taken greater risk to earn abnormal returns and credit card debt is related to bankruptcy filings (Kidane & Mukherji, 2004).
2.2.4 Education and credit card default
Different levels of formal education could influence the risk of credit card default. Households with a lower level of formal education tend to be deliberate with their borrowing. However, if university educated households were factored the findings would be the opposite. This could be explain by the finance and economics courses available in the universities and colleges.
2.2.5 Credit limit and credit card default
The possible amount a person can obtain from a credit card could influence the risk of paying back the debt. Thus the credit limit could adversely or positively affect the repayment rate. The credit limit is set depending on an assumed person’s ability to pay back a certain amount and in some instances their credit score.
There exists a strong positive correlation between credit card debt and personal bankruptcy filings (Domowitz & Sartain, 1999). This could lead to an impact on the economy which thus encouraged the research of credit card default. As such, a higher credit limit gives a greater incentive since it may offer a lower interest rate.
2.2.6 Marital status and credit card default
Generally the finances of spouses are joint and are therefore allocated and spent as one but when it comes to cohabiters finances are dealt with more individually (Brines & Joyner, 1999). This difference would therefore also impact debt. Credit card debt is considered by several youth as an investment debt similar to college loans. The average college loan debt, credit card default is low. (Chiteji, 2007).
2.3. EMPIRICAL STUDY
2.3.1Empirical study on credit card default in developed countries
The fact that credit cards do not require consumers to post collateral, unlike traditional banks, places a greater risk on lenders. The traditional loan market theoretically uses the tools of asymmetric information and adverse selection (Stigliz & Weiss, 1981).
The growth of credit cards debt in the US economy hassled researchers to increasingly turn their attention to the various aspects of credit card debt. The empirical study carried out by Ausubel in 1991 found that abnormally high profit and sticky interest rates exist in the industry in spite of its competitive structure of over 6,000 credit card issuers. He speculated that search costs and a type of irrational consumer behavior might be involved in such market outcomes. In 1995, Brito and Hartley responded to Ausubel’s argument by introducing the aspect of the liquidity service of credit cards which save the consumers the opportunity cost for holding money for payment, thus, arguing that it is rational for consumers to hold positive balances even in the face of high interest rates.
High and sticky interest rates could exist without irrationality on the part of consumers because of information problems for the credit card banks (Mester, 1994). The situation is explained by the open ended nature of credit card loans and the high risk involved with this for banks (Park, 1997). Defaulters have higher interest elasticities and this could induce banks to keep their interest rates high (Stavins, 1996).
Default in credit card debt is due to the fact that card holders with higher balances have higher probabilities of default (Mester & Calem, 1995). Revolving products, such as credit cards, information about borrowers’ repayment ability plays a crucial role in their determining their credit limits. Asymmetric information between borrowers and lenders and lack of collateral to mitigate the informational asymmetric are mainly responsible for credit rationing in some credit markets, hence, banks refuse credit to some borrowers. Credit bureau reports help banks improve the quality of loan supply decision (Stigliz & Weiss, 1981).
2.4.2 Empirical evidence on credit card default in Kenya
Married customers are more credit worthy than single ones (Mokaya, 2011).Also, the longer a consumer stays in employment the more credit worthy they were, savings accounts holders were more credit worthy than the current accounts holders, consumers with house telephone defaulted twice as much as those with none, and the highest default rate was among those earning between 50,000/= and 70,000/=.
Currently in Kenya, credit cards are increasingly becoming an essential tool since a credit card offers a cardholder convenience safety and higher purchasing power. Screening out credit risky customers is a crucial step in card application acceptance process (Mbijiwe, 2005).
CHAPTER THREE:RESEARCH METHODOLOGY.
3.1. INTRODUCTION
The general objective of this study is to model the probability of default of credit card holders. This chapter describes the methods used to achieve the specific objectives of the study which will aid in achieving the general objective wholesomely. The chapter starts off by describing the research design adapted for the study and goes on to give details about the data collection procedure as well as the logistic regression model used for the study.
3.2. RESEARCH DESIGN
Research design refers to the framework of methods and techniques chosen by a researcher to combine various components of research in a reasonably logical manner so that the research problem is efficiently handled. This study took on an analytical design where we used already available information and analyzed it in order to make critical evaluations.
3.3. DATA COLLECTION
Secondary data obtained from a crowd sourced forum called Kaggle was used in the study. The data set contained information of various credit card holders in Taiwan.
3.4. DESCRIPTIVE ANALYSIS
In this study we used the logistic regression model to fit the data and then analyzed it using R.
3.4.1 Logistic Regression Model
The Logistic Regression model seeks to estimate that a given event will occur for a randomly selected set of observations against the probability that the event will not occur. This model is best used when the problem being handled is a classification problem. A classification problem is one where the independent variables are continuous in nature while the dependent variable takes on a categorical nature. A categorical variable is also sometimes referred to as a nominal variable and it is one which has two or more categories but has no intrinsic ordering of these categories. These categorical variables take on two values that is success or failure. In the case of this study the dependent variable will be the probability of default. Where “not defaulting” will be our success and “defaulting” our failure. Under logistic regression this outcome is to be predicted on the basis of one or more independent variables. In the case of this study, we chose these independent variables as sex (gender), age, marital status, limit balance and the level of education. These variables were chosen in order to determine their significance when predicting their probability of default. Hence the aim when using the logistic regression credit scoring model is to be able to identify the conditional probability of each credit card holder to belong to one class. That is the class of default or the class of not defaulting in which case a “good” customer or a “bad” customer would be evaluated based on the values of these predictor variables for each credit card applicant.
The logistic regression has similarities with a linear regression model however, the difference between the logistic regression model and the linear regression model is that the linear regression model is incapable of dealing with outliers that fall outside of a certain set threshold point or value. The logistic regressionmodel on the other hand uses the sigmoid function to deal with such outliers. It also uses the Logit function to show the non-linear relationship between the predictor variables and the response variable in the cases where it’s not linear. The logit function is preferred to other functions such as he probit function because its results are relatively easy to interpret.
3.5 THE LOGISTIC REGRESSION EQUATION.
The logistic regression is defined as:
…… (3.1)
where;
- pi = probability of default
- i = function of the explanatory variables
- x1= Limit balance, x2= sex and x3=education level,x4= marriage,x5= age
- β0 = intercept
- βj= coefficients associated with the corresponding predictor variables χi , for j =1,2,3,4,5 and i=1,2,3,4,5
- represents the default event Yi
- ϵi = error term
We then take the antilog of equation3.1 and hence obtain an equation that gives the probability of default that is Yioccurring and in order to obtain the critical points of this log likelihood function, we will set the first derivative of each Beta to be 0.
Differentiating equation 3.1 we obtain
………. (3.2)
Hence the probability of an event
………. (3.3)
Where Pi is the probabilityof the outcome of the event of default.
3.5.1 Parameter Estimation
The Maximum Likelihood method of parameter estimation is used to estimate the parameters in the logistic regression model.
3.5.1.1 Maximum Likelihood Estimation
The outcomes Yi are binomially distributed that is Yi~Bin(n,p) with n being the number of successes and p the probability of success. This implies that every Yi represents a binominal count in the ith population and hence the joint probability function also called the likelihood function of Y is;
………. (3.4)
The Maximum Likelihood Estimators (MLE) are the values of β that maximizes the likelihood function of equation(3.4).
Rearranging the equation:
……….. (3.5)
Using the logistic regression model we are able to equate the logit transformation to the log odds of the probability of success. That is;
…………… (3.6)
Taking the exponent of both sides of equation(3.6)yields:
………………(3.7)
Solving for p we obtain
…………….. (3.8)
We then substitute the first term of equation(3.5) with equation (3.7) and the second term we substitute with equation (3.8)
…………….(3.9)
Next we simplify the first product equation and then replace equation(3.1) with in the second product, to obtain:
………………….(3.10)
Equation(3.10) is the kernel of the likelihood function that is to be maximized.
NOTE: The logarithm is a monotonic function, and therefore the maximum of the likelihood function will also be a maximum of the log likelihood function and the contra wise will be true too.
Now, we can take natural log of equation(3.9) in order to simplifying its differentiation and hence obtain the log likelihood function as
…… (3.11)
In order to be able to find the critical points of the log likelihood function, we set the first derivative with respect to each βto be equal to zero and then differentiate equation(3.11).
However take note that:
………………(3.12)
And as the other terms in the summation do not depend on βj, then they can be treated as constants.
Differentiating the second half of the equation(3.12), we take note that the general rule that
And proceed to differentiate equation (3.12) with respect to each βjsuch that
=
=
= –
3.7STUDY SITE.
The data we obtained from the crowd sourced forum Kaggle was fitted into the model and analyzed using R.
CHAPTER FOUR:RESEARCH FINDINGS
4.1. MODELLING
This research paper models 30,000 samples of credit card holders’ repayment information. Basic user information is put under keen consideration. For this research, “0” indicates non-default whereas “1” indicates default.
Table 1 Probability of Default
| Default | Non-Default | Total | Default Ratio |
| 6636 | 23364 | 30000 | 22.12% |
The findings show that the probability of default of the sample is 22.12%.
The explanatory variable credit limit takes a numerical status due to the revolving nature of credit cards ranging from 10,000 to 1,000,000. According to our data set, the explanatory variable sex refers to gender. Sex assumes integer numbers 1 and 2. “1” indicates female while “2” indicates male. Education assumes integer values with a minimum of 0 and a maximum of 6 “1” being Graduate school, “2”being university , “3” being high school, “0”, “4”, “5” and “6” being others. Age assumes integer values ranging from 21 years to 79 years. Marriage assumes integer values “1” being married,“2” being single, “3” being divorced and “0” being others.
Figure 1 Histogram of Age distribution
Figure 2 Histogram of Credit Card Balance
A histogram of the credit limit graphically displays a positively skewed distribution with a range boundary on its left side of 0.
Figure 3 Barplot showing distribution of gender
A bar plot on the gender distribution distinctly shows that the sample has more males than females. A bar plot shows that the majority of the sample falls under category 2.
Figure 4 Barplot showing marital status
A majority of the sample have a marriage status of either 1 or 2 that is they are either married or single as graphically evident in the bar plot of marriage status.
The model under study is the logistic regression model. As such, this paper sets forth a regression formula with the explanatory variables credit limit, sex, education, marriage, and age with the output variable being the default status. 2500 test samples are selected for this research due to its relatively smaller number compared to the size of the train samples.
This research is conducted on the basis of both financial and personal information of the credit card holders. The 30,000 samples under study present a majority of personal information in comparison to the small amount of information on their financial information. The personal information of the sample of study was pivotal in understanding essential data such as demographic data. On the other hand, the financial information was vital in determining and modeling the probability of credit card default. The logistic regression model at hand underscores the willingness of repayment across the various variables under study.
The developed logistic regression model concisely estimates the probability of credit card default in the sample of study. The five explanatory variables present banks and financial institutions with a platform for mitigating against credit card default.
Fitting the logistic regression model on the test set has an AUC of 0.635 and the corresponding Receiver Operating Curve is provided below.
Figure 5 Receiver Operating Curve with AUC
4.2. RESULTS
4.2.1 Fitting a Logistic Regression Model
A logistic regression model was used to compute the probability of default of the credit card holders. Our data set was comprised of 30,000 observations, a random sample of 2,500 observations was split from the main dataset and was used as the testing set for the model. The remaining 27,500 observations were used as the training set for the fitting of the model. During the fitting of the model we used the glm() function in R.
Table 2 Summary of Logistic Regression Model
From the table above showing the summary of the Logistic regression model, we can deduce that
Marriage2is statistically insignificant due to its p-value < 0.05. However, if fitted at 10% significance level all the explanatory variables are statistically significant. Credit Card Balance limit (LIMIT_BAL) has a very low p-value as compared to others suggesting that credit card default has a strong association with credit card balance.
4.2.2 Determining Significant variables for predicting credit card default
In the assessment of the ANOVA from the proposed model we were able to deduce the following:
Table 3 Analysis of Deviance Table
Assessing the Analysis of Deviance, we need take a look at the difference between the null deviance, (deviance of the model with only the intercept, the null model) and the residual deviance. The bigger the difference the better our model is doing against the null model. Adding the credit card balance reduces the deviance from 29111 to 28410. Adding gender into the equation also causes a significant shift in the deviance. The deviance from Education level is relatively small, this in turn means we can either include it in the model or leave it out without sacrificing the performance of the model by a great deal.
From Table 3, based on both the p-values and deviance; Education is statistically insignificant with relation to fitting the model.
Building the model without Education variable.
Table 4 Summary of Model without Education Variable
From the table above, the model without the Education variable has all its variables being statistically significant since all p-values < 0.05.
From the analysis of deviance table below; we get to see that all the variables now add a significant effect into the model.
Table 5 ANOVA of Model without Education Variable
The resulting fitted model:
Log(odds) = intercept + β0(balance) + β1(female) + β2(marriage1) + β3(marriage2) + β4(marriage3) + β5(age) ……………… (4.1)
Due to the nature of logistic regression and its response variable we are unable to deduce R2. However, there are different measures that help determine the percentage deviance explained by the data. In our case we will use McFadden’s R2. This is usually given by
1 – LogLikelihood of Model / LogLikelihood of Null Model. …………. (4.1)
The table below shows the relevant pseudo R2 measures including McFadden’s R2;
McFadden’s R2 = 0.027743
4.2.3 Estimating the probability of credit card default
From the predicted values we were able to obtain a count of prediction in terms of default and non-default. The table below shows the default and non-default values from the model prediction.
Table 6 Probability of Default as predicted by Model
| Default | Non-Default | Total | Default Rate |
| 534 | 1966 | 2500 | 21.36% |
4.2.4 Determining predictive power of the model.
In order to determine the predictive power of the model we conducted an accuracy score on the testing data. Since default was denoted by 1 and non-default by 0, any prediction classified as greater than 0.5 is classified as default while any other value is classified as non-default.
Upon checking for misclassified values, the error rate was 21.36%. The accuracy of the model stood at 78.64%.
CHAPTER FIVE:CONCLUSION AND RECOMMENDATIONS
5.1. CONCLUSION
This research has addressed crucial personal and financial information that impacts the probability of credit card default. The explanatory variables in this research are evidently crucial in enabling the banks and financial institutions mitigate against credit card default. After fitting the logistic regression model, one can conclude that it is effective in modelling credit card default. Also, this paper offers a room for the development of new paradigms in deepening the studies on credit card default.
The explanatory variables in this research study can enable banks and financial institutions determine the credit rating of individuals. As such, the credit rating will directly impact the credit limit of one’s credit card thus mitigating against credit card default. Banks and financial institutions will be better equipped to reduce the probability of credit card default to a rate that does not heavily reduce their net profits. A development of an applicable credit-management measures is a pertinent strategy that banks and financial institutions should consider. Thus, banks and financial institutions will only be required to put in extra attention and measures on individuals with a higher probability of credit card default. This logistic regression model will improve the efficiency of banks’ credit management.
5.2. RECOMMENDATIONS
At the moment, the credit card penetration in developing countries is low. As such, banks and financial institutions should carry out educational seminars and training on credit cards. This effort will maintain existing holders while also tapping in on potential credit card holders.
Continuous research by banks the ever changing finance dynamics is highly recommended. Such an effort will enable banks and financial institutions to stay adept with the characteristics of their customer base. As such, banks will be empowered to capitalize on any competitive edge in the credit card market.
Wage policy is an issue affecting most countries, especially developing nations. It is high time for banks and financial institutions to join efforts with their respective governments to deal with for instance on the acceptable minimum wage in line with the prevailing economic conditions. An increase in the minimum wage payable increases one’s disposable income. Thus, the citizenry may significantly result to an uptake of credit cards.
LINES OF CODE
## STEP 1
#importing data
credit.data<-read.csv(file.choose(),header=TRUE)
#view first 6 rows
head(credit.data)
#Data Preview
dim(credit.data)
#Variable Names
names(credit.data)
#show how data is structured
str(credit.data)
## STEP 2
# Data Transformations For Analysis
credit.data$default.payment.next.month <- as.factor(credit.data$default.payment.next.month)
credit.data$SEX <- as.factor(credit.data$SEX)
credit.data$EDUCATION <- as.integer(credit.data$EDUCATION)
credit.data$MARRIAGE <- as.factor(credit.data$MARRIAGE)
#rename column 7
colnames(credit.data)[7] <- “DEFAULT_STATUS”
## STEP 3
# Sample data anlysis
#obtain summary of dataset
summary(credit.data)
#display graphs
hist(credit.data$LIMIT_BAL, main=”LIMIT BAL”)
#gender distribution
barplot(table(credit.data$SEX), main = “GENDER BARPLOT”, ylab = “COUNT”, xlab = “GENDER (1 = FEMALE, 2 = MALE)”)
#education level distribution
barplot(table(credit.data$EDUCATION), main = “EDUCATION BARPLOT”, ylab = “COUNT”)
#marriage status distribution
barplot(table(credit.data$MARRIAGE), main = “MARRIAGE BARPLOT”, ylab = “COUNT”)
#default level distribution
barplot(table(credit.data$DEFAULT_STATUS), main = “DEFAULT BARPLOT”, ylab = “COUNT”)
#Age distribution
hist(credit.data$AGE, main=”Age Distribution Histogram”)
#remove any missing values
credit.data <- na.omit(credit.data)
## STEP 4
# Building the model
# create formula with the variables
credit.regression.formula <- formula(DEFAULT_STATUS ~ LIMIT_BAL + SEX + EDUCATION + MARRIAGE + AGE)
#split the data set into two.
#generate random data positions to split
testpositions <- sample(30000, 2500, replace = FALSE)
#generate testing table
credit.data.test <- credit.data[testpositions,]
#generate training table
credit.data.train <- credit.data[-testpositions,]
#fit the model using training data
credit.model <- glm(credit.regression.formula, family = binomial(link = ‘logit’), data = credit.data.train)
#obtain summary
summary(credit.model)
#log(DEFAULT_STATUS/1-ds) = Intercept + (B1)LIMIT_BAL + (B2)SEX2 + (B3)EDUCATION + MARRIAGE + AGE
## STEP 5
# Model Analysis
anova(credit.model, test=”Chisq”)
#analyze variation in deviance
#install pscl
install.packages(“pscl”)
library(pscl)
#estimate the r2
pR2(credit.model)
#ROC
install.packages(“pROC”)
## model building without education
credit.regression.formula <- formula(DEFAULT_STATUS ~ LIMIT_BAL + SEX + MARRIAGE + AGE)
#fit the model using training data
credit.model <- glm(credit.regression.formula, family = binomial(link = ‘logit’), data = credit.data.train)
#obtain summary
summary(credit.model)
# Model Analysis
anova(credit.model, test=”Chisq”)
#pseudo r2
pR2(credit.model)
## STEP 6
# Model prediction on test sample
fitted.results <- predict(credit.model,newdata=credit.data.test,type=’response’)
#load pROC
library(pROC)
test_roc <- roc(credit.data.test$DEFAULT_STATUS ~ fitted.results, plot = TRUE, print.auc=TRUE)
#convert values > 0.5
fitted.results <- ifelse(fitted.results > 0.5,1,0)
#get misclassification error
fitted.results.error <- mean(fitted.results != credit.data.test$DEFAULT_STATUS)
#display accuracy of model
print(paste(‘Accuracy’,1-fitted.results.error))
#displaying a confusion matrix
table(fitted.results, credit.data.test$DEFAULT_STATUS)
Ausubel, L. M. (1991). The failure of competition in the credit card market. The American Economic Review, 50-81.
Brito, D. L., & Hartley, P. R. (1995). Consumer rationality and credit cards. Journal of Political Economy, 103(2), 400-433.
Mester, L. J. (1994). Why are credit card rates sticky? Economic Theory, 4(4), 505-530.
Pirog, S. F., & Roberts, J. A. (2007). Personality and credit card misuse among college students: The mediating role of impulsiveness. Journal of Marketing Theory and Practice, 15(1), 65-77.
Wickramasinghe, V., & Gurugamage, A. (2009). Consumer credit card ownership and usage practices: empirical evidence from Sri Lanka. International Journal of Consumer Studies, 33(4), 436-447.
Abdul-Muhmin, A. G., & Umar, Y. A. (2007). Credit card ownership and usage behaviour in Saudi Arabia: The impact of demographics and attitudes toward debt. Journal of Financial Services Marketing, 12(3), 219-234.
Joireman, J., Kees, J., & Sprott, D. (2010). Concern with immediate consequences magnifies the impact of compulsive buying tendencies on college students’ credit card debt. Journal of Consumer Affairs, 44(1), 155-178.
Mae, N. (2005). Undergraduate students and credit cards in 2004. Undergraduate students and credit cards in 2005: An analysis of usage rates and trends.
Hamilton, R., & Khan, M. (2001). Revolving credit card holders: Who are they and how can they be identified?. Service Industries Journal, 21(3), 37-48.
White, M. J. (2007). Bankruptcy reform and credit cards. Journal of Economic Perspectives, 21(4), 175-200.
Scott, R. H. (2007). Credit Card Use and Abuse: A Veblen ian Analysis. Journal of Economic Issues, 41(2), 567-574.
Stauffer, R. F. (2003). Credit cards and interest rates: theory and institutional factors. Journal of Post Keynesian Economics, 26(2), 289-302.
Kidane, A., & Mukherji, S. (2004). Characteristics of consumers targeted and neglected by credit card companies. FINANCIAL SERVICES REVIEW-GREENWICH-, 13(3), 185-198.
Domowitz, I., & Sartain, R. L. (1999). Determinants of the consumer bankruptcy decision. The Journal of Finance, 54(1), 403-420.
Brines, J., & Joyner, K. (1999). The ties that bind: Principles of cohesion in cohabitation and marriage. American Sociological Review, 333-355.
Chiteji, N. S. (2007). To have and to hold: An analysis of young adult debt. Young, 60, 70.
Stigliz, J., & Weiss, A. (1981). Credit Banks Rationing in Markets with Imperfect Information” American Economic Review.
Park, S. (1997). Option value of Credit Lines as an explanation of high credit card rates (No. 9702). Federal Reserve Bank of New York.
Stavins, J. (1996). Can demand elasticities explain sticky credit card rates?. New England Economic Review, 43-55.
Calem, P. S., & Mester, L. J. (1995). Consumer behavior and the stickiness of credit-card interest rates. The American Economic Review, 85(5), 1327-1336.
Mokaya, C. N. (2011). The relationship between credit default risk and cardholder characteristics, credit card characteristics, behavioral scoring process among commercial banks in Kenya (Doctoral dissertation, University of Nairobi, Kenya).
Mbijiwe, J. M. (2005). Application of multiple discriminant analysis credit scoring models, for credit card consumers-the case of Barclaycard Kenya (Doctoral dissertation, University of Nairobi).
Kothari, C. R. (2004). Research methodology: Methods and techniques. New Age International.