Development: You’re Averagin’ It Wrong

Development is a fascinating topic because, like many big concepts, everyone kinda knows what it means and no one can precisely agree on how to define or measure it. One logical candidate for development (specifically, economic development) is GDP per capita, or some variation (GNP per capita, real GDP per capita, etc.). In 1990, the UN began publishing the Human Development Index (HDI) as a proposed metric for development that tried to move beyond just measuring income/production. The original HDI averaged three components, each of which was scaled from 0 to 1: GDP per capita, life expectancy, and education.

Now, you might ask, how do you measure and scale those three things? And how do you average them? There are a lot of options, of course, and recently the UN changed the formula. In response to an article about the weak correlation between HDI and GDP growth, a development economics grad student friend of mine linked me to a recent working paper by Martin Ravallion, who argues that the new HDI has serious problems, in part because it switched from an arithmetic average ((A + B + C)/3) to a geometric mean ((A^1/3)*(B^1/3)*(C^1/3)). Ravallion argues that this new formula obscures the implicit tradeoffs in the HDI, and that in particular the value of longevity is now a strange function of income such that the value of a poor life is much lower than that of a rich life.

Why does this change make a big difference? In the old system, the value of an extra year of life expectancy (LE) was the same for all countries. Slightly more technically, the marginal increase in the overall index was .0054 for every year of life expectancy. Zimbabwe adding one year of LE increased its HDI the same as the US adding one year to its LE. The new HDI is much less straightforward. For reasons discussed (and criticized) in the Ravallion piece, the UN decided that the HDI should lower the HDI of countries where one of the three variables was out of line with the others – imagine a rich country with low life expectancy and low literacy rates because most of the money is held by oligarchs – because the three are “imperfect substitutes”. By using the geometric mean, the HDI implicitly values “balanced” development – increasing all three components of the index in tandem. But, as Ravallion shows, by using a geometric mean, the HDI no longer has a constant marginal effect for increasing life expectancy, and in fact, the poorer a country is, the less one year of extra LE will benefit it. In particular, Ravallion computes the marginal rates of substitution for increasing income per capita vs. life expectancy. That is, Ravallion asks, how much more money would a country have to make in order for its HDI to remain the same if it lost 1 year of life expectancy?

The answer is quite shocking. Because the derivative of the geometric mean function mentioned above is always in terms of the other two variables, there is not a constant marginal effect. Instead:

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 HDI implicitly values a year of life expectancy in Zimbabwe at something like 1/10000th the value of a year of life in the US. Oops? What does this all mean?

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 VLEnew for the richest country with the poorest. Serious objections would naturally be raised to any proposal for public action within one country that rested on assigning a lower value to life to poor citizens than to rich ones, let alone a relative value that is such a tiny fraction. The same objections arise in a global context.

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.

I don’t know that any policymaker takes the HDI so seriously that they would consider a policy that cost a country a year of life expectancy (on average) to produce a per capita income gain of only a few dollars. But the HDI as currently calculated would measure such a policy as an improvement in the poorest countries. Ravallion proposes some alternative averaging methods that avoid this problem, but as he notes, no measurement of development will be free from value judgments. And no measurement of development which includes a monetary component will avoid an implicit tradeoff between economic growth and other forms of development. We will always be able to ask the question, how does this metric implicitly value (in money) a year of life or education?

More generally, in reference to my last post on Wallerstein and the split between science and the humanities, for development economists, “the radical separation…in the world of knowledge between the true, the good, and the beautiful” is illusory.


1 Comment

  1. Nathan E

     /  December 21, 2010

    I think you touch on a core idea that makes this difficult, in that people value their own lives differently, and even at the most fundamental level does someone feel that they are developing personally? I would have to look at my life at a very micro level to come up with a reasonable answer to that. Trying to extrapolate that much data from billions of people is both impractical and counterproductive to the goal of understanding and measuring progress.

    Rather than trying to come up with a still-pretty-complicated 3 axes representation of growth, you’ll find that you might need something more like a 1,347-axis graph to accurately represent the needed information. At which point, statistics do not clarify, but obfuscate. Statistics are are just numbers if they confuse. They aren’t necessarily useful metrics.

    If everyone knows what development is, but can’t define or measure it, it starts sounding a lot more like an emotion, like love. We can describe it in many different ways and has different meaning to different people. Trying to quantify love (or any emotion) sort of misses the point: cultures and “growth” are constantly moving, evolving, shrinking and expanding, but nonetheless growing in rich history. Even at “defining” events, you come up with the actual dilemma, of Heisenberg’s Uncertainty Principle.

    You can measure one thing, but miss the other equally important aspect. If you ever put the two together, they change each other and are no longer true representations. You can tell if something has grown, but can’t quantify that growth. You can quantify a statistical point of that growth, but then lose perspective of other factors.

    “Development” should be used as an anecdote, at most, due to this fundamental issue…just like if you went about measuring the “love” in a country.

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