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Journal of Human DevelopmentA Multi-Disciplinary Journal for People-CenteredDevelopmentPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713431425
The Income Component of the Human DevelopmentIndexSudhir Anand; Amartya Sen
To link to this article: DOI: 10.1080/14649880050008782URL: http://dx.doi.org/10.1080/14649880050008782
The Income Component of the HumanDevelopment Index
SUDHIR ANAND and AMARTYA SENSudhir Anand is Professor of Economics, University of Oxford, and AmartyaSen is Master, Trinity College, Cambridge
Issues and research strategies
Human beings as ends and means
The over-arching understanding that has motivated the Human Develop-ment Reports (United Nations Development Programme, several years)since their inception in 1990 is the elementary recognition that humanbeings are the primary ends as well as the principal means of development.These two aspects of the ‘human’ side of development are related but quitedistinct, and recognizing the special demands of each is important foranalytical clarity in this dif�cult subject.
As it happens, both these roles were typically neglected in the analysesof growth and development that came into fashion in the years followingthe Second World War. Both needed correction, but they called for ratherdifferent types of recti�cation. The rhetoric on ‘the importance of humanelements’ in the process of development often confounds the disparatedemands of the two emendations, each important in their own right, butquite dissimilar in their implications for the concepts, measures and priori-ties of development. As it happens, focusing on human beings as theprincipal means of development has been reasonably well addressed by theplacing of ‘human capital’ at the centre of the stage. But this, on its own,is quite inadequate for the appreciation of human beings as the ‘primaryends’ of development. The Human Development Reports attempt to takeon the task of incorporating the view of human beings as ends in theaccounting and assessment of development.
Human capital and beyond
The importance of human efforts, skills and talents needs adequate acknowl-edgement. When these were systematically neglected (as was the case, withsome notable exceptions, in the post-World War emergence of developmenteconomics as a subject), there were excellent grounds for drawing attentionto the role of people as the promoters of development and progress. The
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need to emphasize ‘human capital’ as opposed to ‘physical capital’ wasstrongly felt by many who saw the overwhelming concentration on theaccumulation of physical capital to be very inadequate for a proper under-standing of the process of economic growth as well as of social change.1
By now, the needed evolution in the understanding of development —with appropriate acceptance of the pervasive role of ‘human capital’ — haslargely occurred. Even some early sources of resistance have basicallymoved on to recognize the central part that the productive roles of humanbeings play in the promotion of economic and social development.2 It is asunfashionable today to be sceptical of ‘human capital’ as it was to doubt thepower and reach of physical capital some decades earlier.
However, this much-needed change addresses only one of the twomajor tasks related to the neglect of the human aspects of economic andsocial development. The view of human beings as the ‘primary ends’ of theprocess of development calls for emphasis to be placed on what people getfrom development, not only what they put into it. To see the importance ofhuman qualities in the promotion and sustaining of economic growth,momentous as it is, tells us nothing about the reasons for seeking economicgrowth in the �rst place, nor about the fact that the quality of life can varygreatly between different countries with much the same level of per-capitaGross National Product (GNP) and real income. If the expansion of educa-tional facilities or of health care has the effect of increasing productivity andthus the income level, the approach of ‘human capital’ would give it animmediate and elevated status. But, if these changes in educational andhealth facilities directly make our lives longer and more ful�lled, and add toour ability to avoid preventable diseases and miseries, without necessarilychanging labour productivity or increasing commodity production, then thatachievement would simply not get the recognition it deserves in theaccounting of ‘human capital’.
Something serious is thus missed even in the broadened perspective ofdevelopment that emphasizes ‘human capital’. To rectify what is missed inthe perspective of ‘human capital’, we need a broader conception ofdevelopment that concentrates on the enhancement of human lives andfreedoms, no matter whether that enhancement is — or is not — interme-diated through an expansion of commodity production.
Human development, capabilities and the quality of life
The object of the particular focus chosen by the Human DevelopmentReports was to examine the progress of the conditions of human living —the ability of people to lead the kind of life they have reason to value. It isthe enhancement of the capability to live better and richer lives, throughmore freedom and opportunity, that became the central concern of theseReports (see Haq, 1995).
This motivation is not, in fact, different from that expressed in AdamSmith’s (1790) resentment of seeing people merely as instruments ofusefulness. Even Smith’s friend David Hume, with his interest in the ‘utility’
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Income Component of the HDI
of people, received some criticism from Smith on this ground (although thiswas perhaps a little undeserved, since Hume was inclined to take a ratherbroad view of ‘utility’ itself). Adam Smith complained about the tendency tojudge a person by his ‘usefulness’ or, as he put it, for “that for which wecommend a chest of drawers”.3
Adam Smith’s concern with the ability of people to choose a reasonablelife relates closely to the approach of human development, which concen-trates on people’s capabilities in some �elds that are crucial for the qualityof life. The approach also has clear Aristotelian connections — indeed,Aristotle was a major in�uence on Adam Smith’s thinking. In the Aristotelianview, there is much focus on ‘functionings’ that people need for‘�ourishing’ as human beings.
The Human Development Reports have tended to focus on a variety ofcentral functionings. While the coverage is necessarily restricted by datalimitations, the ultimate object is to include all the crucial functionings thatare central for quality of life, varying from such elementary ones as avoidingescapable morbidity and preventable mortality to being educated, havingcomfortable lives, achieving self-respect and respect from others, beingsocially integrated, and so on. In line with the signi�cance of freedom injudging the advantages enjoyed by adult people, it is important, in thiscontext, to esteem not just people’s actual functionings, but their capabilityto achieve the functionings they have reason to choose (see Sen, 1980,1987; Nussbaum and Sen, 1993).
Human development index and broader concerns
The domain of the Human Development Reports is much wider than whatcan be captured by one index, useful though such an index may be. Therole of any overall ‘development index’ is thus rather complex, and calls forsome scrutiny of research strategy. There are limits to the different valuesthat can be re�ected in one real number. Insofar as more variables are added(to make the measure more ‘inclusive’), the already-included ones decline insigni�cance and emphasis. There is thus a real dilemma in choosing what toinclude in the list.
The Human Development Reports have chosen a two-tiered approachto address this issue:
(i) presenting a variety of relevant information in detail (with investigationof their respective roles, analyzed in different Reports, varying from yearto year); and
(ii) providing a summary picture of some of the major components ofhuman development through a Human Development Index (HDI) toserve as an alternative focal point to the traditional concentration on theGNP, Gross Domestic Product (GDP), and other standard measures ofeconomic development.
The scope of the latter was necessarily much more limited than that of theformer, but its easy communicability and salience has made it, nevertheless,
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a much used and appreciated indicator of parts of the complex process ofhuman development.
Direct and indirect measures
The �rst Report, Human Development Report 1990, identi�ed three keyaspects of the quality of life of people, to be enhanced by the process ofdevelopment: longevity, education and “command over resources to enjoya decent standard of living” (Human Development Report 1990, p. 1).There is a clear asymmetry here. Both longevity and education are clearlyvaluable as aspects of a good life, and also valued as constituents of thecapability to do other things.4 In contrast, ‘command over resources’ is onlyan instrument for other ends — indeed, income is just one way of seeingthis command. The purpose of including this in the HDI was to note the factthat there are many important capabilities which are critically dependent onone’s economic circumstances. The income level enjoyed, especially closeto poverty lines, can be very crucial information on the causal antecedentsof basic human capabilities.
The use of ‘command over resources’ in the HDI is strictly as a residualcatch-all, to re�ect something of other basic capabilities not already incor-porated in the measures of longevity and education. The concentration on‘command over resources’ would have taken the HDI away from the basicapproach of measuring ‘human development’ had it been the sole compo-nent of this index. Indeed, there is much evidence that a country’s GNP percapita is often not a very good indicator of its achievements in health andsurvival. Much depends on how the national resources are used: forexample, how much public health care is provided, and how the totalincome is distributed between the poor and non-poor (see Anand andRavallion, 1993). Also, some countries do very much better than others —both in using the fruits of economic growth and in making use of low-costhealth care in combatting preventable illness and morbidity (see Dreze andSen, 1989; and the literature cited therein). Thus, the command overmaterial resources could not have served as a ‘proxy’ for health andlongevity. The same applies to education.
On the other hand, after taking note of longevity and education, therestill remain some basic concerns that have to be captured in any accountingof elementary capabilities. For example, going hungry is a deprivation thatis serious not just for its tendency to reduce longevity, but also for thesuffering it directly causes. Similarly, resources needed for shelter and forbeing able to travel may be quite important in generating the correspondingcapabilities.
It is, in this sense, that the income component of the HDI has beenused — as an indirect indicator of some capabilities not well re�ected,directly or indirectly, in the measures of longevity and education.5 The roleof the income component of the HDI has to be assessed in this light. Thisis what we proceed to do now, including a re-examination of the way this
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‘component’ has been used in the series of Human Development Reportsthat have been produced.
Human Development Repor ts: 1990–1995
The initial move: 1990
The HDI was �rst proposed in the Human Development Report (HDR)1990. As has already been mentioned, it had three components: longevity(re�ected by life expectancy at birth), education (re�ected by literacy), andcommand over resources. It is this third component that we now scrutinize.
The HDR 1990 (p. 12) states:
The third key component of human development — commandover resources needed for a decent living — is perhaps the mostdif�cult to measure simply. It requires data on access to land,credit, income and other resources. But given the scarce data onmany of these variables, we must for the time being make the bestuse of an income indicator. The most readily available incomeindicator — per capita income — has wide national coverage. Butthe presence of nontradable goods and services and the distor-tions from exchange rate anomalies, tariffs and taxes make percapita income data in nominal prices not very useful for inter-national comparisons. Such data can, however, be improved byusing purchasing-power-adjusted real GDP per capita �gures,which provide better approximations of the relative power to buycommodities and to gain command over resources for a decentliving standard.
A further consideration is that the indicator should re�ect thediminishing returns to transforming income into human capabili-ties. In other words, people do not need excessive �nancialresources to ensure a decent living. This aspect was taken intoaccount by using the logarithm of real GDP per capita for theincome indicator.
The Human Development Index is constructed by specifying a minimumvalue for each indicator (maximum deprivation set equal to one) and adesirable or adequate value (no deprivation set equal to zero). For the 1990HDR, the minimum values were chosen by taking the lowest 1987 nationalvalue for each indicator. For the purchasing-power-adjusted GDP percapita, the minimum value was $220 (log value 2.34), in Zaire. The valuesof desirable or adequate achievement were Japan’s 1987 life expectancy atbirth of 78 years and adult literacy rate of 100%, and the average of�cial‘poverty line’ income in nine industrial countries, adjusted by purchasingpower parities, of $4,861. The nine countries were Australia, Canada, theFederal Republic of Germany, the Netherlands, Norway, Sweden, Switzer-land, the UK and the US (HDR 1990, p. 13).
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Follow-ups: Human Development Reports 1991–1995
The HDR 1991 made a series of ‘re�nements’ to the HDI. Thus, it stated that“… income beyond the poverty level is no longer considered to make nocontribution and thus is given not a zero weight but a progressivelydiminishing weight” (p. 2). It went on to suggest that: “The idea of diminish-ing returns to income is now better captured by giving a progressively lowerweight to income beyond the poverty cut-off point, rather than the zeroweight previously given. That zero weight was found to be too drastic anadjustment, particularly for higher income societies” (p. 15).
In Technical Note 1 of HDR 1991, an explicit formulation is given ofthe treatment of income in the new HDI. Speci�cally, HDR 1991 assigns‘different weights’ for income above and below the poverty line (p. 89):
In the HDI, income up to the poverty line (y*) has a full weight,and income above it has a zero weight. [In the variations above,all income has the same weight. To explore alternatives betweenthese two extremes,] we tried using a full weight for income upto the poverty line and a fractional weight above it. The newvariable (call it W) was:
W 5 y for y < y* (1a)
W 5 y 1 2(y 2 y*)1/2 for y . y* (1b)
The fractional weight assigned to income above the poverty linecomes from a general formula:
W(y) 51
1 2 «y1 2 «
In this formula « 5 0 puts full weight on all income, with nodiminishing returns. As « gets close to 1, W(y) becomes log y. Inequations (1a) and (1b), the assumption is that « 5 0 for y , y* and« 5 1/2 for y . y*.
In Technical Note 2 of HDR 1991, the modi�cation to the incomevariable is described as follows.
The original HDI was based on the premise of diminishing returnsfrom income for human development (or human well-being). Lastyear, this fact was re�ected by using the logarithm of income andgiving a zero weight to income above the poverty line. A moresystematic way is to use an explicit formulation for the diminish-ing return. A well-known, and frequently used, form is the Atkin-son formulation for the utility of income:
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W(y) 51
1 2 «y1 2 « .
Here W(y) is the utility or well-being derived from income,and the parameter measures the extent of diminishing returns.It is the elasticity of the marginal utility of income with respect toincome. If « 5 0 there are no diminishing returns. As « approaches1, the equation becomes:
W(y) 5 log y.
The modi�cation adopted in this HDI is to let the value of « riseslowly as income rises. For this purpose, the full range of incomewas divided into multiples of the poverty line y*. Thus, mostcountries are between 0 and y*, some between y* and 2y*, evenfewer between 2y* and 3y* and so on. Now for all countries forwhich y , y*, that is, the poor countries, « is set equal to 0. Thereare no diminishing returns here. For income between y* and 2y*,« is set equal to 1/2. For income between 2y* and 3y*, « is set at2/3. In general, if ay* # y # (a 1 1)y*, then « 5 a/(a 1 1). This gives:
W(y) 5 y for 0 , y # y*5 y* 1 2(y 2 y*)1/2 for y* # y # 2y*5 y* 1 2(y*)1/2 1 3(y 2 2y*)1/3 for 2y* # y # 3y*and so on.
So, the higher the income relative to the poverty level, the moresharply the diminishing returns affect the contribution of incometo human development. Income above the poverty line thus hasa marginal effect, but not a full dollar-for-dolla r effect. Thismarginal effect is enough, however, to differentiate signi�cantlyamong industrial countries. The original HDI formulation, bycomparison, was:
W(y) 5 log y for 0 , y # y*W(y) 5 log y* for y . y*.
The revision thus does not take « 5 1, but allows it to varybetween 0 and 1.
For example, the Bahamas has a real GDP per capita of$10,590. With the poverty line set at $4,829, there are three termsin the equation to determine the well-being of the Bahamas:
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W(y) 5 y* 1 2(y*)1/2 1 3(y 2 2y*)1/3
5 4,829 1 2(4,829)1/2 1 3(10,590 2 9,658)1/3
5 4,829 1 139 1 29 5 $4,997. (HDR 1991, p. 90)
Note that the well-being of the Bahamas is described in terms of a dollar�gure. However, the income ‘discounting’ is done not by a rate of discount(pure number per time), but rather by raising dollar income to a power lessthan unity (to make the utility function strictly concave), which here iseither 1/2 or 1/3. The number this calculation generates will be a utility orwell-being number (utils or units of well-being), not a dollar �gure.6
The treatment of income in the subsequent Human DevelopmentReports from 1992 to 1995 is essentially similar to that in HDR 1991(already described). Exactly the same W(y) function is used to transform or‘discount’ real per-capita income in HDR 1991–1995. However, there is achange to the threshold income level y* in HDR 1994 (p. 91):
It was always questionable, however, whether the poverty level ofindustrial countries was an appropriate income target for develop-ing countries. So, for the 1994 HDI, the threshold value has beentaken to be the current average global value of real GDP percapita in PPP$. … On the new basis of real GDP per capita, thethreshold is $5,120.7
In HDR 1994, there is also a change in the method of choosing theminimum and maximum values for the three components of HDI. In thecase of the earlier HDRs, namely those of 1990–1993, the contribution ofthe ‘discounted income’ component W(y) to HDI is expressible as (seeAnand and Sen, 1993):
S 1
3 D W(y) 2 Mini[W(yi)]
Maxi[W(yi)] 2 Mini[W(yi)]
where yi is the real per-capita income (in PPP$) of country i. The inter-coun-try minimum and maximum values of yi and W(yi) for each of the years1990–1993 are shown in Table 1. However, this method of normalizing thecomponents of HDI is not appropriate for measuring a given country’shuman development performance over time, because the HDI constructedin this way will be affected by the performance of the worst- and best-per-forming countries. Thus, Anand and Sen (1993) recommended �xing the‘goalposts’ for each of the HDI components.
For the income component, HDR 1994 chose to �x the real per-capitaincome levels (in 1990 PPP$) at a minimum of $200 and a maximum of$40,000 (see HDR 1994, Table 5.1, p. 92). In terms of the W(y) function,this corresponded to a minimum of W(200) 5 200 and a maximum ofW(40,000) 5 5,385 (see HDR 1994, p. 108). In HDR 1995, the minimumvalue of real per-capita income has been revised from PPP$200 to PPP$100:
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This revision was made because in the construction of the gender-related development index (GDI) for different countries, theminimum observed value of female income of PPP$100 is used asthe lower goal post. It is necessary to use this �xed minimum forconstruction of the overall HDI to maintain consistency betweenthe construction of the HDI and that of the GDI and to ensurecomparability between the two indices. (HDR 1995, p. 134)
For this reason (and a change in the education component in 19958), theHDI values in HDR 1995 are not strictly comparable with those in HDR1994.9
TABLE 1. Income bounds and threshold income for HDI 1990–1995
Discounted realReal per capita per capitaincome (PPP$) income, W(y) Threshold
aFor HDR 1990–1993, the threshold income y* was “derived from thepoverty-level income of the industrial countries in the Luxembourg IncomeStudy, with values updated and translated into purchasing power paritydollars (PPP$)” (HDR 1994, p. 91). For HDR 1994–1995, the thresholdvalue has been taken to be “the current [1992] average global value of realGDP per capita in PPP$” (HDR 1994, p. 91).
Source: HDR 1990–1995.
The HDR 1991–1995 formula for ‘Discounted Income’ W(y): anevaluation
The motivation for using the already presented formula for W(y) was toincorporate the consideration that “the higher the income relative to thepoverty level [y*], the more sharply the diminishing returns affect thecontribution of income to human development”. This was achieved byconstructing a W(y) function that simply adds on the concave pieces
1
1 2 «(y 2 jy*)1 2 «
with different values of « for different income intervals de�ned throughsuccessive integer multiples j of the poverty level y*. For income interval[jy*, (j 1 1)y*] the value of « assumed is j/(j 1 1), for j 5 0, 1, 2, 3, etc. Wecan thus write the HDR 1991–1995 function W(y) in general form as:
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W(y) 5 O kj 5 1
j(y*)1j 1 (k 1 1)(y 2 ky*)
1(k 1 1) for ky* # y # (k 1 1)y*
This form is valid for all integers k > 1. For k 5 0, i.e. for the incomeinterval 0 # y # y*, the function is given by W(y) 5 y.
Note that although this function is piecewise concave, it is not concavethroughout its range. Where each new piece gets added on, the right-handderivative of the function has an in�nite slope. The derivative of W(y) at anyy in the income interval [ky*, (k 1 1)y*] is given by
W
y5 (y 2 ky*)
2 k(k 1 1)
® ` as y ¯ ky*.
Hence, the right-hand derivative of W(y) is in�nite at y 5 ky* for k 5 1, 2, 3,etc. The left-hand derivative of the function W(y) at y 5 ky* is given byevaluating W/ y at the right end-point of the previous income interval,namely [(k–1)y*, ky*]. For any y in this interval, W/ y is given by
W
y5 [y 2 (k 2 1)y*]
2 (k 2 1)k .
Therefore, as y ky*, we have
W
y® (y*)
2 (k 2 1)k
which is a �nite positive number for all integers k > 1.10 Thus the functionW(y) is not concave in income y. In other words, it does not re�ect“diminishing returns” in the “contribution of income to human develop-ment” (HDR 1991, p. 90, etc.).
The second problem with the formulation of the presented W(y)function is that the elasticity of the marginal valuation function W 9 (y) doesnot, in fact, lie between 0 and 1. Nor does the elasticity of W 9 (y) increasefrom 0 to 1 as income y increases. The elasticity of the W 9 (y) function isde�ned as
h (y) 5 2 log W 9 (y)
log y5 2 y
W 0 (y)
W 9 (y).
In the interval [0, y*], we do therefore have h 5 0. However, in the intervals[ky*, (k 1 1)y*] for k > 1, we have
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log W 9 (y) 5 2k
(k 1 1)log (y 2 ky*).
Therefore,
h (y) 5 2 log W 9 (y)
log y5
k
(k 1 1)
y
(y 2 ky*).
Thus within the interval [ky*, (k 1 1)y*] itself, we have
h (y) ® ` as y ® ky*
and
h (y) 5k
(k 1 1)
(k 1 1)y*
(k 1 1)y* 2 ky*5 k as y ® (k 1 1)y*.
In other words, the elasticity of the marginal valuation function varies from` to k between the left end-point and the right end-point of the incomeinterval [ky*, (k 1 1)y*]. Therefore, the elasticity h (y) neither lies between 0and 1 nor increases with income y, both within and across income intervalscorresponding to multiples of the poverty line y*.
If the intention of the HDRs was to introduce a ‘variable elasticity’valuation function that is both concave throughout the income range andfor which the elasticity of marginal valuation increases with income (“thehigher the income relative to the poverty level, the more sharply thediminishing returns affect the contribution of income to human develop-ment” (HDR 1991, p. 90, etc.)), there are alternative functions that satisfythese conditions. Take, for example, the class of constant absolute in-equality aversion functions noted in Anand and Sen (1995, p. 27):
W(y) 5 2 e 2 g y where g . 0
up to a positive af�ne transformation. For this class, we have
W 9 (y) 5 g e 2 g y . 0
W 0 (y) 5 2 g 2e 2 g y , 0
and
h (y) 5 2 yW 0 (y)
W 9 (y)5 g y.
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Here, the elasticity h (y) starts at 0 when y 5 0 and increases linearly withincome y.
A more general class of valuation function that combines the constantrelative and constant absolute inequality aversion forms is given by
W(y) 5 2 y 2 a . e 2 g y where a $ 0, g $ 0
up to a positive af�ne transformation. By differentiation and a certainamount of manipulation, it can be shown that for this class we haveW 9 (y) . 0, W 9 9 (y) , 0 (i.e. W(y) is concave throughout), and that
h (y) 5 (a 1 g y) 1a
(a 1 g y).
Note that when a 5 0, this reduces to the constant absolute inequalityaversion class and h (y) 5 g y as above. When g 5 0, this reduces to theconstant relative inequality aversion class (Anand and Sen, 1995, p. 25) andh (y) 5 a 1 1. In the general case, for y 5 0 we have h (y) 5 a 1 1, and asy ® ` , we have h (y) ® ` .11
Thus, if a ‘variable elasticity’ valuation function for discounted incomeis sought, there is considerable �exibility in providing one that satis�es therequired properties. In this section, we have noted a number of problemsand inconsistencies with the HDR 1991–1995 function for discountedincome. However, by way of recti�cation, we have also suggested twoclasses of income function W(y) which are increasing, everywhere concavein the income range y, and have a ‘variable and increasing’ elasticity ofmarginal valuation h (y).
Distr ibutional adjustment to the income component
Practice: distribution adjustment procedures used
The 1990 HDR had foreshadowed a need to make distributional correctionsfor income, although no estimates for a distribution-adjusted HDI werepresented until the 1991 HDR. According to HDR 1990 (p. 12), the ration-ale for making distributional corrections was that “[A]ll three measures ofhuman development suffer from a common failing: they are averages thatconceal wide disparities in the overall population”.
The 1991 HDR was the �rst Human Development Report to adjust theincome component of HDI for inequality. As well as formulating the‘diminishing returns’ function W(y) (see previous section), the 1991 HDRintroduced another re�nement:
A second improvement in the HDI has been to make it moresensitive to the distribution of income within a country (technicalnote 4). Actual or interpolated Gini coef�cients (measures ofdistribution) were obtained for 53 countries — and used to
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compute human development indices modi�ed by income distri-bution (table 1.4) … The compilation of this modi�ed index onceagain drives home the point that a country’s human developmentachievements are greatly modi�ed if they are not shared by all itspeople. (HDR 1991, p. 17)
The precise method for making the HDI sensitive to income distribution isdescribed in Technical Note 4 of HDR 1991.
Adjusted income [i.e. W(y)] was multiplied by (1 2 G) — with Gbeing the Gini coef�cient — to modify income even further.Because this was done for the adjusted income, W(y), rather thanfor the actual income, the diminishing return effect could beincorporated before the distributional adjustment modi�es in-comes further. This modi�ed income W(y)[1 2 G] is then used asthe third variable in addition to life expectancy and educationalattainment to compute a distribution-adjusted HDI. (HDR 1991,p. 94)
Exactly the same method of modifying income was employed in HDR 1992and HDR 1993. There appears to be some discrepancy between this methodand what is stated to have been done in HDR 1994 (discussed later). Finally,no such distributional adjustment to the income component was undertakenin HDR 1995.
The method of interpolating distributional data for countries with nodirect estimate of the Gini coef�cient is also common to HDR 1991–1993.Thus, HDR 1991 (p. 94) describes the estimation technique as follows.
Some 45 countries have data on the ratio of the income share ofthe highest 20% to the lowest 20%. Of these 45 countries, 17 havedata on the Gini coef�cient as well, and there was found to be avery strong association between the two — the logarithm of theratio being a good predictor of the Gini coef�cient. This re-gression result was used to interpolate the Gini coef�cient for theremaining 28 countries. Some countries had data only on the Ginicoef�cient. In all, 53 countries with directly estimated or interpo-lated Gini coef�cients were available.
A word of caution is in order. The Gini coef�cients are registeredfor various years between 1967 and 1985, and the ratios of the top20% to the lowest 20% for years between 1975 and 1986. This isnot a serious problem, since these coef�cients are unlikely tochange quickly. But the Gini coef�cient is not always trulyrepresentative of the entire country. It is sometimes only for asubsection, such as the urban population. (HDR 1991, p. 94)12
The results of this distributional adjustment are described in HDR 1991(p. 94) as:
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For all but two countries the HDI is reduced by making it sensitiveto income distribution, and in over a third of them, it is reducedby 5% or more.13
The two countries for which the distribution-adjusted HDI value is higherthan the HDI value are Republic of Korea and Indonesia (HDR 1991,Technical Note, Table 2, p. 95).
It is dif�cult to understand what meaning can attach to the reductions(and increases for Korea and Indonesia) in HDI values that result frommaking it sensitive to income distribution. A percentage reduction would bea meaningful calculation if the ‘goalposts’ (i.e. the minimum and maximumof the income component) are unaltered. This would require estimating thedistribution-adjusted income component as
S 1
3 D W(y)[1 2 G] 2 Mini[W(yi)]
Maxi[W(yi)] 2 Mini[W(yi)].
But then it is impossible for Korea and Indonesia to show rises, becauseW(y)[1 2 G] # W(y) for G > 0 (by de�nition of G).14
On the other hand, if the minimum and maximum levels of discountedincome are altered to re�ect the new inter-country range for distribution-ad-justed (or modi�ed) income W(y)[1 2 G], the contribution of the incomecomponent to HDI would be
S 1
3 D W(y)[1 2 G] 2 Mini[W(yi)[1 2 Gi]]
Maxi[W(yi)[1 2 Gi]] 2 Mini[W(yi)[1 2 Gi]]
where Gi is the Gini coef�cient for country i. In this case, it is possible fora country’s distribution-adjusted HDI value to be higher than its HDI value.But then little sense can be made of percentage reductions (by 5 or 10%)in the HDI by making it sensitive to income distribution.15 The baselinevalue of HDI without distributional adjustment (obtained by putting G 5 0)is not the same in the two cases. Therefore, any reduction that occurs fora country cannot be attributed to its own Gini coef�cient G alone, but alsoto the Gini coef�cients Gi and the W(yi) levels in the countries for which[W(yi)[1 2 Gi]] is, respectively, minimized and maximized.
Statements of the following kind, then, do not seem to be altogethercoherent:
Brazil has one of the most unequal distributions of income — thetop 20% of the population receives 26 times the income of thebottom 20%. When the income component of its HDI is reducedby a factor to re�ect this maldistribution, its overall HDI falls by16%. The same correction also causes a major drop in the HDI ofmany other countries … (HDR 1992, p. 22; emphasis added)
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The compilation of this modi�ed index once again drives homethe point that a country’s human development achievements aregreatly diminished if they are not shared by all its people. (HDR1991, p. 17; emphasis added)
HDR 1994 appears to use a somewhat different basis for an income-distri-bution-adjusted HDI. The Gini coef�cient is no longer used as the measureof inequality of incomes. Rather, HDR 1994 (p. 97) states that:
For the income disparity factor, we have divided the share of theincome of the bottom 20% of the population by the share of thetop 20%. Multiplying this ratio by the country’s overall HDI givesthe income-distribution-adjusted HDI. This information is availablefor 55 countries.
No country has a perfect income distribution, so adjustingthe HDI for income distribution reduces the score for all. (HDR1994, p. 97; emphasis added)
In Brazil itself, HDR 1994 (p. 98) states that the ratio between the incomeshare of the bottom 20% to the top 20% is 1 to 32 (and in Botswana it is 1to 47). But, if the overall HDI is multiplied by 1/32 5 0.03, then the value forthe distribution-adjusted HDI for Brazil would become 0.03 3 0.756 5 0.02,whereas the value given in Annex Table A5.5 (p. 107) is 0.436.
As a result perhaps of such problems coming to light, no distribution-adjusted HDI was presented in HDR 1995. But ‘income discounting’ contin-ued in that Report, in the form of using the same formula W(y) forthe income component of the HDI as earlier HDRs (1991–1994) had done.If W(y) stands for achievements other than those of longevity and education,it may reasonably be asked why distributional adjustment is undertaken onlyfor that component of HDI.16 Sensitivity to inequality in achievementsrequires that we adjust all three components of the HDI for inequality(discussed in the context of gender, for example, in Anand and Sen, 1995).Yet, as we show in the next section, even with no concern for inequality inachievement levels, diminishing returns to income is a suf�cient reason fortaking note of the distribution of incomes. Inequality in incomes reduces theaverage achievement level made possible by income.
Critique of distribution adjustment procedures used
As we have suggested earlier, the income component of HDI (justi�ed interms of ‘command over resources needed for a decent living’) is supposedto re�ect elementary capabilities for which adequate quantitative indicatorsare not available, at any rate not on a comparable cross-country basis.Suppose that the income variable is indeed used as a proxy for achieve-ments other than life expectancy and literacy. It may be posited that suchachievements of an individual are represented through a concave functionA(y) of her income y, say, by the isoelastic form
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A(y) 51
1 2 «y1 2 «
up to a positive af�ne transformation. The arithmetic average of people’sachievements in a country of n persons is then given by
A 51
n O ni 5 1
A(yi)
51
n O ni 5 1
1
1 2 «yi
1 2 «
51
1 2 «yede
1 2 « by de�nition of yede (Atkinson, 1970)
5 A(yede).
Here yede, the equally distributed equivalent income, is de�ned as that levelof income per head which, if distributed equally among the n persons,would generate the same (total and) average achievement A (see Atkinson,1970). For « . 0, i.e. for a strictly diminishing returns to income functionA(y), we will obtain
A(yede) Þ A(y)
where y is the per-capita income. As shown in Anand and Sen (1995), for« . 0, we in fact have yede , y, and therefore A(yede) , A(y) since A(.) is amonotonic increasing function. Like the �rst two components of HDI, thethird component is supposed to represent the average achievement A in therelevant dimension. For this purpose, therefore, as a measure of averageachievement, one should use yede as the argument of the function A(.) ratherthan y, as has been done in previous HDRs.
It should be emphasized that this adjustment for inequality (use of yede
rather than y in A(.) or W(.)) arises simply because inequality of incomesdetracts from the (total and) average achievement
A 51
n O ni 5 1
Ai
where Ai 5 A(yi), not because we are concerned about inequality of theachievement levels Ai themselves. Also, using the average achievement levelA for the third component of HDI is consistent with what is done for the
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�rst two components, where average life expectancy and average literacy(or educational attainment) are the achievements measured.
If one were concerned with inequality of the Ai levels among people,then a different — and further — adjustment would be needed. A methodfor doing this is possible to devise, but we would then have to �x the af�netransformation in the A(.) function, i.e. the constants a and b , becausecomparability of both the Ai levels and units would be required. Theinequality correction, whether through the Gini coef�cient or some otherindex, would then be in the space of the Ai (not the yi) — and theadjustment to A done through a measure of inequality of the Ai (not the yi).
Hitherto, the HDR method of distributional adjustment has been to useW(y)[1 — G] for the third component, where y is per-capita real income,W(y) is the ‘discounted income’ function referred to earlier (piecewiseconcave with an in�nite slope at the start of each new piece), and G is theGini coef�cient of incomes, not of the Wi 5 W(yi). Although it is possible tocorrect this formula by using a measure of inequality of the Wi or Ai
themselves,17 such an adjustment alone in computing a ‘distribution-ad-justed’ HDI would be partial and incomplete. An intrinsic concern forinequality in human development requires adjustment of average achieve-ment in each of the three dimensions (by the extent of measured inequalityin each) — as well as an accounting of the covariances in achievementalong the different dimensions.
The income component of the HDI: purpose and functions
As was discussed earlier, the income component does play an importantpart in making the HDI a broad indicator. This purpose cannot be easilyful�lled by some other readily usable variable. In this �nal section, we comeback to the motivational issues, and present some further scrutiny of the useof this third component.
We have shown how the precise uses of the income component inthe previous Human Development Reports have sometimes been ratherproblematic, and it is clear that there has been ambiguity as well asoccasional inconsistencies in the utilization of the income variable. Butthese problems, as already discussed, can be entirely remedied, and thepurpose for which the income component was brought into the story canbe fully served by a precisely structured and consistent use of income-related variables, along with making corrections for inequalities in incomedistribution (for example, through yede).
Longevity and education are, of course, important components ofhuman development, and no attempt at constructing a human developmentindex can be successful without giving a major place to information relatedto survival and learning. Yet it would be a mistake to con�ne attention onlyto these two components of HDI. The role of the income component is toserve as a proxy for some of the important aspects of the quality of life thatare missed out in the exclusive concentration on life expectancy and basiceducation. The ability to command resources with which a person can lead
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a positively freer life in a number of �elds gives us an indirect account ofmany signi�cant aspects of human development.
Even the elementary freedom from hunger, as was discussed earlier, isnot just a matter of survival (nor of course of education), but includes, interalia, not being forced to live on a half-empty stomach. Similarly, havingadequate shelter can be important to leading a reasonable life, without thiscapability being re�ected — directly or indirectly — by either longevity oreducation. Again, elementary pleasures of entertainment, or visiting andseeing friends, or taking part in the life of the community, may requireresources that somehow must be considered in devising a human develop-ment index. It is these gaps that point to the need for something more thanan exclusive concentration on life expectancy and schooling.
Having an income is not, of course, comparable with being educated orliving long, which are valued for their own sake. Having an income-relatedcontrol over purchasable commodities can scarcely be intrinsically valuable.Nevertheless, in an indirect way — both as a proxy and as a causalantecedent — the income of a person can tell us a good deal about herability to do things that she has reason to value. As a crucial means to anumber of important ends, income has, thus, much signi�cance even in theaccounting of human development. While something is lost in terms of‘purity’, in not sticking only to variables such as life expectancy and beingeducated which are valuable in themselves, a major practical gain is madein indirectly extending the coverage to take note of various capabilities thatpeople do value intensely and which cannot be adequately re�ected in�gures of life expectancy and literacy. The need to take a transformation —to be exact, a strictly concave transformation — of the income variablerelates to the fact that the valued object ultimately is not income itself, butthe things we are able to do with the help of income, and it also givesrecognition to the further fact that there is likely to be some diminishingreturns in that conversion. We have already discussed these technical issues.
There is, however, a further — rather pragmatic — considerationconnected with the need for the income component. The need to includeany variable in addition to others depends a little on the extent to whichthese variables move with each other. If a variable x is already included, andanother variable y , re�ecting something important, is proposed for furtherinclusion, the case for that inclusion would be somewhat undermined if itwere to turn out that x and y move very closely together, so that x itselfserves as a proxy for y . It is, therefore, useful to see how per-capita income(a transformation of which is to be included in a three-component humandevelopment index) relates to life expectancy and basic education (theother variables already covered in the putative index).
There is, in fact, much evidence that life expectancy and GNP per headdo move together to some extent. For example, in inter-country compari-sons, there is typically a signi�cantly positive correlation between GNP percapita and life expectancy at birth. While that relation is often invokedin the standard literature on economic development to make the claim thatGNP itself can serve as a good development indicator (without supplemen-
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tation by life expectancy, since it is correlated with GNP), we could alsotry to turn the argument on its head to suggest that once we had lifeexpectancy included in the human development index, there would nolonger be much need to include additionally any GNP-based third variable.However, an empirical scrutiny does not provide much support either forthe defence of the adequacy of GNP per head as a ‘total’ indicator ofdevelopment, or for the proposed adequacy of life expectancy as a proxyfor GNP per head.
The reasons for this empirical scepticism include the fact that there aremany crucial divergences, even in inter-country comparisons, betweenrankings of GNP per head, and those of life expectancy achievements.Policy signi�cance may be attached to the experience of ‘outliers’ in eitherdirection — some countries (such as Costa Rica or Sri Lanka) doing muchmore to enhance life expectancy than their GNP per capita would suggest,while some other countries faring even worse than what their low GNP perhead would lead us to expect (see Dreze and Sen, 1989). Underlying thedisjointedness is the important fact that the connection between GNP perhead and life expectancy, insofar as it is there, depends very much on theway income is used in developing countries. For example, more provisionof public health care and reduction of poverty, both of which help to raiselife expectancy, can go with a higher per-capita income, but that relation-ship is not very tight. Once the variations of health care and poverty arethemselves taken directly into account, the need to include income perhead as a separate variable would, to that extent, be reduced in explainingvariations in life expectancy.18 Thus, in responding to the standard defenceof the use of GNP per head alone, it can be argued that this is simply notadequate, since we can get much closer to life expectancy by concentratinginstead on poverty removal and public health care.
This issue does not, of course, arise in that form in dealing with theputative formulae for human development, since life expectancy is directlyincluded in every form of the proposed human development indicator.However, the same basis of scepticism operates to undermine the statisticaladequacy of life expectancy to re�ect indirectly the ranking of GNP perhead. Life expectancy captures, in this view, the role of GNP per headmainly to the extent that it correlates with public health care and povertyremoval. But that is just not adequate enough, if our focus, instead, is onthose impacts of GNP per head that in�uence the quality of life in waysother than enhancing life expectancy. Income �gures can still serve toindicate the basic resources that people have to achieve some other typesof functionings (dependent on incomes), even though life expectancycannot serve this purpose because its effectiveness depends on a different,and not very tight, intermediate connection with public policies.
For example, in dealing with the achievements of the Indian state ofKerala, it would be right to record its great success in raising life expectancyas well as basic education, but some of the deprivations connected with thelow income levels of people in Kerala (such as inadequate housing, or eventhe prevalence of undernourishment) would also seem to need some
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recognition, which cannot be obtained from its high life expectancy orliteracy �gures. The fact that good public health care can dramaticallyreduce mortality rates, even without eliminating undernourishment, is atribute to the reach of public health care, but it also provides the basis ofan argument for looking at undernourishment through some other direct orindirect indicator, rather than through mortality rates alone.19 Similar re-marks can be made about some other aspects of quality of life that mayremain signi�cantly de�cient even as longevity is radically expanded bygood public policy. Life expectancy can soar and literacy come close tobeing total, and yet there could be major shortfalls in achievements whichseverely restrain the lives that people can lead.
Thus, the use of the income component in HDI is not dispensable, butit is important to know precisely why it is needed. It plays a part that theother two components of HDI cannot serve — either directly or as proxyvariables through correlation. To keep track of human development, weneed a broader picture than that provided by just education and health. Itis because of this set of underlying concerns that we have focused, in thispaper, speci�cally on ‘the income component of the Human DevelopmentIndex’.
In moving away from the traditional indicators of development, pri-marily GNP per head, the Human Development Reports have accomplisheda major re-orientation of focal attention, by bringing into the limelightthe neglected but crucial perspectives of survival and basic education as apart of development. But we have to avoid the opposite danger of takingsurvival and basic education to be all, in judging the progress of quality oflife. There is a need for balance, and the rationale for having this thirdcomponent of the Human Development Index relates to that reasoning.In this paper, we have discussed how this income component can be evenmore effectively used, particularly through corrections for inequalities,and what can be learned from the experiences and experiments in pre-vious Human Development Reports. The third component is needed and itcan be consistently and effectively used to serve the purpose for which it isneeded.
Notes
1 An early indication of the presence of a lacuna here was Robert Solow’s (1956)identi�cation of the immensely high proportion of the causation of per-capita economicgrowth that remained to be explained even after taking full note of the accumulation ofcapital, within the interpretative structure of neo-classical growth theory.
2 A good indication of the accepted status of this change can be seen in the plentifulrecognition, in the World Bank’s (1993) study of the ‘East Asian Miracle’, of the roles ofeducation, training, health care, and related changes in bringing about economictransformation in the east Asian economies.
3 Smith (1790), section IV.2.4 (in the 1975 edition, p. 188). The connections between thedifferent issues related to this question are discussed in Sen (1995).
4 Longevity is a crucial determinant of basic capabilities (one has to be alive to be able topursue actively one’s objectives), and being educated helps to advance other objectives(through knowledge and understanding as well as respect, status, and relative power).
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5 There is some evidence that conditions of health and morbidity are reasonably wellre�ected, despite some obvious imperfections, by measures of life expectancy. Indeed,direct questioning on the level of health and illnesses suffered seem often to producemisleading answers, re�ecting the differences in the knowledge and understanding of ill-health. For example, Kerala, with the best care in India and the highest life expectancyat birth, produces also the highest reported levels of ill-health. Greater medical knowl-edge and the possibility of treatment generates more awareness of ill-health, just as it alsoleads to treatment for ill-health (see Sen, 1993). It appears that longevity may well be abetter proxy for health conditions than the psychological perceptions of ill-health. Thereare also problems with going by medical reports of ill-health, since they depend on theavailability of medical services — again, better provided in states with greater healthcare, and little present in the more deprived states.
6 W(y) is the sum of (PPP$), (PPP$)1/2, (PPP$)1/3, etc., and thus cannot be readilyinterpreted as a PPP$ �gure.
7 In HDR 1995 also, the world average income of PPP$5,120 in 1992 is taken to be thethreshold level y* (p. 134).
8 This was the replacement of mean years of schooling with the combined enrolment ratioand the adoption of new series of data in constructing the 1995 HDI (HDR 1995, p. 19).
9 There is also an anomaly in the maximum value of W(y) assumed in HDR 1994 and inHDR 1995. Thus, in HDR 1994 (p. 108), the value used for W(40,000) is 5,385, whilein HDR 1995 (p. 134), the value derived for W(40,000) is ‘PPP$5,448’ — for exactly thesame W(y) function and poverty threshold y*.
10 Hence, the left-hand derivative of the function W(y) at y 5 ky* decreases monotonicallywith k, from a value of 1 at k 5 1 to (1/y*) as k ® ` .
11 It can be shown that h (y) is monotonic increasing for y . (a 1/2 2 a )/ g . This certainly holdsfor a > 1, if incomes are positive.
12 A virtually verbatim statement is found in HDR 1992 (pp. 94–95) with the followingexceptions: (i) 41 instead of 45 countries (as in HDR 1991) are stated to have data onthe ratio of the income share of the highest 20% to the lowest 20%; and (ii) the Ginicoef�cients are registered for various years between 1975 and 1988 (rather thanbetween 1967 and 1985 as in HDR 1991), and the ratios of the top 20% to the lowest20% are for years between 1980 and 1988 (rather than between 1975 and 1986 as inHDR 1991). HDR 1993 (pp. 101–102) also contains a similar statement, with data for 41countries available on the ratio of the income share of the highest 20% to the lowest 20%(of which 17 also have data on the Gini coef�cient), and the regression result being“used to interpolate the Gini coef�cient for another 11 countries, for a total of 52countries” (HDR 1993, Technical Note, Table 1.2).
13 A similar result is reported in HDR 1992 (p. 95): “For all but two countries, the HDI isreduced by making it sensitive to income distribution, and in a half of them, it isreduced by 4% or more. This is particularly marked in the developing countries, where24 of the 32 developing counties have a reduction of 4% or more and seven show areduction in excess of 10%.” The two countries for which the value of the distribution-adjusted HDI is higher than the HDI are Republic of Korea and Indonesia (HDR 1992,Technical Note, Table 1.2, p. 93).
14 The only way for W(y)[1 2 G] to be higher than W(y) is if G is negative (contrade�nition). Obviously, negative values of G should not be used even if interpolation ofthe Gini coef�cient (through the regression equation) produced negative values forKorea and Indonesia.
15 See HDR 1991 (Table 1.4, p. 18, or Technical Note, Table 2, p. 95) for estimates of thepercentage difference between HDI and distribution-adjusted HDI.
16 By applying the Gini coef�cient G of income inequality to inequality in ‘discountedincomes’ W(y), the HDRs 1991–1994 were not altogether consistent with an attempt toadjust for inequality in the achievements represented by income. A more consistentprocedure would have been to adjust W(y) by an index of inequality of the W(y)themselves (rather than of incomes y).
17 In the case of a separable, constant elasticity formulation, this becomes tantamount to
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computing yede for an elasticity of social marginal value of income greater than « , theincome elasticity of the individual marginal achievement function A9 (y).
18 See Anand and Ravallion (1993), where it is shown that once public health expenditureand a measure of poverty are used as separate variables on their own, the use of GNPper head as a further explanatory variable does not add signi�cantly to the explanation.
19 The need for additional concern with undernourishment was forcefully argued by Kumar(1987); on related matters, see also Panikar and Soman (1984), Kumar and Vaidyanathan(1988), Anand and Harris (1992), and Kumar and Stewart (1992).
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