5.2 Factors associated with debt servicing costs relative to income
In this section we summarise our more detailed analysis of factors associated with the variation in debt servicing costs relative to income across family units.
The analysis uses two types of regression models to quantify relationships between a wide range of characteristics and debt servicing costs relative to income: Ordinary Least Squares (OLS) models, and Logistic models.[36] With the exception of income, which is excluded from these models,[37] the explanatory variables are identical to those used in our debt regressions in Section 4.3. As was the case for the debt regressions, these models may suffer from endogeneity and they are not intended to be used for prediction.
The form of the OLS model follows, in which the log of ratio of debt servicing to income was the dependent variable:
Log (debt servicing/income) 
where the Xi are the set of characteristics, the 
are the regression coefficients, and 
is the error term. On the basis of the regression coefficients, we have estimated the marginal effect on the debt servicing ratio of changes in characteristics, and the change in the probability that debt servicing costs exceeded 30% of income.[38]
We also estimated logistic regression models where the dependent variable was a binary variable taking the values of 0 or 1 depending whether the individual or couple has debt servicing costs of less than or greater than 30% of their income. In this regression we were seeking to identify the characteristics associated with the probability that debt servicing exceeds 30% of income.
Logit[39] (probability that debt servicing/income > 0.3)
In both models the data sets were restricted to those having both debt servicing costs and positive income.[40] The regression models were re-estimated excluding those who had equivalised income above the median, but as the results were broadly consistent they have not been reported. We initially included various interaction terms in the models, but found none that significantly improved the fit of the models to the data.
The factors found to be associated with the likelihood of having debt servicing costs in excess of 30% of income are summarised in Table 11 for non-partnered individuals and Table 12 for couples. Full details of the regression results are given in Appendix Tables A.5 and A.6. As with the debt regressions in Section 4.3, many of our explanatory variables were themselves correlated and so the estimated coefficients and marginal effects should be treated with caution.
The first column of Tables 11 and 12 reports the sample mean or proportion of each of the significant variables. For example, 36% of non-partnered individuals were home owners in 2003/04. In the next two columns we report the results of the OLS model. The first of these is the marginal change in debt servicing as a percentage of income associated with a change in the value of an explanatory variable relative to the stated base category. For example, non-partnered individuals in the highest asset decile tended to have debt servicing costs that were 2.9 percentage points more of their income than those in the lowest asset decile, holding all other variables at their sample means. The second OLS column reports the marginal change in the probability of having debt servicing costs greater than 30% of income for one category relative to another. For example, those not in the labour force were 3.2% percentage points less likely to have debt servicing costs greater than 30% of their income than individuals who were employed, holding all other variables at their sample means.
| Sample mean or proportion | Least squares regression | Logistic regression | ||
|---|---|---|---|---|
| Marginal change in debt servicing as a percentage of income | Marginal change in the probability that debt servicing exceeds 30% of income | Marginal change in the probability that debt servicing exceeds 30% of income | ||
Relative to mean age |
||||
| Age + 10 yrs | 38.5 | -1.2% | -4.0% | |
Relative to renters |
||||
| Home owner | 36% | 4.3% | 12.2% | |
Relative to bottom asset decile |
||||
| Asset decile 3 | 10% | 0.7% | 2.3% | |
| Asset decile 4 | 10% | 1.1% | 3.5% | |
| Asset decile 5 | 11% | 1.7% | 5.6% | |
| Asset decile 6 | 10% | 0.9% | 3.1% | |
| Asset decile 7 | 11% | 2.8% | 8.6% | 4.6% |
| Asset decile 8 | 11% | 3.3% | 10.2% | 7.7% |
| Asset decile 9 | 11% | 2.9% | 9.1% | 10.9% |
| Asset decile 10 | 10% | 2.9% | 8.9% | 15.8% |
Relative to European |
||||
| Non-Euro, non-Maori/Pacific | 5% | 6.4% | ||
Relative to Auckland |
||||
| Canterbury | 15% | -0.7% | -2.1% | |
Relative to employed |
||||
| Unemployed | 3% | 5.6% | ||
| Not in labour force | 24% | -1.0% | -3.2% | |
Relative to maximum income from earnings |
||||
| Maximum income from government | 27% | 1.3% | 3.8% | 5.1% |
| Maximum income from other source | 12% | 4.6% | ||
Relative to never married |
||||
| Divorced | 15% | 2.2% | 6.4% | |
| Separated | 11% | 1.2% | 3.7% | 2.4% |
1Marginal effects are non-linear and have been evaluated relative to the stated category, holding all other variables at sample means.
Notes
- [36]Median regressions were also estimated but it was not possible to correctly account for the sampling weights (using Stata) and so the results have not been reported.
- [37]Income is used in the construction of the dependent variable and so has not been used as an explanatory variable.
- [38]The predicted probability of an observation having a debt servicing ratio above any given level can be obtained from the results of the debt servicing ratio OLS regression. Under the standard OLS assumptions, the residuals are normally distributed with zero mean and variance σ2. Therefore the probability of an observation with characteristics represented by x having a debt servicing ratio exceeding 0.3 is F[(βx-ln(0.3))/σ)], where F is the standard normal cumulative distribution function with mean of zero and standard deviation of 1. Ravallion (1996) argues that there is no need for a binary response estimator when the underlying “latent” variable is actually observable. In fact, replacing the observable variable with a binary variable is essentially throwing away information about the variation in the dependent variable.
- [39]The transformation is the log of the ratio of the probability of a positive outcome to a negative outcome, (ie, the log of the odds). The logit transformation results in a dependent variable that can be linearly related to the explanatory variables.
- [40]These are the requirements for our dependent variable (the log of debt servicing to income) to be defined. Those reporting non-positive income represented 1.8% of non-partnered individuals with debt and 0.3% of couples with debt. Further, a debt servicing ratio cannot be logged for those with debt who have no debt servicing costs. Respondents in this situation were those with student loans (but no other debt) who had earnings below the threshold for repayments. They represented 7.2% of the sample of non-partnered individuals with debt, and 0.6% of the sample of couples with debt.
