Data sources
We used data from the most recent Multiple Indicator Cluster Survey (MICS) of three countries (Democratic Republic of Congo, Guinea Bissau and Mali) in sub-Saharan Africa. These countries were selected based on the fact that they are at the top in sub-Saharan Africa with the lowest HDI and for which data are available for the period 2014–2019.
As an international household survey program, the MICS program was developed by UNICEF from 1990 and aims to support countries in the collection of internationally comparable data on a wide range of indicators. Among other things, the MICS provides: (i) detailed information for the assessment of the situation of children and women (children's nutritional status, women's fertility history, water and sanitation, characteristics of household; (ii) basic data to assess the Millennium Development Goals (MDGs) and monitor the Sustainable Development Goals (SDGs) [27].
For the Democratic Republic of Congo, the sixth round of MICS conducted in 2017–2018 concerned a sample size of 20,792 households, representative at the national level, for both urban and rural areas and at the level of twenty-six provinces of the country. Information is also collected from 21,756 women and 6113 men aged 15 to 49 and 21,456 children under five. In Mali, data from the fifth round of MICS conducted in 2015 were collected from 11,830 households with a coverage rate of 99.8%. It is a representative survey of the population which provides detailed information on 18,409 women and 7430 men in 15–49 years and 16,468 children under five. The Guinea-Bissau MICS-5 conducted in 2014 from 6601 households and provides information on 10,234 women and 4232 men aged 15–49 and 7573 children under five.
Variables and measurements
Access to healthcare variables
Based on insight from Ersado and Aran [28] study, we selected seven variables for the analysis of inequalities in healthcare outcomes. These are: i. Antenatal care or prenatal care (women’s routine health control during pregnancy); ii. Birth’s place (birth in health facilities or elsewhere); iii. Birth attended (assisted birth skilled health personnel or others); iv. Child’s postnatal check-up (children medical checkup after delivery); v. Regular immunizations within 1 year after birth (vaccines to protect children from diseases); vi. Access to safe water (water from official sources of drinking water); vii. Access to toilet (availability of toilet in the house). These variables were used to construct three composite healthcare outcome indicators. The first indicator (HA1) relates to access to healthcare services before and after birth. This indicator was constructed by considering that children have access to healthcare services before and after birth if, at the same time, the mother received medical check-ups during pregnancy, gave birth in a health center assisted by qualified medical personnel and the child received postnatal check-up. The second (HA2) concerns access to immunizations. This indicator was built using the same information as that of the variable immunizations. The third indicator (HA3) considers access to housing services (water and sanitation facilities). This indicator was obtained by considering that an individual has access to housing services if, at the same time, he uses water from official sources of drinking water and has toilet in the house in which he/she lives.
Nutrition outcome variables
In order to explore the levels and trends in malnutrition and micronutrient intake, we selected nutrition outcome variables such as: blood tests (blood samples taken for the purpose of the assessment of nutritional status), stunting, wasting and underweight. The last three are related to common anthropometric measures [22, 29] and were used to construct a composite indicator noted NUT1. This indicator (NUT1) is related to the growth status of children. It is constructed by considering that children have good growth status if, at the same time, all the anthropometric indicators are normal. The second one, is noted NUT2 and is related to the first nutrition outcome variable (blood tests). This indicator (NUT2) was obtained by using information related to blood tests.
We consider that children have access to nutrition outcome or opportunity if they have good growth status or a blood sample has been taken from them for the purpose of the assessment of nutritional status.
In this research work, the opportunities are related to the two groups of variables above (healthcare and nutrition). The idea is to consider that the available services relating to health and nutrition are opportunities for children’s health. But access to these opportunities is influenced by certain characteristics that are beyond the control of these children.
Circumstances variables
For each country, we retained the same variables of circumstances which are determinants of the health and nutritional status of children. A total of seven circumstance variables were considered: (i) residence area; (ii) gender of child; (iii) number of children under 5; (iv) age of household head; (v) father’s education; (vi) mother’s education; (vii) economic wellbeing. These circumstance variables were then used to subdivide the sample of children into several sub-groups ranging from the most favorable to the least favorable group. The objective here was to bring together children with identical life circumstances in order to capture the influence of the gap between the different groups on access to healthcare and nutritional outcome. These groups are built from a set of circumstantial variables having the same effects on access to healthcare and nutritional outcome. The idea of building groups is to take into account the interactive effects of the different circumstantial variables and not their individual effects given, for example, that a child in a poor family in a rural area will not necessarily have the same difficulties than one who is in a poor family but in urban area. The rest of this article will focus much more on the two extreme sub-groups (the most and the least favorable group). Thus, the least favorable group is built with characteristics recognized in the economic literature as having negative effects on access to healthcare and nutritional outcome such as: rural areas, poor households with more than two children for which the head has a low level of education. The most favorable group is characterized by circumstances recognized as having positive effects on access to healthcare and nutritional outcome such as urban areas, rich households with at most two children for which the head has a high level of education.
Analytical steps
To analyze the patterns and extent of inequality of opportunity in health and nutrition among children under-five, we used the methodological framework of some previous studies [30, 31] to compute the human opportunity index (HOI) and the dissimilarity index (D-index). The interest given to IoP in children lies in the fact that they do not constitute a decision center and cannot choose between having access or not to the variables of health and nutrition results. Also, policies to combat inequalities in childhood are more effective than those implemented later.
In the first step of this analysis, we define a binary variable as follows [30, 31]:
$$ {z}_i=\left\{\begin{array}{c}1\kern1.5em if\ the\ {i}^{th} child\ has\ access\ to\ health\ or\ nutrition\ opportunity\\ {}0\kern0.5em if\ not\end{array}\right. $$
(1)
It follows from the preceding expression that the probability that the ith child i has access to the opportunities retained is given by:
$$ {p}_i=E\left({z}_i\right) $$
(2)
By considering the fact that this probability is influenced by the life circumstance variables which are out of the children’s control, Eq. 2 can be redefined by means of a simple logit model as follows:
$$ {p}_i=\frac{e^{\left({\beta}_0+{\sum}_{j=1}^k{\beta}_j{x}_{ij}\right)}}{1+{e}^{\left({\beta}_0+{\sum}_{j=1}^k{\beta}_j{x}_{ij}\right)}} $$
(3)
K is a set of circumstance variables: xij, xi1, xi2, …, xik.
We used the maximum likelihood method to estimate the vector of parameters βj of the logit model and obtain the maximum likelihood estimate \( {\hat{\boldsymbol{p}}}_{\boldsymbol{i}} \). The latter is an estimate of the probability of access depending on the selected variables of circumstances. From this probability, we can now determine the dissimilarity index which represents the inequality of opportunity. This index gives information on the dissimilarity of access rates to a given service or available opportunities. It is estimated as follows:
$$ \hat{D}=\frac{1}{2\overline{p}}{\sum}_{i=1}^n{w}_i\left|{\hat{p}}_i-\overline{p}\right| $$
(4)
$$ Where=\left\{\begin{array}{c}\hat{\boldsymbol{D}\ } is\ the\ estimated\ relative\ mean\ deviation\ \\ {}{\boldsymbol{w}}_{\boldsymbol{i}} is\ the\ population\ weight\ associated\ to\ the\ specific\ opportunity\\ {}\overline{\boldsymbol{p}\ } is\ \mathrm{is}\ \mathrm{the}\ \mathrm{average}\ \mathrm{prevalence}\ \mathrm{of}\ \mathrm{access}\ \mathrm{to}\ \mathrm{selected}\ \mathrm{services}\end{array}\right. $$
The average prevalence of access to services or opportunity selected, called level of coverage, is obtained as follows:
$$ \overline{p}={\sum}_{i=1}^n{w}_i{\hat{p}}_i $$
(5)
The dissimilarity index (D-index) which measures the level of inequality of opportunity depending on different circumstances ranges from 0 to 1 (0 to 100 in percentage terms), and takes the value zero in a situation when opportunities are equal in terms of benefits for each child. To measure equity of opportunity, we use the difference between the unit and the D-index. This difference is noted E and is given by the expression:
$$ E=\left(1-D\right) $$
(6)
Human opportunity index
The HOI is obtained by the following expression:
$$ HOI=\overline{p}\left(1-D\right) $$
(7)
This equation shows an inverse relationship between the HOI and the D-index. The latter takes values between 0 and 1. When it increases and becomes close to 1, the HOI decreases. Thus, an increase in the value of the human opportunity index (HOI) can be done by increasing both coverage (\( \overline{p}\Big) \) and equity (E) or increasing only the coverage and decreasing the dissimilarity index.
All these indices were calculated on the basis of the two extreme groups constructed as follows:
$$ Groups=\left\{\begin{array}{c}1\ \left(\boldsymbol{Most}\ \boldsymbol{advantage}\ \boldsymbol{group}\right)\ if\ children\ live\ in\ \mathrm{urban}\ \mathrm{areas},\mathrm{rich}\ \mathrm{households}\ \mathrm{with}\ \mathrm{a}\mathrm{t}\ \mathrm{most}\ \mathrm{t}\mathrm{wo}\ \mathrm{children}\\ {}\mathrm{for}\ \mathrm{which}\ \mathrm{the}\ \mathrm{head}\ \mathrm{has}\ \mathrm{a}\ \mathrm{high}\ \mathrm{level}\ \mathrm{of}\ \mathrm{education}\\ {}2\ \left( Least\ \boldsymbol{advantage}\ \boldsymbol{group}\right)\ if\ children\ live\ in\ \mathrm{rural}\ \mathrm{areas},\mathrm{poor}\ \mathrm{households}\ \mathrm{with}\ \mathrm{more}\ \mathrm{than}\ \mathrm{t}\mathrm{wo}\ \mathrm{children}\\ {}\mathrm{for}\ \mathrm{which}\ \mathrm{the}\ \mathrm{head}\ \mathrm{has}\ \mathrm{a}\ \mathrm{low}\ \mathrm{level}\ \mathrm{of}\ \mathrm{education}\end{array}\right. $$
Decomposition of the inequality by the Shapley value
Following Shorrocks [32], we used Shapley decomposition method to estimate the contribution of each circumstance defined above to inequality in access to health and nutrition outcome variables selected. If we assume that the D-index and the HOI are influenced by the set of circumstance variables defined above, it is also important to emphasize that the increase in the circumstance variables can increase the dissimilarity index. This effect can be measured by the expression below:
$$ {D}_A={\sum}_{s\subseteq N\backslash \left\{A\right\}}\frac{\left|s\right|!\left(n-\left|s\right|-1\right)!}{n!}\left[D\left(S\cup \left\{A\right\}\right)-D(S)\right] $$
(8)
In this equation: A is the additional circumstance variable, DA the impact of adding a circumstance A, N represents the set of the n circumstances, S is the subset of N circumstances obtained without the circumstance A, D(S) is the dissimilarity index obtained with the set of circumstances S without the circumstance A, D(S ∪ {A}) is the dissimilarity index considering with the set of circumstances S and circumstance A.
The application of the shapely decomposition method allowed us to capture the contribution of each circumstance variable omitted to the dissimilarity index as follows:
$$ {\theta}_A=\frac{D_A}{D(N)} $$
(9)
In the previous expression, \( {\sum}_{i\in N}{\theta}_A=1 \) meaning that the contribution of all the variables of circumstance must amount to 1 (100%). All the steps of this methodological approach are used to achieve the objectives of this article.