It is shown that the component statistics of the HDI are highly correlated with one another. The paper demonstrates that an implication of this correlation is that a wide range of index weights produce indexes that are statistically identical to the HDI. Indexes with only two of the three HDI components are very highly correlated with the HDI. These results can be interpreted two ways: either the HDI is robust to a wide range of index weights, or it is largely redundant.Development

Miles Cahill

English

Research Papers in Economics

1
Eastern Economic Journal, Vol. 31, No. 1, Winter 2005
Miles B. Cahill: Department of Economics, College of the Holy Cross, One College Street,
Worcester, Massachusetts 01610. E-mail: mcahill@holycross.edu.
IS THE HUMAN DEVELOPMENT INDEX
REDUNDANT?
Miles B. Cahill
College of the Holy Cross
INTRODUCTION
Since its inception in the 1990 Human Development Report (HDR), the Human
Development Index (HDI) has been controversial. It was set up to replace Gross Domes-
tic Product (GDP) as the main gauge of development. As the 1993 HDR quote of Anand
and Sen [1992] summarizes, “Income, commodities (“basic” or otherwise), and wealth
do of course have instrumental importance but they do not constitute a direct mea-
sure of the living standard itself” [UNDP 1993, 106].1 Some researchers have sug-
gested, however, that since other development index statistics are so closely corre-
lated with GDP or GNP per capita, they are redundant in forming an index.2
But how much correlation renders a statistic redundant? McGillivray [1991] sug-
gests that a correlation coefficient of greater than zero for any component statistic
and the HDI is sufficient to dismiss the HDI of presenting new information. This
article further suggests that the degree of redundancy can be measured by how close
the correlation coefficient is to one. Finally, McGillivray [1991] suggests that the very
high rank-order correlation between the HDI and GNP per capita indicates that the
HDI does not present any new information above what can be learned from per capita
GNP. McGillivray and White [1993] propose alternative criteria for redundancy. First,
a variable is considered to be redundant if the correlation coefficient is above 0.90
(“Level 1 redundancy”) or 0.70 (“Level 2 redundancy”) [McGillivray and White 1993,
187]. Second, a variable is considered redundant if a “restricted” HDI computed with
the component excluded is highly correlated with the excluded component [McGillivray
and White 1993, 188].
This article updates these earlier studies to show that the individual indexes used
as component statistics in the current HDI are indeed highly correlated, using meth-
ods similar to those developed by McGillivray [1991] and McGillivray and White [1993].3
The analysis is then extended by presenting a unique illustration of the impact of this
correlation: alternative weighting schemes are found that form two sets of indexes
that are 1) statistically indistinguishable; and 2) very highly correlated with the origi-
nal HDI. These weights vary widely from the original HDI weights. For example, it is
shown that it is possible to exclude any one of the HDI components and still achieve a
correlation of 0.95 (or higher) to the original HDI.2 EASTERN ECONOMIC JOURNAL
THE HDI
In its current formulation (last revised in 1999), the HDI is a composite index of
four statistics: life expectancy at birth, the adult literacy rate, a combined school
enrollment ratio, and GDP per capita in purchasing power parity terms. The HDI does
not, however, employ raw statistics in its index, partly because it is not possible logi-
cally to combine statistics with unlike units of measure. Instead, the HDI methodol-
ogy creates intermediate component statistics that rate each country’s relative per-
formance in each category. Specifically, each country is rated on a scale from zero to
one, in which zero and one are theoretical lower and upper limits of society’s capabil-
ity (see UNDP [2001] for details). The enrollment and literacy statistics are then
combined to form an education index, in which literacy is given a weight of two-thirds
and enrollment one-third. GDP is also transformed by taking the natural logarithm to
give it diminishing returns. The three component indexes are then averaged together,
each with an equal weight of one-third.
CORRELATION BETWEEN COMPONENT STATISTICS
Table 1 displays the Pearson (zero-order) and Spearman (rank-order) correlation
matrices for the three component indexes for the 2001 HDI. The correlation coeffi-
cients are indeed large, and each of the correlation coefficients is significantly greater
than zero. Each of the coefficients is significantly less than one, however, implying
that some information is unique to each series. Nevertheless, the McGillivray [1991]
and McGillivray and White [1993] standards would reject the HDI as being redundant,
and to a high degree.
TABLE 1
Correlation Coefficients for Adjusted HDI Component Statistics
Pearson zero-order correlation
educ. index GDP index HDI
life exp. index. 0.791* 0.816* 0.936**
educ. index. 0.774* 0.922**
GDP index 0.928**
Spearman rank-order correlation
educ. index GDP index HDI
life exp. index 0.796* 0.857* 0.945**
educ. index 0.791* 0.905**
GDP index 0.942**
*significantly different from 0 and 1 at the 99.9 percent level of significance.
**significantly different from 0 at the 99.9 percent level of significance, significantly different from 1 at
the 98 percent level of significance.
Interestingly, the adjusted statistics are indeed more highly correlated (in terms
of zero-order correlation) with each other than the unadjusted statistics, as Table 2
shows.4 That is, some diversity of information may be lost in the adjustment calculation.3 IS THE HUMAN DEVELOPMENT INDEX REDUNDANT?
TABLE 2
Correlation Coefficients for Raw HDI Component Statistics
Pearson (zero-order) correlation
school
Adult lit. rate enroll. ratio GDP per capita HDI
Life exp. at birth 0.757* 0.758* 0.673* 0.936**
Adult lit. rate 0.812* 0.553* 0.883*
school enroll. ratio 0.663* 0.885*
GDP per capita 0.777*
Spearman (rank-order) correlation
school
Adult lit. rate enroll. ratio GDP per capita HDI
Life exp. at birth 0.753* 0.729* 0.860* 0.945**
Adult lit. rate 0.796* 0.732* 0.860*
school enroll. ratio 0.788* 0.843*
GDP per capita 0.943**
*significantly different from 0 and 1 at the 99.9 percent level of significance.
** significantly different from 0 at the 99.9 percent level of significance, significantly different from 1
at the 97 percent level of significance.
INDEX WEIGHT RESULTS
It has been established that the component statistics of the HDI are highly, but
not perfectly, correlated with each other. But what is the implication for this high
degree of correlation for the HDI results? One way to consider this is to find alterna-
tive weighting schemes that produce indexes that are highly correlated with the origi-
nal HDI. Specifically, the goal is to find the extremes for weights that produce an
index very much like the HDI. Table 3 presents six sets of alternative weights that
produce an index that has a Pearson correlation coefficient with the original HDI of
0.99. A correlation coefficient of 0.99 is significantly different from zero at the 99.9
percent confidence level; however, we can not reject the hypothesis that the correla-
tion is equal to one at the 85 percent confidence level.5 Table 4 presents weights for an
index that has a correlation coefficient with the original HDI of 0.95. A correlation
coefficient of 0.95 is significantly different from zero at the 99.9 percent confidence
level and significantly different from one at the 97 percent level. The Spearman rank-
order correlation coefficients are also reported on Tables 3 and 4, and are not signifi-
cantly different from the Pearson correlation coefficients.
Table 3 shows that an index may be statistically indistinguishable from the HDI
and still have a wide variety of weights, as low as 9 percent for a statistic in two
examples, and as high as 59 percent in another example. Table 4 shows that when the
criterion is lowered somewhat so that the alternative index is not indistinguishable
from, but very closely correlated with, the HDI, it is possible to compute an index in
which any of the statistics is eliminated and one of the statistics is given a weight of at
least 85 percent. Most dramatically, when GDP is eliminated, an index with a weight
of 92 percent on life expectancy and 8 percent on education has a 0.95 correlation with
the original HDI.4 EASTERN ECONOMIC JOURNAL
TABLE 3
Alternative Index Weights for Index with 0.99 Correlation with HDI
HDI index weights Rank-order
Goal life exp. education GDP correlation
high life exp. weight 0.585 0.228 0.187 0.991*
low life exp. weight 0.085 0.439 0.476 0.990*
high educ. weight 0.216 0.556 0.228 0.986*
low educ. weight 0.454 0.111 0.435 0.989*
high GDP weight 0.187 0.238 0.575 0.990*
low GDP weight 0.483 0.429 0.088 0.984*
*not significantly different from 0.99 at 75 percent level of significance.
TABLE 4
Alternative Index Weights for Index with 0.95 Correlation with HDI
HDI index weights Rank-order
Goal life exp. education GDP correlation
high life exp. weight 0.153 0.847 0.000 0.931*
high life exp. weight 0.137 0.000 0.863 0.957*
low life exp. weight 0.000 0.850 0.150 0.939*
low life exp. weight 0.000 0.115 0.885 0.953*
high educ. weight 0.064 0.854 0.082 0.936*
low educ. weight 0.903 0.000 0.097 0.953*
low GDP   weight 0.917 0.083 0.000 0.952*
*not significantly different from 0.95 at 80 percent level of significance.
CONCLUSION
The statistics used in the HDI are so closely correlated with one another that
indistinguishable alternative indexes can be created from the same statistics with
very different weights. In fact, an index that consists of a 58 percent weight on adjusted
GDP, 24 percent on the education index and 19 percent on the life expectancy index is
statistically indistinguishable from the HDI. An index that consists of an 89 percent
weight on adjusted GDP and the remaining weight on the education index has a 0.95
correlation with the HDI. Therefore, this paper not only updated the McGillivray
[1991] and McGillivray and White [1993] studies of the earlier HDI, but expanded the
analysis to show the implications.
There are two ways of interpreting these results. A view supportive of the HDI is
that it is robust to a wide variety of index weights. That is, the debate over the relative
weighting scheme is largely irrelevant. The conclusions of the HDI therefore cannot
be dismissed on the basis that the relative weights bias the results towards favoring a
particular aspect of development.6 This is important because several studies have
suggested that the HDI weighting scheme is subjective, or even random (see, for
example, Noorbakhsh [1998], Ravallion [1997], and Desai [1991]).
The view critical of the HDI is that it appears that a second or third statistic adds
only a relatively small amount of information about development to any one statistic.
To focus on GDP, an index very close to the HDI can be constructed with either an 895 IS THE HUMAN DEVELOPMENT INDEX REDUNDANT?
percent weight on per capita GDP, or a 0 percent weight on per capita GDP; both
results suggest that most information about the HDI is captured in per capita GDP.
Based on an analysis with similar results, McGillivray [1991, 1467] concluded, “…the
UNDP’s index is yet another redundant composite intercountry development indicator.”
NOTES
The author wishes to thank John F. O’Connell, John R. Carter, and an anonymous referee for
helpful comments.
1. Qizilbash [1996] surveys a large number of variables and concepts to consider when measuring
development in the context of critiquing Sen’s work. This paper suggests that composite indexes
like the HDI are useful, but is concerned that the components of the HDI do not perfectly match
the theory laid out in the paper and are not broad enough. Alkire [2002] provides a more recent
and more extensive list of development indicators.
2. McGillivray [1991] was among the first to do so, and concluded that it would be helpful to develop
new indicators to assess development. Larson and Wolford [1979] and Hicks and Streeten [1979]
performed similar analyses of earlier indexes.
3. These articles study the first (1990) version of the HDI; the current (1999 method version) HDI
uses different data and construction methods.
4. Cahill [2002] shows that the natural logarithm of GDP is more highly correlated with the other
statistics.
5. The p-value is 0.186 for the one-tailed t-test.
6. This is similar to a conclusion made by McGillivray and White [1993] on the topic of measurement
error. The article noted that even when assuming a 10 or 15 percent error applied to each of the
HDI index statistics, the assumed true HDI and reported HDI had a very high rank-order correlation.
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Is the Human Development Index Redundant?

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