2014/05/22 by Jonathan Andreas
After percapita GDP, the second most important measure of economic welfare is The United Nations’ Human Development Index (HDI) as you can see in the above graph comparing the frequency of the words in Google’s database. If we add the abbreviation “GDP” to the graph, it dominates the other measures so much, they become almost too small in comparison to be able to see.
It is unfortunate that the HDI has not replaced GDP, because in most ways, the HDI is a newer, better, and more comprehensive measure of welfare than GDP. Unfortunately, the HDI has a tragic flaw. Its creators’ gifts were more mathematical than scientific and they added excessive complexity to the HDI formlua. They created a monstrous formula that even experts have difficulty applying to the real world. Their excessive mathematical creativity defeated their main purpose in trying to create a more accurate measure of welfare.
Norman Hicks & Paul Streeten (1979) give some history of work by the UN beginning in the 1960s which ultimately evolved into the first HDI ranking which was published in 1990. The HDI is a measure with three equallyweighted dimensions of welfare: income, lifespan, and education. The income component was GDP, so the HDI is sometimes criticized for being a descendant of the GDP. Other critics complain that the HDI, like GDP, it is too oversimplified, but all human knowledge is a simplification of reality because human brains cannot reproduce reality in all its detail, so some simplification is inevitable and desirable. GDP, HDI, and MELI are all attempts to compress reality into a crude, simple number which is inevitably a simplification. For this reason one of the creators of the HDI, Amartya Sen, “did not initially see much merit in the HDI”:
At ﬁrst I had expressed to Mahbub ul Haq, the originator of the Human Development Report, considerable skepticism about trying to focus on a crude index of this kind, attempting to catch in one simple number a complex reality about human development. (UNDP, 1990, p. 23)
But Sen and Hahbub Haq wanted to reduce the dominance of GNP which they considered to be “an overused and oversold index.” They decided that GNP could never be supplanted except by another measure that was just as “crude and convenient”. Haq said, “We need a measure of the same level of vulgarity as GNP – just one number – but a measure that is not as blind to social aspects of human lives as GNP is.” (UNDP, 1990, p. 23)
This is the whole point of any statistical analysis. Statistics exist to create crude and convenient oversimplifications because simplifications are the only way for puny human brains to hope to be able to deal with the complexity of the real world. Good statistics make smart people smarter. MELI can make people smarter than GDP or the HDI because MELI combines the best features of both rivals.
The biggest problem with the HDI is that it adds excessive complexity which makes it very difficult to explain and interpret compared with MELI. Even experts have difficulty completely understanding what the HDI measures. One reason the HDI is a mess to explain is because the HDI lacks units. When the UN discarded the units of the underlying data, important information was lost from the HDI. Because the HDI lacks units, it is impossible to compare it to any realworld measurements except ordinal comparisons with itself and that makes it hard to interpret. Suppose a HDI measurement goes from 0.87 to 0.78. What does that mean? I have often asked professional economists this question and nobody I have ever asked has been able to answer. Most people do not even know whether a bigger HDI is better or worse! Only a tiny minority of specialists who directly work with the HDI can interpret the numbers without looking up a HDI rankings for comparison. In this example, 0.78 happens to be the 2012 HDI for both Cuba and Saudi Arabia and 0.87 is the measure for the United Kingdom, but even that information is somewhat vague and unsatisfying compared with their mean GDP measures below.
HDI 
GDP/capita (PPP) World Bank Data 

Cuba 
0.78 
$18,796 
Saudi Arabia 
0.78 
$51,679 
Britain 
0.87 
$35,722 
The GDP measures are more seductive because they have units (dollar signs) that make the numbers easier to understand. Almost nobody knows what a drop in HDI from 0.87 to 0.78 means, but if the median expected lifetime income dropped from $87k to $78k, even a lay person could understand something about the magnitude of that tragedy because of experiencing these units in daily life. MELI has cardinal (ratioscale) dimensions^{[1]} and the HDI is a purely ordinal measure which means that the number itself gives less information.
Because the HDI lacks units, the UN can arbitrarily change the formula and almost nobody notices or cares. For example, the UN completely changed the formula 2010. They abandoned literacy data and adopted years of education instead. They switched from mean GDP to mean GNI and they began aggregating the three components using geometric means rather than arithmetic means. Martin Ravallion and Dan Hirschman were some of the few people who noticed and Hirschman summarized one disadvantage of the last change:
Martin Ravallion, …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… 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?
Ravallion’s paper points out that:
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.
MELI is less susceptible to wholesale changes in measurement methodology because it has realworld units and the calculations are more transparent. Debraj Ray says that,
The HDI might look scientific and the formulae used to create the final average might look complex, but that is no reason to accept the implicit weighting scheme that it uses, because it is just as ad hoc as any other. (1998, p. 28)
There are numerous problems with using GDP as a measure of welfare, but it is the king of welfare measures anyhow because most people think that it has the best combination of simplicity and explanatory power. Both MELI and the HDI retain most of the oversimplifications of GDP and they both make significant improvements in only two areas. They both 1) adjust for inequality and 2) include more dimensions of wellbeing than just monetary income. MELI is better on both factors.
The first improvement is adjusting for inequality. The HDI only adjusts GNP for inequality between nations by taking the logarithm of income (a common way to mathematically express dimmeu). That doesn’t change the rankings; it just deemphasizes income in rich countries compared with income in poor countries. The HDI doesn’t adjust for withincountry inequality at all. The HDI implicitly recognizes dimmeu because it uses the logarithm of income for international comparisons, but if dimmeu is important for international inequality, then inequality within each nation should also be important, but the HDI uses mean income within each country and this implicitly assumes constant marginal utility of money. This shortcoming is why the UN started publishing an inequalityadjusted HDI in 2010. The inequalityadjusted HDI is probably a better measure than the traditional HDI, but it is hard to tell because the calculations add even more complexity and that makes it even harder to analyze what the index is really measuring. That is probably why nobody uses the inequalityadjusted HDI. Even the UN prefers its simpler HDI measure. MELI adjusts for inequality by using the median income of each nation which is a stronger adjustment than the HDI because it changes the rankings of different nations. And the MELI adjustment is a much simpler and therefore more transparent way to adjust for inequality than the UN’s methods.
The second improvement is increasing the dimensions of welfare in the measurement. There are usually tradeoffs to increasing the dimensions of a measure because more dimensions add complexity which makes the measure more difficult to understand. Although MELI seems to add a second dimension to mean income (GDP) by including lifespan, it does not really add a second dimension, so it does not increase complexity at all. It only makes the second dimension more meaningful. Mean GDP already has a time dimension, but it is an arbitrary yearlong measurement that adds zero information about welfare. MELI simply makes the time dimension more meaningful by making it the most important and bestmeasured dimension of human welfare: life expectancy.
The MELI’s approach to measuring life expectancy is better than the HDI’s approach because the more complex HDI formula distorts the meaning of life expectancy, as explained earlier, so that the value of another year of life is bigger in rich nations that already have long lives than in poor nations that have short lives. That is a perversion of the value of life that was unintentionally introduced because of the adhoc complexity of the HDI measure.
It would seem like the HDI is better at including more dimensions of welfare than MELI because MELI only measures 2/3 of the data used in the HDI: income and longevity. But this is by far the most important part of the HDI. The other third, education, should be dropped or at least deemphasized because it is a much weaker measure of human welfare than either of the other two measures, it adds unavoidable complexity, and it adds large measurement errors to the HDI.
It does not deserve equal weight alongside lifespan and income. Amartya Sen himself once said that lifespan is the single best measure of welfare, so he would probably agree that it deserves more weight than education. The HDI measure itself implicitly prioritizes GDP over education because GDP is more closely correlated with the HDI than education which has the weakest correlation with the HDI of its three components. Even though the HDI’s formula weighs each of the three components equally, there is considerable redundancy in including all three because income, longevity, and education are highly correlated with each other. GDP has the highest correlation with the HDI of the three components which implies that it is the most important component for determining the HDI. Many authors have noted the extremely high correlation between GDP and the HDI and Srinivasan (1994) wondered if the HDI even adds enough information that makes any improvement on GDP measures. More recently, Justin Wolfers calculated the correlation for 2008 between GDP and HDI and found:
The correlation between the two is …a massive 95 percent! … For all the work that goes into the Human Development Index, it just doesn’t tell you much that you wouldn’t learn from simple comparisons of G.D.P. per capita. But you do get the veneer of something broader, with a normatively loaded name for this index.
This is a major reason why almost everyone uses GDP rather than the HDI. People, even economists, understand GDP better and the two measures give almost the same information anyhow. You can see how closely the HDI correlates with GDP below.
Nowadays the HDI is slightly more closely correlated with a related variant of GDP called GNI: Gross National Income which gives the very similar graph below. This is because GNI replaced GDP in official HDI calculations in 2010.
The outliers to the bottom right of the trend line are punished by the HDI relative to their GNI measure. Interestingly, most of them (labeled above) rely on natural resource extraction for a large share of their income. The natural resource curse seems to make them particularly inefficient at converting income into lifespan and education.
MELI would also be highly correlated with the HDI, but, like GDP, it would have units that everyone can understand, and MELI would measure welfare better than the HDI measurement for two reasons.
First, MELI does a better job of correcting for inequality than the HDI. I explained this earlier. Intranational inequality only has an indirect effect on the HDI. Inequality only hurts an HDI ranking if it makes a nation less efficient at converting income into lifespan and education as seems to be the case with many economies that rely upon naturalresource extraction.
Secondly, education is the only component of the HDI that MELI lacks is and education has the most measurement error of the three components, so it adds error to the overall measure. Of the three measures, the best quality data is lifespan because it is easy to define when someone dies and cheap for governments to accurately measure. But education is very hard to measure because the quality of education varies tremendously and we have no way to measure quality. For example, if Egypt gives women more years of schooling than Vietnam, does that mean that Egyptian women are really more educated than Vietnamese women? The total quality of education is what matters, not the quantity of years. It is even difficult to measure educational quality within a single nation like the US. Twelve years of public school in innercity New Orleans is completely different from twelve years in a wealthy Minneapolis suburb, but they would be counted exactly the same on the HDI. That adds error to the overall HDI measure.
Furthermore, education has a smaller impact on wellbeing than lifespan or income, so it does not deserve to have equal weight with the other two components of the HDI. Education measures have less correlation with measures of wellbeing. For example, education measures are less correlated than income or longevity with the HDI itself. Literacy was the main measure of education in the HDI until 2010 and it has much lower correlation with the HDI.
Years of schooling is currently the HDI’s main measure of education and it also has much less correlation with the HDI than GDP has.
In conclusion, MELI is better than the HDI because:
 MELI is simpler to understand, more transparent in its formula, and less ad hoc.
 MELI has units that give it more empirical meaning.
 MELI is better at correcting for inequality.
 MELI eliminates the overemphasis on the education measure that probably adds more noise than signal because of the high measurement error in educational quality and the high correlation between true educational attainment and the other two measures, lifespan and income.
^{[1]} All summary statistics must have a cardinal dimension. For example, to measure a median one must have at least one cardinal dimension, the discrete number of observations, because one must be able to know what half of the observations are. So even if one is using ordinal data, there must be a discrete, cardinal dimension if one is going to use statistics. MELI uses cardinal measurement of people, years of lifespan, and money income, but the latter two are only considered to have ordinal correspondence with welfare because people cannot agree upon how lifespan and money affect welfare. But just because we cannot agree on how lifespan and money affect welfare does not mean that they do not cardinally affect each person. So there is no point discarding the cardinal information that exists in the years and dollars in the MELI measurement. The HDI arbitrarily transforms the cardinal information into a purely ordinal number and discards information (including units) without gaining any additional clarity. Statistics should only discard information if they can increase clarity through making the simplification. The HDI does not achieve this.
References (In addition to the hyperlinks above)
Hicks, N., & Streeten, P. (1979). Indicators of development: The search for a basic needs yardstick. World Development, 7(6), 567–580. doi:10.1016/0305750X(79)900937
Ray, D. (1998). Development Economics. Princeton University Press.
Srinivasan, T. N. (1994). Human Development: A New Paradigm or Reinvention of the Wheel? The American Economic Review, 84(2), 238–243.
UNDP. (1990). Human Development Report 1990. Concept and measurement of human development. New York: United Nations Development Program. Retrieved from http://hdr.undp.org/en/content/humandevelopmentreport1999