## Inequality Decomposition in the Distribution of Income and Child Health in Cameroon

**Francis Menjo Baye**^{1}, **Boniface Ngah Epo**^{1,}, **Simon Alain Song Ntamack**^{1}

^{1}Faculty of Economics and Management, University of Yaoundé II, Cameroon

2. The Shapley Value Framework and Gini Decomposition Methods

3. Child Height as an Appropriate Non-Income Indicator of Child Health

4. Presentation of Household Surveys and Adjustments

### Abstract

We undertake a spatial and inter-temporal decomposition of the S-Gini inequality index using the Shapley Value-based approach, and both money-metric and child health indicators collected by the government’s statistics office in 1996 and 2001. Changes in income inequalities are driven largely by changes in between-zone inequalities; for child health, the within-zone component remains more important. Results point to the wisdom of considering the redistribution of health facilities and services within-zones rather than across if the intention is to cost-effectively reduce overall health inequalities. In the monetary space, an optimal-mix of within- and between-zone distributive measures is important in addressing inequality.

**Keywords:** Gini decomposition, Shapley value, income, child health and Cameroon

*American Journal of Rural Development*, 2013 1 (1),
pp 6-14.

DOI: 10.12691/ajrd-1-1-2

Received December 28, 2012; Revised May 05, 2013; Accepted May 06, 2013

**Copyright:**© 2013 Science and Education Publishing. All Rights Reserved.

### Cite this article:

- Baye, Francis Menjo, Boniface Ngah Epo, and Simon Alain Song Ntamack. "Inequality Decomposition in the Distribution of Income and Child Health in Cameroon."
*American Journal of Rural Development*1.1 (2013): 6-14.

- Baye, F. M. , Epo, B. N. , & Ntamack, S. A. S. (2013). Inequality Decomposition in the Distribution of Income and Child Health in Cameroon.
*American Journal of Rural Development*,*1*(1), 6-14.

- Baye, Francis Menjo, Boniface Ngah Epo, and Simon Alain Song Ntamack. "Inequality Decomposition in the Distribution of Income and Child Health in Cameroon."
*American Journal of Rural Development*1, no. 1 (2013): 6-14.

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### 1. Introduction

Cameroon encountered an adverse international environment from 1986 as the CFA franc became overvalued against the US dollar and concomitantly the world market prices of commodity exports from the country declined drastically. This engendered substantial budgetary shortfalls and Cameroon adopted the IMF/World Bank structural adjustment programme (SAP) from 1988 as the structure of the economy was deficient to contain external shocks.

In the context of the SAP, the government implemented a package of expenditure-reducing measures. Non-profit making public enterprises were liquidated and some marginal profit-making ones were privatised. Government expenditures on education and health delivery systems were compressed. 1993 witnessed a double salary cut in the public service – one in January and another in November – cuts that amounted to an average of about 60 per cent of the salaries of public sector workers. Public sector workers were massively retrenched from the mid 1990s. Following the wage leadership role of the government, salary cutbacks in the private sector were believed to bring about an overall decline in the cost of production, which was expected to enhance the global competitiveness of the economy.

After implementing all these internal measures, it became apparent that expenditure-reducing measures alone could not overturn the gloomy economic outlook; hence an expenditure-switching component was added. To enhance the global competitiveness of the economy, a 50 per cent devaluation of the CFA franc against the French franc was effected on January 12, 1994. Being a centre-piece of adjustment, the devaluation was intended to slowdown domestic absorption of imported goods as the level of foreign prices were increased in domestic currency terms and to reallocate resources away from non-tradable to tradable commodities, notably agricultural exports.

Following the relative success in its macro-economic stabilisation effort, Cameroon registered an annual average growth of around 4.5 per cent for the period 1996-2001, despite the continuing decline of the oil sector. Over the same period, per capita income rose annually at about 2 per cent. Social conditions, however, have deteriorated considerably over the last two decades, as a result of the economic and social crisis, and growth has been neither durable enough nor sufficiently redistributive to reverse these trends. Consequently, by 2001, indicators of public health, education and access to basic services were still alarmingly low, and in some cases worse than they were in the 1980s ^{[1]}.

Overall monetary poverty and inequalities in Cameroon deepened in the period 1984-1996 and rural deprivation remained more widespread, deeper and severer than urban ^{[2]}. As observed, the increasing levels of deprivation and inequalities in rural communities induced many young people to migrate into cities and larger towns where they expected to find better conditions ^{[3]}. More generally, the economic crisis and the immediate effects of the SAP amalgamated and forced many Cameroonians to adopt coping devices such as moonlighting, seeking for survival in the informal sector, occupational and geographical mobility, changing regional patterns of activities and productivity, and adopting “behavioural innovations” like corruption and other malpractices for survival ^{[4]}. These adaptations are thought to have defined specific patterns of both income and non-income distribution of well-being, knowledge of which is required to guide public policy on redistributive issues across economic sectors and regions.

Moreover, in the period 1980-2001, Cameroon witnessed all the possible phases of the business cycle: economic prosperity (up to 1985); economic and social crisis (1986-1994); and renewed economic fortunes (from 1995). In such a context, a comprehensive spatial and inter-temporal evaluation of the pattern and investigation of the relative importance of mobility between zones and zonal specific effects on measured inequalities are of interest to both analysts and the political entrepreneurs, who want to better understand elements that inform disparities in the distribution of both income and non-income indicators of well-being.

In addition to income, improvements in well-being in terms of health and education may not be equally distributed. For example, the same level of average health in a population in terms of the rate of growth in children that is consistent with good health may differ regionally depending on how health infrastructures and providers are distributed. Of equally relevance is a change in a given average level of health that may be distributed differently, thereby affecting the extent to which healthcare infrastructural investments will impact the share of the population that is malnourished.

Informed knowledge on both income and child health inequalities by socio-economic characteristics, gender, zone of residence and region of the country though vital for public policy, is unfortunately still fragmented in Cameroon. The only studies that tackle some aspects of monetary inequality decomposition in Cameroon exist ^{[4, 5, 6, 7]}. Very little (if any) is known about the exact contributions of within- and between-zone components of levels and changes in monetary and non-monetary inequality using 1996 and 2001 household surveys. Moreover, confronting both money and non-money metric indicators in a consolidated framework of inequality decomposition is yet to be realised in many African countries including Cameroon. Yet, such information is important to complement each other, especially in an era where distributive issues are becoming prominent in the policy menu. This constitutes some value addition of this paper.

To better inform public debate in the aftermath of or during policy adjustments that engender distributional changes, it is necessary to measure the evolution of inequality and its components, notably the decomposition of levels and changes, with a view to assessing the importance of factors explaining them. Some conventional inequality decomposition techniques in distributive analysis involving the Gini coefficient do not yield exact meaningful components because residuals or interaction terms are included to ensure their identity. Shorrocks ^{[8]} proposes a unified theoretical framework driven by the Shapley Value introduced by Lloyd Shapley in 1953, which rationally eliminates the residual term when an attempt is made to decompose the S-Gini class of inequality measures. This is the research methodology adopted in this paper.

This research is limited in scoop and timeframe. This study focuses only on child a specific child-health indicator and the S-Gini class of inequality measure. Further research could entail undertaking a comparative analysis with other indicator and measures of inequality. Likewise, another limit is that it focuses only on Cameroon. Further research could also entail undertaking a cross country analysis with neighbouring countries.

The foregoing research concerns condense to the following key questions: Does economic growth necessarily produce similar inequality patterns in all dimensions of well-being? What is the relative importance of within- and between-group components of inequality trends? This paper mainly seeks to compare the within- and between-group effects of changes in both income and child health inequalities. The specific objectives are: (1) to decompose spatial and inter-temporal trends in monetary inequalities into effects within-group versus between-group; (2) to decompose spatial and inter-temporal trends in child health inequalities into effects within-group versus between-group; (3) to examine the extent to which the story on income inequalities and child health inequalities converge or diverge; and (4) to derive policy implications on the basis of the findings.

The rest of the paper is in five main sections. Section 2 reviews the Shapley Value-based S-Gini decomposition framework. Section 3 provides a justification of child height as an appropriate non-monetary indicator that reflects child health and can complement income indicators of well-being. Section 4 presents the household surveys used in the analysis. Section 5 reports the empirical findings and Section 6 submits concluding remarks.

### 2. The Shapley Value Framework and Gini Decomposition Methods

**2.1. Description of the Shapley Value**

One of the concerns in distributive analysis would be how to assign weights to the factors that contribute to an observed level or change in an inequality measure in the distribution of living standards. For instance, the level and/or change in a distributive index between two dates may be attributable to factors such as within-group and between-group effects and analysts are interested in quantifying the relative importance of each component. There are different methods to perform the attribution, all of which must have to deal with the fact that the contribution of a factor depends on the presence of the other factors. This issue is similar to problems that arise in cooperative game theory, and recent literature in distributive analysis is proposing and applying an attribution according to the Shapley Value ^{[3, 5, 8, 9]}.

Let K = 1, 2, …, k,…, m be a finite set of factors. Non-empty sub-sets of K are called coalitions. To accomplish the attribution process, the factors may be considered as belonging to coalitions and the strength of each coalition is expressed as a characteristic function v. For any coalition or sub-set S ⊆ K, v(S) measures the share of the surplus or loss that the coalition, S, is capable of appropriating independently of factors belonging to other coalitions.

For each factor k, k∉S, Shapley ^{[10]} proposes a value based on the factors marginal contribution – defined as the weighted mean of the marginal contributions v(S∪*k*) - v(S) of factor *k* in all coalitions S ⊆ K- *k*. That is, factor *k* is attributed the extra amount that it brings to the existing coalition of factors. To identify this value, we imagine that the m factors are randomly ranked in some order, or join coalitions in a random order, defined by σ:

(1) |

and then successively eliminated in that order. The elimination of factors reduces the share accruing to the group of those not yet eliminated. When the coalition, S, is composed of s elements, we can only find the value they will obtain, v(S), when the first s elements of σ are exactly the elements of S. The weight of the coalition S, is measured by the probability that the first s elements of σ are all elements of S. This probability is found by dividing the number of ordered arrangements of which the first s elements are all in S by the total number of possible ordered arrangements. The numerator can be obtained by imagining that the first s factors are orderly arranged in a sequence and the remaining m-s-1 factors are also orderly arranged in another sequence.

The number of possible ordered arrangements is the number of permutations of m factors taken m at a time, which is m! By the same reasoning, since the first s factors yield s! number of permutations, the remaining m-s-1 factors would yield (m-s-1)! number of permutations. The number of ordered arrangements in which the first s factors are all elements of S is thus given by s!(m-s-1)!.

(2) |

where by convention, 0! = 1 and v(∅) = 0. The Shapley Value given in Equation 2 satisfies all three of Shapley’s axioms ^{[8]}. The Shapley value can also be interpreted as the expected marginal contribution made by the factor to the value of a coalition, where the distribution of coalitions is such that any ordering of the factors is equally likely.

**2.2. Gini Inequality Measurement and Decomposition**

Several measures have been proposed in the literature for characterising inequality in the distribution of living standards ^{[10, 11, 12, 13, 14]}. According to these authors, any appropriate measure of inequality that can conveniently facilitate welfare analysis must lend itself to at least five axiomatic conditions: (1) the mean independence condition, (2) the population-size independence condition, (3) the Pigou-Dalton transfer sensitivity, (4) the symmetry condition, and (5) the decomposability condition.

The Mean independence condition holds if multiplying all elements of well-being by a constant, k, leaves the measure of inequality unchanged. The population-size independence condition holds if increasing or decreasing the population by the same amount across all well-being classes does not affect the measure of inequality. The Pigou-Dalton transfer sensitivity condition holds if a transfer from a wealthier to a poorer person brings about a decrease in the measure of inequality without reversing the direction of well-being. The symmetry condition requires that the inequality measure be independent of any characteristic of households other than the well-being indicator whose distribution is being measured. The decomposability condition takes three forms: group decomposability, source decomposability and decomposability of shared household income. For a comprehensive analysis of source decomposition ^{[15, 16]}. The latter two are not considered in this paper. In what follows, we defined and review the group decomposition of the Gini coefficient of inequality.

**2.2.1. The S-Gini Class of Inequality Indices**

The popularity and attractive properties of the Gini coefficient makes it an indispensable measure in any study of inequality. The Gini coefficient tends to satisfy axioms 1-4 above, but will fail the decomposability condition if subgroups of the distribution of well-being overlap. After ordering living standards in a Lorenz consistent manner, the class of S-Gini (or “Single-Parameter” Gini) inequality indices can be shown to be equal to the covariance formula ^{[17]} in Equation 3:

(3) |

where Q(P) is the level of living standard below which we find a proportion P of the population. P ∈ [0, 1]^{[, 1]} is the proportion of individuals/households in the population who enjoy standards of living that are less than or equal to the quantile Q(P). ρ is a parameter of inequality aversion that determines our ethical concern for the deviation of quantiles from the mean at various ranks in the population. The larger the value ρ, the more weight is given to the deviation of living standards from the mean, μ, at the lower tail of the distribution. When ρ becomes very large, the index G(ρ) equals the proportional deviation from the mean of the lowest living standard. When ρ=1, the same weight is given to all deviations from the mean, which then makes the inequality index G(ρ=1) always equal to 0, regardless of the distribution of living standards under consideration.

The conventional Gini index is then obtained by letting ρ=2 (Equation 4):

(4) |

which is just a proportion of the covariance between living standards and their ranks. An interesting property of the conventional Gini index is that it equals half the mean-normalised average distance between all living standards. Thus, if the standard Gini index is found to be 0.3 the interpretation is that the average distance between the living standards of that distribution is of the order of 60 per cent of the mean. The Gini coefficient for ρ=2 can be portrayed graphically as twice the area lying between the lorenz curve and the 45° line divided by the total area in such a diagram. The denominator ensures that this measure will vary between 0 (perfect equality) and 1 (perfect inequality).

**2.2.2. Subgroup Decomposition of the Gini: The Analytical Approach**

As noted, there are ways of decomposing the Gini by group but the component terms of total inequality are not always intuitive or mathematically appealing ^{[13]}. The analytical decomposition of the Gini coefficient of inequality into between-group and within-group contributions raises a legitimate concern because it generates a troublesome and little understood residual term if subgroup well-being ranges overlap ^{[18]}.

Let G(y) be the Gini coefficient and let the population subgroups be indexed by k=1,2,…,n. The decomposition takes the form ^{[19]}:

(5) |

where G_{k} is the Gini coefficient for well-being within subgroup k, G(μ_{1,…,} μ_{k}) is between-group Gini coefficient, defined as the one which would result if every well-being in every subgroup were to be replaced by the relevant subgroup mean, * *is the product of the population share and well-being share accruing to subgroup k, and ε is the residual which will not vanish if subgroups well-being ranges overlap.

**2.2.3. Subgroup Decomposition of the Gini: The Shapley Value Approach**

The Shapley Value decomposition rule has been used to obtain exact decomposition of the Gini coefficient into between-group and within-group components that sum to the total inequality with no residual ^{[5]}. The application of the Shapley value involves two steps. The first step is to decompose total inequality into between-group and within-group contributions. The second step is to express global within-group contribution as a weighted sum of the within-group contributions by the different subgroups. Let us denote the within-group inequality factor by W_{g} and the between group inequality factor by B_{g}, so that total Gini index G(y) = v(W_{g},B_{g}), expressed in terms of the characteristic function v.

In the first step, we suppose that the two Shapley contributions that account for the overall Gini coefficient G(y) are within-group inequality component () and between-group inequality component (), given by: . The basic rules followed to compute the marginal contributions of each of these factors are:

(1) Eliminate the between-group inequality and compute the within-group inequality by using a vector of well-being where each household’s well-being has been multiplied by the ratio μ/μ_{k}. This operation renders the average well-being of each group to equal μ.

(2) Eliminate the within-group inequality and compute the between-group inequality, G (μ_{1,…,} μ_{k}), by using a vector of well-being were each household has the average well-being of its group, denoted by μ_{k};

(3) Eliminate between- and within-group inequality simultaneously and each household remains with the average well-being of the entire distribution. In this case, G(μ) = 0.

The elimination order of factors following these rules is arbitrary and the arbitrariness is purged when the Shapley Value approach is used as in Table 1.

#### Table 1. Application of the Shapley Value (Equation 2) to the within-group and between-group inequality factors (W_{g} and B_{g})

As shown in Table 1, from Equation 2 and the elimination rules defined earlier, the Shapley Value within-group and between-group contributions can be given as in Equations 6 and 7, respectively.

(6) |

(7) |

From the within-group contribution to total inequality expressed in equation (6), the second step consists in decomposing global within-group inequality as a sum of within-group inequality across groups. Note that the term G (μ) = 0, which implies that the within-group contribution is based on three inequality indices. The same rule is used for determining the impact of eliminating the marginal contribution of group k, notably the attribution of group k’s average well-being to all its members in order to eliminate the group’s contribution to global within-group inequality. This gives the Shapley Value of group k’s contribution to total within-group inequality.

To illustrate this procedure, we suppose that there are only two groups, A and B and restate Equation 6 as follows:

(8) |

The Shapley Value contribution of group A to global within-group inequality is given as:

(9) |

This procedure can be applied symmetrically for the second group. Fortunately, this decomposition is already generalised to include more than two groups and programmed in the software DAD 4.4. This procedure is also applicable to inter-temporal changes in S-Gini class of indices of the distribution of well-being.

### 3. Child Height as an Appropriate Non-Income Indicator of Child Health

Most analysts accept, at least in theory, that deprivation/inequality is a multi-dimensional phenomenon. There is no doubt that the distribution of income is significantly instrumental in gauging inequality status. Yet, disparities with respect to a variety of other basic capabilities or functionings (health, literacy, security, political voice, etc.) should complement standard measures of income or expenditures to fully tease-out the ramifications of deprivation and inequalities ^{[20]}. In addition, there is growing concern among policymakers and stakeholders that non-income measures of well-being such as infant mortality and children’s nutritional status may not be similarly distributed over time when the distribution of incomes shift substantially ^{[22]}.

In the same spirit, we use as measures of well-being both household real expenditures per adult equivalent, the standard variable, and children’s standardized heights (their height-for-age z-scores), a good measure of young children’s nutrition and overall health status. In this context, medical and public health research show that children’s height is a good and objective indicator of their general health status, providing us with an observable measure of one of Sen’s basic functionings. Thus, a good measure of the extent of children’s health inequalities is the deviation of the distribution of heights in a population from the distribution for a reference population of healthy children who reach their genetic potential.

Moreover, economic literature modelling health status in developing countries typically uses children’s height as its dependent variable. The main determinants of the distribution of children’s height in a population are the accumulation of episodes of inadequate nutrient intake, disease, and deprivation that result in stunted growth. Most analyses of children’s height are limited to young children (under 36 months old) because the distributions of heights of healthy children among populations are strictly independent of race and ethnic composition.

The standard procedure for analyzing anthropometric data, such as height, is to transform it into age and gender standardized z-scores, or standard deviation scores, to assess the extent to which a child is above or below the median of the distribution of healthy children. The height-for-age indicator can, therefore, be used for assessing malnutrition disparities in children. Prolonged under-nutrition causes retardation of growth in both height and weight to a roughly comparable degree. As indicated above, impaired height gain is called “stunting”, and height gain is most affected by long-standing environmental and socio-economic factors; hence, it reflects snowballing socio-economic conditions the children and their parents have witnessed. Thus, height-for-age is an indicator of long-term nutritional status because it measures both current and past nutritional status.

In particular, the z-scores standardize a child’s height by age and gender as (h_{ik} − h_{k})/σ_{k}, where *h*_{ik}* *is height of a specific child i in a group k, which is defined by age and gender. *h*_{k }* *is the mean height of children in a healthy and well-nourished reference population of the same age and gender, and σ_{k}* *is the standard deviation of the indicator for children within the same group in the reference population. Thus, the z-score measures the number of standard deviations that a child’s height is above or below the mean for a reference population of healthy children of the same age and gender. Since z-scores will typically be negative for height poor children, they will not be quite appropriate in defining most distributive statistics.

The standardized height measure is constructed such that a child’s position in the distribution, in terms of percentiles, is the same for actual height in the actual age/gender group and the transformed height in the reference group WHO distribution. More formally:

(10) |

where *F* is the distribution function of heights in the WHO population for age/gender group defined by *a* (age) and g (gender), *h* is the actual height, months, = female, and *H* is standardized height.

### 4. Presentation of Household Surveys and Adjustments

This study is based on two household surveys: the 1996 Cameroon Households Consumption Survey (CHCS I) (DSCN, 1996), February-April 1996; and the 2001 Cameroon Households Consumption Survey (CHCS II, 2001), September – December 2001, carried out by the National Institute of Statistics formally the Department of Statistics and National Accounts [23,24]^{[23, ]}.

These snapshots represent points during and after SAPs in which household surveys are available. These surveys are different in a number of respects: the duration – three months for the first; and four months for the second. The CHCS II covered all 10 provinces of Cameroon, and was conducted in both urban and rural areas using a sample of 12,000 households, of which 10,992 were actually visited. In all, data were collected for 22 strata – 10 rural and 12 urban. In particular, Yaoundé and Douala were considered as separate strata, then each of the ten provinces was divided into two strata – one rural and one urban. By contrast, for the CHCS I, the country was divided into six regions (Yaoundé, Douala, Other Towns, Rural Forests, Rural High Plateaus, Rural Savannah) and the sample size was 1800 households, of which 1731 were actually interviewed. The strategy was to adjust stratification in the 2001 survey data to approximate the nomenclature of the 1996 household survey.

The sampling frames of both CHCS I and CHCS II are based on the 1987 general population and housing survey augmented to correct for its age. They are similar in (1) the partitioning of the various regions, in the sense that the 2001 survey could easily be regrouped to mimic the structure of the 1996 survey, and (2) the sampling techniques used. To select households in semi-urban and rural areas in the two surveys, a three-stage sampling frame was adopted following the sequence City-primary sampling unit-household. As concerned the political and economic capitals (Yaoundé and Douala), a two-stage stratified probabilistic sampling was carried out to select households [23,24]^{[23, ]}.

The recall period in the 1996 survey was 7 days for both rural and urban areas. The National Institute of Statistics adjusted the 2001 survey data to reflect the same 7 day recall period for rural and urban areas by using a multiplicative correction factor to adjust for declarations made by rural households [23,24]^{[23, ]}.

To account for inherent price differences, Yaoundé was chosen as the reference region, and then a purchasing power parity spatial price index computed by National Institute of Statistics from the price component of the CHCS II data was used to deflate household expenditure per adult equivalent per day of the different regions to render them comparable with Yaoundé prices. The implicit assumption is that the structure of regional price differences did not changed significantly in the period 1996-2001.

The 1996 total expenditures were scaled up, employing consumer price indices, to express them in terms of 2001 prices. For all practical purposes, these surveys are considered suitable for the present endeavours. The welfare indicators used is real expenditures per adult equivalent and standardized heights in percentiles, which captured child health. Since the composition of households by age was captured by the surveys, we followed previous studies in Cameroon to adopt a hybrid of the Oxford Equivalent Scale by attributing adult equivalent scales of 0.5 for household members aged below 15 years and 1 for those aged 15 and above [23,24]^{[23, ]}.

### 5. Empirical Results and Discussion

**5.1. Evolution of Income and Child Health Inequalities in Cameroon**

Table 2 presents the evolution of inequality in both the income and health dimensions in terms of Gini coefficients for the period 1996-2001. At the national level and in urban areas, income inequality regressed by 2.7 percentage points. In semi-rural areas the retreat was about 2.5 percentage points, while rural income inequality actually aggravated by 1.4 percentage points.

Estimates for nutrition inequality in terms of standardised heights increased significantly at the national level by 27 percentage points in the period under review (Table 2). The significant increase in rural areas was slightly more than the overall change and much more than for other zones. Apart from rural areas that yielded similar inequality trends, inequality results at the national level, and urban and semi-urban areas contrast drastically in terms of the two dimensions of well-being. What is clear from the results is that rural areas experienced worsening inequality in both income and health dimensions in the period under review. Hence, in both dimensions, trends in inequality are more of a rural than an urban worry in Cameroon (Table 2), although in terms of levels, the reverse is true in the income dimension.

These results indicate that health facilities are likely to be unequally distributed in Cameroon, but more so for rural than urban areas. This could be in terms of medical personnel, vaccination coverage, better dissemination and comprehension of information about HIV/AIDS and antiretroviral drugs. Indeed, social sector workers, especially those in the education and health sectors in Cameroon, typically avoid working in rural areas and rural dwellers are likely to be less capable to lobby for health infrastructures than their urban counterparts. On the average, the influential local politicians and landlords generally determine the location of such facilities in rural areas and it is not uncommon for facilities to be highly concentrated.

In the income dimension, the indication may be that low income earners, with the economic rebound, have reduced the gap between themselves and the rich, or the rich may have confronted circumstances that adversely affect their incomes or both. A decisive fight against corruption by the political entrepreneurs may engender such effects on the incomes of the more influential elite, who are generally corrupt and well to do.

**5.2. Decomposition of Income and Health Inequalities**

The decomposition of inequality trends is performed using both income and child health well-being indicators. The decomposition of income inequality in the period 1996-2000 is presented in Table 3. In 1996, of the income Gini of 42.9 per cent, the within-group contribution was much more (28.4 per cent) compared to the between-group component of 14.5 per cent. By 2001, the within-group contribution was slightly reinforced, while the between-group contribution retreated. The -2.7 percentage points change in income inequality was over accounted for by the between-group contribution (-3.7 percentage points), while the within-group component (1.0 percentage points) worked contrary to the decline. The bulk of the within-group income inequality was captured in the rural areas in both 1996 and 2001.

Table 4 presents zonal decomposition of levels and changes in health inequalities into within and between subgroup effects. Rural areas accounted for up to 72.7 per cent of national health inequality in 1996, while urban areas accounted for 21 per cent and semi-urban areas only accounted for 5.2 per cent. In 2001, the rankings are maintained but the contribution of the rural areas dropped in favour of that of urban and semi-urban areas. For the two periods, total health inequality is overwhelmingly accounted for by the within-group component, 99 per cent and 94.4 per cent, respectively. Table 4 also presents a decomposition of changes in health inequalities. While the relative contribution of urban and semi-urban areas augmented between 1996 and 2001, the relative contribution of rural areas retreated substantially. Of the 27 percentage points increase in health inequalities, the within-group contribution was 23.6 percentage points and the between-group contribution was only 3.4 percentage points. Rural areas contributed to mitigate the rise in the within-group health inequality.

Both dimensions of well-being do confirm the dominant contribution of within-group inequality in the distribution of well-being in Cameroon. However, while the between-group contribution is negligible in the health dimension, it is non-negligible in the income dimension of inequality (see, Table 3 and Table 4). These results reveal that greater efficiency could be achieved in reducing overall health inequalities if policy objectives are aimed at tacking inequality within the different zones and very little appears to be gained if emphasis is placed on zonal disparities. In terms of the income dimension, adopting an optimal-mix of within- and between-group considerations appears to be more appropriate in scaling down income inequality rather than concentrating only on one of them.

The dominance of the within-group health inequality and its zonal distribution indicate that children of the same cohort spatially experience different nutritional outcomes that reflect differences in epidemiological environments, access to healthcare providers and health infrastructures.

These results point to the wisdom of considering the redistribution of health facilities and services within-zones rather than between-zones if the intention is to reduce overall health inequalities in Cameroon. This is the case because within-group health inequalities appear to be more of a problem than between-group inequalities. This again indicates that the locally powerful political elite may be quite influential in diverting health infrastructures and personnel to their specific areas of origin within the different zones of the country. This is likely to engender substantial variation within than between zones in the health and nutritional status of children.

**5.3. Discussion**

These results highlight the importance of using non-income well-being measures to complement money-metric measures in distributive analysis. Results from health inequality decomposition in the period 1996-2001 sharply contrast those obtained from income inequality decomposition, but for the evolution of income inequalities in rural areas. This is an indication that these measures may be capturing different aspects of well-being disparities. Different instruments and targeting strategies are, therefore, likely to be required to scale down inequality in each dimension of well-being. Moreover, the divergence in the evolution of money-metric inequalities and child health inequalities points to more pervasive disparities than measures of inequality based on income or consumption expenditure would imply. Indeed, since stunting inequalities reflect cumulative nutritional and health disparities, it is likely to persist despite a tendency to equalizing incomes. In addition, the decompositions suggest that changes in income inequalities are driven largely by changes in the between-group inequalities, while for child health; the within-group component seems to be more important.

In the backdrop of these contrasting results, does economic growth necessarily produce significant reduction in all dimensions of inequalities? The answer is apparently no. These findings need to be explained. Are they evolving from the nature of the measures, a problem with the data, and/or do they capture something about the actual constraints and opportunities being faced by households? These concerns may contribute in accounting for the observed divergences in the two measures of well-being.

Money-metric indicators are generally skewed to the right, while child nutrition is likely to be skewed to the left because of biological factors. The long rightward tail of income distributions implies that poverty/inequality can be unduly influenced by the welfare of the rich. As incomes improve from low levels, the associated improvements in health dissipate quickly, precisely because height has a genetic upper bound while income does not. These patterns may also emanate because income does not typically include the benefits received from social expenditures on health and nutrition that themselves are likely to face enormous spatially disparities.

Although the characteristics of the measures may be responsible to an extent for some of the discrepancies, they cannot account for all. The actual constraints and opportunities faced by households in the different zones may be responsible for the bulk of the contrast. While household income growth may be attributed mainly to their labour market participation in an era of renewed growth, health is largely a function of the availability of public goods. Moreover, the underlying factors that determine income disparities are different from those that contribute to health differences. For example, the income discrepancies are undoubtedly explained by the nature of the labour market, the role of non-earned incomes, including the large flows of remittances from urban migrants and overseas workers, and the distribution of productive assets.

While these factors may also affect health outcomes, perhaps of greater importance is the long-term commitment of the state to promoting social welfare and equity through investments in services and institutions that affect health inequalities directly. The length of time that it takes to upgrade or renovate abandoned health infrastructures after an economic rebound may imply a time lag for these infrastructures to respond to favourable economic fortunes in terms of adequately providing health services, which are likely to take-off at different times in different areas because of budgetary constraints.

Furthermore, the economic rebound in Cameroon is attributable to the 1994 devaluation of the CFA franc and subsequently to fall-outs from the HIPC process, which was preceded by fiscal austerity measures. The austerity measures requiring the state to scale down public expenditures were embedded in the initial SAPs, designed to re-establish macroeconomic stability. This resulted in a declined in the quality and availability of public goods. With the attainment of the completion point of the HIPC initiative, efforts directed at scaling up the provision of social services including access to affordable healthcare services and infrastructures as enshrined in the PRSP are taking time to materialise. Hence, it is plausible that with economic growth, (1) monetary inequalities may be retreating, while health inequalities are still persisting, and (2) rehabilitation of health infrastructures and redistribution of health personnel is likely to start from the main urban areas before ever reaching the country-side.

Downsizing expenditures as conditioned by exigencies of the SAP lead to: (1) a halt in the construction and equipping of health facilities; (2) a freeze in the hiring of public health workers; and (3) the public sector salary cutbacks in 1993. These measures conspired and deteriorated the quality of the health delivery systems in Cameroon against WHO standards. For example, by 2001, Cameroon had one physician for every 10000 inhabitants (compared to 1 for every 3000), and one nurse for every 2250 inhabitants (compared to 1 for every 1000) ^{[1]}.

These difficulties were experienced just at a time when new challenges were plaguing the health sector. For example, (1) malaria is still accounting for 40-50 per cent of morbidity and 28 per cent of hospitalisation; (2) the incidence of HIV/AIDS rose from 2 per cent to 11.8 per cent between 1992 and 2002, and is affecting the working and most reproductive age group and their offspring more than others; and (3) tuberculosis has intensified in conjunction with HIV/AIDS. These outcomes are further undermining and reducing both the quantity and quality of the health delivery systems in Cameroon with far-reaching impacts on medium to long-term economic growth via spatial disparities in child health and human capital deficiencies. These outcomes could, at least in part, account for the observed discrepancies in our findings.

Moreover, as opposed to income, anthropometric indicators that reflect child health are influenced by the psychological state of the primary care-giver, who like other public sector workers is subjected to poor working conditions and surging prices of basic consumables. In this context, the weaning and other child feeding practices that are largely conditioned by the natural occurrence of trace minerals and vitamin availability in soils and foods also suffer. Community factors that influence public health such as the quality of water, sanitation, and vaccination coverage, which have been shown to be at least equal to income in determining child health, may also be important in determining the availability and quality of the healthcare system, which is also spatially unevenly distributed.

### 6. Concluding Remarks

This paper attempted to comprehensively study the group decomposition of the S-Gini class of inequality measures using a Shapley Value-based approach and both money-metric and child health indicators of well-being. It advanced two questions: does economic growth produce similar distributional patterns in all dimensions of well-being? What is the relative importance of within- and between-group components of inequality trends? Specifically, the paper: (1) decomposed spatial and inter-temporal trends in monetary inequalities into effects within-group versus between-group; (2) decomposed spatial and inter-temporal trends in child health inequalities into effects within-group versus between-group; and (3) examind the extent to which the story on income inequalities and child health inequalities converge or diverge.

Rural areas experienced worsening inequality in both income and child health dimensions in the period 1996-2001. At the national level, and urban and semi-urban areas income inequalities retreated, while child health inequalities aggravated over the same period. In both dimensions, trends in inequality were more of a rural than an urban worry in Cameroon, although in terms of levels, the reverse is true in the income dimension.

These results indicate that health facilities are likely to be more unequally distributed than income in Cameroon, but more so for rural than urban areas. This could be fathomed out in terms of medical personnel, vaccination coverage, better dissemination and comprehension of information about HIV/AIDS and antiretroviral drugs. Indeed, social sector workers, especially those in the education and health sectors in Cameroon, typically avoid working in rural areas and rural dwellers are likely to be less capable to lobby for health infrastructures than their urban counterparts. Moreover, the influential local politicians and landlords generally determine after allocation, the location of such facilities in rural areas and it is not uncommon for facilities to be highly concentrated. In the income dimension, the pointer is that with the exception of rural areas the low income earners, with the economic rebound, could have reduced the gap between them and the rich, or the rich may have confronted circumstances that prevented a similar rise in their incomes.

Both income and non-income dimensions highlighted the dominant contribution of within-group inequality in the distribution of well-being in Cameroon. While the between-group contribution to inequality trends was found to be negligible in the health dimension, it was found to be non-negligible in the income space. Meanwhile, results also suggested that changes in income inequalities are driven largely by changes in the between-group inequalities; for child health, the within-group component remains more important. This is indication of substantial variation within- than between-groups of households in the health and nutritional status of children. These results point to the wisdom of considering the redistribution of health facilities and services within-zones rather than between-zones if the intention is to cost-effectively reduce overall health inequalities in Cameroon. In the monetary space, an optimal-mix of within- and between-group measures would be required in addressing overall inequality.

### Acknowledgement

This paper is inspired from a research supported by the African Economic Research Consortium (AERC), Nairobi, Kenya.

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