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Fundación de Estudios de Economía Aplicada

Measuring Poverty: Taking a Multidimensional Perspective^* by Jacques Silber DOCUMENTO DE TRABAJO 2007-14

June 2007

This paper is the written version of the opening lecture that the author gave at the annual meeting of the Spanish Symposium on Public Economics (Encuentros de Economía Pública) in Santander on February 1 2007. Jacques Silber wishes to thank the organizers of this conference, and in particular, Luis Ayala, for inviting him to give this lecture. He is also very thankful to FEDEA (Fundación de Estudios de Economia Aplicada, Madrid) for its warm hospitality. Very useful comments on a previous draft of this paper have been received from Luis Ayala, Jose-Maria Labeaga and Amedeo Spadaro. The author is evidently responsible for all remaining errors.

** Department of Economics. Bar-Ilan University – Israel. Visiting FEDEA, Madrid. Los Documentos de Trabajo se distribuyen gratuitamente a las Universidades e Instituciones de Investigación que lo solicitan. No obstante están disponibles en texto completo a través de Internet: http://www.fedea.es. These Working Paper are distributed free of charge to University Department and other Research Centres. They are also available through Internet: http://www.fedea.es.

Jorge Juan, 46 28001 Madrid -España Tel.: +34 914 359 020 Fax: +34 915 779 575 infpub@fedea.es

Abstract

This paper attempts to review the main problems that have to be faced when taking a multidimensional approach to poverty and to give a survey of the solutions that have hitherto been proposed to solve these issues.

It starts by a quick summary of the cardinal approach to uni-dimensional poverty analysis. It then presents the cardinal approach to multidimensional poverty measurement. An attempt is also made to describe the ordinal approach to poverty measurement and a short section at the end describes some aspects of a more qualitative approach to poverty measurement.

I. Introduction

The social philosopher Alexis de Tocqueville (1805-1859), who is known for his famous Democracy in America, and eventually also for his The Old Regime and the Revolution, wrote also a monograph entitled Memoir on Pauperism. His Memoir on Pauperism was written in 1835, immediately after he completed the first volume of Democracy in America.

In the first part of this Memoir Tocqueville stressed that there was a difference between individuals who are “poor” and those who are “indigents”. The latter are people who can be clearly distinguished within a population (hence the modern concept of “social exclusion”). Tocqueville makes in fact an interesting comparison between England on one hand and Spain and Portugal on the other.

“Cross the English countryside and you will think yourself transported into the Eden of modern civilization….There is a pervasive concern for well-being and leisure, an impression of universal prosperity which seems part of every air you breathe…

Now look more closely at the villages: examine the parish registers and you will discover with indescribable astonishment that one-sixth of the inhabitants of this flourishing kingdom live at the expense of public charity…

Now, if you turn to Spain, or even more to Portugal, you will be struck by a very different sight. You will see at every step an ignorant and coarse population; ill-fed, ill-clothed, living in the midst of a halfuncultivated countryside and in miserable dwellings. In Portugal, however, the number of indigents is insignificant….”

This is a description of three countries in the middle of the nineteenth century, even before. But it seems that this distinction between the “poor” and the “indigents” remains valid today. The only difference is that today specialists use other words, making, for example, a distinction between the “income poor” and the “socially excluded” or between uni- and multidimensional poverty.

The goal of the present paper is to attempt to review the main problems that have to be faced when taking a multidimensional approach to poverty and to give a survey of the solutions that have hitherto been proposed to solve these problems.

The paper is organized as follows. Section II gives a quick summary of the cardinal approach to uni-dimensional poverty analysis while the focus of section III is the cardinal approach to multidimensional poverty measurement. In section IV an attempt is made to describe the ordinal approach to poverty measurement and section V stresses that there is also a qualitative approach to poverty measurement. Concluding comments are given in Section VI.

II. The Cardinal Approach to Uni-dimensional Poverty Analysis: a Quick Summary

In his pathbreaking paper Sen (1976) made the by now well-known distinction between the issue of identifying those who are poor and that of deriving an aggregate measure of poverty. Here is a short summary of these two issues (see, Deutsch et al., 2007, for more details).

A) Identifying the poor:

Several problems have to be solved before being able to precisely identify the poor.

1) Determining a Poverty Line:

Various options are available. One can take an absolute approach to poverty measurement (e.g. Rowntree, 1901, but also Orshansky, 1965), a relative approach to poverty (e.g. Fuchs, 1967) or even a subjective approach to poverty measurement (e.g. Hagenaars, 1986). The European Union, for example, takes a relative approach to poverty and defines the poverty line as being equal to 60% of the median income.

2) Choosing an indicator of welfare:

The definition of the poverty line may be based on the distribution of incomes. Selecting income as an indicator of welfare is however subject to criticism (Income data in surveys are often not reliable, income does not take into account the fact that some goods and services are provided on a free or subsidized basis and self-production is often ignored in income surveys).

Other studies rely on the expenditures of the household, a concept which is assumed to be closer to that of permanent income.

3) The unit of observation:

In most studies of poverty, the unit of observation is the household. But one could also think of selecting the individual or the family (a household is defined as including all those who live in a given dwelling so there could be more than one family in a dwelling).

4) The concept of equivalence scales:

The topic of equivalence scale concerns the possibility of comparing households of different size or composition (e.g. age structure), assuming data are collected at the level of the household. The general idea of equivalence scales is to compute for each household the number of "equivalent adults", often called the number of standardized adults. This means giving a certain weight to each individual in the household in order to derive the weight (equivalence scale) of the household. Various proposals have appeared in the literature to build equivalence scales. The Oxford scale, for example, gives a weight of 1 to the first adult, of 0.7 to any additional adult and of 0.5 to any child younger than 14 years old. The OECD scale on the other hand gives a weight of 1 to the first adult, of 0.7 to any additional adult and 0.5 to any child who is less than 14 years old. There are several approaches in the literature as to the determination of equivalence scales. One can derive econometrically equivalence scales (see, for example, Ayala et al., 2003, Prais and Houthakker, 1955, Barten, 1964, but also Engel, 1895, and Rothbart, 1943).

Another possibility is to use parametric equivalence scales (see, Buhman et al., 1988, and Cowell and Mercader-Prats, 1999). The idea here is to assume that the equivalence scale depends on the size of the household. Buhman et al. (1988) suggest defining , the equivalence scale of household with respect to the reference household (assumed to be anh adult living alone), as:

\[\mathbf {E} _ {\mathrm{h}} = (\mathbf {N} _ {\mathrm{h}}) ^ {\mathrm{s}}\tag{1}\]

where represents the number of individuals in household and is ah s parameter summarizing the extent of economies of scale, varying between zero and one. More accurately, is the elasticity of the equivalence scales with respect to the size of the household. The closer is to one, the lesss economies of scale there are, which implies that it is assumed that most goods are of the private goods type. The closer is to zero, the greater thes extent of economies of scale, so that it is assumed that most goods are of the public good type. Obviously when is equal to one, it is assumed thats the “corrected income’ is in fact the per capita income, while when iss equal to zero it is equal to the actual household income. One may think also of more sophisticated formulations taking into account the composition of the household as well (see, for example, Cutler and Katz, 1992). Another approach would make use of subjective equivalence scales (for more details, see, van Praag and van der Saar, 1988).

5) The Weighting of the Units of Observation:

This issue was raised in an interesting paper by Danziger and Taussig (1979) and amounts more or less to deciding whether the goal is to measure poverty among individuals or households. One may, for example, assume that the welfare indicator is the per capita income (which implies that all goods consumed are of the private goods type) but that one wants to measure poverty among households (e.g. the percentage of poor households with respect to such an indicator). One could also select as welfare indicator total household income (which implies that all goods are of the public goods type) but be interested in determining the percentage of individuals that are poor with respect to such an indicator.

B) The Aggregation Issue: Deriving Indices of Poverty

Once the poor have been identified, one has to find a way to derive an overall measure of poverty in the society .

1) The desirable properties of a (uni-dimensional) poverty index:

a) Focus: The idea here is that the poverty index should be independent from the incomes of the rich (non poor).

b) Monotonocity: This axiom assumes that if the income of an individual below the poverty line decreases, poverty should increase.

c) Principle of Transfer: Here it is supposed that when δ units are transferred from a poor individual i to another poor individual j who is richer than i, poverty should increase (such a transfer is regressive)

d) Transfer Sensitivity: This axiom assumes that if a transfer is regressive, poverty will increase more, the poorer the individual who is the poorer of the two individuals concerned by the transfer.

¹ For a thorough review of this topic, see, Zheng, 1997.

e) Impartiality: This principle implies that only income is taken into account when measuring poverty. The other characteristics of the individuals (such as age, gender,…) are irrelevant.

f) Impact of a change in the poverty line: Here it will be assumed that the poverty index will increase when the poverty line increases.

g) Continuity : This axiom is important because it implies, for example, that if there are errors of measurement, a small error will not lead to a big change in the value of the poverty index.

h) Principle of population replication: This axiom which is also often called Dalton´s principle of population says that if a population is “replicated” (“cloned” to use a more modern language) the value taken by the index of poverty should not change.

i) Implication of a growth in population: The idea here is that if a poor individual is added to the population, poverty increases.

2) An incomplete list of poverty indices:

a) The headcount ratio

This is clearly the most popular poverty index. It may be defined as

\[\mathrm{H} (\mathrm{x}, \mathrm{z}) = \mathrm{q} / \mathrm{n}\tag{2}\]

where x is the distribution of income, is the poverty line, n the number of individuals in the population and q the number of poor. The headcount ratio represents hence the proportion of poor in the population.

b) The income gap ratio

This index is defined as

\[\mathrm{I} (\mathrm{x}, \mathrm{z}) = (\sum_ {\mathrm{i} = 1 \text { to q }} \mathrm{g} _ {\mathrm{i}}) / (\mathrm{q} \mathrm{z})\tag{3}\]

where and corresponds to the "poverty gap" for individual i. That is, g_i tells us how far i’s income is from the poverty line. The numerator in (3) indicates therefore what the sum of the poverty gaps is (what amount of money would be necessary to suppress poverty) . The income gap ratio (called also poverty gap) tells us how far on average the poor are from the poverty line as a proportion of the income corresponding to the poverty line.

c) Sen’s poverty index

Another familiar index was derived axiomatically in Sen’s (1976) famous paper. Sen’s index, Sen(x,z), is expressed as

\[\operatorname{Sen} (x, z) = \{2 / [ (q + 1) n z ] \} \sum_ {i = 1 \text { to } q} (z - x _ {i}) (q + 1 - i)\tag{4}\]

This index may also be written as

\[\operatorname{Sen} (x, z) = H (x, z) \left\{1 - \left[ (1 - I (x, z)) [ 1 - G _ {p} (q / (q + 1)) ] \right] \right\}\tag{5}\]

where refers to the Gini index of the incomes of the poor. If the number of poor q is sufficiently high, it may be easily shown that

\[\operatorname{Sen} (\mathrm{x}, \mathrm{z}) = \mathrm{H} (\mathrm{x}, \mathrm{z}) [ \mathrm{I} (\mathrm{x}, \mathrm{z}) + (1 - \mathrm{I} (\mathrm{x}, \mathrm{z})) \mathrm{G} _ {\mathrm{p}} ]\tag{6}\]

Thus Sen’s index is an increasing function of the headcount ratio, of the income gap ratio and of the Gini index of the incomes of the poor.

d)The Foster, Greer and Thorbecke poverty index FGT

This index, proposed by Foster, Greer and Thorbecke (1984), has become one of the most popular poverty indices. This index is expressed as

\[\mathrm{FGT} = (1 / \mathrm{n}) \sum_ {\mathrm{i} = 1 \text { to q }} ((\mathrm{z} - \mathrm{x} _ {\mathrm{i}}) / \mathrm{z}) ^ {\alpha}\tag{7}\]

It is easily observed that when , the FGT index is equal to the headcount ratio since in such a case

Similarly when , expression (7) may be rewritten as FGT =

e) The Watts Index

This is, in fact, one of the oldest indices that has appeared in the literature (see, Watts, 1967). It may be expressed as:

\[\mathrm{W} (\mathrm{x}, \mathrm{z}) = (1 / \mathrm{n}) \sum_ {\mathrm{i} = 1 \text { to q }} \log (\mathrm{z} / \mathrm{x})\tag{8}\]

where, as in previous cases, z is the (relative) poverty line.

It may be shown that the Watts index may be also expressed as

\[\mathbf {W} (\mathbf {x}, \mathbf {z}) = \mathbf {H} (\mathbf {x}, \mathbf {z}) [ \mathbf {W} _ {\mathrm{IGR}} + \mathbf {L} _ {\mathrm{poor}} ]\tag{9}\]

where and denote respectively the headcount ratio, what has been called (see, Chakravarty et al., 2005) the Watts income gap and Theil’s second inequality index (when applied only to the poor population . respectively.

It should be stressed that the Watts index, unlike some more popular poverty indices, has most of the desirable properties of a poverty index that were mentioned previously.

f) Other poverty indices

Other poverty indices have appeared in the literature such as those proposed by Anand (1977), Takayama (1979), Thon (1979), Kakwani (1980), Blackorby and Donaldson (1980), Clark-Hemming and Ulph (1981), Chakravarty (1983). Their formulation will not be given here.

III. The Cardinal Approach to Multidimensional Poverty Measurement:

In what follows a distinction will be made first between on one hand approaches that lead to the derivation of an aggregate indicator on the basis of which a poverty threshold (line) will be determined and traditional measures of uni-dimensional poverty will be derived and on the other hand truly multidimensional approaches where a poverty threshold is determined for each dimension and which lead to the definition of multidimensional indices of poverty.

In the second case two possibilities again arise, depending on whether one first aggregates the dimensions and then the individuals or one first aggregate the individuals and then the dimensions.

In figure 1 an attempt is made to describe the various ways of deriving a multidimensional poverty index.

² This so-called “Watts income gap ratio” is more or less equal to the percentage income difference between the poverty line and the (arithmetic) average of the incomes of the poor.

Figure 1

Various Approaches to Multidimensional Poverty Analysis

Before these approaches are reviewed, additional issues have to be mentioned that are specific to the multidimensional case.

A) On Some Important Issues in Multidimensional Poverty Analysis:

1) The Choice of Poverty Dimensions:

Several questions have to be asked here:

a) Which dimensions of poverty are relevant?

b) Should more than one indicator per dimension be used, and if so which ones should be selected?

c) Which kind of interaction between dimensions should one assume? Are dimensions substitutes or complements?

d) How to deal with interactions between indicators representing a given dimension?

The issue of the interaction between the dimensions or/and between the indicators will be analyzed in another section. As far as the selection of dimensions is concerned one may mention that Sabina Alkire (forthcoming) listed five possible ways of selecting dimensions:

Decide in function of the availability of data or because of an authoritative convention

- Make implicit or explicit assumptions about what people value

Follow “Public Consensus” (e.g. list of Millenium Development Goals or MDG´s)

- Rely on deliberative participatory processes

- Accept empirical evidence concerning people´s values

To illustrate the issue of the selection of dimensions one may cite Ramos and Silber (2005) who tried to translate empirically some of the approaches mentioned by Alkire (2002a). One of the approaches Ramos and Silber (2005) attempted to implement is that of Allardt (1993) who stressed three main dimensions: Having, Loving and Being.

Using the British Household Panel Survey, they took therefore into account the following dimensions:

HAVING

For this dimension the following sub-dimensions were used

1) Economic resources

2) Housing

3) Employment

4) Working Conditions

5) Health

6) Education

Naturally for each of these sub-dimensions several indicators were proposed (see, Ramos and Silber, 2005).

LOVING

This dimension covers what is concerned with the degree of satisfaction with social life (family, friends,…) and here again several indicators were introduced.

BEING

Here again several sub-dimensions were taken into account and several indicators introduced for each sub-dimension.

1) Self-Determination (ability to make decisions,…)

2) Political Activities

3) Leisure Time Activities

4) Opportunities to Enjoy Nature

5) Meaningful Work (Satisfaction with work,…)

Clearly selecting dimensions is not a simple issue and Clark and Qizilbash (2005) have labelled this problem the “horizontal vagueness” of poverty.

2) The “Fuzzy Aspect” of Poverty:

The problem here is that it is often very difficult to determine a clear threshold making a difference between those who are poor and those who are not. A reasonable solution may be found, say, in the “nutrition dimension” (e.g. minimum number of calories needed as a function of age, location, …). The issue is more complex when dealing with, for example, a “shelter” or an income dimension. This issue will be mentioned again when the so-called Fuzzy Approach to Multidimensional Poverty will be described.

3) The “Vertical Vagueness” of Poverty:

Clark and Qizilbash (2005) have used the expression “vertical vagueness” to emphasize the fact that deciding which individual (household) is poor becomes even more complicated in a multidimensional framework. Should be called “poor” only those individuals (households) who are poor in all dimensions or is it enough to be poor in one dimension to be called “poor”? This question will be raised again when in another section the choice between a “union” and an “intersection” approach will be discussed.

4) The “temporal vagueness” of poverty:

Finally Clark and Qizilbash (2005) have also introduced the concept of “temporal vagueness” which refers to the unit of time one should select when analyzing poverty. The importance of time may in fact be considered from different angles.

- the contrast between Chronic and Transitory Poverty

- the idea of Vulnerability

a) On Chronic versus Transitory Poverty:

As stressed by Hulme and McKay (forthcoming) “for many people poverty is not a transitory experience or a seasonal problem: it is a situation from which escape is very difficult, most emphatically illustrated by deprivation which is transmitted from one generation to the next”. As indicated previously, a similar distinction was actually made in eighteenth century France when a difference was made between the pauvres and the indigents. “The former experienced seasonal poverty when crops failed or demand for casual agricultural labour was low. The latter were permanently poor because of ill health (physical and mental), accident, age, alcoholism or other forms of ‘vice’ “ (Hume and McKay, forthcoming).

Hulme and Shepherd (2003) identify in fact four main ways in which people may experience chronic poverty:

- those who experience poverty for a long time

those who experience poverty throughout their entire lives (life course poverty)

- the transfer of poverty from parents to children (inter-generational poverty)

- those who experience a premature death that was easily preventable

This is why, following work by Carter and Barrett (2005), these authors recommend using an asset approach to poverty measurement and make eventually a distinction between structural and stochastic poverty. They suggest considering a transitorily poor household that is poor in the first period but above the poverty line in the second period. This may reflect structural change, because, for example, the household has been able to accumulate assets over this period. Alternatively it may reflect stochastic factors: the fact that the household was poor in one of the two periods may just be the consequence of bad luck in that period.

This is why the question to be asked is whether on average the level of assets is sufficient to put a household above the poverty line, hence the idea of an asset poverty line. The goal is to be able to distinguish among the income poor (as well as non-poor) between those for whom this situation appears to be temporary because they have (do not have) a sufficiently high level of assets, and those for whom this seems to be permanent. Carter and Barrett (2005) think in fact in terms of a dynamic asset threshold which is somehow the level above which households will save and accumulate assets (keeping them above the poverty line), and below which they will reduce their asset holdings and find themselves in a situation of long term poverty (poverty trap).

b) The concept of “vulnerability”:

To introduce this concept Calvo and Dercon (forthcoming) stress the importance of the ex-ante consequences of the possibility of future hardship. For them vulnerability is viewed as the magnitude of the threat of poverty, measured ex-ante, before the veil of uncertainty has been lifted. To illustrate this point Calvo (forthcoming) gives a nice citation from Voices of the Poor (2000): “Security is peace of mind and the possibility to sleep relaxed” (a woman from El Gawaber, Egypt).

To explain what vulnerability is, Calvo and Dercon (forthcoming) cite also Sen (1981) when he discusses the famine in Sahel: “Compared with the farmer or the pastoralist who lives on what he grows and is thus vulnerable only to variations of his own output (arising from climatic considerations or other influences), the grower of cash crops, or the pastoralist heavily dependent on selling animal products, is vulnerable both to output fluctuations and to shifts in marketability of commodities and in exchange rates.…[Thus] while commercialization may have opened up new economic opportunities, it has also tended to increase the vulnerability of the Sahel population”.

To be more explicit vulnerability has to do with “the probability of outcomes failing to reach some minimal standard and on the uncertainty about how far below that threshold the outcome may finally turn out to be. States of the world where outcomes are above the poverty threshold are paid no attention, so that vulnerability is not lessened by simultaneous ex ante possibilities of very high outcomes” (Calvo, forthcoming).

In the framework of multidimensional poverty analysis Calvo and Dercon (forthcoming) emphasize the importance, for each individual, of the degree of correlation between the various dimensions over the set of possible states of the world. The relevance of these outcome correlations would come in addition to the well-known role of outcome correlations over the set of individuals, a question that will be mentioned again in another section.

B) The Case where Dimensions are Aggregated Immediately

The desire to take into account multiple deprivation indicators implies clearly that looking only at low incomes would provide only an “indirect” rather than a “direct” measure of poverty, as stressed by Ringen (1988). There are many ways of aggregating such indicators. Assuming the deprivation indicators are dichotomous indicators referring to the lack of specific items or activities as in Townsend’s (1979) pathbreaking study, a straightforward way of combining indicators into a single scale is evidently to compute the sum of these dichotomous indicators (see, Atkinson, 2003, for a careful analysis of what is implied by such a “counting approach”) or use relatively simple weighting schemes (e.g. Martinez and Ruiz-Huerta, 2000). Note that the lack of a given item or activity may be either the consequence of a voluntary decision or the sign of deprivation, as emphasized by Mack and Lansley (1985) or Halleröd (1994), for example. Most researchers however use more sophisticated techniques of aggregation. We cannot review here of all of them (for more details, see, Kakwani and Silber, forthcoming, 2) but will at least mention some of them, following in fact Krishnakumar (forthcoming).

1) Approaches using traditional multivariate analysis:

These approaches are generally based on the idea of latent variable.

a) Principle Components Analysis:

Principal Components Analysis (PCA) seeks linear combinations of the observed indicators in such a way as to reproduce the original variance as closely as possible. It is thus an “aggregating technique” but lacks an underlying explanatory model which factor analysis offers. An interesting illustration of this approach is given in Klasen (2000).

b) Factor Analysis (FA):

Here the observed values are postulated to be linear functions of a certain number of unobserved latent variables (called factors). In the framework of a capability approach, for example, FA would provide a theoretical framework for explaining the (observed) functionings by means of capabilities represented by the latent factors but such a model will not explain the latent variables.

\[\text { In short: } \quad y = \Lambda f + \varepsilon\]

where y refers to observed variables, f to latent variables, Λ to a coefficient matrix.

Applications of this approach to the study of deprivation may be found, for example, in the studies of Schokkaert and Van Ootegem (1990), Nolan and Whelan (1991) or Lelli (2001).

c) The MIMIC Model:

The MIMIC model (Multiple Indicators, Multiple Causes, see, Joreskog and Goldberger, 1975) represents a step further in the explanation of the phenomenon under investigation as it is not only believed that the observed variables are manifestations of a latent concept but also that there are other exogenous variables that “cause” and influence the latent factor(s).

In short: y = λ f + ε

\[\textbf {f} = \beta \textbf {x} + \zeta\]

As in FA y refers to indicators, f to latent variables while here x refers to “causes”.

For an application of the MIMIC model to poverty analysis, see, Abul Naga and Bolzani, forthcoming.

d) Structural Equations Model (SEM):

We can summarize this model by writing that it includes the following equations (see, Krishnakumar, forthcoming):

\[\mathrm{Ay} ^ {*} + \mathrm{Bx} ^ {*} + \mathrm{u} = 0\]

\[\mathbf {y} = \boldsymbol {\Lambda} \mathbf {y} ^ {*} + \varepsilon\]

\[\mathbf {x} = \boldsymbol {\Phi} \mathbf {x} ^ {*} + \boldsymbol {\zeta}\]

where

y* refers to latent endogenous variables

x* refers to latent exogenous variables

y and x are the observed indicators corresponding to and x*.

(for a nice empirical illlustration on Bolivia, in a capability analysis framework, see, Ballon and Krishnakumar, 2006).

e) Cluster Analysis:

This is a technique allowing the classification of similar objects into different groups, or more precisely, the partitioning of an original population into subsets (clusters), so that the data in each subset (ideally)

share some common trait – proximity according to some defined distance measure. The goal is thus to bring together individuals having relatively similar characteristics, while individuals belonging to different groups are as disparate as possible.

Ferro-Luzzi et al. (forthcoming) have thus combined factor and cluster analysis to identify the subpopulation of poor in Switzerland.

f) Multiple Correspondence Analysis (MCA):

MCA is interesting because it can easily combine quantitative variables and categorical variables, although clearly the latter should be ordinal in a poverty analysis (for an application of MCA to poverty analysis in Vietnam, see, Asselin and Vu Tuan Anh, forthcoming).

MCA has also the advantage that one can plot on the same graph the variables and the observations so that it becomes easy to undertake a proximity analysis (to see which variables are next to a given observation, provided evidently that there are not too many observations)

2) Other approaches based on the idea of latent variables: the socalled Rasch model and its extensions

The Rasch model (Rasch, 1960) belongs originally to the field of psychometrics, a discipline that attempts to measure latent traits such as intelligence, sociability or self-esteem, which cannot be observed directly and must be inferred from their external manifestations. This model was applied to poverty by Dickes (1983, 1989) who made the assumption that poverty (a latent variable) is a continuum and that on the basis of a set of heterogeneous information (e.g. on health and housing), it is possible to rank individuals according to a criterion that would be homogeneous: poverty. This approach has also been used by Ayala and Navarro (forthcoming a and b) and is also mentioned in Capellari and Jenkins (2006).

Two points must be stressed (see, Fusco and Dickes, forthcoming): a) A same set of items of deprivation belonging to several domains can measure either a single or several latent characteristics. Poverty is considered as unidimensional if only one continuum of poverty is measured and as multidimensional if one needs more than one continuum to grasp this phenomenon. Hence it is necessary to determine

- whether poverty is a unique phenomenon that manifests itself equally in different domains of life

or whether it is a concept constituted by separated continua that manifest themselves in a differentiated way in different domains of life

b) Moreover, two different ways of considering the relationship between the items are possible. Items in a set are homogeneous if the correlation between them is high and then they measure the same latent characteristic. There is however also the possibility that the relationship between the items is hierarchical. This means that if an individual suffers from the more severe deprivations, he (she) is likely to suffer also from the less severe ones: not having a house can make it difficult to participate fully in society.

When we combine these two criteria we obtain four theoretical representations of the idea of continuum.

1- In the unidimensional homogeneous model, poverty can be considered as a single phenomenon that manifests itself homogeneously in different domains of life.

2- The second possibility is the unidimensional homogeneous and hierarchical model. Here we suppose again that there is only one continuum on which we can classify the individuals but there is a hierarchy among the items (see, Gailly and Hausman, 1984).

3- The multidimensional homogeneous model assumes that poverty affects the different domains of life in differentiated ways. There are thus several types of poverty and an individual can be considered as poor in one dimension and not in another. Poverty is therefore a homogeneous phenomenon for each of its constitutive dimension but the dimensions are heterogeneous.

4- The multidimensional homogeneous and hierarchical model of poverty implies also the identification of several dimensions but the relationships between the items is hierarchical. This case corresponds to a multidimensional extension of the Rasch model.

For Dickes (1989) the selection of one of the models is not a logic operation but must be the result of an empirical procedure. The question of the uni- or multi-dimensionality of poverty must be resolved in applying specific multidimensional and confirmatory methods. This is also true for the choice between the homogeneous or hierarchical nature of the items of the continuum. For more details and an illustration, see, Fusco and Dickes (forthcoming).

A nice presentation of the possible extensions of the Rasch (item response) model is given in Cappellari and Jenkins (2006). Among the studies using this type of latent variable approach one may cite Pérez-Mayo (2004 and 2005), Ayala and Navarro (forthcoming a and b),

3) Efficiency Analysis and Multidimensional Poverty:

a) The concept of input distance function:

Let q represent an arbitrary quantity vector and u an arbitrary utility indifference curve. The distance function , defined on u and q, represents the amount by which q must be divided in order to bring it on to the indifference curve, so that . Geometrically, in Figure 2, is the ratio OB/OA. Note that if q happens to be on u, B and A coincide so that if and only if

This concept of distance function may naturally be also used when relating an output y to inputs x.

Figure 2

Using the input distance function defined previously (see, Figure 2) we could assume that the inputs are various indicators relevant for a given wellbeing dimension (e.g. measures corresponding to various aspects of health) while the output would be the health standard of reference against which to judge the relative magnitudes of the vectors of health indicators.

This reference set is assumed to be a lower bound so that individuals located on the isoquant will have the lowest level of health, with an health index value of unity, whereas individuals with larger values of the health indicators will be assumed to have a higher overall health level (health index above unity).

b) The concept of output distance function:

Efficiency analysis may be also applied when using the concept of production possibility frontier (PPF) and will then show by how much the production of all output quantities could be increased while still remaining within the feasible production possibility set for a given input vector (see, Figure 3).

Clearly here the production possibility frontier will be considered as a standard of reference and will correspond to an upper bound. Therefore the further inside the output set an individual is, the more it must be radially expanded in order to meet the standard and hence the lower its “overall production level” for a given set of inputs.

When applied to the evaluation of well-being, the various outputs could correspond to various dimensions of well-being such as financial well-being, health, level of social relations, etc…and so, the further inside the “PPF” an individual is, the lower his overall level of well-being

Various techniques may be applied in efficiency analysis to estimate these input and output distance functions:

Data envelopment analysis (DEA):

In its simplest form Data Envelopment Analysis is linear programming. But there are more sophisticated approaches. Anderson et al. (forthcoming) have, for example, applied a technique called Lower Convex Hull Approach, to data on life expectancy, literacy rate, school enrollment and gross domestic product per capita for 170 countries in the years 1997 and 2003, and used this technique to determine which countries could be considered as the “poorest” on the basis of these four indicators (dimensions).

Econometric Approaches:

Others, starting with Lovell et al. (1994), have adopted an econometric approach to efficiency analysis. Deutsch, Ramos and Silber (2003) have applied such an approach to data from the British Household Panel Survey (BHPS) and estimated the percentage of poor in terms of standard of living as well as of quality of life. The standard of living was assumed to be a function of income, the quality of the dwelling, other property, the amount of durables available for homework and that available for leisure. Quality of life was assumed to be a function of the environment (type of neighbourhood) in which the individual lived, the degree of his mobility and his ability to undertake usual physical tasks, his ability to undertake usual mental tasks, the degree of his “self-respect and self worth” (e.g. feeling of playing a useful role in society), his ability to socialize and network, and various aspects of his health. The correlation between standard of living and quality of life was quite low (0.07). It appeared also, using a relative approach to poverty, that the percentage of poor in both standard of living (SL) and quality of life (QL) was low (less than 10% in both cases, with a poverty line ranging from 50% to 80% of the median value of the corresponding distribution), probably because both SL and QL are weighted averages.

4) Information Theory:

Maasoumi (1986) was the first to use concepts borrowed from information theory to derive measures of multidimensional well-being and of multidimensional inequality in well-being. Assume n welfare indicators have been selected, whether they be of a quantitative or qualitative nature. Call the value taken by indicator j for individual (or household ) i, with i = 1 to n and 1 to m. The various elements may be represented by a matrix X.

Maasoumi’s idea is to replace the m pieces of information on the values of the different indicators for the various individuals by a composite index which will be a vector of n components, one for each individual.

In other words the vector corresponding to individual i will be replaced by the scalar . (c stands for composite). This scalar may be considered either as representing the utility that individual i derives from the various indicators or as an estimate of the welfare of individual i, as an external social evaluator sees it.

The question then is to select an “aggregation function” that would allow deriving such a composite welfare indicator . Maasoumi (1986) suggested finding a vector that would be closest to the various m vectors giving the welfare level the various individuals derive from these m indicators. Using concepts borrowed from the idea of generalized entropy, Maasoumi (1986)

³ Theil (1967) was probably the first to apply information theory (on this topic, see, Shannon, 1948) to economic issues.

showed that this composite indicator will be an arithmetic, geometric or harmonic mean of the various indicators.

While Maasoumi (1986) computed then an index measuring the degree of inequality of the distribution of this composite indicator using evidently entropy related inequality indices, Miceli (1997), using a relative approach to poverty, estimated the percentage of poor in the population, on the basis of the distribution of this composite index

Deutsch and Silber (2005) have applied information theory to Israeli census data for the year 1995 and, using an approach similar to that adopted by Miceli (1997), they computed indices of multidimensional poverty in Israel, for the year 1995. This study will be mentioned again when various approaches to multidimensional poverty measurement will be compared.

5) The concept of order of acquisition of durable goods:

Forty years ago Paroush (1963, 1965 and 1973) suggested using information available on the order of acquisition of durable goods to estimate the standard of living of households. Assume we collect information on the ownership of three durable goods α, β and A household can own one two, three or none of these goods. There are therefore possible profiles of ownership of durable goods in this example. An illustration is given in Table 1 where the letter Y indicates that the household owns the corresponding good and the letter N that it does not.

If we assumed that every household followed the order α, β, γ (that is, that a household first acquires good α, then good β and finally good γ) there would be no household with the profiles 3, 4, 6 and 7. We do not want to assume however that every household has to follow this order α, β, γ . More generally, for a given order of acquisition and k durable goods, there are k+1 possible profiles in the acquisition path.

There are evidently always households that slightly deviate from this most common order of acquisition and this possibility will be taken into account. Deutsch and Silber (forthcoming) have worked with 11 durable goods so that discovering this most common order of acquisition required a very high number of computations.

For each individual i in the sample, they had to determine the minimum distance of his profile to each of the possible profiles in a given order of acquisition. As mentioned before, with 11 goods, there are 12 such comparisons. Since the sample used was based on 204,098 households, 2,449,176 comparisons were needed in order to determine some proximity index R (for more details on this index, see, Deutsch and Silber, forthcoming) for a single order of acquisition. Since they worked with 11 durable goods, this procedure had to be repeated times. This is the total number of possible orders of acquisition resulting from 11 durable goods. As a consequence was the total number of computations necessary to find the order of acquisition with the highest index of proximity R.

Once the most common order of acquisition was found, they worked only with the households who selected (more or less) this order. There were 65,333 such households (out of the 204,098 original households). Each of these individuals had therefore 0,1,2…, or 11 of the durable goods.

Table 1: List of possible orders of acquisition when there are 3 goods

Deutsch and Silber (forthcoming) then assumed that those who did not have any of the goods had the highest level of deprivation while those who had all of them had the lowest level of deprivation. This allowed them to estimate an ordered logit regression where the level of deprivation was a function of variables such as age, size of the household, education, etc…Then they computed the probability that a household with given characteristics belonged to one of the profiles permitted by the order of acquisition of durable goods that was finally found to be the most common. Using the results of this ordered logit regression they estimated for each household the expected value of its deprivation index (the latent variable in the procedure). They then decided that the households with the highest levels of deprivation (e.g., those belonging to the upper quartile) should be considered as poor and checked what characteristics these poor had.

Analyzing data from the 1995 Israeli Census, Deutsch and Silber (forthcoming) thus found that the probability of being poor decreased with the schooling level of the head of the household, first decreases and then increased with his/her age and with the size of the household. Poverty was found to be higher when the head of the household was single and lower when he/she is married. Poverty was lowest when the head of the household was Jew and highest when he/she is Muslim. Poverty was also higher among households whose head had immigrated in recent years.

Let us now turn to another set of approaches to multidimensional poverty measurement, one where poverty lines are first determined for each poverty dimension. Only afterwards will an attempt be made to aggregate the information.

But even then there are two possibilities:

- Aggregating first the dimensions and then the individual observations

- Or aggregating first the individual observations and then the dimensions.

C) Determining first poverty lines for each dimension, then aggregating the dimensions and finally aggregating the individual observations

1) The axiomatic approach to multidimensional poverty measurement:

Chakravarty et al. (1998) made the following assumptions when deriving some multidimensional poverty indices.

• Symmetry: This property assumes that the multidimensional poverty index depends only on the various attributes j that the individuals have and not on their identity.

Focus: Cal the amount of attribute j than individual i has. Call the poverty line for attribute j. Then if for any individual i an attribute j is such that , the overall multidimensional poverty index P(X;z) will not change if there is an increase in (X is the matrix of the ´s and z the vector of the .

• Monotonicity: If for any individual i an attribute j is such that does not increase if there is an increase in

• Principle of Population: A m-fold replication of X will not affect the value of the poverty index.

• Continuity: An index of multidimensional inequality M(X) should be a continuous function, that is, it should be only marginally affected by small variations in

• Non-Poverty Growth:

If the matrix Y is obtained by adding a rich person to the population defined by

X, then

• Non-decreasingness in Subsistence Levels of Basic Needs: If increases for any j, P(X;z) does not decrease.

• Scale Invariance: This implies that the ranking of any two matrices of attributes is preserved if the attributes are rescaled according to their respective ratio scales.

• Normalization: whenever for all i and j.

Subgroup decomposability: Assume is the population size of subgroup i (i=1 to m) with n the total size of the population. Then the poverty index for the whole population (where the data on each subpopulation is represented by a matrix may be expressed as

\[\mathrm{P} \left(\mathrm{X} _ {1}, \dots , \mathrm{X} _ {\mathrm{m}}\right) = \sum_ {\mathrm{i} = 1 \text { to m }} \left(\mathrm{n} _ {\mathrm{i}} / \mathrm{n}\right) \mathrm{P} \left(\mathrm{X} _ {\mathrm{i}}; \mathrm{z}\right)\]

• Factor Decomposability:

\[\mathrm{P} (\mathrm{X}; \mathrm{z}) = \sum_ {\mathrm{j} = 1 \text { to k }} a _ {\mathrm{j}} \mathrm{P} (\mathrm{x} _ {. \mathrm{j}}; \mathrm{z} _ {\mathrm{j}})\]

where is the jth column of is the weight attached to attribute j such that

\[\sum_ {j = 1 \text { to } k} a _ {j} = 1.\]

Transfer Axiom: Let be the submatrix of X corresponding to the poor. If Y is derived from X by multiplying by a bistochastic matrix (not a permutation matrix), then given that the bundles of attributes of the rich remain unaltered.

• Nondecreasing Poverty under Correlation Increasing Arrangement:

This property refers to switches of some attribute(s) between individuals, that increase the correlation of the attributes. This property will be analyzed at length in another section below.

Chakravarty et al. (1998) derived then axiomatically a generalization of the FGT index which may be expressed as:

\[\mathrm{P} \alpha (\mathrm{X}; \mathrm{z}) = (1 / \mathrm{n}) \sum_ {\mathrm{j} = 1 \text { to k }} \sum_ {\mathrm{i} \in \mathrm{Sj}} a _ {\mathrm{j}} [ 1 - (\mathrm{x} _ {\mathrm{ij}} / \mathrm{z} _ {\mathrm{j}}) ] ^ {\alpha}\]

In another paper Chakravarty and Silber (forthcoming) derived the following multidimensional generalization of the Watts index:

\[\mathrm{PW} (\mathrm{X}; \mathrm{z}) = (1 / \mathrm{n}) \sum_ {\mathrm{j} = 1 \text { to k }} \sum_ {\mathrm{i} \in \mathrm{Sj}} a _ {\mathrm{j}} \log (\mathrm{z} _ {\mathrm{j}} / \mathrm{x} _ {\mathrm{ij}})\]

Using the Shapley decomposition, Chakravarty et al. (2005) have shown that changes over time in this index may be easily decomposed into components reflecting respectively

- changes in the overall headcount ratio (overall percentage of poor, all poverty dimensions combined)

- changes in the share of the various poverty dimensions in the sum of the poor in the various dimensions (note that this sum is likely to be greater than the overall number of poor)

- changes in the ratio between the overall number of poor and the sum of the poor in each dimension (somehow a measure of the correlation between the poverty dimensions)

- changes, in each dimension, in the percentage gap between the poverty line and the average level of the corresponding attribute

- changes in the degree of the inequality of the distribution of the corresponding attribute among the poor.

In their empirical illustration Chakravarty et al. (2005) applied this decomposition technique to data on the per capita GDP, life expectancy and literacy rates of the countries for which the figures were available in 1992 and 2002 (164 countries representing a population of 5.3469 billions of individuals in 1992 and 5.9980 in 2002). These three variables are the main elements determining the Human Development Index HDI which is computed every year by the World Development Programme. The index HDI depends also on school enrollment rates but this variable was not taken into account in order to maximize the number of countries for which data were available.

For each of these three dimensions the authors had to determine a “poverty line”. For life expectancy they decided that any country in which life expectancy was smaller than 60 years should be considered as a “poor country” from the point of view of this dimension. Similarly, whenever the literacy rate in a country was smaller than 60%, that country was “labeled” poor as far as the literacy dimension is concerned. Finally, for the per capita GDP the authors did not adopt the 1$ or 2$ a day criterion which is often adopted by international agencies but assumed that any country in which the per capita GDP was smaller than 5$ day should be classified as poor from the point of view of income (per capita GDP). This corresponds to an annual per capita GDP of $1825.

Using the multidimensional Watts index the authors found that world poverty decreased by close to 50% between 1993 and 2002 (the Watts index decreased from 0.247 to 0.131). It turns out that this decrease was essentially the consequence of the decrease in the overall headcount ratio. The contributions of the other determinants mentioned previously were small and cancelled out.

In a second stage of the analysis Deustch, Chakravarty and Silber (forthcoming) excluded China and India whose weight in the world population is very high.

It then appears that both in 1993 and in 2002 the weights of the three dimensions were almost equal. (Recall that the weight of a given dimension is equal to the ratio of the number of the poor computed on the basis of that dimension over the sum of the number of poor computed on the basis of the different dimensions.) They also observed that whereas when all countries are included, the share of the poor (all dimensions included) in the world population decreased significantly between 1993 and 2002 (from 36.1% to 19.6%), it slightly increased (from 31.6% to 32.2%) when China and India are excluded.

As far as the five determinants of the multidimensional Watts poverty index are concerned, the results are quite different from what was observed when China and India were included in the analysis. The decrease in the Watts index was much smaller (from 0.252 to 0.216) and more than two thirds of this decrease was due to an increase in the degree of correlation between the three dimensions of poverty on which this analysis is based. The other component which played a role in the decrease in the Watts index is the percentage change in the gap between the poverty lines and the average level of the attributes among the poor. This percentage decreased for life expectancy and the literacy rate and increased for the per capita GDP.

2) Information Theory:

In an interesting paper Maasoumi and Lugo (forthcoming) have defined multidimensional poverty indices that are derived from information theory and in which, at the difference of what was mentioned earlier, poverty lines are defined separately on each dimension. Their empirical illustration is based on the 2000 Indonesian Family Life Survey and the poverty dimensions they used are the real per capita expenditure, the level of hemoglobin and the years of education achieved by the head of household. The reason for using the level of hemoglobin is that low levels of hemoglobin indicate deficiency of iron in the blood and iron deficiency is thought to be the most common nutritional deficiency in the world today. As expected, the measured poverty rates increase as the parameter measuring substitutability between attributes decreases.

3) The Subjective Approach to Multidimensional Poverty Measurement:

The subjective approach starts by asking households how they evaluate their own situation in terms of verbal labels such as 'bad', 'sufficient', 'good‘,…Such an approach to poverty was already proposed in the late 1970s (see Goedhart et al., 1977, Van Praag et al., 1980, as well as Hagenaars, 1986).

Let us assume that one of the poverty dimensions is the financial situation of an individual and call an individual’s financial satisfaction. We can assume that depends, for example, on his income and possibly other variables like family size.

In short where stands for personal variables, including income.

Assuming is distributed as a normal variable with mean 0 and variance 1, the probability that an individual gives a satisfaction of (on a scale from 0 to 10) may be expressed as

\[\mathrm{P} [ 0. 6 5 < \mathrm{S} _ {1} < 0. 7 5 ] = \mathrm{P} [ \mathrm{N} ^ {- 1} (0. 6 5) < \beta_ {1} \mathrm{x} _ {1} + \beta_ {0} + \varepsilon \leq \mathrm{N} ^ {- 1} (0. 7 5) ]\]

The can then be estimated by maximizing the log-likelihood. Such an approach has been called Cardinal Probit (CP) by Van Praag and Ferrer-i-Carbonell (2004).

The same approach may be followed with respect to other domains of life, such as job and health. It is obvious that such domain satisfactions might be correlated so that the likelihood would involve a bi-variate normal integral. With six domains, the likelihood might then be a six-dimensional integral. To solve this issue Van Prrag and Ferrer-i-Carbonell (forthcoming) have proposed an alternative approach, the details of which will not be given here.

One may then ask whether there is a trade-off between domain satisfactions and whether there is a natural aggregate of domain poverties, which may be interpreted as an aggregate poverty concept or ‘overall poverty’? Since in many of these types of surveys there is also a question about ‘satisfaction with life as a whole’ it is possible to explain this General Satisfaction by the specific domain satisfactions

The authors used the German Socio-Economic Panel (GSOEP) and made a distinction between six domain satisfactions: satisfaction with financial situation, job, health, leisure, environment, and housing. They assumed, for each domain, that when an individual´s answer was 0,1,2,3 or 4, he should be considered as poor with respect to this domain. They thus found that financial poverty was 6.8% but the poverty rate with respect to health was 11.3% and that with respect to job satisfaction 10.4%. The authors also found that in general there is a significant positive correlation between the domain satisfactions. But there are some exceptions. For instance, older people live in better houses or at least enjoy more housing satisfaction, while at the same time their health is worse than that of younger people. This may explain the negative correlation between health and housing. A similar explanation may hold for the low correlation between health and environment and leisure satisfactions.

Van Praag and Ferrer-i-Carbonell (forthcoming) conclude that it is possible to interpret overall-poverty as a weighted sum of domain poverties and that there is a trade-off between the domains (e.g. less job satisfaction may be compensated by a higher financial satisfaction).

D) Determining first poverty lines for each dimension, then aggregating the individual observations and finally aggregating the dimensions

This is the procedure that is in fact adopted by the so-called Fuzzy Approach to Multidimensional Poverty Measurement.

The mathematical theory of “Fuzzy Sets” was developed by Zadeh (1965) on the basis of the idea that certain classes of objects may not be defined by very precise criteria of membership. In other words there are cases where one is unable to determine which elements belong to a given set and which ones do not.

This simple idea may be easily applied to the concept of poverty. There are thus instances where it is not clear whether a given person is poor or not. This is especially true when one takes a multidimensional approach to poverty measurement, because according to some criteria one would certainly define an individual as poor whereas according to others one should not regard him as poor. Such a fuzzy approach to the study of poverty has taken various forms in the literature. A detailed presentation is given in a recent book on the topic edited by Betti and Lemmi (2006).

One of the approaches is called the Totally Fuzzy and Relative Approach (TFR). Assume a specific question j (e.g. health status) on which one can give answers from 0 to 5, 5 corresponding to the highest level of deprivation (lowest level of health status). Calling the distribution function of deprivation, one of the ways of defining the deprivation (i) of individual i with respect to dimension j is to assume that , that is, i´s deprivation is equal to the proportion of individuals who are not more deprived than he is.

The second stage of the analysis is to compute the overall level of deprivation of individual i (over all dimensions). There it is usually assumed that

\[\mu_ {j} (i) = \sum_ {j = 1 \text { to } J} w _ {j} \mu_ {j} (i),\]

where the weight of each dimension j is inversely related to the average level of deprivation in the population for dimension j. In other words the lower the frequency of poverty according to a given deprivation indicator, the greater the weight this indicator will receive. The idea, for example, is that if owning a refrigerator is much more common than owning a dryer, a greater weight should be given to the former indicator so that if an individual does not own a refrigerator, this rare occurrence will be taken much more into account in computing the overall degree of poverty than if some individual does not own a dryer, a case which is assumed to be more frequent.

In the final stage of the analysis the average level of deprivation in the population will be computed as

\[\mu_ {\mathrm{mean}} = (1 / \mathrm{n}) \sum_ {\mathrm{i=1ton}} \mu (\mathrm{i})\]

so that the average level of deprivation in the population is assumed to be equal to the simple arithmetic mean of the levels of deprivation of the different individuals.

Any individual whose deprivation level will be greater than will be assumed to be poor and this allows us then to compute the percentage of poor in the population.

Working again with Israeli Census data for the year 1995 (for which only information on the ownership of durable goods was available) Deutsch and Silber (2006) concluded, combining this Fuzzy Approach with a Logit regression, that, ceteris paribus, the probability of being poor is lower, the higher the educational level of the head of the household, that it first decreases, then increases again with the size of the household as well as with the age of the head of the household. Ceteris paribus this probability is highest when the head of the household is Muslim and lowest when he/she is Jewish, is lowest when the head of the household is married and highest when he/she is single. Ceteris paribus it is also higher when he/she is a new immigrant and the head does not work. Finally, ceteris paribus, the gender of the head of the household was found to have no significant impact on the probability to be poor.

Finally, applying a Shapley type of decomposition, Deutsch and Silber (2006) were able to determine the exact impact on poverty of each of the explanatory variables of the logit regression. The three categories of variables that were found to have the greatest impact were the age of the head of the household, his/her religion and the size of the household. Other variables that play an important role were the year of immigration, the educational level and the marital and working status of the head of the household.

E) Does the selection of a specific approach make a difference?

There is no study that systematically compared all the various approaches previously described. Deutsch and Silber (2005) attempted to compare four approaches on the basis of the same data base (1995 Israeli Census): the fuzzy approach, information theory, the efficiency approach and the axiomatic approach.

They found that in most cases there were no big differences between the various multidimensional poverty indices that have been used, at least as far as the impact on poverty of various explanatory variables was concerned. Thus poverty was found to first decrease, then increase with the size of the household and the age of its head. Poverty was also lower when the head of the household had a higher level of education, worked, was self-employed, married, Jewish, lived in a medium-sized city and had been for a longer period in Israel.

To what extent do these different approaches identify the same households as poor?

In order to be able to make relevant comparisons, Deutsch and Silber (2005) assumed that, whatever the approach used, 25% of the households were poor.

They found that 53.2% of the households were never defined as poor while 15.4% of them were considered as poor according to one poverty index (and one only). Note that 11% of the households were defined as poor according to all the indices, which is not a small percentage. They also observed that 31.4% of the households were defined as poor according to at least two indices, 25.4% according to at least 4 indices and almost 20% (19.8%) according to at least 6 indices.

Deutsch and Silber (2005) based their analysis, as was mentioned earlier, on information drawn from the 1995 Israeli Census concerning the ownership of durable goods. No information on income was available for the sample used.

In another study Silber and Sorin (2006) used data from the 1992-1993 Israeli Consumption Expenditures Survey and attempted to compare results based on a fuzzy approach with the more traditional approach using directly consumption or income data. For the Fuzzy Approach the following variables were taken into account:

1) Non ownership of an oven or a microwave oven

2) Non-ownership of a refrigerator

3) Non-ownership of a TV set

4) Non-ownership of at least two of the following durables: washing machine, vacuum cleaner, air conditioning, videotape, stereo, phone

5) Non-ownership of a car

6) Non-ownership of an apartment (house)

7) Negative savings

Three different fuzzy approaches were used, that of Cerioli and Zani (1990), that of Cheli et al. (1994) and Cheli and Lemmi (1995) and that of Vero and Werquin (1997). Silber and Sorin (2006) computed also the percentage of poor on the basis of a unidimensional approach using either income or expenditures as welfare indicator. They thus used five different approaches in computing the proportion of poor. They then observed that only 2% of the households were poor according to all the five approaches, more than 25% (in fact 28.9%) of the households were poor according to at least one of the five estimation methods. This is an important result that could show that multidimensional approaches to poverty are a useful complement to the more traditional (and unidimensional) approaches to poverty measurement

IV. The Ordinal Approach to Poverty Measurement:

A) The Case of Uni-dimensional Poverty:

The advantage of an ordinal approach to poverty analysis is that it eventually allows making poverty comparisons that are valid for a wide range of poverty lines as well as for a broad class of poverty measures (see, Atkinson, 1987, and Fields, 2001).

Assume we plot the cumulative density functions for income, with income on the x-axis. One may then think of the values on the x-axis as potential poverty lines and of the corresponding value on the y-axis as headcount ratios. This particular cumulative density function is sometimes called a “poverty incidence curve” (see, Fields, 2001).

If the poverty incidence curve for one distribution is everywhere below the poverty incidence curve for another over a bottom range of poverty lines, it can be proven that poverty will be lower in the first distribution for all those poverty lines and for all poverty measures that obey two conditions: nondecreasingness and anonymity.

Non-decreasingness implies that if any one person’s income increases, then the poverty measure cannot increase as well. Anonymity means that only the incomes of individuals (and no other characteristic) will be taken into account when measuring poverty. Following Duclos et al. (forthcoming) call P1 the class of all poverty measures that have these characteristics. It then turns out that P1 includes in fact almost every standard poverty measure. What has just been defined is in fact called “first-order poverty dominance”.

What happens if the cumulative density functions cross one or more times? Then we do not have a clear ordering. There are two ways of dealing with this problem.

First, it is possible to conclude that poverty in one distribution is lower than in another for the same large class of poverty measures, but only for poverty lines up to the first point at which the cumulative density functions cross (see Duclos and Makdissi, 2005). Second, it is possible to make comparisons over a smaller class of poverty measures. Thus if we add the condition that the poverty measure respects the Pigou-Dalton transfer principle, it turns out that we can compare the areas under the crossing poverty incidence curves. So if the area under one curve is less than the area under another for a bottom range of reasonable poverty lines, poverty will be lower for the first distribution for all poverty measures that are: non-decreasing, anonymous and obey the principle of transfer.

This is called “second-order poverty dominance” and, following Duclos et al. (forthcoming) let us call the associated class of poverty measures P2. Note that while not as general as the one drawn under first order dominance, it is still quite a general conclusion. The curve that plots these areas as a function of income is often called “poverty deficit curve” (see, Fields, 2001).

What if two poverty deficit curves cross each other? Here again we will try to define smaller class of poverty measures. Following Duclos et al. (forthcoming) the third class of poverty indices will be denoted by P3 and will include the indices belonging to the second class that obey also the principle of diminishing transfers (when a transfer is made from a poor to a poorer individual, the decrease in poverty will be greater, the poorer the recipient of the transfer).

Thus if we add the condition that the poverty measure respects the principle of diminishing transfers, we will be able to compare the areas under the crossing poverty deficit curves. So if the area under one such curve is less than the area under another for a bottom range of reasonable poverty lines, poverty will be lower for the first distribution for all poverty measures that are: non-decreasing, anonymous and obey the principles of transfers and diminishing transfers.

This is called “third-order poverty dominance” and we can call the associated class of poverty measures P3. The curve that plots these areas as a function of income is often called “poverty severity curve” (see, Fields, 2001).

B) The Case of Multidimensional Poverty:

In what follows, at the difference of what was assumed previously, there will be a poverty threshold for each dimension. At this stage different concepts need to be introduced and various questions have to be asked before stating some interesting propositions.

1) Which concept is relevant: Union or Intersection

Assume that in each dimension there is a threshold so that if for an individual the level of the attribute corresponding to a given dimension (e.g. years of education) falls short of this threshold, he will be considered as poor with respect to this dimension (attribute). If the level that an individual has reached on each attribute is known, what can be said about his overall level of poverty? Or more precisely when can we say that this individual is poor? To answer this question one has to ask which concept is more relevant, Union or Intersection?

a) The Union approach:

This approach will say that as soon as an individual is poor with respect to one attribute, he should be considered as poor. Figure 4, which is borrowed from Atkinson (2003), shows that in such a case any individual located in the area OPQRST should be considered as poor.

b) The Intersection Approach:

This approach will say that an individual is poor only when he is poor with respect to each dimension. In such a case Figure 4 shows that the set of poor includes only the individuals located in the area

Figure 4: Multidimensional Poverty Union versus Intersection

It should be clear that if we choose the Union interpretation, the sum over all dimensions of the number of individuals who are poor with respect to a given dimension is likely to be higher than the total number of poor obtained on the basis of a union approach. Note that this possibility of double counting increases rapidly with the number of dimensions. The opposite conclusion is evidently true when adopting the intersection approach.

2) Are the dimensions substitutes or complements?

The concepts of “substitutability” and “complementarity” used here are not based on the well-known Hicks-Allen (1934) definitions of “substitutability” and “complementarity” , but on what is known today as the ALEP approach (Auspitz, Lieben, Edgeworth and Pareto). Auspitz and Lieben (1889, cited in Lenfant, 2006) have in fact an interesting statement. Starting their story with an original decrease in the price of coffee, they then state that

⁴ The Hicks-Allen (1934) approach assumes that a price rise will eventually lead to a decrease in the consumption of complementary goods.

“…A rise in the consumption of coffee will always result in an increase in the quantity of sugar used to sweeten it, but, if the same individual is also reducing his consumption of tea as a consequence of an increased use of coffee, it may happen that, instead of increasing, its total consumption of sugar will decrease…

This so-called ALEP approach was evaluated as follows by Schultz (1935, cited by Lenfant, 2006):

“…according to [the ALEP definition] if we wish to know whether two commodities are completing, independent, or competing to an individual, we must ask him (and he must be able to tell us) whether, as we increase the quantity of one of the goods, the final utility of the other increases, remains constant or decreases. The operation calls for an introspective comparison of final degrees of utility, on his part…

In other words the ALEP definition assumes that in a two goods world, if two goods are substitutes, the marginal utility of one good will decrease when the quantity of the other increases.

Let us go back to the topic of this article and, for simplicity, assume that the degree of poverty of an individual is a function of only two attributes. Then it is possible to state, on the basis of the ALEP approach, that if these two attributes are substitutes, poverty will decrease less with an increase in attribute 1 for individuals with greater amounts of attribute 2. The contrary is evidently true when the two attributes are complements.

Duclos et al. (forthcoming) give the following illustration:

“If we are able to improve a child´s health, it seems ethically right that this should reduce overall poverty the most when the child is very poor in the income dimension. But there are some plausible exceptions. For example, suppose that only healthy children can learn at school. Then it might reduce poverty more if we concentrate health improvements on children who are at school (better off in the education dimension), because of the complementarity of health and education”.

3) The concept of Correlation Increasing Switch:

Assume there are two individuals (i = a and i = b) and two attributes and denotes the amount of attribute j that individual i has. Assume that and that

Consider now a “switch” of attribute 2 between the two individuals. Such a “switch” increases the correlation between the two attributes because now individual a has more of attribute 1 as well as more of attribute 2. If the two attributes are considered as substitutes in the ALEP sense, then such a switch cannot decrease poverty. This is the principle of “non-decreasing poverty under a correlation increasing switch” (see, Bourguignon and Chakravarty, 2002 and 2003). If however the two attributes are complements, such a switch should not increase poverty. This is then the principle of “non-increasing poverty under a correlation increasing switch”.

4) Some basic assumptions:

Here is a list of properties that will always be assumed to hold in what follows:

a) Focus (FOC): For any person i and attribute j, assume that where is the poverty line for attribute j. Then an increase in , assuming that all other attribute levels in the matrix X (the matrix of the remain fixed, will not change the value of the poverty index.

b) Symmetry (SYM): This property assumes in fact that multidimensional poverty depends only on the values taken by the elements of the matrix X and on no other characteristics of the individuals (e.g. their race, gender,…).

c) Principle of Population (POP): This is Dalton´s famous replication principle which says more or less that a “cloning” of the existing population will not affect poverty.

d) Subgroup Decomposability (SUD): It is assumed that overall multidimensional poverty in a population is a weighted average of multidimensional poverty in the various population subgroups, the weights being the population shares of the various subgroups.

e) Differentiability (DIF): It will be assumed that the poverty measure is twice differentiable.

Following Bourguignon and Chakravarty (2002) three categories of poverty indices will now be defined. The three categories of indices will be assumed to have the five properties mentioned previously, that is, FOC, SYM, POP, SUD and DIF.

1- The class P+: The indices in this family are assumed to have, in addition to the five common properties, two additional properties: MON and NDP:

- Monotonicity (MON): For any person i and attribute j such that an increase in given that all the other elements of the matrix X remain constant, will not increase poverty.

- Non-Decreasing Poverty under a Correlation Increasing Switch (NDP):

Assume, for simplicity, two attributes only and two individuals a and b who are poor with respect to both attributes with individual a having more of attribute 1 than individual b while individual b has more of attribute 2 than a. Assume now a switch of attribute 2 between the two individuals so that individual a has now more of attribute 1 and more of attribute 2 than individual b. Note that in such a case the marginal distributions of the attributes does not change. Then if a matrix Y is derived from a matrix X by such a correlation increasing switch of an attribute between two persons who are poor in both attributes, poverty will not have decreased (when moving from X to Y) if the attributes are substitutes.

2-The class P-: The indices in this family are assumed to have, in addition to the five common properties, two additional properties: MON and NIP:

- Non-Increasing Poverty Under a Correlation Increasing Switch (NIP): Using the same example as previously, but assuming this time that the two attributes are complements, increasing the correlation between the two attributes must not increase poverty (remember the case assuming that health and education are complements).

3-The class P0: The indices in this family are assumed to have, in addition to the five common properties, two additional properties: MON and NCP:

- Non-Changing Poverty under a Correlation Increasing Switch (NCP): This is evidently an intermediate case where poverty is not assumed to change under a correlation increasing switch.

We can now state the following propositions (see Bourguignon and Chakravarty, 2002, for the proofs).

Proposition 1: Assume that all the properties listed for category P+ hold (FOC, SYM, POP, SUD, DIF, MON and NDP). Then poverty dominance requires

- Uni-dimensional Poverty Dominance in each dimension

- Two-dimensional Poverty Dominance over the set of persons who are poor simultaneously in both dimensions (the headcount should be lower in the intersection of the single dimension poverty spaces).

Proposition 2: Assume that all the properties listed for category P- hold (FOC, SYM, POP, SUD, DIF, MON and NIP). Then poverty dominance requires

- Uni-dimensional Poverty Dominance in each dimension.

- Two-dimensional Poverty Dominance over the set of persons who are poor in either one of the dimensions (the headcount should be lower in the union rather than in the intersection of the single dimension poverty spaces).

Proposition 3: Assume that all the properties listed for category P0 hold (FOC, SYM, POP, SUD, DIF, MON and NCP). Then poverty dominance requires - Uni-dimensional Poverty Dominance in each dimension.

We can therefore conclude that when two poverty dimensions are substitutes, analyzing the dominance conditions of one distribution over another implies working with the concept of intersection whereas when the dimensions are complements one should work with the concept of union.

As stressed by Atkinson (2003) these conclusions do not imply that when measuring multidimensional poverty one should work with the intersection when the dimensions are substitutes and with the union when they are complements. The conclusions drawn by Bourguignon and Chakravarty (2002) concerning the choice between union and intersection apply only to the issue of dominance analysis (as in fact they emphasized themselves).

V. The Qualitative Approach to Poverty Analysis and Learning from Other Social Sciences:

Robert Chambers (forthcoming) has the following citation of a book by Beck (1994): “..the central preoccupation of the majority of authors on poverty has been the accuracy of the statistics and the statistical techniques used”. Chambers then goes on and writes: “A tempting caricature of the concept of poverty implied by such debates could be of a top-down, centre-outwards, ivory tower, mathematical construct, overfed and driven by questionnaires, statistics, computers, regressions, equations, graphs and tables. In this view, it could be seen as sustained by erudite, incestuous and self-reproducing systems of high status organizations and departments, and by teaching, textbooks, international conferences, prestigious journals and rigorous professional peer review”.

This may be a harsh statement but the truth is that qualitative studies are often a nice complement to quantitative surveys. Thus London et al. (2004) stressed that ethnographic data suggest that material hardship, domestic violence and health problems are underestimated in survey data. For example, in a survey conducted in 1999 on Urban Change in the United States aimed at studying the impact of welfare reforms on poor families, the authors found that not only were women in this specific population considerably less healthy than women in the whole population. They also discovered that several respondents who initially said their health was good went on, at some stage, to describe relatively serious health problems (a serious foot injury that would require surgery, a recent really bad case of bronchitis, a recent surgery to have a cyst removed from her breast, …). It thus seems that some women may be reluctant to reveal health problems when standard survey techniques are used.

Let us now review some more specific views concerning a qualitative approach to poverty analysis.

A) On the contribution of anthropology to poverty analysis

Berry (forthcoming) writes that “ethnographic insights can enhance understanding of the meaning and limitations of quantitative indicators as tools for describing and explaining both the causes of poverty and its consequences for people´s aspirations, actions and relations with one another and the conditions in which they live”.

A good example of the usefulness of an ethnographic approach concerns the use of the household as a unit of observation in many surveys. Berry (forthcoming) writes that defining a household may be very difficult in African societies “where one residential structure may house dozens of people who relate to one another in different ways, and individuals move in and out continually, leaving their everyday lives, so to speak, in motion…Children often move among several domiciles as they grow up…In southern Ghana husbands and wives may reside in different houses, sending children to carry meals and messages between them, visiting each other when circumstances permit, and travelling separately to trade, work, or visit distant relatives, sometimes for extended periods of time”.

B) On Participatory Approaches:

Robb (2002), cited by Chambers (forthcoming), states that “the moral imperative for giving the poor a voice in the poverty debate is self-evident” (see also, Narayan et al., 200a and 200b). Chambers (forthcoming) goes on saying that “the bonus is that engaging with the poor also leads to better technical diagnosis of problems and implementation of solutions. Through PPAs (Participatory Poverty Assessments), the poor deepen our understanding of poverty and can influence policymaking. This new approach challenges traditional power relations…When undertaken in an environment of increased trust, PPAs can present opportunities for a more open dialogue and greater understanding between the powerless and those in power.”

Citing Booth et al. (1998) Chambers gave the following list of types of information that could be only obtained via Participatory Poverty Assessments:

A sense of isolation, from services, markets, government institutions and information, with physical isolation a key factor

The key importance of water supplies

• Security of life and livelihood as a primary concern

Access to curative health as a consistently high priority

Local visions of poverty relating to prevailing community norms

Differential vulnerability according to inherent or socially constructed characteristics of individuals (gender, age, childlessness, health status, disability and individual pathologies such as drunkenness)

Hunger and dietary inadequacy as a distinct dimension of deprivation

The seasonality of access and vulnerability

Intra-household poverty dynamics

The decline of traditional, and insufficiency of, alternative safety nets

Community-level poverty versus household or individual poverty

C) Taking Psychology into account:

Palomar Lever (forthcoming) stresses the fact that “…diverse studies link the type of beliefs held by individuals in relation to the causes of poverty with the way in which they perceive their own possibilities for overcoming this precarious condition.

These studies generally show that individuals with a low socioeconomic level are more likely to have beliefs that connote victimization (for example, blaming society,…, the government) and that are associated with perceptions of a lack of control over their own lives, plus low self-esteem, low psychosocial adjustment, and a lack of optimism in regard to overcoming their poverty…

Other studies found that individuals inclined to explain the causes of poverty in terms of the characteristics or life styles of poor people, tend more often to think that they have the means of overcoming poverty, in comparison to those adopting fatalistic or structural explanations. This is particularly true among young individuals with high levels of schooling”.

VI. Concluding comments:

Alkire (2002b) writes that “theories that are not user-friendly do not spread”. This is certainly a pertinent remark and the question one should ask is evidently whether approaches stressing the multidimensional aspects of poverty will gain strength. There are certainly signs of an increasing concern with the multidimensional aspects of poverty. This is probably the main reason for the growing popularity of the Human Development Index published each year by U.N.D.P., although clearly per capita G.D.P., as an indicator of development, has not been evicted. What may be less known is that already in the late 1960´s there was a whole literature in development economics, stressing the importance of a basic needs approach. There was thus a proposal for a Physical Quality of Life Index (P.Q.L.I.) depending on per capita income, the infant mortality rate and life expectancy at age 1. Similarly the development economist Streeten (1980) stressed the need to emphasize outputs rather than inputs when measuring development and suggested that life expectancy might be the best available measure of development. Silber (1983) extended Streeten´s ideas by taking into account not only the mean duration of life but also its dispersion and proposed a new index called the Equivalent Length of Life, which was an application to life tables of Atkinson´s equally distributed equivalent level of income.

But clearly these efforts were not very successful and one may wonder why. Alkire (2002) argues that the problem with the basic needs approach is that those who tried to implement it (at the World Bank and at the International Labour Organization) focussed their attention on the commodities needed to meet such basic needs as health, education, clothing, shelter sanitation and hygiene. This was indeed not the point of view adopted by Amartya Sen (1999a and 1999b) when he formulated his Capability Approach which has become so popular and from which the Human Development Index is probably derived.

So why had two theories, that both stressed the concept of human development, the basic needs and the capability approaches, such a different fate? To answer such a question one has to raise the concept of competition of ideas. A “natural selection” approach to this issue will certainly stress the importance of the degree of problem solving that each approach has, as emphasized by Alkire (2002b).

It is however likely that another factor played an important role, the presence or absence of “successful entrepreneurs of ideas”. It is quite clear that without the clarity of Sen´s contributions, the capability approach would not have been as successful as it is. As an illustration of the convincing power of his contributions here are two citations of Sen describing his capability theory.

“The capability approach to a person´s advantage is concerned with evaluating it in terms of his or her actual ability to achieve various valuable functionings as a part of living.” (Sen, 1993).

“The claims in favor of the capability approach to poverty are:

Poverty can be sensibly identified in terms of capability deprivation; the approach concentrates on deprivations that are intrinsically important (unlike low income, which is only instrumentally significant).

There are influences on capability deprivation – and thus on real poverty – other than the lowness of income (income is not the only instrument in generating capabilities)

The instrumental relation between low income and low capability is variable between different communities and even between different families and individuals…”.

The arguments put forth by Sen are indeed strong and may explain his success. It should however be stressed that the capability approach is only one of several multidimensional approaches to human development and poverty. In addition it should be emphasized that among those advocating such a capability approach there are at times important differences. The philosopher Martha Nussbaum has thus published a detailed list of “Central Human Capabilities” (see, for example, Nussbaum, 2006) while Sen has always refused to give such a list. Sen has probably also never endorsed a specific empirical approach to multidimensional poverty measurement. The reason may be that more work remains to be done in this field before an economist and philosopher like Sen makes any recommendation. This paper, after all, did not intend to summarize the final state of the arts in the field of multidimensional poverty measurement. Its more modest goal was to show that there are quite a few research directions in this field and to suggest that there is certainly room for important additional contributions.

Bibliography

References

1. Abul Naga, R. and E. Bolzani, forthcoming, “Permanent Income, Poverty Measurement and the MIMIC Model,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Alkire, S., 2002a, “Dimensions of Human Development”, World Development, 30(2): 181-205.

References

1. Alkire, S., 2002b, Valuing Freedoms: Sen´s Capability Approach and Poverty Reducation, Queen Elizabeth House Series in Development Studies, Oxford University Press.

References

1. Alkire, S., forthcoming,”Choosing Dimensions: The Capability Approach and Multidimensional Poverty,” in N. Kakwani and J. Silber, The Many Dimensions of Poverty, London, Palgrave-Macmillan.

References

1. Allardt, E., “Having, Loving and Being: An Alternative to the Swedish Model of Welfare Research”, in M. C. Nussbaum and A. Sen, editors, The Quality of Life, Clarendon Press, Oxford, 1993.

References

1. Anand, S., 1977, “Aspects of Poverty in Malaysia,” Review of Income and Wealth, 25(1): 1-16.

References

1. Anderson, G., I. Crawford and A. Leicester, forthcoming, “Efficiency Analysis and the Lower Convex Hull,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Asselin, L.-M. and V. Tuan Anh, forthcoming, “Multidimensional Poverty and Multiple Correspondance Analysis,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Atkinson, A.B., 1987, “On the Measurement of Poverty,” Econometrica, 55, 749-764.

References

1. Atkinson, A.B., 2003, "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches", The Journal of Economic Inequality 1(1), 51-65.

References

1. Auspitz, R. and R. Lieben, 1889, Untersuchungen über die Theorie des Preises, Duncker and Humblot, leipzig.

References

1. Ayala, L., R. Martinez and J. Ruiz-Huerta, 2003, “Equivalence Scales in Tax and Transfers Policies,” Investigaciones Económicas, XXVII(3): 343-367.

References

1. Ayala, L. and C. Navarro, forthcoming a, “The dynamics of housing deprivation,” Journal of Housing Economics.

References

1. Ayala, L. and C. Navarro, C., forthcoming b, “Multidimensional indices of housing deprivation with applications to Spain,” Applied Economics.

References

1. Ballon, P. and J. Krishnakumar, 2006, “Estimating Basic Capabilities: A Latent Variable Approach Based on Bolivian Data,” mimeo, Geneva.

References

1. Barten, A., 1964, “Family Composition, Prices and Expenditures Patterns,” in P. Hart et al., editors, Econometric Analysis for National Economic Planning, Butterworth, London, 1964.

References

1. Beck, T., 1994, The Experience of Poverty: Fighting for Respect and Resources in Village India, Intermediate Technology Publications, London.

References

1. Berry, S., forthcoming, “Poverty Counts. Living with Poverty and Poverty Measures,” in N. Kakwani and J. Silber, The Many Dimensions of Poverty, London, Palgrave-Macmillan.

References

1. Betti, G. and A. Lemmi, 2006, Fuzzy Set Approach to Multidimensional Poverty Measurement, Springer, pages 155-174.

References

1. Blackorby C. and D. Donaldson, 1980, “Ethical Indices for the Measurement of Poverty”, Econometrica, Vol. 48, No. 4, pp. 1053-1060.

References

1. Booth, D., J. Holland, J. Hentschel, P. Lanjouw and A. Herbert, 1998, Participation and Combined Methods in African Poverty Assessments: Renewing the Agenda, Report commissioned by DFID for the Working Group on Social Policy, Special Program of Assistance for Africa.

References

1. Bourguignon, F. and S. R. Chakravarty, 2002, “Multidimensional Poverty orderings,” mimeo, Paris.

References

1. Bourguignon, F. and S. R. Chakravarty, 2003, “The measurement of multidimensional poverty,” Journal of Economic Inequality 1, 25 – 49.

References

1. Buhman, B.,L. Rainwater,G. Schmaus and T.M. Smeeding, 1988, “Equivalence Scales, Well-Being, Inequality and Poverty: Sensitivity Estimates across Ten Countries Using the Luxembourg Income Study (LIS) Database”, Review of Income and Wealth, Vol. 34, pp. 115-142.

References

1. Calvo, C., 2005, “Vulnerability to Multidimensional Poverty. Peru: 1998-2002,” paper presented at the International Conference on The Many Dimensions of Poverty, International Poverty Centre, Brasilia, August 2005.

References

1. Calvo, C. and S. Dercon, forthcoming, “Risk and Vulnerability to Poverty,” in N. Kakwani and J. Silber, The Many Dimensions of Poverty, London, Palgrave-Macmillan.

References

1. Capellari, L. and S. P. Jenkins, 2006, “Summarizing Multiple Deprivation Indicators,” ISER (Institute for Social and Economic Research), Working Paper 2006-40, University of Essex, UK.

References

1. Carter, M and C. Barrett, 2005, “The Economics Of Poverty Traps And Persistent Poverty: An Asset-Based Approach”, mimeo.

References

1. Cerioli, A., Zani S., 1990, “A Fuzzy Approach to the Measurement of Poverty”, in C. Dagum & M. Zenga (eds.) Income and Wealth Distribution, Inequality and Poverty, Studies in Contemporary Economics, Springer Verlag, Berlin, pp. 272-284.

References

1. Chakravarty, S., 1983, “A New Index of Poverty,” Mathematical Social Sciences, 6(3): 307-313.

References

1. Chakravarty, S. R. and J. Silber, forthcoming, “The Axiomatic Approach to Multidimensional Poverty Measurement,” in N. Kakwani and J. Silber,

References

1. Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Chakravarty, S. R., Deutsch, J. and J. Silber, “On The Watts Multidimensional Poverty Index,” paper presented at the International Conference on The Many Dimensions of Poverty, International Poverty Centre, Brasilia, August 2005.

References

1. Chakravarty, S. R., Mukherjee, D. and R. R. Ranade, 1998, “On the Family of Subgroup and Factor Decomposable Measures of Multidimensional Poverty,” in D. J. Slottje, editor, Research on Economic Inequality, vol. 8, JAI Press, Stamford, Connecticut and London.

References

1. Chambers, R., forthcoming, “Participation, Pluralism and Perceptions of Poverty,” in N. Kakwani and J. Silber, The Many Dimensions of Poverty, London, Palgrave-Macmillan.

References

1. Cheli, B., Ghellini A., Lemmi A, and Pannuzi N., 1994, “Measuring Poverty in the Countries in Transition via TFR Method: The Case of Poland In 1990- 1991”, Statistics in Transition, Vol.1, No.5, pp. 585-636.

References

1. Cheli, B. and Lemmi A., 1995, "Totally" Fuzzy and Relative Approach to the Multidimensional Analysis of Poverty”, Economics Notes by Monte dei Paschi di Siena, Vol. 24 No 1, pp. 115-134

References

1. Clark, S., R. Hemming and D. Ulph, 1981, “On Indices for the Measurement of Poverty,” The Economic Journal, 91: 515-526.

References

1. Clark, D. A. and Qizilbash, M. (2005), ‘Core Poverty, Basic Capabilities and Vagueness: An Application to the South African Context’, GPRG Working Paper, Universities of Manchester and Oxford, UK, forthcoming. Available online at http://www.gprg.org/pubs/workingpapers/default.htm

References

1. Cowell, F. and M. Mercader-Prats, 1999, “Equivalence Scales and Inequality,” in J. Silber, editor, Handbook on Income Inequality Measurement, Kluwer Academic Publishers, Dordrecht and Boston.

References

1. Cutler, D. and L. Katz, 1992, "Rising Inequality: Changes in the Distribution of Income and Consumption in the 1980s," American Economic Review, Papers and Proceedings 82: 546-551.

References

1. Danziger, S. and M. K. Taussig, 1979, “The Income Unit and the Anatomy of Income Distribution,” The Review of Income and Wealth, 25(4): 365-375.

References

1. Deutsch, J., X. Ramos and J. Silber, 2003, “Poverty and Inequality of Standard of Living and Quality of Life in Great Britain," Advances in Quality-of-Life Theory and Research, J. Sirgy, D. Rahtz and A.C. Samli, editors, Kluwer Academic Publishers, Dordrecht, The Netherlands.

References

1. Deutsch, J. and J. Silber, 2005, “Measuring Multidimensional Poverty: An Empirical Comparison of Various Approaches,” Review of Income and Wealth, 2005, 51(1): 145-174.

References

1. Deutsch, J. and J. Silber, 2006, “The Fuzzy Set Approach to Multidimensional Poverty Analysis: Using the Shapley Decomposition to Analyze the Determinants of Poverty in Israel,” in A. Lemmi and G. Betti Editors,

References

1. Fuzzy Set Approach to Multidimensional Poverty Measurement, Springer, pages 155-174.

References

1. Deutsch, J. and J. Silber, forthcoming, “The Order of Acquisition of Durable Goods and the Measurement of Multidimensional Poverty,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Deutsch, J., O. Israeli and J. Silber, 2007, Multi-dimensional Approaches to the Measurement of Poverty: A Study Based on the Last Israeli Census, Israel’s Central Bureau of Statistics.

References

1. Dickes P., 1983, “Modèle de Rasch pour items dichotomiques: Théorie, Technique et application à la mesure de la pauvreté“, Université de Nancy II.

References

1. Dickes P., 1989, “Pauvreté et Conditions d'Existence. Théories, modèles et mesures“, Document PSELL n°8, Walferdange, CEPS/INSTEAD

References

1. Duclos, J.-Y. and P. Makdissi, 2005, “Sequential stochastic dominance and the robustness of poverty orderings”, Review of Income and Wealth 51, p.63- 88.

References

1. Duclos, J.-Y., D. Sahn and S. D. Younger, forthcoming, “Using an Ordinal Approach to Multidimensional Poverty Analysis,” ,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Edgeworth, F. Y., 1897, “La teoria pura del monopolio,“ Giornali degli economisti 2, 13-31, 307-320 and 405-414. Partial translation “The pure theory of monopoly” in Papers Relating to Political Economy (3 vols), 1925, by F. Y. Edgeworth, Macmillan, London. Reprinted in The Foundations of Price Theory (6 vols), 2001, by Pascal Bridel, Ed. Pickering and Chatto, London.

References

1. Engel, E., 1857, “Die Production und consumtionsverhältnisse des Königreichs Sachsen,” in Ernst Engel, Die lebenkosten belgischer arbeiter-familien, Dresden, 1895, C. Heinrich.

References

1. Engel, E., 1895, Die lebenkosten belgischer arbeiter-familien, Dresden, C. Heinrich.

References

1. Ferro Luzzi, G., Y. Flückiger and S. Weber, forthcoming, ”Multidimensional Poverty. Factor and Cluster Analysis,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Fields, G., 2001, Distribution and Development: A New Look at the Developing World, Russell Sage Foundation and MIT Press.

References

1. Foster, J., Greer J. and Thorbecke E., 1984, “A Class of Decomposable Poverty Measures”, Econometrica, Vol. 52 No. 3, pp. 761- 765.

References

1. Fuchs, V., 1967, “Redefining Poverty and Redistributing Income,” The Public Interest, 8: 88-95.

References

1. Fusco, A. and P. Dickes, forthcoming, “The Rasch Model and Multidimensional Poverty Measurement,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Gailly B. and Hausman P., 1984, 'Des Désavantages Relatifs à une Mesure Objective de la Pauvreté', in Sarpellon G. (ed.), Understanding poverty, Franco Angeli Editore, pp. 192-216.

References

1. Goedhart, T., Halberstadt, V., Kapteyn A. and B. M. S. Van Praag, 1977, “The Poverty Line: Concept and Measurement,” The Journal of Human Resources, number 12.

References

1. Hagenaars, A.J.M., 1986, The Perception of Poverty, North-Holland, Amsterdam.

References

1. Halleröd, B., 1994, “A new approach to the direct consensual measurement of poverty,” Social Policy Research Centre Discussion Paper No. 50, University of New South Wales, Sydney.

References

1. Hicks, J. and R. Allen, 1934, “A Reconsideration of the Theory of Value, Parts I and II, Economica, N. S. 1, 52-76 and 196-219.

References

1. Hulme, D. and A. McKay, forthcoming, “Identifying and Measuring Chronic Poverty: Beyond Monetary Measures?,” in N. Kakwani and J. Silber, The Many Dimensions of Poverty, Palgrave-Macmillan, London.

References

1. Hulme, D. and Shepherd, A., 2003, “Conceptualizing chronic poverty”, World Development, 31(3), 403-424.

References

1. Jöreskog, K. and A. Goldberger, 1975, “Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable”, Journal of the American Statistical Association, Vol. 70, No. 351.

References

1. Kakwani, N., 1980, “On a Class of Poverty Measures”, Econometrica Vol. 48, No. 2, pp. 437-446.

References

1. Kakwani, N. and J. Silber, forthcoming 1, The Many Dimensions of Poverty, London, Palgrave-Macmillan.

References

1. Kakwani, N. and J. Silber, forthcoming 2, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Klasen, S., 2000, “Measuring poverty and deprivation in South Africa,” Review of Income and Wealth, 46: 33-58.

References

1. Krishnakumar, J., forthcoming, “Multidimensional Measures of Poverty and Well-Being Based on Latent Variable Models,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Lelli, S., 2001, “Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen's Functioning Approach”, available as http://www.econ.kuleuven.ac.be/ew/academic/econover/Papers/DPS0121.pdf

References

1. Lenfant, J.-S., 2005, “Complementarity and Demand Theory. (From the Twenties to the Forties),” mimeo, Paris.

References

1. London, A. S., Schwartz, S. and E. K. Scott, 2004, “Models of Integration: The Promises and Pitfalls of Combining Quantitative and Qualitative Research,” Paper presented at the conference Q-Squared in Practice: Experiences of Combining Qualitative and Quantitative Methods in Poverty Appraisal, University of Toronto, May 15-16.

References

1. Lovell, C.A.K, S. Richardson, P. Travers and L. Wood (1994) “Resources and functionings: A new view of inequality in Australia”, in Models and Measurement of Welfare and Inequality (ed. W. Eichhorn), Springer-Verlag, Heidelberg.

References

1. Maasoumi, E., 1986, “The measurement and decomposition of multidimensional inequality”, Econometrica, 54: 991-97.

References

1. Maasoumi, E. and M. A. Lugo, forthcoming, “The Information Theory Approach,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Mack, J. and S. Lansley, 1985, Poor Britain, George Allen and Unwin, London.

References

1. Martinez, R. and J. Ruiz-Huerta, 2000, “Income, multiple deprivation and poverty : an empirical analysis using Spanish data, “ paper presented at the 26th General Conference of the International Association for Research in Income and Wealth (IARIW), Cracow.

References

1. Miceli, D., 1997, Mesure de la pauvreté. Théorie et Application à la Suisse. Thèse de doctorat ès sciences économiques et sociale, Université de Genève.

References

1. Narayan, D., R. Chambers et al., 2000a, Voices of the Poor. Crying Out for Change. New York. The World Bank and Oxford University Press.

References

1. Narayan, D., R. Patel et al., 2000b, Voices of the Poor. Can Anyone Hear Us?, New York. The World Bank and Oxford University Press.

References

1. Nolan, B. and C. T. Whelan, 1991, “Resources, deprivation and the measurement of poverty,” The Economic and Social Research Institute Working Paper No. 21, Dublin.

References

1. Nussbaum, M. C. and A. Sen, editors, The Quality of Life, Clarendon Press, Oxford, 1993.

References

1. Nussbaum, M., 2006, Frontiers of Justice. Disability, Nationality, Species Membership, Harvard University Press.

References

1. Orshansky, M., 1965, "Counting the Poor: Another Look at the Poverty Profile," Social Security Bulletin, 28(1): 3-29.

References

1. Palomar Lever, J., forthcoming, “The Subjective Dimension of Poverty. A Psychological Viewpoint,“ in N. Kakwani and J. Silber, The Many Dimensions of Poverty, London, Palgrave-Macmillan.

References

1. Pareto, V., 1909, Manuel d´économie politique, V. Giard and E. Brière, Paris.

References

1. Paroush, J., 1963, "The order of Acquisition of Durable Goods," Bank of Israel Survey (in Hebrew), September, (no.20): 47-61.

References

1. Paroush, J., 1965, "the Order of Acquisition of Consumer Durables," Econometrica 33(1): 225-235.

References

1. Paroush, J., 1973, "Efficient Purchasing Behavior and Order Relations in Consumption," Kyklos XXVI (1): 91—112.

References

1. Pérez-Mayo, J., 2004, “Consistent Poverty Dynamics in Spain,” IRISS Working Paper Series N0. 2004-09, Differdange, Luxembourg.

References

1. Pérez-Mayo, J., 2005, “Identifying Deprivation in Spain: A New Approach,” Applied Economics, 37: 843-955.

References

1. Prais, S. J. and H. S. Houthakker, 1955, The Analysis of Family Budgets, Cambridge University Press, Cambridge.

References

1. Rasch G., 1960, Probabilistic models for some intelligence and attainment tests, Copenhagen, Nielsen and Lydiche.

References

1. Ramos, X. and J. Silber, 2005, “On the Application of Efficiency Analysis to the Study of the Dimensions of Human Development,” Review of Income and Wealth, 51(2): 285-309.

References

1. Ringen, S., 1988, “Direct and indirect measures of poverty,” Journal of Social Policy, 17: 351-365.

References

1. Robb, C., 2002, “Can the Poor Influence Policy? Participatory Poverty Assessments in the Developing World,” The World Bank and International Monetary Fund, Washington DC.

References

1. Rothbarth, E., 1943, “Note on a Method of Determining Equivalent Income for Families of Different Composition,” in C. Magdge, editor, War-Time Pattern of Saving and Expenditure, Cambridge University Press, Cambridge.

References

1. Rowntree, S., 1901, Poverty. A Study of Town Life, London, Mac Millan.

References

1. Schokkaert, E. and L. Van Ootegem, 1990, “Sen’s concept of the living standard applied to the Belgian unemployed,” Recherches Economiques de Louvain, 56: 429-450.

References

1. Schultz, H., 1935, “Interrelations of Demand, Price and Income,” Journal of Political Economy 43, 433-81.

References

1. Sen, A.K., 1976, “Poverty: An Ordinal Approach to Measurement”, Econometrica, Vol. 44, No. 2, pp.219-231.

References

1. Sen, A., 1981, Poverty and Famines. An Essay on Entitlement and Deprivation, Oxford, Oxford University Press.

References

1. Sen, A., 1993, “Capability and Well-Being,” in The Quality of Life, M. Nussbaum and A. Sen, editors, Oxford, Clarendon Press.

References

1. Sen, A., 1999a, Commodities and Capabilities, Oxford University Press, Oxford India Paperbacks.

References

1. Sen, A., 1999b, Development as Freedom, Oxford, Oxford University Press.

References

1. Shannon, C. E., 1948, “The Mathematical Theory of Communication,” Bell System Tech Journal, 27: 379-423 and 623-656.

References

1. Silber, J., 1983, "E.L.L. (The Equivalent Length of Life) or Another Attempt of Measuring Development," World Development, 11(1):21-29.

References

1. Silber, J., 1999, Handbook on Income Inequality Measurement, Kluwer Academic Publishers, Dordrecht and Boston.

References

1. Silber, J. and M. Sorin, 2006, “Poverty in Israel: Taking a Multidimensional Approach,” Chapter 9 in Petmesidou M. & Papatheodorou C, eds: Poverty and Social Deprivation in the Mediterranean Area: Trends, Policies and Welfare Prospects in the New Millennium. London: Zed Books / CROP Series.

References

1. Streeten, P., 1979, “Indicators of development: The search for a basic needs yardstick,” World Development, 6: 567-580.

References

1. Takayama, N., 1979, “Poverty, Income Inequality and Their Measures: Professor Sen’s Axiomatic Approach Reconsidered,” Econometrica, 47(3): 747-759.

References

1. Theil, H., 1967, Economics and Information Theory, North Holland, Amsterdam.

References

1. Thon, D., 1979, “On Measuring Poverty,” Review of Income and Wealth, 25(4):429-439.

References

1. De Tocqueville, A., 1997, Memoir on Pauperism, translated by S. Drescher, Civitas, London.

References

1. Townsend, P., 1979, Poverty in the United Kingdom, Harmondsworth, Penguin.

References

1. Van Praag, B. M. S. and N. L. Van der Sar, 1988, “Household Cost Functions and Equivalence Scales,” Review of Income and Wealth, Number 28.

References

1. Van Praag, B.M.S., Th. Goedhart, and A. Kapteyn, 1980. “The Poverty Line - A Pilot Survey in Europe,” The Review of Economics and Statistics, 62(3): 461-465.

References

1. Van Praag, B.M.S. and A. Ferrer-i-Carbonell, 2004. Happiness Quantified: A Satisfaction Calculus approach. Oxford University Press, Oxford: UK.

References

1. Van Praag, B. M. S. and A. Ferrer-i-Carbonell, forthcoming, “The Subjective Approach to Multidimensional Poverty Measurement,” ,” in N. Kakwani and J. Silber, Quantitative Approaches to Multidimensional Poverty Measurement, London, Palgrave-Macmillan.

References

1. Vero, J., Werquin P., 1997, “Reexamining the Measurement of Poverty: How Do Young People in the Stage of Being Integrated in the Labor Force Manage”, Economie et Statistique, No. 8-10, pp. 143-156 (in French).

References

1. Watts, H. W., 1967, “The Iso-Prop Index: An Approach to the Determination of Differential Poverty Income Thresholds,” The Journal of Human Resources, 2:3-18.

References

1. Zadeh, L.A, 1965, “Fuzzy Sets,” Information and Control, No. 8, pp. 338-353.

References

1. Zheng, B., 1997, “Aggregate Poverty Measures”, Journal of Economic Surveys Vol.11, No 2. 1997, pp. 123-162.