Taxes, Transfers and Redistribution

This subsection examines how inequality indices vary for post-tax-and-transfer incomes, compared with the inequality of GTI. The measures used are the Gini, Atkinson, Kakwani and Reynolds-Smolensky indices described in Section 3. These have been constructed for different units of analysis. Table 3 shows three cases: using individual incomes, household incomes and income per adult-equivalent person. Using the household as the unit of analysis recognises that, with income sharing within households, it may be more appropriate to consider inequality in the distribution of income between households. The ‘household income’ inequality measures in Table 3 are estimated across individuals but where each adult within the household is assumed to receive an equal share of household income.[18]

The use of household income per adult-equivalent person further recognises that sharing economies may depend on household composition and size - where there are several adults and/or children within a household. For example, adding a second or third adult to a household, and the inclusion of children may provide differing opportunities to share income. A number of adult equivalence scales are used in the literature, many of which can be captured by the simple form:

where m is the number of adult-equivalents, 0 ≤ q ≤1 captures the weight attached to each additional child in the household, and 0 ≤ α ≤ 1 captures scale economies. Table 3 adopts a commonly used scale in NZ Treasury's tax projections - the ‘Jensen scale’, which approximately equates to θ = 0.7; α= 0.6.[19] Sensitivity to this scale is examined below.

A feature of the inequality indices reported below is that in all cases these relate to inequality across individuals where, in the case of ‘household income’ and ‘adult-equivalent household income’, the income is assumed to be shared equally among the adult household members, or the adult-equivalents as measured by (13). For example, consider a two-adult household with a household income of $50,000. With no weighting, the household is considered to have two adults with $25,000 each. Alternatively, using an adult equivalence scale such as (n_a + qn_c)^a with α = 0.6, there are 2^0.6 = 1.516 adult-equivalents in the household yielding 2 individuals each with an adult-equivalent income of $32,988.

Table 3 reports inequality measures using the following abbreviations: Y = gross taxable income; T = tax; W = income after tax; S = transfers; Z = income after tax and transfers; g = ratio of tax to income. In discussing the results, the focus is mainly on the indices for incomes per adult-equivalent, as other results reveal a similar pattern. Inequality of gross taxable income, using either G_Y or A_Y, is generally lower for comparisons across households than across individuals, with the use of the adult-equivalence scale reducing inequality further. This is not surprising since inequality indices based on household incomes effectively remove intra-household inequality.

Using an adult-equivalence scale gives relatively higher income to individuals within larger households compared to weighting all adults equally. Hence the use of an adult equivalence scale improves inequality (compared to no scaling) if households on lower incomes tend to have lower ‘adult equivalents’ - either due to fewer additional adults or a higher ratio of children to adults.[20]

Table 3 - Inequality Measures for Incomes, Taxes and Transfers

Inequality measure	Based on distribution across individuals using:
	Individual incomes	Household incomes	Adult-equivalent H'hold incomes
Gini (G) & Concentration (C) Indices:
GY	0.464	0.407	0.391
CW	0.432	0.381	0.363
CZ	0.406	0.352	0.333
CT	0.565	0.490	0.479
CS	0.362	0.304	0.489
Atkinson Index:	AY	AY	AY	[AZ]
A (ε = 0.2)	0.077	0.057	0.052	[0.038]
A (ε = 0.5)	0.190	0.139	0.128	[0.094]
A (ε = 0.8)	0.305	0.221	0.202	[0.149]
A (ε = 1.0)	0.392	0.277	0.252	[0.187]
A (ε = 1.5)	0.730	0.492	0.453	[0.291]
Kakwani (K) and Reynolds-Smolensky (L) Progressivity Indices:
KW	0.101	0.083	0.088
KZ	0.218	0.213	0.216
LW	0.032	0.025	0.027
LZ	0.052	0.050	0.055
Tax ratios:	g (tax) = 0.238
	g (tax - transfers) = 0.212

Considering the Gini and Concentration indices in Table 3 it can be seen that the tax system modestly reduces inequality from G_Y = 0.391 to C_W = 0.363, with transfers inducing a further reduction to C_Z = 0.333. The C_T and C_S indices also reveal the redistributive nature of taxes and transfers since these exceed the value of G_Y = 0.391; for a proportional tax the concentration curve coincides with the Lorenz curve, such that G_Y = C_T. Note that this does not apply to transfers since if these are progressive the concentration curve for transfers (unlike the Lorenz curve) lies above the 45^o line; the more progressive are transfers, the further above the 45^o line is their concentration curve, and hence larger C_S.[21]

Table 3 shows that, when considering the distribution across adult-equivalent household incomes, taxes and transfers (essentially WfF) are similarly redistributive: C_T = 0.479, C_S = 0.489. However, across individuals or households, transfers are noticeably less redistributive than taxes. This likely reflects the fact that, since WfF is related to child numbers and ages, it has a greater impact when these are given greater weight via the adult equivalence scale. However, across individuals, because WfF affects a relatively small fraction of taxpayers, it has less redistributive effect than taxes.[22]

The L indices of tax and transfer progressivity in Table 3 (where L = G_Y - G_Z) show that the gross income Gini is reduced by about 2.5 points (0.027) by the tax system and by a similar further amount by WfF. The same message emerges from the Kakwani, K, indices measuring the concentration of tax (or tax & transfers) relative to gross incomes. Tax can be seen to be more concentrated (relative to a proportional tax) by almost 9 points (0.088) and taxes and transfers by over 20 points (0.22). The Atkinson indices in Table 3 also confirm that the inequality across individuals using income per adult-equivalent is less than for individual incomes or household incomes. For example, A_Y (ε = 0.5) falls from 0.19 for individual incomes to 0.13 for adult-equivalent incomes. A_Z (ε = 0.5) is noticeably lower at 0.094.

The Kakwani and Reynolds-Smolensky measures of progressivity and redistribution are all Gini-based and thus related to Lorenz and concentration curves. These are illustrated in Figure 3, where all curves are based on adult-equivalent incomes. The Lorenz curve of post-tax-and-transfer income is closer to the line of equality than that of post-income-tax income, which in turn is closer to the line of equality than that of gross income. Figure 3 also shows the concentration curve for tax payments. This lies substantially outside the various Lorenz curves, reflecting the disproportionality (progressivity) of personal taxes. Adding transfers (not shown) would magnify the progressivity effect observed for taxes alone.

Figure 3 - Lorenz and Concentration Curves

 

The inequality indices for New Zealand in Table 3 may be compared with similar measures estimated for Australia. For example Creedy and Kalb (2006) estimate Atkinson indices for ‘net income’ (post-tax-and-transfer income), for 1997/98, similar to those in Table 3. For an adult-equivalence scale with a = 0.6 (close to the value used in Table 3) they obtain A_Z(e = 0.5) ≈ 0.07. Creedy et al (2008) provide estimates for 2003/04; they estimate G_Z = 0.285, A_Z(ε = 0.2) = 0.027, and A_Z(ε = 0.5) ≈ 0.06.[23] These values compare to our New Zealand estimates of G_Z = 0.336, A_Z(ε = 0.2) = 0.043 and A_Z(ε = 0.5) = 0.108. Though differences in income definitions, equivalence scales etc make cross-country comparisons tricky, these measures tend to suggest that net incomes are more equally distributed in Australia than New Zealand.[24]