Multidimensional Poverty Analysis:
           Looking for a Middle Ground


                            Francisco H. G. Ferreira † Maria Ana Lugo


Widespread agreement that poverty is a multifaceted phenomenon encompassing depriva-
tions in multiple dimensions clashes with the vociferous disagreement about how best to
measure these deprivations. Drawing on the recent literature, this short paper reviews
three methodological alternatives to the false dichotomy between scalar indices of multi-
dimensional poverty, on the one hand, and a “dashboard” approach that considers only
marginal distributions, on the other. These alternatives include simple Venn diagrams of
the overlap of deprivations across dimensions, multivariate stochastic dominance analy-
sis, and the analysis of copula functions, which capture the extent of interdependency
across dimensions. Examples are provided from the literature on both developing and de-
veloped countries. JEL codes: I32, O15



Over the last 10 years, interest in multidimensional poverty measurement has
grown steadily. Since the pioneering works of Bourguignon and Chakravarty
(2003) and Tsui (2002), a number of approaches have been proposed to measure
or analyze deprivation in multiple dimensions. This rapidly growing literature
now includes Alkire and Foster (2011a), Chakravarty, Deutsch, and Silber
(2008), Deutsch and Silber (2005), Duclos, Sahn, and Younger (2006), and
Maasoumi and Lugo (2008), among others.
   Multidimensional poverty analysis has been transformed from a purely academ-
ic discussion into a broad domestic and international policy debate, both within
and between many countries. In December 2009, for example, Mexico’s National
Council for the Evaluation of Social Policy (CONEVAL) adopted a multidimensional
index as the country’s official poverty measure.1 In 2011, the government of
Colombia followed suit by adopting a poverty-reduction strategy that focused on
five separate dimensions and relied on a variant of Alkire and Foster’s (2011a)

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doi:10.1093/wbro/lks013           Advance Access publication January 20, 2013                                28:220–235
approach to quantify progress in the reduction of poverty. Internationally, the
Multidimensional Poverty Index of Alkire and Santos (2010), which was reported
for over 100 countries in the UNDP’s Human Development Report 2010, has also
gained prominence (UNDP 2010).
   The driving force behind this rising popularity is the acknowledgment that
poverty involves much more than just low income. Low consumption and inade-
quate living standards are at the heart of the concept of “poverty,” to be sure. The
associations conjured up by that term also include aspects of poor health, such as
a shortened lifespan; limited access to education, knowledge, and information;
and powerlessness in various domains. Poor people often mention nonincome di-
mensions as being crucial to their perceptions of their own hardships. The follow-
ing quote from a person from Georgia illustrates this point: “Poverty is lack of
freedom, enslaved by crushing daily burden, by depression and fear of what the
future will bring” (quoted in Narayan et al. 2000, p. 37). It is now quite common
for poverty analysts, whether from academia, the World Bank, or other agencies,
to face enquiries about how best to summarize information on “multidimensional
poverty” in a particular country.
   However, the various new multidimensional poverty indices have not been uni-
versally welcomed. Serious criticism of these indices centers on the manner in
which information on deprivation is aggregated across dimensions. One powerful
critique is that the weights used to aggregate across dimensions lack the intrinsic
meaning associated with prices, which are used to add the components of con-
sumption expenditure (or, implicitly, its dual, the incomes used to finance con-
sumption). Under the law of one price, and given relatively weak assumptions on
preferences, relative prices are equal to the rate at which consumers themselves—
regardless of their income levels and allowing for different utility functions—are
willing to trade one such component (e.g., bread) for another (e.g., a bicycle).
   Of course, there are a number of practical reasons why prices may not be ideal
welfare weights. These reasons range from the existence of externalities to the fact
that price data are often geographically coarse, so actual price variation in space
is missing from the information available to the researcher. Nevertheless, as
Ravallion (2011, p. 247) argues,


      It is widely agreed that prices can be missing for some goods and decep-
      tive for others. There are continuing challenges facing applied economists
      in addressing these problems. However, it is one thing to recognize that
      markets or prices are missing or imperfect, and quite another to ignore
      them in welfare and poverty measurement. There is a peculiar inconsisten-
      cy in the literature on multidimensional indices of poverty whereby prices
      are regarded as an unreliable guide to the tradeoffs, and are largely

Ferreira and Lugo                                                                  221
      ignored, while the actual weights being assumed in lieu of prices are not
      made explicit in the same space as prices.
Because multidimensional indices adopt arbitrary weights, which are often equal
weights across dimensions, they inherently involve specific tradeoffs between the
constituent components of welfare in the mathematical sense: A certain extra
amount of one component will exactly offset the change in another component to
leave the index unchanged. These tradeoffs are seldom stated explicitly, and it is
not obvious that they are frequently revised by public debate (Ravallion 2011).


What Is the Disagreement?
The debate between proponents and skeptics of multidimensional poverty mea-
surement was featured in the Forum Section of the June 2011 issue of the Journal
of Economic Inequality (e.g., Alkire and Foster 2011b; Ravallion 2011; Lustig
2011). These articles suggest strong agreement on at least one basic point:
“poverty is multidimensional” (Ravallion 2011, p. 236). There is little dispute
that deprivation exists in multiple domains, which are often correlated. Therefore,
considering information on these various dimensions (rather than on incomes or
consumption expenditures only) is likely to be useful for designing policies that
effectively combat poverty.
   The disagreement between proponents and skeptics involves how best to
measure this multidimensional poverty—that is, how best to convey information
about the extent of these various deprivations in a way that is useful for both ana-
lysts and policy makers. Some studies, such as those by Alkire and Foster (2011a)
and Maasoumi and Lugo (2008), have proposed scalar indices that seek to
combine information from various dimensions into a single number. A key advan-
tage of such scalar indices is that they generate a complete ordering of countries,
regions, or individuals, even when the rankings conflict across individual dimen-
sions. The Multidimensional Poverty Index (or the Human Development Index, in
the space of attainments) attracts a good deal of international attention, in large
part because it ranks countries according to how well they perform on various di-
mensions through a simple summarizing tool.
   In contrast, Ravallion (2011) suggests a “dashboard” approach, whereby “we
may need to focus our efforts and resources on developing the best possible dis-
tinct measures of the various dimensions of poverty [. . .] aiming for a credible set
of ‘multiple indices’ rather than a single ‘multidimensional index’ ” (Ravallion
2011, p. 13; our emphasis). An important limitation of multidimensional indices,
as noted earlier, is that they require the use of relative weights for each dimension,
which are chosen somewhat arbitrarily by the analyst. Other analysts, policy
makers, and the public may disagree with these specific weights. Instead of

222                                    The World Bank Research Observer, vol. 28, no. 2 (August 2013)
imposing a specific weighting system, the dashboard approach allows the user to
attach more or less importance to any particular dimension.




Is There a Policy-relevant Middle Ground for Multidimensional
Poverty Analysis?
In this short paper, we argue that this debate—a single index versus a
dashboard—is a false dichotomy. In other words, we suggest that the analysis of
multidimensional poverty can and should move beyond both scalar indices and
dashboards of deprivation based on marginal distributions. Multidimensional
poverty analysis is interesting because the joint distribution of achievements pro-
vides more information than that provided by its margins. The dependency struc-
ture in a joint distribution—how closely correlated various achievements (or
deprivations) are—can affect how we assess poverty in a society or how we
compare it across time periods, even given identical margins. A dashboard that
reports on poverty indices for each dimension separately may overlook this aspect
of the joint distribution.
   This point was made eloquently by Duclos, Sahn, and Younger (2006). In one
instance, these authors compare the joint distributions of two dimensions of
health (nutrition and survival probabilities) in Cameroon and Madagascar and
find that both marginal distributions in Cameroon first-order dominate the corre-
sponding marginal distributions in Madagascar. However, there is no dominance
of the joint distribution. In this example, a dashboard approach would lead a
researcher to naively conclude that poverty was unambiguously greater in
Madagascar, whereas a truly multidimensional assessment (i.e., one that took
into account the correlations) would enable the researcher to conclude that no
clear ranking was possible.
   The discrepancy arises because the correlation between the two dimensions
may differ substantially from one place to another, so the cumulative concentra-
tion of deprivations could make overall poverty worse in a place that has better
marginal distributions. As Duclos et al. put it, “It is possible for a set of univariate
analyses done independently for each dimension of well-being to conclude that
poverty in A is lower than poverty in B while a multivariate analysis concludes
the opposite, and vice-versa. The key to these possibilities is the interaction of the
various dimensions of well-being in the poverty measure and their correlation in
the sampled populations” (Duclos, Sahn and Younger 2006, p. 945).
   In the remainder of this paper, we briefly describe three alternative empirical
approaches for the analysis of the dependency structure in joint distributions. All
three illustrations are drawn from the recent literature, and we make no claim to

Ferreira and Lugo                                                                   223
originality. Each is suitable to a specific purpose, but all of the approaches focus
on interactions among the dimensions, so the menu of options may be useful not
only to analysts but also to policy makers.
   The first approach is the set of multivariate stochastic dominance techniques
proposed by Duclos et al. (2006), which enable poverty analysts to investigate
joint distributions of multiple deprivations without making the specific assump-
tions about tradeoffs that understandably worry Ravallion (2011). If the correla-
tion between deprivations matters—as surely it must—then this approach must
be regarded as superior to the dashboard approach, which considers only the
marginal distributions.
   Multivariate stochastic dominance compares two multidimensional distribu-
tions to determine whether one distribution dominates the other (i.e., consistently
lies always above or always below) for all reasonable poverty frontiers. If this is
the case, then one could conclude that poverty in, say, A is always higher (or
lower) than poverty in B for all additive poverty indices. Below, we reproduce two
examples given in Duclos et al. (2006). These graphs represent the bidimensional
dominance surfaces—that is, the difference between two joint distributions.
   The graph on the left of Figure 1 represents the difference in the surfaces of
two hypothetical distributions. In this case, “[a]though differences in the univari-
ate dominance curves in both dimensions clearly cross the origin (at the extreme
left and right of the figure), there is a significant interior section where the first
surface is entirely above the second” (Duclos et al. 2006, p. 954). In other words,
there is intersection dominance without marginal dominance.


Figure 1. Differences in Dominance Surfaces




 Source: Reprinted from Duclos, J.-Y., D. Sahn, and S. Younger. 2006. “Robust Multidimensional Poverty
 Comparisons.” Economic Journal 116 (514): 943-68.



224                                          The World Bank Research Observer, vol. 28, no. 2 (August 2013)
   The graph on the right of Figure 1 depicts the dominance surface comparing
rural and urban children in Vietnam on two dimensions: household expenditure
per capita and height-for-age Z scores. This case indicates that over almost the
entire range of expenditures and stunting, rural children are poorer than their
urban counterparts. This dominance is found for all reasonable poverty lines, so
the finding that “rural children are poorer than urban ones is valid for almost
any intersection, union or intermediate poverty frontier” (Duclos et al. 2006,
p. 959).
   Of course, it is true that multivariate stochastic dominance analysis tends to be
of limited use when the number of dimensions or margins is large. In these cases,
a seldom-discussed natural alternative involves complementing the dashboard ap-
proach with a direct representation of the dependency structure. In poverty
studies, the degree of interdependence can be presented in terms of the extent of
the overlap between individuals who are identified as deprived under the various
criteria. For instance, if poverty were defined by three dimensions (such as educa-
tion, health, and income), the dependency could be illustrated—at least in part—
by the proportion of individuals who were deprived in all three dimensions, those
who were deprived in (different) pairs of dimensions, or those who were deprived
in only one dimension. Atkinson and Lugo (2010) provide such an example for
the case of Tanzania.
   Table 1 below (reproducing Table 5 in Atkinson and Lugo 2010) presents infor-
mation on deprivations in three dimensions of well-being measured at the house-
hold level and the extent of overlap between them. The dimensions chosen are
school attendance of children between 5 and 16 years old, access to safe sources
of drinking water ( piped or protected), and an indicator of ownership of durable
assets. These indicators are closely related to the goals set by the government in
the Tanzanian National Strategy and are obtained at the household level from the
(same) Household Budget Surveys. The example shows the following:
      Between 2001 and 2007, school attendance and availability of durable
      assets have improved significantly, whereas access to protected sources of
      drinking water has deteriorated. Despite the latter, the combined effect is
      to reduce the proportion of Tanzanians who suffer from any of the three
      forms of deprivation: this has fallen from 90 per cent to 80 per cent.
      Equally there has been a fall in the proportion deprived on all 3 dimen-
      sions: from 19 per cent to 10 per cent. At the same time, there has been
      an increase in one category of the deprived: those lacking only access to
      water (Atkinson and Lugo 2010, p. 15).
The implication of these results for assessing the progress of the country between
the two years is clear: “If it were decided that access to water were the sole
concern, then deprivation would have increased from 46 per cent in 2001 to 51

Ferreira and Lugo                                                                   225
Table 1. Deprivations in schooling, access to protected water and durable assets in Tanzania
Proportion of the individuals living in households . . .                                         2001              2007

School deprived: at least one child 5– 16 years old not in school                                55.2              34.5
Assets deprived: no car and fewer than on "small asset"                                          66.6              47.4
Water deprived: no access to piped or protected source of drinking water                         45.8              50.7
Distributions of individuals
  Not deprived in school, water or assets                                                        10.3              20.1
  Only school deprived                                                                            8.9               7.5
  Only water deprived                                                                             4.7              14.4
  Only assets deprived                                                                           17.3              15.1
  School and water deprived                                                                       9.5              10.7
  Water and assets deprived                                                                      12.5              15.9
  School and assets deprived                                                                     17.6               6.6
  School, water and assets deprived                                                              19.1               9.8
   Source: HBS 2001 and 2007. Reproduced from Atkinson and Lugo (2010), "Growth, poverty and distribution
in Tanzania." International Growth Centre, Working Paper 10/0831. November. Page 15.
   Note: small assets include television, radio, telephone (including mobile phones), refrigerator bicycle, and
motorcycle.




per cent in 2007. [. . .] [If instead, one wanted to] assess overall performance
simply in terms of the proportion deprived on all dimensions [. . .] this proportion
has fallen, indicating definite progress” (Atkinson and Lugo 2010, p. 15).
   An effective way of diagrammatically presenting this kind of information on
the degree of overlap across dimension-specific deprivations is through Venn dia-
grams, as Atkinson et al. (2010) do for the EU-27, the 27 countries of the
European Union. The larger the overlap between deprivations is, the greater the
extent of interdependence will be. Figure 2 (reprinted from Atkinson et al. 2010)
shows the number of people who are at risk of poverty (EU definition),
the number of people who are materially deprived, and the number of people aged
0–59 years who are living in jobless households.2 Data come from European
Union Statistics on Income and Living Conditions surveys. The authors note,
“A little over 80 million people live in households at risk of poverty, a further
40 million live in households that are not at risk of poverty but are defined as
jobless and/or materially deprived.” Indeed, “well over two-thirds are identified
under only one of the criteria.” This especially insightful example suggests that, in
this particular context, policies that are directed exclusively toward one of the
indicators may fail to reduce the degree of deprivation of a large proportion of
households. The authors astutely conclude that it is important not only to
monitor the three indicators but also to understand that the degree of overlap
among them will help to shape policies to address these shortfalls.



226                                                        The World Bank Research Observer, vol. 28, no. 2 (August 2013)
Figure 2. Multiple Indicators from the Europe 2020 Target




  Note: Figures for EU-27 in million of persons.
  Source: EU-SILC, Eurostat-CEPS/INSTEAD calculations. Reprinted from Atkinson, A. B., E. Marlier, F.
  Monatigne, and A. Reinstadler. 2010. “Income Poverty and Income Inequality.” In A.B. Atkinson and E.
  Marlier, eds., Income and Living Conditions in Europe, 127. Luxemburg: Eurostat.




   When the objective is to evaluate well-being rather than deprivation, the repre-
sentation of interdependencies between dimensions is less straightforward, and
some “lateral thinking” (Atkinson 2011) might be necessary. Sklar’s Theorem,
from the statistics literature, tells us that any joint distribution function can be de-
composed into the marginal distribution functions of each dimension (corre-
sponding to the dashboard approach) and a copula function, which captures the
degree of interdependency between the dimensions. Copulas, which are the third
approach we want to highlight, have been used to study the relationship between
health and income (Decancq 2009, Quinn 2007). Formally, the copula function
is the joint distribution function of n vectors whose elements are the relative posi-
tion of every individual in each of the n dimensions of well-being. As in the case


Ferreira and Lugo                                                                                 227
Figure 3. The Evolution of the Dependence between the Dimensions of Well-being over Time
in Russia




 Source: RLMS 1995-2003. Reprinted from Decancq, K. 2009. “Copula-based Measurement of Dependence
 Between Dimensions of Well-being.” HEDG Working Paper 09/32. University of York, Health Economics
 Resource Centre, York, UK.


of the margins, once the copula function is constructed, a stochastic dominance
analysis could be performed to assess whether the degree of interdependency
between the components has changed in an unambiguous way. In addition, and
in the same way that information on unidimensional inequality can be summa-
rized by an index (such as the Gini coefficient or the mean log deviation), mea-
sures of rank correlation allow us to order distributions unambiguously in terms
of their degree of interdependency (Decancq 2009).
   As an example, we reproduce from Decancq (2009) a graph showing the evolu-
tion of the Spearman correlation coefficient, a commonly used measure of rank
correlation, in Russia between 1995 and 2003 (Figure 3). The author considers
three dimensions, standard of living, health, and schooling, represented respec-
tively by household income, self-assessed health, and years of schooling as
primary ranking variables (three other variables are used as secondary ranking
variables in case of ties). For context, the Russian Human Development Index in-
creased from the beginning to the end of the period, albeit with a deterioration
around the time of the 1998 financial crises.
   In this figure, the dashed line represents the 95 percent confidence interval ob-
tained by Monte Carlo simulations, whereas the dotted line represents an alterna-
tive computation of the same confidence interval by bootstrapping. The figure


228                                        The World Bank Research Observer, vol. 28, no. 2 (August 2013)
shows that the degree of dependence across these three dimensions of well-being
has increased throughout most of the period; as average well-being was rising, so
was the degree of interdependency between the dimensions of well-being.
   Although they differ in technical complexity, these three alternative techniques
(Venn diagrammatic representations of the dependency structure, multivariate
stochastic dominance, and the analysis of copula functions) seem to avoid the dis-
advantages associated with both the scalar indices and the dashboard approach.
Like the dashboard approach (but unlike scalar indices), these techniques do not
require the use of generally arbitrary weights to aggregate across dimensions,
with their unpalatable implications in terms of tradeoffs. Like scalar indices (but
unlike the dashboard approach), these techniques incorporate information about
how deprivations are jointly distributed and allow analysts to take into account
different levels or changes in the extent of overlap or correlation between them.
This is a menu of analytical approaches that represents an advantageous middle
ground in multidimensional poverty analysis and that may add value to some of
the poverty analyses currently undertaken at the World Bank (and elsewhere).
   There is one important caveat, however. This kind of analysis requires that in-
formation on the various dimensions be observed for each unit of observation
(typically, the individual or the household). In other words, the dimensions must
be observed in the same survey (or census) or, at least, in different surveys that
cover the same set of households and contain common identifiers. Otherwise, it is
clearly impossible to observe the joint distribution.
   An especially important argument proposed by Ravallion (2011) for the dash-
board approach is that the best data on separate dimensions (say, health status
and consumption expenditures) are often found in different data sets, from which
no joint distribution can be constructed. In these cases, a tradeoff may arise
between data quality and information on the joint distribution, and such tradeoffs
must be evaluated on a case-by-case basis. If the quality of information is thought
to differ only marginally—if, for example, anthropometric information about chil-
dren in a health survey is thought to be superior to that contained in an Living
Standards Measurement Study-type survey, but the latter has some information—
some analysts may be sufficiently interested in the extent of the overlap of depri-
vation in health and consumption to incur the cost of using the slightly worse
data. Conversely, analysts who place sufficient weight on the accuracy of the infor-
mation on marginal distribution would choose to analyze each margin separately,
drawing from the best survey in each case.3
   In many cases, of course, reliable information on relevant dimensions, such as
health status, anthropometrics, education, and consumption, exists in the same
survey. This is the case, for instance, for the Russia Longitudinal Monitoring
Survey used by Decancq (2009), the Indonesia Family Life Survey, and various
Living Standards Measurement Study-type surveys. In these cases, it is difficult to

Ferreira and Lugo                                                               229
find a justifiable excuse for any analyst who fails to complement his marginal
analysis with information on the dependency structure. Furthermore, one should
not underestimate the power of the demand for better data. If there are certain
aspects of well-being and deprivation that are not regularly captured in household
surveys but whose joint distribution with other dimensions (such as income) is of
real policy interest, then more frequent analysis of the kind we suggest might en-
courage statistical institutes or other data providers to collect information on such
aspects.



What about Scalar Multidimensional Poverty Indices?
Finally, we turn briefly to the question of whether the analytical approaches we
propose should completely preclude the computation of scalar multidimensional
poverty indices. It is clear that they do not preclude the dashboard approach in
that considering the marginal distributions is inherent in considering the joint
distributions. The three approaches described above are best understood as com-
plementing the dashboard approach with information on the dependency struc-
ture between the dimensions, when this information is available.
   What role do we see for the definition and computation of scalar multidimen-
sional poverty indices? We see this question as another instance of choice given a
tradeoff. A scalar multidimensional index provides a complete ordering, with the
ability to rank two years, countries, or regions, even when their joint distributions
(or copulas) cross. Just as in unidimensional poverty or inequality analysis, the
ability to generate a complete ordering comes at a cost in terms of specific func-
tional form assumptions. In the case of multidimensional well-being and poverty,
this price is high, for two key reasons.
   The first reason is that the identification step (in the sense of Sen 1976) is con-
siderably more complex for multidimensional poverty than for unidimensional
poverty. This complexity results not only because one has to define a threshold for
each individual dimension but also because a difficult choice must be made at the
identification step about how many deprivations constitute poverty. This situation
recalls the fundamental choice between the union and intersection approaches
(e.g., Bourguignon and Chakravarty 2003), the establishment of an intermediate
cutoff in the number of dimensions (Alkire and Foster 2011a), or whether the
depth of deprivation in one dimension should be allowed to offset well-being in
another dimension at the identification stage (e.g., Duclos et al. 2006). In this
paper, we have largely ignored issues of identification, although these issues are
clearly important if one decides to pursue the scalar-index route.
   The second reason is the need for weights to aggregate across dimensions. Even
conditional on a particular identification algorithm, the issue of weights remains.

230                                   The World Bank Research Observer, vol. 28, no. 2 (August 2013)
Whether a price is worth paying is therefore likely to depend on, first, the impor-
tance of the ability to rank for the purpose of the analysis at hand and, second,
the arbitrariness (and number) of the weights.
    Therefore, it is difficult to take a definitive position in the abstract. As in the case
of unidimensional poverty measurement, it seems that two extreme positions are un-
tenable. The first position would be to say that a particular multidimensional
poverty index is the one true measure of poverty. The second position would be to
argue that any particular index that makes an unpalatable assumption is inadmissi-
ble. In the same way that we recognize the limitations of the headcount index but
continue to report it (ideally, alongside other measures and more disaggregated and
robust analysis), there are clear uses for various indices of multidimensional poverty.
    In our view, such scalar indices would be most useful if they relied, to the
greatest possible extent, on (shadow or market) prices to aggregate across differ-
ent goods and services. Only the aspects of well-being for which there can truly
be no sensible estimate of relative prices should be treated as separate dimensions.
Although food, cooking utensils, toilets, clothing, and vehicles may be resources
that affect different “functionings” (in the sense of Amartya Sen), they are best
treated as components of a single dimension of well-being—command over private
goods—whose internal weights are given by relative prices.
    Equilibrium prices, as noted earlier (and in elementary first-year economics
courses), reflect people’s preferences and constraints as well as market structures.
If individual choices can be reasonably approximated by the result of maximizing
a utility function subject to a budget constraint, and if the law of one price holds,
then it follows that (regardless of people’s individual utility functions or income
levels) the rate at which every person trades off one unit of a good against one
unit of another good will be the same. In other words, relative prices reflect the
marginal rate of substitution between the goods.
    Naturally, price data are often problematic. Very often, the available data on
prices do not accurately represent the prices actually encountered by individuals
for the indicators that we would include in the analysis. This is largely because
there is price heterogeneity across regions (or even cities) within a country and in
the quality of products and services, whereas price data tend to be collected at a
higher level of aggregation and for a representative (average) item in each catego-
ry. However, it is questionable whether these problems are so severe that choosing
arbitrary weights across dimensions, such as the availability of cooking utensils
and, say, the ownership of certain means of transport, would yield a preferable
metric. In this regard, Ravallion’s (2011) arguments for greater reliance on
market prices seem overwhelmingly compelling.
    The true value of the analysis of multidimensional poverty (or well-being) lies
in the existence of certain aspects of well-being that we deem important but for
which there can be no sensible estimate of relative prices. It is reasonable to

Ferreira and Lugo                                                                     231
include in this category items such as political and personal freedoms, health,
and, arguably, education. Although various inputs into the production of health
and education are marketable, this is not true of all of them. Health is influenced
by environmental quality and by a number of other public goods. Education, once
embodied in human capital, generates so many externalities that it is difficult to
think that school fees or costs are suitable approximations of its true shadow
price. These things—not the material from which a ceiling is made or the kind of
stove one uses—are the true dimensions of welfare.
   In these cases, multidimensional analysis becomes particularly relevant. If, for
the purpose at hand, the analyst decides that the price of selecting weights is
worth paying (to obtain a complete ordering), then the question is whether one
can choose relative weights that at least attempt to represent the existing tradeoff
between the different components of deprivation (or well-being). There are
various approaches to setting these weights; some are based exclusively on the ob-
served distribution of attributes, others are based on people’s opinions, and others
use both sorts of information (Decancq and Lugo, 2013). Regardless of the
weighting scheme and the precise functional form chosen, multidimensional
indices of deprivation (or well-being) should be allowed to be sensitive to the
essence of the multidimensional approach, that is, to the degree of dependency
between its components.



Conclusions
There is widespread agreement that poverty is a multifaceted phenomenon.
Income shortfalls, which translate into an inability to consume certain basic com-
modities, are central to this phenomenon. However, income poverty is typically as-
sociated with deprivation in other realms, such as health, education, social
status, and political power, which are more difficult to price. These associations or
correlations between the constituent dimensions of poverty vary over time and
from place to place, and they are often believed to be significant. Recent advances
in multidimensional poverty analysis seek to capture these interactions, and re-
vealed preference seems to suggest that they are of interest to policy makers in
many developing countries.
   Despite this widespread agreement on the essential fact that poverty is multidi-
mensional, there has been a lively debate about whether this implies that scalar
indices should be constructed that summarize information on these various di-
mensions into a single number or whether multiple indices should be provided,
one for each dimension, in a dashboard approach. Drawing on the existing litera-
ture, we have argued here that such a dichotomous view misses the point.
The most interesting aspects of the multidimensionality of poverty arise from the

232                                   The World Bank Research Observer, vol. 28, no. 2 (August 2013)
interdependence among dimensions. The joint distribution of dimensions over the
population contains more information than the corresponding marginal distribu-
tions, and the correlation patterns in that joint distribution may change how we
compare poverty across two countries or time periods. This dependency structure
is overlooked entirely by the dashboard approach and is often obscured by scalar
indices.
   Drawing on examples from both developed and developing countries, we
provide three alternative approaches that allow researchers and policy analysts to
focus on the dependency structure of a joint distribution. The first approach is sto-
chastic dominance analysis, which permits partial orderings across joint distribu-
tions that are robust not only to poverty lines and welfare weights (as in the
unidimensional case) but also to dimension weights. The second approach is a
representation of the overlap of deprivations over the population by means of
simple tabulations or Venn diagrams. Given the agreement on the identification
criterion along each dimension, this extremely simple tool can complement the
dashboard statistics on the marginal distributions in informative ways. The third
approach involves the use of copula functions to study the multivariate association
among different components of well-being across two or more joint distributions.
   Finally, we argue that multidimensional poverty indices, like most other tools,
can be accommodated in the economist’s toolkit, and the risk of serious injury de-
creases with reliance on relative prices and a focus on a few core, truly irreducible
dimensions. If such indices are used, fodder will remain for future controversies
on the choice of weights, poverty lines, and functional forms, but these controver-
sies would largely be a distraction from what really matters to policy makers: the
pattern of associations and overlaps across the core dimensions of well-being.




Notes
Francisco H. G. Ferreira is with the Development Research Group at the World Bank and the
Institute for the Study of Labour (IZA); email address: fferreira@worldbank.org. Maria Ana Lugo is
in the Poverty, Equity and Gender Group at the Latin America Region of the World Bank. This paper
is an expanded version of a short comment that was published as Ferreira (2011). We are grateful
to three anonymous referees and to Sabina Alkire, Peter Lanjouw, Nora Lustig, and Martin
Ravallion for comments on earlier versions of the paper. We are also grateful for illuminating con-
versations with James Foster on this subject. All remaining errors are ours. This paper is a product
of the Equity and Development Research Project (P099861). The views expressed here are those of
the authors. They should not be attributed to the World Bank, its Executive Directors, or the coun-
tries they represent.
    1. The Executive Secretary of the National Council for the Evaluation of Social Policy,
Dr. Gonzalo Herna  ´ ndez Licona, is quoted as saying, “Mexico is proud to be the first country in the
world to measure poverty, not narrowly on economic grounds alone, but to take full account of
crucial social components of poverty such as quality of housing and access to healthcare and food,


Ferreira and Lugo                                                                                233
which are all too often neglected by established poverty measures.” See http://www.ophi.org.uk/
launch-of-mexico%E2%80%99s-new-poverty-measure/.
    2. Persons “at risk of poverty” are defined as those who have an equivalized disposable income
below 60 percent of the national median equivalized disposable income, after social transfers.
Material deprivation covers indicators relating either to economic strain or to the ownership of dura-
bles. Severely materially deprived persons cannot afford at least four of the following: to pay rent or
utility bills; to keep their home adequately warm; to pay unexpected expenses; to eat meat, fish, or a
protein equivalent every second day; a one-week holiday away from home; a car; a washing
machine; a color TV; or a telephone. Finally, a “jobless household” is one in which none of the
members aged 18 –59 years are working or the members aged 18 –59 years have very limited work
attachment.
    3. The question of whether data on a particular variable are more reliable in one survey than in
another may, in some cases, be investigated empirically. At a minimum, survey-to-survey imputation
techniques can be used to assess the sensitivity of results to using information from different
sources. This remains an area for future work.



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