4.3 Factors associated with the level of family debt

This section summarises the findings from our analysis of the variation in debt levels across families. We estimated basic regression models to test whether certain characteristics could be identified as being significantly related to variation in debt levels. The purpose of the models was to identify associations in the data and they are not intended to be used for prediction. Note it is possible they may suffer from presence of various forms of endogeneity, as it is difficult to account for this with one cross section of data.[22]

Models were estimated for non-partnered individuals and couples separately with the log of debt as the dependent variable. Singles and couples who reported no debt were excluded from the models. The general form of the regression models is given by:

ln(Debt) = f(Age, Ethnicity, No. children, Migrant status, Education, Health, Region, Assets, Income, Income source, Employment, Marital status, Home ownership) + ε

in which the log of debt is associated with a set of explanatory variables and an error term (ε). Ordinary Least Squares (OLS) was used to estimate the coefficients.[23] Selection models were considered but we were unable to find a variable in the dataset that was theoretically related to the choice to have debt but not related to the level of debt.[24]

Many of our explanatory variables were themselves correlated. Examples are: home ownership and assets; age and income; employment and income. While this does not affect the overall fit of the model to the data, it can reduce the precision of the estimated coefficients on the correlated variables and make them difficult to interpret. The coefficient on a variable is usually interpreted as the effect of a unit change in that variable on the dependent variable, holding all other variables constant. In the presence of multicollinearity, this interpretation is less valid. For example, in our dataset, there were very few home owners in the lower part of the asset distribution. Given this data, it would have been unreasonable to expect the models to untangle the home ownership and asset level effects. It is therefore not sensible to think of the coefficient on home ownership as the effect on debt due to becoming a home owner, independent of asset levels. In this case, it is the simultaneous change in home ownership and asset levels that is associated with a change in debt levels, and the actual effect is likely to be larger than that implied by the coefficient on home ownership.

Tables 8 and 9 present a summary of the factors found to be associated significantly, in a statistical sense,[25] with either a higher or lower level of debt.[26] A finding of statistical significance is not particularly meaningful on its own and so, in order to quantify the effect of each significant factor, marginal effects were computed. The marginal effect measures how the model's estimate of total debt changes in response to a change in one of the explanatory variables, while all other variables are held constant.[27] As an example, consider the first factor, age, listed in Table 8. The mean age of all non-partnered individuals in the sample was 37.5 years. The marginal effect is given for the average age plus 10 years.[28] The estimated level of debt in 2003/04 for a person aged 47.5 is $3,867 lower than for one aged 37.5 when all other variables are held at their sample mean values. Although the marginal effects have been calculated holding all other factors constant, as noted earlier, the presence of collinear variables means they should be interpreted cautiously.

The regression model for non-partnered individuals accounted for 33% of the variation in (log) debt. The largest statistically significant marginal effect was estimated for home owners relative to renters, where home owners were estimated to have had about $17,000 more debt, all else constant. Asset decile effects were also relatively large; being in the top three deciles was associated with debt levels being about $10,000 higher than decile 1, all else constant.[29] Having a degree was associated with debt levels of about $8,000 more than those with no qualifications, and being separated or divorced was found to be associated with debt levels being about $4,000 and $5,000 higher respectively than those who had never married. All else constant, those unemployed or out of the labour force were estimated to have total debt some $3,000 lower than those in employment.[30] Income effects were not particularly significant although being in income decile 5 or 6 was associated with slightly lower levels of debt than deciles 1 ($3,000 lower) and 10 ($5,000 lower). The smallest significant marginal effects were school qualifications relative to no qualifications ($2,000 more debt) and for males relative to females ($1,000 more debt). Ethnicity, number of dependent children, migrant status, self-reported health, region of residence and maximum source of income were all found to have statistically insignificant coefficients, meaning there was insufficient evidence to reject the hypothesis that they had no effect on debt after controlling for the other variables in the model.

The regression model for couples (see Table 9) accounted for 40% of the variation in (log) debt. The largest statistically significant marginal effects were estimated for asset deciles 9 and 10, at $42,000 and $55,000 respectively relative to decile 1; further, a large significant effect of about $30,000 relative to deciles 4 to 8 was also estimated for decile 10. The home ownership effect for couples was estimated at $27,000. Relative to couples in the bottom income decile, those in deciles 9 and 10 tended to have about $20,000 more debt.[31] A large positive effect was estimated for couples where both partners were employed, at about $25,000 relative to couples where one partner was unemployed and the other was out of the labour force[32], $16,000 relative to couples where both were out of the labour force and $5,000 relative to couples where one partner was employed. The model estimated a negative age effect over the relevant range, where couples with an average age of 54.5 tended to have about $17,000 less debt than couples with an average age of 44.5. Couples with at least one partner identifying as Maori/Pacific tended to have about $7,000 more debt than European couples.[33] The ethnicity classification associated with the lowest debt levels was both partners classifying as “other” (ie, non-European and non-Maori/Pacific) with a marginal effect of -$8,000 relative to European, and about -$15,000 relative to couples where at least one partner is Maori/Pacific. Couples living in the South Island outside of Canterbury tended to have debt levels that were about $10,000 less than couples living in Auckland or Waikato. Distinct marital status effects were identified: both partners responding as never married was associated with $8,000 less debt than married couples; couples with other mixtures of marital status tended to have levels of debt that were about $12,000 higher than married couples. Education, maximum source of income, number of dependent children, migrant status, self-reported health status and years in employment all had statistically insignificant effects.

¹ Marginal effects on debt are non-linear and have been evaluated relative to the stated category, holding all other variables at sample means. The base estimate of debt level to which the marginal effect relates appears in brackets. The criteria for statistical significance is <0.05.

² The share in each asset and income decile does not necessarily equal 10% because the deciles are calculated over all non-partnered individuals, including those without debt.

¹ Marginal effects on debt are non-linear and have been evaluated relative to the stated category, holding all other variables at sample means. The base estimate of debt level to which the marginal effect relates appears in brackets. The criteria for statistical significance is <0.05.

² The share in each asset and income decile does not necessarily equal 10% because the deciles are calculated over all couples, including those without debt.