Mon, 10 Jan 2011 18:00:37 GMT
By Eduardo Zambrano*
Associate Professor, Department of Economics at the Orfalea College of Business, Cal Poly
In 2010 the Human Development Report Office (HDRO) introduced a new methodology for the computation of the HDI. This new methodology takes the geometric mean of the suitably normalized achievements for each country in regards to life expectancy, educational attainment and income, and ranks the countries based on the index that arises as a consequence.
There are essentially three ways of understanding the rationale and implications of any such methodological change: (1) by identifying the normative principles that the new methodology satisfies, (2) by studying the tradeoffs between the different dimensions that are implicit in the resulting index, and (3) by looking at the ranking of countries that arises as a result. In my forthcoming papers “Functionings, Capabilities and the 2010 Human Development Index” (Zambrano, 2011a) and “An Axiomatization of the Human Development Index” (Zambrano, 2011b) I study the new methodology introduced by the HDRO in these three ways. In Zambrano (2011a) I also investigate some alternative formulations for the HDI proposed by Martin Ravallion in his paper “Troubling Tradeoffs in the Human Development Index” (Ravallion, 2010). What one learns is the following: The new methodology chosen by the HDRO in 2010 is a vast improvement over both the old formulation and the numerous alternatives that at one point or another have made it to the drawing board.
In this post I focus specifically on what one learns from comparing the rankings that arise from the alternative formulations suggested by Ravallion to the methodology adopted by the HDRO.
The different formulas
The new HDI is computed using a multiplicative function of the normalized values of health, education, and (log) income.[1] Ravallion in his paper suggested using an additive function of concave transformations of the normalized values of health, education and income[2], parameterized by a number, r, between zero and one. I compute the indices and the corresponding rankings suggested by Ravallion for three values of r: 0.9, 0.5 and 0.1 although for simplicity of exposition I focus below on comparing the case where r=0.5 to the 2010 HDI ranking.
The results
The first thing to notice is that there is a very strong linear association between these rankings[3], as Figure 1 shows.
Figure 1. Rank scatterplot between the HDI ranking and the Ravallion ranking
One immediately learns that there is far more agreement between the designers of these indices than there is disagreement.
Having said this, there are a number of countries for which the different rankings differ substantially. When the rankings differ we can take a closer look to see why the methodologies vary in their assessment of human development. Consider, for example, the seven countries outside of the 95% density ellipse highlighted in Figure 1 above. All but one of these countries (New Zealand) rank much better according to the Ravallion index than according to the new HDI. Why?
Table 1 below reveals the answer. It contains the rankings of these seven countries according to these two indices, and also according to the health, education and income variables alone.
Table 1. The rankings of selected countries according to assorted criteria
|
|
2010 HDI |
Ravallion index |
Life exp. rank |
Education rank |
Income rank |
|
New Zealand |
3 |
17 |
15 |
1 |
33 |
|
Luxembourg |
24 |
7 |
24 |
48 |
6 |
|
Singapore |
27 |
10 |
14 |
56 |
8 |
|
United Arab Emirates |
32 |
11 |
37 |
79 |
4 |
|
Qatar |
38 |
4 |
47 |
97 |
2 |
|
Kuwait |
47 |
26 |
35 |
107 |
5 |
|
Liberia |
162 |
143 |
133 |
133 |
167 |
Luxembourg, for example, ranks in the top 10 according to the Ravallion index even though it ranks 24th in life expectancy and 48th in educational attainment. Qatar, in turn, ranks in the top 5 according to the Ravallion index even though it ranks 47th in life expectancy and 97th in educational attainment. Similar points can be made about the top 15 position of Singapore and the United Arab Emirates according to the Ravallion index despite their rankings in terms of educational attainments being outside of the top 50 and about the top 30 position in terms of the Ravallion index for Kuwait despite its life expectancy and educational attainment rankings being outside of the top 30. What all these countries have in common is that they are all top ten countries in terms of income per capita and that is just enough for the Ravallion index to rank these countries pretty high up despite their low, or uneven, development in the other dimensions. This is something that the new HDI tends to avoid.
Table 1 also features Liberia, which is on the other end of the income spectrum. Not only its income is comparatively low but it is also very close to the normatively determined minimum level for income of $163 per capita per year. As a consequence of this, the new HDI would have this country stay at the bottom of the ranking even though Liberia has comparatively better numbers for life expectancy and education than income.
One can test the soundness of the new HDI and of the Ravallion index further by asking the question: when the new HDI and the Ravallion index differ significantly, which index provides the ranking that goes most in accordance with what these indices are intended to measure? Let’s look at an example of how to answer this question for the case of New Zealand, the only country in Table 1 which does significantly worse according to the Ravallion index vs. the new HDI.
New Zealand is not in the top 20 in terms of income alone. But it is by no means a poor country, as it has a level of income per capita that is about 3.5 times the median per capita income worldwide. It does have, however, a top 20 position in both life expectancy and in educational attainment. These attainments, and a high enough income, are sufficient for the new HDI to rank New Zealand as a top 5 country in terms of human development. The Ravallion index, however, gives New Zealand a spot that is 14 positions lower than the new HDI does, placing New Zealand (in terms of the countries in Table 1), behind Luxembourg, Singapore, The United Arab Emirates and Qatar. The question then becomes: If the Human Development Index is intended to measure “what a person can do and not what he can purchase as the ultimate metric of wellbeing,” (Chakravarty, 2003, p. 100) are the rankings implied by the Ravallion measure for these countries (versus, say, those produced by the new HDI) warranted?
Further robustness checks
Ravallion presents his proposal as a version of the family of generalized (additive) Human Development Indices developed by the great Indian economist Satya Chakravarty in 2003. But there is a crucial sense in which the Ravallion index and the Chakravarty index differ: the way in which they deal with income. Chakravarty treats his HDIs as capabilities indices, dependent on income only to the extent that income contributes to enhancing the capabilities set of the individuals in society. This is the same approach taken by Haq and Sen in their original 1990 formulation, and it is also the general approach taken by the 2010 HDI. Indeed, in his empirical implementation of his generalized HDI formulations Chakravarty uses precisely the same (concave) transformation of income that was being employed by the HDRO at the time he conducted his research (and which HDRO replaced later by the logarithm of income). As a consequence, the country rankings one gets from Chakravarty’s exact formulation are closer to the new HDI rankings than they are to the ones generated by the Ravallion indices, as Figure 2 below illustrates.
Figure 2. The Chakravarty ranking, the HDI ranking and the Ravallion ranking
To conclude
These seemingly different methodologies work in similar ways a lot of the time and, when they disagree, the new HDI appears to produce the most intuitive ranking of countries in terms of what the HDI is intended to be a measure of: capabilities and human development.
Endnotes
* I am indebted to Francisco Rodríguez and Jeni Klugman for their input and to Martin Heger for excellent research assistance.
1. The new HDI is computed as 
, where 
and 
. The variables h, e and y stand for health, education and income, respectively. The parameters ho,eo and yo are to be thought as normative values below which subsistence is not known to be possible. The interpretation of h*, e* and y* is that they’re the highest level any society has been known to achieve in those dimensions. The HDRO has determined these parameters based on long run historical evidence in the corresponding dimensions. See Kovacevic, M., “Review of Critiques to HDI and Potential Improvements.” Human Development Research Paper 33/2010.
2. Ravallion in his paper suggested using the formula: 
, where Ih and Ie are as before, 
and r is a number between zero and one.
3. The Spearman’s rank correlation coefficients between the HDI ranking and the Ravallion ranking is 0.9923. The Kendall’s rank correlation coefficients between the HDI ranking and the Ravallion ranking is 0.9420.
4. The Spearman and Kendall rank correlation coefficients between the HDI ranking and the Chakravarty ranking are, 0.9906 and 0.9272, respectively, whereas the Spearman and Kendall rank correlation coefficients between the Ravallion ranking and the Chakravarty ranking are, 0.9784 and 0.8891, respectively. Furthermore, among those countries for which the Chakravarty ranking differs substantially from the Ravallion ranking the following is true: For very high income countries the Ravallion ranking ranks countries much higher than the Chakravarty ranking, despite low or uneven development for these countries in the other dimensions of interest. For lower income countries the Ravallion ranking ranks countries uniformly lower than the Chakravarty ranking. This is, then, a specific sense in which the Chakravarty index is closer to the new HDI than it is to the Ravallion index.
This is not to say one would necessarily want to choose the Chakravarty measure over the new HDI formulation, as the new HDI has a number of advantages over these (additive) Chakravarty measures: (1) It is invariant to irrelevant aspects of the normalization of the core dimensions (Herrero, Martínez and Villar, 2010a, p. 4) (2) it recognizes that the contribution of one of the dimensions towards human development may critically depend on the level of achievement in the other dimensions (Herrero, Martínez and Villar, 2008, p. 9), (3) it is a fully axiomatized index (Zambrano, 2011b), and (4) it produces a more intuitive capabilities ranking whenever it disagrees with the Chakravarty measures (Zambrano, 2011a).
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Julio Antonio Pérez Espinosa, Etnólogo Ex funcionario Federal INI méxico y actual académico wrote: "Este trabajo es digno de estudiarse, no obstante cualquier esfuerzo tendiente a obtener mediciones más precisas y más alejadas de ciertos prejuicios, nos ayudará mucho. Gracias" |
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Siddieq Noorzoy, Professor of Economics, Emeritus U of Alberta, Canada wrote: "I wonder where in these formulations there is a role for the utility of the spirituality of different activities within the framework of different religions? I know as a Muslim that sharing what others need in material things gives a utility that no index can define for we believe this act is recorded by means unknown to humans. Thus, concentrating on the gains in this life for those believing in the next permanent life leaves a vacuum unfulfilled by any index measuring activities relating to this kind of phenomena present in many societies and communities." |
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Martin Ravallion, Director of the Research Department World Bank wrote: "It can hardly be surprising that these various indices are highly correlated with each other; they are after all just positively weighted aggregates of the same data. But that does not address my concerns about the “troubling tradeoffs” built into the HDI, notably the huge gradient in the value attached to an extra year of life (“value” measured in either money units of “HDI units”). This was an ethically troubling feature of the old HDI, but now it is even more problematic with the changes made to the index in the 2010 Human Development Report. Who could accept that an extra year of life is worth 17,000 times more in the richest country than the poorest? My proposed alternative index shows that one can go a long way toward avoiding these troubling tradeoffs. I do hope that the HDR team will think again about the properties of the index, and the signals they are sending to poor countries trying to improve their HDI ranking." |
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K.L.N. Reddy, Professor Department of Economics. SSSIHL (Deemed University) Prasanthinilayam-515134. A.P. INDIA wrote: "The model is good and a realistic measure of HDI." |
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Dominique Alheritiere, Hon. Chair International Association for Water Law wrote: ""The proof of the cake is in the eating". There must be something wrong with your methodology to see a country like the US ranking better than Canada, Sweden, Germany or France. A quick trip to these countries immediately shows that there are more inequalities, less solidarity in the first one compared to the latter 4. How can a country with 50 million without health coverage, with a declining life expectancy, etc. ranks 4th !! You must also introduce something regarding peace, because a country at war must not rank high on human development. Thanks" |
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David Hastings, Curator HumanSecurityIndex.org wrote: "@ Dominique Alheritiere: Perhaps you are looking for something more comprehensive and targeted differently than the HDI, particularly as it went in 2010? Such indicators as the Global Peace Index, the World Prison Brief (and related World Prison Population List) appear to be admirably approached indicators. They are included in the inputs to the Human Security Index (http://humansecurityindex.org), which just had version 2 released. The one country you refer to lies about midway down the ~230 countries enumerated on that list. The others are rather higher." |
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Suzatmo Putro, Central Board of Statistics, Mojokerto City - Indonesia wrote: "What about indonesia? Indonesia has moved 3 steps ahead to a higher rank, is it because of new methodology or our development progress? It could be a disputable political discussing. Is UN prompt all countries to use this kind of methodology in 2010?" |
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Jean-Yves Hamel, HDRO/UNDP wrote: "The Human Development Report Office prepares explanation documents for all HDI ranked countries. These files explain the changes to the HDI values and ranks, and are available in the country profiles of each UN member state. Click on the "Countries" tab in the top of our website to access the profiles." |
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Mehmet Tolga Taner, Senior Lecturer wrote: "Does anybody know whether (from now on) the HDI will be based on the estimate values of three dimensions?" |
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Jean-Yves Hamel, HDRO/UNDP wrote: "@Mehmet Tolga Taner: The new methodology for calculating the HDI will continue to be used in upcoming editions of the Human Development Report. For more information on this issue, please consult the 2010 |
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Dr. Udaya S Mishra, Associate professor Centre for Development Studies wrote: "I consider the new multiplicative aggregation procedure of HDI more accurate in the sense that it accommodates inter-dimensional dependence on one hand and rates greater equivalence across dimensions to be ideal on the other." |
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Dominique Alhéritière, Honorary Chair of an NGO Retired from FAO wrote: "In my search for brevity I forgot 2 things: 1) to congratulate you for your highly interesting work; and 2) to make a disclaimer that my comments do not commit at all the NGO for which I am a volunteer; I thought that to enter the name of my NGO was a compulsory field but I did not realize it would appear on my posted comment. Many thanks again." |
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Diosdado Ebang Ebang, Estudiante 4º Licenciado en economia Universidad de Zaragoza wrote: "Yo siempre he pensado que el PIB no es una medida exacta para medir el nivel de desarrollo de un país estaría bien que los organismos internacionales tuvieran mas en cuenta el IDH que personalmente considero el mejor indicador de crecimiento." |
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David Moore, Senior Project Manager Global Footprint Network (unaffiliated comment) wrote: "Firstly, I'd like to express my gratitude for the work that has been put in to attempt improvement of the HDI for this 20th Anniversary report. Despite Ravallion's thoughtful critique, I believe that although the data CAN be used for putting an implicit value on an extra year of life, this is quite an obscure abstraction and none which any country (hopefully) would attempt to use in evaluation of their development pathways. Rather, this characteristic should just be taken for what it shows: diminishing returns to HDI for increases in single indicators. The doubling of the diminishing returns to income reflects both this and the assumed diminishing ability for income to provide for "freedoms". Secondly, it has come to my attention that there may be an increased focus on inter-generational sustainability of human development in upcoming reports. I applaud this move, and would like to discuss the potential for natural resource measures such as the Ecological Footprint in augmenting the HDI. The Ecological Footprint is a tool which aggregates renewable natural resource use across a number of different land uses to produce a composite measure of human demand on the biosphere. Although Global Footprint Network's typical publications emphasize the consumption-based Ecological Footprint, it is equally possible to look at the production-based Ecological Footprint. If carbon dioxide emissions are excluded from the production-based Ecological Footprint, then we gain a measure of pressure on the domestic capacity of ecosystems. When this is set against another measure which describes the inherent ability of a country's ecosystems to provide resources, biocapacity, we gain information about the long-term sustainability of production. If we take this resource extraction to underlie the income component of the HDI, then we can scale the HDI in a similar way to the inequality-adjusted HDI, and derive a measure that scales the index based on how sustainable it may be in the long-term. Using this methodology, I have found that there are generally small changes to country's rankings. Countries that are highly industrialized fare better, since they generally place their environmental demands in terms of globally dispersed carbon emissions. Although this is an unfortunate outcome, it remains a challenge to incorporate negative global externalities within national measures. For example, would African countries at risk of severe drought due to climate change be penalized, since their production is likely to be further constrained? It is my hope to publish a white paper containing a detailed proposed methodology on an adjusted HDI on Global Footprint Network's website soon (www.footprintnetwork.org); until then, these comments remain unaffiliated." |
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Oscar Francisco Natalichio, Contador-Economista-Escritor-Docente Centro de Investigaciones Económico-sociales wrote: "El ingreso per cápita distorsiona el IDH. Si hay que incluirlo ello no debería tener más de un 10% de incidencia en la construcción del índice. Con un 33% lo que oculta es la pobreza La mortalidad infantil debe integrarse con la esperanza de vida en un 50 y 50% y debe ocupar un 50% del índice. El restante 40% la educación. Mayor ingreso no significa mayor calidad de vida." |
