Dynamics of inequality in child under-nutrition in Ethiopia

Introduction: Although Ethiopia has already achieved a remarkable progress in reducing under-five mortality in the last decades, undernutrition among children is still a common problem in this country. Socioeconomic inequalities in health outcomes in Ethiopia have been thus of focus in academia and policy spheres for a while now. This study provides new evidence on child undernutrition inequalities in Ethiopia using longitudinal perspective. Method: Using three round of household panel survey (from 2012 to 2016), we use concentration index (associated curve), different mobility index approaches for measuring inequalities and its dynamics, and decomposition method to identify contributing factors. Results: In all concentration index computing approaches and socioeconomic status ranking variables, the concentration indices are significant with negative value. This implies that in either of short-run or long-run inequality estimates, the burden of unequal distribution of undernutrition remains on the poor with significant difference across regions. While employing different SES ranking variables, the difference in the concentration indices is only found significant in case of Height-for-age Z-score. It signifies that relatively higher inequality is measured using consumption as ranking variable. Significant difference in inequality is also shown across regions. With respect to dynamics of inequalities, results on mobility indices computed based on Allanson et al. (Longitudinal analysis of income-related health inequality. Dundee Discussion Working Paper No. 214, 2010) approach show that inequality remain stable (persistent) in Height-for- age Z-score, and reduction of inequality in Weight-for- age Z-score while in case of Weight-for- height Z-score, there is no clear trend over subsequent waves. Results on decomposition of inequalities show that the major contributors are wealth index, consumption and mother’s education. Conclusion: The argument of the choice of welfare indicator can have a large and significant impact on measured socioeconomic inequalities in a health variable which it depends on the variable examined. Employing longitudinal perspective rather than weighted average of cross-sectional data is justifiable to see the dynamic of inequality in child malnutrition. In both socioeconomic status ranking variables, the bulk of inequality in malnutrition is caused by inequality in socioeconomic status in which it disfavours the poor in both cases. This calls for enhancing the policy measures that narrow socioeconomic gaps between groups in the population and targeting on early childhood intervention and nutrition sensitive.

Data for the study comes from the ESS collected jointly by the CSA of Ethiopia and the World Bank as part of the Living Standard Measurement Study-Integrated Surveys on Agriculture (LSMS-ISA). It is a longitudinal survey with three waves (2011/12, 2013/14 and 2015/16). The ESS5 sample is a two-stage probability sample. It employs a stratified, two-stage design where the regions of Ethiopia serve as the strata. The first stage of sampling entails selecting enumeration areas (i.e. the primary sampling units) using simple random sampling (SRS) from the sample of the Agriculture Sample Survey (AgSS) enumeration areas (EAs). The AgSS EAs were selected based on probability proportional to size of population (PPS). The sample design of the first wave provides representative estimates at the national level for rural-area and small-town households while subsequent waves include large towns and cities. The samples are also regionally representative for the major regions of the country (Oromia, Amhara, Tigray, and SNNP) as well as Addis Ababa since the second wave. The second stage of sampling is the selection of households to be interviewed in each EA. The surveys provide household-level data on a range of issues such as consumption expenditure, assets, food security shocks, copying strategies, non-farm enterprises, credit. Very importantly, individual- level data are available on socioeconomic, demographics, education, health and time use (labor and leisure). Moreover, as traditional in LSMS surveys, community-level data on a host of issues such as health infrastructure as well as market price data from two nearest local markets are collected. Finally, data are obtained from 3969, 5262 and 4954 households in the first, second and third waves respectively. However, the sample for health variable data is restricted to children whose age is below 5 years, which is considered in this study. Our health outcome interest is malnutrition using anthropometric indicator. Theoretically, the body of a child responds to malnutrition in two ways that can be measured by anthropometric survey. First, a reduction in growth over the long-term results in low height-for-age or stunting. Second, a short-term response to inadequate food intakes is assessed by weight relative to height (wasting). The combination of short-term and long-term food shortage and growth disturbances produces low weight-for-age (underweight) (ONIS, 2000). Survey data often contain measures of weight and height, in particular for children. Weight and height do not indicate malnutrition directly. Besides age and sex, they are affected by many intervening factors other than nutrient intake, in particular genetic variation. However, even in the presence of such natural variation, it is possible to use physical measurements to assess the adequacy of diet and growth, in particular in infants and children. This is done by com-paring indicators with the distribution of the same indicator for a healthy reference group and identifying extreme or abnormal departures from this distribution [31]. Irrespective of what particular reference data are used, anthropometric indices are constructed by com-paring relevant measures with those of comparable individuals (in regard to age and sex) in the reference populations. There are three ways of expressing these comparisons: Z-score (standard deviation score), percent of median and percentile. However, the preferred and most common way of expressing anthropometrics indices is in the form of Z-scores. More specifically, Z-score for an individual i is calculated using eq. 1: Where Xi  is an observed value for ith child in a target population; Xr is a median of the reference population; and δ is a standard deviation (SD) of the reference population. Thus, the health outcome variables used in this study are the three anthropometric indicators (Height-for-age Z-score (HAZ), Weight-for-Height Z-score (WHZ), and Weight-for-Age Z-score (WAZ). First, those anthropometric indicators from age, height/length and weight data following the World Health Organization, WHO [32] child growth standards are computed. It is then stated that stunting, wasting and underweight levels for children aged less than 5 years as shown in Table 1. List and description of child undernutrition indicators Those are used as explanatory variables for regression -based decomposition analysis as well as SES ranking variables in computing SES – related health inequalities. Broadly, they can be grouped as child level characteristics, household and community level characteristics. The child level characteristic includes child’s age, age square, sex, and illness. Under household level, wealth index, consumption, mother’s education, toilet facilities6 and household sizes are considered. At community level, health facilities, access to safe drink water and spatial dimension such as household’s place of residence in the form of rural urban or regions. Detail on each variable definition and measurement are given in Table ​Table2.2. However, among those household socioeconomic characteristics, wealth index and consumption are chosen as SES ranking variables for household position in measuring inequalities. Let’s see below in detail how those values are constructed: Description and measurement of variables used in decomposition analysis Households were asked whether they owned from a list of asset items (such as farm implements, furniture and kitchenware, entertainment and communication equipment, electronic item, personal items) or not7. It also considers various indicators of housing condition of household such as walls, roof, and floor of the main dwelling; type of kitchen, cooking and bathing facilities. Then, following the standard approach of assessing economic status of the household, the study uses household asset and housing conditions to compute wealth index using principal component analysis (PCA) while sampling weight is taken in to account. Unlike DHS and other data sets’ wealth index which is constructed from urban-based social and economic amenities and may be measuring more of urban/city condition instead of inclusive socioeconomic status, this study uses ESS data which also includes rural based socioeconomic asset indicators. The surveys include questions on expenditure on food and non-food items, food security, shocks, and coping mechanisms. The total consumption expenditure (available from the survey) is constructed from food consumption, non-food consumption and education expenditure. Initially, a common reference period is established for all items, and values are imputed in cases in which they are not available (converted to a uniform reference period for example, a year). Then, it follows three steps in constructing a consumption-based living standards measure: (a) construct an aggregate of different components of consumption, (b) make adjustments for cost of living differences, and (c) make adjustments for household size and composition. Household size and a measure of adult-equivalency 9 are constructed based on scale factors such as categorizing age in to different ranges(13 age categories) for both male and female by allocating different weights for each categories. In addition, it uses a regional price index (for 10 regions), based on the index created by the Ministry of Finance and Economic Development (MoFED) in their Household Consumption Expenditure (HCE) 2010/2011, 2013/14 and 2015/16 reports. Nominal and real per adult equivalent consumption were then calculated, and real consumption was re-scaled to have the same overall mean value as nominal consumption. The calculated per capita amounts winsorised at the 97th percentile for non-zero consumption for each item (for details, see LSMS annual report of each wave, guideline for constructing aggregate consumption). In this study, we also group the households into quintiles based on the wealth index and consumption adjusted by sample weights for nationally representative inferences. Of course, using consumption expenditure as socioeconomic ranking variable has its own drawbacks. One constraint is that households might overestimate their level of consumption expenditure for different reasons. Measurement problem is also another limitation. Here, consumption is considered as flow measurement while wealth index is as stock variable. A flow is a quantity which is measured with reference to a period of time. It has time dimension. However, a stock has no time dimension (length of time) as against a flow which has time dimension. A flow shows change during a period of time whereas a stock indicates the quantity of a variable at a point of time. Thus, wealth is a stock since it can be measured at a point of time, but consumption expenditure is a flow because it can be measured over a period of time. Hence, using consumption expenditure which is a flow variable enable us to exploit the time dimension aspect of the variable. This is again in line with the main intention of the study. The study aims to examine the child undernutrition inequalities in socioeconomic status and spatial dimensions. For socioeconomic inequalities in child health, we use consumption expenditure and wealth index as alternative welfare measures and see the gap between the worse-off (bottom 60%) and better off (40%) as well as between the poorest (1st quintile) and the richest (5th quintile). And for the spatial dimension, inequalities are traced between rural and urban children as well as among those in various regions of the country. The study also computes absolute and relative inequalities from rate differences and rate ratios. When there are only two subgroups to compare, difference and ratio are the most straightforward ways to measure absolute and relative inequality. However, the differences and ratios between different groups do not consider inequalities by the whole population. Hence, concentration curves are used to illustrate the trend of the socioeconomic and spatial inequalities in child undernutrition over time. The concentration curve plots the cumulative proportion of the population ranked by a measure of socioeconomic status (such as an index of household wealth and consumption) against the cumulative proportion of the health measure (undernutrition indicators). If concentration curve lies above the diagonal (45 degree line of equality), it is interpreted as child malnutrition is disproportionately concentrated among the poor and the reverse is true while it lies below line of equality. The study also conducts tests of dominance between concentration curves following the procedures in O’Donnell et al. [34]. Since a concentration curve does not give a measure of the magnitude of inequality that can be com-pared conveniently across many time periods, countries, regions, or whatever groups may be chosen for comparison, the study examines inequalities using CI [23, 34] and with possible extension. The CI is defined as twice the area between the concentration curve and the line of equality (the 45-degree line). It provides a summary measure of socioeconomic related health inequality, i.e. a measure of the extent to which the concentration curve diverges from the diagonal. The convention is that the index takes a negative value when the curve lies above the line of equality, indicating disproportionate concentration of the health variable among the poor, and a positive value when it lies below the line of equality. However, when there is no socioeconomic-related inequality, the concentration index becomes zero. In this study, with availability of panel data, we follow dynamic approach to measure inequality in health rather than a static one used in cross-sectional data. The basic rationality behind is that longitudinal data are more relevant for policy making analysis. The cross-sectional data, static approach is often used to compare inequality at two different points in time while the panel, dynamic approach is essentially useful when interest lies in the long -run rather short-run inequality (which can be the case for example, policy makers). As Jones and Lopez [24] prove theoretically, looking at a different point in time using short-run CI does not give a complete picture rather in panel, it enables us to follow each individual in every year and have thus a complete picture of their relative evolution. To this end, there are various ways of expressing the CI algebraically. For the measurement of inequality at one point in time, the study uses the CI stated in eq. 2, that is mostly used in the literature for its convenience. It is derived by ranking the population by a measure of SES and then com-paring the cumulative proportion of health with the cumulative proportion of the population ranked by SES. Where yit represents the health level of individual i in period t, and Rit denotes the relative fractional rank of ith individual in the distribution of SES in period t; N is the sample size at period t . y¯t=∑i=1NyitN is the mean of health of the sample in the period t. Equation 2 shows that the value of concentration index is equal to the co-variance between individual health (yi) and the individual’s rank Rit, scaled by the mean of heath in the population (yi).Then to ensure the CI ranges between −1 and +1, the whole expression is multiplied by 2. Alternatively, it can be defined as a measure of the degree of association of between an individuals’ level of health and their relative position in the SES distribution. The negative and positive sign of CI tells us that health outcome is concentrated among poor and rich people respectively. It is important to highlight that a value of CI is equal to zero does not mean an absence of inequality, but an absence of socioeconomic gradient in the distribution, i.e. an absence of inequality associated with socioeconomic characteristics. However, Jones and Lopez [24] illustrate that cross-sectional CIs can lead to wrong conclusions when trying to measure socioeconomic-related health inequality in the long- run as these do not take into account the possibility that people may change in socioeconomic rank. As such, they derive a formula to measure inequality in the long- run, which is similar to the cross-sectional CI. They find that the CI for the distribution of average health after T periods can be written as the difference between two terms: the weighted sum of the CIs for each of the sub periods (term1) minus a residual which is the difference between period specific SES Rit and ranks for average specific SES over all periods RiT and their relationship to health over time ( term2) as stated below in eq. 3. where y==∑i∑iyitNT is the overall average health status/population/ in T periods; ∑y¯tT=y¯T is the average health of the individual over the T periods, y¯t=∑iyitN is the mean of the health of individual in each t period, wt=y¯tTyT= can be seen as the share of total health in each period; and CIT is defined as long-run CI and CIt is short-run CI of each health variable under consideration in period t. The CI can be computed easily in stata software either using covariance method or regression-based method. Accordingly, this study adopts the user-written stata command conindex developed by O’Donnell et al. [34]10. It calculates rank-dependent inequality indices while offering a great deal of flexibility in considering measurement scale and alternative attitude to inequality. Estimation and inference is via a regression approach that allows for addressing the issue of sampling design, misspecification and for testing for differences in inequalities across population or sub-populations. The magnitude and sign of concentration index depends on the method used to compute the required index. These results also affect the inequality analysis. When the variable of interest has an infinite upper bound on a fixed scale, the main normative choice is between absolute and relative invariance. Matters are more complicated when the measurement scale is not unique. Applying the generalized CI to a ratio or cardinal variable requires one to accept that the inequality ordering may depend on the scaling adopted. This can be avoided for the relative inequality invariance criterion if one replaces the standard CI with the modified one. When the variable has a finite upper bound, one should first choose between relative inequality invariance and the mirror condition. If one prioritizes the relative invariance criterion (in attainments or shortfalls), then the standard CI or its modified version can be used. When priority is given to the mirror condition, one faces a choice between the Erreygers index, which focuses on absolute differences, and the Wagstaff index, which mixes concern for relative inequalities in attainments and relative inequalities in shortfalls [35]. In this study, for standard and generalized CI, the health variable (the dependent variable) is negative of Z-score which is continuous and unbounded variables while in case of Erreygers and Wagstaff, it is binary which is bounded variables taking a value either 1 if stunted, wasted and underweighted or 0 otherwise. Since this study prefers to use longitudinal data, its other basic concern is examining the measurement of malnutrition inequality with variation of SES variables over time (SES related health inequality mobility). In this regard, even if individuals do not experience health changes, long-run SES- related inequality can be greater or less than that obtained with snapshot cross-sectional estimates, as long as the patterns of SES mobility are systematically related to health. Averaging the short-run measures of inequality will then tend to underestimate or overestimate the long-run picture. However, in situations where SES- related inequality tends to fade either solely due to health mobility or solely due to SES mobility, the mobility index would be zero. In these cases, the information obtained from the series of cross-sectional CIs would be sufficient to capture the dynamics of interest. Hence, it is useful to measure how much the longitudinal perspective alters the picture that would emerge from a series of cross-sections, in the same spirit as Shorrocks’ [36] index of income mobility. With same notational representation used above for computing long-run CI, Jones and Lopez [24] put mobility index MT for any SES variables: Here, mobility index would be different from zero if the following two conditions hold: i) The SES rank of individuals is sensitive to the length of the time window over which measurement is taken, i.e. there is SES mobility, as defined by Shorrocks [36]11. ii) These changes in SES rank are associated with systematic differences in health variable considered. If mobility index is negative in sign, it implies that short-run CI (cross-sectional) underestimates long-run one (longitudinal data) while it is positive, it shows that short-run CI overestimate long-run one. Jones and Lopez [24] provide an index that measures the difference between short-run and long-run income-related health inequality and suggest that it can be interpreted as an index of health-related income mobility. Nonetheless, as of Allanson et al. [25], it is questionable whether this index is more appropriate to health policy makers other than to illustrate that income-related health inequalities may be slightly more important than might be inferred from cross-sectional estimates. Moreover, they note that, initially, health policy-makers are more likely to be interested in income-related health changes, less so in health-related income changes, especially since a large amount of health-related income changes are likely to be unavoidable. Jones and Lopez [24] measure is equal zero if there is no income mobility regardless of whether there is health mobility. Conversely, the measure may not equal zero even if there are no health changes. Second, the index provided by Jones and Lopez [24] is symmetric in the sense that the value of the index is invariant to the ordering of the years. Yet, policy makers may want to distinguish between equalizing and dis-equalizing income changes since these have diametrically opposed implications for the level of income-related health inequality over time. Finally, the value of the Jones and Lopez [24] index is likely to be little more than a reflection of the unimodal shape of the income distribution and the strength of the association between income and health in the long- run compared to the short-run. As a remedy for these shortcomings, Allanson et al. [25] propose an alternative approach based on the simple observation that any change in income-related health inequality over time must arise from some combination of changes in health outcomes and income ranks. By decomposing the change in between two periods, they provide an index of income-related health mobility that captures the effect on short-run income-related health inequality of differences in relative health changes between individuals with different initial levels of income. Thus, the measure addresses the question of whether the pattern of health changes is biased in favour of those with initially high or low incomes, providing a natural counterpart to measures of income-related health inequality that address the issue of whether those with better health tend to be the rich or poor. In addition, like Jones and Lopez [24], they also obtain a health-related income mobility index that captures the effect of the reshuffling of individuals within the income distribution on cross-sectional socioeconomic inequalities in health. Accordingly, in this study, Allanson et al. [25] approach is adopted to decompose the change in the short-run CI between any initial or start period s and any final period f into two part: Where yis and Ris are health and relative fractional rank of individual at starting period. Similarly, yif and Rif denote health and relative fractional rank of individual at final period. yf and ys represent mean of health at final and starting period respectively. CIss and CIff are the CI ′ s in periods starting (s) and final (f) respectively, and CIfs is the CI obtained when health outcomes in the final period are ranked by income in the initial period. In equation 5, the mobility index, MH = CIfs − CIss provides a measure of income-related health mobility, which captures the effect of differences in relative health changes between individuals with different initial levels of income. MH is positive (negative) if health changes are progressive (regressive) in the sense that the poorest individuals either enjoy a larger (smaller) share of total health gains or suffer a smaller (larger) share of total health losses compared to their initial share of health ,and equals zero if relative health changes are independent of income. MH in turn depends on the level of progressivity and scale of health changes. However, the income-related health mobility index, MH is not exactly equal the change in income-related health inequality because it does not allow for the effect of changes in the ranking of individuals in the income distribution between the initial and final periods. This effect is captured by the health-related income mobility index, MR = CIff − CIfs. It may be negative since the concentration index of final period health outcomes ranked by initial income can exceed that ranked by final income. MR can be equal to zero, irrespective of the degree of reshuffling of individuals in the income distribution, if final period health is uncorrelated with changes in income rank [25]. In this part of the study, the CI of each child undernutrition indicator is decomposed in order to identify the major contributing factors to the inequality. Such decomposition method enables us to know what extent of inequality in child malnutrition is explained by inequalities in socioeconomic status such as education, health access to maternal and child health care, etc? Wagstaff, van Doorslaer, and Watanabe (2003) demonstrate that the health CI can be decomposed into the contributions of individual factors to income-related health inequality, in which each contribution is the product of the sensitivity of heath with respect to that factor (the elasticity) and the degree of income-related inequality in that factor (the respective CI). To explain variations in a child’s under-nutrition level, a standard household production-type anthropometric regression framework [37, 38] is adopted , in which negative of each child’s anthropometrics indicators (Z-score) is specified to be a linear function of a vector of child-level variables, a vector of household-level variables, and community level. The study interprets this estimating equation as a reduced-form demand equation rather than a production function. Here, the study focuses on inequalities in all malnutrition indicators measured using the negative of the child’s height-for-age z-score, weight-for-height z-score, and weight-for -age z-score respectively following the World Health Organization, WHO [32] child growth standard data. Like Wagsta et al. [27] and many others in the literature, it has two reasons for favouring the z-score over a binary variable indicating whether or not the child in question was undernutritioned or not. First, it conveys information on the depth of malnutrition rather than simply whether or not a child was malnourished. Second, it is amenable to linear regression analysis, which is favourable to the decomposition method employed in this study. Since the equation used for decomposing the CI requires linearity of the underlying regression model, most of the decomposition result holds for a linear model of health outcomes. Moreover, It uses the negative of the z-score to make the malnutrition variables easier to interpret. Rising of negative of the z-score indicates an increasing in malnutrition level. Accordingly, for its regression based -decomposition, it relies on malnutrition level rather than binary outcome as dependent variable. Since this study employs longitudinal data, the specification of its model for decomposing socioeconomic related inequality in health could be simple pooled OLS model, random effect model and fixed effect model. Most studies in this topic use simple pooled linear model, estimating by ordinary least square (OLS) but it doesn’t take in to account potential error components structure and dynamics. This study rather uses both random and fixed effect to model and estimate the regression equation for decomposing inequality. It thus considers linear panel models12 as it is indicated in eq. 6. Where Yihct indicates that malnutrition level of child i in a household h, community c and in time t, X1, X2, and X3 are vectors of child level, household level and community level explanatory variables respectively (for details on variable definition and measurement, see Table ​Table2).2). While β is a vector of regression coefficients which show the effect of X on Y; μihct = αi + εihct, αi 13 is individual specific effect (could be random or non- random) effect) and εihct is idiosyncratic error term. In decomposing CI, this study follows the formula proposed by Wagsta et al. [27] while linear panel data is taken in to account in this case. Then, the decomposed CI as stated in eq. 7 shows that it is equal to the weighted sum of the CIs of the K regressors: Where CIT is overall long-run CI for health, y¯T is the mean health over all periods, βk are coefficients obtained from regression of eq. 6, X¯k is mean of the kth regressor taken over all periods, CIkT is the long-run CI of the kth regressor and GCϵT is long-run generalized concentration index for each error term14 and ηk=βkX¯ky¯T is elasticity of health variable under consideration with respect to the explanatory variables (Xk). Since the main objective of decomposition analysis is to offer an explanation of socioeconomic inequality of health by including the contributions of each explanatory variable to such inequality, the product of elasticity ( k) and CI of kth regressor (CIkT) gives us the contribution of each explanatory variables in the variation of inequality in health variables. It is common to raise why do gaps in health outcome exist between the poor and better-off in many countries despite health systems explicitly aimed at eliminating gap in health outcome? Hence, the Oaxaca-type decomposition [34, 39] is employed to explain the difference between two groups. Such type of decomposition explains the gap in the means of an outcome variable between two groups (For example, between the poor and the non-poor). The gap is decomposed into group differences in the magnitudes of the determinants of the outcome in question and group differences in the effects of these determinants. But, such method does not allow us to decompose inequalities in health outcome across the full distribution of SES variable, rather we simply restricted to analysis between the poor and the better-off. The decomposition equation this study uses to estimate the health outcome gap between two groups is given in eq. 9. However, it takes panel data rather than different cross-sectional data for our estimate. where Yit is individual child undernutrition level at time t, Xihc t is vector of child, household and community level characteristics at time t. X¯ represents mean of individual child undernutrition level for each group and X¯ represents vector of child, household and community level characteristics evaluated at mean for each groups and β′s also represents estimated coefficients including intercepts for poor and non-poor . So, the gap in Y between the poor and the non-poor might come from differences in the coefficients (β) including intercepts (difference in effects), and differences in those determinants level (X). Estimates of the difference in the gap in mean outcomes can be obtained by substituting sample means of the X ′ s and estimates of the parameter’s into eq. 8. As it is stated in eq. 12, the mean health outcome difference between the two considered gaps can be attributable to (i) differences in the X ′ s (sometimes called the explained component); (ii) differences in the β ‘s (sometimes called the unexplained component) and interaction effect (change in product of X and; β, βX).

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• yayo negasi, mengesha