The Distribution of Pre-Tax Incomes

There are number of possible income distributions we could consider, such as for earned income only, wage and salary income only, and all income excluding benefits. Similarly there are various alternative units of analysis, such as all individuals, individuals in the labour market, households, or families. We begin by considering only private/personal taxable income, PGTI, (quadrant I in Table 1) and gross taxable income, GTI, (quadrants I & II) for individuals, both including and excluding those with zero incomes.[11] Figure 2 shows the distribution of GTI including zero incomes, and Table 2 shows Gini and Atkinson indices for the various definitions. The Atkinson index necessarily includes only positive incomes.[12]

Figure 2 shows the large number of individuals on zero income (around 340k out of a total of around 3.2 million individuals in the distribution). These are largely 15-18 year olds, students and non-workers within households. There is a second mode of around 140k individuals at $13k. Thereafter the number of individuals drops so that there are generally around 10-20k individuals in each $1000 class between $20k and $60, with numbers dropping again to under 10,000 per $1000 class in excess of $60k.[13]

Figure 2 – Distribution of Gross Taxable Income, 2006-07

Table 2 treats the individual as the appropriate unit of analysis. However, concern may be with the inequality of income over all individuals, including those who may have zero income or small amounts of unearned income, despite the possibility that they live within high income households.

The table shows Ginis in this case to be: G_PGTI = 0.608 and G_GTI = 0.512. That is, before receipt of government benefits, income is relatively unequally distributed (recall 0 ≤ G ≤ 1; with G = 0 implying complete equality). Unsurprisingly, the inclusion of benefits reduces the inequality of taxable incomes by around 0.1, or 15 per cent ((0.608 - 0.512)/0.608). When those on zero incomes are excluded, both Ginis are reduced: to G_PGTI = 0.569 and G_GTI = 0.464.

Table 2 also highlights the differences in the Atkinson measures depending on assumed inequality aversion. This indicates that, given the current distribution of income across individuals, and mild inequality aversion at ε = 0.2, A(ε) = 0.077 is obtained for GTI; that is a 7.7 per cent reduction in mean income would be tolerated to achieve complete equality. For greater degrees of inequality aversion of ε = 0.5 and 0.8, the inequality index rises substantially to 0.24 and 0.41 respectively. These results suggest that, given the relatively large numbers of individuals on low incomes in New Zealand, even relatively moderate aversion to inequality, such as e around 0.5, generates a relatively high value of A involving a relatively large drop in mean incomes.

Whether individuals on zero or low incomes are of concern in welfare terms may depend on the choice of unit of analysis.[14] The way in which inequality indices vary depending on this classification is examined below.