On the Measurement of Multidimensional Well-Being in Some Countries in Eastern and Southern Africa

Joseph Deutsch; Herman Musahara; Jacques Silber

doi:10.1007/978-3-319-30981-1_9

Poverty and Well-Being in East Africa pp 191-214 | Cite as

On the Measurement of Multidimensional Well-Being in Some Countries in Eastern and Southern Africa

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Joseph Deutsch
Herman Musahara
Jacques SilberEmail author

Chapter

First Online: 01 May 2016

Part of the Economic Studies in Inequality, Social Exclusion and Well-Being book series (EIAP)

Abstract

Using data from the AfroBarometer survey, this chapter derives measures of overall well-being for six Eastern African countries (Burundi, Madagascar, Kenya, Tanzania, Malawi, and Mozambique) for which enough data were available to take a broad enough view of well-being. Correspondence analysis is implemented to aggregate variables in each domain of well-being while overall well-being is derived through efficiency analysis. The chapter compares the findings concerning overall well-being with those based on its narrow view, one whose focus is only on material well-being. It appears that the two main determinants of material well-being are the educational level of the individual and his/her area of residence. For the measure of overall well-being the findings were less clear-cut.

Keywords

Afrobarometer Correspondence analysis Efficiency analysis Shapley decomposition Well-being

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Appendix 1: List of Questions for Each Domain of Well-Being

1.
Material conditions:
- In general, how would you describe your own present living conditions? (possible answers: very good; fairly good; neither good nor bad; fairly bad; very bad)
- In general, how do you rate your living conditions compared to those of other Tanzanians? (possible answers: Much worse; Worse; Same; Better; Much better)
- Looking back, how do you rate your living conditions compared to twelve months ago? (possible answers: Much worse; Worse; Same; Better; Much better)
- Looking ahead, do you expect your living conditions in twelve months’ time to be better or worse? (possible answers: Much worse; Worse; Same; Better; Much better)
- Over the past year, how often, if ever, have you or anyone in your family gone without enough fuel to cook your food? (possible answers: Never; Just once or twice; Several times; Many times; Always)
- Over the past year, how often, if ever, have you or anyone in your family gone without a cash income? (possible answers: Never; Just once or twice; Several times; Many times; Always)
- Do you own a radio? (possible answers: yes; no)
- Do you own a TV? (possible answers: yes; no)
- Do you own a motor vehicle, car, or motorcycle? (possible answers: yes; no)
- How many mobile phones are owned in total by members of your household, including yourself?
- Please tell me whether your main source of water for household use is available
  
  inside your house
  
  inside your compound
  
  outside your compound
- Please tell me whether a toilet or latrine is available
  
  inside your house
  
  inside your compound
  
  outside your compound
- In what type of shelter does the respondent live?
  
  Non-traditional/formal house 1
  
  Traditional house/hut 2
  
  Temporary structure/shack 3
  
  Flat in a block of flats 4
  
  Single room in a larger dwelling structure or backyard 5
  
  Hostel in an industrial compound or farming compound 7
  
  Other
- What was the roof of the respondent’s home or shelter made of?
  
  Metal, tin, or zinc
  
  Tiles
  
  Shingles
  
  Thatch or grass
  
  Plastic sheets
  
  Asbestos
  
  Multiple materials
  
  Some other material
2.
Health
- Over the past year, how often, if ever, have you or anyone in your family gone without enough food to eat? (possible answers: Never; Just once or twice; Several times; Many times; Always).
- Over the past year, how often, if ever, have you or anyone in your family gone without enough clean water for home use? (possible answers: Never; Just once or twice; Several times; Many times; Always).
- Over the past year, how often, if ever, have you or anyone in your family gone without medicines or medical treatment? (possible answers: Never; Just once or twice; Several times; Many times; Always).
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Services are too expensive/unable to pay (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Lack of medicines or other supplies (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Lack of attention or respect from staff? (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Absent doctors? (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Long waiting time? (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Dirty facilities? (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
- Have you encountered the following problem with your local public clinic or hospital during the past 12 months: Long waiting time? (possible answers: No experience with public clinics in last 12 months; Never; Once or Twice; A few times; Often)
3.
Personal Security
- Over the past year, how often, if ever, have you or anyone in your family felt unsafe walking in your neighborhood? (possible answers: Never; Just once or twice; Several times; Many times; Always)
- Over the past year, how often, if ever, have you or anyone in your family feared crime in your own home? (possible answers: Never; Just once or twice; Several times; Many times; Always)
- During the past year, have you or anyone in your family had something stolen from your house? (possible answers: No; once Yes; Yes twice; Yes, three or more times)
- During the past year, have you or anyone in your family been physically attacked? (possible answers: No; once Yes; Yes twice; Yes, three or more times)
- During election campaigns in this country, how much do you personally fear becoming a victim of political intimidation or violence? (possible answers: Not at all; A little bit; Somewhat; A lot)
4.
Access to information
- How often do you get news from the radio? (possible answers: Every day; A few times a week; A few times a month; Less than once a month; Never)
- How often do you get news from the television? (possible answers: Every day; A few times a week; A few times a month; Less than once a month; Never)
- How often do you get news from newspapers? (possible answers: Every day; A few times a week; A few times a month; Less than once a month; Never)
- How often do you get news from the internet? (possible answers: Every day; A few times a week; A few times a month; Less than once a month; Never)
- How often do you use a computer (possible answers: Every day; A few times a week; A few times a month; Less than once a month; Never)
- How often do you use the internet (possible answers: Every day; A few times a week; A few times a month; Less than once a month; Never)
- Do you ever use a mobile phone? If so, who owns the mobile phone that you use most often? (possible answers: No, I never use a mobile phone; Yes, I use a mobile phone that I own; Yes, I use a mobile phone owned by someone else in my household; Yes, I use a mobile phone owned by someone outside my household)
- How often do you normally use a mobile phone to make or receive a call? (possible answers: Never; Less than one time per day; One or two times per day; Three or four times per day; Five or more times per day)
- How often do you normally use a mobile phone to send or receive a text message or SMS? (possible answers: Never; Less than one time per day; One or two times per day; Three or four times per day; Five or more times per day)
- How often do you normally use a mobile phone to send or receive money or pay a bill (possible answers: Never; Less than one time per day; One or two times per day; Three or four times per day; Five or more times per day)
5.
Freedom
- In your country, how free are you to say what you think (possible answers: Not at all free; Not very free; Somewhat free; Completely free)
- In your country, how free are you to join any political organization you want (possible answers: Not at all free; Not very free; Somewhat free; Completely free)
- In your country, how free are you to choose who to vote for without feeling pressured (possible answers: Not at all free; Not very free; Somewhat free; Completely free)
- Overall, how satisfied are you with the way democracy works in your country (possible answers: Very satisfied; Fairly satisfied; Not very satisfied; Not at all satisfied; the country is not a democracy)
6.
Participation in organization
- How related are you to groups such as a religious group that meets outside of regular worship services (possible answers: you are an official leader; an active member; an inactive member; not a member)
- How related are you to some other voluntary association or community group (possible answers: you are an official leader; an active member; an inactive member; not a member)
7.
Corruption
- In the past year, how often, if ever, have you had to pay a bribe, give a gift, or do a favor to government officials in order to get a document or a permit? (possible answers: No experience with this in past year; Never; Once or Twice; A few times; Often)
- In the past year, how often, if ever, have you had to pay a bribe, give a gift, or do a favor to government officials in order to get water or sanitation services? (possible answers: No experience with this in past year; Never; Once or Twice; A few times; Often)
- In the past year, how often, if ever, have you had to pay a bribe, give a gift, or do a favor to government officials in order to get treatment at a local health clinic or hospital? (possible answers: No experience with this in past year; Never; Once or Twice; A few times; Often)
- In the past year, how often, if ever, have you had to pay a bribe, give a gift, or do a favor to government officials in order to avoid a problem with the police, like passing a checkpoint or avoiding a fine or arrest? (possible answers: No experience with this in past year; Never; Once or Twice; A few times; Often)
- In the past year, how often, if ever, have you had to pay a bribe, give a gift, or do a favor to government officials in order to get a place in a primary school, or extra lessons on the side, for a child? (possible answers: No experience with this in past year; Never; Once or Twice; A few times; Often)
- During the last election in 2010, how often, if ever did a candidate or someone from a political party offer you something, like food or a gift or money, in return for your vote? (possible answers: Never; Once or Twice; A few times; Often)
8.
Trust
- How much do you trust your relatives (possible answers: Not at all; Just a little; Somewhat; A lot)
- How much do you trust your neighbors (possible answers: Not at all; Just a little; Somewhat; A lot)
- How much do you trust other people you know (possible answers: Not at all; Just a little; Somewhat; A lot)
9.
Employment
- If you have a job that pays cash income, is it full-time or part-time?

Appendix 2: On Correspondence Analysis

Correspondence analysis (CA) was originally introduced by Benzécri and Benzécri (1980). It is strongly related to the principal components analysis (PCA) but while PCA assumes that the variables are quantitative, CA has been designed to deal with categorical variables. More precisely, CA offers a multidimensional representation of the association between the row and column categories of a two-way contingency table. In short CA’s goal is to find scores for both the row and column categories on a small number of dimensions (axes) that will account for the greatest proportion of the chi² measuring the association between the row and column categories. There is thus a clear parallelism between CA and PCA, the main difference being that PCA⁶ accounts for the maximum variance. A clear presentation of CA is given in Asselin and Vu Tuan Anh (2008: Chap. 5) and in Kakwani and Silber (2008).

Let us first recall the main features of PCA. It is a data reduction technique that consists of building a sequence of orthogonal and normalized linear combinations of the K primary indicators that will exhaust the variability of the set primary indicators. These orthogonal linear combinations are evidently latent variables and are usually called as ‘components’. In PCA the first component has the greatest variance and all subsequent components have decreasing variances.

Let N be the size of the population, K the number of indicators $ I_{k} $. The first component $ F^{1} $ may be expressed for observation i as:

$$ F_{i}^{1} = \sum\limits_{k = 1}^{K} {\omega_{k}^{1} I_{i}^{*k} } . $$

Where $ I^{*k} $ refers to the standardized primary indicator $ I^{k} $. Note that $ \omega_{k}^{1} $ is the (first) factor score coefficient for indicator k. It turns out that the scores $ \omega_{k}^{1} $ are in fact the multiple regression coefficients between the component $ F^{1} $ and the standardized primary indicators $ I^{*k} $. It is important to understand that PCA has some limitations, of which the most important is probably the fact it has been developed for quantitative variables.

It is therefore better not to use PCA when some of the variables are of a qualitative nature. (Multiple) Correspondence Analysis (MCA) is in fact a data reduction technique that should be used in the presence of categorical variables.

Let us therefore assume now that the K primary indicators are categorical ordinal and that the indicator $ I^{k} $ has $ J^{k} $ categories. Note that if some of the variables of interest are quantitative, it is always possible to transform them into a finite number of categories. To each primary indicator $ I^{k} $ we therefore associate the set of $ J^{k} $ binary variables that can only take the value 0 or 1.

Let us now call $ X(N,J) $ the matrix corresponding to N observations on the K indicators which are now decomposed into $ J^{k} $ variables. Note that $ J = \sum\nolimits_{k = 1}^{K} {J^{k} } $ represents now the total number of categories. Call $ N_{j} $ the absolute frequency of category j. Clearly $ N_{j} $ is equal to the sum of column j of the matrix X. Let $ N_{..} $ refer to the sum of all the $ (N\,by\,K) $ elements of the matrix X. Let also $ f_{j} $ be the relative frequency $ (N_{j} /N_{..} ) $, $ f^{i} $ be the sum of the ith line of matrix X, $ f_{ij} $ be the value of cell (i, j), and $ f_{j}^{i} $ be equal to the ratio $ (f_{ij} /f^{i} ) $. Finally, call $ \{ f_{j}^{i} \} $ the set of all $ f_{j}^{i} $’s for a given observation i (j = 1 to J). This set will be called the profile of observation i.

As stressed previously CA is a PCA process applied to the matrix X, but with the $ \chi^{2} $-metric on row/column profiles, instead of the usual Euclidean metric. This $ \chi^{2} $-metric is in fact a special case of the Mahalanobis distance developed in the 1930s. This metric defines the distance $ d^{2} \left( {f_{j}^{i} ,f_{j}^{{i^{\prime}}} } \right) $ between two profiles i and i′ as:

$$ d^{2} \left( {f_{j}^{i} ,f_{j}^{{i^{\prime}}} } \right) = \sum\limits_{j = 1}^{J} {(1/f_{j} )} \left( {f_{j}^{i} - f_{j}^{{i^{\prime}}} } \right)^{2} $$

Note that the only difference with the Euclidean metric lies in the term $ (1/f_{j} ) $. This term indicates that categories which have a low frequency will receive a higher weight in the computation of distance. As a consequence CA will be overweighting the smaller categories within each primary indicator. It can be shown that:

$$ \omega_{j}^{1,k} = \frac{1}{{\left( {N_{j}^{k} /N} \right)}}{\text{Cov}}\left( {F^{1*} ,I_{j}^{k} } \right) $$

where $ \omega_{j}^{1,k} $ is the score of category $ j_{k} $ on the first (non-normalized) factorial axis, $ I_{j}^{k} $ is a binary variable taking the value 1 when the population unit belongs to the category $ j_{k} $, $ F^{1*} $ is the normalized score on the first axis, and $ N_{j}^{k} $ is the frequency of the category $ j_{k} $ of indicator k.

It is also interesting to note that CA offers a unique duality property since it can be shown that:

$$ F_{1}^{i} = \frac{{\sum\nolimits_{k = 1}^{K} {\sum\nolimits_{j = 1}^{{J_{k} }} {\frac{{w_{j}^{1,k} }}{{\lambda_{1} }}I_{i,j}^{k} } } }}{K} $$

where K is the number of categorical indicators, $ J_{k} $ is the number of categories for indicator k, $ w_{j}^{1,k} $ is the score of category $ j_{k} $ on the first (non-normalized) factorial axis, $ I_{i,j}^{k} $ is a binary variable taking the value 1 when unit i belongs to category $ j_{k} $, and $ F_{1}^{i} $ is the (non-normalized) score of observation i on the first factorial axis.⁷

Reciprocally it can be shown that:

$$ \omega_{j}^{1,k} = \frac{{\sum\nolimits_{i = 1}^{N} {\frac{{F_{1}^{i} }}{{\lambda_{1} }}} }}{{N_{j}^{k} }} $$

This duality relationship implies that the score of a population unit on the first factor is equal to the average of the standardized factorial weights of the K categories to which it belongs. Conversely the weight of a given category is equal to the average of the standardized scores of the population units belonging to the corresponding category.

Appendix 3: On Frontier Efficiency Measurement

1.

Duality and the Concept of Input Distance Function in Production Theory:

Let $ x_{i} = (x_{1i} , \ldots ,x_{ji} , \ldots ,x_{ki} ) $ denote the vector of levels of social exclusion in the various k domains of social exclusion for individual i and let $ y_{i} $ denote the overall level of social exclusion for individual i. An individual’s performance, as far as social exclusion is concerned, may hence be represented by the pair $ (x_{i} ,y_{i} ) $, i = 1, …, I.

A theoretical social exclusion index SE can then be estimated using a Malmquist input quantity index:

$$ {\text{SE}}(y,x^{s} ,x^{t} ) = D_{\text{input}} (y,x^{s} )/D_{\text{input}} (y,x^{t} ) $$

where x ^s and x ^t are two different ‘social exclusion inputs’ vectors and $ D_{\text{input}} $ is an input distance function. The idea behind the Malmquist index is to provide a reference set against which to judge the relative magnitudes of the two vectors of ‘social exclusion inputs’. That reference set is the isoquant $ L(y) $ and the radially farther $ x_{i} $ is from $ L(y) $, the higher the overall level of social exclusion of individual i is, for $ x_{i} $ must be shrunk more to move back onto the reference set $ L(y). $

There is, however, a difficulty because the Malmquist index depends generally on y. One could use an approximation of this index such as the Tornquist index, but such an index requires price vectors as well as behavioral assumptions.⁸ Since we do not have prices for ‘social exclusion inputs,’ we have to adopt an alternative strategy. The idea is to get rid of y by treating all individuals equally and assume that each individual has the same overall level of social exclusion: one unit for each ‘social exclusion input’. Let e represent such a vector of ‘social exclusion inputs’—a k-dimensional vector of ones. Thus, the reference set becomes L(e) and bounds the vectors of ‘social exclusion inputs’ from below. Individuals with ‘social exclusion vectors’ on to L(e) share in fact the lowest level of ‘overall social exclusion’, with an index value of unity, whereas individuals with large vectors of ‘social exclusion inputs’ will then have higher overall levels of social exclusions, with index values above unity.

To estimate the distance function, let $ \lambda = (1/x_{k} ) $ define a $ (k - 1) $ dimensional vector $ z $ as $ z = \{ z_{j} \} = (x_{j} /x_{k} ) $ with $ j = 1, \ldots ,k - 1 $. Then $ D_{\text{input}} (z,e) = (1/x_{k} )D_{\text{input}} (x,e) $ and, since $ D_{\text{input}} (x,e) \ge 1, $, we have:

$$ (1/x_{k} ) \le D_{\text{input}} (z,e) $$

This implies that we may also write it as:

$$ (1/x_{k} ) = D_{\text{input}} (z,e)\exp (\varepsilon ),\quad \varepsilon \le 0. $$

By assuming that $ D_{\text{input}} (z,e) $ has a translog functional form, we have:

$$ \ln (1/x_{k} ) = \alpha_{0} + \sum\limits_{j = 1}^{k - 1} {\alpha_{j} \ln z_{j} } + (1/2)\sum\limits_{j = 1}^{k - 1} {\sum\limits_{h = 1}^{k - 1} {\alpha_{jh} \ln z_{j} \ln z_{h} + \varepsilon } } $$

Estimates of the coefficients $ \alpha_{j} $ and $ \alpha_{jh} $ may be obtained using corrected ordinary least squares (COLS) or maximum likelihood methods (see later) while the input distance function $ D_{\text{input}} (z_{i} ,e) $ for each individual i is provided by the transformation

$$ D_{\text{input}} (z_{i} ,e) = \exp \{ \hbox{max} (\varepsilon_{i} ) - \varepsilon_{i} \} . $$

This distance will, by definition, be greater than or equal to one (since its logarithm will be positive) and will hence indicate by how much an individual’s ‘social exclusion input vector’ must be scaled back in order to reach the ‘social exclusion inputs’ frontier. This procedure guarantees therefore that all ‘social exclusion input vectors’ lie on or above the resource frontier $ L(e). $ The overall level of social exclusion for individual i will then be obtained by dividing $ D_{\text{input}} (z_{i} ,e) $ by the minimum observed distance value—which by definition equals 1.

2.

Estimation Procedures: The Stochastic Production Frontier Approach

Let us take as a simple illustration, the case of a Cobb–Douglas production function. Let $ \ln y_{i} $ be the logarithm of the output of a firm i $ (i = 1\,{\text{to}}\,N) $ and $ x_{i} $ a $ (k + 1) $ row vector, whose first element is equal to one and the others are the logarithms of the k inputs used by the firm. We may then write that:

$$ \ln (y_{i} ) = x_{i} \beta - u_{i} \quad i = 1\;{\text{to}}\;N. $$

where $ \beta $ is a $ (k + 1) $ column vector of parameters to be estimated and $ u_{i} $ a nonnegative random variable, representing technical inefficiency in production of firm $ i $.

The ratio of the observed output of firm i to its potential output will then give a measure of its technical efficiency $ {\text{TE}}_{i} $ so that:

$$ {\text{TE}}_{i} = y_{i} /\exp (x_{i} \beta ) = \exp (x_{i} \beta - u_{i} )/\exp (x_{i} \beta ) = \exp ( - u_{i} ) $$

One of the methods that allows the estimation of this output-oriented Farrell measure of technical efficiency TE_i (see, Farrell 1957) is to use an algorithm proposed by Richmond (1974) which has become known as corrected ordinary least squares (COLS). This method starts by using ordinary least squares to derive the (unbiased) estimators of the slope parameters. Then in a second stage the (negatively biased) OLS estimator of the intercept parameter $ \beta_{0} $ is adjusted up by the value of the greatest negative residual so that the new residuals all become nonnegative. Naturally the mean of the observations does not lie any more on the estimated function; the latter has become in fact an upward bound to the observations.

One of the main criticisms of the COLS method is that it ignores the possible influence of measurement errors and other sources of noise. All the deviations from the frontier have been assumed to be a consequence of technical inefficiencies. Aigner et al. (1977) and Meeusen and van den Broeck (1977) have independently suggested an alternative approach called the stochastic production frontier method in which an additional random error $ v_{i} $ is added to the nonnegative random variable $ u_{i} $. We can therefore write:

$$ \ln (y_{i} ) = x_{i} \beta + v_{i} - u_{i} $$

The random error $ v_{i} $ is supposed to take into account factors such as the weather and luck and it is assumed that the $ v_{i} $’s are i.i.d. normal random variables with mean zero and constant variance $ \sigma_{v}^{2} $. These $ v_{i} $’s are also assumed to be independent of the $ u_{i} $’s, the latter being taken generally to be i.i.d. exponential or half-normal random variables. For more details on this maximum likelihood estimation procedure, see Battese and Corra (1977) and Coelli et al. (1998), as well as programs such as FRONTIER (Coelli 1992) or LIMDEP (Green 1992). The same methods (COLS and maximum likelihood) may naturally also be applied when estimating distance functions.

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Joseph Deutsch
- 1
Herman Musahara
- 2
- 3
Jacques Silber
- 4
- 1
Email author

1.Department of EconomicsBar-Ilan UniversityRamat GanIsrael
2.Department of EconomicsUniversity of RwandaButareRwanda
3.OSSREA (Organization for Social Science Research in Eastern and Southern Africa)Addis AbabaEthiopia
4.Senior Research FellowLISEREsch-sur-AlzetteLuxembourg

On the Measurement of Multidimensional Well-Being in Some Countries in Eastern and Southern Africa

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