Valuing longevity in the Human Development Index

Martin Ravallion

23 January 2011



The 20th edition of the annual Human Development Report has introduced a new version of its famous Human Development Index (HDI) (UNDP 2010). The HDI aggregates country-level attainments in three dimensions: life expectancy at birth, education, and income per capita. Each year’s country rankings by the index have been keenly watched (in both rich and poor countries) since they first appeared in 1990. UNDP (undated) documents many examples of the influence of the HDI, including on policymakers in developing countries.

As for any composite index, we need to know the trade-offs built into the HDI if it is to be properly assessed and used (Ravallion 2010a). The trade-off can be defined as how much of one desired component must be given up for an extra unit of another, keeping the overall HDI constant. In other words, the trade-off is what economists call the “marginal rate of substitution”. If one of the positively-valued dimensions increases at the expense of another, then it is the marginal rate of substitution that tells us whether human development is deemed to have risen or fallen.

What then are the trade-offs embodied in the HDI, and how have they changed?

The new Human Development Index

While there have been some changes to the HDI over its 20 year history, these are clearly the biggest yet. Only one of the three components is the same, namely life expectancy. Gross national income has replaced GDP, both at purchasing power parity and logged. The measures for education have also changed. And new bounds are used to map each component into a common (0,1) scale. But the change with greatest bearing on the implied trade-offs is that the HDI now uses the geometric mean of its three components, rather than the arithmetic mean. This was done to avoid the long-standing feature that the three dimensions of the HDI were assumed to be perfect substitutes (UNDP, 2010, p.15), as implied by the arithmetic mean.1

What do these changes mean for the HDI’s implicit valuations? Here I focus on the implications for the valuation of longevity. In Ravallion (2010b) I also examine the HDI’s valuations of schooling and discuss an alternative aggregation function for the HDI that would go a long way toward avoiding the problems identified here.

Country-level trade-offs between income and longevity

Aggregating income with life expectancy in a single index implicitly puts a monetary value on an extra year of life. The HDI’s marginal rate of substitution between life expectancy and income gives the extra income needed to compensate for one year less life expectancy, keeping the HDI constant.

The Human Development Reports have never discussed explicitly the marginal rate of substitutions embedded in their index, and they can be questioned. Past comments on the HDI have pointed out the seemingly low value attached to longevity in poor countries (Ravallion 1997). As we will see, it turns out that the changes introduced in the 2010 Report have lowered the HDI’s valuations of longevity even further.

Using the geometric mean changes the implied trade-offs. The direction of this effect is theoretically ambiguous, and depends crucially on both the data and the bounds used for rescaling the variables. As it turns out, for the vast bulk of countries (all but eight of the 169 countries for which the HDI is reported), switching to the geometric mean lowers the index’s valuation of longevity (see Ravallion 2010 for more detail).

So what are the HDI’s new trade-offs? Figure 1 gives my calculations of the new valuations of an extra year of life expectancy for each country, plotted against national income (logged to avoid bunching up at low incomes). The HDI’s valuation for the poorest country, Zimbabwe, is $0.51 per year, representing less than 0.3% of that country’s (very low) mean income in 2008. Thus the new 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 now has an unusually low GNI per capita. The next lowest valuation of longevity is for Liberia, at $5.51 per year (1.7% of annual income). The value tends to rise with income and reaches about $9,000 per year in the richest countries (Figure 1). The implicit value of extra longevity as a proportion of mean income also rises with mean income (Figure 2). (The highest proportion of GNI is 16%, in Equatorial Guinea, though this is clearly an outlier).

Figure 1. Monetary valuations of extra longevity in the 2010 HDI

Source (this figure and all following ones): Author’s calculations from data for 2008 provided in the 2010 Human Development Report. The fitted line is a locally smoothed (nonparametric) regression.

Figure 2. Valuations of longevity as a percentage of national income

So the trade-offs embedded in the HDI imply that, in the interests of promoting “human development”, poor countries should only be willing to pay a small sum (in dollars and as a percentage of national income) to attain an extra year of life expectancy, but that rich countries should be willing to pay about 10% of their mean income.

The changes introduced by the 2010 Report have markedly lowered the value of longevity relative to the old HDI. The change is particularly notable among low and middle income countries. This can be seen in Figure 3, which provides a “blow up” of Figure 1 for the poorest half of countries (in terms of GNI per capita), as well as the values implied by the old HDI aggregation formula using the arithmetic mean. (I also give the old valuation of longevity using the arithmetic mean and old bounds.)

Figure 3. HDI’s revised values of life expectancy in the poorest half of countries

It can be seen from Figure 3 that changing the bounds alone did not produce this large downward revision to the HDI’s valuation of longevity. It was the switch to the geometric mean that did the work, although it can be shown that different assumptions about the bounds would have made the HDI’s valuations less sensitive to the new aggregation method (Ravallion 2010).


The changes introduced in the new HDI have reduced its (seemingly low) valuations of longevity in poor countries even further. The Human Development Report’s implicit valuation on an extra year of life expectancy is now over 17,000 times higher in the richest country than in the poorest – a far greater difference than in their average income (which is 460 times higher in the richest country than the poorest). A poor country experiencing falling life expectancy due to (say) a collapse in its healthcare system could still see its HDI improve with even a small rate of economic growth.

A rich person will be able to afford to spend more to live longer than a poor person, and will typically do so. But how much should one build such inequalities into our assessment of a country’s progress in “human development”? That is a difficult question, which has certainly not been resolved here. However, given that the last 20 Human Development Reports have clearly intended to support a high value in development policymaking on attainments in health, it is puzzling that the 2010 Report has chosen a trade-off that puts such seemingly low value on the gains from longevity in poor countries. Possibly the construction of the HDI did not adequately consider what trade-offs were acceptable. Good intentions alone do not make for good measurement.

Note: These are the views of the author, and need not reflect those of the World Bank or any affiliated organisation.


Ravallion, Martin (1997), “Good and Bad Growth: The Human Development Reports”, World Development, 25(5):631-638.

Ravallion, Martin (2010a), "Your new composite index has arrived: Please handle with care",, 14 October.

Ravallion, Martin (2010b), “Troublesome Tradeoffs in the Human Development Index”, Policy Research Working Paper 5484, World Bank, Washington DC.

United Nations Development Programme, undated, Ideas, Innovation and Impact: How Human Development Reports Influence Change. United Nations Development Programme, New York.

United Nations Development Programme (2010), Human Development Report: The Real Wealth of Nations, New York: Palgrave Macmillan for the UNDP.

1 Strictly speaking, since income enters on a log scale, income and life expectancy (or schooling) were not in fact perfect substitutes even in the old HDI.



Topics:  Development Health economics

Tags:  development, longevity, human development index

Edmond D. Villani Chair of Economics, Georgetown University