Methodology

Our study uses logit analysis¹ on financial ratios² of commercial banks in Indonesia and Japan to compare the two domestic models with a cross-country model of bank failure prediction.

A. Data

Our data on financial ratios is drawn from the balance sheets and income statements for the entire population of commercial banks in Indonesia and Japan. In Indonesia, the sample includes state-owned banks, private national foreign exchange and non-foreign exchange banks, regional development banks, joint-venture banks, and foreign banks for fiscal years 1997-2003. The population of Japanese commercial banks includes city banks, long-term credit banks, trust banks and regional I and II banks for fiscal years 1978-2001³.

We investigate the failure prediction value of 17 financial variables that proxy for the fundamental condition and performance of the banks’under analysis.

The variables are as follows:

1. CaD = Capital to Deposits
2. EtD = Equity to Deposits
3. LtE = Loans to Equity
4. LtC = Loans to Capital
5. FAE = Fixed Assets to Equity
6. FAC = Fixed Assets to Capital
7. ETA = Total Equity Capital to Assets
8. ROE = Return on Equity
9. ROA = Return on Assets
10. LAD = Liquid assets-short term borrowing to total deposits
11. ERA = Equity to risk assets (= assets - cash – CB DD - government securities)
12. LTA = Loans to Assets
13. STA = Treasury Securities to Assets
14. OTA = Other Securities to Assets
15. CTA = Capital to Assets
16. CDL = Core deposits to Total Liabilities
17. NPL = Non Performing Loans to Total Loans
18. LtD = Total Loan to Total Deposit

B. The Logistic Function

The logistic function, given as varies from 0 to 1 as θ varies from -∞ to +∞⁴. Replacing θ with an index of bank characteristics xb, the logistic model can be used to express the likelihood of bankruptcy (Y=1) or survival (Y=0) as follows:

where: P_it : probability that ith bank will fail (Y=1); 0 ≤ Pi ≤ 1 X_i : predictor variable for ith bank Z_i : linear function from predictor variable; -∞ ≤ Z_i ≤ +∞ t : time k : period (yearly) before bank goes bankrupt e : natural logarithm; e = 2,7182 β : regression coefficients

After estimating the logistic model with the full set of financial data, we do a stepwise logistic regression that uses factor analysis⁵ to reduce the number of independent variables in the regression by identifying those variables which are most informative in predicting bankruptcy.

In the logistic estimation, we also employ maximum likelihood technique as an approach to calculate the intercept and coefficient parameters. We

P is the probability of Y_i = 1 given X_i(P_i = P(Y_i=1/X_i)
P is the probability of Y_i = 0 given X_i(P = P(Y_i= 0/Xi)=1 - P_i

The probability of N values of sample Y given all N sets of values X_i is calculated by multiplying the N probabilities:

The maximum likelihood estimation (MLE) chooses estimates of the intercept and coefficients of parameters from a set of K independents variables (i.e. ) which would make the likelihood produces estimate of Y as large as possible. The likelihood function is:

Intercept and coefficient of b’s are solved from the following method:

Recall the following equation:
L(Y/X, b) = P(Y/X)

To obtain the slope estimates of and we differentiate log L with respect to α and β, set the result to zero and solve:

C. Diagnostic Tests

After estimating both the full logistic model and the stepwise logistic model, we conduct some diagnostic tests on the appropriateness of the three prediction models: the domestic models for Japan and Indonesia and the cross-country model. A goodness of fit test is conducted using the likelihood ratio statistics as proposed by Aldrich and Nelson (1984) and McFadden (1973), which measures the difference between observed value and predicted value of dependent variable (the probability of bankruptcy) and tests the null hypothesis that there is no statistically significant difference between actual observed bank failure and classification using the bank failure prediction model.

We also look at the predictive power of our models. This is a test of the power of the model to predict bankruptcy or survival of the population of banks. Our bankruptcy prediction model generates a number between 0 (zero) and 1 (one) representing the probability of bankruptcy. Depending on the set cut-off-point for classification, the predictive power of the model can be expressed by four ratios: accurate estimation of bankruptcy, accurate estimation of survival, false classification of a surviving bank as a bankruptcy (type I error) and false classification of a failed bank as a survivor (type II) error (refer to Santoso (1996)). The cut-off-point represents the probability level where a bank is classified as signaling bankruptcy or not and therefore plays a critical role in determining the predictive power of the model. We follow the suggestion of Santoso (1996) suggests the use of the proportion of bankrupt and non-bankrupt bank in the sample (or in our case actual population) as the idea cutoff- point.

Finally, we include some graphical representations of the specificity, the fraction of observed survivals that are correctly classified by the model, and sensitivity, the fraction of observed bankruptcies that are correctly classified, of the prediction models and compare these for the three models.

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