5  Alternative Equivalence Scales

Inequality and poverty measures were analysed in section 3 using the equivalence scale:

(22)    

However, this scale is just one of many which are used in policy evaluation. This section contrasts the inequality and poverty measures which arise from using different equivalence scales. Table 1 describes the 29 equivalence scales analysed; there is no suggestion that this is exhaustive as they consist of an arbitrary selection concentrating largely on New Zealand and Australia. The scales are grouped according to the regions for which they were designed and the sources from which they were obtained.[24]

As the equivalence scales are based on a variety of different approaches and functional forms, they are not directly comparable. To overcome this, for each scale the equivalent sizes, , were used to fit the two-parameter form. This was achieved by carrying out regressions using:

(23)    

As this is nonlinear in the parameters, regressions were carried out for a range of values, and the value producing the highest was taken as the estimate, with the corresponding value. Table 1 shows the value of from these regressions together with the estimates of the parameters, and . Where NA is given in the column (1, 2, 15 and 16), the coefficients directly apply to the two-parameter functional form, so no estimation was required. As shown by the high values of , the two-parameter form of equivalence scales provides a very good fit for all scales analysed; the lowest value of is 0.956.

Table 1 shows substantial variation in the parameter estimates, and . The weight attached to children, , ranges from 0.300 (scale no. 25) to 0.916 (scale no. 15), while the parameter reflecting economies of scale, , ranges from 0.395 (scale no. 14) to 1.014 (scale no. 13). Due to the nonlinear nature of the poverty and inequality profiles, observed variations in and provide little indication as to the variation in inequality and poverty measures that would result from the different equivalence scales. For this reason, each scale was in turn applied to the New Zealand expenditure data, from which inequality and poverty measures were then calculated.

Figure 30 shows the inequality profiles produced using the equivalent adult unit of analysis and an inequality aversion coefficient of 1.2, for four different values of . Plotted on this figure are the measures of inequality produced using each of the 29 equivalence scales. There is clearly a considerable range of inequality measures resulting from these scales. The two extremes are provided by scales 25 and 11, where inequality for the latter is 18 percent higher than the former. In terms of inequality comparisons over time and for tax policy microsimulation studies, this order of magnitude is very large. Figure 30 shows that a number of the scales differ mainly in the size of and lie roughly on the relatively flat section of the inequality profiles, where inequality is not particularly responsive to changes in . The use of only those scales would give the misleading impression that the choice of scales is not important.

Table 1 – Equivalence Scales Analysed and Regression Results