4. Gender Differences in Earning and Rewarded Employment

5. Extent of Inequality Aversion 

6. Gender-Equality Measures and GESI

7. On Spaces and Formulas
 

The human development index H for a country has been defined to be
 

 
 

where is the average life expectancy attained in the country, LIT is the average percentage literacy rate among adults, and LPCY is the logarithm of per capita GDP (in "purchasing power parity" dollars) truncated at the average official poverty line income in nine developed countries, with 3.687 being the-then value of the logarithm of the poverty level (Anand and Sen 1993).

For the gender-equity-sensitive HDI, we simply replace the arithmetic average attainments in each component by the equally distributed equivalent achievements. Thus the first component ( - 35)/50 is replaced by (L_ede - 35)/50. The second component LIT/100 is replaced by X_ede/100, where X_ede is now the (1-)-average of the female and male literacy rates. No corresponding correction can be made for the third component of HDI, because gender-specific attributions of income per head cannot be readily linked to the aggregate GDP per capita used in these calculations, and inequalities within the household are difficult to characterize and assess (Sen 1992a; Anand and Sen 1993).

It is important to distinguish between two different aspects of incomes, viz. earning and use. If we wish to concentrate on the use aspect, the within-family division of income use between women and men would have to be identified to assess income use by gender. But the empirical and conceptual problems in getting at these divisions within the family are formidable indeed.

In contrast, the earning aspect looks at women and men not as income users, but as people who earn incomes. The total gross national product can then be seen in terms of aggregate earnings of all women and all men, making up something like the total national income. An approximate idea of the income earnings of women and men can be obtained by looking at their respective employment ratios and their relative wages.

What significance can be attached to such income earning estimates? Indeed, there is some tension in concentrating on the earning aspect when the entire approach of the Human Development Report has been based on identifying what people get out of the means they can use, rather than on the means they earn — possibly to be used by their families. On the other hand, the earning contrasts between men and women do point to an important asymmetry between them in most — nearly all — existing societies. While women very often work as hard as — or harder than — men, much of their work is of the unpaid kind that does not yield remuneration.¹⁴ There is also considerable evidence to indicate that earning explicitly recognized "incomes", and working in sectors that are treated as evidence of being "economically active", can significantly and favourably influence the "deal" that women tend to get in the division of benefits and chores within the family.¹⁵

There is, thus, a case for doing some gender division even for the "real income" component of HDI, trying to note the differences between the earnings of women and men. It would be hard to get anything like the degree of precision with earnings "allocated" between women and men on the basis of rough calculations that gender-specific measures of literacy or life expectancy can offer. But even some estimates of relative earnings of women and men would give the gender equity-sensitive indicator (GESI) another component with some bite. If this were to be done, then the total GDP per head can be notionally "split" between women and men in the ratio of the respective products of employment rates and wage rates per unit of employment. It would, however, be necessary then to explain clearly that (1) this procedure looks at income from the "earning" perspective rather than the "use" perspective (even though gender inequalities seem to link the latter to the former), and (2) the evaluations of earnings of women and men are fairly "soft" estimates, to be interpreted with much caution.

5. Extent of Inequality Aversion 

As was discussed earlier, the values of the parameter can be taken to range from zero to infinity, reflecting the extent of social preference for equality. In fact,  as a parameter stands for the elasticity of the marginal social valuation of the respective achievement, and tells us how quickly the marginal value falls as the achievement level rises (that is, how strongly diminishing the marginal social returns are).  can, in fact, be seen as a reflection of the extent of inequality aversion. When  is taken to be zero, there is no decline in marginal values, so that the simple arithmetic mean does well enough. At the other extreme, when  is taken to be infinity, the sensitivity is so great that we end up picking only the lower of the two numbers in a pair, ignoring the achievement of the better-off. It would be interesting to calculate the gender-equity-sensitive (GESI) adaptation of HDI for several parametric values of  , such as 0, 1, 2, 3, 5, 10, . We call this class of "corrected" HDI the gender-related development index, or GDI for short. Typically we will use the value = 2.

The implications of different choices of  can be gauged by examining the effects on X_ede, the equally distributed equivalent achievement. We can compare the relative increase in X_ede through a unit increase in female achievement X_f compared to a unit increase in male achievement X_m. From equation (2) in Appendix A.1, we have
 

 

if the social valuation function V(X) has a constant elasticity of marginal valuation  .

According to this, if male achievement X_m is twice female achievement X_f, i.e. (X_m/X_f) = 2, and if  = 1 (i.e. we have the logarithmic form for V(X)), then a unit increase in female achievement will contribute twice as much to X_ede as a unit increase in male achievement (see Table 1). If (X_m/X_f) remains equal to 2, but = 2, then a unit increase in female achievement contributes four times as much as a unit increase in male achievement. Holding (X_m/X_f) constant (at any value above 1), as  is increased there is an increase in the relative contribution to X_ede from a unit increase in X_f compared to a unit increase in X_m.¹⁶ Table 1 estimates the relative contribution to X_ede of a unit increase in female achievement compared to a unit increase in male achievement for different values of and different ratios of male-to-female achievement (X_m/X_f).

For particular values of , how different would GDI be from HDI (bearing in mind that HDI is, in fact, a special case of GDI, with  = 0)? Clearly, the distributional correction would tend to pull down the value of HDI, and we expect GDI to be quite significantly below the corresponding HDI values in a systematic way, for relatively high values of .
 

Relative Contributions to X_ede of Unit Increases in X_f and X_m, i.e.,

(Xm/Xf)	0.0	1.0	1.5	2.0	2.5	3.0	5.0	10.0
1.0	1	1	1	1	1	1	1	1	1
1.5	1	1.5	1.8	2.3	2.8	3.4	7.6	57.7
2.0	1	2.0	2.8	4.0	5.7	8.0	32.0	1,024.0
2.5	1	2.5	4.0	6.3	9.9	15.6	97.7	9,536.7
3.0	1	3.0	5.2	9.0	15.6	27.0	243.0	59,049.0
4.0	1	4.0	8.0	16.0	32.0	64.0	1,024.0	1,048,576.0

Note: The relative contributions to X_ede in this table are estimated under the assumptions that p_f = p_m = 1/2, and that V(X) has a constant elasticity of marginal valuation  .

This does not, however, imply that the rankings would be necessarily much changed. That would depend on the relative differences in the extent of gender inequality. While there are often substantial differences between the gender inequality levels of the relevant parameters between high-achieving and low-achieving countries, the patterns of gender inequalities may often be quite close to each other for countries at similar levels of human development. This would tend to make the rankings of GDI rather similar to those of HDI. However, some differences can be expected between low-achieving countries in Asia and low-achievers in Sub-Saharan Africa, since the extent of gender inequality in many fields has tended to be substantially less in the latter countries.¹⁷
 

 
6. Gender-Equality Measures and GESI

The Appendix A.3 ("Properties of the Relative Gender-Equality Index E") draws attention to the fact that the relative level of gender equality can be well captured by comparing the values of GESI with the uncorrected average measure. That average (gender-blind) measure is based on taking an arithmetic average (as with HDI) over the entire population, whereas the formula for GESI permits an entire class of "(1-)-averaging" to take note of — and to weigh against — inequalities. In the special case in which  is taken to be 2, the GESI formula corresponds to the harmonic mean. The equally distributed equivalent achievement corresponding to  = 2, i.e. X_ede(2), is then given (for equal proportions of women and men) by the formula

Hence,
 

which is the harmonic mean of X_f and X_m. If we take the ratio of the harmonic mean to the arithmetic mean, we then get a measure of "gender equity" that has obvious interest.

For reasons discussed in the last section, the values of GDI and HDI may not diverge in a way that makes the respective rankings very different. When the values of GDI and HDI are shifted in similar ways — without much of a relative change — the ratios may not tell us very much either. It must, however, be remembered that the GESI formula can be applied to other variables as well, specifically chosen to highlight differences in gender disparities. We must, in general, distinguish between (1) the GESI formula of (1-)-averaging, and (2) the "space" on which it is applied (that is, the variables for which achievements and gender disparities are scrutinized).

It should be noted here that the procedure used for inequality correction in GDI involves the estimation of inequality-corrected achievements in terms of different focus variables, and then putting them together in one aggregate measure of inequality-adjusted performance. In some respects, this procedure is a little deceptive, since the different variables might, in principle, work in somewhat opposite directions, moderating the influence of each other in the inequality between individuals. For example, if person A has a higher achievement in longevity while person B does better in terms of education, it could be thought that these inequalities must, to some extent, counteract each other, so that in terms of a weighted average of achievements, A and B may be less unequal than in terms of each of the two variables. And this opposite-direction case would be different from the one in which one of the individuals, say A, is better off in terms of both the variables. In terms of the procedure used here, we cannot discriminate between these two types of cases, since the aggregation is done, first, in terms of specific variables, and then they are put together in an index of overall achievement.

This defect is, however, fairly inescapable at the individual level, given the data availability. There is no obvious way of relating the individual identities in the distribution of one variable with those for the other variable. There is, thus, no serious alternative to the kind of procedure we have used. As a matter of fact, this is not, however, a very serious limitation in the present context. This is partly because the individual deprivations very often go together and reinforce — rather than counteract — each other. For example, the educationally deprived person is often also the one with the lower longevity, as we know from statistical studies of development characteristics.

More importantly, it should be borne in mind that the exercise of gender-equity adjustment is being made here at a high level of aggregation, dealing with the mean positions of women and men. At this aggregated level, the inequalities almost always go together, with women being in a more deprived position, on the average, than men. The exceptions come from a handful of countries — such as the Scandinavian ones — where in terms of one variable, viz. life expectancy, women seem to have actually gone significantly ahead of men in terms of the standard correction for expected longevity (with five extra years expected in female longevity). In such cases, the disparity in life expectancy may go in the opposite direction to the disparity in education or income earning. If note were to be taken of this connection, these countries would be placed higher in terms of overall achievement, since the inequality adjustments would have, to some extent, counteracted each other. But since these countries are, in any case, towards or at the top of the international "league tables", the effect of this correction would be only to reinforce that positional lead.

7. On Spaces and Formulas

This paper has been primarily concerned with proposing, explaining, and defending a particular approach to constructing gender-equity-sensitive measures of human development. It has not been directly concerned with the choice of variables, even though the argument has been developed in terms of the "classic" components of human development indicators, beginning with Human Development Report 1990.

The choices of variables — in particular, life expectancy and literacy — were primarily governed by the ability to discriminate among the relatively less affluent countries. For the high-achieving developed countries, there is relatively little sensitivity in the use of these variables, at least as far as the rankings are concerned. It is for this reason that we had earlier suggested (in Anand and Sen 1993) that different variables may be used in a supplementary way to discriminate between middle- and high-achieving countries, respectively. We stick to the logic behind that position, since the variables needed to discriminate between the advanced countries tend to dilute the importance of some of the basic features of human development that the "classic" variables capture, thereby turning a partially blind eye to the relative failures and successes of poorer countries in bringing about achievements in basic fields (such as literacy and life expectancy). However, it is not the purpose of this paper to insist that we must use only the classic HDI variables, or the pyramid structure proposed in Anand and Sen (1993). That is ultimately a question to be determined at the UNDP. But we would like to emphasize that even if we depart from the variables with which this note has been specifically concerned, there will be scope for using the methodology developed here. For example, replacing literacy by "total gross enrollment ratio" would not require any basic change in the methodological approach developed here. We have reasons to question the quality of these data and their perspicuity in "telling" between poorer countries in terms of what has been called "first things first" (on which see Streeten et al. 1981), but the methodology has enough catholicity to deal with that option if it were chosen. The ball should now be at the UNDP's court.
 

14. See, for example, Goldschmidt-Clermont (1982, 1993), Folbre (1991), Folbre and Wagman (1993), Urdaneta-Ferrán (1993), and the references cited there. Many of the diverse underlying issues are discussed in Chen (1983), Bergmann (1986), Jayawardena (1986), Brannen and Wilson (1987), Sen and Grown (1987), Okin (1989), Goldin (1990), England (1992), Ferber and Nelson (1993), Folbre (1994), Agarwal (1995), and Nussbaum and Glover (1995).

15. For references to the literature on this, and an analysis of why this relationship is observed in situations of "cooperative conflict" (as family-living typically is), see Sen (1990). See also Anand (1979), Manser and Brown (1980), McElroy and Horney (1981), Lundberg and Pollak (1994), and the references cited there.

16. By partial differentiation with respect to , it is straightforward to show that

and

17. On this see Kynch (1985) and Sen (1988), and the references cited there.