metadata: authors: 0: author: Ravallion, Martin
count: World
docna: 0: docna: Troubling tradeoffs in the Human Development Index
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,Health Care Services Industry,Population & Development,Educational Sciences,Economic Growth
teratopic: Macroeconomics and Economic Growth,Social Protections and Labor,Poverty Reduction,Finance and Financial Sector Development
abstracts: cdata!: The 20th Human Development Report has
            introduced a new version of its famous Human Development
            Index (HDI). The HDI aggregates country-level attainments in
            life expectancy, schooling and income per capita. Each
            year's rankings by the HDI are keenly watched in both
            rich and poor countries. The main change in the 2010 HDI is
            that it relaxes its past assumption of perfect
            substitutability between its three components. However, most
            users will probably not realize that the new HDI has also
            greatly reduced its implicit weight on longevity in poor
            countries, relative to rich ones. A poor country
            experiencing falling life expectancy due to (say) a collapse
            in its health-care system could still see its HDI improve
            with even a small rate of economic growth. By contrast, the
            new HDI's valuations of the gains from extra schooling
            seem unreasonably high -- many times greater than the
            economic returns to schooling. These troubling tradeoffs
            could have been largely avoided using a different
            aggregation function for the HDI, while still allowing
            imperfect substitution. While some difficult value judgments
            are faced in constructing and assessing the HDI, making its
            assumed tradeoffs more explicit would be a welcome step.
repnme: repnme: Troubling tradeoffs in the Human
            Development Index
display_title: Troubling tradeoffs in the Human
            Development Index
listing_relative_url: /research/2010/11/13170524/troubling-tradeoffs-human-development-index
topicv3: Economic Growth m1326241 471,Education m1327048 470,Aging Population m1327275 643,Life Expectancy m1504363 2666,Health m1504661 3480
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Social Protections and Labor,Poverty Reduction,Finance and Financial Sector Development
no_of_pages: 32
model_extractions: WPS5484 Policy Research Working Paper 5484 Troubling Tradeoffs in the Human Development Index _Martin Ravallion_ The World Bank Development Research Group Office of the Director November 2010
Policy Research Working Paper 5484

# **Abstract**

The 20<sup>th</sup> Human Development Report has introduced a new version of its famous Human Development Index (HDI). The HDI aggregates country-level attainments in life expectancy, schooling and income per capita. Each year’s rankings by the HDI are keenly watched in both rich and poor countries. The main change in the 2010 HDI is that it relaxes its past assumption of perfect substitutability between its three components. However, most users will probably not realize that the new HDI has also greatly reduced its implicit weight on longevity in poor countries, relative to rich ones. A poor country experiencing falling life expectancy due to (say) a collapse in its health-care system could still see its HDI improve with even a small rate of economic growth. By contrast, the new HDI’s valuations of the gains from extra schooling seem unreasonably high—many times greater than the economic returns to schooling. These troubling tradeoffs could have been largely avoided using a different aggregation function for the HDI, while still allowing imperfect substitution. While some difficult value judgments are faced in constructing and assessing the HDI, making its assumed tradeoffs more explicit would be a welcome step.

This paper—a product of the office of the Director, Development Research Group—is part of a larger effort in the department to assess whether prevailing development indices are providing a reliable guide to assessing country performance and guiding policy making. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at mravallion@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Troubling Tradeoffs in the Human Development Index

## Martin Ravallion<sup>1</sup>

_Development Research Group, World Bank 1818 H Street NW, Washington DC, 20433, USA_

> 1    The author is grateful to Satya Chakravarty, Deon Filmer, Emanuela Galasso, John Quiggin, Suman Seth, Dominique van de Walle, Adam Wagstaff and staff of the Human Development Report Office, UNDP, for helpful comments and discussions. These are the views of the author, and need not reflect those of the World Bank or any affiliated organization.
# **1. Introduction**

The _Human Development Index_ (HDI) aims to provide a broader characterization of “development” than is possible by focusing on national income alone. For this purpose, the HDI aggregates country-level attainments in life expectancy and education, as well as income. The index has been published since 1990 in the UNDP’s _Human Development Reports_ (HDRs).

Each year’s scores and rankings by the HDI are keenly watched in both rich and poor countries. The countries that do well on the index are congratulated by each new HDR.<sup>2</sup> Politicians and the media often take note. The HDI aims not only to monitor human development, but to encourage countries to take actions that promote it. The latest (2010) HDR claims that the HDI and its various descendants “...yield many novel results—and insights—that can guide development policy debates and designs” (UNDP, 2010, p.8). UNDP (undated) documents numerous examples of the policy influence of the HDRs, including the HDI.

As in any composite index, users should know what weights are attached to the HDI’s dimensions, to properly judge if it has got the balance right.<sup>3</sup> The weight in any given dimension can be defined as the index’s first partial derivative (“slope”) with respect to that dimension. Since the units of the index are arbitrary (the HDI is normalized to lie in the 0, 1 interval) what really matters is the relative weights of its component dimensions. In other words, we need to know the assumed tradeoffs, as given by the HDI’s marginal rate of substitution (MRS), i.e., how much of one desired component of the HDI must be given up for an extra unit of another component, keeping the overall index constant. If a policy or economic change entails that one of the positively-valued dimensions increases at the expense of another dimension, then it is the MRS that tells us whether human development is deemed to have risen or fallen.

> 2 In answer to the question: “Which countries have been most successful in furthering the human development of their people?” (UNDP, 2010, p.41) the HDR looks at HDI indices over 1970-2010 for 135 countries and identifies the “top 10 movers,” defined by the rate of increase in their HDI relative to its 1970 value; the countries are Oman, China, Nepal, Indonesia, Saudi Arabia, Lao PDR, Tunisia, South Korea, Algeria and Morocco. At the other extreme, the report identifies three countries for which the 2008 HDI is lower than its 1970 value: Democratic Republic of the Congo, Zambia and Zimbabwe.

> 3 On the importance of knowing the weights built into a composite index of development see Ravallion (2010a), which also discusses a number of other issues not touched on here, including the robustness of country rankings and whether aggregation of the core dimensions is useful for policy.

2
While the HDI has clearly aimed to influence policy makers, and appears to have had some success, the interest in identifying its tradeoffs does not rest on a view that the HDI is the maximand of some policy calculus. The interest stems instead from the need to understand the properties of the index. We can all agree that GDP is an incomplete metric of development.<sup>4</sup> The real issue is how we form a better composite index, should we feel the need for one.<sup>5</sup> What tradeoffs does the index attach to the various components? Only if we accept those tradeoffs can we be confident that the composite index is adequately measuring what it claims to measure.

In common with other “mashup indices” (Ravallion, 2010a), the HDI’s tradeoffs are not constrained by theory, though economic theory can offer some insights into how one might form a composite index of human development.<sup>6</sup> The authors of the HDR set themselves free to pick the HDI’s variables and weights. From 1990 to 2009 the HDI gave equal (linear) weights to three functions of its core dimensions for health, education and income.<sup>7</sup> While the choice of variables and their weights can certainly be questioned, the HDI has at least appeared to be transparent and simple. That appearance is not quite so evident on closer inspection. Indeed, the HDI has never made explicit its tradeoffs across the core dimensions; users are only told the weights on its three derived functions of those core dimensions, even though the deeper tradeoffs between the core dimensions are clearly more salient. Since income is one of those core dimensions, the tradeoffs can also be monetized, which makes them easier to understand, and to assess whether they are appropriate by comparison with other research findings, including on the economic returns to better health and education.<sup>8</sup>

> 4 The claims regularly made by the HDR’s that “development” is typically defined solely in terms of GDP have surely been exaggerated, as Srinivasan (1994) argued in an early critique of the HDI.

> 5 Saying that there is more than one relevant indicator of development does not in itself imply that we need to force them into one dimension; see Ravallion (2010a) on this point.

> 6 In the context of aggregating mean income and life expectancy, Dowrick et al. (2003) show how revealed preference theory can guide the methodological choices. Also see the more structural economic models in Becker et al. (2005) and Jones and Klenow (2010), and the latent-variable statistical model used by Høyland et al. (2010) to set the weights for a version of the HDI. 7

The income variable has been somewhat controversial, with some observers arguing against its inclusion in the HDI; on the case for including income, see Anand and Sen (2000). 8 Advocates of making human development the overarching development goal often reject monetary valuations. However the fact of using money _per se_ as the metric of value cannot be objectionable; rather the issue is how we assess “value.” For further discussion and references to the literature on money metrics of social welfare see Ravallion (2010a).

3
x — xmin =x ~ <u>ymax</u> ~~_~~ <u>ymin</u> (x = LE, S) InY— myTMn LeY= <u>Inymax</u> ~~—~~ <u>Inymin</u> (1.1) (1.2)
ADI gig = Cig + 1s +1y )/3 HDInew = [ie1/3 le!,1/3 ly!,;1/3 I, = (MS/MSTM2*)°5 (ES /ESTMAx) 05 <!-- Start of picture text --> (2)<br>(3)<br>ADInew<br><!-- End of picture text --> ADInew
Why did the 2010 HDR switch from equation (2) to (3)? The report offers the following explanation:<sup>10</sup> “Poor performance in any dimension is now directly reflected in the HDI, and there is no longer perfect substitutability across dimensions. This method captures how well rounded a country’s performance is across the three dimensions. As a basis for comparisons of achievement, this method is also more respectful of the intrinsic differences in the dimensions than a simple average is. It recognizes that health, education and income are all important, but also that it is hard to compare these different dimensions of well-being and that we should not let changes in any of them go unnoticed.” (UNDP, 2010, p.15) These reasons are not as compelling as they may seem at first glance. It is true that the old HDI assumed that the scaled indices (���, �� and �� ) were perfect substitutes (constant MRS), but this was not true of the core dimensions. Since income enters on a log scale (and is only then rescaled to the 0, 1 interval), income and life expectancy (or income and schooling) were not in fact perfect substitutes even in the old HDI. And relaxing perfect substitutability between ���, �� and �� does not imply that one should switch to the form in (3); one can do so by using instead the generalized (old) HDI proposed by Chakravarty (2003). (I will return to Chakravarty’s index in section V.) The other arguments made by the 2010 HDR for switching to the geometric mean are also less than fully compelling. It is not evident in what sense using the geometric mean makes poor performance more “directly” reflected in the HDI, or more “well rounded,” or “more respectful of the intrinsic differences in the dimensions,” or that using this aggregation formula means that we do “not let changes in any dimension) go unnoticed.” Indeed, one can argue, to the contrary, that the HDI’s new aggregation formula hides partial success amongst countries doing poorly in just one dimension. As dimension � approaches �<sup>���</sup> we see that ������ approaches zero no matter what value is taken by the other dimensions.

Consider, for example, Zimbabwe, which has the lowest ������ of 0.14 (UNDP, 2010)—and it is the lowest by far, at about 60% of the next lowest. Yet this is due to one component that currently scores very low, namely income; Zimbabwe’s ��=0.01—the lowest of any country, and by a wide margin (60% of the next lowest value)—while ��=0.52 and ���=0.43, both well above the bottom. Indeed, there are 56 countries with a lower schooling index than Zimbabwe’s, yet this relative success is hidden by the HDI’s new aggregation formula, given its

> 10 A number of commentators in the literature have advocated a multiplicative form for the HDI, such as (3), including Desai (1991), soon after the HDI first appeared, and Sagar and Najam (1998) (although the 2010 HDR does not refer to these antecedents in the literature).

6
multiplicative form. Using the arithmetic mean instead (with other data unchanged), Zimbabwe still has a low HDI, but it ranks higher than six countries. (And Zimbabwe does even better using the alternative HDI discussed in Section V.) The rest of this paper examines the country-specific tradeoffs implied by the 2010 HDI, and how they have changed. On _a priori_ grounds it is unclear what effect relaxing perfect substitutability between the scaled indicators (���, �� and ��) would have on the tradeoffs in the core dimensions. Whether the MRS increases or decreases will depend on the data. This is illustrated in Figure 2, which plots the contours (holding the HDI constant) between log income per capita and life expectancy for both the arithmetic mean (the straight line contour) and the geometric mean (the convex one). As usual, the MRS is the absolute value of the slope of the contour. For convenience, countries A and B are taken to have the same HDI either way.<sup>11</sup> For country A, the switch implies a higher MRS, while for B the MRS is lower. The fact that we are more interested in the MRS with the core dimension of income (“unlogged”) adds further theoretical ambiguity to the effect of this change in the HDI.

While the focus here is on the HDI’s implicit tradeoffs, knowing those tradeoffs is clearly not sufficient for deciding whether policies that promote health care or education will promote human development. Even leaving aside the issue of whether the HDI is an adequate representation of that goal, we would also need to know the costs, assuming that it is national income net of those costs that is valued for human development.<sup>12</sup> And those costs will vary across countries. The costs of lengthening life or raising school attainments are also likely to be higher in richer countries, given that health and education services are labor intensive, and (hence) will tend to be more expensive in rich countries where wages are higher.

I will note some comparisons with the costs of increasing longevity, drawing on the literature. However, this paper’s focus on the valuations built into the HDI is primarily intended

> 11 In other words, the scaled values of log income and life expectance are swapped between A and B. More generally, depending on the data and assumed bounds, the switch to the geometric mean may alter the HDI ranking of A and B. 12

> For example, let _VLE_ denote the monetary valuation (MRS) for longevity and let _MCLE_ denote its marginal cost i.e., the income forgone for other purposes when life expectancy is increased by one year. Then higher life expectancy will increase the HDI if (and only if) _VLE_ > _MCLE_ .

7
lie Is ly OHDInew OHDIoa _ ~~Ox~~ Ox ~~HDInew~~ I, (x = LE.S.Y) HDInew < Ig (3(LETM* — LETM”))-1 = 0,0054 ~~dHDInew HD Inew OLE~~ 3(LE — LETMn)|

(4) (s)
HDInew > ly _ VLEoa ~~Y(nyTMTM — InyTM”)~~ = ~~—S~~ <u>pmax</u> ~~— min~~ = VLEnew ~~Y(InY — InyTM*”) LE —LEmin~~ VLE 51a Y (6.1) (6.2) VLEo1aq > VLEnew Ig > ly
2008. Figure 4 plots the valuations against national income. (I return to explain the “marginal cost” series in Figure 4.) The HDI’s value of longevity in the poorest country, Zimbabwe, is a remarkably low $0.51 per year, representing less than 0.3% of that country’s (very low) mean income in 2008. Thus the 2010 HDI implies that if Zimbabwe takes a policy action that increases national income by a mere $0.52 or more per person per year at the cost of reducing average life expectancy by one year, then the country will have promoted its “human development.” Granted Zimbabwe has an unusually low GNI. The next lowest valuation of longevity is for Liberia, for which the HDI attaches a value of $5.51 per year to an extra year of life expectancy; this is 10 times Zimbabwe’s valuation, though it is still only 1.7% of Liberia’s annual income. The value tends to rise with income and reaches about $9,000 per year in the richest countries (Figure 4). The highest valuation of longevity is 17,000 times higher than the lowest. Even dropping Zimbabwe’s (exceptionally low) valuation, the differential is 1,600.

The least-squares elasticity (the ordinary regression coefficient of �������� on ���) is 1.208 (with a robust standard error of 0.033; n=169). This is significantly greater than unity, implying that the HDI’s valuation of longevity as a proportion of mean income tends to rise with mean income. The elasticity is also higher than most past estimates of the income elasticity of market-based estimates of the value of statistical life.<sup>15</sup> The fact that the valuation of longevity as a proportion of mean income tends to rise with mean income is confirmed by Figure 5. (The highest value as a proportion of GNI turns out to be almost 16%, in Equatorial Guinea, though this is clearly an outlier.) By contrast, the old HDI had an income elasticity of unity, and (when evaluated with the HDI’s new bounds) ������ is almost exactly 10% of each country’s annual income.

The changes to the HDI have devalued longevity, especially in poor countries. Given the construction of the index, ������/������ is directly proportional to ������/� (equations 6.1 and 6.2); the constant turns out to be 10.014. So by dividing the vertical axis of Figure 5 by 10 (noting that the axis is in percent), we can also read it as a graph for ������/������. (Selected

> 15 A review of the evidence by Viscussi and Aldy (2003) concludes that the income elasticity is in the range 0.5-0.6.

10
points for ������/������ are indicated on the vertical axis in parentheses.) There was a roughly 25% downward revision on average (mean ������/������ �0.748). If one focuses on the poorest half of countries (GNI per capita below the median) then the average downward revision was close to 40% (mean ������/������ �0.620 ; n=84); for the poorest quarter, the valuation of longevity has been almost halved ((mean ������/������ �0.545; n=42)).

Figure 6 provides a “blow up” of Figure 4 for the poorest half of countries (in terms of GNI per capita), as well as the values implied by the old HDI aggregation using the arithmetic mean. (I also give the old valuation of life using the arithmetic mean and old bounds.) It can be seen that changing the bounds alone in the old HDI would not have produced this large downward revision to the index’s monetary valuation of longevity. Rather it was the combined effect of switching to the geometric mean, the form of the scales used and (of course) the data. Given the scales and aggregation formulae, the marked devaluation of longevity stems from the fact that ��� ��� for all except eight of the 169 countries, implying that ������ �������. (This difference in the distributions was already evident in Figure 1.) Whether this holds depends on the assumed bounds built into the HDI. For example, a higher upper bound for _LE_ would have lowered the value of life implicit in the old HDI; I find that ������ would have been quite close to the level of ������ at ��<sup>���</sup> �100. The somewhat arbitrary and time varying choice of bounds has played an important role in the HDI’s devaluations of longevity.

The income gradient in the HDI’s monetary valuations of longevity appears to be substantially greater than the gradient in the marginal costs of longevity. Dowrick, Dunlop and Quiggin (DDQ) (1998) estimate marginal costs of an extra year of life expectancy for 58 countries in 1980, which I have simply converted to 2008 prices using the US CPI. There are a number of comparability problems between the DDQ estimates and my calculations of _VLE_ , so these calculations should only be considered as broadly indicative for the present purposes.<sup>16</sup> The DDQ estimates are also given in Figure 4. Their estimated marginal cost of a one year increase in life expectancy is 400 times higher in the country with the highest cost (Denmark in their

> 16 Probably most importantly, updating solely for inflation in the US misses the structural changes in growing developing economies, which entail changes in their relative prices; in particular, we can expect that the cost of attaining higher longevity may have risen more in rapidly growing economies such as China than these estimates indicate. This is suggested by comparisons of PPP estimates across different rounds of the International Comparison Program; see Ravallion (2010b).

11
sample) than the lowest (Madagascar). This is far less than my calculations of the differential in the valuation of longevity implicit in the HDI. The DDQ estimates are only roughly similar to the HDI’s valuations for the poorest countries, but the HDI’s valuations greatly exceed marginal costs among most countries, and the gap is very large for the richest countries.

Across individuals, one expects the value attached to extra longevity to rise with income. Even if (instantaneous) utility depends only on consumption, a high income allows more to be consumed in the extra years of life, giving higher expected utility.<sup>17</sup> Similarly, one would expect people in rich countries to be willing to pay more for extra longevity, and they clearly do. However, such observations do not justify building an income gradient (let alone a steep gradient) into the valuation of longevity. The HDI is clearly intended to embody social values, which need not accord with private ones.

With reference to the private valuations of “statistical life”—such as derived from contingent valuation questions in surveys or wage premia paid for risky jobs—Ackerman and Heinzerling (2001, p.18) note a similar concern: “Calculation of the link between average income and the value of a statistical life could, if applied indiscriminately, lead to the unacceptable implication that rich people, or residents of rich nations, are worth more than the poor.” While the HDI is not deriving its valuations of longevity from such sources, the fact that it puts a higher value to an extra year of life for people in rich countries than poor ones is arguably no less of an example of the “unacceptable implication” that Ackerman and Heinzerling refer to.

This troubling tradeoff in the 2010 HDI will clearly influence its rankings of performance in human development. However, a more worrying concern arises if the index influences (domestic and international) policy making. The HDI’s embedded tradeoffs imply that, in the interests of promoting human development—or at least improving its HDI—the government of a poor country should not be willing to pay more than a very small sum (in $’s and as a percent of national income) for an extra year of expected lifespan for its citizens, while the government of a rich country would be encouraged to spend vastly more for the same gain in longevity—17,000 times more if one compares my calculation of ������ for the richest country with the poorest.

> 17 Suppose instead that (i) utility is strictly increasing in both life expectancy and income; (ii) the marginal utility of higher life expectancy does not fall with higher income, and that (iii) there is declining marginal utility of income. Then the MRS will be an increasing function of income.

12
HDInew > Is VSo1a = Y(InyTMTM — InyTM”)((MSTM*)~+ + (ESTM4*)~1)/2 VSnew = Y(InY — InyTM”)(MS~1 + ES~1)/2 (7.1) (7.2) VSo1d VSnew
�����=$33 per year, or 11% of annual income. At the other extreme, ����� rises to $53,000 per year in the country with the second highest GNI per person, representing 67% of that country’s GNI. The valuation of schooling has increased in 94 countries, though the increase is more marked amongst high-income countries. Given the cross-country differences in schooling, the valuation of schooling as a proportion of GNI does not rise with GNI above some point; Figure 8 plots �����/� against GNI. (The highest �����/� is for Burkina Faso, but this is an outlier.) While the HDI’s implicit valuations of longevity seem low, it’s valuations on schooling seem high. In constructing a composite index such as the HDI, there is a (rather poorlyunderstood) issue about what dimensions are intrinsically, versus instrumentally, important. We can all agree that a longer life is valued intrinsically, independently of income. However, it is not quite so clear that education has such a large intrinsic value (as assumed by the HDI), rather than being (very) important instrumentally to income and (hence) welfare.

In defense of the HDI, one might argue that the benefits of extra schooling are not fully reflected in current incomes; better educated parents pass advantages onto their children, leading to higher future incomes. (Possibly the new HDI’s introduction of the variable for expected schooling is trying to capture this effect.) But it is a moot point just how much extra one would allow for such an effect, on top of the economic return to schooling. The HDI is presumably measuring a country’s current human development not its future value.

If we compare the HDI’s valuations on schooling with the returns implied by earnings regressions, the HDI’s valuations are clearly very much higher. The regression coefficient of log earnings on years of schooling is typically around 0.1; see Psacharopoulos and Patrinos (2002). So it seems that the HDI is putting a much larger value on the returns to schooling than is reflected in current earnings. Indeed, the HDI’s valuation in developing countries appears to be roughly four times the labor market returns to schooling.<sup>19</sup> Finally, Figure 9 compares the new HDI’s valuations for longevity and schooling. What is most striking is how much higher the HDI’s implicit valuation of schooling is than its

> 19 For high-income countries, the ratios of the valuation of extra schooling to mean income in Figure 6 are roughly seven times the coefficients on years of schooling reported by Psacharopoulos and Patrinos (2002, Table 4, p.14). However, Banerjee and Duflo (2005) question whether the evidence supports the claim that returns to education vary much across countries.

14
HDI = [f(ie) + fs) + fUy)1/3 ~~a~~ f Ux) f Ux) fdJ=IF O<r<1) HDIf£ (8) Yr I, r ly = (vy -yminy/ (ymax _ ymin)
HDIE HDIE Vx ~~ly~~ 1-r ~~(ymax _ ymin)~~ = ~~(7) Gracgmm~~ (ALES) HDInew ©) HDInew HDIE Tr Ire Is HDI new HDIE HDI¢« HDI<.

HDInew HDIE
0.987 for _r_ =0.25), there are some large changes. For _r_ =0.5, Zimbabwe’s index rises by over 300%, from the lowest value (by far) of 0.140 based on ������ to 0.454; it also rises relatively, to be the 12<sup>th</sup> lowest—reflecting the fact that the additivity property of the Chakravarty index puts a higher premium on Zimbabwe’s schooling attainment. Using _r_ =0.25, the upward revision to Zimbabwe’s index is even more dramatic, with ����.��� =0.583. The largest decrease is that for New Zealand, for which the index falls by 0.094 in switching to ����.�� , and the ranking falls from third place to 18<sup>th</sup> . The differences are small at high HDIs using _r_ =0.25 (Figure 12).

# **6. Conclusions**

The Human Development Index was introduced in 1990 as an alternative to using national income per capita as the metric of development success. Until 2010 the index was an equally-weighted mean of scaled attainments in three dimensions: life expectancy, education and income. The simplicity of the HDI gave it a transparency that was clearly appealing to many users, although the HDI was never quite as simple as one might think at first glance, given the transformations embedded in its components. Over 20 years, the Human Development Reports (and numerous offshoot reports at national level) have applauded those countries that do well in the HDI, and offered advice to others on how they might do better in the HDI stakes.

A new version of the index was introduced in the 2010 edition of the HDR. The main change was to switch from the original additive aggregation function (the arithmetic mean of the three components) to a multiplicative function (their geometric mean). The main reason given for this change was to allow for imperfect substitutability between the HDI’s three components.

However, good intentions alone do not make for good measurement. The 2010 HDI is both more complicated and more problematic in its tradeoffs across core dimensions. Longevity in poor countries has been substantially devalued, though it seems unlikely that this was intended. The HDI’s valuation of longevity in the poorest country is now a mere 0.006% of its value in the richest country—a far greater difference than in their average incomes (for which the poorest country has 0.2% of the national income per capita of the richest). A poor country experiencing falling life expectancy due to (say) a collapse in its already weak health-care system could still see its HDI improve with even a small rate of economic growth. By contrast, 17
the valuations of extra schooling have risen for most countries and they seem high—some four times higher than the valuations typically placed by the labor market on extra schooling.

There are some contentious value judgments buried in the maths of the HDI. It can be granted that a rich person will be able to afford to spend more to live longer than a poor person, and will typically do so. But that does not justify building such inequalities into our assessment of progress in “human development.” Given what we know about the marginal costs of extending life expectancy, if one accepted the tradeoffs embodied in the new HDI, one would be drawn to conclude that the most promising way to promote human development in the world would be by investing in higher life expectancy in rich countries—surely an unacceptable implication of the HDI’s tradeoffs. And it is unclear why we would want to put so much higher a value on schooling than implied by its economic returns.

Setting the tradeoffs in a composite index is never going to be easy and it is ultimately up to users to judge for themselves if they accept the HDI’s valuations. However, the troubling tradeoffs in the new HDI are not in fact essential to relaxing the perfect substitutability property of the old HDI. The less appealing properties of the new index could have been avoided to a large extent, while allowing imperfect substitutability, by using an alternative aggregation function already found in the literature—in fact a straightforward generalization of the old HDI.

An important lesson for future composite indices is the need for transparency about the implicit tradeoffs, especially in more complicated indices. Those tradeoffs are the key to understanding the properties and implications of the index. I would hazard to guess that if the authors of the 2010 Human Development Report had calculated the tradeoffs implicit in their index they would have had second thoughts about it, and looked for alternatives.

18