PREDICTING THE PROBABILITY OF CONSUMER FINANCING DEFAULT IN ISLAMIC BANK: LOGISTIC BINARY REGRESSION MODEL

(Proposal Riset ini dipresentasikan di INCEIF ISLAMIC BANKING AND FINANCE EDUCATIONAL COLLOQUIUM 2006 - Bank Negara Malaysia (BNM), Kuala Lumpur - MALAYSIA)

Penulis mendapatkan juara ketiga untuk kategori proposal Phd

I. INTRODUCTION

I.A. Rationale
The expansion of Islamic banking industry in Indonesia was rapidly developed in the last two years. Apart from the increase of people’s trust, such positive development could be observed from the emergence and the growth of shariah banking chain. Within the last two years time frame, until December 2005, Bank Central of Indonesia (BI) reported that there exist three full-fledged Islamic banks (BUS) and 19 business shariah units (UUS), with 183 branch offices in all over Indonesia compare to BI report in the year December 2003 with only two BUS, 8 UUS and 116 branch offices.
Such a good achievement is also challenge for Islamic Banking industry to present and perform a well manage institution in the sight of customers. It is therefore, Islamic Banking industry obliged to deliver excellent services to their customer. One of bank’s tasks that have to be extra paid attention is risk management in credit for both borrowers and lenders. For this reason, banks and financial institutions started to revise their lending policies.
Analysis and management of credit risk has taken on an increased importance in recent years. New regulations such as BASEL II force banks and other financial institutions to make credible efforts to chart and manage the risks associated with their client portfolio. In addition, harder competition in the financial markets has also increased the need to monitor the risk/reward relationship for various customers.
Credit defaults are one of the main sources of loss for a bank. The definition of corporate default risk is the counterpart failure to comply with their obligations to service debt. This risk is critical since the default of a small number of important customers can get generate large losses, potentially leading the bank to insolvency.
It is therefore according to Prof. Sam N. Basu (1994), well credit analysis will have great contribution toward proper decision making. Further, he stated that credit analysis has two major objectives; first, to assist bankers in credit lending decision correctly. second, to assist bankers keeping away from unviable credit lending decision.

There are basically six functional responsibilities associated with credit lending activities; (1) assessment of the customers credit risk, (2) making the credit granting decision with regard to credit terms and, where relevant, credit limits, (3) collecting receivables (debts) as the fall due and taking action against defaulters, (4) monitoring customer behavior and compiling management information, (5) bearing the risk of default or bad debt, (6) financing the investment in receivables (debtor) (Summer and Wilson, 2000).

On top that, there at least five standards (5C) that has been applied so far by banking industry to deal with lending process (Kasmir, 2005); character, capacity, capital, condition and collateral. It is 5C that being used by bankers to analyze whether customers credit worthy. These five standards are having similarities with the data being used in the research done by Ozlem Ozdemir et. al (2004). The study aimed to examine the relationship between the consumer credit clients’ payment performance and some demographic variables (such as marital status, sex, age, residential status, occupation) and some financial variables (such as income, loan size, interest rate, maturity, credit category).

The present research is important for three reasons. First, the research will go beyond what have been done by many previous studies. Many previous studies were focused more on the relationship between lender’s decision and the characteristics of the consumer credit applicants and the relationship between the characteristics of people that are already accepted (clients) and whether they are paying back their loans on time or not i.e. payment performance. Second, by predicting credit default probabilities, a bank will have a chance to minimize the expected default or misclassification rate subject to some exogenous acceptance rule (Carling et al., 1998). Third, no research has been done on characteristics consumer financing applicant and/or clients of any Islamic bank, which will be different from conventional one.

For the purpose of the study, we collect the data on the characteristics of the credit clients (by mean of 5C) of the two biggest full-fledged Islamic banks in Indonesia, namely Bank Muamalat Indonesia (BMI) and Bank Syariah Mandiri (BSM).

I.B. Research Objectives
In line with the above rationale, therefore, the objectives of this research are:
1. To deliver the relationship between lender’s decision and the characteristics of the consumer applicants.
2. To analyze the relationship between the characteristics of applicants that are already accepted (clients) and whether they are paying back their loans on time.
3. To deliver strategic analysis for shariah banking to minimize the probability of default (non performing loan).
4. To deliver information with regard to the potential development of shariah banking which based on the analysis of applicants characteristics.


I.C. Research Benefits
The potential benefits from the finding of this of research are as follow:
1. As information with regard to potential development of shariah banking from lending strategy model side.
2. As information with regard to potential factors that might influence the probability of default.
3. As information with regard to the importance of prudentially aspect by looking at applicants characteristics.
4. As information with regard to the characteristic of shariah banking clients

I.D. Research Coverage
The scope of this research is will be encompassing the analysis of shariah banking improvement by looking at the probability of its clients default. The research will look deeply into the characteristics of Islamic bank clients that might have positive/negative relationship with default ness.

Research coverage analysis will be comprise of the two biggest full-fledged Islamic banks in Indonesia, namely Bank Muamalat Indonesia (BMI) and Bank Syariah Mandiri (BSM). It will cover approximately 100 respondents from both of these banks, which are granted loan between the years 2003-2004. The criteria of the area is based on the potential and actual condition, whereby both of the banks are the two biggest full-fledged in Indonesia recently.

The following section gives a brief review of related research and theoretical framework, then, the conceptual model used in this study followed by explanations on data, methodology, and statistical analysis used. Last but not least, the schedule and the flow of the research are presented for the purpose of consistency.


II. Previous Research and Theoretical Framework

The previous literature on consumer credit can be categorized in two parts; the studies on consumer credit applicants examining the lenders’ decision to grant the loan and the studies on consumer credit clients examining the borrowers' ability to pay the loan. There are many studies on scrutinizing and improving the rejection and acceptance criteria of credit lenders’ decisions.

Jappelli (1990), for example, investigates lenders’ and borrowers’ behaviors in consumer rationing activities for the United States’ credit market in 1983. He found that most of the applicants are rejected because of their credit history, their age or their income. Amount of collateral, which is a property, offered by borrowers to secure a loan in case of delinquency, is another important factor affecting credit-granting decision. Time spent at current job, time spent at current address, job, type of work, family size, sex, and race is found to be less effective on credit decision.

Crook (1996) replicates Jappelli’s (1990) study with 1989 data and examines whether the client characteristics, which predict the probability of households being credit constrained, have changed or remained the same between years 1983 and 1989 in the United States. According to his study, more years of schooling of a household head would also be expected to increase future income, with consequent increases in the household’s demand for credit and the supply. Unlike Jappelli, he argued that having received more education enables a potential borrower to be more capable to forecast his/her payback ability, helping the decision of lender. There is tenuous evidence that the probability of default decreases with age. In the case of family size, there is clear evidence that the probability of default increases as the number of children increases.

Roszbach K. and Jacobson T. (1998) built a statistical model in order to measure the risk of sample loan portfolio and show how the model helps to evaluate alternative lending policies. They found that income does not affect credit-granting decision and being a male significantly decreases the chance of being granted a loan. In addition, homeowners have more chance of being granted a loan. Although researches are mostly interested in evaluating the lenders’ decisions on granting loans to credit applicants, the results of previous studies are contradictory.

Not many studies are done to investigate the relationship between characteristics of people that are already accepted (client) and whether they are paying back their loans on time or not. Carling K., Jacobson T., and Roszbach K (1998) examine the Swedish consumer credit clients’ payment performance. According to their study, married applicants tend to pay back their loans faster. A possible reason might be the existence of two wage earners in the Swedish families, which leads to a stable flow of income.

Alternatively, it could reflect the fact that married couples is simply more diligent. Surprisingly, they found a negative relationship between incomes and default risk and the size of limit having no influence on payment performance, whereas increasing the loan size delay payback. Sexton D. E. (1977) analyzes the credit risk in two types of American families: (i) low-income families; (ii) high-income families. Aim of his study is to find out whether or not the variables associated with good credit risks among high-income families are similar to those for low-income families. His study does not analyze the extent of the impact of the independent variables on the dependent variable. However, its numerical results indicate that married couples and homeowners tend to pay their debt on time. On the other hand, credit default risk decreases when the income and age increase.

Ozlem Ozdemir and Levent Borant came up with a logistic binary regression model to explore the relationship between consumer credit client’s payment performances i.e. credit default risk and some demographic and financial variables. Their empirical results indicated that financial variables rather than the demographic characteristics of clients have a significant influence on customers’ pay back performance. Thus, the longer the maturity time, the higher the interest rate, and the higher the credit default risks.

Different from these studies, the current research examines not only the relationship or the effect of regressors on the payment performance of consumer credit clients of a bank, but also trying to predict the probability of consumer default. The following section gives brief information about the empirical model used for this purpose and its data as well.

III. Research Methodology and Data
III.A. Data
We construct a conceptual model to predict the probabilty of consumer credit default in Islamic Bank by using primary data obtained from consumer loans and through consumer credit records as well (Bank annually report). The dataset will be individuals from Bank Muamalat Indonesia (BMI) and Bank Shariah Mandiri (BSM) who were granted a loan between the year 2003-2005. In this case, the loans are either still paying regular installments and its margin or has been amortized completely. Our data contains credits, which are repaid monthly with installments that are constant along the payback period.

The hypothesis for each independent variable to express our expectation about the relationship between each independent and the consumer financing default are stated below:

1. H1 : There exist the relationship between character and the probability of consumer financing default in Islamic Bank.

2. H1 : There exist the relationship between capacity and the probability of consumer financing default in Islamic Bank.

3. H1 : There exist the relationship between capital and the probability of consumer financing default in Islamic Bank.

4. H1 : There exist the relationship between condition and the probability of consumer financing default in Islamic Bank.

5. H1 : There exist the relationship between collateral and the probability of consumer financing default in Islamic Bank.

III.B. Research Methodology
For researh purposes, we employ Logistic Binary Regression Model (LBRM) which will be discussed briefly in the following:
III.B.1. Chi-Squared Test of Contingency Table
Chi-Squared test of contingency table is used to determine whether two variables in population are independent.
Hypothesis :
H0 = The two variables are independent
H1 = The two variables are dependent
Chi-Squared test of contingency table between observed frequency with expected frequency based on:
whereby :
χ2 = Value for random variable which sampling distribution approches chi-squared distribution.
oi = observed frequency for cell-i
ei = expected frequency for cell-i
III.B.2. Logistic Binary Model
Logistic regression method as linear regression, is statistic analysis tool which trying to describe the relationship between dependent variable and one or more independent variables. (Agresti, Alan 1990)

The basic different between linear regression and logistic regression is lies on its dependent variable. Dependent variable in linear regression is binary variable or dichotomous in logistic regression. The independent variable in logistic regression coul be categorical variable or interval variable. Whereas in linear regression, either dependent variable or independent variable must be scaled interval.

Conditional opportunity for dependent variable which has criteria determined by , therefore logistic binary regression model for such function is:
In the comprehension of Generalized Linier Model, relationship function that well fitted with logistic regression model is logit function. Logit transformation as a function of stated as follow (Hosmer and Lemeshow, 1989):
Logistic regression analysis is used to detect the influence of independent variable integratedly toward dependent variable. To obtain the best model, required some crucial steps. First, creating model which accomodate all independent variables and reduce unobvious independent variables statistically by mean of Wald-test statistic. Following afterward comparing the original model with its reductional one by employing G-test statistic.
III.B.3. Parameter Estimation Logistic Regression
Parameter estimation in logistic regression model could be done by using maximum likelihood method which obtained by reducing its probability of density joint function. Such probability of density joint function is expressed by:

Logistic regression coefficient could be found by maximazing logarithm from its maximum likelihood function.

III.B.4. G-test Statistics
Once we have the above probability regression model, following afterward is doing test for the compatibility of logistic model being made. Statistical test for this purpose is G-test. G-test statistic is likelihood ratio test used to test the role of independent variables jointly. General formula for G-test statistic is (Hosmer and Lemeshow, 1989):
L0 = Likelihood value without indpt varbls
L1 = Likelihood value with all indpt varbls

III.B.5. Wald-test Statistics
Wald-test is used to test parameter βi partially (Hosmer and Lemeshow, 1989), based on the hypothesis below:
H0 :
H1 : ; i = 1, 2, 3, ..., p

whereas, its statistical test is:
; whereby:
= estimation of
= Standard Error estimation of
The decision theorem is that rejecting null hypothesis if , which meant that (Hosmer & Lemeshow, 1989).

III.B.6. Coefficient Interpretation
Coefficient interpretation in logistic regression model uses odds ratio value. Odds ratio is a tool to measure association as to estimate how identical, close that has dependent variable for the purpose of estimation result. Odds ratio needs not normal distribution variables and do not exist homoskedastic between variables. In logistic regression, Odds ratio defined as follow:
where is coefficient from logistic regression model. Odds ratio has confidence interval as stated below (Hosmer and Lemeshow, 1989): .

III.C. Methodology Flow
The flow of methodology is as follow:
1. Find out the relationship between independent variables and dependent variable one by one.
2. Parameter estimation using logistic regression.
3. Parameter testing in logistic regression by mien of G-test statistics and Wald-test statistics to observe the influence of independent variable toward dependent variable.
4. Eliminate independent variables that having no significant influence toward dependent variable so that repeat the third step; until find out the best independent variable that having significant influence toward dependent variable.
5. For the purpose of coefficient interpretation (prediction), we employ odds ratio value as a tool.


IV. Research Flow Chart
Formulation of an Estimate Theoretical Model
Collection of Data
Model Estimation
Interpret Model
Economic or Financial Theory (Previous study)

Is the model statistically adequate?

Reformulate Model
No
Yes
Use for Analysis

V. Research Schedule (Tentative)
The detailed research schedule is attached.

VI. References
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