2.3.2  Case Two: A Sole Parent With One Child

Figures 6 and 7 show EMTR profiles and budget constraints of a sole parent with one child (aged nine) based upon the person’s income and the different sources of this income (market income and Family Assistance and welfare payments). Figure 6 is based on an assumed wage rate of $10 per hour and figure 7 is based on an assumed wage rate of $15 per hour. Net incomes are shown on the vertical axes at the left of the figures. EMTRs are shown on the vertical axes at the right of the figures. Hours of work are shown on the horizontal axes of the figures. The extent that personal income taxes reduce gross total income is also shown in the figures. Vertical lines in the figures indicate the hour levels corresponding to personal income tax thresholds applying to market income.

Figures 8 and 9 show the frequency distributions of the hours of work of sole parents. These figures exclude those people with zero hours of work. Given that there are likely to be few observations of particular family types at certain wage rates, wage bands (of below and above median wages for particular demographic groups) have been used to calculate the frequency distributions of hours of work. Figure 8 shows the distribution of hours for those people receiving wage rates up to and including the median wage rate for this demographic group. Figure 9 shows the distribution of hours of work for people receiving wage rates above the median wage rate for this demographic group. The median wage for this demographic group is $11.08 per hour. As the median wage differs from the wage rates assumed in the calculation of EMTR profiles and budget constraints, some variance in the measured distribution of hours of work and the measured distribution of incentives would be expected.

The net Domestic Purposes Benefit abates at a rate of 30% against increases in gross non-benefit income between $80 per week ($4,160 per annum) and $180 per week ($9,360 per annum). When the gross family non-benefit income increases above $180 per week the net Domestic Purposes Benefit abates at a rate of 70% against increases in gross non-benefit income.

As the gross Domestic Purposes Benefit is greater than $9,500, when the person’s non-benefit income is below $80 per week the EMTR is made up of a combination of the 21% tax rate and the 1.2% ACC earners’ levy. When non-benefit income increases to $80 per week the net Domestic Purposes Benefit begins to abate against gross non-benefit earnings at a rate of 30%. The gross benefit abatement is thus 0.380 (given by 0.3 / (1 – 0.21)), the change in gross income is 0.620 (given by 1 – 0.380), the change in disposable income is 0.478 (given by 0.620 (1 - 0.21) – 0.012), and the EMTR is thus 52.2%. (The method for calculating EMTRs is explained in appendix 3.)

This 52.2% EMTR continues until the person’s total gross income (including market and benefit income) equals $20,000. At this point the Family Support Tax Credit begins abating against increases in gross income at 18%.[12] The Family Support abatement is 11.2% (given by 0.62 x 0.18) and the EMTR increases to 63.4%.

When the person’s gross non-benefit income reaches $9,360 the net Domestic Purposes Benefit begins abating at the rate of 70%. The net benefit abatement rate thus increases to 0.886 (given by 0.7 / (1 – 0.21)), the change in gross income is 0.114 (given by 1 – 0.886), the change in disposable income is 0.078 (given by 0.114 (1 – 0.21) – 0.012), and the EMTR thus increases to 92.2%. This EMTR continues until the gross Domestic Purposes Benefit falls below $9,500 and the marginal tax rate applying to this benefit thus falls to 15%. The gross benefit abatement is thus 0.824 (given by 0.7 / (1 – 0.15)), the change in gross income is 0.176 (given by 1 – 0.824), the change in disposable income is 0.127 (given by 0.176 (1 - 0.21) – 0.012), and the EMTR is 87.3%.

The EMTR remains at this rate until the Domestic Purposes Benefit is fully abated. When the benefit is fully abated the family begins to receive the Child Tax Credit. This payment is added together with the Family Support Tax Credit and it is this total figure that abates. The abatement of the Family Assistance programmes is 18% and the EMTR becomes 40.2% (given by 0.18 + 0.21 + 0.012). When the family’s gross income increases to $27,000 the abatement of the Family Assistance programmes increases to 30% and the EMTR increases to 52.2%. When the Family Assistance programmes are fully abated the EMTR is based on only the personal income tax scale, Low Income Earner Rebate, and ACC earners’ levy and initially falls to 22.2%.

A sole parent with one child receiving the Domestic Purposes Benefit faces relatively little disincentive from part-time work, but this disincentive increases so that by about 18 hours of work at $10 per hour (or 12 hours at $15 per hour) there is little incentive to increase market income unless it is possible to work for more than 46 hours per week at $10 per hour (or 30 hours at $15 per hour). At above this point the Domestic Purposes Benefit is fully abated and the family receives the Child Tax Credit. There is thus a reduction in the disincentive to supply labour above this point (although this is weakened by the abatement of the Family Support and Child Tax Credits).

As the median wage differs from the wage rates assumed in the calculation of EMTR profiles and budget constraints, some variance in the measured distribution of hours of work and the measured distribution of incentives would be expected. In spite of this, however, the financial incentives from social assistance programmes do appear to play an important role in influencing the frequency distribution of hours of work of different demographic groups.

Relatively small numbers of sole parents with one child and with hourly wages equal to or below the median for the demographic group ($11.08) locate in the abatement-free zone. The earlier data on the distribution of EMTRs among beneficiaries, however, suggests that there could be a significant proportion of beneficiaries with zero hours of work. The frequency distribution of hours of work of these sole parents demonstrates a mode at around 15 hours. This mode reflects changes in the budget constraint that arise between the $80 abatement-free zone and the increase in the net benefit abatement rate to 70%. Further, reflecting the relatively flat nature of the budget constraint between the point at which the benefit begins abating at 70% and the point at which the benefit is fully abated, fewer people work as the hours of work increase along this segment of the budget constraint. At this wage rate few people locate at the point above which the benefit is fully abated.

As with sole parents with one child and wages equal or below the median ($11.08), relatively small numbers of sole parents with one child and wages above the median locate in the abatement-free zone and there is a small mode at around 15 hours (reflecting changes in the budget constraint that arise between the $80 abatement-free zone and the increase in the net benefit abatement rate to 70%). However, with a higher hourly wage rate the abatement of the Domestic Purposes Benefit occurs over a shorter range of hours. The anti-mode at around 25 hours reflects the change in the slope of the budget constraint due to the completed abatement of the Domestic Purposes Benefit and the payment of the Child Tax Credit. Significant numbers of sole parents who work at wage rates above the median hourly wage also work for 30 hours per week or more. The incentives that arise from the personal income tax scale, Low Income Earner Rebate, and abatement of the Family Assistance programmes are relatively significant for people who work these hours.

Overall, few people seem to locate in the abatement-free zone for the Domestic Purposes Benefit, but there may be a large number of people at zero hours of work who could nevertheless be affected by a change to this zone. Further, small modes at around 15 hours per week reflect the changes in the slopes of the budget constraints due to the abatement of the Domestic Purposes Benefit. Roughly similar numbers of sole parents work these hours at both hourly wage bands. At the higher wage band, however, larger numbers of sole parents locate at the point above which the benefit is fully abated. The lower the hourly wage the greater the significance of the abatement of the benefit and the abatement-free zone for financial incentives.

In comparison to other family types, the numbers of people in both distributions of sole parents by hours of work are relatively small. Significant numbers of sole parents who work do so for around 15 hours per week. Significant numbers of sole parents who work at wage rates above the median hourly wage also work for 30 hours per week or more.

Figure 6: EMTR Schedule and Budget Constraint of a Sole Parent with One Child (aged 9) and with a Wage Rate of $10 per Hour

Figure 7: EMTR Schedule and Budget Constraint of a Sole Parent with One Child (aged 9) and with a Wage Rate of $15 per Hour

Figure 8: Frequency Distribution of Hours of Work of Sole Parents (Wages up to and including Median ($11.08) for Group)

Figure 9: Frequency Distribution of Hours of Work of Sole Parents (Wages over Median ($11.08) for Group)

Notes

• [12]From 1 April 2004 the Family Assistance abate thresholds will increase to $20,356 (from $20,000) and $27,481 ($27,000).