1. Partnership for Child Development Imperial College London
Multidimensional poverty measurement
Elisabetta Aurino
Partnership for Child Development
Imperial College London
& University of Oxford

2. Recalling unidimensional approach?
Limits – spell out

3. Problems with unidimensional approach
Appropriateness of utility as the measure for welfare
Interpersonal heterogeneity
Assumptions of perfect markets, no increasing returns, and no externalities
Targeting and means testing: information distortion; incentive distortion; disutility and social stigma; administrative costs and corruption; political sustainability
Joint-distribution of deprivations

4. How about another approach?
Alternatively approaches propose to measure well-being directly by observing outcomes
Sen: poverty as the inability of individuals to achieve a minimum level in a set of outcomes
(such as the inability to be healthy, well-fed, clothed, sheltered...).
Hence, Sen’s approach to poverty is inherently multidimensional.
NOTE: not all the multidimensional measures are theoretically linked to Sen’s approach!
This implies a change in the informational basis for assessing poverty
Shift from a resources-centered paradigm to a people-centered one. People become the focus of the process of development, which aims at enlarging people’s choices and not just their income

5. Advantages of the CA for measuring poverty
Focuses directly on achievements:
Personal heterogeneities in their ability to convert resources in well-being levels;
Can capture the impact of public goods on welfare
Aggregation and equivalence scales: by observing capabilities directly, it does not need to make assumptions about adult equivalence and household specific economies of scale.
Revealing joint deprivations for the same person at the same time.
Direct targeting and means testing.

6. Which are the key issues related to this approach?
Choose the space:
Capabilities of functionings?
Which dimensions are important?
Which indicator(s) best measure that dimension?
Set the “poverty line” for each dimension/indicator
Which weights to assign to each of these dimensions?
What about dimensions for which no data are available?
Can we implement a real measure of capabilites and functionings?

7. Note 1: Plural methods essential
The CA is incomplete. It does not provide a definitive list of capabilities which should be relevant for all the people and in all contexts.
Theoretically, there are many degrees of freedom in how to implement the CA (standard of living (resources), functionings, capabilities...)
However, in practice, there are far fewer realistic options, due to theoretical and empirical difficulties.
Magari qua accennare alla disputa teorica tra Sen e Nussbaum sul fatto che esista o meno una lista di CA fondamentali!
Sen: there may be different purposes you can cosnstruct your CA analysis. A single list is not enough for all purposes, plus unchangeable constraint. Need for public debate.
Nussbaum: broad cross-cultural consensus on a list of basic capabilities. The list provides the underpinning of basic political princioples that can be embodied in constitutional guarantees and the basis for determining a decent social minimum for a variety of areas. N’s work is UNIVERSALISTIC!

8. Note 2: Measure reflects context
“What we focus on cannot be independent of what we are doing and why” (Sen 2004, p. 79)
Particular objectives of the exercise:
a. The purpose of the evaluation
b. The region, or sector, or years of interest
c. The methodologies
2. Unchangeable constraints (might include)
a. Data
b. Political powers
c. Time and costs (e.g. of participation)
Questo deriva dal fatto che il CA approach sia open

9. Note 3. functionings or capabilities?
Capability = functionings + freedom
Capability is the freedom to enjoy valuable functionings.
Functionings are valuable activities and states that make up people’s well-being
Most frequently focus on functionings or resources data rather than capabilities.
This might seem disappointing, given the importance given to freedom in the CA!
A key dilemma for the capabilities approach has been how to measure what people could do (their opportunity freedom), as opposed to what they actually do (their achieved functionings).
Capabilities are the alternative combinations of functionings a person is feasibly able to achieve. Formulations of capability have two parts: functionings and opportunity freedom – the substantive freedom to pursue different functioning combinations. Consequently, the capability set outlined by this approach is not merely concerned with achievements; rather, freedom of choice, in and of itself, is of direct importance to a person’s quality of life. For this reason, while the combination of a person’s functionings represents their actual achievements, their capability set represents their opportunity freedom – their freedom to choose between alternative functioning combinations.

10. Minimal capabilities
Sen recognises that in contexts where extreme poverty is prevalent, it is sufficient to measure deprivation in “minimal capabilities” (Sen 1997)
Functionings (and the corresponding basic capabilities) of crucial importance for the life of an individual, (e.g. the ability to be well-nourished and well-sheltered, the capability of escaping avoidable morbidity and premature mortality, and so forth)

11. Functionings and Indicators
Which are direct indicators of functionings?
A. Asset index
B. Subjective well-being/Happiness
C. Body mass index
D. Literacy
E. Years of schooling
F. Self-reported health
G. Income of Euro per month.
H. To be safe from violence.

12. From Concept to Implementation:
The introduction of a multidimensional framework leads to additional theoretical and empirical difficulties in the measurement of poverty. Every choice in the context of multidimensional poverty analysis implies a specific value judgement, which have to be clearly specified. Moreover, those choices should be based on PUBLIC DISCUSSION about the nature, the relative merits and the importance of various capabilities, together with a debate on more technical issues, such as the weighting scheme.

13. Steps for constructing MD Poverty Measures
Choice of Unit of Analysis
Choice of the Dimensions
Choice of the Variables/Indicators
Choice of Normalisation
Choice of Poverty Cutoffs for each indicator/dimension
If relevant, Aggregation within dimensions.
Choice of Weights within and across dimensions.
Identification (Who is poor)
Aggregation (How much poverty does a society have)

14. 1. Choice of the Unit of Analysis
Individuals
Households
Choice depends upon purpose and data.

15. 2. Choice of Dimensions (theory)
It’s a value judgement!
Sen (2004), 2 criteria:
Value and priority (for relevant group(s)):
basic importance.
ii) Appropriateness for institutional response: social influenciability.

16. 2. Choice of dimensions (in practice)
Existing data or convention.
Theory: implicit assumptions on what people do value or should value (e.g. Nussbaum’s list).
Public ‘consensus’: a list that has achieved a degree of legitimacy due to public consensus (e.g. universal human rights; MDGs).
Ongoing deliberative participatory process: a process that periodically elicit the values and perspectives of stakeholders
Empirical evidence regarding people’s values: empirical data on values, or on consumer’s preferences and behaviour.

17. 2. Choice of dimensions (in practice) (2)
REMEMBER: Try always to justify why and the methodology according to which you chose a particular set of dimensions, in order to favour open discussion and debate. Mention the other dimensions that you wanted to include, but you couldn’t for lack of data.
Questo si lega con il fatto che CA e’ un approccio incompleto.

18. Can you think about some possible dimensions?

19. Often Observed Dimensions
An interesting result is that lists of dimensions developed by researchers of different backgrounds are surprisingly similar.
Life, Health, Reproduction.
Security.
Work and Leisure.
Education, Knowledge, Skills.
Relationships.
Self-direction, Empowerment, Agency.
Political life, Governance.
Inner Peace and Self Expression.
Culture and Spirituality.

20. 3. Choice of Variables/Indicators
Normative Justification
Kind of indicator (functioning/resource/utility)
(input/output/outcome; stock/flow)
Data Availability
Institutional/Historical Considerations
Literature on that indicator/database
Interrelations with other indicators
Accuracy of individual level data for hh or hh level data for individual

21. 4. Normalisation
Transformation of the original variables into commensurable units in order to avoid to sum up “apples and oranges”. Normalisation is required prior to any data aggregation as the indicators in a data set often have different measurement units.

22. 5. Choice of Poverty Cutoffs
For each indicator there is the need to choose a poverty threshold, in order to assess deprivation in that specific indicator. The idea is: “Beneath a certain level of capability, in each area, a person has not been enabled to live in a true human way” (Nussbaum 2000, p. 74).
since the achievements xi are often measured in different measurement units, they need to be transformed or standardised to a common basis before they can be sensibly aggregated.
Per quanto riguarda la scelta normalizzazione ci sono due metodi di normalizzazione (vedi saisana et al.):
Rescaled values (come undp fa per hdi)
Standardizzazione

23. Example of Deprivation cutoffs
Examples: Not deprived (in bold) in dimension x if:
Schooling: how many years of school have you completed?
6 or more (NOT DEPRIVED)
1-5 years
b. Drinking water: What is the main source for drinking?
Piped water
Well/Pump (electric hand)
Rain water
River water
Water collection basin

24. 7. Setting weights Rationale
1. Normative
Importance: absolute importance of a dimension for poverty
Priority: urgency of making progress in a dimension at a given time (e.g. 3-year plan)
2. Statistical
Data driven: (i) frequency-based; (ii) quality of data; (iii) most favourable weights.
Descriptive statistics: (i)principal components analysis; (ii) cluster analysis (latent variable models).
Regression-based
FREQUENCY BASED: the smaller the proportion of individuals with a certain deprivation, the higher should be the weight, on the grounds that a hardship shared by few has more impact than one shared by many (‘mal comune mezzo gaudio’)
Problema fondamentale di statistical weights (Decancq & Lugo 2008, p. 18): “there is no a priori reason to believe that statistical weights are in accord with people’s perceptions about priorities and relative importance of each dimensions”.

25. Weights, where?
Within dimensions (e.g. Asset index in the MPI; education index in HDI).
Between dimensions (e.g. across 3 dimensions of HDI/HPI/MPI).
Among people in the distribution, i.e. to give greater priority to the most disadvantaged (e.g. think at the role of α in FGT).

26. Normative weights: Equal weights
Most common approach (e.g. HDI, HPI).
Underlying hypothesis: dimensions of well-being are perfect substitutes.
‘Agnostic viewpoint’: all the indicators are presumed to be equally important. This, at a first sight, might seem a ‘neutral’ choice of the researcher.
However, as we saw, weights reflect an important aspect of the trade-offs between the dimensions, which, in turn, imply value judgement.
With equal weighting, trade-offs and value judgements are hidden.

27. Weights and Choice of Dimensions
In the capability approach, because capabilities are of intrinsic value, the relative weights on different capabilities or dimensions that are used in society-wide measures are value judgments. Weights can represent (Alkire & Santos 2010): 1) the enduring importance of a capability relative to other capabilities or 2) the priority of expanding one capability relative to others in the next phase. Need for public debate!

28. 8. Aggregation
Aggregation is concerned with summarising all the available information in order to get a synthetic index. There are many ways to aggregate: - means, -statistical-based models, -and poverty indices, such as the Alkire & Foster.

29. Review: Unidimensional Poverty
Variable – income Identification – poverty line Aggregation – Foster, Greer & Thorbecke (1984) E.g. x=(7,3,4,8), poverty line z=5 Deprivation vector g0=(0,1,1,0) Headcount Ratio: P0=μ(g0)=2/4 Normalised gap vector g1=(0, 2/5, 1/5, 0) Poverty Gap: P1= μ(g1)=3/20 Squared gap vector g2=(0, 4/25, 1/25, 0) FGT measure: P2= μ(g2)=5/100

30. Multidimensional data
DOMAINS j=1, …d
Achievement of person i for dimension j
INDIVIDUALS i=1, …n
CUTOFFS VECTOR

31. Multidimensional data: example
Matrix of well-being scores for n persons in d domains.
DOMAINS j
Income Health Edu Nutri
CUTOFFS

32. The Alkire & Foster (2010) Multidimensional Poverty Measure

33. Some preliminary tools…
In order to understand how the AF works, we need to understand some basic building blocks of the methodology, that will be useful to calculate our poverty measures.

34. 1. From the original matrix to the deprivation matrix
Replace entries: 1 if deprived, 0 if not deprived.
These entries fall below cutoffs.

35. Identification in multidimensional settings
Unidimensional poverty: y <= z
MD poverty:
Set z for each dimensions, AND
Decide the number of dimensions needed in order to identify somebody as poor.
If a person meets a given identification criterion, then the person is considered to be ‘poor’.
Def.: Deprivation: we use this term to indicate that a person’s achievement in a given dimension falls below the poverty line for that specific dimension (=cutoff).

36. Identification – Counting Deprivations
DOMAINS
PERSONS
Question: who is poor?
It depends on how we set the identification criterion, i.e. on how many dimensions we require a person is deprived at the same time in order to be considered poor.

37. 3 approaches to Identification
Union approach: the person must be deprived in AT LEAST ONE DIMENSION (e.g. Tsui 2002; Bourguignon & Chakravarty 2003).
Intersection approach: in order to be considered poor, the person must be deprived in ALL DIMENSIONS.
Counting Approach (Alkire & Foster 2007)
DUAL CUTOFF: gives priority to those people who are deprived in several (but not necessarily all!) dimensions. It sets a number of deprivations (or, if the dimensions are not equally weighted, the weighted sum of the dimensions) for which a person is considered being poor.

38. Identification – Union approach
Q/ Who is poor?
A1/ poor if deprived in any dimension|ci ≥ 1 ci
DOMAINS
q=3
Union approach often predicts high numbers.

39. Identification – Intersection approach
Q/ Who is poor?
A2/ poor if deprived in all dimensions|ci =d ci
DOMAINS
q=1
Demanding requirement (especially if d is large).
Often identifies a very narrow slice of population.

40. Identification – Counting approach
Q/ Who is poor?
A3/ Fix cutoff k  d; then identify as poor if ci ≥k
(E.g. k=2) ci
DOMAINS
q=2
NOTE: Includes both union (k=1) and intersection (k=d) approaches.
Developed by Alkire & Foster (2007).

41. Identification – The problem empirically (Alkire & Seth 2008)
Poverty in India for 10 dimensions:
91 % of population would be targeted using union,
0% using intersection.
Need something in the middle!
Note: as k rises, the focus shifts to the poorest of the poor (acute deprivation). k=
1 Union H
91.2% 2 3
75.5 %
54.4 % 4 5
33.3 %
16.5 % 6 7
6.3 %
1.5 % 8 9
0.2 %
0.0 %
10 Intersection

42. The role of k
k is a policy variable that governs the range of simultaneous deprivations each poor household necessarily must have in order to be considered poor.
As k goes up,the number of households who will be considered poor goes down,
but the intensity or breadth of deprivations in any poor household goes up.
The problem is how to set k.

43. 9. Aggregation
In the past years, boom of the literature on aggregation methods for MD measures of poverty.
Why? Recognition of the multidimensionality of well-being and poverty + increase availability of data.
Different approaches:
Axiomatic: Chakravarty et al. (1998); Tsui (2002); Bourguignon & Chakravarty (2003); Alkire & Foster (2007; 2009).
Non Axiomatic: Information Theory; fuzzy set; counting, etc...

44. 9. Aggregation (ctd.)
We will examine more deeply Alkire & Foster (2007, 2009).
Theoretical approach: Capability Approach;
Extension to the multidimensional case of the FGT family of poverty measures;
Easy to understand;
The method was used to construct UNDP’s Multidimensional Poverty Index (Alkire & Santos 2010), that we will analyse later.

45. Aggregation: Alkire & Foster 2007
Once you set k, the first thing to do is to censor data of nonpoor (e.g. k=2).
DOMAINS
c(k)
PERSONS
Similarly per g1(k) etc...
This is an implication of the FOCUS axiom: we are not interested to what happens to the non-poor.

46. a. Headcount Ratio H = q/n [k=2] Two poor persons out of four: H=1/2
DOMAINS
c(k)
PERSONS
H = q/n
Two poor persons out of four: H=1/2

47. Critique to the Headcount Ratio
Suppose the number of deprivation rises for person 2:
DOMAINS
c(k)
PERSONS
The number of the poor remains the same: H=1/2.
It does not take into account the depth of poverty in that dimension (violates dimensional monotonicity).

48. Average deprivation share among poor
As we know, the Headcount Ratio is a very crude measure of poverty. It is insensitive to both monotonicity and transfer.
We need to broaden our informational basis, by including more information on the share of deprivation among the poor.
A =c(k)/qd
A includes additional information on the breadth of deprivations experienced by the poor.
This partial index conveys relevant information about MD poverty, namely, the fraction of possible dimensions d experienced by a poor person i.

49. Aggregation – Including the share of deprivations among poor
Deprivation shares among poor
c(k)
c(k)/d
DOMAINS
PERSONS
A = average deprivation share among poor:
A= (2/4 + 4/4)/2 = 3/4

50. b. Adjusted Headcount Ratio (1)
Adjusted Headcount Ratio: M0=HA=μ(g0(k))
c(k)
c(k)/d
DOMAINS
M0=HA= (2/4)*(3/4) = 6/16 =

51. b. Adjusted Headcount Ratio (2)
Adjusted Headcount Ratio = M0=HA=μ(g0(k))
M0 is a MD poverty measure which combines information on:
The prevalence of poverty (H)
The average breadth of deprivations poor people suffer (A).
The equivalent definition M0=μ(g0(k)) interprets M0 as the total number of deprivations experienced by the poor, c(k)=|g0(k)|, divided by the maximum number of deprivations that could possibly experienced by all people, nd.

52. b. Adjusted Headcount Ratio (3)
As a simple product of the two partial indices H and A, M0 is sensitive to the frequency (H) and the breadth (A) of MD poverty.
It is similar to the FGT measure for the poverty gap P1=HI; here M0=HA.
Easy to calculate and to interpret.
UNDP’s MPI is a form of M0.
In particular, M0 satisfies dimensional monotonicity, as we will see from the following example.

53. M0 is sensitive to the breadth of deprivation
Suppose the number of deprivation rises for person 2:
DOMAINS
c(k)
c(k)/d
M0=HA= (2/4)*(7/8) = 7/16 =
M0 is increased for the additional deprivation of person 2. It hence satisfies dimensional monotonicity.

54. b. Adjusted Headcount Ratio (4)
However, it does not provide any information regarding the depth of deprivation in one dimension. In other words, M0 doesn’t satisfy the traditional monotonicity requirement, according to which poverty should increase as a poor person becomes more deprived in any given dimension. Consequently we will need another measure, that we can develop for cardinal data only.

55. identify the set of poor people.
To Sum Up...
Matrix of information: n people and d dimensions. Who is MD poor?
a. Identification:
z vector (dx1) of poverty cutoffs  dimension d
identification criterion (union, intersection, dual cutoff approach) Define k of interest.
identify the set of poor people.

56. Summarise all the available information in only one number.
b. Aggregation – Alkire & Foster (2007, 2009)
Summarise all the available information in only one number.
How?
1. Censor data of non poor  g0(k)
2. Headcount Ratio
H=q/n
problem: no breadth and depth of poverty.
Define A= c(k)/qd, average deprivations share across the poor.

57. 3. Adjusted Headcount Ratio
M0=HA=μ(g0(k))
Satisfies dimensional monotonicity (breadth of poverty).
Problem: no info on the depth of poverty (monotonicity within dimensions).
Define G= |g1|/| g0|, average poverty gap across all instances in which poor persons are deprived.

58. Define: S=|g2(k)|/|g0(k)|Average severity of deprivations
4. Adjusted Poverty Gap
M1=HAG=μ(g1(k))
Combines information on the prevalence of poverty, the average range of deprivation and the average depth across deprived dimensions.
Problem: it does not take into account whether the increase in deprivation occurs for a person who is slightly or acutely deprived.
Define: S=|g2(k)|/|g0(k)|Average severity of deprivations

59. 5. Adjusted FGT Measure M2 = HAS = μ(g2(k)) Sensitive to inequalities in the distribution of deprivations among the poor. We can generalise these results to a class of MD poverty measures: 6. Adjusted FGT class Mα= μ(gα(k)) for α ≥ 0.

60. UNDP’s Multidimensional Poverty Index

61. The MPI and the HPI
In November 2010, UNDP has launched the new ‘Multidimensional Poverty Index (MPI)’, that has substituted the Human Poverty Index in the global estimates of multidimensional poverty.
The MPI was developed by Alkire & Santos (2010), by adopting the Alkire&Foster methodology to measure multidimensional poverty.

62. The MPI (Alkire & Santos 2010)
Developed by following Alkire & Foster (2007,2009).
Captures the number of households which experience multiple deprivations at the same time (acute poverty)  Micro analysis now!
Portrays the composition of poverty for those households, i.e. in which dimensions or indicators they are deprived.
It is also decomposable by geographic location (in order to show variation in poverty within countries) and subgroups of population.

63. Our steps and the MPI Choice of Unit of Analysis
Choice of the Dimensions
Choice of the Variables/Indicators
Choice of Normalisation
Choice of Poverty Cutoffs for each indicator/dimension
If relevant, Aggregation within dimensions.
Choice of Weights within and across dimensions.
Identification (Who is poor)
Aggregation (How much poverty does a society have)

64. Weights Dimensions 1/3 Weights Indicators 1.67 0.55
Electricity and floor non sono MDGs! We are aware that all the living standard indicators are means rather than
ends; they are not direct measures of funtionings.

65. Source: Alkire & Santos (2010)

66. Choice of weights and poverty cutoff k
There are 10 indicators. Equal weights between and within indicators. Alkire & Santos (2010) computed the MPI for two values of k: k=2, k=3. Here we will consider k=3, that means that a household is to be considered poor if the weighted sum of its deprivations exceeds 3. Let’s do an example in order to understand how the index works in practice.

67. Example of Identification: Tabitha
Source: Alkire & Santos (2010)

68. Why is it important to decompose?
Alkire & Santos (2010)

69. Problems with the MPI?
From the CA perspective, problems with some of the indicators chosen. Are the means confused with the ends?
Loss of information due to composite indicators.
Data comparability and update issues.

70. Further references
Alkire, S. & Seth, K. (2008). Measuring Multidimensional Poverty in India. A New Proposal. OPHI WP 15.
Alkire, S. and Santos, M.E Acute Multidimensional Poverty: A New Index for Developing Countries. OPHI Working Paper 38.
Bourguignon, F., & Chakravarty, S. R. (2003). The Measurement of Multidimensional Poverty. Journal of Economic Inequality. 1(1), pp
Deutsch, J., & Silber, J. (2005). Measuring Multidimensional Poverty. An Empirical Comparison of Various Approaches. The Review of Income and Wealth 51, pp

71. References
Ravallion, M. (1992). Poverty Comparisons. A Guide to Concepts and Methods. Living Standards Measurement Study Working Paper No. 98.
Rawls, J. (1971). A Theory of Justice. Cambridge, Massachusetts: Belknap Press of Harvard University Press.
Ruggeri Laderchi, C. (2008). Do Concepts Matter? An Empirical Investigation of the Differences Between a Capability and a Monetary Assessment of Poverty. In Comim,F., Qizilbash,M., & Alkire,S. (eds). The Capability Approach. Concepts, Measures and Applications. Cambridge: Cambridge University Press.
Sen, A. (1999). Development as Freedom. Oxford: Oxford University Press.
Sen, A.K. (1987). The Standard of Living: Lecture II, Lives and Capabilities. In G. Hawthorn (ed.). The Standard of Living: The Tanner lectures on Human Values. Cambridge: Cambridge University Press
Sen, A. K. (1976). Poverty: An Ordinal Approach to Measurement. Econometrica, 44(2), pp
World Bank. (1990), World Development Report: Poverty, Oxford University Press for the World Bank.
Rowntree, S. (1901). Poverty. A Study of Town Life. MacMillan.

72. Thanks!