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6  Conclusions

This paper has examined the sensitivity of several inequality and poverty measures to the choices of the adult equivalence scale, used to adjust total household income, and the unit of analysis, along with the choice of poverty line. In considering alternative scales, extensive use was made of a highly flexible two-parameter functional form of the adult equivalence scale, allowing for economies of scale and a separate weight added to children. Three units of analysis (or weights in computing summary measures), namely the household, the equivalent adult and the individual were examined. The use of individuals was seen to be consistent with an anonymity principle, while the use of the number of equivalent adults is consistent with the principle of transfers.

The main empirical comparisons were for New Zealand, using pooled information about total household expenditure, from several Household Economic Surveys. The results demonstrated the sensitivity of New Zealand’s inequality and poverty measures to the parameters of the equivalence scales and, in addition, to the chosen unit of analysis. Profiles of inequality against the economies of scale parameter, for a given weight attached to children, were found to be U-shaped, consistent with other studies. The role of the correlation between the total expenditure per adult equivalent and the size of the household was found to be crucial in generating the U-shape. A negative correlation (despite the positive correlation between total household expenditure and household size) is more likely, the lower is the weight attached to children and the higher is the economies of scale parameter. It was shown that a negative correlation is equivalent to the ‘reranking’, identified by Coulter et al (1992), that arises as the scale parameter increases. The profiles of inequality and poverty for individuals and equivalent adults as the unit of analysis (or weights) were found to intersect over a range of parameter values. For poverty measures, the profiles of poverty with the economies of scale parameter were upward sloping, with a higher scale parameter increasing poverty over the whole range in all cases.

The effect of alternative equivalence scales and income units on the reranking arising from the direct tax system were also examined. Using a decomposition of the redistributive effect of taxation, horizontal inequity was found to be extremely small in all cases. Profiles of reranking for an increasing scale parameter were found to be J-shaped. A reranking minimising set of parameters were investigated, and were found to be substantially lower than the scales commonly used in New Zealand.

Finally, a wide range of equivalence scales designed for New Zealand, the United Kingdom, Australia and the OECD were examined. The two-parameter form was found to provide a very good fit to these scales. The scales were applied to the New Zealand data and the resulting inequality and poverty measures were contrasted.

The results demonstrate that considerable care needs to be taken in the choice of adult equivalence scales and the income unit. Applied studies of inequality and poverty often use only a single set of scales, claiming that results are not affected. However, given the different patterns of variation in summary measures found, much caution is required before declaring that analyses are not affected by the choice of scale.

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