Human Capital, Household Prosperity, and Social Inequalities in Sub-Saharan Africa

Abstract

This article examines the relationship between human capital accumulation, household income, and shared prosperity using 2005–2018 household surveys in Cameroon, Ethiopia, Kenya, Nigeria, and Uganda. Human capital is found to be positively and significantly correlated with household wellbeing in all five nations. Health’s indirect benefits in Cameroon, Ethiopia, and Kenya augment its direct benefits. Education has monotonic welfare benefits from primary to tertiary levels in all countries. Human capital and labour market participation are strongly associated with household wellbeing. The equalization of human capital endowments increases income for the 40% of the least well-off groups in three of the sample countries. All countries except Uganda record a decrease in human capital deprivation over the period studied. Redistribution is associated with a reduction in human capital deprivation, although less systematically than in the growth scenario. These results suggest that sizeable reductions in human capital deprivation are more likely to be accomplished by interventions that focus on boosting general human capital outcomes than those that redistribute the human capital formation inputs. In countries with declining human capital deprivation, the within-sector interventions seem to account for this success. Substantial heterogeneity in human capital poverty exists within and across countries and between rural and urban areas.

1. Introduction

1.1. Background

Addressing shortages of human capital stocks in Africa is instrumental in improving the standards of living in the region. The level and distribution of human capital endowments (general education, technical skills, health, and nutrition) are among the main determinants of inequality and poverty in Africa. The unequal distribution of human capital endowments at the individual and household levels is a source of disparities in access to current and future incomes, especially as mediated through labour markets.

According to Sen (1997) and Bebbington (1999), the individuals endowed with human capital are not only more skilled, productive, and efficient, but are also more capable of transforming capabilities into functioning. In analysing the relationship between human capital and welfare outcomes, it is important to determine whether a specific dimension of human capital fosters functioning or is a means to a specific end. For example, health can be an end in itself, if it reflects specific welfare dimensions, such as being well-nourished or being free from illness (Sen, 1998), but is a means to higher income or prosperity if it is an input into a production process (Grossman, 1972). However, from an ethical, individual perspective, average health levels should receive little weight in personal health assessments because an individual with poor health is deprived, irrespective of the general health prevailing in the population (Dotter & Klasen, 2020). This notwithstanding, the average perception of health in one’s neighbourhood may influence his/her self-perceived health status.

A framework for investigating the drivers, processes and welfare consequences of human capital dimensions is an important tool in generating evidence on what works to improve household prosperity in Africa and elsewhere. For instance, understanding the drivers of individual and household-level human capital endowments, and how the endowments can be translated into poverty and inequality reductions via labour market participation, is key to advancing the United Nations’ sustainable development goals. High initial inequality is detrimental to future economic growth and to poverty reduction efforts (Christiansen et al., 2002). The negative consequences of inequality occur through several channels, such as people’s engagement in rent-seeking activities and non-peaceful agitation for equal human rights. These are endemic behaviours in sub-Saharan countries due to the excessive marginalization of some communities, especially those in slums, and in rural and semi-arid areas.

1.2. Research Issues

The multidimensional nature of human capital and its different effects on welfare and shared prosperity have inspired policy advocates to place the question of human capital accumulation at the centre of the development process. From a long-run economic perspective, human capabilities (education, technical skills, nutrition and health) are key ingredients in consolidating social and technological processes that sustain shared growth (Lucas, 1988; Romer, 1990; Hanushek, 2013). Thus, substantial investments in human capital are required to transform and industrialize African economies. At the individual and household levels, it is important to understand the processes of human capital formation and to gauge its effects on economic prosperity. However, potential endogeneity, sample selectivity bias, and unobserved heterogeneity present major challenges in a proper assessment of the welfare effects of human capital formation. To that end, it is important to understand the mechanisms through which individual, household, and community characteristics affect human capital accumulation. Understanding drivers of human capital and its role in lifting households out of poverty and in empowering them to build prosperous livelihoods is the first contribution of this research endeavour, using the control function modelling and neighbourhood identification strategies, which can address endogeneity (for both continuous and dummy variables), sample selectivity, and unobserved heterogeneity biases simultaneously.

Evidence on how poverty changes over time and how the changes are linked to individual-level capabilities is vital for the design of anti-poverty interventions. Unfortunately, this sort of evidence is rare in African countries. Thus, explaining changes in household welfare in a way that accounts for effects due to inter-temporal differences across households in endowments and effects due to inter-temporal differences in returns to endowments is an indispensable intermediate step to understanding household prosperity and how it is shared.

Low levels of investments in education, nutrition, and health hinder inclusive growth by preventing vulnerable social groups from participating in its process (Appleton & Teal, 1998). Evidence on household shares in collective prosperity is a necessary task in devising public strategies to address social inequalities. The literature on equity and equal opportunities suggests that human capital plays a significant role in accounting for household prosperity (Roemer, 2002; Lefranc et al., 2008; Baye & Epo, 2015). An appraisal of the impacts of investments in human capital (education, skill, nutrition and health) on wellbeing through factual and counterfactual distributions analysis is an important policy simulation exercise. Designing factual and counterfactual human capital equalizing policy schemes and assessing their impacts on shared prosperity and on reduction in poverty and inequality is the second contribution of this paper.

The overarching idea that ties together the aforesaid two contributions is that the accumulation of human capabilities improves the level and distribution of wellbeing at both the household and community levels (Moser, 1998, 2006). Human capital constitutes one of the main inputs into the equalization of economic opportunities across social groups and across genders; especially overtime. Thus, generating evidence on how human capital endowments affect the shifting or movements of individuals or social groups in and out of some well-defined economic categories is key to designing workable social safety nets. In this regard, it is important to understand the extent to which deprivations in human capital sources of wellbeing are attributable to effects due to inter-sector mobility, those due to location-based improvements, and effects arising from location-based redistribution. Thus, understanding drivers of social mobility in Africa, and how this mobility is linked to human capabilities and functioning, is important in animating public policy debates on social inequalities. We make this third contribution by demonstrating the power of regression-based decomposition analysis of the level and distribution of household wellbeing. This type of analysis can be used to obtain multiple dimensions or a combination of dimensions in money metric units derived from drivers of a wellbeing/income-generating function.

1.3. Research Question and Objectives

This paper endeavours to answer the following question: What are the drivers and consequences of human capital formation on household income, shared prosperity, poverty, and social inequalities? The related specific objectives are to (1) determine the drivers of human capital and measure its effects on household wellbeing and growth accounting; (2) assess the impact of human capital sources of wellbeing on shared prosperity; (3) examine the role human capital plays in poverty and inequality reductions; and (4) explore changes in human capital (measured as income sources) deprivations over time and decompose the changes into those related to location-based growth, location-based redistribution, and mobility components.

1.4. Literature Review and Knowledge Gaps

In a presidential address to the American Economic Association, T. W. Schultz (1961) argued for the need to improve human capital, defined as the education, skills, health, and nutrition of individual household members. These dimensions of human capital increase prospects of labour market participation and household prosperity, which are reflected in gains in income, human wellbeing, and shared prosperity, as well as in reductions in inequality and poverty. According to Thirlwall (1999), human capital development takes several forms, such as spending on health and education facilities, formally organized education, adult education, in-service and institutional training, and retraining. Investments related to child nutrition and healthcare are also part and parcel of early human capital accumulation. In this context, impediments to greater productivity and household prosperity, such as illiteracy, poor health, malnutrition, unreceptiveness to new ideas, lack of initiative, and immobility, can be overcome by human capital investments.

An important component of theoretical literature in this field highlights a strong interactive effect between human capital and poverty reduction. There is consistent evidence that human capital formation reduces the unequal distribution of income, improves productivity, and promotes employment readiness (Fisher, 1946; T. W. Schultz, 1961, 1962; Becker, 1975; T. P. Schultz, 1993; Roemer, 1998; World Bank, 2005; Santos, 2009; Teixeira, 2014). A review of the literature indicates that the role of human capital in reducing poverty (Becker, 1995) cannot be well understood without decomposing human capital into its various dimensions and learning about the effects of individual dimensions on household income.

Human capital endowments enable people to contribute to and benefit from the growth process (Punam, 2014; Cumming et al., 2019). Moreover, the ‘Commission on Growth and Development [CGD] (2008)’ acknowledges that human capital investments through education and health promote the equality of opportunity, including in wages and employment. Components of human capital—education, nutrition, and health—are expected to have a positive effect on the creation of equal opportunity for all citizens (Mincer, 1991; Riddell & Song, 2011; Larionova & Varlamova, 2015).

Human capital theory suggests that education and health are the key determinants of current and future wellbeing (Becker, 1964; Grossman, 1972). These factors raise prospects of employment and employability, as well as people’s receptiveness to innovative ideas. Indeed, since the seminal works of Becker (see Becker, 1964; Becker & Tomes, 1976), recent advances in human capital formation frameworks have confirmed the role of human capital in the process of achieving household prosperity (Cunha et al., 2006; Cunha & Heckman, 2008; Heckman, 2007). Concerning the relationship between poverty traps and human capital accumulation, Ceroni (2001) finds that persistent inequalities in human capital follow from the observation that the poor require relatively higher financial returns to invest in human capital, because basic necessities such as food and shelter take the lion’s share of their incomes. This indicates that human capital accumulation has a non-negligible public good feature that requires government support.

A report by the World Bank (2015b) suggests that low levels of health and education, poor access to clean water, and sanitation are among the deprivations that cause low levels of income and wellbeing. Thus, improvements in the education, skills, health, and nutrition of household members, especially those who participate in the labour market, can considerably increase their productivity and earnings, as well as their receptiveness to advanced ideas and new technologies. In this way, the quality of labour can be enhanced by education, by improved health and nutrition for children and adults, by the migration of workers to places with better job opportunities, and by fertility reduction.

Studies analysing inter-temporal decomposition of poverty into growth and redistribution parts have identified the growth components as the one largely accounting for changes in the level of poverty when compared to the income redistribution component (Kakwani, 2000; Bigsten et al., 2003). Similarly, studies undertaking the sectoral decomposition of poverty changes typically attribute the bulk of the effects to the within-sector/group component. However, researchers are slow in extending these approaches to the decomposition of deprivations in regression-based sources of wellbeing, which turns out to attribute money metric units to otherwise non-monetary dimensions or a combination of dimensions of wellbeing. Up until now, nonmonetary dimensions of welfare have typically been captured in scalar form, making the determination of the attendant thresholds, a less transparent process. Thus, to better understand the processes of human capital formation, there is a need to explore the decomposition of changes in the deprivation of human capital regression-based sources of wellbeing along the mobility, sector-based growth and sector-based redistribution components.

The remainder of the paper is organized as follows. The methodology is outlined in Section 2, followed by a detailed description and interpretation of the empirical results in Section 3, and Section 4 concludes the paper.

2. Methodology

2.1. Modelling, Estimation and Computation Methods

This paper adopts a battery of approaches embedded in a framework in which results from preceding analyses are typically used as inputs in subsequent analyses.

2.2. The Wellbeing-Generating Function

Denoting the household economic wellbeing function with Y, contingent on a set of vectors of exogenous and endogenous variables, an income-generating function specified in Equation (1) can be envisaged. The key variables determining Y may include human capital—education, skills, nutrition, labour market employment, and health—and household, community, and regional characteristics, which serve as controls. In the setup shown in Equation (1) (Heckman, 2004), human capital endowments are the endogenous covariates of policy interest.

$$LnY=a_0+{{\displaystyle \sum }}_{k=1}^K{a}_k{Z}_k+{\eta }_1{E}_1+{{\displaystyle \sum }}_{j=2}^J{\eta }_j{E}_j+{\epsilon }_1$$

(1)

where $LnY$, E₁, and $E$, respectively, are the log of household income, a labour market indicator and human capital endowments (education, skills, nutrition, health, and/or mobility). The vector, $Z$, comprises K exogenous variables; $a$ is a vector of K parameters of the exogenous explanatory variables; $\eta$ is a vector of parameters of the potential endogenous explanatory variables; $a_0$ is the constant term; and ${\epsilon }_1$ is the error term that captures both random terms and unobservable variables that are typically correlated with the endogenous regressors.

Since the parameter set η shows the effects of human capital endowments on household prosperity, with important policy implications, care is needed to estimate it. In particular, since household economic wellbeing and human capital endowments are jointly observed, endogeneity is a potential problem that should be addressed, if present. An appropriate estimation strategy to use in this case is the instrumental variables (IV) method. In this vein, the reduced form of the jth human capital, Equation (2) can take the form:

$$E_j=b_{0j}+{{\displaystyle \sum }}_{k=1}^K{b}_k{Z}_{kj}+{{\displaystyle \sum }}_{k=K+1}^{K^{\prime }}{b}_k{Z}_{kj}+{\epsilon }_{2j}$$

(2)

where $K^{\prime }$ is an expanded vector of exogenous variables encompassing K covariates that belong in the economic welfare function and a vector of $\left(K^{\prime }-K\right)$ instrumental variables that affect the human capital endowment (E) but have no direct effect on household economic wellbeing $\left(LnY\right)$, except through the jth human capital endowment. The vector $b_k$ is a set of $K^{\prime }$ parameters of exogenous explanatory variables in the reduced form of the human capital endowments equation to be estimated, and ${\epsilon }_2$ is the error term that captures both the random effects and other relevant but unobservable characteristics that influence human capital endowments.

In addition, the heterogeneity of responses due to the non-linear interaction of human capital endowments with unobservable variables could bias the estimated effects. The heterogeneity in household preferences, sometimes originating from inherited traits, could affect human capital endowments, whose effect on household economic wellbeing is captured by the interaction of the human capital endowments with their respective residuals derived from the reduced form estimates. We appeal to control functions to address these two potential issues (Heckman, 1976; Wooldridge, 2002, 2015).

Another potential endogenous variable is the labour market indicator, E₁, which in our present endeavour is formal sector employment, modelled as a probit in Equation (3).

$$P\left(E_1=1\parallel z\right)=\mathsf{\Phi }\left(z\delta \right)$$

(3)

where P, E₁, and z are probability, formal sector employment, and a vector of exogenous variables (including those in Equation (1) and instrumental variables). $\mathsf{\Phi }$(.) is the standard normal cumulative function and δ is the vector of parameters to be estimated. Following Wooldridge (2015, pp. 427–428), Equation (3) can be considered a probit reduced form of that equation. To purge the potential endogeneity of formal employment resulting from its correlation with the error term of the structural equation (Equation (1)), we estimate the probit model, compute the inverse Mills ratio, thus generating the generalized residual, $\widehat{r}$.1

To address potential endogeneity and unobserved heterogeneity biases, Equation (1) can be augmented by including reduced form residuals (both linear and non-linear) and the interaction of the linear reduced form residuals with their corresponding endogenous counterparts, as shown in Equation (4):

$$LnY={\alpha }_0+{{\displaystyle \sum }}_{k=1}^K{\alpha }_k{Z}_k+{{\displaystyle \sum }}_{j=1}^J{\eta }_j{E}_j+{{\displaystyle \sum }}_{j=2}^J{\alpha }_j{\widehat{\epsilon }}_{2j}+{{\displaystyle \sum }}_{j=2}^J{\lambda }_j\left({\widehat{\epsilon }}_{2j}\ast E_j\right)+\phi \widehat{r}+u$$

(4)

where ${\widehat{\epsilon }}_{2j}$ (j = 1, 2, …, J) are residuals of the endogenous regressors resulting from the reduced form model (Equation (2)). The residuals $\left({\widehat{\epsilon }}_{2j}\right)$ serve as the controls for unobservable variables that correlate with $E_j$, thus permitting these endogenous inputs to be treated as if they were exogenous covariates during estimation. The term, $\left({\widehat{\epsilon }}_{2j}\ast E_j\right)$ is the interaction of the residuals with the actual values of each of the potential endogenous explanatory variables. The disturbance term, u is the random error and $\alpha , \eta , \lambda \mathrm{and} \phi$ are vectors of parameters to be estimated. Equation (4) is expected to produce parameter estimates that are unbiased and consistent (see Wooldridge, 2015). In the setup in Equation (4), testing the hypothesis of the exogeneity of human capital is equivalent to testing whether the coefficients on the reduced form residuals are jointly statistically insignificant.

2.3. The Identification Strategy

To instrument for health and formal sector work, we used the non-self-cluster mean of the health variable and the non-self-cluster proportion of formal sector employment, exploiting cluster-level information in the household surveys. These neighbourhood-based instruments are relevant bearing in mind the sociological constructs of emulation and imitation emerging from social interactions (Becker, 1975) norms that are practised widely in the countries under study. The expectation is that the higher the extent of wellness-reporting in a given neighbourhood, the more likely the excluded household head will report wellness, and vice versa. Similarly, if a higher proportion of formal sector workers is observed in a neighbourhood, the more likely is the excluded worker in the same cluster to be observed in formal sector work, especially if formal sector workers appear to be faring well.

The assignment of non-self-cluster means correlates with the endogenous variables but is not directly correlated with household spending, except through the wellness and sector of the activity of the key breadwinner or through other neighbourhood average characteristics that correlate with the non-self-cluster-based instruments. Because of the tendency for emulation within a cluster, assigning to a household belonging to the cluster a neighbourhood-level measure of an endogenous variable is equivalent to asserting that the assigned variable affects the household’s decisions, behaviours or status, but not the vice versa. This context reflects the exogeneity of the instruments.

Analysts familiar with the literature are likely to agree that the non-self-cluster mean/proportion may mitigate the endogeneity concerns, but some are likely to argue that such instruments may be associated with the excluded household’s wellbeing through unobserved channels. If, for example, formal sector workers are living in wealthier clusters, with both greater wellness and job availability, this context could equally affect their labour market decisions and wellbeing opportunities. Yet, the fundamental point here is that these are indirect channels, which we capture with the interaction term in our theoretical regression model stated in Equation (4).

2.4. Procedure for Accounting for Growth in Household Wellbeing

This section shows how to use the Shapley–Oaxaca–Blinder decomposition procedure to account for income growth in household wellbeing and then compare the relative contributions of human capital endowments to those associated with other individual, household, and community characteristics. In our setup, we consider estimated coefficients obtained from the structural model (Equation (4)) and from descriptive statistics of the different variables used in this equation to compute the contribution of endowments and returns to endowments between two periods, (t) and (t + n). After removing any arbitrariness in selecting the base year by using the Shapley value approach, which is equivalent to averaging the quantities at the two potential reference points, we can write down the following model:

$$Ln{\overline{Y}}_{t+n}-Ln{\overline{Y}}_t={\displaystyle \sum _{m=1}^{M}0.5\left({\overline{X}}_{t+n,m}-{\overline{X}}_{t,m}\right)}({\widehat{\beta }}_{t+n,m}+{\widehat{\beta }}_{t,m})+{\displaystyle \sum _{m=1}^{M}0.5\left({\overline{X}}_{t,m}+{\overline{X}}_{t+n,m}\right)}({\widehat{\beta }}_{t+n,m}-{\widehat{\beta }}_{t,m})$$

(5)

where X_m (m = 1, 2, …, M) represents each of the variables captured in Equation (4)—both observed and predicted. The left-hand side captures growth in household wellbeing, as proxied by income, between period t and t + n. The first right-hand-side term of Equation (5) simply shows the part of the growth in household wellbeing between t and t + n that can be explained by endowments in the different characteristics. The second term is the part of growth in household wellbeing between period t and t + n that can be explained by differentials in returns to the endowments. Note that various refinements of the standard Oaxaca-Blinder decomposition (Oaxaca, 1973; Blinder, 1973) can also be used to account for the growth in household wellbeing, asset endowment, or anthropometric indicators. In a context where sample selection is accounted for, the Neuman and Oaxaca (2004) method is relevant.

2.5. Assessing Welfare Impacts of Human Capital Endowments

To characterize the impact of human capital on shared prosperity, poverty, and inequality, we first simulate factual and counterfactual distributions of household welfare. To compute the factual and counterfactual distributions, we appeal to Bourguignon et al. (2007) and Baye and Epo (2015). The underlying idea here is to obtain two welfare distributions where the factual distribution equals the initial household wellbeing distribution and the counterfactual distribution is derived from the factual distribution when differences in human capital endowments are eliminated, say by assigning the mean value or the cluster mean value to all households. To get the counterfactual benchmarks, we first obtain the factual distribution by expressing the estimated counterpart-form of Equation (4) as shown in Equation (6).

$$Ln\widehat{Y}={\widehat{\alpha }}_0+{{\displaystyle \sum }}_{k=1}^K{\widehat{\alpha }}_k{X}_k+{{\displaystyle \sum }}_{j=1}^J{\widehat{\eta }}_j{E}_j+{{\displaystyle \sum }}_{j=2}^J{\widehat{\alpha }}_j{\widehat{\epsilon }}_{2j}+{{\displaystyle \sum }}_{j=2}^J{\widehat{\lambda }}_j\left({\widehat{\epsilon }}_{2j}\ast E_j\right)+\widehat{\phi }\widehat{r}$$

(6)

It is worth stressing that Equation (6) represents the estimated factual distribution of household income or wellbeing. From Equations (4) and (6), the factual or observed household welfare distribution in log form is obtainable as $LnY=Ln\widehat{Y}+\widehat{u}$, so that taking the antilog, we have $Y=Exp\left(Ln\widehat{Y}+\widehat{u}\right)$, which is expressed in full as in Equation (7).

$$Y=Exp[{\widehat{\alpha }}_0+{{\displaystyle \sum }}_{k=1}^K{\widehat{\alpha }}_k{Z}_k+{{\displaystyle \sum }}_{j=1}^J{\widehat{\eta }}_j{E}_j+{{\displaystyle \sum }}_{j=2}^J{\widehat{\alpha }}_j{\widehat{\epsilon }}_{2j}+{{\displaystyle \sum }}_{j=2}^J{\widehat{\lambda }}_j\left({\widehat{\epsilon }}_{2j}\ast E_j\right)+\widehat{\phi }\widehat{r}+\widehat{u}]$$

(7)

where $\widehat{u}$ is the predicted error term from the estimation of Equation (4). From the factual distribution, we can derive the counterfactual distribution to study the impact of human capital interventions on a wide range of household welfare outcomes, such as the poverty–growth–redistribution relationships, sectorial decomposition, and shared prosperity. The counterfactual value function is as stated in Equation (8).

If the household heads are allocated the mean value (or their cluster mean value) of the human capital endowments $({\stackrel{-}{E}}_j)$, while allowing exogenous circumstance-related variables to enter the function as observed, we have the distribution of wellbeing $Y_{\stackrel{-}{E}}$, defined as:

$$Y_{\stackrel{-}{E}}=Exp[{\widehat{\alpha }}_0+{{\displaystyle \sum }}_{k=1}^K{\widehat{\alpha }}_k{Z}_k+{{\displaystyle \sum }}_{j=1}^J{\widehat{\eta }}_j{\stackrel{-}{E}}_j+{{\displaystyle \sum }}_{j=2}^J{\widehat{\alpha }}_j{\widehat{\epsilon }}_{2j}+{{\displaystyle \sum }}_{j=2}^J{\widehat{\lambda }}_j\left({\widehat{\epsilon }}_{2j}\ast {\stackrel{-}{E}}_j\right)+\widehat{\phi }\widehat{r}+\widehat{u}]$$

(8)

Equation (8) is a counterfactual distribution in which human capital endowments are equalized at mean or cluster mean values. It is called counterfactual because it is not observed in real life; human capital endowments are not equalized across households, but public policy interventions may generate effects that mimic such a scenario.

2.6. Analysing the Impact of Human Capital on Shared Prosperity

To gauge the effect of human capital on shared prosperity, we use the factual (Equation (7)) and counterfactual (Equation (8)) distributions of wellbeing. Precisely, we compare shared prosperity using these two settings. To undertake this analysis, we adopt the World Bank (2013) definition of shared prosperity, which is the difference in average wellbeing at the bottom 40% of the distribution of a wellbeing metric between two periods. In this context, we consider the growth in average expenditure of the bottom 40 per cent in the factual and counterfactual distributions, and the impact of human capital is elicited by comparing the two scenarios.

For both distributions, the weighted average wellbeing per adult equivalent at the bottom 40 per cent is defined as:

$${\overline{Y}}_{B40}={\displaystyle \frac{{\displaystyle \sum _{h=1}^z{y}_{h}P\left(Y=y_h\right)}}{P\left(Y\le z\right)}}\hspace{0.17em}$$

(9)

where B40 is the poorest 40 per cent of the population, or the 40 per cent least well-off households, and ${\stackrel{-}{Y}}_{B40}$ is the weighted average wellbeing per adult equivalent of the least well-off households. $P\left(Y=y_h\right)$ is the probability density function of nonnegative values of wellbeing of households, $y_h$ in vector $Y$ represents the wellbeing of household h, and $P\left(Y\le z\right)=0.4$ represents an ordering of Y until the 40th percentile.

Following the World Bank (2015a), we measure shared prosperity by growth in average expenditure at the bottom 40 per cent of the wellbeing distribution between two periods. Given ${\stackrel{-}{Y}}_{t+n,B40}$ and ${\stackrel{-}{Y}}_{t,B40}$, the mean wellbeing per adult equivalent at the bottom 40 per cent at the two time periods (years) t and t + n, then shared prosperity is given as:

$${\theta }_{B40}\hspace{0.17em}={\left({\displaystyle \frac{{\overline{Y}}_{t+n,B40}}{{\overline{Y}}_{t,B40}}}\right)}^{\left(n\right)}-1\hspace{0.17em}$$

(10)

where ${\theta }_{B40}$ is the World Bank’s shared prosperity index (SPI). When observations are recorded over years, the shared prosperity index presents the annualized growth in average expenditure at the bottom 40 per cent of the welfare distribution. The corresponding annualized growth rate in population mean welfare is defined as:

$$\theta \hspace{0.17em}={\left({\displaystyle \frac{{\overline{Y}}_{t+n}}{{\overline{Y}}_t}}\right)}^{\left(n\right)}-1\hspace{0.17em}$$

(11)

where ${\stackrel{-}{Y}}_t$ and ${\stackrel{-}{Y}}_{t+n}$ are the population mean welfare in time t and t + n, respectively; $\theta$, the annualized growth in population mean welfare, represents average prosperity; and the shared prosperity premium is given by SPP = ${\theta }_{B40}-\theta$. Notice that the realization of a positive SPP is harder than that of a positive SPI because, in growing their incomes, the poorest groups compete with everyone else in the economy. In contrast, negative quantities of SPI and SPP occur comparatively easily because the poor face large relative human capital deprivations that work against their prosperity.

As indicated earlier, to measure the impact of human capital on shared prosperity, we compute the difference in shared prosperity or shared prosperity premium between the factual and counterfactual distributions. To verify the robustness of our approach, other social welfare functions, such as Sen’s (1976) social welfare function (SWF) or Atkinson’s SWF, can be used to assess the impact of a human capital intervention on household economic outcomes. Furthering our analysis, we also compute the Palma ratio, which focuses on the income disparities between those at the bottom and top of the wellbeing distribution, to supplement our shared prosperity analysis. This ratio is defined as the wellbeing share of the richest 10% divided by the share of the poorest 40 per cent. However, the downside of the Palma ratio is that it may satisfy the Pigou–Dalton transfer principle only weakly, if at all.

The factual–counterfactual analysis can also serve a broader policy purpose by eliciting the impact of human capital endowments on poverty, inequality, the components of growth–redistribution decomposition, and the sectoral intertemporal decomposition of measured poverty.

2.7. Derivation of Regressed Income Sources and Deprivation Lines

Without a loss of generality, we can express Equation (7) as Equation (12), in which case, the total welfare for the $i\mathrm{th}$ household is the income sum from all estimated welfare sources, M, plus the predicted error term, which is given as:

$$y_i=\exp \left({\widehat{\alpha }}_0+{\displaystyle \sum _{m=1}^M{\widehat{\beta }}_m{X}_{i,m}+{\widehat{u}}_i}\right)$$

(12)

where y_i, is the income of household i from source m, m = 1, 2, …, M; ${\widehat{\alpha }}_0$ is the estimated constant term; ${\displaystyle \sum _{m=1}^M{\widehat{\beta }}_m{X}_{i,m}}$ is the sum of income from M-estimated sources of household wellbeing; and ${\widehat{u}}_i$ is the residual. Equation (13) gives the expression for generating the value for the estimated welfare source, m, for each household.

$$\exp ({\widehat{\beta }}_m{X}_{i,m})={\displaystyle \frac{y_i}{\exp \left({\widehat{\alpha }}_0+{\displaystyle \sum _{j\ne m}^{M-1}{\widehat{\beta }}_j{X}_{i,j}+{\widehat{u}}_i}\right)}}$$

(13)

Notice that expression (13) is not a share or ratio equation but a compact mathematical way of separating out the income associated with source m from the incomes derived from all other sources, M − 1. Operationalizing Equation (13) for each regressed income source, we can sum utilities (revenues) from different income sources to obtain the total welfare for each household in money-metric units. After predicting the different regressed sources of welfare, growth–redistribution decomposition and the sectoral decomposition of changes in deprivation in each of the different sources between the two time periods are performed. Official monetary poverty lines and non-parametric regressions of each regressed welfare/income source on total expenditure per adult equivalent are used to obtain the relevant welfare cut-off line of each regression-based source of wellbeing.

Particularly, we performed non-parametric regressions with data from each of the five countries using the DAD 4.1 software. A non-parametric regression does not impose a functional form between the human capital income source and total expenditures per adult equivalent (PAE). Instead, it allows for some flexibility in the estimation of the relationship between the two variables following a weighting scheme based on the human capital income source of those households with total expenditures PAE in the neighbourhood of the predetermined monetary poverty line. This technique assigns a weighting scheme that attributes smaller weights as the absolute gaps between household total expenditures PAE and the predetermined poverty line increase. The results obtained by this process are less affected by outliers in the data and therefore unlikely to suffer from specification bias attributable to wrong functional forms.2 In each case, we project the value of the monetary poverty line from the total expenditures PAE axis to the non-parametric line, and then read the corresponding value on the human capital income source axis as the cut-off point, below which a household is considered as suffering from human capital deprivation.

2.8. Analysing Growth–Redistribution Decomposition of Changes in Human Capital Deprivation

To investigate the impact of human capital on the poverty-redistribution relationship, we make use of the well-known growth–redistribution decomposition framework attributed to Datt and Ravallion (1992) and Kakwani (2000). Particularly, we adopt the general framework for exact decomposition that can admit more than two factors using a Shapley value-based approach (Shorrocks, 1999). This method is considered a rationalization of the averaging procedure to eliminate the residual term that remains in the standard growth–redistribution decomposition (Datt & Ravallion, 1992). Given a welfare threshold, change in wellbeing between the initial period (t) and the final period (t + n) can be expressed as a contribution of growth, ${\phi }_G^{Sh}$, and that of redistribution, ${\phi }_R^{Sh}$, in the decomposition of changes in any measure of deprivation or poverty that is additively decomposable.

In the present endeavour, the welfare sub-indicators are the M regressed income sources, extracted from our estimated income-generating functions (Equations (12) and (13)). The relevant predicted income or welfare sources could be limited to regressed sources of human capital endowments, in which changes in their deprivation between two time periods are decomposed into growth and redistribution components.

Adopting the $P_{\alpha }$ class of deprivation measures (Foster et al., 1984), the aggregate change in the deprivation of the regressed income source, m, can be expressed as:

$$\Delta P_{\alpha }^m=P_{\alpha }^m\left({\mu }_{t+n}^m,L_{t+n}^m\right)-P_{\alpha }^m\left({\mu }_t^m,L_t^m\right)={\nu }_{\alpha }^m\left(G,R\right)$$

(14)

$\Delta P_{\alpha }^m$ is expressed as a function of the growth (G) and redistribution (R) components. The Shapley growth component $\Delta P_{\alpha }^m$ takes the form:

$$\begin{array}{cc}{\varphi }_G^{Sh,m}\left(2,v\right)& ={\displaystyle \frac{1}{2}}\left[{\nu }_{\alpha }^m\left(G,R\right)-{\nu }_{\alpha }^m\left(R\right)+{\nu }_{\alpha }^m\left(G\right)\right]\hfill \\ & =0.5\left[P_{\alpha }^m\left({\mu }_{t+n}^m,L_{t+n}^m\right)-P_{\alpha }^m\left({\mu }_t^m,L_{t+n}^m\right)+P_{\alpha }^m\left({\mu }_{t+n}^m,L_t^m\right)-P_{\alpha }^m\left({\mu }_t^m,L_t^m\right)\right]\hfill \end{array}$$

(15)

The Shapley redistribution component $\Delta P_{\alpha }^m$ can be expressed as:

$$\begin{array}{cc}{\phi }_R^{Sh,m}\left(2,v\right)& ={\displaystyle \frac{1}{2}}\left[{\nu }_{\alpha }^m\left(G,R\right)-{\nu }_{\alpha }^m\left(G\right)+{\nu }_{\alpha }^m\left(R\right)\right]\hfill \\ & =0.5\left[P_{\alpha }^m\left({\mu }_{t+n}^m,L_{t+n}^m\right)-P_{\alpha }^m\left({\mu }_{t+n}^m,L_t^m\right)+P_{\alpha }^m\left({\mu }_t^m,L_{t+n}^m\right)-P_{\alpha }^m\left({\mu }_t^m,L_t^m\right)\right]\hfill \end{array}$$

(16)

Equations (15) and (16) express the decomposition of wellbeing changes of regressed income source, m, into growth and redistribution components, respectively. The change in deprivation can now be expressed as the sum of the growth and redistribution components with:

$$\Delta P_{\alpha }^m={\phi }_{\alpha G}^{Sh,m}\left(2,\nu \right)+{\phi }_{\alpha R}^{Sh,m}\left(2,\nu \right)$$

(17)

2.9. Addressing Sectoral Decomposition of Changes in Human Capital Deprivation

The generation of regressed income sources as indicated in Equation (13) is inspired by the regression income source framework suggested by Morduch and Sicular (2002) and Wan (2004). To explore the extent to which changes in human capital deprivation are due to mobility, location-based growth and location-based redistribution effects, we implement the sectoral decomposition of changes in deprivation. Subgroup consistency constitutes one of the most desirable properties of a good measure of deprivation once the welfare cut-off is established (Foster & Shorrocks, 1991; Balisacan, 1995). This implies that, all else being equal, the overall level of deprivation would fall whenever deprivation decreases within some subgroups of the population and is unchanged outside of those groups. In terms of the principle of additive decomposability, overall deprivation is the weighted average of subgroup deprivation levels. These weights are the respective population shares of the different subgroups.

We compute the within-location and between-location components in accounting for observed changes in deprivation. To attain this task, we exploit the sectoral decomposition approach (Ravallion & Huppi, 1991) of changes in deprivation between two dates, t and t + n, and the Shapley value decomposition framework (Shorrocks, 1999). To undertake the decomposition, let $f_s^m$ and $P_s^m$ represent the population share and deprivation level of a particular regressed source, m, that reflects the level of deprivation for sector/location s ∈ S. Hinging on the property of subgroup decomposability of the P_α class of deprivation measures, let aggregate levels of deprivation of regressed source m be expressed as $P_{\alpha ,t}^m={{\displaystyle \sum }}_{s\in S}{f}_{s,t}^m{P}_{\alpha s,t}^m$. Change in the level of aggregate deprivation between period t and t + n yields:

$$\Delta P_{\alpha }^m=P_{\alpha ,t+n}^m-P_{\alpha ,t}^m={\displaystyle \sum }_{s\in S}[f_{s,t+n}^m{P}_{\alpha s,t+n}^m-f_{s,t}^m{P}_{\alpha s,t}^m]$$

(18)

Extending the analysis, we can account for the overall change in deprivation ($\Delta P_{\alpha }^m$) in terms of changes in deprivation within given sectors or groups $\Delta P_{\alpha s}^m=P_{\alpha s,t+n}^m-P_{\alpha s,t}^m$, $s\in S$, and the population shifts between sectors/groups, $\Delta f_s=f_{s,t+n}^m-f_{s,t}^m$, $s\in S$.

To obtain an exact decomposition, we adopt the Shapley value-based decomposition framework. We then express the exact within-sector effects ${{\displaystyle \varphi }}_{\alpha W}^{Sh,m}$ and between-sector effects ${{\displaystyle \varphi }}_{\alpha B}^{Sh,m}$ of aggregate deprivation changes of source, m, as:

$${{\displaystyle \varphi }}_{\alpha W}^{Sh,m}= 0.5{{\displaystyle \sum }}_{s\in S}[f_{s,t}^m+f_{s,t+n}^m]\Delta P_{\alpha s}^m$$

(19)

$${{\displaystyle \varphi }}_{\alpha B}^{Sh,m}= 0.5{{\displaystyle \sum }}_{s\in S}[P_{\alpha s,t}^m+P_{\alpha s,t+n}^m]\Delta f_s^m$$

(20)

The overall change in deprivation, as expressed in Equation (18), can now be rewritten in terms of exactly two components: within-location changes in deprivation and between-location population shift effects:

$$\begin{gathered} \Delta P_{\alpha }^m= {{\displaystyle \varphi }}_{\alpha W}^{Sh,m}+ {{\displaystyle \varphi }}_{\alpha B}^{Sh,m} \\ =Within\text{-}location effects + Between\text{-}location population shifts effect \end{gathered}$$

(21)

The within-sector effects can be further decomposed into within-location growth and within-location redistribution effects, where the groups are urban, semi-urban, and rural locations.

3. Empirical Results and Discussions

It is worth noting that the statistical procedures outlined in the methodological section above are designed to identify impacts of policies or interventions on the level or distribution of the household wellbeing. However, due to the cross-sectional nature of the data we use, our estimation results are best interpreted as associations, rather than as impacts or causal effects, except in simulation scenarios where we appeal to a ceteris paribus assumption.

3.1. Determinants of Household Wellbeing

We report only results for estimations using the control function for the five countries studied, as the results from the OLS, 2SLS (residual inclusion method), and the reduced form estimates can be viewed in the Appendix A and Appendix B. The control function generalized residual version accounts for the potential endogeneity of health and labour market inputs into the wellbeing-generating function. The coefficients on the predicted residual for health, the interaction of health with its predicted residual, and the generalized residual for formal sector labour market participation are statistically different from zero. This statistical significance of the coefficients on the control function variables is the validation of our choice to prefer the control function estimates.

Table 1. Wellbeing-generating function estimates using the control function method. The dependent variable is the log of total household expenditure per adult equivalent.

Variables	Cameroon Col. (1)	Ethiopia Col. (2)	Kenya Col. (3)	Nigeria Col. (4)	Uganda Col. (5)
Health	0.415 ***	0.320 **	0.334 ***	0.814 ***	2.653 ***
	(0.161)	(0.155)	(0.086)	(0.269)	(0.591)
Health times year dummy				−1.606 ***
				(0.313)
Primary education (1 = yes and 0 = otherwise)	0.017	0.082 ***	0.146 ***	0.095 ***	0.107 ***
	(0.012)	(0.015)	(0.009)	(0.021)	(0.042)
Secondary education (1 = yes and 0 = otherwise)	0.089 ***	0.293 ***	0.282 ***	0.231 ***	0.209 ***
	(0.012)	(0.027)	(0.010)	(0.025)	(0.056)
Tertiary education (1 = yes and 0 = otherwise)	0.287 ***	0.529 ***	0.440 ***	0.588 ***	0.596 ***
	(0.017)	(0.031)	(0.011)	(0.030)	(0.085)
Age	−0.012 ***	−0.024 ***	−0.013 ***	−0.020 ***	−0.069 ***
	(0.002)	(0.002)	(0.001)	(0.004)	(0.008)
Age squared ×10−2	0.015 ***	0.030 ***	0.015 ***	0.025 ***	0.100 ***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
Gender (female = 1 and 0 = otherwise)	0.068 ***	0.085 ***	−0.066 ***	−0.072 *	0.057
	(0.015)	(0.025)	(0.011)	(0.040)	(0.057)
Rural area (1 = yes and 0 = otherwise)	−0.234 ***	−0.301 ***	−0.430 ***	−0.211 ***	−0.318 ***
	(0.011)	(0.020)	(0.009)	(0.019)	(0.050)
Married (1 = yes and 0 = otherwise)	−0.070 ***	−0.024	−0.094 ***	−0.248 ***	−0.269 ***
	(0.011)	(0.021)	(0.011)	(0.037)	(0.061)
Non-self-cluster average farmland ownership	−0.187 ***	−0.123 ***	−0.028 **	−0.302 ***	−0.340 ***
	(0.022)	(0.030)	(0.014)	(0.030)	(0.069)
Formal sector (1 = yes and 0 = otherwise)	0.627 ***	0.085 *	0.075 ***	0.123 **	−0.599 ***
	(0.042)	(0.047)	(0.017)	(0.057)	(0.223)
Locality A	−0.190 ***	−0.090 **	−0.068 ***	−0.279 ***	−0.732 ***
	(0.027)	(0.035)	(0.015)	(0.025)	(0.050)
Locality B	−0.199 ***	−0.229 ***	−0.104 ***	−0.397 ***	−0.711 ***
	(0.023)	(0.028)	(0.012)	(0.027)	(0.049)
Locality C	−0.467 ***	−0.046	−0.219 ***	−0.373 ***	−0.602 ***
	(0.016)	(0.028)	(0.012)	(0.025)	(0.094)
Locality D	−0.406 ***	−0.095 **	−0.137 ***	−0.092 ***
	(0.018)	(0.037)	(0.012)	(0.030)
Locality E	−0.380 ***	−0.173 ***	−0.136 ***	−0.138 ***
	(0.017)	(0.061)	(0.010)	(0.025)
Locality F	−0.135 ***	−0.351 ***
	(0.017)	(0.029)
Locality G	−0.110 ***	−0.247 ***
	(0.025)	(0.086)
Locality H	−0.112 ***
	(0.018)
Year dummy	0.341 ***	0.817 ***	0.847 ***	1.931 ***	0.500 ***
	(0.023)	(0.033)	(0.011)	(0.280)	(0.053)
Health residual	−0.569 ***	−0.473 ***	−0.420 ***	−0.914 ***	−2.386 ***
	(0.165)	(0.163)	(0.092)	(0.283)	(0.601)
Health times year dummy residual				1.667 ***
				(0.338)
Health times its residual	0.151 ***	0.143 *	0.205 ***	−0.020	−0.361 *
	(0.056)	(0.080)	(0.050)	(0.139)	(0.187)
Health times year dummy times its residual				−0.106
				(0.201)
Generalized residual for formal sector	−1.570 ***	−0.369	0.825 ***	−0.572 *	3.104 ***
	(0.242)	(0.291)	(0.110)	(0.327)	(1.200)
Constant	12.922 ***	9.085 ***	7.969 ***	11.260 ***	9.515 ***
	(0.160)	(0.159)	(0.082)	(0.257)	(0.400)
R-squared/adjusted R-squared	0.374/0.373	0.462/0.461	0.414/0.413	0.391/0.390	0.209/0.208
F-Stat [df; p-val]	544.77	459.00	1230.5	244.61	88.89
Prob > F	0.000	0.000	0.000	0.000	0.000
Number of observations	20,982	11,763	34,817	8794	6040

Source: Computed by authors. *** 1%, ** 5%, and * 10%. Notes: Values are reported in three decimal places. For Cameroon, the localities are A = Adamaoua, B = East, C = Extreme North, D = North, E = Northwest, F = West, G = South, and H = Southwest. For Ethiopia: A = Tigray, B = Amhara, C = Oromia, D = Somali, E = Benishangul Gumuz, F = SNNP, G = Gambelia. For Kenya: A = North East province, B = Eastern province, C = Rift Valley province, D = Western province, E = Nyanza province. For Nigeria: A = North Central, B = North East, C = North West, D = South East, E = South West. For Uganda: A = Eastern region, B = Northern region, C = Western region.

, Columns 1 to 5, shows that human health capital is positively and significantly related to household economic wellbeing in all five countries. These results indicate that a unit (percentage) increase in the health index (wellness) produces a 0.32 to 2.65 log-point increase in household economic wellbeing, with Uganda (Table 1, Column 5) registering the highest value and Ethiopia the lowest (Table 1, Column 2). The indirect effect of health, as captured by the interaction of health with its reduced-form residual, shows that the reduced-form unobservable variables significantly complement health in explaining household economic wellbeing in Cameroon, Ethiopia, and Kenya (Table 1, Columns 1 to 3). This is a technical point worth elaboration.

The coefficient on health is the direct effect of health on household wellbeing. As can be readily checked from the regression results, the coefficient on the interaction between health and its predicted residual (interaction term) is the indirect effect of health on household economic wellbeing. The indirect effects of health on wellbeing depend on the estimated coefficients of the interaction of wellness and its residual captured at the mean value of the residual. Table 1, in the case of Cameroon, Ethiopia, and Kenya, shows the indirect effects of health on household wellbeing to be positive and statistically significant. This is evidence of important complementarities between health and unobserved correlates of health in advancing household prosperity. In Uganda, the unobservable variables are substituting for health (reducing the direct effect) in explaining household economic wellbeing (Table 1, Column 5). In Nigeria, the substitution effect is statistically insignificant. Thus, in four of the five countries, there is evidence of important unobserved heterogeneities. These unobserved heterogeneities may originate from inherited genetic endowments from parents or geographical-based circumstances that are generally beyond individual or household control but are affecting the effect of health on wellbeing.

Table 1, Columns 1 to 5, suggests that, compared with no education, the positive and significant effects of levels of education on household welfare increase monotonically from a primary to a tertiary level of education. Comparing these effects by level of education reveals that Kenya registered the highest effect for a primary level of education (0.15 log-points), Ethiopia for secondary education (0.29 log-points), and Uganda for tertiary education (0.6 log-points). Thus, the promotion of human capital (education and health) would increase household wellbeing through two key mechanisms—namely, improved employment opportunities (Mincer, 1962) and the enhancement of the decision-making abilities of individuals (Becker, 1964; Grossman, 1972; T. Schultz, 1975).

Formal sector engagement is contingent on participation in the labour market and obtaining a job. In four of the five countries, Kenya, Ethiopia, Nigeria, and Cameroon, formal sector work is associated with 0.08 to 0.63 log-points of positive and significant effects on household welfare (Table 1, Columns 1 to 4). On the contrary, formal sector work tends to dampen household wellbeing in Uganda (by 0.59 log-points). This negative effect of formal sector work in Uganda is attributable to the possibility that there is a relatively high phenomenon of job mismatch, which is characterized as underemployment.

Age portrays a significant U-shaped relationship with household wellbeing in all five countries. The age range above which any additional year improves household welfare is between 35 and 45 years (Table 1, Columns 1 to 5). Deviating from the general beliefs about gender bias, female household heads have 0.07 to 0.09 log-points higher household income relative to their male counterparts in Cameroon and Ethiopia (Table 1, Columns 1 and 2). However, this finding is not evidence that the mean incomes of female heads in Cameroon and Ethiopia are higher than the average incomes of their male counterparts. Instead, the estimates show that female household headship in the two countries is correlated with factors that have higher income returns relative to factors that matter for male headship. For example, females with tertiary education or entrepreneurial talent might have higher chances of heading households in certain contexts.

Meanwhile, the incomes of female household heads in Kenya and Nigeria are 0.07 log-points less than those of their male counterparts. Land ownership, measured at the cluster level (Table 1), is negatively associated with household economic wellbeing in all countries studied. This finding likely reflects the difficulties that households in rural communities face in converting land into consumable or marketable produce. However, land in Africa is highly valued and much sought after, but arguably for non-income reasons (Berry, 1993). The prevalence of farmer–grassier conflicts may also be at the root of the estimated negative returns of land ownership.

Household heads residing in rural areas are 0.23 to 0.43 log-points less on an income scale compared to their urban counterparts, with Kenya registering the highest estimate (Table 1, Columns 1 to 5). As opposed to the general belief that there is a wellbeing premium in marriage, our results show that couples register welfare deficits in all five countries. In terms of regions, the main takeaway from Table 1 is that dwellers in localities that do not host the political or economic capital, as well as in regions that are arid or likely to suffer from droughts, registered household economic wellbeing deficits ranging from 0.04 log-points to 0.73 log-points in the five countries. Over time, households incurred wellbeing gains in the order of 0.34 to 1.93 log-points, with Nigeria recording the highest values.

Table 1 also reports the estimated coefficients of the generalized residuals for formal sector engagement in the five countries. A negative effect of the generalized residual suggests that a formal sector worker selected into the estimation sample enjoys a smaller amount of economic wellbeing than a formal sector worker drawn randomly from the general population. Meanwhile, a positive effect suggests that a formal sector worker selected into the estimation sample spends more than a formal sector worker drawn randomly from the general population. Specifically, in the case of Cameroon, because the sample mean of the generalized residual is 0.039 (see

Table A1. Descriptive statistics.

	Cameroon		Ethiopia		Kenya		Nigeria		Uganda
Variables	Mean	Sd.	Mean	Sd.	Mean	Sd.	Mean	Sd.	Mean	Sd.
Household expenditure per adult equivalent	723,665	737,539	15,391	18,119	5530	7224	121,822	169,100	22,904	104,601
Health	0.732	0.313	0.807	0.312	0.823	0.311	0.862	0.291	0.684	0.429
Health times year dummy							0.366	0.406
No education (1 = yes and 0 = otherwise)	0.221	0.415	0.472	0.499	0.238	0.426	0.116	0.320	0.157	0.364
Primary education (1 = yes and 0 = otherwise)	0.328	0.470	0.270	0.444	0.249	0.432	0.209	0.406	0.513	0.500
Secondary education (1 = yes and 0 = otherwise)	0.357	0.479	0.120	0.325	0.156	0.363	0.209	0.407	0.225	0.417
Tertiary education (1 = yes and 0 = otherwise)	0.092	0.289	0.121	0.326	0.133	0.340	0.127	0.333	0.072	0.259
Age	42.68	15.52	43.17	15.45	44.603	15.929	51.24	14.96	43.45	15.639
Age squared	2062	1531	2103	1527	2243	1632	2849	1630	2132	1550
Gender (female = 1 and 0 = otherwise)	0.278	0.448	0.305	0.460	0.324	0.468	0.150	0.357	0.303	0.460
Rural area (1 = yes and 0 = otherwise)	0.455	0.498	0.543	0.498	0.617	0.486	0.678	0.467	0.736	0.441
Married (1 = yes and 0 = otherwise)	0.558	0.497	0.681	0.466	0.712	0.453	0.799	0.400	0.724	0.447
Non-self-cluster average farmland ownership	0.340	0.240	0.385	0.267	0.489	0.255	0.565	0.317	0.510	0.195
Formal (1 = yes and 0 = otherwise)	0.167	0.373	0.178	0.382	0.143	0.350	0.163	0.369	0.244	0.429
Locality A	0.061	0.239	0.089	0.285	0.137	0.344	0.165	0.371	0.303	0.460
Locality B	0.075	0.263	0.055	0.228	0.095	0.294	0.153	0.360	0.230	0.421
Locality C	0.056	0.230	0.148	0.355	0.139	0.346	0.189	0.392	0.236	0.425
Locality D	0.119	0.323	0.041	0.197	0.059	0.235	0.159	0.366	0.230	0.421
Locality E	0.060	0.237	0.067	0.249	0.078	0.268	0.159	0.366
Locality F	0.081	0.272	0.052	0.222	0.178	0.383	0.175	0.380
Locality G	0.111	0.314	0.059	0.236	0.197	0.397
Locality H	0.101	0.302	0.150	0.357	0.115	0.319
Locality I	0.050	0.218	0.157	0.364
Locality J	0.090	0.286	0.075	0.263
Locality K			0.107	0.309
Year dummy	0.491	0.500	0.563	0.496	0.622	0.485			0.395	0.489
Health residual	−0.001	0.302	−0.010	0.288	−0.008	0.302	−0.001	0.279	−0.018	0.420
Health times year dummy residual							0.000	0.190
Health times its residual	0.089	0.141	0.074	0.150	0.084	0.140	0.077	0.115	0.162	0.173
Health times year dummy times its residual							0.035	0.083
Generalized residual for formal sector	0.039	0.049	−0.035	0.060	−0.057	0.057	−0.041	0.059	−0.060	0.077
Non-self-cluster average of health	0.732	0.089	0.807	0.099	0.823	0.107	0.801	0.105	0.681	0.130
Non-self-cluster average of health times year dummy							0.366	0.405
Non-self-cluster average of formal employment	0.167	0.136	0.177	0.166	0.143	0.147	0.155	0.164	0.240	0.128
Non-self-cluster average for labour market participation	0.932	0.085	0.721	0.159	0.869	0.165	0.880	0.103	0.850	0.125
Factual distribution for household expenditure per capita	787,107.8	781,335.1	15,447.9	18,160.9	5531.1	7224.7	121,431.6	170,008.4	23,012.4	104,929
Counterfactual distribution when human capital is equalized	735,009.3	720,076.2	18,955.8	21,115.9	6431.7	8006.7	301,665.9	540,281.1	66,134.7	863,941.7
Being sick (1 = yes and 0 = otherwise)	0.341	0.474	0.135	0.342	0.275	0.447	0.202	0.402	0.380	0.485
Visited a hospital for treatment (1 = yes and 0 = otherwise)	0.349	0.477	0.074	0.262	0.055	0.228	0.077	0.266	0.167	0.373
Visited a health centre for treatment (1 = yes and 0 = otherwise)	0.332	0.471	0.114	0.318	0.024	0.154	0.012	0.111	0.083	0.276
Consulted by a health practitioner (1 = yes and 0 = otherwise)	0.171	0.377	0.274	0.446	0.204	0.403	0.144	0.351	0.328	0.469

Source: Computed by authors. Notes: Values are reported in three decimal places. For Cameroon, the localities are A = Adamaoua, B = East, C = Extreme North, D = North, E = North West, F = West, G = South, and H = South West. For Ethiopia: A = Tigray, B = Amhara, C = Oromia, D = Somali, E = Benishangul Gumuz, F = SNNP, G = Gambelia. For Kenya: A = North East province, B = Eastern province, C = Rift Valley province, D = Western province, E = Nyanza province. For Nigeria: A = North Central, B = North East, C = North West, D = South East, E = South West. For Uganda: A = Eastern region, B = Northern region, C = Western region.

in the Appendix A), formal sector workers captured in the estimation sample are about 6.1% (0.039 × (−157)) less endowed in wellbeing compared to their counterparts randomly drawn from the general population. In the case of Nigeria, the sample mean of the generalized residual is −0.041 (see Table A1 in the Appendix A), which suggests that formal sector workers in the estimation sample are about 2.3% ((−0.041) × (−57.2)) more endowed in economic wellbeing relative to their counterparts randomly drawn from the general population. Lastly, it is worth noting that the estimated coefficients on dummy covariates can be adjusted as in Halvorsen and Palmquist (1980, p. 474).

3.2. Explaining Household Wellbeing Growth: The Shapley–Oaxaca–Blinder Decomposition Estimates

To gauge household wellbeing growth for each of the five countries in the study, we use the household wellbeing function and the Shapley–Oaxaca–Blinder decomposition framework to analyse the contributions of the different household income sources in explaining wellbeing growth (

Table 2. Components of household wellbeing growth—access and returns to endowment effects: Shapley–Oaxaca–Blinder decomposition.

	Cameroon			Ethiopia			Kenya			Nigeria			Uganda
Variables	AE Col. (1)	RE Col. (2)	Total Col. (3)	AE Col. (4)	RE Col. (5)	Total Col. (6)	AE Col. (7)	RE Col. (8)	Total Col. (9)	AE Col. (10)	RE Col. (11)	Total Col. (12)	AE Col. (13)	RE Col. (14)	Total Col. (15)
Health	−0.019	0.137	0.118	0.017	1.609	1.626	0.046	−1.358	−1.312	0.004	4.073	4.077	0.404	−5.839	−5.435
Primary education (1 = yes and 0 = otherwise)	0.000	−0.020	−0.020	−0.002	−0.009	−0.011	0.006	0.025	0.031	0.000	0.025	0.025	−0.001	0.074	0.073
Secondary education (1 = yes and 0 = otherwise)	0.002	−0.060	−0.058	0.011	0.004	0.015	0.006	0.040	0.046	0.000	0.037	0.037	0.001	0.129	0.130
Tertiary education (1 = yes and 0 = otherwise)	0.010	−0.039	−0.029	0.023	0.005	0.028	−0.014	0.077	0.063	0.006	0.022	0.028	0.011	0.073	0.084
Age	−0.019	0.683	0.664	0.049	−0.736	−0.687	−0.002	−1.337	−1.339	0.107	−5.142	−5.035	−0.262	1.707	1.445
Age squared	0.015	0.000	0.015	−0.038	0.423	0.385	0.003	0.425	0.428	−0.152	4.013	3.861	0.251	−1.297	−1.046
Gender (Female = 1 and 0 = otherwise)	0.001	−0.008	−0.007	0.001	0.058	0.059	−0.002	−0.007	−0.009	0.001	0.115	0.116	0.007	−0.244	−0.237
Rural area (1 = yes and 0 = otherwise)	−0.007	0.101	0.094	0.054	−0.057	−0.003	0.017	0.081	0.098	0.000	0.012	0.012	−0.006	−0.399	−0.405
Married (1 = yes and 0 = otherwise)	0.001	−0.014	−0.013	0.000	0.000	0.000	0.002	0.041	0.043	0.002	−0.777	−0.775	0.000	0.429	0.429
Non-self-cluster average farmland ownership	0.013	0.111	0.124	0.012	0.082	0.094	0.001	0.117	0.118	0.001	−0.041	−0.040	−0.016	−0.194	−0.210
Formal (1 = yes and 0 = otherwise)	−0.014	0.123	0.109	−0.001	0.010	0.009	−0.002	−0.008	−0.010	−0.002	0.008	0.006	−0.010	0.086	0.076
Locality A	−0.003	−0.014	−0.017	0.002	−0.010	−0.008	0.006	−0.046	−0.040	−0.002	−0.070	−0.072	−0.009	0.075	0.066
Locality B	−0.001	−0.005	−0.006	0.020	−0.002	0.018	−0.011	0.020	0.009	0.007	−0.024	−0.017	−0.021	0.074	0.053
Locality C	0.010	−0.051	−0.041	0.005	−0.001	0.004	−0.091	0.044	−0.047	−0.006	−0.035	−0.041	−0.001	0.219	0.218
Locality D	−0.009	−0.032	−0.041	−0.002	−0.022	−0.024	0.008	−0.039	−0.031	0.000	0.044	0.044
Locality E	0.013	−0.050	−0.037	−0.007	0.009	0.002	0.017	−0.011	0.006	−0.001	−0.105	−0.106
Locality F	0.003	−0.021	−0.018	0.045	−0.008	0.037
Locality G	−0.001	−0.009	−0.010	−0.013	0.001	−0.012
Locality H	0.002	−0.024	−0.022
Health residual	−0.004	0.000	−0.004	0.004	0.024	0.028	0.016	−0.009	0.007	0.004	0.015	0.019	−0.064	−0.132	−0.196
Health times year dummy residual										−0.099	−0.869
Health times its residual	0.000	0.046	0.046	−0.043	0.058	0.015	−0.023	−0.033	−0.056	−0.013	−0.001	−0.014	0.013	0.075	0.088
Health times year dummy times its residual										−0.019	−0.104
Generalized residual for formal sector employment	0.003	−0.133	−0.130	0.000	0.010	0.01	0.014	−0.051	−0.037	0.000	−0.005	−0.005	0.015	0.124	0.139
Constant	0.000	−0.678	−0.678	0.000	−1.067	−1.067	0.000	1.763	1.763	0.000	−1.936	−1.936	0.000	4.737	4.737
Total	−0.002	0.042	0.040	0.138	0.380	0.518	−0.003	−0.265	−0.268	−0.163	−0.744	−0.907	0.311	−0.303	0.008

Source: Computed by authors. Notes: Values are reported in three decimal places. The values are reported in log-points. AE = Access to Endowments. RE = Returns to Endowments. For Cameroon, the localities are A = Adamaoua, B = East, C = Extreme North, D = North, E = North West, F = West, G = South, and H = South West. For Ethiopia: A = Tigray, B = Amhara, C = Oromia, D = Somali, E = Benishangul Gumuz, F = SNNP, G = Gambelia. For Kenya: A = North East province, B = Eastern province, C = Rift Valley province, D = Western province, E = Nyanza province. For Nigeria: A = North Central, B = North East, C = North West, D = South East, E = South West. For Uganda: A = Eastern region, B = Northern region, C = Western region. Considering countries that registered growth in household wellbeing, we note three scenarios. In Cameroon, observed growth in household wellbeing was driven by the returns to endowment components rather than access to endowments (Table 2, Columns 1 and 2). In Ethiopia, both access (Table 2, Column 4) and returns (Table 2, Column 5) to endowments explained registered growth rates. In Uganda, while access to endowment components (Table 2, Column 13) enhanced the growth in household welfare, the returns to endowment components (Table 2, Column 14) eroded the growth. In countries that register growth deficits in household wellbeing, both the access and returns to endowment components contributed to dwindling growth in household welfare in Kenya (Table 2, Columns 7 and 8) and Nigeria (Table 2, Columns 10 and 11).

). Descriptive statistics of variables used to carry out the Shapley–Oaxaca–Blinder decompositions and the control function-generalized residual estimates by year used to implement the Shapley–Oaxaca–Blinder decompositions are available in the Appendix B.

Cameroon (2007–2014), Ethiopia (2013–2018), and Uganda (2005–2015) reported growth in household wellbeing of 0.04, 0.52, and 0.01 log-points, respectively (Table 2, Columns 3, 6, and 15). On the contrary, Kenya (2005–2015) and Nigeria (2010–2015) recorded deficits in household wellbeing growth of 0.27 and 0.91 log-points, respectively (Table 2, Columns 9 and 12).

To assess the net effects of the different household wellbeing sources, we considered the sum of access and returns to endowments components for the different sources of the wellbeing function (Table 2, Columns 3, 6, 9, 12, and 15). In all five countries, we observe the important role that human capital (health, education, and labour mobility) plays in enhancing growth in household welfare or in attenuating the effects of adverse factors. Additionally, we observe the relatively important role of returns to endowments in general, and particularly the returns associated with human capital in driving the welfare gaps in the five countries (See Table 2, Columns 3, 6, 9, 12, and 15).

We observe that human health capital is key in accounting for growth or deficits in household wellbeing. While in Cameroon, Ethiopia, and Nigeria (Table 2, Columns 3, 6 and 12), health largely explains growth in household wellbeing, in Kenya and Uganda, it largely accounts for the shortfalls in growth (Table 2, Columns 6 and 15). Education has a net positive effect on household wellbeing growth in all the countries in the study, except in Cameroon, where it has a negative net contribution to growth. In terms of formal sector employment, Table 2 shows that the net effect of formal sector employment on household welfare growth is positive in four of the five countries. In Kenya, the net effect of formal sector employment on welfare growth is negative, perhaps due to a large share of unregistered but profitable firms in the informal sector. Farmland ownership is household growth-ameliorating in Cameroon, Ethiopia, and Kenya (Table 2, Columns 3, 6 and 9), but household income growth-reducing in Nigeria and Uganda (Table 2, Columns 12 and 15).

Table 2 also shows that female household heads contribute positively towards expanding household welfare in Ethiopia and Nigeria (Table 2, Columns 6 and 12). Meanwhile, female headship is household income growth-eroding in Cameroon, Kenya and Uganda (Table 2, Columns 3, 9 and 15).

Although largely driven by returns to endowments, the location dummy in Table 2 suggests the following: (a) households residing in rural areas in Cameroon positively accounted for growth in household wellbeing, unlike the regional dummies—excluding the political and economic capitals (Table 2, Column 3); (b) rural households and regional dummies in Ethiopia, except for the Amhara, Oromia, Benishangul Gumuz, and SNNP provinces, negatively accounted for observed growth in household wellbeing (Table 2, Column 6); (c) rural Kenyan households, as well as those residing in the Eastern and Nyanza provinces, appear to contribute negatively to household wellbeing growth, unlike their urban counterparts and the other provinces (Table 2, Column 9); (d) residing in rural areas and the South East regions of Nigeria positively contributed to household welfare improvements relative to their urban colleagues and the other regions (Table 2, Column 12); and (e) whereas rural areas accounted negatively for growth in household welfare, regional dummies accounted positively to growth in household wellbeing (Table 2, Column 12).

3.3. Shared Prosperity Analysis

Table 3. Impact of human capital equalization on mean wellbeing among the 40% of the least well-off households.

Cameroon
	2007			2014
Location	Factual Col. (1)	Counterfactual Col. (2)	Impact:	Factual Col. (4)	Counterfactual Col. (5)	Impact:
			Abs. [Rel.] Col. (3)			Abs. [Rel.] Col. (6)
Urban	379,685.9	370,940.2	−8745.7 [−0.02]	358,274.9	373,181.1	14,906.2 [0.04]
Rural	194,339.9	190,941.0	−3398.9 [−0.02]	209,302.4	228,485.3	19,182.9 [0.09]
Cameroon	224,765.6	221,562.2	−3203.4 [−0.01]	252,823.2	273,202.8	20,379.6 [0.08]
Ethiopia
	2013			2018
Location	Factual	Counterfactual	Impact:	Factual	Counterfactual	Impact:
			Abs. [Rel.]			Abs. [Rel.]
Urban	4169.0	5232.8	1063.8 [0.26]	9586.7	11,885.1	2298.4 [0.24]
Rural	2443.1	3450.4	1007.3 [0.41]	5300.1	7061.2	1761.1 [0.33]
Ethiopia	2596.6	3649.9	1053.3 [0.41]	5952.5	7878.9	1926.4 [0.32]
Kenya
	2005			2015
Location	Factual	Counterfactual	Impact:	Factual	Counterfactual	Impact:
			Abs. [Rel.]			Abs. [Rel.]
Urban	1307.1	1546.7	239.6 [0.18]	3550.9	4178.1	627.2 [0.18]
Rural	877.5	1038.1	160.6 [0.18]	2178.5	2659.2	480.7 [0.22]
Kenya	938.6	1113.0	174.4 [0.19]	2404.1	2927.9	523.8 [0.22]
Nigeria
	2010			2015
Location	Factual	Counterfactual	Impact:	Factual	Counterfactual	Impact:
			Abs. [Rel.]			Abs. [Rel.]
Urban	46,155.9	54,174.7	8018.8 [0.17]	77,318.9	236,015.5	158,696.6 [2.05]
Rural	26,706.7	33,189.9	6483.2 [0.24]	43,517.6	145,297.3	101,779.7 [2.34]
Nigeria	31,308.7	38,692.6	7383.9 [0.24]	50,737.3	167,429.2	116,691.9 [2.30]
Uganda
	2005			2015
Location	Factual	Counterfactual	Impact:	Factual	Counterfactual	Impact:
			Abs. [Rel.]			Abs. [Rel.]
Urban	2798.7	2494.7	−304 [−0.11]	7076.7	5275.1	−1801.6 [−0.25]
Rural	1721.3	1804.7	83.4 [0.05]	3676.1	2813.6	−862.5 [−0.23]
Uganda	1909.8	1932.6	22.8 [0.01]	4135.4	3137.8	−997.6 [−0.24]

Source: Computed by authors using the software component by Barriga-Cabanillas (2014). Notes: Values for Cameroon are reported in FCFA; Ethiopia in Ethiopian birr; Kenya in Kenyan shilling; Nigeria in Naira; Uganda in Ugandan shilling. Relative values in brackets.

and

Table 4. Impact of equalizing human capital on shared prosperity among 40% of the least well-off.

Location	Factual Col. (1)	Counterfactual Col. (2)	Impact: Abs. [Rel.] Col. (3)
Cameroon (2007–2014)
Urban	−0.83 (1.36)	0.09 (2.40)	0.92 [1.11]
Rural	1.07 (4.70)	2.60 (5.90)	1.53 [1.43]
Overall	1.69 (3.56)	3.04 (4.67)	1.35 [0.80]
Ethiopia (2013–2018)
Urban	18.1 (21.6)	17.8 (20.5)	−0.3 [0.02]
Rural	16.7 (19.8)	15.4 (18.1)	−1.3 [0.08]
Overall	18.0 (21.7)	16.6 (19.8)	−1.4 [0.08]
Kenya (2005–2015)
Urban	10.5 (6.98)	10.4 (6.42)	−0.10 [0.01]
Rural	9.52 (7.41)	9.86 (7.36)	0.34 [0.04]
Overall	9.86 (7.81)	10.2 (7.49)	0.34 [0.04]
Nigeria (2010–2015)
Urban	10.9 (12.8)	34.2 (35.2)	23.3 [2.14]
Rural	10.3 (11.3)	34.4 (32.8)	24.1 [2.34]
Overall	10.1 (11.9)	34.0 (33.8)	23.9 [2.37]
Uganda (2005–2015)
Urban	152.8 (76.3)	111.5 (135.8)	−41.3 [0.27]
Rural	113.6 (44.6)	55.9 (16.4)	−57.7 [0.51]
Overall	116.5 (56.6)	62.4 (51.5)	−54.1 [0.46]

Source: Computed by authors using software component by Barriga-Cabanillas (2014). Notes: Relative values in square brackets [ ]. Overall annualized growth in parentheses ( ).

report the results of shared prosperity, whilst

Table 5. Inequality impacts of equalizing human capital endowments: Palma ratios.

Variable	Factual Col. (1)	Counterfactual Col. (2)	Impact: Abs [Rel.] Col. (3)
Cameroon (2007–2014)
Urban	1.88	1.96	0.08 [0.04]
Rural	1.82	1.97	0.15 [0.08]
Cameroon	2.03	2.10	0.07 [0.03]
Ethiopia (2013–2015)
Urban	2.36	2.16	−0.20 [0.08]
Rural	2.46	2.31	−0.15 [0.06]
Ethiopia	3.09	2.67	−0.42 [0.14]
Kenya (2005–2015)
Urban	2.34	2.15	−0.19 [0.08]
Rural	1.95	1.93	−0.02 [0.01]
Kenya	2.53	2.34	−0.19 [0.08]
Nigeria (2010–2015)
Urban	2.39	5.01	2.62 [1.10]
Rural	2.36	4.72	2.36 [1.00]
Nigeria	2.64	5.11	2.47 [0.94]
Uganda (2005–2015)
Urban	17.8	70.6	52.8 [2.97]
Rural	7.16	27.3	20.1 [2.81]
Uganda	12.7	45.0	32.3 [2.54]

Source: Computed by authors.

displays the Palma ratios. Table 3 suggests that over the period under review for each country (Cameroon 2007 and 2014; Ethiopia 2013 and 2018; Kenya 2005 and 2015; Nigeria 2010 and 2015; and Uganda 2005 and 2015), the average expenditure of households at the 40th percentile of the wellbeing distribution increases when human capital inequality is eliminated in the counterfactual distribution, except in Cameroon in 2007 (Table 3, Column 3) and Uganda in 2015 (Table 3, Column, 6). In addition, the relative gains reported across locations (overall, urban and rural) are higher in rural areas than in urban areas and in all locations. This points to the observation that the bottom 40% of the population registered far greater improvements in wellbeing in rural areas than in urban areas.

Table 4 enables the assessment of shared prosperity and its nature in all five countries. Column 1 shows that in the factual distribution, shared prosperity is depicted overall and by location, except for urban Cameroon. In addition, Uganda (2005–2015) and Ethiopia (2013–2018) reveal high rates of growth in household wellbeing of the bottom 40 per cent of the wellbeing distribution. Except for Cameroon, urban areas in other countries experienced higher rates of shared prosperity than their rural counterparts in the factual distribution.

Considering the counterfactual distribution (Table 4, Column 2), we observe that the bottom 40th percentile registered positive growth overall and for both rural and urban areas in the five countries. The higher values for urban areas imply that putting in place interventions that level human capital differences would lead to shared prosperity improvements, more so in urban than in rural locations. Additionally, equalizing human capital is shared prosperity-enhancing in Cameroon, Kenya (excluding urban Kenya), and Nigeria overall and by location, as revealed by the growth rates of the bottom forty per cent in the counterfactual relative to the factual distribution (Table 4, Column 2 versus Column 1). While Ethiopia and Uganda registered shared prosperity in the counterfactual distributions, the shared prosperity rates were lower than in the corresponding factual distributions.

In terms of shared prosperity premium, Kenya stands out distinctly in registering shared prosperity premiums in both the factual and counterfactual distributions—overall and by location. In both factual and counterfactual distributions, Uganda registered shared prosperity premiums overall and in rural settings. In addition, Nigeria registered shared prosperity premiums in the counterfactual distribution overall and in rural areas. (Table 4, Column 2). Meanwhile, Cameroon and Ethiopia experienced shared prosperity deficits in both distributions over the periods under analysis. This is an indication that in these two countries, although the share of benefits from growth accruing to the population increased over the different periods under review, the 40% least well-off households gained proportionately less from the rising prosperity compared to their well-off counterparts.

To assess inequality between households at the bottom and top of the distributions, Table 5 presents the Palma ratios for the factual and counterfactual distributions. Results illustrate that in all five countries, in both distributions, inequality is worsening between the top 10% and the bottom 40% of the less well-off. Particularly, in Cameroon, Nigeria, and Uganda, equalizing human capital endowments is inequality-increasing in the counterfactual distribution between the richest 10th percentile and the bottom 40th percentile compared to the factual distribution (Table 5, Columns 2 versus 1). This outcome is probably due to lower returns to higher stocks of human capital endowments among the least well-off, engendered by equalization. On the contrary, the negative inequality impacts for Kenya and Ethiopia suggest that eliminating human capital disparities is Palma ratio-decreasing in the counterfactual distribution. This is a signal that by adopting interventions that level disparities in human capital in Ethiopia and Kenya, the shares of average household expenditure of the top 10th percentile of the population in terms of wellbeing divided by the bottom 40th percentile would decrease over time. Thus, allowing interventions that level the playing field in terms of human capital differences would have an inequality-reducing tendency between the tails of the distribution of wellbeing. The findings in Table 4 and Table 5 suggest that the growth and inequality effects of human capital equalization are context-specific.

3.4. The Role of Human Capital Endowments on Poverty and Inequality

Table 6. Effect of human capital equalization on household income poverty.

Cameroon
	Factual P0 Col. (1)	Counterfactual P0 Col. (2)	Change P0 Col. (3)	Factual P1 Col. (4)	Counterfactual P1 Col. (5)	Change P1 Col. (6)	Factual P2 Col. (7)	Counterfactual P2 Col. (8)	Change P2 Col. (9)
Urban	0.168 ***	0.165 ***	−0.003 ***	0.049 ***	0.047 ***	−0.002 ***	0.021 ***	0.020 ***	−0.001 ***
	(0.007)	(0.007)	(0.004)	(0.002)	(0.002)	(0.001)	(0.001)	(0.001)	(0.000)
Rural	0.508 ***	0.477 ***	−0.031 ***	0.180 ***	0.170 ***	−0.010 ***	0.084 ***	0.080 ***	−0.004 ***
	(0.011)	(0.012)	(0.005)	(0.005)	(0.005)	(0.001)	(0.003)	(0.003)	(0.001)
Overall	0.375 ***	0.355 ***	−0.020 ***	0.129 ***	0.122 ***	−0.006 ***	0.059 ***	0.056 ***	−0.003 ***
	(0.010)	(0.009)	(0.003)	(0.004)	(0.004)	(0.001)	(0.002)	(0.002)	(0.001)
Ethiopia
	Factual P0	Counterfactual P0	Change P0	Factual P1	Counterfactual P1	Change P1	Factual P2	Counterfactual P2	Change P2
Urban	0.065 ***	0.033 ***	−0.032 ***	0.017 ***	0.008 ***	−0.009 ***	0.007 ***	0.003 ***	−0.004 ***
	(0.008)	(0.005)	(0.005)	(0.002)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)
Rural	0.251 ***	0.116 ***	−0.135 ***	0.074 ***	0.029 ***	−0.045 ***	0.031 ***	0.012 ***	−0.019 ***
	(0.015)	(0.010)	(0.009)	(0.005)	(0.003)	(0.002)	(0.002)	(0.001)	(0.001)
Overall	0.210 ***	0.098 ***	−0.112 ***	0.061 ***	0.025 ***	−0.036 ***	0.025 ***	0.009 ***	−0.016 ***
	(0.012)	(0.007)	(0.007)	(0.004)	(0.002)	(0.002)	(0.002)	(0.001)	(0.001)
Kenya
	Factual P0	Counterfactual P0	Change P0	Factual P1	Counterfactual P1	Change P1	Factual P2	Counterfactual P2	Change P2
Urban	0.191 ***	0.147 ***	−0.044 ***	0.070 ***	0.052 ***	−0.018 ***	0.036 ***	0.026 ***	−0.010 ***
	(0.011)	(0.010)	(0.003)	(0.005)	(0.004)	(0.001)	(0.003)	(0.002)	(0.001)
Rural	0.425 ***	0.337 ***	−0.087 ***	0.172 ***	0.130 ***	−0.042 ***	0.093 ***	0.068 ***	−0.025 ***
	(0.009)	(0.009)	(0.003)	(0.005)	(0.004)	(0.001)	(0.003)	(0.003)	(0.001)
Overall	0.361 ***	0.285 ***	−0.075 ***	0.144 ***	0.109 ***	−0.035 ***	0.077 ***	0.056 ***	−0.021 ***
	(0.007)	(0.007)	(0.002)	(0.004)	(0.003)	(0.001)	(0.002)	(0.002)	(0.001)
Nigeria
	Factual P0	Counterfactual P0	Change P0	Factual P1	Counterfactual P1	Change P1	Factual P2	Counterfactual P2	Change P2
Urban	0.182 ***	0.109 ***	−0.073 ***	0.054 ***	0.031 ***	−0.023 ***	0.023 ***	0.013 ***	0.010 ***
	(0.020)	(0.013)	(0.010)	(0.007)	(0.005)	(0.003)	(0.004)	(0.003)	(0.001)
Rural	0.466 ***	0.228 ***	−0.237 ***	0.170 ***	0.085 ***	−0.085 ***	0.085 ***	0.043 ***	−0.042 ***
	(0.015)	(0.009)	(0.010)	(0.007)	(0.005)	(0.003)	(0.004)	(0.003)	(0.002)
Overall	0.361 ***	0.184 ***	−0.176 ***	0.128 ***	0.065 ***	−0.063 ***	0.062 ***	0.032 ***	−0.030 ***
	(0.017)	(0.010)	(0.009)	(0.007)	(0.004)	(0.003)	(0.004)	(0.002)	(0.001)
Uganda
	Factual P0	Counterfactual P0	Change P0	Factual P1	Counterfactual P1	Change P1	Factual P2	Counterfactual P2	Change P2
Urban	0.127 ***	0.182 ***	0.054 ***	0.056 ***	0.080 ***	0.024 ***	0.035 ***	0.049 ***	0.014 ***
	(0.023)	(0.020)	(0.014)	(0.012)	(0.012)	(0.004)	(0.009)	(0.009)	(0.003)
Rural	0.240 ***	0.276 ***	0.036 ***	0.107 ***	0.128 ***	0.021 ***	0.063 ***	0.079 ***	0.015 ***
	(0.017)	(0.013)	(0.010)	(0.009)	(0.008)	(0.004)	(0.006)	(0.005)	(0.003)
Overall	0.214 ***	0.254 ***	0.040 ***	0.095 ***	0.117 ***	0.022 ***	0.057 ***	0.072 ***	0.015 ***
	(0.015)	(0.010)	(0.008)	(0.008)	(0.007)	(0.003)	(0.005)	(0.005)	(0.002)

Source: Computed by authors using the DASP software (version 2.1). Notes: Values in parentheses are standard errors. *** 1%, ** 5%, and * 10%. P₀: poverty incidence; P₁: poverty depth; P₂: poverty severity. Poverty lines of the counterfactual distribution are calculated using a non-parametric approach to correspond to the official factual distribution poverty lines reported by the National Institute of Statistics for each country.

shows factual and counterfactual poverty indices, and

Table 7. Impact of human capital equalization on Gini income inequality.

Cameroon
	Factual Col. (1)	Counterfactual Col. (2)	Change Col. (3)
Urban	0.382 ***	0.390 ***	0.008 ***
	(0.005)	(0.005)	(0.001)
Rural	0.377 ***	0.392 ***	0.015 ***
	(0.004)	(0.004)	(0.001)
Overall	0.413 ***	0.419 ***	0.006 ***
	(0.004)	(0.004)	(0.001)
Ethiopia
	Factual	Counterfactual	Change
Urban	0.430 ***	0.416 ***	−0.014 ***
	(0.012)	(0.012)	(0.001)
Rural	0.418 ***	0.412 ***	−0.006 ***
	(0.010)	(0.010)	(0.001)
Overall	0.451 ***	0.432 ***	−0.019 ***
	(0.008)	(0.008)	(0.001)
Kenya
	Factual	Counterfactual	Change
Urban	0.434 ***	0.411 ***	−0.023 ***
	(0.011)	(0.009)	(0.002)
Rural	0.382 ***	0.379 ***	−0.003 ***
	(0.004)	(0.004)	(0.001)
Overall	0.439 ***	0.420 ***	−0.019 ***
	(0.006)	(0.005)	(0.001)
Nigeria
	Factual	Counterfactual	Change
Urban	0.417 ***	0.533 ***	0.116 ***
	(0.011)	(0.011)	(0.007)
Rural	0.413 ***	0.522 ***	0.109 ***
	(0.010)	(0.008)	(0.003)
Overall	0.439 ***	0.538 ***	0.099 ***
	(0.009)	(0.007)	(0.004)
Uganda
	Factual	Counterfactual	Change
Urban	0.652 ***	0.802 ***	0.150 ***
	(0.018)	(0.019)	(0.018)
Rural	0.539 ***	0.754 ***	0.214 ***
	(0.011)	(0.007)	(0.011)
Overall	0.618 ***	0.781 ***	0.162 ***
	(0.013)	(0.009)	(0.012)

Source: Computed by authors using the DASP software by Araar and Duclos (2009). Notes: Values in parentheses are standard errors. *** 1%, ** 5%, and * 10%.

indicates the impact of human capital equalization on inequality in all five countries. We employ the Foster–Greer and Thorbecke indices for the incidence, depth/intensity, and severity of poverty. Table 6, Columns 3, 6, and 9, portrays the changes in the incidence, depth, and severity of poverty when we compare the counterfactual and the factual distributions. These results show that levelling human capital disparities reduces the incidence, depth, and severity of poverty in Cameroon, Ethiopia, Kenya, and Nigeria.

In Table 6, the poverty reduction gains were higher in rural than in urban areas in these four countries. Results also indicate that eliminating human capital differences, achievements in reducing the incidence and depth of poverty become more pronounced in Nigeria and Ethiopia (Table 6, Columns 3 and 6). Meanwhile, Nigeria and Kenya registered the greatest success in the alleviation of the severity of poverty—that is, in reducing the inequality among the poor (Table 6, Column 9). However, equalizing human capital disparities is poverty-exacerbating in all three measures in Uganda. This is some indication that the actual distribution of human capital is inequality-reducing in Uganda.

Regarding the dynamics of inequality measured by Gini in Table 7 above, we observe that equalizing human capital disparities as in the counterfactual distribution reduced inequality overall and by location in Ethiopia and Kenya (Table 7, Column 3). Considering the urban–rural dynamics in Ethiopia and Kenya, the differences between the counterfactual and factual distributions show that the inequality-reducing tendency due to human capital equalization is more of an urban than a rural phenomenon. On the contrary, levelling disparities in human capital is Gini inequality-increasing in Uganda, Nigeria, and Cameroon by large orders of magnitude (Table 7, Column 3). In addition, an increase in inequality became more acute in rural areas in Cameroon and Uganda and more severe in urban areas in Nigeria, unlike in their rural counterparts after equalization.

3.5. Components of Inter-Temporal Changes in Human Capital Deprivations

Estimates of Human Capital Deprivations

The monetary poverty and human capital income source cut-off points are shown in

Table A3. Monetary poverty and human capital income source deprivation lines.

Country	Monetary Poverty Lines	Human Capital Deprivation Lines
Cameroon	369,100	441,500
Ethiopia	7510	6010
Kenya	1295	1556
Nigeria	24,410	293,500
Uganda	45,240	40,790

Source: computed by authors. Notes: Values for Cameroon are reported in FCFA. Ethiopia in Ethiopian birr; Kenya in Kenyan shilling; Nigeria in Naira; Uganda in Ugandan shilling.

and

Table A4. Weighted descriptive statistics of the human capital income source.

	Observations	Mean	Standard Deviation	Minimum	Maximum
Cameroon
Initial period–2007	10,679	451,076	50,305	281,468	601,633
Final period–2014	10,303	380,697	50,599	217,734	538,159
Pooled survey	20,982	411,810	61,391	217,734	601,633
Ethiopia
Initial period–2013	4993	6465	1921	3144	14,002
Final period–2018	6770	8261	2130	4797	14,678
Pooled survey	11,763	7446	2226	3144	14,678
Kenya
Initial period–2005	13,158	1339	653	479	2507
Final period–2015	21,746	1632	782	594	3085
Pooled survey	34,904	1621	783	576	3085
Nigeria
Initial period–2010	4763	297,172	22,962	251,755	354,676
Final period–2015	4034	33,270	23,068	0.044	94,795
Pooled survey	8797	171,528	133,800	0.044	354,676
Uganda
Initial period–2005	3678	40,644	7735	10,017	62,698
Final period–2015	2371	45,421	8896	8366	67,892
Pooled survey	6049	43,539	8772	8366	67,892

Source: Computed by authors. Notes: Values for Cameroon are reported in FCFA. Ethiopia in Ethiopian birr; Kenya in Kenyan shilling; Nigeria in Naira; Uganda in Ugandan shilling.

in Appendix A.

Table 8. Human capital deprivations by location.

Cameroon
	2007				2014
	Population share Col. (1)	Incidence of deprivation Col. (2)	Depth of deprivation Col. (3)	Severity of deprivation Col. (4)	Population share Col. (5)	Incidence of deprivation Col. (6)	Depth of deprivation Col. (7)	Severity of deprivation Col. (8)
Urban	0.353 ***	0.108 ***	0.008 ***	0.0005 ***	0.423 ***	0.137 ***	0.012 ***	0.002 ***
	(0.017)	(0.007)	(0.001)	(0.0001)	(0.006)	(0.005)	(0.001)	(0.0001)
Rural	0.647 ***	0.376 ***	0.029 ***	0.004 ***	0.577 ***	0.316 ***	0.032 ***	0.004 ***
	(0.017)	(0.014)	(0.002)	(0.0001)	(0.006)	(0.008)	(0.001)	(0.0001)
Overall		0.484 ***	0.037 ***	0.004 ***		0.452 ***	0.044 ***	0.006 ***
		(0.011)	(0.001)	(0.0001)		(0.009)	(0.001)	(0.0001)
Ethiopia
	2013				2018
	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation
Urban	0.185 ***	0.082 ***	0.011 ***	0.002 ***	0.264 ***	0.102 ***	0.008 ***	0.001 ***
	(0.018)	(0.009)	(0.001)	(0.0002)	(0.025)	(0.011)	(0.001)	(0.0001)
Rural	0.815 ***	0.509 ***	0.051 ***	0.007 ***	0.736 ***	0.421 ***	0.032 ***	0.003 ***
	(0.019)	(0.017)	(0.002)	(0.001)	(0.025)	(0.022)	(0.002)	(0.0003)
Overall		0.591 ***	0.062 ***	0.009 ***		0.523 ***	0.040 ***	0.004 ***
		(0.013)	(0.002)	(0.001)		(0.018)	(0.002)	(0.0003)
Kenya
	2005				2015
	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation
Urban	0.235 ***	0.145 ***	0.043 ***	0.013 ***	0.304 ***	0.168 ***	0.021 ***	0.003 ***
	(0.013)	(0.009)	(0.002)	(0.001)	(0.011)	(0.008)	(0.001)	(0.0002)
Rural	0.765 ***	0.539 ***	0.171 ***	0.056 ***	0.696 ***	0.555 ***	0.078 ***	0.014 ***
	(0.013)	(0.011)	(0.004)	(0.001)	(0.011)	(0.010)	(0.001)	(0.001)
Overall		0.684 ***	0.214 ***	0.069 ***		0.722 ***	0.097 ***	0.017 ***
		(0.009)	(0.003)	(0.001)		(0.007)	(0.001)	(0.001)
Nigeria
	2010				2015
	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation
Urban	0.366 ***	0.171 ***	0.008 ***	0.001 ***	0.357 ***	0.134 ***	0.056 ***	0.029 ***
	(0.024)	(0.015)	(0.001)	(0.0001)	(0.023)	(0.013)	(0.006)	(0.003)
Rural	0.634 ***	0.473 ***	0.020 ***	0.001 ***	0.643 ***	0.414 ***	0.198 ***	0.112 ***
	(0.024)	(0.020)	(0.001)	(0.0001)	(0.023)	(0.019)	(0.011)	(0.008)
Overall		0.644 ***	0.028 ***	0.002 ***		0.549 ***	0.254 ***	0.141 ***
		(0.012)	(0.001)	(0.0001)		(0.015)	(0.010)	(0.007)
Uganda
	2005				2015
	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation	Population share	Incidence of deprivation	Depth of deprivation	Severity of deprivation
Urban	0.240 ***	0.078 ***	0.011 ***	0.003 ***	0.231 ***	0.068 ***	0.009 ***	0.002 ***
	(0.023)	(0.009)	(0.001)	(0.001)	(0.023)	(0.009)	(0.001)	(0.001)
Rural	0.760 ***	0.382 ***	0.053 ***	0.013 ***	0.769 ***	0.363 ***	0.053 ***	0.014 ***
	(0.023)	(0.018)	(0.003)	(0.001)	(0.023)	(0.021	(0.003)	(0.001)
Overall		0.459 ***	0.064 ***	0.016 ***		0.431 ***	0.063 ***	0.016 ***
		(0.017)	(0.003)	(0.001)		(0.019)	(0.003)	(0.001)

Source: Computed using DAD 4.6 software. Notes: Figures in parentheses represent standard errors. Results are reported in three decimal places. These are absolute contributions. *** 1%, ** 5%, and * 10%.

shows results of the incidence (Table 8, Columns 2 and 6), depth (Table 8, Columns 3 and 7), and severity (Table 8, Columns 4 and 8) of human capital deprivations. The evolution of the population shares (

Table 9. Growth and redistribution decomposition of changes in human capital deprivation.

Cameroon	Growth Component Col. (1)	Redistribution Component Col. (2)	$\Delta P_0$ Col. (3)	Growth Component Col. (4)	Redistribution Component Col. (5)	$\Delta P_1$ Col. (6)	Growth Component Col. (7)	Redistribution Component Col. (8)	$\Delta P_2$ Col. (9)
Urban	−0.013	−0.020	−0.033	−0.002	0.013	0.011	−0.0003	0.003	0.0033
	(0.004)	(0.004)	(0.018)	(0.002)	(0.002)	(0.002)	(0.0004)	(0.0004)	(0.001)
Rural	−0.017	0.033	0.016	−0.002	0.008	0.006	−0.0002	0.001	0.0012
	(0.001)	(0.001)	(0.015)	(0.001)	(0.001)	(0.001)	(0.001)	(0.001)	(0.0002)
Overall	−0.029	−0.003	−0.032	−0.004	0.011	0.007	−0.001	0.003	0.002
	(0.002)	(0.002)	(0.014)	(0.001)	(0.001)	(0.001)	(0.002)	(0.002)	(0.0004)
Ethiopia	Growth Component	Redistribution Component	$\Delta P_0$	Growth Component	Redistribution Component	$\Delta P_1$	Growth Component	Redistribution Component	$\Delta P_2$
Urban	−0.078	0.028	−0.050	−0.012	−0.007	−0.019	−0.002	−0.002	−0.004
	(0.006)	(0.006)	(0.028)	(0.005)	(0.005)	(0.003)	(0.001)	(0.001)	(0.001)
Rural	0.063	−0.119	−0.056	0.012	−0.041	−0.029	0.002	−0.010	−0.008
	(0.013)	(0.013)	(0.030)	(0.007)	(0.007)	(0.005)	(0.001)	(0.001)	(0.001)
Overall	−0.081	0.015	−0.066	−0.013	−0.009	−0.022	−0.002	−0.003	−0.005
	(0.005)	(0.005)	(0.013)	(0.005)	(0.005)	(0.003)	(0.001)	(0.001)	(0.001)
Kenya	Growth Component	Redistribution Component	$\Delta P_0$	Growth Component	Redistribution Component	$\Delta P_1$	Growth Component	Redistribution Component	$\Delta P_2$
Urban	−0.016	−0.051	−0.067	−0.124	0.009	−0.115	−0.050	0.005	−0.045
	(0.022)	(0.022)	(0.024)	(0.009)	(0.009)	(0.006)	(0.002)	(0.002)	(0.001)
Rural	−0.001	0.094	0.093	−0.066	−0.045	−0.111	−0.029	−0.024	−0.053
	(0.001)	(0.001)	(0.012)	(0.007)	(0.007)	(0.004)	(0.003)	(0.003)	(0.001)
Overall	−0.001	0.038	0.0395	−0.096	−0.019	−0.115	−0.042	−0.010	−0.052
	(0.003)	(0.003)	(0.011)	(0.006)	(0.006)	(0.003)	(0.002)	(0.002)	(0.001)
Nigeria	Growth Component	Redistribution Component	$\Delta P_0$	Growth Component	Redistribution Component	$\Delta P_1$	Growth Component	Redistribution Component	$\Delta P_2$
Urban	−0.272	0.180	−0.092	−0.062	0.199	0.137	−0.043	0.123	0.080
	(0.013)	(0.013)	(0.035)	(0.002)	(0.002)	(0.002)	(0.001)	(0.001)	(0.008)
Rural	−0.375	0.275	−0.100	−0.034	0.311	0.277	−0.015	0.190	0.175
	(0.019)	(0.019)	(0.021)	(0.004)	(0.004)	(0.013)	(0.003)	(0.003)	(0.010)
Overall	−0.352	0.257	−0.095	−0.052	0.279	0.227	−0.032	0.173	0.141
	(0.007)	(0.007)	(0.020)	(0.002)	(0.002)	(0.010)	(0.001)	(0.001)	(0.007)
Uganda	Growth Component	Redistribution Component	$\Delta P_0$	Growth Component	Redistribution Component	$\Delta P_1$	Growth Component	Redistribution Component	$\Delta P_2$
Urban	−0.053	0.024	−0.029	−0.004	−0.0015	−0.006	−0.001	−0.002	−0.003
	(0.009)	(0.009)	(0.040)	(0.004)	(0.004)	(0.007)	(0.001)	(0.001)	(0.002)
Rural	−0.008	−0.022	−0.030	−0.0011	0.0003	−0.0008	−0.0003	0.0010	0.0007
	(0.001)	(0.001)	(0.031)	(0.004)	(0.004)	(0.003)	(0.001)	(0.001)	(0.001)
Overall	−0.016	−0.013	−0.029	−0.002	0.0002	−0.0022	−0.0005	0.0004	−0.0001
	(0.002)	(0.002)	(0.025)	(0.003)	(0.003)	(0.004)	(0.0009)	(0.0009)	(0.0001)

Source: Computed using DAD 4.6. Notes: Figures in parentheses represent standard errors. Results are reported in three decimal places.

, Columns 1 and 5) suggests that in Cameroon (2007–2014), Ethiopia (2013–2018), and Kenya (2005–2015), rural areas experienced declining population shares in contrast to urban areas. This may reflect rural–urban migration. Meanwhile, in Nigeria and Uganda, rural population shares increased, and urban population shares contracted—a possible reflection of reverse migration. These shares inform the weights used to compute changes in the incidence, depth, and severity of human capital poverty. The incidence of human capital deprivation declined in four of the five countries in the periods under study. Only in Kenya did the incidence of human capital poverty worsen.

3.6. Estimates of the Growth and Redistribution Effects of Changes in Human Capital Deprivations

Table 9 presents the growth and redistribution effects of intertemporal changes in human capital deprivation. In all five countries, we observe the important role of growth in attenuating the incidence, depth, and severity of human capital poverty (Table 9, Columns 1, 4 and 7). There is some indication that growth might be a credible channel to improve human capital endowments.

The largest effects of growth on the incidence of human capital deprivation were registered in Nigeria and Ethiopia and in Kenya and Nigeria for the depth and severity of human capital deprivation. In addition, the results suggest that to eradicate human capital deprivations in a substantive way in all five countries, there is a need for interventions that enhance human capital both in urban and rural areas.

The ability of the redistribution component to alleviate human capital deprivation is less systematic (Table 9, Columns 2, 5, and 9) than the case of the growth component. However, we observe higher benefits in mitigating human capital deprivations in situations where the redistribution components are negative. These results indicate that to significantly reduce human capital deprivation, interventions that improve investments in human capital are likely to be more inclusive than those that redistribute it in the process of bridging disparities in these endowments. However, in countries like Ethiopia and Uganda that register declining overall incidence, depth, and severity of human capital deprivation, we observe that the redistribution components declined overall and by location, especially in Ethiopia. For Uganda, the redistribution component was negative for the incidence of deprivation and only in urban areas for the depth and severity of human capital deprivation.

On the contrary, in countries with worsening overall incidence or depth and severity of human capital deprivation, like Kenya, Cameroon, and Nigeria, the positive redistribution components overwhelm the growth components. Meanwhile, in Cameroon, Kenya, and Nigeria, the effects of redistribution in rural areas were more effective than those in urban areas in affecting the incidence of human capital deprivation.

3.7. Estimates of Sectoral Decomposition of Changes in Human Capital Deprivation

Regarding the sectoral decomposition of changes in human capital deprivation by location,

Table 10. Intra- and inter-sectoral components of changes in human capital deprivation.

Cameroon	Intra-Sectoral Effects Col. (1)	Inter-Sectoral Effects Col. (2)	Impact on $\Delta P_0$ Col. (3)	Intra-Sectoral Effects Col. (4)	Inter-Sectoral Effects Col. (5)	Impact on $\Delta P_1$ Col. (6)	Intra-Sectoral Effects Col. (7)	Inter-Sectoral Effects Col. (8)	Impact on $\Delta P_2$ Col. (9)
Urban	0.006	0.022	0.028	0.002	0.002	0.004	0.001	0.000	0.001
			(0.008)			(0.001)			(0.0001)
Rural	−0.020	−0.040	−0.060	0.007	−0.004	0.003	0.002	−0.001	0.001
			(0.016)			(0.002)			(0.0004)
Overall	−0.014	−0.018	−0.032	0.009	−0.002	0.007	0.003	−0.001	0.002
			(0.014)			(0.001)			(0.0004)
Ethiopia	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_0$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_1$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_2$
Urban	−0.013	0.033	0.020	−0.006	0.003	−0.003	−0.002	0.001	−0.001
			(0.015)			(0.001)			(0.0003)
Rural	−0.041	−0.047	−0.088	−0.015	−0.004	−0.019	−0.003	−0.001	−0.004
			(0.028)			(0.001)			(0.001)
Overall	−0.053	−0.015	−0.068	−0.021	−0.001	−0.022	−0.005	0.000	−0.005
			(0.022)			(0.003)			(0.001)
Kenya	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_0$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_1$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_2$
Urban	−0.018	0.041	0.023	−0.031	0.009	−0.022	−0.012	0.002	−0.010
			(0.012)			(0.003)			(0.001)
Rural	0.068	−0.052	0.016	−0.081	−0.012	−0.093	−0.039	−0.003	−0.042
			(0.016)			(0.004)			(0.001)
Overall	0.050	−0.011	0.039	−0.112	−0.003	−0.115	−0.051	−0.001	−0.052
			(0.011)			(0.003)			(0.001)
Nigeria	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_0$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_1$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_2$
Urban	−0.033	−0.004	−0.037	0.049	−0.001	0.048	0.028	−0.0004	0.028
			(0.020)			(0.006)			(0.003)
Rural	−0.065	0.006	−0.058	0.176	0.002	0.177	0.111	0.000	0.111
			(0.028)			(0.011)			(0.001)
Overall	−0.098	0.003	−0.095	0.225	0.001	0.226	0.139	0.0004	0.139
			(0.020)			(0.010)			(0.007)
Uganda	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_0$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_1$	Intra-Sectoral Effects	Inter-Sectoral Effects	Impact on $\Delta P_2$
Urban	−0.007	−0.003	−0.010	−0.001	−0.0003	−0.001	−0.0007	−0.0001	−0.0008
			(0.013)			(0.001)			(0.0007)
Rural	−0.023	0.004	−0.019	−0.0006	0.0006	−0.000	0.0006	0.0002	0.0007
			(0.028)			(0.004)			(0.0007)
Overall	−0.030	0.002	−0.029	−0.002	0.0003	−0.002	−0.0005	0.0004	0.0001
			(0.025)			(0.004)			(0.0001)

Source: Computed using DAD 4.6. Notes: Figures in parentheses represent standard errors. Results are reported in three decimal places.

shows estimates of the incidence (Columns 1 to 3), depth (Columns 4 to 6), and severity (Columns 7 to 9) of deprivation. In the different scenarios portraying a decline in human capital deprivation, we observe that the within-sector effects largely account for the decrease in countries achieving such improvements (Table 10, Columns 1, 4, and 7). The importance of a decline in human capital (HC) deprivation within rural areas significantly accounts for the reduction in the incidence of human capital deprivation in Cameroon, Ethiopia, Nigeria, and Uganda (Columns 1 and 3). On the contrary, in Kenya, the within-sector effects worsen the incidence of human capital deprivation, and the contribution of rural areas appears to be the main driving force (Columns 1 and 3).

Considering the between-sector effects, Table 10 (Columns 2, 5, and 8) depicts two distinct scenarios. In Cameroon, Ethiopia, and Kenya, rural settings register negative values, suggesting a contribution to the alleviation of human capital (HC) deprivation. Meanwhile, urban localities posted positive values, although their effects were lower than those in rural areas. The revelation here is that the fall in the proportion of human capital deprived households in rural areas affects the overall deprivation rates and therefore deserves some policy attention. In Nigeria and Uganda, the overall between-sector effects are positive, but the negative within-sector effects overwhelm the positive effects to yield a favourable effect on the alleviation of human capital deprivation (Columns 1–3). In this setting, both urban and rural areas register net favourable effects in the deprivation-alleviation process (Column 3).

In terms of the depth and severity of HC deprivation, (1) Nigeria stands out prominently in that, both within- and between-sector effects exacerbate HC deprivation; (2) in the case of Ethiopia and Kenya, both within- and between-sector effects are HC poverty-reducing; and (3) meanwhile, in Cameroon and Uganda, the two effects show opposing signals on HC depth and severity rates.

Nonetheless, the outcome of the overall dynamics of deprivation at the national level and by location appears to hinge largely on the extent of the within-sector components for the incidence depth and severity of HC poverty, except in the case of the severity of HC poverty in Uganda.

4. Discussion

As a framework paper in distributive analysis, this work has made the following contributions to the related literature:

(i)

The power of the control function procedure in policy analysis has been shown to lie in simultaneously netting out endogeneity, sample selectivity, and unobserved heterogeneity biases from the evidence generated to support policy decisions and actions.

(ii)

While this method has been widely implemented in the literature (Heckman, 1976; Wooldridge, 2002, 2015), we are probably the first to use it to analyse the nexus between growth, shared prosperity, and inequality in Sub-Saharan Africa, thus showing how to strengthen the evidence needed to address slow growth while also reducing social inequalities in the region.

(iii)

The estimated welfare-generating function allows for factual and counterfactual analyses of the impacts of public policies on welfare outcomes of interest (Bourguignon et al., 2007), thus showing the difference that interventions can make in people’s wellbeing.

(iv)

Our empirical procedure facilitates the monetization of otherwise non-monetary dimensions of wellbeing, such as human capital or its components, e.g., health, education, nutrition, and labour market engagements.

(v)

As noted previously, up until now, nonmonetary dimensions of welfare have typically been captured in a scalar form, thus masking their optimal thresholds and constituent parts, particularly in poverty and inequality reduction analyses.

5. Conclusions

This study investigated the drivers and consequences of human capital on household income, income growth, poverty, inequality, and shared prosperity, as well as the decomposition of changes in human capital deprivation using household survey data from Cameroon, Ethiopia, Kenya, Nigeria, and Uganda collected in the period 2005–2018. To achieve these objectives, we deployed (a) control functions to estimate parameters of the income generating functions; (b) the Shapley–Oaxaca–Blinder decomposition to account for growth in household welfare; (c) factual and counterfactual distribution analyses to capture the impact of human capital endowments on poverty, inequality, and shared prosperity; and (d) deprivation indices and inter-temporal decomposition methods to configure changes in human capital deprivation into growth–redistribution and within–between location components.

The results showed that human capital positively and significantly correlates with household wellbeing in all five countries. The indirect effects of human health capital complement the direct effects in explaining household economic wellbeing in Cameroon, Ethiopia, and Kenya. The welfare effects of education increase monotonically, from primary to tertiary levels, in all five countries. Compared with the informal sector, formal sector work correlates positively with household welfare in Cameroon, Ethiopia, Kenya, and Nigeria. Households residing in rural areas are on a lower wellbeing level than their urban counterparts in all countries.

Cameroon, Ethiopia, and Uganda registered appreciable growth in household wellbeing, unlike Kenya and Nigeria. Returns to endowments in Cameroon, access and returns to endowments in Ethiopia, and access to endowments in Uganda correlated favourably with improvements in household wellbeing. In Kenya and Nigeria, both access and returns to human capital endowments affect growth in household income. The results also showed the role of human capital (health, education, and labour) in enhancing household income or attenuating unfavourable effects on it. There is evidence that human health capital is key in accounting for growth in household income. While in Cameroon, Ethiopia, and Nigeria, health largely explains growth in household wellbeing, in Kenya and Uganda, it accounts for growth shortfalls. Education has a net positive effect on growth in household income, except in Cameroon, where it has a negative net contribution. The effect of formal sector employment on growth in household welfare is positive in four of the five countries—Kenya being the odd one.

The average expenditure of households at the bottom 40th percentile of the income distribution increases with human capital equalization, except in Cameroon in 2007 and Uganda in 2015. Households at the bottom 40th percentile of income distribution registered positive growth overall and by location in the five countries. The higher values for urban areas imply that putting in place interventions that level human capital differences would improve shared prosperity, more so in urban than in rural areas. Human capital equalization is shared-prosperity enhancing in Cameroon, rural Kenya, and generally in Nigeria. Kenya and Uganda stood out distinctly in registering large shared-prosperity premiums in both the factual and counterfactual distributions. Meanwhile, Nigeria registered shared-prosperity premiums only in the counterfactual distribution overall and in rural areas. Cameroon and Ethiopia experienced shared-prosperity deficits in both distributions over the study period. This is an indication that in these two countries, although the share of benefits from growth accruing to the population increased over time, the 40% least well-off households gained less from the rising prosperity.

An analysis of the incidence, depth, and severity of poverty by comparing these indices between the factual and counterfactual distributions reveals that they fell for all countries except Uganda. Considering the urban–rural patterns, the benefits associated with equalizing human capital disparities are higher in rural than urban areas in Cameroon, Ethiopia, Kenya, and Nigeria. The Gini indices declined in rural and urban settings when disparities in human capital were removed, but only in Ethiopia and Kenya. To eradicate human capital deprivation in a substantive way in the five countries, there is a need for interventions that expand human capital provision to cover both urban and rural areas. The ability of the redistribution component in alleviating human capital deprivation is non-negligible but less systematic than the growth component. These results indicate that to significantly reduce human capital deprivations, interventions that improve human capital outcomes are more likely to be inclusive than those that redistribute human capital inputs. However, in Kenya, Cameroon, and Nigeria, the positive redistribution components overwhelm the growth components; meanwhile, the effects of redistribution in rural areas are more effective than those in urban areas in stemming the incidence of human capital deprivation.

In countries experiencing reductions in human capital deprivation, we observed that the within-sector effects largely account for this success. In Cameroon, Ethiopia, and Kenya, rural settings seem to account for observed reductions in human capital deprivation. This is evidence that differential interventions may be needed for rural and urban areas. In Nigeria and Uganda, the negative within-sector effects overwhelm the positive between-sector effects in alleviating human capital deprivation. In this setting, both urban and rural areas register net reductions in human capital poverty. Nonetheless, the overall change in human capital deprivation at the national and local levels is largely driven by within-sector interventions.