The Treasury

Global Navigation

Personal tools

Treasury
Publication

Adult Equivalence Scales, Inequality and Poverty in New Zealand - WP 04/21

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

Scale No. Title R2 θ α
Scale No. Title R2 θ α
  New Zealand      
  Brashares, Edith and Aynsley, Maryanne (October 1990) Income Adequacy Standards for New Zealand      
1 Jensen's 1978 Equivalence Scale (Annex 5, p.1) NA 0.781 0.737
2 Jensen's 1988 Equivalence Scale (Annex 5, p. 2) NA 0.730 0.621
  Michelini, Claudio (April 1999) New Zealand Household Consumption Equivalence Scales from Quasi-Unit Record Data      
3 Commodity-specific and household-type equivalence scales: ELES model (p.14, Table 1 - Total Expenditure) 0.999 0.490 0.711
4 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - PS-AID(θj) (p.17, Table 2 - PS-AID(qi) 0.987 0.620 0.949
5 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - PS-QAID(θj) (p.17, Table 2 - PS-QAID(qj)) 0.991 0.650 0.896
6 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - PS-QAID(θj) - H (p.17, Table 2 - PS-QAID(qi) - H) 0.956 0.720 0.622
7 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - EPS(θ)-QAID(θj) (p.17, Table 2 - EPS(a)-QAID(θi)) 0.999 0.670 0.782
8 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - EPS(α)-QAID(θj)d (p.17, Table 2 - EPS(α)-QAID(θi)d) 0.999 0.670 0.775
9 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - EPS(βλ-QAID(θj) (p.17 Table 2 - EPS(βλ )-QAID(θi)) 1.000 0.580 0.799
10 Estimates of the household Equivalence Scales for total consumption when the equivalence parameter mo is commodity-invariant - EPS(βλ)-QAID(θj)d (p.17 Table 2 - EPS(βλ)-QAID(θi)d) 0.998 0.630 0.797
11 Commodity-specific and household-type equivalence scales obtained from the PS-AID(qij) model (p.18, Table 3 - PS-AID(qij), Tot.Expenditure) 0.992 0.890 0.904
12 Commodity-specific and household-type equivalence scales obtained from the PS-QAID(θij) model (p.18, Table 3 - PS-QAID(qij), Tot.Expenditure) 0.963 0.890 0.825
13 Commodity-specific and household-type equivalence scales obtained from the EPS(α)-QAID(θij) model (p.20, Table 4 - EPS(a)-QAID(θij), Tot.Expenditure) 0.957 0.670 1.014
14 Commodity-specific and household-type equivalence scales obtained from the EPS(βλ)-QAID(θij) model (p.20, Table 4 - EPS(βλ)-QAID(θij), Tot.Expenditure) 0.986 0.890 0.395
15 Heuristic Household Equivalence Scales - Easton, 1980 (p.21, Table 6 - Easton, 1980) NA 0.916 0.606
16 Heuristic Household Equivalence Scales - Smith, 1989 (p.21, Table 6 - Smith, 1989) NA 0.713 0.972
  United Kingdom      
  Brashares, Edith and Aynsley, Maryanne (October 1990) Income Adequacy Standards for New Zealand      
17 Townsend's Equivalence Scale (Annex 5, p.49, Table 38 - Townsend) 0.995 0.890 0.551
18 The United Kingdom Supplementary Benefit Equivalence Scale 1968/69 (Annex 5, p.49, Table 38 - Supplementary Benefit) 0.997 0.650 0.658
  Van de Ven, Justin (November 18, 2003) Demand Based Equivalence Scale Estimates for Australia and the UK      
19 Equivalence Scales by Estimation Method for Engel Estimates for the UK (p.15, Table 3 - UK, Engel) 0.999 0.470 0.928
20 Equivalence Scales by Estimation Method for Rothbarth Estimates for the UK                                 (p.15, Table 3 - UK, Rothbarth) 0.997 0.370 0.876
21 Equivalence Scales by Estimation Method for DS(a) Estimates for the UK                                       (p.15, Table 3 - UK, DS(a)) 1.000 0.630 0.576
22 Equivalence Scales by Estimation Method for DS(b) Estimates for the UK                                    (p.15, Table 3 - UK, DS(b)) 1.000 0.640 0.501
  Australia      
  Brashares, Edith and Aynsley, Maryanne (October 1990) Income Adequacy Standards for New Zealand      
23 Henderson Equivalence Scale (Annex 5, p.40, Table 30 - Head Working - All Costs) 0.989 0.810 0.562
  Van de Ven, Justin (November 18, 2003) Demand Based Equivalence Scale Estimates for Australia and the UK      
24 Equivalence Scales by Estimation Method for Engel Estimates for Australia                          (p.15, Table 3 - Australia, Engel) 0.999 0.530 1.013
25 Equivalence Scales by Estimation Method for Rothbarth Estimates for Australia                            (p.15, Table 3 - Australia, Rothbarth) 0.994 0.300 0.886
26 Equivalence Scales by Estimation Method for DS(a) Estimates for Australia                                   (p.15, Table 3 - Australia, DS(a)) 1.000 0.600 0.676
27 Equivalence Scales by Estimation Method for DS(b) Estimates for Australia                            (p.15, Table 3 - Australia, DS(b) 0.999 0.470 0.639
  OECD      
28 The OECD scale (p.172) 0.998 0.700 0.884
29 The Modified OECD scale (p.172) 0.994 0.580 0.763

Notes

  • [24]As mentioned above, the scales are price independent, but of course differences in relative prices between countries may be thought to affect their applicability to more than one country.
Page top