Estimates for the cumulative logistic regression

We begin the discussion in this section by examining the result of using a single ex- planatory variable. The regression results shown in Table 5.7 use Score10 as the reference category. So a negativeβmeans more borrowers move to a state with a higher behavioural score whenever the explanatory macroeconomic variable increases one unit.

Initiali CPI GDP Interest rate Stock Unemployment

(k,w) β -2Log(L) (k,w) β -2Log(L) (k,w) β -2Log(L) (k,w) β -2Log(L) (k,w) β -2Log(L) 3+Cycle (6,1) -1.7764** 848 (3,1) 0.1119** 855 (6,1) -5.2234* 843 N N N (9,.8) 1.7812** 854 Inactive (12,1) -6.4673* 101530 (12,1) -0.9764* 106849 (6,.8) -9.9927* 99844 (2,.2) 7.8655* 110248 (12,1) 6.016* 106520 Score1 (12,1) -0.9668* 7747 (12,1) -0.1098** 7758 (12,1) -1.8927* 7746 (2,.2) -3.0851** 7749 (12,1) 1.5825* 7739 Score2 (6,1) -1.0983* 87751 (12,1) -0.1692* 88073 (6,.8) -3.4636* 87881 (1,1) -0.6749* 88225 (12,1) 1.7241* 87916 Score3 (6,1) -1.2022* 430217 (12,1) -0.1863* 432117 (12,1) -2.5571* 431345 (3,.8) -3.2326* 432565 (12,1) 2.0705* 430555 Score4 (12,1) -1.0462* 845059 (12,1) -0.1251* 846900 (12,1) -1.844* 844964 (3,.8) -5.8616* 845166 (12,1) 2.2039* 842108 Score5 (12,1) -0.5408* 730487 (12,1) -0.0745* 730792 (12,1) -0.9525* 730495 (3,.8) -3.0535* 730480 (12,.8) 1.2364* 729680 Score6 (9,1) -0.8268* 385572 (12,1) -0.1345* 385961 (12,1) -1.7219* 385425 (3,.8) -3.6684* 385876 (12,.8) 1.6059* 385116 Score7 (12,1) -1.5348* 428421 (12,1) -0.1968* 429894 (12,1) -1.8635* 429469 (3,.8) -4.1701* 430120 (12,1) 2.252* 427946 Score8 (6,1) -1.7928* 680673 (12,1) -0.4607* 683939 (12,1) -2.9207* 684962 (3,.8) -3.0955* 689597 (12,1) 3.5824* 680296 Score9 (12,1) -1.9308* 549049 (12,1) -0.1276* 553407 (12,1) -2.6738* 550782 (1,1) -4.1888* 551750 (12,1) 2.6247* 549195 Score10 (9,1) -2.9673* 428366 (12,1) -0.6563* 433237 (12,1) -2.5793* 434126 (3,.8) -15.8883* 433483 (12,1) 3.8103* 427040

”‘*”’ indicates the parameter is significant at 99% level. ”‘**”’ indicates the parameter is significant at 95% level.

”‘N”’ represents the stepwise cumulative logistic regression cannot find any significant explanatory macroeconomic variable.

Table 5.7: Summary of cumulative logistic model estimates

The number of borrowers moving to a high behavioural score increases with inflation. This is different from the general perception which holds that inflation is an indicator of more challenging times ahead and thus the risk score of consumers will be lower, and the results in corporate research (Figlewski et al., 2006) which indicates inflation is associated with increased risk of a rating downgrade. Our results indicate that behavioural score and CPI move in the same direction. This is because the behavioural scores of borrowers go up during expansion, and so does CPI. One can observe in Figure 1.1 that the year-on-year CPI percentage change was positive from 2005 to 2007. This result shows one should use not only inflation or deflation to predict the direction of the behavioural score movement but also add other economic indicators to help make such estimates.

tion of the macroeconomic variable is the mean of the previous twelve months. So if GDP goes up, borrowers’ behavioural score improves gradually and it takes one year for credit card holders to gain the real benefit. Similar results hold in the corporate risk research which says there is a lower number of credit rating downgrade (Figlewski et al., 2006) or higher default risk (Helwege and Kleiman, 1997) when GDP grows.

Consumers’ scores tend to increase when interest rate goes up as all coefficient esti- mates with respect to the Interest Rate model are positive. The coefficient estimate of 3+Cycle is high and the lag is only six months. This shows interest rate has a more se- vere impact on those in arrears than for standard behavioural score accounts. Moreover, interest rate has a significant impact on Inactive accounts. These people tend to activate their credit card account when the interest rate goes up.

The estimates of the Stock variable show stock market performance is a key indicator. It is however rather hard to find a consistent trend in the regression coefficients. It is evident that there is a huge dependence between Score 10 and Stock market, with regression parameters β = −15.8883. So if stock market goes up, people’s behavioural score improves. (A similar result found by Figlewski et al. (2006) which show reduced credit rating downgrade if the stock market is doing well.) Conversely, when it goes down, their score goes down and it is those in scoreband 10 (the highest) who are most hit.

Unlike the findings in Figlewski et al. (2006) which show labour market have volatile impact on the credit rating, our finding show that the effect of the labour market is clear in our parameter estimates. The parameters are positive and thus indicate the behavioural scores are moving inversely with unemployment rate. The coefficient estimates for Inactive borrowers are significantly higher than those of the other accounts. This indicates that borrowers tend to use their credit cards when the labour market is not doing well.

Initiali Model A Model B

CPI GDP Stock

-2Log(L) Stock Unemployment -2Log(L)

β β β β β 3+Cycle -1.6538** 0.0811 N 846 N N N Inactive -6.2968* -0.1634* 9.9704* 100046 12.1121* 6.7087* 104552 Score1 -0.9267** -0.0314 -3.3048* 7731 -2.4069** 1.3978* 7731 Score2 -1.1747* -0.0227 -1.8722* 87659 -0.2523 1.7104* 87914 Score3 -1.4405* 0.0025 -5.874* 428739 -1.8103* 1.9667* 430410 Score4 -0.9516* -0.0183** -5.6601* 842854 -4.0862* 1.9673* 841003 Score5 -0.448* -0.0351* -3.148* 729955 -3.1522* 1.2489* 729141 Score6 -0.9523* 0.0114 -4.3578* 385007 -3.4841* 1.5761* 384748 Score7 -1.366* -0.0359* -3.105* 428121 -1.463* 2.1433* 427886 Score8 -1.7587* -0.1467* -6.4164* 677831 0.0597 3.5864* 680296 Score9 -1.9944* 0.0805* -3.3807* 547479 -3.0181* 2.36* 548145 Score10 -3.7399* 0.3292* -2.1302* 427866 -0.1625 3.7916* 427040

”‘*”’ indicates the parameter is significant at 99% level. ”‘**”’ indicates the parameter is significant at 95% level.

”‘N”’ represents the stepwise cumulative logistic regression cannot find any signifi- cant explanatory macroeconomic variable.

Table 5.8: Summary of cumulative logistic model estimates - Model A and Model B

more than one variable into the cumulative logistic regression changes the signs of some regression coefficients (highlighted in bold). This is because macroeconomic variables are correlated with each other (as presented in Table 5.2). These collinear variables contain the same information about the behavioural score migration. When one puts all these variables together in a multivariate regression, the coefficient parameters are adjusted in order to give a precise estimation of the behavioural score.

For example, say we examine the linear relationship between the dependent variableZ

and independent variables X and Y. The equations describing the relationships between the dependent variable and each independent variable are:

z = 10 + 0.5x, z = 10 + 0.01y (5.8) Hypothetically, if x and y are independent from each other, then the equation line de- scribes the relationship between z and x and y is:

z = 10 + 0.5x+ 0.01y (5.9) One can interpret this equation as ”‘if the value of x is unchanged and the value of y

increases one unit, the value of z increases 0.5.”’ However, if x and y are correlated, any change in y essentially changes the value of x. In that case, if we still use the above equation to estimate z, then the value of z is too high or too low. Therefore if one puts x

and y together as independent variables of a regression analysis, the coefficient estimates of x and y are different to those presented in (5.9) and are as follows:

z = 10 + (0.5 +δ1)x+ (0.01 +δ2)y, whereδ1, δ2 ∈ <. (5.10)

If one would like to observe the actual impact of the independent variable, s/he should use (5.8). Whereas if the objective is to predict the value of z from x and y, equation (5.10) is used.

Note that as the magnitude of the coefficient estimates of these macroeconomic vari- ables is small, it is possible that any adjustment in these coefficient estimates could change their sign. Model A and Model B can be used later as a prediction of the behavioural score migration whereas one should not use the models’ coefficient estimates to investigate the impact of each individual macroeconomic measurement.