Understanding Multidimensional Measures of Living Conditions

1. ON MULTIDIMENSIONAL MEASURES OF LIVING CONDITIONSLecture to be given at the S.A.M.P.L.E. CONFERENCESiena, October 6 2010 Jacques Silber Department of Economics Bar-Ilan University – Israel

2. Let me start this talk with a few citations taken from Voices of the Poor: Can Anyone Hear Us?, a book published by the World bank 10 years ago, where poor people around the world were asked to define what poverty for them means: • “It’s the cost of living, low salaries, and lack of jobs. And it’s also not having medicine, food and clothes” (Brazil, 1995) • “Being poor is being always tired” (Kenya, 1996) • “Poverty is lack of freedom, enslaved by crushing daily burden, by depression and fear of what the future will bring” (Georgia, 1997). • “Poverty means working for more than 18 hours a day, but still not earning enough to feed myself, my husband, and two children” (Cambodia, 1998)

3. From this same book, here is a summary of poverty indicators as described by the Poor in Vietnam (1999): Poor households: • Live in unstable houses, often made with mud • Have no television or radio • Are not able to save money • May have children who cannot go to school, or who have to leave school prematurely • Usually have enough food until the next harvest, although sometimes lack food for one or two months per year • Are unable to utilize surrounding natural resources to their benefit Very Poor Households: • Live in very unstable houses that often need to be rebuilt every two to three years • Have no wells or easy access to fresh water

4. A few weeks ago, Duncan Green, Head of Research for Oxfam, seemed to agree with these features of poverty when he wrote in his blog “Ask poor people what poverty is like, and they typically talk about fear, humiliation and ill health, at least as much as money.” He then added “But can the non-income dimensions of poverty be measured in a way that allows policy makers to weigh priorities and allocate resources?” These sentences were written, following a recent debate between Martin Ravallion, Director of the World Bank Research Department, and Sabina Alkire, Director of OPHI, the Oxford Poverty and Human Development Initiative, who were arguing about a new multidimensional measure of poverty (MPI) recently proposed by Alkire and Foster, and about which I will talk later on.

5. Although both Alkire and Ravallion agree with the fact that poverty is not only a matter of limited resources but that it affects in fact all aspects of life, the health of an individual (“malaria”), her education, etc..., Ravallion does not believe in attempts to build a Multidimensional Poverty Index. His position is that “Everyone agrees that poverty is not just about low consumption of market commodities by a household.  There are also important non-market goods, such as access to public services, and there are issues of distribution within the household. It is agreed that consumption or income poverty measures need to be supplemented by other measures to get a complete picture. But does that mean we should add up the multiple dimensions of poverty into a single composite index? Or should we instead measure consumption poverty with the best data available, while also looking for the best data on other dimensions of poverty as appropriate to the country context?”

6. Even if one does not agree with Ravallion and decides to take a multidimensional approach to poverty measurement, another issue arises, that of making a distinction between the concept of poverty and that of social exclusion. One may want to use the term “multidimensional poverty” to refer to what the EU called in fact “social exclusion”, a distinction being made here by the EU between primary indicators (which encompass poverty risk, unemployment and joblessness, low educational qualifications, the employment situation of migrants, material deprivation, housing, access to health care and child well-being) and secondary indicators (which comprise a more detailed disaggregation of some of these indicators).

7. I would prefer to reserve the term “social exclusion” to what Sen (2000) called the “relational features in deprivation.“ For Sen “being excluded can sometimes be in itself a deprivation and this can be of intrinsic importance on its own. For example, not being able to relate to others and to take part in the life of the community can directly impoverish a person’s life. It is a loss on its own, in addition to whatever further deprivation it may indirectly generate. This is a case of constitutive relevance of social exclusion. In contrast, there are relational deprivations that are not in themselves terrible, but which can lead to very bad results.

8. For example, not using the credit market need not be seen by all to be intrinsically distasteful. Some do, of course, enjoy borrowing or lending, while others do not feel this to be a matter of inherent importance... But not to have access to the credit market can, through causal linkages, lead to other deprivations, such as income poverty, or the inability to take up interesting opportunities that might have been both fulfilling and enriching but which may require an initial investment and use of credit. Causally significant exclusions of this kind can have great instrumental importance: they may not be impoverishing in themselves, but they can lead to impoverishment of human life through their causal consequences (such as the denial of social and economic opportunities that would be helpful for the persons involved). Landlessness is similarly an instrumental deprivation….".

9. This more sociological approach to poverty was already mentioned in the work of Tocqueville. Alexis de Tocqueville who is known for his famous “Democracy in America” and eventually also for his “The Old Regime and the Revolution” wrote also a monography entitled “Memoir on Pauperism”. I must say that until I looked two or three years ago at a book by the French sociologist Serge Paugam entitled “The Elementary Forms of Poverty” I was totally unaware of Tocqueville´s Memoir. Tocqueville was born in 1805 and died in 1859. 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”.

10. The latter are people who can be clearly distinguished within a population (hence the modern concept of “social exclusion” ). In the first part of his Memoir Tocqueville makes 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”

11. 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 half-uncultivated 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 to me that this distinction between the “poor” and the “indigents” remains a valid one today. The only difference is that today specialists use other words, making a distinction, as I suggested previously, between the “income poor and deprived” and the “socially excluded”.

12. The purpose of my talk is to attempt - to review the main problems that have to be faced when taking a multidimensional approach to the measurement of living conditions - to give a brief survey of the solutions that have hitherto been proposed to solve these problems We will see that several avenues are open to researchers working in this field and I will not attempt to recommend one multidimensional approach over another. Given the limited amount of time I have, I will not talk about the unidimensional approach to poverty and will immediately concentrate my attention on the multidimensional approach to poverty.

13. On the Cardinal Approach to Multidimensional Poverty Measurement In what follows a distinction will be made first between • 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 (2) truly multidimensional approaches where a poverty threshold is determined for each dimension and which lead to the definition of multidimensional indices of poverty. But in the case of (2) two possibilities again arise: • Aggregate first the dimensions and then the individuals • Aggregate first the individuals and then the dimensions The following graph attempts to describe the various ways of deriving a multidimensional poverty index.

15. Before reviewing these approaches I would like to mention additional issues that are somehow specific to the multidimensional case. I) On Some Important Issues in Multidimensional Poverty Analysis: A) The Choice of the Poverty Dimensions: Several questions have to be asked: a) Which DIMENSIONS are relevant? b) Should MORE THAN ONE INDICATORPER DIMENSION be used, and if so which ones? 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?

16. The issue of the interaction between the dimensions or/and between the indicators will be analyzed later on. Just a few words on the selection of dimensions: Sabina Alkire (2007) 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

17. An Illustration: Ramos and Silber (2005) This paper attempted to translate empirically some of the approaches mentioned by Alkire (2002) in her paper on “The Dimensions of Human Development”. One of the approaches she mentioned is that of Allardt whose ideas were presented in his paper on “Having, Loving, Being: An Alternative to the Swedish Model of Welfare Research” (in Nussbaum and Sen, The Quality of Life).

18. Thus, using the British Household Panel Survey, we took into account the following dimensions: A) HAVING: • Economic resources • Housing • Employment • Working Conditions • Health • Education B) LOVING: Satisfaction with social life (family, friends,…) C) BEING: • Self-Determination (ability making decisions,…) • Political Activities • Leisure Time Activities • Opportunities to Enjoy Nature • Meaningful Work (Satisfaction with work,…)

19. Clearly selecting dimensions is not a simple issue and Clark and Qizilbash (2005) have labelled this problem the “horizontal vagueness” of poverty. B) The “Fuzzy Aspect” of Poverty: The problem here is that determining a clear threshold making a difference between those who are poor and those who are not is not an easy task. 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.

20. C) The “Vertical Vagueness” of Poverty: Clark and Qizilbash (2005) have used the expression “vertical vagueness” to emphasize that deciding which individual (household) is poor is not an easy task 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”? We will come back to this issue when discussing the choice between a “union” and an “intersection”.

21. D) The “temporal vagueness” of poverty: Finally Clark and Qizilbash 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

22. 1) On Chronic versus Transitory Poverty: A citation from Hulme and McKay (2007): “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 stressed by these authors a similar distinction was made in eighteenth century France when a distinction 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’ “.

23. Hulme and Shepherd (2003) identify four main ways in which people may experience chronic poverty: • those who experience poverty for a long time (five years, more?). • 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.

24. This is why, following work by Carter and Barrett (2006), these authors recommend using an asset approach to poverty measurement. 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 idea is therefore to make a distinction 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.

25. 2) The concept of “vulnerability”: Calvo and Dercon (2007) 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. There is a nice citation from Voices of the Poor (2000) which can be found also in Calvo (2008): “Security is peace of mind and the possibility to sleep relaxed” (a woman from El Gawaber, Egypt). Calvo and Dercon give the following illustration borrowed from Sen (1981) who 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”.

26. II) The Case where Dimensions are aggregated immediately: Many techniques of aggregation have been proposed. We cannot review all of them (for more details, see, Kakwani and Silber, 2008) but will at least mention some of them. A) Approaches using traditional multivariate analysis: These approaches are generally based on the idea of latent variable. Here we should mention the following techniques: • Principal Components Analysis (PCA) • Factor Analysis (FA) • MIMIC models • Structural Equation models • Cluster Analysis • Multiple Correspondance Analysis (MCA)

27. B) Another approach based on the idea of latent variable: the so-called Rasch model 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 (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.

28. Two points must be stressed (see, Fusco and Dickes, 2008): A same set of items of deprivation belonging to several domains can measure either a single or several latent characteristics. Poverty is considered as unidimensionalif only one continuum of poverty is measured and as multidimensionalif one needs more than one continuum to grasp this phenomenon. Hence we have 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.

29. C) Efficiency Analysis and Multidimensional Poverty: Without entering into technical details we can say that this approach is based on the concept of distance function which is a well-known notion in consumption and production theory. There are thus input and output distance functions. For example, 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.

31. Various techniques may be applied in efficiency analysis to estimate these input and output distance functions: • Data envelopment analysis (DEA) which is, in its simplest form, linear programming. But even then there are various approaches, one of them being called the Lower Convex Hull Approach. - Econometric Approaches: This is, for example, the approach adopted by Lovell et al. (1994) and later on by Deutsch, Ramos and Silber (2003) who, using data from the British Household Panel Survey (BHPS), estimated the percentage of poor in terms of standard of living as well as of quality of life.

32. As an illustration let me quickly report on the interesting work of Anderson et al. (2008) who applied the Lower Convex Hull Approach, to data on life expectancy, literacy rate, school enrolment 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).

33. A distinction is made between • the lower convex hull where the reference household is the worst off • the upper monotone hullwhere the reference is the best off

34. Lower Convex Hull

35. Upper monotone hull

36. The resulting distance measuresreflect the minimum amount one would have to scale each observation so that they shared equal ranking with the best and worst off observations. It appears that agent (2) is the best off. It ties with (1) and (3) when using the upper monotone hull approach as all are potentially the best off under some measure, but it is the agent which has to be deflated most when compared to the worst off (when using the lower convex hull approach). Similarly household (6) is the worst off. It ties with (5) as potentially the worst off (when using the lower convex hull approach) but compared to the best off it has to be scaled up by more than (5).

37. Anderson et al. (2008) applied this approach, using data from the World Bank on the life expectancy, literacy rate, school enrolment and gross domestic product per capita for 170 countries in the years 1997 and 2003. They found that the following countries were members of the Rawlsian Frontier or “Poorest Countries Club”: Bhutan (1997), Central African Republic (2003), Ethiopia (1997), Niger (2003), Niger (1997), Sierra Leone (2003), Sierra Leone (1997) and Zambia (2003)

38. D) 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 xij the value taken by indicator j for individual (or household ) i, with i = 1 to n and j = 1 to m. The various elements xij 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 xc which will be a vector of n components, one for each individual. In other words the vector (xi1,…xim ) corresponding to individual i will be replaced by the scalar xci. (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.

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

40. E) 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 A, B and C. A household can own one two, three or none of these goods. There are therefore 23 = 8 possible profiles of ownership of durable goods in this example. A number 1 will indicate that the household owns the corresponding good, a zero that it does not.

42. If we assumed that every household followed the order A, B, C (that is, that a household first acquires good A, then good B and finally good C) 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 A, B, C. More generally, for a given order of acquisition and k durable goods, there are k+1 possible profiles in the acquisition path. There are always households that slightly deviate from this most common order of acquisition and this possibility will be taken into account.

43. Bérenger, Deutsch and Silber (2009), using data from using data from the Demographic and Health Surveys (DHS) for Egypt, Morocco and Turkey, considered 10 durable goods and access to services: ownership of dwelling, fuel for cooking, car, television, refrigerator, phone, washing machine, video, phone, air conditioning To derive the most common order of acquisition a very high number of computations was required. For each individual i in the sample, we had to determine the minimum distance Siof his profile to each of the possible profiles in a given order of acquisition. With 10 goods, there are 11 such comparisons. The data for Egypt, for example, included 21972 individuals so that 241692 comparisons (21972 times 11) were needed in order to determine the proximity index R for a single order of acquisition.

44. This procedure has to be repeated 10! =3628800 times. This is the total number of possible orders of acquisition resulting from 10 durable goods. As a consequence 241692  3628800 = 8.7711011 was the total number of computations necessary to find the order of acquisition with the highest index of proximity . The determination of a most common order of acquisition of durable goods allowed us to use an ordered logit procedure to better understand the factors affecting this order of acquisition, or more generally the factors having an impact on the standard of living. Here are the results concerning the order of acquisition.

47. On the basis of the logit regression where the dependent variable was the probability to have a given "welfare score“, we concluded that households whose head has a higher educational level have, ceteris paribus, a higher "welfare score". This "welfare score" increases and then decreases with the size of the household. As a whole it also seems to increase with the age of the head of the household and to be higher when the head of the household is married.

48. We now turn to another set of approaches to multidimensional poverty measurement, one where poverty lines are first determined for each poverty dimension. Only afterwards does one attempt to aggregate the information. But even then there are two possibilities: • First aggregating the dimensions and then the individual observations • Or first aggregate the individual observations and then the dimensions.

49. I) The axiomatic approach to multidimensional poverty measurement: We will not review here the axioms that are at the basis of the derivation of these multidimensional poverty indices. We will just give the formulation of the indices and present an illustration. Chakravarty et al., for example, derived then axiomatically a generalization of the FGT index which may be expressed as: P(X;z)=(1/n)j=1 to ki  Sj aj [1-(xij/zj)]

50. In another paper Chakravarty and Silber (2008) derived the following multidimensional generalization of the Watts index: PW(X;z)=(1/n)j=1 to ki  Sj aj log(zj /xij) Then, using the so-called Shapley decomposition, Deutsch, Chakravarty and Silber (2008) have shown that changes over time in this index may be easily decomposed into components reflecting respectively