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Abstract
This paper illustrates the effects of using different distributions and summary measures, using New Zealand data for the period 2007–2011. Using an annual accounting period, alternative welfare metrics and units of analysis are investigated. In addition, the sensitivity to assumptions about economies of scale within households is examined, and changes in inequality are decomposed into those arising from population and tax structure changes. When considering the period 2007–2010, all measures agree that inequality fell, although the extent of the reduction varies. For the period 2007–2011 (after the tax reforms of 2010) the answer to the question of whether inequality in New Zealand has risen or fallen depends crucially on the combination of welfare metric, income unit, adult equivalent scale and inequality measure used. In empirical studies, it is therefore important to explore a wide range of alternative approaches, providing information for readers to make their own judgements.
Acknowledgements
Access to data used in this paper was provided by Statistics New Zealand under conditions designed to give effect to the security and confidentiality provisions of the Statistics Act 1975. The tables and graphs presented in this report are the work of staff at the New Zealand Treasury and not Statistics New Zealand. The views, opinions, findings and conclusions are strictly those of the authors and do not necessarily reflect the views of the New Zealand Treasury. We are grateful to Christopher Ball, Peter Lambert, Angela Mellish, Robert Stephens and two referees for comments on an earlier version of this paper.
Notes
1. Results were obtained using the Treasury's microsimulation model, Taxwell (the ‘well’ in the name of the model comes from Ivan Tuckwell, who made extensive and valuable contributions to tax and benefit modelling in New Zealand).
2. It is recognised that judgements about income distribution changes may well depend on mobility characteristics and thus income measured over a longer period.
3. Furthermore, no attempt is made to allow for changes over time such as the introduction of new commodities, or relative price changes which may have differential impacts on different income groups.
4. The choice of metric and unit, prerequisites for drawing the Lorenz curve, also involves value judgements, as discussed further below.
5. It is tempting to think of as representing a (cardinal) utility function, assumed to be the same for all individuals. The case where
(implying no aversion to inequality) thus corresponds to the ‘Classical utilitarian’ case. However, it is necessary to think of
as simply representing the contribution of
to
, reflecting the independent judge's views.
6. For details and elaborations for special cases where further assumptions regarding value judgements can be used to establish dominance results when curves intersect, see Lambert Citation(2001).
7. Reference is sometimes made inappropriately to ‘society's aversion to inequality’.
8. The expression in (Equation1(1) ) is usually used though strictly the numerator is
, for continuity with the case where
.
9. It is obviously possible to modify the form of to allow, for example, for constant absolute inequality aversion rather than constant relative aversion, but for convenience the latter specification is used here.
10. Instead of writing , as in (Equation1
(1) ), in terms of all individual incomes, the abbreviated form is expressed in terms of summary measures of the distribution; see Lambert Citation(2001). The abbreviated form is also convenient to avoid negative values of
in cases where
.
11. Among New Zealand studies, Hyslop and Yahanpath (Citation2005, p. 7) compute Ginis including negative values.
12. Of course, distributions of these sources may be considered separately, but are combined here, as discussed below.
13. As mentioned earlier, in common with most studies no allowance is made here for utility from leisure.
14. Further examples are given in Decoster and Ooghe Citation(2003) and Creedy and Scutella Citation(2004).
15. In the empirical analysis reported below, when this sharing rule is applied, sharing is actually restricted to family members within a household.
16. This formulation actually corresponds to the modified OECD equivalent scale, which does not allow for economies of scale within households.
17. Distribution 11 shares market income. An additional alternative distribution would be to consider individual market incomes as in distribution 9 but with an additional zero values. Comparisons with distribution 12 would then combine the effects of sharing and taxes and transfers.
18. For details of an attribution process, see Aziz, Ball, Creedy, and Eedrah (Citation2014, Appendix C).
19. However, when the incidence of education and health is examined in distribution number 13, GST is deducted before those components are added.
20. The weights used for this study are taken from Taxwell, rather than Statistics New Zealand's HES weights.
21. Some investigators arbitrarily set negative values to zero, rather than removing them from the sample.
22. The HES is conducted from July to June, and Taxwell uses this for modelling the April to March tax year. However, when modelling the so-called ‘2011 year’ we use the 2010–2011 HES but apply the policies that came into force in October 2010.
23. For further discussion of the tax mix change, see Creedy and Mellish Citation(2011).
24. Changes to Portfolio Investment Entities could not be incorporated into the analysis. There was a temporary additional payment to some benefit categories to compensate for price rises due to the GST increase. This was paid from October until April 2011 when benefits would next be indexed by the CPI. As a compromise, benefit payments were modelled according to the Taxwell tax year, thus including only half the temporary payment.
25. For discussion of the precise conditions in terms of the relevant joint distributions and the correlation between equivalent income and the number of individuals in the household, see Creedy and Sleeman (Citation2005, pp. 58–60).
26. On decompositions which allow also for labour supply responses, see Bargain (Citation2012a, Citation2012b), and Creedy and Hérault Citation(2015). The latter paper also considers the use of money metric utility as the welfare metric in decompositions.