Fri, 17 Dec 2010 16:00:44 GMT
Por Martin Ravallion
Director, Development Research Group, World Bank
It is important that users of popular development indices, such as the Human Development Index (HDI), understand their properties. With reference to the HDI, Bill Easterly and Laura Freschi write that “… while their results get huge publicity, the methodology behind the results is interesting to approximately 3 people.” Hopefully this debate will have increased that number.
Francisco Rodriguez has defended the HDI against the recent criticisms by Easterly and Freschi, which drew in part on my paper, “Troubling Tradeoffs in the Human Development Index.” Francisco would make a good lawyer, since he defends his case vigorously on multiple fronts.
But this leaves some puzzles about his true position. On the one hand, Easterly, Freschi and myself are said to be “fretting” that the new HDI puts too low a weight on longevity attainments in poor countries, while on the other hand we are characterized as believing that income is the best measure of development, in which case we would surely have no cause for fretting about a low weight on longevity in poor countries. Does Francisco really think that we are so confused?
Another puzzle is found in Francisco’s defense of the HDI. On the one hand he claims that tradeoffs—including the implied monetary valuation of extra longevity or schooling—are not relevant to the HDI, and that it is even “incorrect” to calculate them. But (on the other hand) he agrees that the old HDI was deficient because it assumed constant tradeoffs (perfect substitution). If he does not care about the HDI’s tradeoffs then why does he care about how much substitution is built into the index, which is all about its tradeoffs?
Let’s look more closely at the second (more important) puzzle.
The tradeoff built into any composite index is just the ratio of the (marginal) weight on one of its underlying variables (such as longevity in the HDI) to another (such as income). When one of the two variables is in money units, the tradeoff is a monetary valuation of the other variable. For example, if the HDI (which lies between 0 and 1) for a given country rises by (say) 0.006 for an extra year of life expectancy, while it rises by 0.000005 for an extra $1 of income per capita then the HDI implicitly values an extra year of life expectancy in that country at $1,200 (which is about the value implied by the data for South Africa, which is also about the mean for all countries).
I find that the valuations in the new HDI vary from an astonishingly low $0.51 for the country with lowest income per capita (Zimbabwe) to $8,800 for the second highest (Qatar).
Francisco rejects my focus on these implied tradeoffs embodied in the new HDI on the grounds that “…the HDI is not a utility function, nor is it a social welfare function. It is an index of capabilities.” This is an appeal to Amartya Sen’s insightful and influential writings arguing that human capabilities are the relevant concept for defining welfare or well-being. The HDR has never made clear how exactly one goes from the theoretical idea of capabilities to the specific form taken by the HDI. It is not an “index of capabilities” in any sense that is obvious to me, so I am inclined to think that this is little more than theoretical hand waving.
But even if one agreed that the HDI is an “index of capabilities,” the weights and implied tradeoffs embodied in that index remain fundamental to assessing it. Making such calculations certainly does not mean that we think that the index is the sole objective of development; it just means we are interested in understanding its properties. There is nothing “incorrect” in wanting to know the weights and implied tradeoffs in the HDI.
Francisco defends the new HDI against our “fretting” about its troubling tradeoffs on the grounds that it allows imperfect substitution between its components. This is a non sequitur. One can introduce imperfect substitution without the questionable features of the new index. Indeed, I showed in my paper that if the HDI had used instead the Chakravarty index—a simple generalization of the old HDI, with a number of appealing properties—it could have relaxed perfect substitution in a far less objectionable and more transparent way.
And I think almost anyone would agree that it IS objectionable to create an index of “human development” that puts such a vastly greater value on longevity in rich countries than poor ones. Instead of a 17,000 to 1 ratio of the HDI’s valuation of longevity in the richest country to the poorest, the ratio would have been about 50 to 1 using the alternative HDI I proposed in my paper. (50 to 1 may seem too high in some readers’ eyes, but it is a lot easier to accept than the tradeoffs embodied in the new HDI.)
Figure 1: The change in methodology has substantially lowered the HDI’s weight on longevity in poor countries
And this striking revaluation of longevity is not just due to the fact that the HDI puts declining marginal weight on income (as Francisco suggests). As can be seen from Figure 1, the weight on longevity itself has declined in almost all countries and substantially so in poor countries. This is due to the change in methodology. (The graph gives the marginal weight on extra life expectancy for each of the 169 countries for which the HDI can be calculated; the graph gives both the weight implied by the old HDI—which was a constant—and the new weight.)
I agree with Francisco that perfect substitutability was a dubious feature of the old HDI, and (as he points out) the index was criticized from the outset for this feature. It is a shame that it took 20 years for the Human Development Report to fix the problem. And it is an even bigger shame that the proposed solution brought with it new concerns.
One such concern is the substantial downward revision to the HDI for many countries in Africa, which Easterly and Freschi pointed out. Francisco questions their claim, but the data are not on his side. Figure 2 shows the pure effect of the change in the HDI’s aggregation method. (I have held everything else constant, at the same data used by the 2010 HDI.) Switching to the geometric mean involves a sizeable downward revision for countries with low HDIs, and these are disproportionately found in SSA.
Figure 2: The change in methodology has created a virtual “HDI crash” in Sub-Saharan Africa
Maybe it is time to go back to the drawing board with the HDI. Deeper consideration of what properties the index should have—especially its tradeoffs—would be a good way to start.
 Francisco notes that I do not apply the log transformation to income when calculating my alternative HDI using the Chakravarty aggregation function and he says I offer no justification for doing so. However, I do explain this choice in my paper. The reason for the log transformation in the old HDI was to assure that there are diminishing marginal returns to income—that the HDI is concave in income. This is a reasonable property. However, concavity is already assured by the Chakravarty functional form. So the log transformation is redundant. The fact that the new HDI kept the log transformation of income is actually rather odd; in effect income is then logged twice (log HDI is linear in the log of the log of income). It would have made more sense for the new HDI to drop the log transformation.