Fri, 17 Dec 2010 18:00:47 GMT
By Francisco R. Rodríguez
Head of Research Team, Human Development Report Office, UNDP
Last week, I responded to recent critics of the HDI by pointing out that many of their observations were based on a misinterpretation of the HDI as a social welfare or utility function. This week, the World Bank’s Martin Ravallion responds. Ravallion characterizes my discussion of the HDI as an index of capabilities as “little more than theoretical hand waving.” He argues that there is a contradiction between my discussion of the desirable properties of the HDI and my argument that the trade-offs implicit in the index should not be interpreted as values. He also presents some new calculations purporting to show that Africa is in fact made worse off by the change in methodology of the HDI. Let’s look at each of his objections in turn.[1]
The HDI as a capabilities index
From the outset, we can find the description of the HDI as an index of capabilities. The 1990 Human Development Report, for example, describes it as “an index that captures the three essential components of human life…longevity and knowledge refer to the formation of human capabilities, and income is a proxy measure for the choices people have in putting their capabilities to use.”[2]
What is an index of capabilities? Simply put, it is an index that tries to measure the opportunities that people have to attain different kinds of lives that they have reason to value. Living a long and healthy life and having access to knowledge expand these opportunities. So do adequate nourishment, shelter and security. The HDI tries to measure some of the basic capabilities that matter to people’s lives and centers on three: health, education, and a decent standard of living.
There are many things that people may care about that are not usefully thought of as capabilities. For example, once one is sufficiently well-off, greater income may contribute to one’s pleasure or enjoyment, but does not radically alter our freedom to carry out the activities that allow us to lead a meaningful life. Thus, buying a flat-screen TV or a cashmere sweater may make us happier, but does not affect our capabilities.
For precisely this reason, the authors of the early HDRs argued that income should be treated differently in the index. Income, they argued, is not a capability but rather an input that people use to develop and use these capabilities. When income is low, its growth helps people to gain access to essential goods and services which constitute relevant capabilities. Yet as income rises its contribution to further expanding capabilities declines. The HDI (in both its old and new versions) captures this by using a logarithmic transformation of income.[3]
Note that this is a completely different issue from whether the index should incorporate imperfect substitutability in capabilities – something that the new index does through its new geometric mean formula. The first issue refers to the rate at which income turns into capabilities. The second is about how capabilities relate to each other. The geometric mean formula captures the fact that the more that you have of a given capability, the greater the contribution that increases in other capabilities will have to expanding people’s opportunities.
Ravallion advocates for a functional form that adopts imperfect substitutability but treats income symmetrically to health and education. He attributes this functional form to Chakravarty (2003), but ignores the fact that Chakravarty treated income asymmetrically from health and education in his calculations.[4] Instead, and in contrast to Chakravarty, he argues that “the log transformation is redundant…. It would have made more sense for the new HDI to drop the log transformation.” Dropping the log transformation, however, would have been equivalent to disregarding the idea that income turns into capabilities at a decreasing rate. Ravallion’s suggestion appears to reflect unfamiliarity with the literature on the treatment of income in the Human Development Index.
How do we interpret trade-offs in the HDI?
Trade-offs are implicit in any aggregate index, and exploration of these trade-offs is meaningful. But before we interpret them, we have to know what they represent. Ravallion makes much of the interpretation of the marginal rate of substitution implicit in the HDI – the amount of, say, income that you would have to receive in order to maintain the HDI constant if life expectancy had declined by a year. He calls this the “value of longevity” and compares it to existing evidence on the monetary values that people and markets assign to these goods. Thus, he argues, the value of longevity according to the HDI is 17,000 times higher in rich than in poor countries.
But if the HDI is an index of capabilities, then such comparisons are incorrect. Because people value other things than their capabilities[5], there is no necessary relationship between the trade-offs implicit in the index and the value that people assign to these components. Trade-offs along a capabilities index reflect rather the amount of one component that you would have to receive if another component has declined in order to keep a constant level of capabilities. Since income contributes nearly nothing to expanding capabilities in rich countries, then the implicit trade-off of longevity for income will be much higher in rich than in poor countries. The above noted 17,000 to 1 ratio simply describes how little income contributes to the expansion of capabilities after you surpass the basic levels necessary to ensure a decent standard of living.
Evaluating the relative performance of countries
Ravallion returns again to the issue of whether the change in HDI methodology has adversely affected the countries of sub-Saharan Africa. He presents a figure comparing two versions of the index (with arithmetic and geometric mean) and argues graphically that the geometric mean leads to a significant decline in values of the HDI for African countries.
The problem with this exercise is that it compares two indices which vary over different ranges. Before the changes introduced in this year’s report, the HDI varied from a minimum of .34 to .97 – after the changes, it went from .14 to .94. In other words, the new HDI methodology “stretched” the range of the HDI by substantially lowering its lower bound. Thus it is trivially true that the index values declined more for countries at the lower end of this spectrum.
It is incorrect to compare two functions which map over different ranges.[6] Saying that African countries suffered an “HDI crash” with the new HDI formula is like saying that more temperate countries will suffer a temperature crash if we shift from a Farenheit to a Celsius scale. Incidentally, this problem affects other comparisons presented in Ravallion’s paper, including the comparisons of weights on different dimensions in different HDI indices, as pointed out by Eduardo Zambrano in a new paper to be published in our research paper series.
A more meaningful comparison would look at functions which map over the same range. Such a comparison is readily available – we can simply look at the relative standing of African countries vis-à-vis the rest of the sample as given by their HDI ranking. The table below shows the variation in ranks for African countries arising from the changes introduced in this year’s report. Africa’s median rank in this year’s report is 141.5. By contrast, in last year’s report it was 143.5 – two positions lower. It would have also been two positions lower if we had kept the arithmetic functional form. Alternatively, if we had adopted Ravallion’s suggested functional form, it would have improved by only one position in comparison to last year. Thus, contrary to what Ravallion argues, the adoption of the geometric mean improved the standing of sub-Saharan countries relative to the rest of the world.
Table: Median rank of Sub-Saharan Africa's HDIs, alternative methodologies
| Rank | Change in rank relative to HDI 2009 | |
| New HDI | 141.5 | 2 |
| New HDI with arithmetic functional form | 143.5 | 0 |
| Ravallion functional form | 142.5 | 1 |
| Old HDI | 143.5 | . |
Note: Old HDI refers to the HDI published in the 2009 Human Development Report. Total observations = 166; SSA observations = 42. Sample includes only countries published in the 2009 and 2010 Reports.
Enabling open debate
HDRO values debate and deliberation around the properties of the Human Development Index and the other composite indices published in the Human Development Report. Although I disagree with the specific points raised by Martin Ravallion in this debate, I agree with his more fundamental observations regarding the need for greater transparency and discussion of the trade-offs implicit in composite indices, as well as of their theoretical underpinning.
In 2010, HDRO has moved to increase that transparency through the publication of research on the theoretical properties of the Human Development Index and the introduction of three new indices with well-specified theoretical foundations, two of which use individual-level household data.[7] This complements the existing space for rigorous academic debate on the measurement of human development that takes place in the HDRO-supported Human Development and Capabilities Association and Journal of Human Development and Capabilities. We have launched a new web application, “Build your own development index” through which users can explore the sensitivity of the country rankings in the HDI to changes in the variables included in the index as well as in the weights assigned to different dimensions. We have also launched this online forum, which has already housed previous discussions on methodology, to enable open discussion and debate about the human development approach. We hope that other institutions publishing composite indices will undertake similar initiatives.
References
Alkire, S., and J. Foster (2010) “Designing the Inequality-Adjusted Human Development Index (IHDI).” Human Development Research Paper 28. UNDP-HDRO, New York.
Alkire, S., and M. E. Santos (2010) “Acute Multidimensional Poverty: A New Index for Developing Countries.” Human Development Research Paper 11. UNDP-HDRO, New York.
Anand, S., and Sen, A. (1993) “Human Development Index: Methodology and Measurement.” Human Development Report Office Occasional Paper 19. UNDP, New York.
Anand, S., and A. Sen (2000) “The Income Component of the Human Development Index.” Journal of Human Development, 1(1), 83-105.
Chakravarty, S. R. (2003) “A Generalized Human Development Index.” Review of Development Economics, 7(1), 99-114.
Gaye, A., J. Klugman, M. Kovacevic, S. Twigg & E. Zambrano (2010) “Measuring Key Disparities in Human Development: the Gender Inequality Index.” Human Development Research Paper. UNDP-HDRO, New York.
Herrero, C., R. Martínez, and A. Villar (2010) “Improving the Measurement of Human Development.” Human Development Research Paper 12. UNDP-HDRO, New York.
Ul-Haq, M. (1995) “Reflections on Human Development.” New York: Oxford University Press.
UNDP (United Nations Development Programme) - Human Development Report Office (1990) “Human Development Report 1990.” New York: Oxford University Press.UNDP (United Nations Development Programme) - Human Development Report Office (1993) “Human Development Report 1993.” New York: Oxford University Press.
UNDP (United Nations Development Programme) - Human Development Report Office (1993) “Human Development Report 1998.” New York: Oxford University Press.
Zambrano, E. (forthcoming) “Functionings, Capabilities and the 2010 Human Development Index.” Human Development Report Office.
[1] The author would like to acknowledge the insightful comments and observations of María Eugenia Boza, Jeni Klugman, Emma Samman and Eduardo Zambrano as well as the research assistance of Martin Heger.
[2] UNDP (1990, p. 12). See also UNDP (1993), Anand and Sen (1993) and Desai (1991)
[3] An extensive discussion of these issues is provided by Anand and Sen (2000). See also Anand and Sen (1993) and ul Haq (1995).
[4] Chakravarty (2003) uses a concave piecewise function of income designed in the early Human Development Reports to capture the idea that income turns into capabilities at a declining rate. See UNDP (1998) for a description of this function. In 1999, this function was replaced by the logarithm of income.
[5] For example, policymakers in high income countries tend to devote significant efforts to raising their growth rates, although there appears to be only a marginal contribution of this growth to furthering the capabilities of the average citizen in these countries.
[6] I thank Eduardo Zambrano for making this point. Note that this also affects the calculations that I presented in the previous blog, which showed that Africa’s HDI had fallen 1.8% compared to the world average. The problem is that that number can be made higher or lower by applying arbitrary affine transformations to the HDI formula, even if they are constrained to keep the number in the 0-1 range.
[7] On the HDI, see Herrero et al. (2010) and Zambrano (forthcoming). On the new indices, see Alkire and Foster (2010), Alkire and Santos (2010) and Gaye et al. (2010).
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Martin Ravallion, Director World Bank wrote: "Whether or not we call the HDI an “index of capabilities” (though I remain of the view that this is quite unclear theoretically) we can still calculate its weights and tradeoffs, as we should with any composite index. To calculate the tradeoff is not to say that this bears any relationship to the value that people actually assign to that component. Nobody except Francisco is saying that. The tradeoff is just a property of the index—the ratio of its weights. |
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Juan Mora, Docente Escuela de Líderes Sociales y Empresariales wrote: "¿Qué debemos discutir? Una posibilidad, es discutir, como parece se está haciendo, sobre la manera, metodología para establecer los déficit o las inequidades, en base a variables como: nivel de longevidad, alcanzado, en un País en concreto ó en África Subsahariana ó cualquier otra. Y nos podemos enfrascar en la discusión o adopción de modelos de medición, matemáticos, estadísticos, mejores o peores. Una segunda opción es, discutir si es el enfoque unilateral de ingresos ó, por el contrario, es un enfoque multidimensional, el que nos permite entender y tomar decisiones de cómo mejoramos la calidad de vida de las personas. Quiere decir, de cómo los Estados generan oportunidades y capacidades para todas y todos. Ciertamente, las dos opciones son útiles. La primera por que pone el acento en la necesidad de medir, de la mejor manera, de manera adecuada y esto, tengo la impresión, debe hacerse en un debate académico, interno, que tenga a la base la suma de esfuerzos y capacidades para mejorar las variables. La segunda por que pone énfasis en que el incremento de los ingresos no es una condición única suficiente para generar capacidades y que por lo tanto hay que mirar, por lo menos, que pasa con la salud, la educación y la vivienda en concreto para poder conocer que desarrollo, qué capacidades y de quiénes se están generando, actualmente. Yo me quedo, obviamente con la segunda opción, me parece mucho más útil tener un diagnóstico, aún aproximado, de si los Estados y las personas pueden, con los ingresos que obtienen, sólo sobrevivir o generar capacidades para ellos y sus familias. Conocer esto con el método que sea es impostergable y construir Políticas y Programas que reviertan la situación es ética y políticamente, poco cuestionable, y urgente. Las personas en situación de Pobreza no son las que decidieron el tipo de desarrollo hegemónico hoy y tampoco pueden esperar nuestros debates teóricos y menos que no hagamos, responsablemente, la suma de capacidades. Con la finalidad no sólo de cuestionar ó tener la razón, en lo que planteamos. ¿Qué debemos Hacer? Avancemos a buscar las posibilidades, que el nuevo IDH 2010, brinda para establecer Políticas y Programas que lleven a tener un mundo más equitativo y justo y que las personas puedan mejorar sus condiciones y calidad de vida al tiempo que seguimos sumando capacidades para mejorar el nivel de observación ó la metodología de investigación." |
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Gregory Durrette, Consultant Summerall Institute wrote: "Thanks for your insight and integrity to lift the barriers that have created plagues." |
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Dickson Abraham Maturo, Student wrote: "There is inadequate information in the report given, since it touched not all human life aspect from its sources. When evaluating,one should consider all human lives foundation as struggles to life." |
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Peter Bartelmus, Prof. Bergische Universität Wuppertal, Columbia University, New York wrote: "Davao, 12/29/10
Source: P. Bartelmus (2008), Quantitative Econ–nomics, How Sustainable Are Our Economies?, Dordrecht and others: Springer Science and Business: Table 5.4." |
