Incorporating income inequality into a welfare index

bution during earlier years of the period are offset by greater inequality in the later years. Again, the trend towards increased inequality since about 1975 is more marked in the UK. In this case, however, Fig. 2 provides an interpretation of this increase in terms of social welfare. The Atkinson index I can be interpreted as the loss of welfare associated with a given level of inequality in the distribution of incomes. Fig. 2 reveals that in 1978 this loss of welfare for the UK was around 6.5, a slight improvement over the 9 loss associated with income inequality in 1950. By 1996, on the other hand, the welfare loss had more than dou- bled to over 14.

4. Incorporating income inequality into a welfare index

It is clear from the discussion above that the Atkinson index has the advantage of offering an immediate interpretation in terms of social wel- fare, and can thus be used to incorporate the effects of income inequality directly into welfare measures. For example, where income is used directly as a proxy for social welfare, we find that Eq. 3 can be recast as: Y adj = Y1 − I 7 Y adj now represents the distribution-adjusted wel- fare measure. This method can be generalised in a straightforward fashion to other kinds of welfare measures W through: W adj = W 1 − I 8 In the following section we present a case study in which the Atkinson index is used to adjust several different kinds of welfare measure in the two case study countries Sweden and the UK. First, however, it is worth pointing out that a number of other suggestions have been made concerning the incorporation of distributional as- pects into welfare measures. In the literature, dis- tributional adjustments have been made, for example, to the GDP, the World Bank’s human development index HDI and Daly and Cobb’s index of sustainable economic welfare ISEW Daly and Cobb, 1989. Each of these indicators incorporates some kind of income concept as its basis, and it this income variable that is most obviously open to adjustment from a distribu- tional perspective. Perhaps the most widely used methodology in- corporates the Gini coefficient in some form. A Gini-based welfare indicator was derived, for ex- ample, by Sen 1976, 1997 and has been used in several empirical works, such as by UNDP 1993 to correct the HDI and by Klasen 1994 to adjust income in the USA. A welfare function adjusted using the Gini coefficient could take the following shape as in the Human Development Index UNDP, 1993:W adj = W 1 − Gwhere W is the welfare index, G is the Gini coefficient and W adj is the distribution-adjusted welfare index. Alternatively, the adjustment could be made using a Gini index formulated relative to a particular base year: W adj = W G rel 100 10 where G rel = 100 G base G n 11 G base is the Gini coefficient in the base year, and G n is the Gini coefficient in the year of interest. Even though this method is quite widely used there are several problems with it. Firstly, al- though the Gini coefficient satisfies the principle of transfers — i.e. a transfer from a rich person to a poor person always reduces the inequality measure — it does not satisfy the principle of diminishing transfers — i.e. that the effect of a transfer diminishes as the absolute level of income increases Schwartz and Winship, 1979. Further, in spite of the classification of the Gini coefficient as an objective measure, it does implicitly include value judgements. For example, distributions to- wards the middle are implicitly preferred in the index. However, these value judgements remain hidden within the index. Perhaps the most in- tractable problem is that there is no direct wel- fare-theoretic interpretation of the Gini index. By contrast, there are several specific advan- tages to the Atkinson index. Firstly, of course, the interpretation in welfare terms is straightforward, since the Atkinson index is formulated from a welfare-theoretic model. In addition, however, there is much greater transparency with regard to value judgements. Given that the conventional summary measures inevitably introduce distribu- tional values, Atkinson 1983 argues that ‘it may be preferable to consider such values explicitly. Only then can it be clear just what distributional objectives are being incorporated as a result of adopting a certain measure.’ The Atkinson index incorporates these value judgements explicitly through the value o in Eq. 2. This allows the user of the index to incorporate particular value judge- ments about the importance of distributional ele- ments to welfare. It should perhaps be mentioned that it would also be possible to construct a distribution-ad- justed welfare model using a relative Atkinson index by a straightforward analogy with the method proposed in Eqs. 10 and 11 for the Gini coefficient. In this case, the distribution-ad- justed measure W adj would be given by: W adj = W I rel 100 12 where I rel = 100 I base I n 13 I base is the Gini coefficient in the base year, and I n is the Atkinson index in the year of interest. It is not clear however, that this method offers any advantages over a direct welfare-theoretic adjust- ment. Table 1 summarises a variety of attempts to adjust welfare measures for distributional properties.

5. Case study: distribution-adjusted welfare measures for Sweden and the UK