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Determinants of child height in Uganda: A consideration of the selection bias caused by child mortality

Namkee Ahn and Abusaleh Shariff

Abstract

This paper reports a methodology for analysis and presents the determinants of child height in Uganda. A two-stage estimation method that evaluated the effects of covariates on child height for age after controlling for the selection bias caused by child mortality was necessary. Important determinants of child health in Uganda are the child's and some maternal characteristics. Some environmental factors (at the levels of both community aggregate and household) have significance. The effects of mothers' characteristics were relatively more sensitive to correction of the selection bias. In particular, mother's secondary education almost doubled its effect and became significant in determining the height of children. Overall results suggest that Uganda is facing a phase of health transition in which the effect of socio-economic variables (at both individual and community levels) are beginning to show up significantly. Although an all-round developmental effort is essential, selective interventions aiming to improve female education and, where that is difficult, extension of appropriate information through radio are likely to improve the survival and health of children.

Introduction

A standardized anthropometric measure, height for age, is considered a good measure of the long-term health of children by nutritionists and social scientists [1]. This indicator also presents conditions determining the levels of mortality in a given population. When it is very low, the risk of mortality increases many times [2]. We assessed determinants of the long-term health of Ugandan children under five years of age.

Although the essential role played by the costly capital-intensive high-technology modern health care system in improving health cannot be disregarded, one cannot ignore a rudimentary and subtle but decisive contribution made by social change in general and mass education in particular in improving health and longevity. Indeed, it may well be the joint effect of education and medical intervention that will lead to improvements in child survival and health. This seems likely because education (especially of mothers) improves child health by increasing the technical efficiency or productivity of health inputs and also by reducing the cost of information on choice of technology [3]. The fact that a woman has some schooling may operate through her increased participation in household decision making, which is likely to improve child health [4]. Measuring education's beneficial impact on market (wage) and especially non-market (household health) production in a developing economy such as Uganda is policy-oriented and highly desirable.

A number of studies report a consistent negative association between education and human fertility [5, 6] and mortality [4, 7-9] in developing countries. More recently, workers have documented significant relationships between child anthropometry (height and weight) and parental education as well as other environmental or community factors [10-16]. Since data on child anthropometry can be obtained for all surviving children, these measures are suitable to put to quantitative estimations even with a relatively small sample. (The study of infant and child mortality primarily suffers from two problems that are relatively difficult to handle: a large sample is required, even in high-mortality countries, to get adequate vital events to construct dependent measures; and the mortality data, especially of infants and young children, are susceptible to reporting errors.) Analyses of child anthropometry in developing countries, especially in Africa, have been meager, mostly for want of data and also for lack of interest. The Demographic and Health Survey (DHS) programme in Uganda now provides data on child anthropometry and many useful covariates, and we have used these data to investigate determinants of child health, with emphasis on parental schooling.

This analysis presents a theoretical formulation and the empirical results applied to Uganda data, focusing on the following three issues:

» What are the determinants of the height of children? In particular, what is the role of parental education, especially the mother's?
» Does the fact that data on health measures are available only for surviving children lead to misestimation of the coefficients meant to represent the whole population? That is, does controlling for the survival status of children affect the health status estimates?
» Does the effect of maternal education on child health differ by information and environmental factors, such as access to radio and place of residence? Does parental education have different effects depending on the sex of children?

Model specification

In the following the health equations to be estimated are conceptualized [2, 3, 17] with the aim of understanding the effects of exogenous risk and parental endowment factors on child health measures when child characteristics and a few other factors are controlled for. Correction of the selection bias is necessary for the analysis of anthropometric data from developing countries [2].

Height for age is an indicator of the long-term cumulative health of children. It is considered to be a function of child characteristics (C_c), risk factors (E_r) emerging from the immediate environment in which the child lives, and characteristics of the parents (E_p) under whose care children grow. To determine the accurate associations among the variables of interest, it is necessary to control for certain variables such as the region and religion.

Besides age and sex, the child characteristics whose effects are controlled for at the outset are previous birth interval, number of siblings, and whether born as a twin. The parental characteristics are their respective ages, levels of education, work status, marital status, and co-residence. The environmental risk factors are water quality, as evidenced by the availability of water supplied through a pipe or tap; the quality of housing, as evidenced cement floors; disease and environmental hygiene, emerging from data on the reported frequency of diarrhoea and fever and access to a private toilet; and the area of residence, rural or urban. This information is available at the household level. However, mean values at the cluster (village) level are necessary to capture community environmental effects. The religious affiliation of the household head and the geographic region in which the respondents live are essential controls.

The mother's access to some external information (Ii) through radio is an additional variable, because the information-flow and place-of-residence (rural or urban) variables are known to have important interactive effects with the mother's education. The interaction terms of the child's sex with the mother's (and father's) education are also included.

The health equation can be written as a function of all these variables and an unobserved error term (u) as follows, where the individual subscript is suppressed for notational simplicity:

H = H(C_c, E_r, E_p, I_i, u) (1)

Assuming that the function can be approximated by a linear form, we can write the health outcome H as a linear function of inputs X1:

H=X₁ß+u (2)

A common empirical practice is to run the ordinary least square (OLS) regression for equation 2.

Selection bias

The standard OLS regression method suffers from a few statistical problems leading to biased estimates. Samples usually include only children who are alive at the time of survey. First, in a one-time cross-sectional survey, the anthropometric measures can be obtained only for children who are alive and present in the home at the time. It could well be that the included (living) children are systematically different from the excluded (dead or fostered out) children in their various health measures. The OLS estimates of these data are likely to be biased. More specifically, suppose that the children of less-educated women suffer higher mortality. Then the surviving children of these women are likely to be genetically stronger (because they have survived despite high risk of mortality) than those of better-educated mothers. If this biological selection is severe in a sample and innate genetic strength is not controlled, the OLS is likely to underestimate the effect of women's education on child health (because the surviving children of educated mothers may be biologically inferior). This selection bias is likely to be great in high-mortality societies such as Uganda.

Suppose the survival status (S) is determined by an unobserved latent variable S* as in equation 3:

S = 1, if S * > 0;
=0, if S*<0. (3)

Suppose that S* is determined, as in equation 4:

S. = X_2g + e (4)

where X₂ is a vector of covariates, g is an unknown parameter vector, and e is an error term. If the error terms, u in equation 2 and e in equation 4, are correlated, the regular OLS estimates of the health-output equation (equation 2) would not be consistent because the expected value of the error term is not zero, as shown here:

(5)

where s ₁₂ is the correlation coefficient between u and e, s ₂ is the standard error of e, and, assuming bivariate normal distribution of u and e,

(6)

where Z= (X₂)g /s ₂ and ø and Ø are the standard normal density and distribution functions.

One of the methods that corrects this bias is a two-stage estimation method [18], which has been applied, for instance, to estimate a wage equation while controlling for the fact that the wage is observed only for wage earners. In the present analysis, the aim was to estimate children's height for age while controlling for the sample including only surviving children. In the first step a probit regression of the child survival status (living or dead) is run, controlling for the age of child. Then, using the probit estimates of g /s ₂, a correcting factor l is constructed by equation 6. In the second stage, a health equation (OLS, anthropometric measures as regressands) for living children is estimated, including l as a covariate. The inclusion of l makes the expected value of the error term zero so that the parameters can be estimated consistently.

A simple example can help to explain more intuitively how this method corrects the selectivity bias. First, it is easy to see that the correction variable l is a monotone decreasing function with respect to Ø (-Z), the probability that an observation is selected into the sample, that is, the probability of being alive at the time of survey. If children of less-educated women face a higher mortality risk, their l values are likely to be larger than those of the children of better-educated mothers. On the other hand, everything else being equal, the surviving children of less-educated mothers are likely to be genetically stronger since they survived despite their higher mortality risk. Then, among the surviving children the A value can be used as a proxy for the unobserved biological factors. Therefore, its inclusion in a height equation is expected to take away the effect of these biological factors from an education coefficient.

A major problem in implementing this method is in identifying the model. That is, one has to find some variables that affect children's survival status but not their anthropometry. Although in principle all the factors that affect child mortality would also affect child height, since both are the consequence of healthiness, in practice some variables can serve as identifying variables if their influence on mortality is much greater than on height. Mother's antenatal immunization against tetanus is presumed to reduce the risk of mortality directly, especially in very young ages, whereas its influence on the height of children is negligible. This variable, therefore, is dropped from the height equation to satisfy the identification condition in the two-stage estimation method.

Including tetanus injection as an identifying variable seems to be supported by a simple test. According to the Ugandan data used here, a child's probability of surviving is much higher if the mother has received an antitetanus injection (88.8%) than otherwise (84.5%). On the other hand, the average height is virtually the same regardless of the injection. (The average heights for age of the living children without a tetanus injection were 95.5%, 95.3%, 92.3%, and 91.7% of the reference standard among the children less than 7, 7-12, 13-24, and 25-59 months old respectively, compared with the corresponding figures of 98.7%, 95.2%, 92.6%, and 91.9% among children with an injection.) In fact, the injection is estimated to have a significant negative coefficient (t ratio -0.55 [2.82]) in the uncorrected OLS estimation of height for age. This means that among surviving children the antitetanus injection has a detrimental effect on height. Since this is highly unlikely, an alternative explanation may be that the surviving children without the injection must be healthier (taller) on average than those with the injection after controlling for other influencing factors.

Data

DHS programmes are the major source of data on human fertility, mortality, and health for many countries. Programmes by Macro International Inc. have undertaken nationally representative sample surveys in about 46 developing countries throughout the world. Data from a sample of 4,730 women were collected in Uganda during 1988-1989. Important components of these data are the height and weight measures of children under five years of age. A total of 3,945 live births and 3,377 living children with anthropometric data are included in this analysis. (Details of the sampling, survey methodology, and quality of data are given in Kaijuka et al. [19].) Tables 1 and 2 present the description of the variables and the sample means. Since the surveys were designed mainly to provide accurate data on fertility, mortality, and contraception, data relating to many types of economic variables were not collected. Information is not available, for example, on income, wages, and prices. Nevertheless, the data are rich enough to assess many correlates of child health, especially the effect of parental education.

TABLE 1. Description of variables, and means for all births and living children

Uganda is a multi-ethnic, multiregional country with the characteristics of a developing country. Education levels, health care use, and the availability of basic utilities and amenities are modest. Uganda also appears to have a tradition-bound society, with practices such as polygamy and childbearing outside marriage. It is characterized also by high fertility and high mortality. In this sample 14.4% of the children who had been born live during the previous five years were dead by the time of survey.

TABLE 2. Probit estimation of survival status

Sample size = 3,945.
* Significant at 10%.
** Significant at 5%.
*** Significant at 1 %.

Determinants of children's height in Uganda

Height is a continuous variable expressed as a percentage of the NCHS/CDC/WHO international reference median height for age. The mean height of the 3,377 children included in this analysis was 93% of the reference. Log of height was used as the dependent variable. (Using the logarithm of the standardized height as a dependent variable improved the model fit (R²) compared with the use of the standardized height. Another convenience of using the logarithm is that the estimated coefficient is interpreted as proportional effects of a unit change in the respective explanatory variable on the standardized height. That is, if logH = x₁ß, then ) Table 3 presents the estimation results of three different specifications: the regular OLS estimations without correction, the second-stage OLS equation with correction, and a second-stage OLS including the interaction terms of the mother's education with place of residence and ownership of a radio. (The first-stage probit estimation of the survival status of children that was later used to compute correction factor l is presented in the Appendix.)

From an examination of the regular OLS result, it is evident that almost all the classified child characteristics except birth order have strong effects. For example, the negative association with child's age continues until 42 months, at which time it is positive. Twin children have a significant and large disadvantage with respect to height (3.9% change). The length of previous birth intervals has a strong and positive association with child height. A female child has a significantly better chance than a male child to improve her own height. The only other variables showing significance at a 10% level are the quality of the house floor, radio ownership, having suffered from diarrhoea during the previous fortnight, and community-level environmental factors such as the availability of treated water. No variables representative of parental characteristics show any significant effects in the regular OLS.

One of the objectives of this paper is to demonstrate that, in the absence of correction of the selection bias, the estimates are not true effects, especially for mother's education and other mother-related covariates. The second column in table 3 shows the second-stage OLS coefficients where the selection bias is corrected. (This computation was performed using LIMDEP econometric software [20], which also corrected the standard errors.) The correction-factor coefficient (l) is large and positive, as hypothesized, and highly significant, suggesting its important role in this analysis. It is evident that many variables, especially those of parental environment, have increased in magnitude and significance, while a few others have decreased. Also, a change in signs occurs in a few instances and must be discussed.

TABLE 3. Estimation of log height for age of children less than 60 months old

Sample size = 3,377.

The dependent variable is the logarithm of the standardized (percentage to the international reference) height measure. The estimated coefficients are multiplied by 100. Therefore. they are interpreted as percentage change in the standardized height with respect to a unit increase in the value of covariates.

*Significant at 10%.
**Significant at 5%.
***Significant at 1%.

The mother's age at the time of the child's birth and her secondary education become significant at the 5% level after correction of selection bias. The child's sex, being born as a twin, and the mother's and father's education increase their influence in the same direction of association. The mother's current work status, her marital status (unmarried, widowed, separated), and community-level radio ownership change their direction of association altogether, but they remain statistically insignificant in both estimations. All these changes are worth discussing in light of the correction for selection bias.

Mother and child characteristics

The mother's age when the child is born shows a positive but declining effect on the height of children after correction for selection bias. The association reaches the maximum at 38.4 years of age, after which it is negative. The standardized height (i.e. the percentage of the reference median height for age) decreases as children grow older, until the minimum is reached at 46 months of age; younger children fare better than older ones in comparison with the standard reference group. This suggests that the adverse health effects accumulate with age during the first few years of childhood, and younger children are exposed to a relatively better development environment than older ones (this factor could be most relevant in a rapidly developing economy). Female children's highly significant advantage over males increases from 0.7% to about 1.0% after the control, and the disadvantage of a child of twin birth increases to 6.6% from 3.9%.

The average duration of breast-feeding for the children (including those still being breast-fed at the time of survey) was 13 months. To capture the effect of differential duration of breast-feeding for a given age, the deviation of the duration of breast-feeding relative to the mean duration for the same age was used as a covariate in the analysis. This measure has a stable significant negative relationship with the height of children (the magnitude and significance do not change even after the correction for selection bias). Children who are breast-fed for a longer time seem to be shorter. It may be that extended breastfeeding is not adequately supplemented with other types of foods and that this adversely affects child health. However, it might be that mothers may consciously breast-feed weaker children for a longer time in Uganda, which leads to the endogeneity bias of the estimation. Yet another possible confounding factor is the effect of household wealth: that is, poorer mothers probably breast-feed their children longer. The coefficient for the length of breastfeeding should be interpreted with caution.

It is suspected that the relationship between the length of breast-feeding and child height would be different depending on the age of the child. Indeed. the separate regression results by the age of the child indicate that the relationship is positive (but not significant) among the children under 18 months old, whereas it is significantly negative among those 18 months old or older. (The estimated coefficients of breast-feeding are 0.20, 0.80, - 2.17, and -1.96 for the samples of children less than 6, 6-17,18-36, and 37 months old or over respectively. The estimated coefficients of the other variables did not vary much by the age of child.)

Parental characteristics

Parental education is measured as a three-level dummy variable uneducated; primary school, up to seven years; and secondary school, eight or more years.* Without correction, the associations are positive but none is significant. After correction for selection bias, secondary education of mothers shows a significant advantage in improving child height by 1.2% compared with the children of uneducated mothers. Furthermore, the magnitude and significance level of primary education also increase. This suggests that the regular uncorrected OLS did underestimate the effect of female education on the dependent measures. It has often been found for many African countries [21; H. F. DeRose, personal communication, 1992] that there is no significant association between height for age and mother's education.

This could largely be due to non-correction for the selection bias. However, this analysis seems to suggest that in societies where female literacy is low, a relatively higher level of maternal education (secondary level in the case of Uganda) is necessary to produce long-term health in children.

The positive, although not statistically significant, associations between height for age and the mother being currently unmarried (never married, widowed, separated) and currently working become negative after correction for selection bias. (Data from rural north-eastern Brazil [22] and from Mali and Senegal [21 ] showed a positive but not significant association between the unmarried status of the mother and the child's height for age. Since infant and child mortality is fairly high in these areas, it is to be expected that the selection bias will be relatively more severe.) These again are good examples of the misestimation of the respective associations in the regular uncorrected OLS estimations. The correction indeed indicates that both a mother's unmarried status and her work adversely affect the long-term growth of children. Previous research has found that female-headed households are normally much poorer across the world, and more so in the developing countries. Many types of women's work outside the home even in some African countries have negative effects on child care and health [H. F. DeRose, personal communication, 1992].

Both the father's primary and secondary education show a positive but insignificant (5%) effect on child height even after correction for selection bias. The magnitude of the effects, however, more than doubles when the correction is performed. This seems to suggest that the father's education, which is a proxy for long-term family income or household wealth, is not important in the African context. It may well reflect specific cultural factors involving the rules of family formation, co-residence, and the pooling and distribution of household resources in Uganda.

Environmental risk factors

The effects of household-level environmental factors are encouraging. All the signs of the seven variables included are in the expected direction and remain consistent even after correction for selection bias, although only floor quality, ownership of a radio, and reported episodes of diarrhoea show significance. The positive associations of better-quality housing and having a toilet in the home suggest their roles in improving overall household hygiene and reducing the risk of infections. Children living in houses with cement floors have a better chance of improving their height than those who live in houses with earthen floors.

Since data on the duration of access to tap or pipe water and the duration of living in a house with a cement floor are not available, these effects have to be considered with care. But, as only children less than five years of age are included in this analysis, it is likely that both are fairly robust. However, household environmental factors such as quality of housing and the presence of a toilet are likely to be highly correlated with income or wealth, in which case the coefficient could reflect some of the income or wealth effect.

The community-level aggregates of the risk factors are included to pick up the effect of the quality of the exogenous environment. Drinking water shows significance that also is corrected from a negative to a positive association, the expected direction. Besides, the coefficient of the quality of housing is positive and large, although not significant. The coefficients of these variables in general are not significant.

The area surveyed by the OHS in Uganda is divided into six geographic regions based on administrative units and dominant language. Kampala, the only city, is treated as a separate region. Each region is considered as one dummy, and Kampala is the omitted category. Only residence in the Southwest has a negative effect on the height of children when compared with Kampala. Two of the remaining four regions show a positive and significant effect on child height. Uganda has a multi-religious society: the three predominant religions are Catholic, Protestant, and Muslim, but there are no significant differences in child height among them.

Interaction effects with parental education

Urbanization and urban living in developing countries are normally considered advantageous mainly because of easy access to utilities, health care, and information. It is expected that children living in urban areas will fare better than their rural counterparts. The effect of the mother's education also may differ between urban and rural areas. To understand these relationships, the interaction terms between place of residence and female education are included as regressors in a separate specification as shown in the third column of table 3. It is important to note that being uneducated and living in urban areas is the worst combination as far as child height is concerned. The effect of the mother's education on child height is much greater in urban than in rural areas, as shown by the large positive coefficients of interaction terms. In urban areas the mother's primary education improves her child's height by 1.5%, but it has negligible effect in rural areas. Secondary education improves the child's height by a much larger 3.7% in urban areas, whereas it improves it by only 1.8% in rural areas. However, the interaction terms are all insignificant. The question of the mechanism by which parental education and urban living affect child health is much more complex. It could work through a better use of health improving facilities and available resources, or by increasing the resources themselves. This issue requires further investigation.

In developing countries ownership and use of a radio is considered a good indicator of the extension and use of knowledge meant to benefit the populations. In fact radio is extensively used for this purpose. It is expected that access to a radio would therefore have a positive effect on improving children's health. The possibility has been discussed that radio may serve as a substitute for education. This proposition would hold if uneducated women with a radio show relatively larger effects. To test this hypothesis, access to a radio and its interaction with the mother's education were introduced into the analysis. It turns out that there is no significant effect at least on child height, but the negative coefficient of the interaction term between having a radio and secondary education suggests that the effect of the radio is likely to be lower among women with more education.

Finally the interaction terms of the mother's and the father's education with the sex of the child arc examined to see whether they indicate any sex preferences in the society. They are in general insignificant, suggesting that parental education does not contribute differentially to child health by the sex of the children.

Summary and conclusions

The bivariate and regular OLS analyses were suspected of misestimating the effects of covariates because of selectivity bias. It is reasonable to assume that the children who have died were usually weak and sickly and that their omission from the sample yields biased estimates. This paper, therefore, presents empirical results correcting for this selection bias and discusses the relative role of the determinants. The analysis illustrates the need to undertake corrections if anthropometric data are used to signify child health, particularly where mortality rates are high, as in sub-Saharan Africa.

Important determinants of child health in Uganda are child characteristics and some maternal characteristics. Environmental factors at both the aggregate community level and the household level are also significant. Mothers' characteristics are relatively more sensitive to the correction for selection bias. In particular, the effect of the mother's secondary education is almost doubled and becomes significant in determining children's height.

The interaction effects of maternal education with urban residence and ownership of a radio are revealing. Urban living and access to a radio are given special emphasis because of their policy relevance. This analysis suggests that urban living and female education are complements, whereas radio and female education are substitutes in the household production of child health. The mother being unmarried (never married, widowed, separated) and her work outside home, which show a positive association with height for age in the regular OLS, become negative when corrected. Although the associations are not significant, the change of signs supports the contention that selection bias indeed is a problem in understanding data on child anthropometry.

Overall, the results lead us to speculate that Uganda may be facing a stage of health transition in which the effect of community and individual socioeconomic variables are beginning to show up significantly. Further exploration is required to find whether this is true for other developing countries. Although an all-round developmental effort is in order, selective interventions aiming to improve female education and, where that is difficult, extension of appropriate information through radio are likely to improve child survival and quality of life.

Appendix: First-stage probit and marginal effects on child survival status

The first-stage probit regression was run on the survival status of children, which is a dichotomous variable (not alive = 0, alive = 1). The maximum likelihood coefficients of this probit are used to compute A, the correction factor used in the subsequent second-stage OLS regressions. The marginal effects of the covariates also are presented for easy interpretation. Overall 14.4% of the children born alive during the previous five years were dead at the time of survey. As expected, the child characteristics show significant relationships with the probability of death. Only a few individual-level (child and mother) variables show significant effects, whereas the exogenous environmental and socio-economic variables appear not to be important in explaining the survival status. For example, child characteristics such as age, sex, previous birth interval, and being born as a twin and maternal characteristics such as age, marital status, and care during pregnancy show significant associations with the probability of survival.

The mother's age at the child's birth significantly influences survival in a positive way; the marginal effect reaches the maximum at about 31.5 years of age, and from then on the association turns negative. Children born out of wedlock and those living with a single parent, mostly the mother, have a substantially lower survival probability than children who normally live with both parents. Females seem to have a significantly higher chance of survival over male children. Whether this suggests a daughter preference or simply the biological differences between sexes or is because of data problems is difficult to resolve. As expected, longer birth intervals are desirable, whereas being born as a twin is highly disadvantageous for survival. The probability of survival improves tremendously if the mother had tetanus toxoid inoculations during pregnancy.

Both parents' education have positive effects but they are not statistically significant. The mother's work and other socio-economic covariates included in this equation do not significantly affect survival probabilities. Only the geographic region where the child lives seems to have some significance. There is a suggestion that in Uganda child death is influenced less by the socio-economic and household-level attributes. The determinants of survival are mostly biological and demographic.

Acknowledgements

This paper was written while the authors were visiting the Economic Growth Center at Yale University during 19911992. We thank T. P. Schultz, Jack Caldwell, Parker Mauldin, Ricardo Barros, Robert Evenson, and T. N. Srinivasan for their comments on an earlier version of the paper. Financial support for Shariff from the Rockfeller Foundation and Ahn from Yale University is acknowledged.

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