Statistics, Development and Human Rights
Session I-PL 6/7
The Human Development Index and Beyond:
Which Are the Prerequisites for a Consistent
Design of Development Indicators - Should
There Be a Human Development Index?
Jacob RYTEN
Montreux, 4. – 8. 9. 2000
Statistics, Development and Human Rights
The Human Development Index and Beyond: Which Are the
Prerequisites for a Consistent Design of Development
Indicators - Should There Be a Human Development Index?
Jacob RYTEN
"Southleigh"
Cirencester, GL7 1TX, United Kingdom
T. + 44 1285 657 606 F. + 44 1285 658 889
Rytenjacob@email.msn.com
ABSTRACT
The Human Developmet Index and Beyond: Which Are the Prerequisites for a Consistent
Design of Development Indicators – Should There Be a Human Development Index?
In this paper, the question is asked under which conditions should an official statistical
agency engage in representing complex social changes by means of a single number. There are
examples of successful single numbers such as the GDP. The circumstances for them to be useful
and credible are examined and found not to exist in the case of the Human Development Index
(HDI). The current method of calculating the HDI comes in for criticism because it does not take
into account a measure of distribution even though social development can be stunted in the
absence of a distribution regarded as fair and equitable by all. The indicators derived from the
Health and Education sectors also come in for criticism because they lack a common structure. One
such structure is proposed as a starting point for future research. The paper’s conclusions are that
while the strength of a single number as a communication device is recognized, at this stage Human
Development should be measured by a set of at least half a dozen numbers. In any event and for the
time being, official statisticians should abstain from publishing a HDI and preferably ought to leave
the publication of related numbers in the hands of either their research arm or with research
institutions.
RESUME
L’Indice du Développement Humain et au-delà : Quels sont les pré-requis pour une
conception cohérente des indicateurs du développement - Devrait-il y avoir un Indice de
Développement Humain?
Dans cette présentation, la question est de savoir dans quelles conditions une agence
officielle des statistiques pourrait s’engager dans la représentation de changements sociaux
complexes moyennant de simples chiffres. Il existe des exemples de simples chiffres couronnés de
succès tels que le GDP. Les circonstances les rendant utiles et crédibles ont été examinées et il se
trouve qu’elles ne sont pas présentes dans le cas de l’Index sur le Développement Humain (HDI).
La méthode habituelle de calcul du HDI est l’objet de critiques car elle ne tient pas compte d’une
mesure de distribution même si le développement social peut être retardé en l’absence d’une
distribution considérée comme loyale et équitable par tous. Les indicateurs dérivés du secteur de la
Santé et de l’Education sont aussi l’objet de critiques car une structure commune leur fait défaut.
Une telle structure est proposée comme point de départ de la recherche future. Les conclusions de
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cette présentation sont les suivantes : quoique la force d’un simple chiffre en tant qu’outil de
communication soit reconnue, à ce stade le développement humain devrait être mesuré par un
ensemble d’au moins une demi-douzaine de chiffres. A l’occasion de tout événement et jusqu’à
nouvel ordre, les statisticiens officiels devraient s’abstenir de publier un HDI et de préférence
laisser la publication de tels chiffres aux mains soit de leur section de recherche, soit des
institutions de recherche.
1. Background
At first I wanted to limit my efforts to debunking the idea of a Human Development Index
(HDI). Official statisticians ought to resist the lure of single numbers designed to represent
complex social changes until such time as those numbers are solidly backed by theory and by
operational definitions of the magnitudes they purport to represent. There are several single
numbers that have been extraordinarily successful in conveying environmental information to the
general public, danger signals to policy makers, and an empirical basis for academics to test
theoretical hypotheses. But not all complex realities lend themselves to representation by a single
number nor does it follow when the matter is still the subject of active research that official
statistical agencies ought to lend their stamp of legitimacy by making the single number public.
The experience of the international statistical community with the International Comparison
Project 1 convinced me that the criteria that allow us to adopt certain numbers as official must be
made explicit. But if a particular number exists, has even acquired some legitimacy by virtue of
being around for some time and yet must be debunked, it is the burden of the debunker to suggest
an alternative. At this stage I have not yet come to the formulation of such an alternative. I do have
arguments to suggest that in the absence of certain initial conditions, one should sacrifice the
simplicity of a single number for the sake of a more robust and more nuanced description, in this
case of “human development”. While I have no operational definitions of what it is that we should
be measuring nor of a proposal to aggregate the various measurements, I do have an outline of the
direction in which I would like to see research go, the underlying assumptions to justify it, and the
steps that should be taken if the proposal below is considered to hold promise.
My paper attempts to discuss – if not to answer - the following questions. Firstly, when is it
legitimate to compile a single figure to represent a complex social (or economic, or environmental)
reality? Secondly, what are the circumstances that make it acceptable for an official statistical
agency to publish a particular statistic? Thirdly, is the Human Development Index a construct with
interesting properties? Fourthly and lastly, are there more useful and more interesting alternatives to
the current HDI?
2. The first question : When is it legitimate to compile a single figure to represent a complex
social (or economic, or environmental) reality?
There are well known examples of single figures used currently to represent complex
changes. To start with the best known of all – the GDP - we have all come across statements of the
following form and content:
“…in the two last quarters, real GDP growth has slowed down considerably making it
virtually impossible to reach the 2 per cent per annum forecast by the Ministry of Finance …”
In this hypothetical example, no one would question the adequacy of the concept of GDP to
provide a warning to the authorities that for reasons to be looked into, the rhythm of economic
J. Ryten: “The International Comparison Project” An Evaluation Report, 29 the Session of the United Nations
Statistical Commission. New York 1998. Ian Castles: Review of the Eurostat-OECD PPP Programme, OECD Paris
1997
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activity was insufficient to attain an official government expectation. Underlying the concept of
GDP are many complex conventions, accepted internationally, and abided by all serious
practitioners. For example, there is the convention on how to separate capital from current
expenditure; where to draw the production boundary; how to separate domestic from foreign
transactions; how to divide changes in values measured in nominal monetary terms into the
components caused by pure price variations and those accounting for all other causes; how to allow
for the effect of seasons –climatic or institutional – on the quarter to quarter variation of GDP
values; how to demarcate private from public transactions; and so on.
Beyond agreement on definitional conventions there is an acceptance that national economies
change slowly and therefore the figures that represent them are strongly auto correlated. What
happens in one quarter is strongly conditioned by what happened in the previous quarter and in turn
is a strong conditioner of what is to happen in the next. Given a particular value for one quarter – so
goes the assumption - it is highly improbable for subsequent values to be very much different from
what went on in the immediate past.
These agreements did not always exist. There was a time when the GDP figure was viewed
much as certain categories of experimental figures - the results of the Purchasing Power Parity
(PPP) comparisons for example - are viewed today. In the early fifties there was a debate whether
the GDP as an aggregate was interesting and suitable as a basis for action by Ministries of Finance;
there was a question about the legitimacy of deflation and whether it led to meaningful results; there
were doubts about the suitability of calculating GDP at quarterly intervals and whether the required
degree of imputation was not such as to invalidate the resulting rates of change; and finally there
was concern that seasonal adjustment distorted figures unjustifiably and that possibly the data
should be left in their original condition.
Even today there is no universal consensus over some of these questions. For example, there
are statistical agencies (NSO’s) that claim that their role is to calculate the best possible basic
statistics. They argue that transformations based on arguable assumptions such as seasonal
adjustment and imputations based on deductive inferences rather than on empirical observation are
best left to research departments and to academic institutions.
The debate over whether a single quarterly GDP figure provided useful and reliable
information lasted more than ten years. And whether it is the role of official statistical agencies to
compile it is still a moot question in many parts of the world.
Today the centre of discussion has shifted. In fact it has shifted to get closer to matters such as
those that underlie the construction of a Human Development Index. The issues faced are whether
the standards for GDP compilation and their definition of the production boundary are socially
acceptable in the light of current public concerns. The fact that the GDP number excludes unpaid
work conducted within the household is questioned by many quarters; that the GDP does not
discriminate among agents and cannot answer how much of current production (and current
income) is imputable to female participation and how much to the rest is reckoned to be a
shortcoming by many critics. Moreover, to add to the current criticism, the income and expenditure
accounts do not take into account the impact of production on natural resources – the rate at which
the latter are being contaminated and depleted.
In spite of these questions – and some of them deserve serious consideration – there is no
serious doubt either among the user constituencies or among the official producers of GDP accounts
that the number itself is necessary, whatever scope there may exist for its future improvement.
Many policies are predicated on the timely publication of the GDP accounts and it is difficult to
imagine how the public sector would organize its fiscal and financial activities if no GDP and
related figures were made available. What are then the properties that a single high impact
synthetic number should have, irrespective of who publishes it?
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Properties of a high profile single number
The following is not an exhaustive list but rather an enumeration of the key attributes of a
high profile single number:
•
•
•
•
•
it must be communicable2 in the sense that if questioned, a short and simple explanation
can be given of what the number pretends to measure and the elements that are required in
order to compile it with the conviction that such an explanation will be accepted and
understood by the majority of potential users;
it must be replicable (more or less) in the sense that an interested user with access to
sufficient resources, the same basic data, and armed with the same book of definitions and
procedures will reach roughly the same results;
it must be related to theory in the sense that if someone asked for the conceptual basis of
the figure, an answer could be given in terms of the interrelationship of the components
and in the particular instance of a HDI, where and how those components fit in a theory of
social and economic development;
it must be related to possible action in the sense that if the estimated figure behaves in a
particular way, one can think of decisions that can and will be taken and policies that will
or will not be adopted as a result; and
it must be credible where credibility is associated with the authority and legitimacy of the
compilers, the expected use of the figure in the framing of policies, and the perception that
its estimation is based on objective methods rather than on partisan views.
The attributes mentioned above are the most basic. In addition, the following technical
characteristics are essential requirements:
•
•
•
the components of a synthetic number must be independent of each other. A sound
construction of the synthetic number implies that subject to constant quality, the number
of components must be minimized (efficiency). Sound construction also implies that
subject to the input being held constant the information yielded by the number must be
maximized (effectiveness);
the attributes must share a common metric or in the absence of a common metric must be
standardized (for example, expressed in units of standard deviation from a natural origin);
the manner in which the attributes are aggregated – the functional form and the weights –
must be the result of a selection from an easily understandable set or else chosen so as to
be robust. It must be possible to claim that there are no policy applications in sight that
would be disadvantaged depending on the choice of the aggregation function and its
weights.
3. Second question: What are the circumstances that prompt an official statistical agency to
publish or refrain from publishing a particular statistic?
In the past serious arguments have been put forward that would have statistical agencies give
up on the compilation of the CPI. The alternative was that they should publish every month or every
week a list of prices and the exact specifications of the goods and services to which those prices
corresponded. They would also make available the latest pattern of consumer expenditure as well as
2
The following quote is reproduced from Ian Castles: Comments on the UNDP response to the Castles Critique of
HDR 1999 “… Amartya Sen has explained that he came to accept Mahbub ul Haq’s view that the HDI was valuable
‘as an instrument of public communication’, in order to ‘[get] the ear of the world through the high publicity associated
with [its] transparent simplicity … ‘ (‘Mahbub ul Haq: The courage and creativity of his ideas’, speech at the Memorial
Meeting for Mahbub ul Haq, 15 October 1998).
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software, which would make it possible for serious users to calculate their own index choosing the
functional form that best suited their needs. This way the statistical agency would do what it knew
best – to measure an operationally defined magnitude under controlled conditions; it would stay
away from opting for one or another of several possible aggregation functions, all of which are
controversial; and would allow users a better understanding of the concept underlying a CPI while
giving them freedom of choice of how to combine many numbers into one, if they so wished. The
tenor of this proposal is the logical consequence of the injunctions to stay away from controversial
assumptions and to maintain objectivity throughout.
But tradition, political realities, general acceptance and expectations, all combine to suggest
that this view is much too extreme and that it is in line with the mission of an NSO to compile the
CPI. Even so, what are the conditions that demand that a line be drawn? There is a category of
aggregates that most if not all statistical agencies would refuse to compile. What are the grounds for
refusal? Or is there virtue in remaining ambiguous because no one is sure of how to describe those
grounds?
Official statistical agencies have not developed or been provided with an international agreed
code of “publishability”. There are codes of quality and texts proffering advice on suitability and
relevance. For example, on the IMF website, the references to data quality in the papers and reports
quoted - address “fitness for use”3 in terms of timeliness, precision, error, cost, and other
dimensions normally associated with quality. But those standard quality attributes do not answer the
underlying question of whether it is appropriate for a statistical agency to lend its legitimacy and
moral endorsement to a particular number nor do they examine the theoretical (as derived from
social science rather than from statistics) attributes that number should have. In other words, they
do not question what statistics a statistical agency should regard as fit to publish. It follows that
ultimately, the decision whether or not to publish is very much in the hands of the head of an NSO
and his immediate advisers.
Suppose the example is “human development” and the management of an NSO identify a user
and a use. The user argues justifiably that the GDP is much too limited a variable. High GDP per
capita is compatible with socially atrophied situations – situations where there is high illiteracy and
health standards are poor. Accordingly the GDP per capita is rated to be an incomplete measure if
not downright misleading for certain policy purposes. The user is prepared to fund the compilation
of an alternative so long as the alternative includes explicitly those social dimensions about which
the GDP has nothing to say and which we shall assume are not strongly related to GDP per capita.
The explicit purpose of the index is to provide an objective measure of “development” to help
with the allocation of funds presumably to combat social deprivation in the form of low life
expectancy, high illiteracy, low rates of access to social services etc. The alternative to having the
official statistical agency compile such a number is to have it compiled and published by a private
research institution, which of course is in no position to stamp the result with the trademark of the
statistical agency. Suppose that there is an international dimension to this initiative and that an
international consensus has been reached on the name, components, and aggregation form for the
new synthetic measure. What is the right course of action for the official statistical agency?
Properties of a number fit to publish (as opposed to a number “fit to use”)
The following may constitute criteria to decide whether or not to publish:
•
3
Relevance. If a number is to be compiled it must have a final user and a final use both of
which the authorities in charge of an official statistical agency can identify and rank as of
sufficient priority to justify the effort;
G. Brackstone: Managing Data Quality in a Statistical Agency, Survey Methodology, December 1999, Ottawa.
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•
•
Robustness. Even though a synthetic number may be well compiled in the sense that all
its components are correctly estimated, the aggregation function may be so sensitive to
small changes in weights or in the functional form that its usefulness as an effective guide
to decision taking is questionable. Moreover, if a number is unstable over time its
credibility. For example, suppose that a group of countries are ranked using an index that
makes inter-country comparisons possible. Suppose two rankings take place at times t and
t+k. Suppose that the rank correlation between the two rankings is no better than if the
two had no relationship. What credibility would we attach to the procedure if we knew
that the ranking variable changed slowly irrespective of the country to which it applied?
The point is that we expect some constancy of characteristics over time and movements
that are too rapid incite our suspiciousness. This gets aggravated if there is no accepted
body of theory capable of explaining the shifts.
Adequacy. For an ongoing statistic to be useful it must keep on answering the right
question. One way to explain this property is by example. Suppose there is the question of
adopting a CPI to measure inflation in a traditional society. The decision is to opt for a
Laspeyres price index on the grounds that to inform the government (assuming that it
wants to be informed) about whether there are any inflationary (or deflationary) pressures
on the horizon, it is sufficient to measure the changes in expenditure on a fixed basket of
goods and services.
Now suppose the society surrenders to a rapidly changing technology and the consequent
changes in expenditure pattern, and the speed at which the pattern is changing become the question
of the day. Even though the CPI answers the earlier question well, the question it answers is no
longer the right one.
4. Third question: Is the Human Development Index a construct that has interesting
properties?
The answer is probably “no”. But a few remarks to set the stage are in order. For a synthetic
number such as the HDI to be interesting it must be sufficiently different from all others not to be
redundant; it must be sensitive to change to provide signals while at the same time time-resistant so
as not to signal in excess; and its changes must lead to questions that in turn provide a basis for
insights. It is not specifically a number designed to settle questions of fact because such questions
are usually settled by reference to a basic statistic. As an example: has the school enrolment gone up
or down this year in relation to last? The answer is settled by looking up a time series of basic
enrolment statistics.
If the variations of a synthetic number are mostly caused by one of its components, it is the
component that is worthy of attention and study. Take the example of the HDI as calculated in the
Human Development Report. It consists of three components: GDP per capita corrected by
purchasing power parities (PPP’s); life expectancy at birth; and a combination of literacy and gross
enrolment rates. In other words, the goal of human development is to produce a citizen who is
affluent, healthy and well educated. Now let us make the reasonable assumption that health and
knowledge (or literacy or education however defined) are long-term functions of income and that
their variation is explained by the lagged variation in GDP. It follows that the synthetic measure
fails on account of redundancy. Moreover the interesting insights the HDI might give rise to are in
fact derivable from those of the responsive component.
Suppose alternatively that the three components are independent but respond to policy at very
different speeds. Imagine that the two social components are slow moving partly because they are
demography driven and partly because they presume very different lengths of what economists
would call “roundaboutness”. If the period of observation is one year and some policy is instituted
to act on all components naturally the driver of the synthetic index will be the most responsive. So
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once again an index constructed on that basis fails the redundancy test.
Suppose that all components of a synthetic index can move up or down but that in the case of
one of them, a downward movement implies a catastrophic event (life expectancy?) whereas
downward movements in the case of the others are subject to relatively quick recovery. In such a
case we do not wish the synthetic index to obscure the movements of the components and would
prefer to see on its own the component that records catastrophic events. In this example, the
synthetic index obscures rather than sheds light on the matter under study.
Suppose a synthetic index is designed in order to construct an international league table and
imagine that all countries are ranked by their shortfall from some average or by the value of their
HDI. And suppose that the probabilities of variation in components other than the GDP are as much
a function of explicit policies as they are of the initial demographic composition of the country. It
follows that for the same amount of effort, assuming that all else is constant, the outcome will be
different depending on the demographic structure about which little if anything can be done and
certainly not in the short run.
These reasons should be sufficient to argue that an HDI – such as we know it - may not have
properties that are analytically interesting.
5. Fourth Question: Index of Human development: are there more useful and interesting
alternatives?
The answer is probably yes. But first consider the following. Other than simplicity and
communicability and other than a residual dissatisfaction with GDP or with a related measure such
as consumption of goods and services per capita, are there reasons to attempt to compile a single
indicator to represent the social and economic sides of human development? The answer is
probably not in the sense that there is no theory other than the trite statement that the richer a
society, the greater its production and consumption possibilities, the faster the increase it
experiences in longevity, probability of surviving the first year of life, literacy, feeling at home with
the achievements of modern technology, participation in community development, etc.
Conversely, there is the argument that sustained growth requires a number of fundamentals
such as high literacy rates, good health and health care etc. The point is that there is no tested theory
to link the social, environmental and economic factors that are required for human development and
therefore the synthetic index is no more than a statistical device to make possible the aggregation of
selected indicators presumed to be relevant but with unknown inter-relationships.
Other attributes
Irrespective of which way the causality links go – they may go both ways but at different
speeds - the list of ingredients that constitute the development index, leaves out for no explainable
reason a number of important factors that one might imagine are also worthwhile considering. For
example:
•
•
•
•
•
Uncertainty, especially uncertainty in the labour market but also uncertainty with respect
of the value of fixed income;
Predictability (the converse of uncertainty) through the absence of corruption, the
sanctity of contract, the openness of government, and the fairness of public administration;
Security (related as a distant cousin to the two above) from internal and external dangers;
Upward mobility. To expect that one’s probability of economic and social success
(however defined) not be conditioned by circumstances of birth, sex, ethnic origin, social
class etc.
Absence of excessive inequality. The situation where neither income nor wealth is
disproportionately concentrated in the hands of the privileged few.
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The list could be considerably longer. Moreover for each of these attributes one could devise
one or more statistical indicators, all of them susceptible of being defined, measured, compiled,
standardized, and used as ingredients to construct a synthetic index. The problem though would
remain in our inability to define a criterion for aggregation because no theory exists that provides an
underlying conceptual framework.
Distribution, concentration, inequality
In addition to the fact that a synthetic indicator such as the HDI is deficient in theoretical
terms, its properties in a number of boundary cases are questionable. Consider that the current HDI
is marked by the absence of a measure of distribution or concentration of income and wealth and
imagine the following:
•
•
•
•
•
•
•
•
There is a country called Kryptonia;
Kryptonia has an index that combines one well known economic indicator (production,
household consumption what have you) with several social indicators (derived from health
and education);
The economic indicator varies relatively fast but the social indicators vary slowly;
Wealth and income are poorly distributed – according to a consensus view. Indicators of
inequality – whatever they are – suggest that a small proportion of the population owns
most wealth and accounts for most income. All the others live as serfs.
The country’s wealth is derived from a unique resource in high demand – let us call it
Kryptonite;
The international prices of Kryptonite went up but since demand for the resource is highly
inelastic so did incomes. There was no short term effect on internal income distribution;
There is trickle through - as is implicitly assumed in human development indexes – but it
is much slower than the increase in incomes and assets experienced by the privileged few;
The HDI of Kryptonia goes up faster than the HDI of other countries particularly of those
that are buyers of kryptonite rather than sellers.
Is this a property that we want a HDI to have? And if not, how should we change it?
6. Ménage à trois, ménage à quatre: a proposal
One possibility to modify the HDI while retaining the same components and supplying it with
a structure that it sorely misses is to consider for each of them three analogous conditions: the ratio
of actual to eligible entrants; the efficiency of transformation of inputs into outputs; and the ratio of
actual to potential outputs. In the case of education the three conditions translate themselves into an
average of enrolments; a ratio of graduates to entrants; and a ratio of graduates to the relevant
portion of the population (after netting out duplication). To find exact measurable counterparts in
the case of health is not that easy. In the case of the GDP derived indicators it is understood that
they must be adjusted for Purchasing Power Parities.
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Purchasing Power parities – a sideline
At the same time as there is an effort to find suitable indicators
for a comparative study of the conditions of human
development, there is still some dithering about the use of
Purchasing Power Parities in the adjustment of values expressed
in nominal monetary terms. 4 The evidence that there is no
alternative to this adjustment and that comparisons made on the
basis of exchange rate terms are wildly misleading is
overwhelming. 5 While there is genuine doubt about the
management and the resources made available for the
corresponding statistical programmes there should be no
hesitation in ruling out the alternatives.
In the discussion that follows it is understood that all GDP
related indicators are PPP adjusted and researchers engaged in
improving the statistics necessary to compare human
development are encouraged to devote some of their rime and
resources to a corresponding improvements in the quality of the
purchasing power numbers.
The following are the elements of my proposal for an alternative to the HDI. The proposal is
addressed to national and international official statistical agencies. It includes a research programme
for official statistical agencies interested in pursuing the matter.
1. Resist the temptation to publish a single number to measure “human development”, a
single figure measuring the shortfall in “human development”, or any other variant that
ends up by being a single figure;
2. Accept the idea that for a suitable description of human development to be given, more
than one figure is necessary. Think in terms of a situation where you are asked to
provide all the expenditure components of GDP but you are barred from adding them
up because they lack a minimum of coherence;
3. Think in terms of a description that improves by adding modules as more research takes
place into the various dimensions of human development and as operational definitions
for each of those dimensions are proposed. As more is known about a certain feature of
human development – access to public services or participation in political life or
engagement in voluntary associations – a corresponding module is drawn up;
4. Refrain from the temptation of compiling international league tables even if there are
solid international agreements that ensure that all modules are calculated in the same
way and there is guaranteed inter country comparability. At this stage of our
knowledge, league tables are silly and give rise to unjustified and invidious
comparisons.
5. Provide all modules with a structure and try and make it the same even if in some cases
– at least at first – the results look somewhat forced. Inevitably there will be gaps either
because the indicator cannot be compiled or because the underlying concept cannot be
found.
Let those gaps constitute a programme of research nationally and
internationally.
4
5
See United Nations Development Report 1999. New York 1999
See Castles and Ryten, op.cit
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6. Examine how sensitive the results are to different types of weighting in the first
instance to be able to reject all attempts at forcing the premature creation of a single
figure.
7. Make very sure that there is clarity in the minds of the public as to who calculates the
basic indicators of human development and explain the inadequacy of an “ersatz” single
figure for the spurious purposes of engaging in international comparisons.
8. For purposes of research, development, and publication use a framework along the lines
of Table 1 below.
Table 1 Framework for an alternative to HDI
Modules
Stages
Economic
growth
Health
Input
Employed as
proportion of
total labour force
Transformation
Ratio of hours
worked to total
number of hours;
labour
productivity
GDP per head
Education
Infantile mortality; rate
of maternal mortality
?
Life expectancy
Output
Distribution
Gini coefficient
of income
distribution or
equivalent
“Healthfulness”
coefficient
Other
Enrolments in
first year of each
stage of the
formal education
system
?
Ratio of
graduations to
enrolments
?
Successful
graduates over
total possible
graduates
?
Rate of functional ?
literacy
Notes to the proposal
A great deal remains to be done within this framework. For example: is there a means of
combining a measure of central tendency – GDP per capita or household consumption per capita –
with a measure of distribution? Ands if so, what would the combined number mean? An arbitrary
score?
What is the most suitable measure of distribution? One possibility is to popularise the Gini
coefficient. But it has known shortcomings. There are more sophisticated alternatives. Measures of
entropy6 have interesting properties but can they be readily explained to politicians and to the
public? And if they cannot, how is a combined figure to gain credibility? Whatever measure is
adopted it is important to bear in mind that it must retain the property of communicability. Thus if a
number is adopted but cannot be explained in as many words as say the CPI or the maternal
mortality at birth, the chances are that it will not flourish. Even so a successful number must take
into account distribution of income and wealth (or at least income). After all, human development
6
The Kullback-Liebler measure or the Theil coefficient of redundancy for example.
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Statistics, Development and Human Rights
as commonly understood would be thwarted if most means of purchase remain in the hand of the
very few.
Nor is the first of the columns the only one that is open ended. What is the output of the
health sector, awkwardly designated as “healthfulness” in the table? Somehow one would like to
have a physical output measure similar in concept to caloric equivalent. For example, can
healthfulness be measured in pain free days? And what is the health sector counterpart of years
spent in school? Is there a counterpart to measure the society’s capacity to restore to health those
afflicted by disease and pain? And subsequently to measure the ratio of those restored to those that
could be restored if the capacity were fully utilized?
Implications of the proposal
The obvious implication is that instead of publishing a single figure – one index or one
shortfall – each country would be characterized by at least a triplet and each component of the
triplet might be a set of two figures. Accordingly:
Table 2 What replaces the single figure
“Achievement”
Distribution
Total goods and
services
X11
X21
Education
Health
X12
X22
X13
X23
7. Conclusions
Before attempting to publish a sextuplet, a study must take place into the most effective
means of aggregating the component indicators. It is not obvious how to combine a number on
unemployment with a number on productivity and one number on the GDP even though the set is
much more coherent than the grouping that constitutes the HDI. The recommendation in this paper
is for a systematic structure that can be expanded over time to span other indicators of development
on the basis of further research.
Assuming that research is crowned with success, it will still be awkward to replace a single
figure by a sextuplet and to have to analyze the evolution of six numbers so as to make them readily
understandable to policy analysts. But ultimately, if the choice is to mislead with a single figure or
to explain awkwardly with six, the latter should be professionally if not emotionally preferable.
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Montreux, 4. – 8. 9. 2000