BIBLIOTECA UNIVERSITARIA DE HUELVA INTRODUCCIÓN

This subsection introduces the two-level credit scoring model which in- cludes group-level characteristics. The scorecard is presented in [2.7]. It expands the random-intercept scorecard given in [2.5] by inserting the microenvironment- level characteristics in the second-level model for the varying-intercept }_~. The microenvironment-level variables are denoted by ´? in the second-level model. Specifying group-level characteristics in a scorecard helps to explore the impact of the microenvironment-level information on the probability of default. It also improves the estimation of the area-specific intercepts.

Similarly to the previous case, the area-specific intercept is modelled as given in [2.8]. Additionally to the population average intercept }₀ and the ran- dom term O_,@ the model for the varying-intercept now includes four microenvironment-level variables _,y , for m=1,..,4. The group-level variables ,y vary across J=61 microenvironments but take the same value for all bor- rowers 1, . . , within a given microenvironment j.

Qz9 1{, O,@| =&0>}~A BC&1A B.1D1E10/A BFGE1744H3 I A BJK)A BLMNO1/A BPQ&%1//&'A BR.S

A B_TS_4UV6 A B_WX1E0A B_@Q/0_63VA BYZ, [2.7]

}~ }@A ´? A O,@,

´? ?n1_C&1A ?nn_{UVI6V I}A ?_F 0&1/A ?_JX&''11, [2.8] O,H | ,  ~ j 0, 3.

Microenvironment-level variables characterize the economic and demog- raphic conditions in the borrowers’ residence areas. The variables are n1_’4HyV- average income in the living area j (measured in thousands of dol-

lars); 0&1/ -percentage of retail, furniture, building materials and auto store sales in the total retail sales in the market; X&''11 - percentage of college gra- duates in the residence area and nn_{UVI6V I} – the share of African-American (Hispanic) residents in the region.

The two-level credit scoring model with the microenvironment-level variables and a varying-intercept is fitted in Stata by using maximum likelihood. Table 2.10 provides the estimated coefficients of the individual and group-level variables, and the standard deviation of the area-specific intercept.

The fixed-effect estimates of the individual-level variables are essentially the same as in the scorecard presented in [2.5]. This is quite reasonable as including the microenvironment-level characteristics only modifies the random- intercept model. The standard deviation of the microenvironment-intercept is smaller than in the credit scoring model without group-level variables. This is due to the fact that the second-level characteristics partly explain the variation between microenvironments.

The estimated coefficients for the microenvironments-level variables show the impact of the living area conditions on the riskiness of applicants for a loan. Higher per capita income has a negative effect on the riskiness of a borrower. Similarly, the living area share of individuals with a university degree negatively impacts the probability of default. The result is intuitive and implies that the effect of higher education on default is negative not only at the borrower-level but also at the microenvironment-level.

In contrast, the impact of the variable share of African-American residents on default is significant and positive. The coefficient of nn_{UVI6V I} explains how the demographic composition of residents in the area influences the probability of default. It is evident that borrowers within microenvironments with a large share of African-American and Hispanic residents have higher exposure to area-specific risks which trigger default.

Variable Coefficient Std.err. z P>|z|

Total Income -0.041 0.004 -9.34 <0.001

Number of dependents 0.114 0.033 3.47 <0.001

Trade accounts -0.038 0.008 -5.02 <0.001

Bank accounts (ch/ savings) -0.426 0.082 -5.19 <0.001

Enquiries 0.373 0.017 22.40 <0.001

Professional -0.332 0.096 -3.47 <0.001

Derogatory Reports 0.615 0.030 20.51 <0.001

Revolving credit balance 0.015 0.004 3.45 <0.001

Previous credit -0.060 0.018 3.16 0.004

Past due 0.221 0.068 3.25 <0.001

Own -0.285 0.100 -2.85 0.004

Constant -0.860 0.210 -4.09 <0.001

Microenvironment-level variables, }_~

Living area per capita income -0.017 0.008 -2.12 0.033 Share of African-American residents 0.012 0.003 4.00 <0.001

Share of college graduates -0.034 0.014 -2.42 0.015

Infrastructure of shopping facilities 0.037 0.029 1.27 0.204 Random-effects Estimate (Std.err.) 95% Confidence interval Standard deviation of intercept, _3‹ 0.38(0.08) [0.24; 0.59]

Table 2.10. Estimation results for the two-level random-intercept model with microenviron- ment-level explanatory variables. The random-intercept variance is given in the last row in the table.

The effect of the infrastructure of shopping facilities on default is positive. One possible interpretation of the result may be that a good access to various department stores and shopping malls provokes spending and initiates borrowing. In addition, I use in the empirical analysis the credit history data on the consumer loans which individuals regularly use for making small purchases of durable goods, buying cars or covering medical bills.

I apply a ROC curve analysis to assess the classification performance of the credit scorecard with group-level characteristics and a varying-intercept. Figure 2.4 shows the ROC curve and pointwise confidence bounds.

Figure 2.4. ROC curve for the two-level credit scoring model with an area-specific intercept and group-level variables. The optimal cut-off point is indicated by the red triangle (₁ 0.2264.

The summary of the ROC curve analysis, the Gini coefficient and a classification table for the optimal cut-off point are provided in Table 2.11.

The area under the ROC curve and the Gini coefficient are increased. The AUC is 0.017 higher than in the case of the credit scoring model without the microenvironment-level variables. The difference is not large; however, the 95% confidence intervals for the AUC values do not overlap which implies the areas are significantly different from each other ([0.811; 0.825 ] versus [0.794; 0.808]).

Another important improvement of the current version of the credit sco- ring model over the scorecard without group-level variables is that the former model has a higher rate of correct classifications. The rate of correct classifications is calculated at the threshold which corresponds to the maximal

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 S e n si ti v it y 1-Specificity

ROC: Microenvironment-intercept credit Scorecard with group-level variables

sensitivity/specificity pair ( 0.2264). The specificity is also higher at this point. True Classified ₁ 0.2264 D ND Total Default 235 308 543 Non-default 190 3447 3637 Total 684 3755 4180 Correctly classified, % 87.16 Sensitivity, % 55.22 Specificity, % 91.81

ROC curve metrics:

Area under the ROC (AUC) 0.818

Standard error 0.005

95% confidence interval [0.811; 0.825]

Gini coefficient 0.636

Accuracy ratio 0.701

Table 2.11. Summary for the ROC curve analysis and the classification table for the optimal cut-off point, 0.2264, for the microenvironment-intercept scorecard with the group-level variables.

2.3.3 Microenvironment-specific coefficients in