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A comparison of empirical models on determinants of infant mortality: A cross-national study on Africa
Health Policy, 24 (1993) 155-174 0 1993 Elsevier Scientific Publishers Ireland Ltd. All rights reserved. 1168-8510/93/506.00
155
HPE 00531
A comparison of empirical models on determinants of infant mortality: A cross-national study on Africa* Kwame P. Gbesemete
and Dick Jonsson
Department of Health and Society, University of LinkGping. Sweden Accepted 25 November
1992
Summary The goal of achieving health for all by the year 2000 has instigated numerous studies on the determinants of health. In this paper, we re-evaluate two models in which infant mortality - across twenty-eight low- and middle-income African states - is explained by socioeconomic, demographic, medical, environmental and political factors. The results indicate that the GNP per capita, school population as a percentage of the population under 19, population density and the percentage of the population with access to health care together explained 80% of the variations in infant mortality in the sample study. Apart from the GNP per capita and the school population as a percentage of the population under 19 which were negative and statistically significant, variables of importance for health policy, e.g. female literacy rate, water supply, food aid, calorie supply, health care expenditure and the degree of urbanization carried a negative sign but were nonsignificant. We interpreted the above thus: a reduction in infant mortality is feasible only with changes on diverse fronts rather than by marginal improvements in a few determining factors. A comparative test of the replicated model and our proposed model has shown that our model produced a better theoretical and statistical fitting than did the replicated model. Africa; Infant mortality; Socio-economic; factors
Demographic;
Medical; Environmental;
Political
1. Introduction International comparisons can hardly be used to give any normative answer on different health issues such as if the right amount of health care Address for correspondence:
Dr. Kwame P. Gbesemete, University of Linkoping, Department of Health
and Society, 58183 Linkoping, Sweden. *The twenty-eight countries in the sample are: Ethiopia, Zaire, Burkina Faso, Malawi, Uganda, Niger. Tanzania, Somalia, Togo, Benin, Liberia, Ghana, Sierra Leone, Kenya, Sudan, Lesotho, Mozambique. Mali, Zambia, Nigeria, Cote D’Ivoire, Zimbabwe, Cameroon, Tunisia, Senegal, Congo, Morocco. Botswana.
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reaches the right consumers, if the production is technically efficient, etc. Such issues according to Gerdtham [ 1] require more detailed cost-benefit analysis of specific health care programmes. However, international comparisons can be used to widen - in this case - our perception of the overall determinants of health levels either worldwide or for a specific geographical region. Determinants of health - the latter measured in terms of life expectancy and or age-specific mortality rate - is a well established field of research (see, for example, Refs. 2-5). Typical for these studies is that they were conducted using international cross-section data although there are exceptions where regional and district aggregates have been used for a given country, (see, for example, Refs. 6 and 7). In the Beenstock and Sturdy study, various socio-economic variables were regressed on infant mortality rates across Indian states to determine the factors that systematically account for variations in the named health variable. A recent addition to the literature is Cumper’s study [8] which examined the relationship between infant mortality rate and a wide range of socio-economic, political, biological and environmental factors. Cumper’s study covered a total of 163 countries and was based on data from 1976. According to the WHO [9] the under-five mortality rate reflects the socioeconomic status of a nation while the infant mortality rate is a measure of the level of health care services. During the past two decades most countries in the Third World improved accessibility and the quality of their health care services [lo]. Despite these efforts the level of infant mortality particularly in Africa remains relatively high. This raised the question whether there are factors outside the medical sphere which affects infant mortality rate. The present study seeks to answer this question using data for 28 low- and middle-income African countries for the year 1984. Apart from the authors personal interest in Africa, we have chosen the African region because there is a dearth of literature on cross-national analysis on determinants of infant mortality in Africa. Initially, the model suggested by Cumper [8] - being one of the most widely cited studies in this field - is replicated. Secondly the study estimates and evaluates a model proposed by us on health determinants including socio-economic, demographic, medical, environmental and political factors. A cross-sectional study of this kind has certain advantages when compared with time-series analysis. For example there is smaller variances of the estimated structural parameters in cross-sectional study because the dispersion of the values of regressor variables is larger than what is usual in timeseries data. However, there are certain limitations with cross-sectional studies. First, the small sample size (countries) imposes restrictions on model size and statistical inferences. Second, in practically every empirical analysis of this kind the presence of n&measured and/or unobserved variables that are correlated with the explanatory variable is incorporated in the model. Third, cross-sectional comparisons are static, whereas the observed differences in health levels are the outcome of real (permanent) differences and transitory differences due to countries being in different stages of some adjustment process. The study proceeds as follows. An analytical framework is outlined in
157
Section 2. In Section 3, data, measurement and statistical methodology are reviewed. In Section 4, the empirical analysis of the determinants of infant mortality is reported. Furthermore some old models from earlier studies are replicated and, within the framework of encompassing tests, the former models are compared with ours. The final section is devoted to the interpretation and discussion of the results.
2. Analytical framework Differences in health levels can be explained as the outcome of a composite of factors namely; socio-economic, demographic, medical, environmental and political factors [8]. Any study on health determinants that does not take into consideration the above factors will therefore be incomplete. However, in practice and where there are conceptual and measurement difficulties there is the problem of how to operationalize and hence assess the quantitative impact of the named factors. In this study, we focus attention on factors that have featured most prominently in the literature. These factors are categorised in the four broadly defined groups as stated above. So&-economic factors Education
In numerous studies, education is pointed out as one of the most powerful predictors of mortality [l l-141. Others noted the role of education in influencing a population’s use of available health and medical services [ 15-171. An educated population seems to be more receptive to medical, sanitary and nutritional information that leads to increased longevity [18-191. The educational level of females is particularly vital to the health of infants [20-211. The educated mother is likely to make use of the numerous alternatives in child care and the treatment of illness that are available in a rapidly changing society. She is also more likely to take personal responsibility in such fields as birth control, etc. [22]. For these reasons a negative association is posited between educational status and infant mortality. Water supply and sanitation
The role of water supply and sanitation in improving health is a widely studied field of research. Improved water supply and sanitation is very effective against bacillary dysentry, cholera and other diarrhoeal diseases [23]. Hence, it is assumed that the higher the proportion of the population with an acceptable standard of water supply, the lower will be the level of infant mortality ceteris paribus. Gross national product per capita
The most general measure of resource availability is the gross national product (GNP) per capita. Numerous studies have found that as incomes decrease, health levels tend to deteriorate [24-261. Others have observed a positive correlation between income levels and health care expenditure [27].
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Income is measured in Cumper’s study in terms of GNP per capita, and it is posited so as to be negatively correlated to infant mortality. Percentage of the population with access to health care
A substantial number of scholars have analyzed the relationship between various measures of health and medical services and mortality. For example in Bangladesh, the provision of medical services such as immunization of children and nonpregnant women led to lower neonatal deaths among children whose mothers had two tetanus injections 9-32 months before delivery than among those in the control group [28]. In Costa Rica, the provision of medical services helped to negate mortality in the nonadult population (291. According to some authors, health and medical services are of much greater importance than measures of social and economic development in determining mortality levels [30-321. In the light of the above, we argue that the more available the health services are to the population - as measured by the percentage of the population with access to health services - the lower will be the infant mortality rate. It should be emphasised that not everyone shares the enthusiasm expressed in earlier works on the importance of medical services in decreasing the mortality rate. In a survey of global mortality, Gwatkin [33] observed a substantial decrease in the capacity of modern medical and health services to combat certain diseases, e.g. diarrhoea, in developing countries. Low birth weight
Clinical studies conducted by Chase [34] found a statistical correlation between birth weight and infant mortality. Birth weight is determined by a number of factors such as the nutrition of the foetus, genetic factors, etc. [35]. Low birth weight babies are not a homogeneous group. A classification of low birth weight babies gives us groups with a specific pathological cause, preterm deliveries and those which are full term but small for gestational age ]8, p.541. Low birth weight babies are disadvantaged in respect of mortality, as has been shown by the experience of groups affected by pathologies or prematurity. In the light of the above, we posited a positive relationship between low birth weight and infant mortality rate. A major problem with this data is that it is likely to be underestimated because the greater part of all births in most African countries take place in the home often with the help of traditional birth attendants who are hardly capable of weighing babies at birth due partly to the fact that most of these birth attendants are illiterate. Economic social standing
The use of the gross national product (GNP) does not tell us much about the quality of life and/or the health of the people. Here instead, we use a different dimension of economic development, ‘economic social standing’ which represents the average of ranks for GNP per capita, educational status of the population and level of health. For an aggregate of countries, an index of overall economic development can serve the purpose of identifying
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development trends. In the light of the above, we posited a negative relationship between a country’s economic social standing and its infant mortality rate. A problem with this variable is that it is likely to be highly correlated with the variables listed above. Health care expenditure
Here we argue that aggregate health care expenditure determines the level of health care services. Infant mortality is determined by a wide range of factors including the level of maternal care. We therefore argue that the provision of health care services, e.g. maternity care, is likely to be poor if the level of health care expenditure is low ceteris paribus. Furthermore, the level of health care expenditure affects the purchase of medical equipment, e.g. incubators for saving the lives of premature babies. Hence, we argue that infant mortality will be inversely related to health care expenditure. The exact component of the health care expenditure per capita is not stated other than as it reflects total government expenditure on health. If the greater part of this expenditure is devoted to salaries, then obviously it will have less impact on infant mortality. More desirable data would be govemment expenditure on pediatric and/or maternity wards. However we do not have this data. Diet and nutrition
The relationship between diet and nutrition and health is a field of research which has been extensively investigated by a number of scholars [36-371. A recent report by the World Health Organization [38] named malnutrition as one of the underlying causes of child mortality in 46 African countries. Improved diet supplementation programs significantly reduced child mortality in Guatemala [39]. Similar conclusions were reached for Peru [40]. In an Indian study, it was observed that improved nutrition is a prerequisite for increased life expectancy [30]. In our study, the diet and nutrition composite is measured by food aid in metric tons and calorie supply as percentage of requirement. The latter variable has been subject to criticism due to doubts about its accuracy in the case of certain developing countries - but also because it does not make any allowance for the disparities in the distribution of food between and within households. Furthermore, the indicator is said to be unsatisfactory if health is measured in terms of infant mortality rate. The argument here is that in most developing countries breast-feeding is widespread in the first year of life [g, p.521. In contrast to the above postulations, we expect a relationship between nutrition and infant mortality partly on the basis of the nutritional status of pregnant and nursing mothers, but also on the basis of foods offered to the infants to supplement breast-feeding. Hence, as stated earlier we expect an inverse relationship between the diet and nutrition composite and infant mortality rate.
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Food aid
According to the World Bank [41] and UNICEF [42] the food deficit on the African continent was most acute during the sample period. The unavailability of food especially in times of war or drought can be detrimental to health particularly for pregnant women, but also in the case of children who have been taken off the breast. In the light of the above, we assume that food aid can help to compensate for the loss of food. Hence, we envisaged a negative relationship between the named variable and infant mortality. Demographic factors Fertility
It is argued that infant deaths increase with ascending number of births and shorter birth intervals. With shorter birth intervals, less care is given to the children. Furthermore, high fertility may lead to competition for the limited resources available to a household [43]. In a study, Oni [44] found that on the average, child mortality could be lowered by 8% if the number of babies born were limited to three or less. In the light of the above, we posited a positive relationship between a high fertility rate and infant mortality. Density
High population density is deleterious to health insofar as it aggravates problems of sanitation and facilitates disease transmission [45]. On the other hand, it is argued that the effectiveness of health service inputs varies inversely with the dispersion of the population, hence a low population density is not conducive to health. According to Cumper, the net effect of the density variable at the international level is to produce a significant negative correlation with health. High population density such as high urban settlement, may lead to greater availability of social services. This in turn may offset negative features such as disease transmission [8, p.481. Medical factors Physicians, nurses and hospital beds
Three categories of medical inputs have been chosen for the regression analysis, namely: the number of physicians, other health workers, e.g. nurses, and the number of beds, all expressed in per 1000 population. The three variables indicate the degree of medical accessibility, hence a negative relationship is posited between the named variables and infant mortality. For example when the stock of physicians increase and the workload decreases doctors may.spend more time on each patient - in this case pregnant women and newborn babies - than otherwise. A similar argument holds for nurses. An increased number of hospital beds may lead to more admissions in hospitals and thereby the diagnosis and cure - provided there are drugs and equipment in the hospital - of potential killers.
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Environmentaland political factors Drought and involvement in war Drought and wars are likely to be positively correlated to infant mortality due to their impact on the individual’s purchasing power. In a study on the causes of famine, it was concluded that famine is not due to drought and wars per se but rather to the disruption in the individual’s power to purchase food and other items conducive to health [46]. Low purchasing power with its consequent impact on food intake especially by pregnant women is likely to affect the development of the foetus. As stated earlier, a poorly developed child - at birth - is more liable to disease and death than a well developed one. Hence we argue that infant mortality will be higher in countries which have been subjected either to war or to drought.
3. Data, measurement and statistical methodology Data The data used in the present study are taken from diverse sources and are for the year 1984. Since these data files have been used in many studies in the area, comparability is likely to be the best among the available data sources. However it should be emphasised at the outset that numerous problems regarding data quality still remain. To judge the quality in terms of validity, reliability and precision of such aggregate archival data is difficult. There is therefore enough room for imperfect reliability with regard to crosssection comparisons basically as a result of differential classifications; particularly in the case of health determinants. Furthermore, there is no homogeneity in international data compiling. From the viewpoint of reproducibility of empirical analyses however, we have opted for the current situation i.e. to use the data which is available instead of embarking on earlier practices where individual investigators performed their own ‘massage’ to the data. The cross-sectional analysis includes observation from 28 low- and middle-income African countries. We have chosen these countries because they have similar causes of mortality, similar demographic distribution, small diferences in socio-economic status and above all they are within the same geographical (African) region. Furthermore we have selected countries for which data is complete for the sample period.
Measurement In order to clarify this paper Table 1 reports the operationalised and the data sources used.
variables
Statistical methodology The construction of the empirical model is deduced from the theoretical framework. A number of variables - percentage of the population with
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Table 1 Dethition of the variables in the empirical model for the determinants of infant mortality Variable
Description
Source
IMR
Infant mortality rate; i.e. deaths under 1 year of age per 1.000 hve births Density: population per square km Degree of urbanization: i.e. urban nonulation & percentage of total population Food aid in metric tons School population (5-19 years) per teacher School population as a percentage of the population 5-19 years Percentaee of the total oonulation with reasonable access (oftkn*not more than 1 km distance) to safe and adequate drinking water supply Fertility rate i.e. the number of children that would be born per woman, if she were to live to the end of her child-bearing years and bears children at each age in accordance with prevailing age-specific fertility rates Physicians per 1000 population Other health workers, e.g. nurses per 1000 population Number of hospital beds per 1000 population Percentage of the population with simple sanitary latrines; safe disposal methods for personal and household wastes Gross national product per capita in US% Calorie supply, i.e. daily per capita calorie supply as percentage of requirement Health care exnenditure ner canita in USS Low birth weight, i.e. children*bom weighing
1101
DEN URBAN FOOD TEA PUPC PWSC
FER
PHY OHW BED PEDC GNP CAL HEXP LBIRTH FLITT HCA
SOCECO
less than 25 000 g Female literacy rate, i.e. percentage of females females aged 15 and over who can read and write Health care access, i.e. percentage of the population that can reach appropriate local health services by the local means of transport in no more than 1 h Socio-economic standing. This represents average ranks for GNP per capita, educational status of the population, and level of health
r::; [10,531 ;::j 1541 [3gJOl
[lo,551
[541 [56,571 [571 UOI
1101
1541
access to health care, low birth weight, socio-economic standing, health care expenditure, nutrition and diet, food aid, drought and involvement in war which we think (intuitively) affects the level of infant mortality but were excluded from Cumper’s models were discussed and tested in our empirical search model. The statistical analysis was carried out as follows. First, we replicated Cumper’s model on a disaggregated African data. Later, we constructed an empirical search model by including variables derived from the analytical framework which minimised the Akaike criterion. The replicated models were later evaluated in relation to our proposed model. Both models are
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evaluated with respect to theoretical consistency, i.e. in accordance with theoretical considerations and statistical performance. The latter is expressed in terms of the R2 (adjusted (adj.)), the log-likelihood value, the parameter of the t-value and the significance level of the J-test. The J-test is an encompassing test of nonnested models. For a technical discussion of the J-test see Refs. 47 and 48. The test is used to evaluate the best of Cumper’s models but also to evaluate the best of Cumper’s models with our proposed empirical model. This test procedure is necessary in assessing the statistical validity of the quoted statistical significance of parameter estimates. The models are estimated in double logarithmic form. However unlike Cumper, we have not done any other data transformation such as deviations, etc. The regression equations are based on the same data set which renders systematic model comparisions free from uncertainties as to data reliability. The models are also estimated with the same estimators. The problem of heteroscedasticity is not present in any of the estimated models because the estimation procedure includes heteroscedasticity invariant covariance matrix. In the first estimation of the model, ordinary least squares (OLS) is applied. This is the same estimator used by Cumper. The OLS estimation is a standard estimator but is sensitive to autocorrelated residuals. In the second estimation, we used the general least squares (GLS) estimator which includes a moving average component (MA) for the error terms. The coefflcients of the moving average component picks up the behaviour of the residuals [48]. In the statistical analysis, countries that suffered war or drought in the year 1983-1984 are given one whereas those that suffered nothing are assigned zero. The statistical method is based on an international cross-section analysis for the year 1984. We have chosen this year due to data availability.
4. Statistical analysis 4.1. Replication of Cumper’s models 4.1.1. Cumper s first model
Cumper’s main hypothesis [8, p.31 is that a change in the factors which improve health at the individual or local community levels could be generalised to be positively correlated to health at the aggregate level, e.g. improved sanitation may lead to low infant mortality rate. The author noted that due to the high correlation between the independent variables and income per capita measured as GNP, the statistical analysis was carried out not in terms of the original data base but in terms of the deviations of the data in logarithmic form from the regression line relating them to GNP per capita. Accordingly, because of the strong correlation between income and the independent variables, the procedure outlined above, standardised for income but also for the independent variables. Furthermore, due to the lack of observations for some variables, multiple regression analysis could not be
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applied uniformly on all the variables. Therefore, an approach was adopted where four variables - GNP per capita, hospital beds, physicians and other health professionals per 1000 population - for which data was complete and for which there is a strong causal connection with health both at the macro and micro levels were selected for multiple regression analysis. The transformed data in Cumper’s empirical model are logged in natural logarithmic form and have the following structure: 1nIMR = Bo + BJnTEA + BJnPUPC
+ BJnPWSC + B&DEN +
BJnFER + BdnPHY + B7LnOHW + BsLnBED + B9LnPEDC + e,
(1)
with Bi, B2, B3, Bq, B6, Br, Bs, & c 0 and Bs > 0 and where IMR, infant mortality rate, i.e. deaths under 1 year of age per 1000 live births; TEA, school population (5-19 years) per teacher; PUPC, school population as a percentage of the population 5-19 years of age; PWSC, percentage of the population with reasonable access (often not nore than 1 km distance) to safe and adequate drinking water supply; DEN, population per square km; FER, fertility rate; PHY, physicians per 1000 population; OHW, other health workers per 1000 population, e.g. nurses; BED, number of hospital beds per 1000 population; PEDC, percentage of the population with simple sanitary latrines; safe disposal methods for personal and household wastes. In his regression analysis, Cumper [8] incorporated two educational variables - the total population in educational institutions as a percentage of the under 15 population and the number of teachers per 1000 of school population - without explaining why these two variables should be incorporated simultaneously in the regression equation. Cumper never defined what constituted adequate excreta disposal. Therefore, we do not know whether adequate excreta disposal meant improved disposal of waste products explained in terms of the daily collection of rubbish or whether it meant better toilet facilities. Information which could have increased our knowledge about what constituted adequate excreta disposal is missing. The main findings of the above model are summarised in Table 21 on p. 110 of Cumper’s book. The model is consistent with the hypothesised theories stated earlier. However the level of significance was not reported for the various variables. This makes interpretation of the results difficult. Furthermore the R-square and R-square (adj.) for the nine independent variables were not stated in the multiple regression results reported in his Table 21. 4.1.2. Cumper’s second model Cumper’s second model including the transformed rithm form has the following structure: 1nIMR = Bo + B&GNP
data in natural loga-
+ BJnPHY + BJnOHW + B JnBED + e,
(2)
19 0.45 0.76 0.66 -113.9
2.27 0.18 -0.02 -0.03 0.01 0.31 -0.04 0.03 0.13
;.;+ -0:9 0.7 1.5f
3.7’ 1.5+ -0.4 -0.6
18 0.41 0.78 0.67 -112.9
-0.94
A:: -0.5
-0.28
4.5;
;.;t -0:9 0.6 1.4%
t
2.27 0.18 -0.02 -0.03 0.01 0.31 -0.04 0.03 0.13
B
B
t
GLS
OLS
23 0.46 0.75 0.71 -114.4
-h5 0.06 0.19 -0.14
3.83
B
OLS
Model 2
??
8.9’
-2.1 * 1.9; -;:;*
t
22 0.37 0.80 0.76 -111.2
-0.72
-0.03 0.06 -0.14 0.19
-
3.83
B
GLS
4.3’
-1:7+
-1.0 1.5:. _;.;**
t
R2, the adjusted coefficient of determination;
&nificant at the 0.5% level. Significant at the 2.5% level. tSignificant at the 5% level. ‘Significant at the 10% level. “The OLS and the GLS in both models are estimated with heteroskedasticity consistent covariance matrixes. bPercentage of the population with adequate excreta disposal (PEDC) is excluded from the regression for lack of data. ‘Log(L) is adjusted for functional transformations.
Statistics
:Y& BED GNP RES:MA (1)
Variableb Constant TEA PUPC PWSC DEN FER
Model 1
log-likelihood value.
d,, degrees of freedom; SSE, sum of square error; R*, coefficient of determination;
Replication of Cumper’s models on infant mortality rate on nine independent variables. Multiplicative functional form’
Table 2
Log(L),
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with Bi B2 B3 B4 < 0 and where IMR, infant mortality rate; GNP, gross national product per capita in US$; PHY, physicians per 1000 population; OHW, other health workers per 1000 population, e.g. nurses; BED, number of hospital beds per 1000 population. The use of variables such as GNP per capita, beds, physicians and other health workers as standardising variables in explaining the effect of other factors on infant mortality rate becomes doubtful when one considers the fact that these variables are highly correlated with GNP per capita. Furthermore, the three last named variables are proxies for medical inputs. Of late however, the role of these inputs in health improvement has been subject to criticism and doubts [49-521. The two models are nonnested because certain variables included in Model 1 are missing in Model 2 and vice-versa. Apart from the inclusion of GNP per capita in Model 2, Model 1 can be seen as a more general model. A plausible question is which of the models is to be preferred from a statistical or a theoretical point of view. 4. I. 3. Results Cumper [8] studied the problem of infant mortality at the aggregate level. Using the same variables as Cumper, we were essentially able to replicate his results on twenty-eight African states. Table 2 summarizes the results of our replication of Cumper’s models on nine independent variables. As evident in Model 1 (OLS), only one variable, the fertility rate (FERT) with a coefficient of 0.31 is significant at the 5% level. Two other variables, school population per teacher (TEA) and number of hospital beds per 1000 population (BEDS) are significant at the 10% level, respectively. The elasticities of the latter variables are 0.18 and 0.13, respectively. The abovenamed variables emerged significant at the 10% level respectively in Model 1 GLS. The other variables incorporated in Model 1 (OLS) and (GLS) namely: school population as a percentage of the population 5- 19 years (PUPC), percentage of the total population with reasonable access (often not more than 1 km distance) to safe and adequate drinking water supply (PWSC), population density per square km (DEN), physicians per 1000 population (PHY) and other health workers, e.g. nurses (OHW) are nonsignificant. Model 1 is theoretically consistent except variables like school population per teacher (TEA), other health workers (OHW) and number of hospital beds per 1000 population (BEDS) which did not carry the expected sign. The R* (adj) for the eight variables included in the ordinary least squares (OLS) regression equation in Model 1 is 66% and 67% for the general least squares (GLS). A re-estimation of Cumper’s Model 2 using the OLS method shows how infant mortality is explained by the number of physicians per 1000 population (PHY), other health workers, e.g. nurses (OHW), number of hospital beds per 1000 population (BEDS) and the gross national product per capita (GNP). The elasticities for the named variables are -0.05, 0.06, 0.19 and -0.14 respectively. As evident above, the reported coeflicients for (BEDS) and (OHW) are positive. A practical explanation may be that the positive
167
signs reported for the variables (BED) and (OHW) could be an artifact indicating increased registration of infant mortality when the number of beds and other health workers, e.g. nurses increase. Furthermore, a theoretical and a statistical explanation may be that the variables in the model are highly correlated and subject to omitted variable bias. It is interesting to note that in Model 2 GLS regression, GNP was the only variable that emerged with any significant negative impact on infant mortality. The number of physicians is nonsignificant in Model 2 GLS. On the other hand, the number of beds per 1000 population (BEDS) and other health workers (OHW) remained positively significant. The reported coefticients for the significant variables in Model 2 GLS regression are similar to those of the OLS. The R2 (adj) for the OLS in Model 2 is 71% and 76% for the GLS. The full model R2 in both regression is 75% and 80%, respectively. We compared Cumper’s Model 1 with his Model 2 and vice-versa. The comparisons were performed using a nonnested hypothesis testing procedure. The results are shown in Table 3 below. Table 3 Comparison of the two models: nomwsted hypothesis testing
Model 21 compared with Model 21
Coefficient
SD
J-test
X:!
0.3999 0.2513
::;
From the results, it is apparent that Cumper’s Model 2 is statistically superior to Model 1 as indicated by the J-test which was significant at the 5% level. We cannot reject the hypothesis that Model 2 encompasses Model 1 but we have rejected the inverse hypothesis. 4.2. The empirical search model 4.2.1. Model construction Having completed the replication we proceed to propose an alternative model to explain the determinants of infant mortality in Africa. The proposed model incorporates variables which were overlooked in Cumper’s models. The empirical search model takes the following expression. 1nIMR = B, + BilnXi + B2lnDi + B,lnMi + BJnEi where IMR, infant mortality rate; Xi, socioeconomic variables; Di, demographic variables; Mi, medical variables; Ei, environmental and political variables. The model is constructed by including variables stepwise in order to minimize the Akaike criterion (AIC)-criterion. The AIC-criterion is a statistical discrimination criterion and not a test procedure from a theoretical point of view. The estimator in detecting the original empirical model is ordinary least squares.
168
In the construction of the empirical model, other variables deduced from the theoretical framework were tested but in accordance with the procedure of minimizing the AIC-criterion’they were excluded from the equation. The following variables - gross national product per capita (GNP), school population as a percentage of the population 5- 19 years of age (PUPC), population density (DEN) and the percentage of the population with access to health care (HCA) - were the only ones that minimised the AIC criterion, hence their inclusion in the empirical model as shown in Table 4 below. The coefficients in the OLS and the GLS regression can be interpreted directly as elasticities. The results indicate that a 1% increase in the gross national product per capita (GNP), school population as a percentage of the population 5- 19 years of age (PUPC) and percentage of the population with access to health care services (HCA), led to a -0.11, -0.26 and -0.13 percent decrease in infant mortality rate, respectively. On the other hand, a 1% increase in the population density led to an 0.06% increase in the dependent variable. The reported coefficients are similar in both the OLS and GLS regressions. The models are rather robust and not so sensitive to the choice of estimators. They are consistent with a priori theoretical considerations and include only significant variables as evident in both the OLS and the GLS equations. The reported R2 (adj.) is 79% for the OLS and 80% for GLS regressions, respectively.
Table 4 Estimation of our model on the determimmts of infant mortality in twenty-eightAfrican states d, degrees of freedom; SSE, sum of square error; R’, coeflticient of determination; t i e adjusted coefftcient of determination; Log(L), log-likelihood value. GLSa
OLY t
B Variable Constant Ft!z DEN HCA RESMA”
6.65 -0.11 -0.26 0.06 -0.13 -
t
B 34.3’ -3.0’ -5.8: -;:;** -
6.65 -0.11 -0.26 0.06 -0.13 -0.33
Statistics
R2 (adj.) Log(L) b
23 0.33 0.82 0.79 -110.1
&nificant at the 0.5% level. Srgnificant at the 2.5% level. ‘Significant at the 5% level. aHeteroscedasticity consistent covariance matrix. bLog(L) is adjusted for functional transformations.
22 0.29 0.84 0.80 -108.3
28.7’ -3.9. -5.7;. -:::t -1.2
R2 (adj.),
169
Variables with a nonsignificant but a priori expected sign were female literacy rate (-), water supply (-), food aid (-), calorie supply (-), fertility rate (+), health care expenditure (-) and degree of urbanization (-). Nonsignificant variables with not expected signs were teachers (+), low birth weight (-), nurses (+) and beds (+). Of all these excluded and nonsignificant variables, calorie supply, urbanization, low birth weight and nurses received statistical t-values between 0 and 1. A surprising finding was that the dummy variable for war was highly nonsignificant. The same holds for the dummy variable for drought. A test of the socio-economic standing variable verified its status as a variable capturing the society’s socio-economic level. When the variable was included in the equation, the relationship between infant mortality and education and between infant mortality and gross national product per capita changed dramatically. Table 5 below compares our GLS to the GLS in the replicated Model 2. The idea is to evaluate the models and compare them with respect to theoretical and statistical performance. As evident in the table, four of our variables - the gross national product per capita (GNP), school population as a percentage of population 5-19 years of age (PUPC), population density (DEN), and the percentage of the population with access to health care (HCA) are significant. This can be
Table 5 A
comparisionof
our GIS with Cumper’s Made1 2 GIS’
d/, degrees of freedom; SSE, sum of square error; R,, coefficient of determination; adjusted coefficient of determination; Log(L), log-likelihood value. Our Model B Variable Constant GNP PUPC DEN HCA PHY OHW BED RES:MAa
Cumper’s Model 2 t
6.65 -0.11 -0.26 0.06 -0.13 -
28.7’ -3.9. -5.7;.
-0.33
-12
-::;t -
B
t 3.83 -0.14 -0.03 0.06 0.19 -0.72
Statistics 22 0.29 0.84 0.80 .108.3 &nificant at the 1% level. Significant at the 5% level. tSigniticant at the 10% level. “Heteroscedasticity consistent. bLog(L) is adjusted for functional transformation.
??
-;::**
22 0.37 0.80 0.76 -111.2
-q :.1** -1:7t
R,, the
170 Table 6
Comparison of our sear& model with Cumper’s models: nonnested hypothesis testing Coefficient
SD
J-test
compared with Cumper’s
0.5
0.1967
2.6
0~;~;1.k21 compared with Cumper’s
0.5
0.2942
1.7
O~r,~;;$l
compared to only three variables, namely, gross national product per capita (GNP), other health workers, e.g. nurses (OI-IW), and the number of hospital beds per 1000 population (BEDS) which were significant in the Cumper GLS regression. The R2, which is the explanatory power of a model, is much higher in our model than the replicated model. The reported R2 (adj.) in our model is 80% as compared to 76% for the replicated model. Table 6 compares our search model with Cumper’s model. Here, the idea is to see if our model encompassed the replicated models. The results indicate that our model encompassed the replicated model 1 and was significant at the 5% level. Our model does not however encompass the replicated Model 2. The J-test for our search model and the replicated Model 2 is significant at the 10% level.
5. Conclusions The main purpose of this study has been to provide a comprehensive analysis of eighteen variables potentially explaining the cross-national differences in infant mortality in Africa. The empirical results from the replicated Model 1 indicates that out of the eight explanatory variables only three, namely, fertility rate (FERT), school population per teacher (TEA), and the number of hospital beds per 1000 population (BEDS) were statistically significant. The reported coefficients in both the OLS and the GLS regressions for the named variables are 0.31, 0.18 and 0.13, respectively. In the replicated Model 2, the following variables, physician per 1000 population (PHY), other health workers, e.g. nurses (OHW), number of hospital beds per 1000 population (BEDS) and the gross national product per capita (GNP) emerged significant in the OLS regression. The physician variable (PI-W) was however insignificant in the GLS regression. The replicated Models 1 and 2 were compared with each other using the J-test. The results indicate that the F-acceptable model containing four variables, i.e. Model 2 is preferable to Model 1. Having replicated Cumper’s models, an alternative model was proposed to explain the determinants of infant mortality. The reported coeflicients both in the OLS and the GLS - in the proposed model indicate that a 1% increase in the gross national product per capita (GNP), school population as a percentage of the population 5- 19 years of age (PUPC) and accessibility to health care (HCA) led to a -0.11, -0.26 and -0.13 percent decrease in
171
infant mortality rate. On the other hand, the infant mortality rate went up by 0.06% whet_ the population density increased by 1%. We used an encompassing test to compare the relative efficiency of our model to the replicated models. The results indicate that our model encompassed the replicated Model 1 and was significant at the 5% level. However, our model does not encompass the replicated Model 2. It appears that the choice of an estimator had great consequences in terms of the results of the statistical analysis in general. The general least squares (GLS) is preferable to the ordinary least squares (OLS) because the former produced more effcient estimates of the parameter variances and more reliable t-statistics. Other variables were found to be of importance and consistent to previous studies but were non-significant. For example, a negative relationship is reported for female literacy rate, water and calorie supplies, degree of urbanization and the infant mortality rate. Health care expenditure and food aid carried the expected sign. Four coefficients, namely, school population per teacher, other health workers, e.g. nurses, low birth weight and hospital beds per 1000 population have ‘wrong’ signs. It is approriate at this point - given the importance of the findings in this study - to conclude with a few problems and remarks. First cross-sectional studies do not show the dynamics of change or issues concerning structural changes, because cross-sectional studies deal with static comparisons. However this problem can be dealt with by pooling the data. A pooled crosssectional time-series has a number of advantages over a pure cross-sectional design. For example it is possible to test for other features in the relationship, such as temporal stability and lags. Furthermore, such a design may lead to an increase in the sample sizes. The small sample size evident in most pure cross-sectional studies constitutes an important limitation in statistical comparisons of different regression models. The GNP per capita appears to be the most important statistical factor in cross-national analysis of infant mortality. However, this variable should be treated with caution because the level of per capita income does not say anything about how the income is distributed. The negative sign reported for female literacy and infant mortality conforms with the results in earlier studies. There are however certain limitations with female literacy. For example child care practices are likely to be related to the mother’s working habits. The educated woman is more likely to work outside the home. Work of any kind may inhibit appropriate feeding, especially breast-feeding, in early life and this may reduce the chances of survival. It would therefore be interesting in future research to test the male literacy rate on mortality levels. The educated male is likely to secure a well paid job. If the husband’s income is high the female is more likely to stay at home and take care of the children and this might have a positive impact on infant and child survival. The health care accessibility variable is significant at the 5% level and carries a negative sign indicating that the level of infant mortality decreases if the population has access to health care services. This finding reinforced the universally accepted view of the World Health Organization [9] that the level of infant mortality is a reflection of the level of health care services and
172
their accessibility. Apparently, pregnant women and those with babies utilize health care services provided they are accessible. The accessibility variable used here should be treated with caution because geographical accessibility says nothing about the individuals’ capacity to pay for health services nor their capacity to communicate with health personnel. Both elements are essential in health care utilization. Both food aid and calorie supply carried a negative sign indicating a decline in infant mortality with improvements in the named variables. The food aid variable is of particular interest. During the sample period, most countries in the African region suffered drought and bush fires. It appears that food aid supplemented domestic food production and this helped to keep infant mortality low. Health care expenditure is negatively correlated to infant mortality. Apart from its effects on infant mortality, an increase in health care expenditure may contribute to economic growth and raise incomes. The two density variables, namely the population per square km and the degree of urbanization, appear to differ in their impact on infant mortality. As is evident in Table 4, infant mortality is positively correlated to population density. On the other hand, the negative sign reported for the urbanization variable implies that the more urbanised a country, the lower the infant mortality rate. It is likely - as argued by Cumper [8] - that a high level of urbanization leads to greater availability of social services and this in turn offsets negative features such as disease transmission. An extension of this study to cover the other geographical regions of the world could help to illuminate the determinants of infant mortality across countries with different ‘endowments’. Therefore, we hope in the future to see more empirically oriented studies including evaluations and comparision of models with policy implications in this field.
References Gerdtham, U.G., Essays on International Comparisons of Health Care Expenditure, Ph.D. Dissertation, LinkBping Studies in Arts and Sciences, No.66, University of Linkbping. Sweden, 1991. Preston, S.H., Mortality Patterns in National Populations with Special Reference to Recorded Causes of Death, Academic Press, New York, 1976. United Nations, Some aspects of socio-economic determinants of mortality in tropical Africa. In Proceedings of the Meeting on socioeconomic Determinants and Consequences of Mortality, United Nations, New York, 1979. Pendleton, B.F. and Yang Shu, O.W., So&-economic and health effects on mortality declines in developing countries, Social Science Medicine, 30 (1985) 453-460. Hobcraft, J.N., McDonald, J.W. and Rutstein, S.O., So&o-economic factors in infant and child mortality: A cross-national comparison, Population Studies, 38 (1984) 193-223. Beenstock, M. and Sturdy, P., The determinants of infant mortality in regional India, World Development, 18 (1990) 443-453. Patel, M., Modelling determinants of health, International Journal of Epidemiology, 10 (1981) 177-180. Cumper, G.E., Determinants of Health Levels in Developing Countries, Research Studies Press Ltd., Letchworth, UK, 1984. World Health Organization, Health Program Evaluation: Guiding Principles for its Application in the Managerial Process for National Health Development, Series No. 6, Geneva, 1981.
173 10 UNICEF, The State of the World’s Children, New York, 1989. 11 Jonsson, D., Socioekonomiska faktorer ock dodhghet: En jiimforande studie av dynamiska regressionsmodeller for sverige 1940/51- 1984, Mimeo Linkoping, Sweden, University of Linkoping, Department of Health and Society, 1990. 12 Grosse, R.N. and Auffrey, C., Literacy and health status in developing countries, Annual Review of Public Health, 10 (1989) 281-297. 13 Al-Hi, I.J., Kanawati, A.A. and McLaren, D.S., The formal education of mothers and their nutritional behaviour, Journal of Nutrition Education, 7 (1975) 22-24. 14 Grossman, M., The correlation between health and schooling. In N.E. Tercleckyj (Ed.), Household Production and Consumption, National Bureau of Economic Research (NBER), New York, 1975. 15 Caldwell, J.C., Education as a factor in mortality decline. An examination of Nigeria data. In Proceedings of the Meeting on Socioeconomic Determinants and Consequences of Mortality, United Nations, New York, 1979, 172-192. 16 Anderson, J.G., Causal models and social indicators: Towards the development of social system models, American Sociological Review, 38 (1973) 285-301. 17 Leigh, J.P., Direct and indirect effects of education on health, Social Science and Medicine, 17 (1983) 227-234. 18 Agarwal, D.K., Katiyar, G.P., Yadav, K.N.S. and Agarwal, K.N., Morbidity patterns in under-five children, Journal of Tropical Pediatrics, 28 (1982) 139- 143. 19 Caldwell, J.C., Reddy, P.H. and Caldwell, P., The causes of demographic change in rural south India, A micro approach, Population Development Review, 8 (1982) 689-727. 20 Cochrane, S.H., O’Hara, D.J. and Leslie, J., The Effects of Education on Health, World Bank Staff Working Paper, No. 405, Washington, DC, 1980. 21 Frozen, P.D. and Hogan, D.P., The impact of class, education and health care on infant mortality in a developing society. The case of rural Thailand, Demography, 19 (1982) 391-408. 22 Caldwell, J.C., The mechanism of demographic change in historical perspective, Population Studies, 35 (1981) 5-27. 23 Azurin, J.C. and Alveron, M., Field evaluation of environmental sanitation measures against cholera, Bulletin of the World Health Organization, 51 (1974) 19-26. 24 Mundle, S., Recent trends in the conditions of children in India. A statistical profile, World Development, 12 (1984) 305-306. 25 Shash, R.S. and Rajalakshmi, R., Vitamin A, status of newborns in relation to gestational age, body weight and maternal nutritional status, American Journal of Clinical Nutrition, 40 (1984) 795-796. 26 Carvajal, M., Burgess, P., Socioeconomic determinants of foetal and child death in latin America. A comparative study of Bogata, Caracas and Rio De Janeiro, Social Science and Medicine, 12 (1978) 89-98. 27 Gbesemete, K.P. and Gcrdtham, U.G., Determinants of health care expenditure in Africa: A crosssectional study, World Development, 20 (1992) 303-308. 28 Black, R.E., Huber, D.H. and Curlin, G.T., Reduction of neonatal tetanus by mass immunization of non-pregnant women: duration of protection provided by one or two doses of aluminiumabsorbed tetanus toxoid, Bulletin of the World Health Organization, 58 (1980) 927-930. 29 Haines, M.R. and Avery, R.C., Differential infant and child mortality in Costa Rica, 1968-1973, Population Studies, 36 (1982) 321-344. 30 Caldwell, J.C., Reddy, P.H. and Caldwell, P., The social component of mortality decline: an investigation in South India employing alternative methodologies, Population Studies, 37 (1983) 185-205. 31 Ruzicka, L.T. and Hansluwka, H., Mortality transition in south and east Asia: technology confronts poverty, Population and Development Review, 8 (1982) 567-588. 32 Hemminki, E. and Paakulainen, A., The effects of antibiotics on mortality from infectious diseases in Sweden and Finland, American Journal of Public Health, 66 (1976) 1180-I 184. 33 Gwatkin, D.R., Indications of change in developing country mortality trends: The end of an era?, Population and Development Review, 6 (1980) 615-644. 34 Chase, H.C., Infant mortality and weight at birth, 1960 United States cohort, American Journal of Public Health, 59 (1969) 1618-28. 35 Sterky, G. and Mellander, L., Weight Distribution an Indicator of Social Development, SAREC Report No. R.2, Stockholm, 1978. 36 Smith, M.F., Paulsen, S.K., Fongere, W. and Ritchey, S.J., Sccio-economic, education and health factors in influencing growth of rural Haitian children, Ecology of Food and Nutrition, 13 (1983) 99-108.
174 37 38 39 40
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
Lind, T., Would more calories per day keep low birth weight at bay?, Lancet i, No. 8375 (1984) 501-502. World Health Organization, Evaluation of the Strategy for Health for All by the Year 2000, Seventh Report on the World Health Situation, Vol. 2, Brazaville, 1987. Scrimshaw, N.S. and Behar, M., Malnutrition in underdeveloped countries, New England Journal of Medicine, 272 (1965) 137-144. Baertl, J.M., Morales, E., Verastegui, G. and Graham, G., Diet supplementation for entire communities: growth and mortality of children, American Journal of Clinical Nutrition, 23 (1970) 707-715. World Bank, World Development Report, Washington, DC, 1984. UNICEF, Within Human Reach: A Future for African Children, New York, 1985. Wolfer, D., Scrimshaw, S., Child survival and intervals between pregnancies in Guayaquil, Ecuador, Population Studies, 29 (1975) 449-496. Oni, G.A., Child mortality in a Nigerian city: Its levels and socio-economic differentials, Social Science and Medicine, 27 (1988) 607-614. Adegbola, O., The impact of urbanization and industrialization on health conditions; the case of Nigeria, World Health Statistics, 40 (1987) 74-83. Sen, A., Poverty and Famine: An Essay on Entitlement and Deprivation, Clarendon Press, Oxford, 1982. Davidson, R. and McKinnon, J., Some non-nested hypothesis tests and the relations among them, Review of Econometrica, 44 (1982) 551-565. Harvey, A.C., The Econometric Analysis of Time-series, Philip Allan, Oxford, 1983. McKeown, T., The Modern Rise of Population, Edward Arnold Publishers Ltd., London, 1976. McKeown, T., Record, R.G. and Turner, R.D., An interpretation of the decline of mortality in England and Wales during the twentieth century, Population Studies, 29 (1975) 391-422. Sharpston, M.J. A health policy for developing countries. In G.M. Meier (Ed.) Leading Issues in Economic Development, 3rd Edn., Oxford University Press, Oxford, 1971, pp. 496-506. Flegg, A.T., Inequality of income, illiteracy and medical care as determinants of infant mortality in underdeveloped countries, Population Studies, 36 (1982) 441-458. World Bank, World Development Report, Washington, DC, 1986. Sivard, R.L. World Military and Social Expenditure, Priority Publishers Inc., Washington, DC, 1987. UNICEF, The State of the World’s Children, New York, 1990. World Health Organization, Statistics Annual, Geneva, 1986. United Nations, Statistical yearbook of national account statistics, New York, 1988.
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HPE 00531
A comparison of empirical models on determinants of infant mortality: A cross-national study on Africa* Kwame P. Gbesemete
and Dick Jonsson
Department of Health and Society, University of LinkGping. Sweden Accepted 25 November
1992
Summary The goal of achieving health for all by the year 2000 has instigated numerous studies on the determinants of health. In this paper, we re-evaluate two models in which infant mortality - across twenty-eight low- and middle-income African states - is explained by socioeconomic, demographic, medical, environmental and political factors. The results indicate that the GNP per capita, school population as a percentage of the population under 19, population density and the percentage of the population with access to health care together explained 80% of the variations in infant mortality in the sample study. Apart from the GNP per capita and the school population as a percentage of the population under 19 which were negative and statistically significant, variables of importance for health policy, e.g. female literacy rate, water supply, food aid, calorie supply, health care expenditure and the degree of urbanization carried a negative sign but were nonsignificant. We interpreted the above thus: a reduction in infant mortality is feasible only with changes on diverse fronts rather than by marginal improvements in a few determining factors. A comparative test of the replicated model and our proposed model has shown that our model produced a better theoretical and statistical fitting than did the replicated model. Africa; Infant mortality; Socio-economic; factors
Demographic;
Medical; Environmental;
Political
1. Introduction International comparisons can hardly be used to give any normative answer on different health issues such as if the right amount of health care Address for correspondence:
Dr. Kwame P. Gbesemete, University of Linkoping, Department of Health
and Society, 58183 Linkoping, Sweden. *The twenty-eight countries in the sample are: Ethiopia, Zaire, Burkina Faso, Malawi, Uganda, Niger. Tanzania, Somalia, Togo, Benin, Liberia, Ghana, Sierra Leone, Kenya, Sudan, Lesotho, Mozambique. Mali, Zambia, Nigeria, Cote D’Ivoire, Zimbabwe, Cameroon, Tunisia, Senegal, Congo, Morocco. Botswana.
156
reaches the right consumers, if the production is technically efficient, etc. Such issues according to Gerdtham [ 1] require more detailed cost-benefit analysis of specific health care programmes. However, international comparisons can be used to widen - in this case - our perception of the overall determinants of health levels either worldwide or for a specific geographical region. Determinants of health - the latter measured in terms of life expectancy and or age-specific mortality rate - is a well established field of research (see, for example, Refs. 2-5). Typical for these studies is that they were conducted using international cross-section data although there are exceptions where regional and district aggregates have been used for a given country, (see, for example, Refs. 6 and 7). In the Beenstock and Sturdy study, various socio-economic variables were regressed on infant mortality rates across Indian states to determine the factors that systematically account for variations in the named health variable. A recent addition to the literature is Cumper’s study [8] which examined the relationship between infant mortality rate and a wide range of socio-economic, political, biological and environmental factors. Cumper’s study covered a total of 163 countries and was based on data from 1976. According to the WHO [9] the under-five mortality rate reflects the socioeconomic status of a nation while the infant mortality rate is a measure of the level of health care services. During the past two decades most countries in the Third World improved accessibility and the quality of their health care services [lo]. Despite these efforts the level of infant mortality particularly in Africa remains relatively high. This raised the question whether there are factors outside the medical sphere which affects infant mortality rate. The present study seeks to answer this question using data for 28 low- and middle-income African countries for the year 1984. Apart from the authors personal interest in Africa, we have chosen the African region because there is a dearth of literature on cross-national analysis on determinants of infant mortality in Africa. Initially, the model suggested by Cumper [8] - being one of the most widely cited studies in this field - is replicated. Secondly the study estimates and evaluates a model proposed by us on health determinants including socio-economic, demographic, medical, environmental and political factors. A cross-sectional study of this kind has certain advantages when compared with time-series analysis. For example there is smaller variances of the estimated structural parameters in cross-sectional study because the dispersion of the values of regressor variables is larger than what is usual in timeseries data. However, there are certain limitations with cross-sectional studies. First, the small sample size (countries) imposes restrictions on model size and statistical inferences. Second, in practically every empirical analysis of this kind the presence of n&measured and/or unobserved variables that are correlated with the explanatory variable is incorporated in the model. Third, cross-sectional comparisons are static, whereas the observed differences in health levels are the outcome of real (permanent) differences and transitory differences due to countries being in different stages of some adjustment process. The study proceeds as follows. An analytical framework is outlined in
157
Section 2. In Section 3, data, measurement and statistical methodology are reviewed. In Section 4, the empirical analysis of the determinants of infant mortality is reported. Furthermore some old models from earlier studies are replicated and, within the framework of encompassing tests, the former models are compared with ours. The final section is devoted to the interpretation and discussion of the results.
2. Analytical framework Differences in health levels can be explained as the outcome of a composite of factors namely; socio-economic, demographic, medical, environmental and political factors [8]. Any study on health determinants that does not take into consideration the above factors will therefore be incomplete. However, in practice and where there are conceptual and measurement difficulties there is the problem of how to operationalize and hence assess the quantitative impact of the named factors. In this study, we focus attention on factors that have featured most prominently in the literature. These factors are categorised in the four broadly defined groups as stated above. So&-economic factors Education
In numerous studies, education is pointed out as one of the most powerful predictors of mortality [l l-141. Others noted the role of education in influencing a population’s use of available health and medical services [ 15-171. An educated population seems to be more receptive to medical, sanitary and nutritional information that leads to increased longevity [18-191. The educational level of females is particularly vital to the health of infants [20-211. The educated mother is likely to make use of the numerous alternatives in child care and the treatment of illness that are available in a rapidly changing society. She is also more likely to take personal responsibility in such fields as birth control, etc. [22]. For these reasons a negative association is posited between educational status and infant mortality. Water supply and sanitation
The role of water supply and sanitation in improving health is a widely studied field of research. Improved water supply and sanitation is very effective against bacillary dysentry, cholera and other diarrhoeal diseases [23]. Hence, it is assumed that the higher the proportion of the population with an acceptable standard of water supply, the lower will be the level of infant mortality ceteris paribus. Gross national product per capita
The most general measure of resource availability is the gross national product (GNP) per capita. Numerous studies have found that as incomes decrease, health levels tend to deteriorate [24-261. Others have observed a positive correlation between income levels and health care expenditure [27].
158
Income is measured in Cumper’s study in terms of GNP per capita, and it is posited so as to be negatively correlated to infant mortality. Percentage of the population with access to health care
A substantial number of scholars have analyzed the relationship between various measures of health and medical services and mortality. For example in Bangladesh, the provision of medical services such as immunization of children and nonpregnant women led to lower neonatal deaths among children whose mothers had two tetanus injections 9-32 months before delivery than among those in the control group [28]. In Costa Rica, the provision of medical services helped to negate mortality in the nonadult population (291. According to some authors, health and medical services are of much greater importance than measures of social and economic development in determining mortality levels [30-321. In the light of the above, we argue that the more available the health services are to the population - as measured by the percentage of the population with access to health services - the lower will be the infant mortality rate. It should be emphasised that not everyone shares the enthusiasm expressed in earlier works on the importance of medical services in decreasing the mortality rate. In a survey of global mortality, Gwatkin [33] observed a substantial decrease in the capacity of modern medical and health services to combat certain diseases, e.g. diarrhoea, in developing countries. Low birth weight
Clinical studies conducted by Chase [34] found a statistical correlation between birth weight and infant mortality. Birth weight is determined by a number of factors such as the nutrition of the foetus, genetic factors, etc. [35]. Low birth weight babies are not a homogeneous group. A classification of low birth weight babies gives us groups with a specific pathological cause, preterm deliveries and those which are full term but small for gestational age ]8, p.541. Low birth weight babies are disadvantaged in respect of mortality, as has been shown by the experience of groups affected by pathologies or prematurity. In the light of the above, we posited a positive relationship between low birth weight and infant mortality rate. A major problem with this data is that it is likely to be underestimated because the greater part of all births in most African countries take place in the home often with the help of traditional birth attendants who are hardly capable of weighing babies at birth due partly to the fact that most of these birth attendants are illiterate. Economic social standing
The use of the gross national product (GNP) does not tell us much about the quality of life and/or the health of the people. Here instead, we use a different dimension of economic development, ‘economic social standing’ which represents the average of ranks for GNP per capita, educational status of the population and level of health. For an aggregate of countries, an index of overall economic development can serve the purpose of identifying
159
development trends. In the light of the above, we posited a negative relationship between a country’s economic social standing and its infant mortality rate. A problem with this variable is that it is likely to be highly correlated with the variables listed above. Health care expenditure
Here we argue that aggregate health care expenditure determines the level of health care services. Infant mortality is determined by a wide range of factors including the level of maternal care. We therefore argue that the provision of health care services, e.g. maternity care, is likely to be poor if the level of health care expenditure is low ceteris paribus. Furthermore, the level of health care expenditure affects the purchase of medical equipment, e.g. incubators for saving the lives of premature babies. Hence, we argue that infant mortality will be inversely related to health care expenditure. The exact component of the health care expenditure per capita is not stated other than as it reflects total government expenditure on health. If the greater part of this expenditure is devoted to salaries, then obviously it will have less impact on infant mortality. More desirable data would be govemment expenditure on pediatric and/or maternity wards. However we do not have this data. Diet and nutrition
The relationship between diet and nutrition and health is a field of research which has been extensively investigated by a number of scholars [36-371. A recent report by the World Health Organization [38] named malnutrition as one of the underlying causes of child mortality in 46 African countries. Improved diet supplementation programs significantly reduced child mortality in Guatemala [39]. Similar conclusions were reached for Peru [40]. In an Indian study, it was observed that improved nutrition is a prerequisite for increased life expectancy [30]. In our study, the diet and nutrition composite is measured by food aid in metric tons and calorie supply as percentage of requirement. The latter variable has been subject to criticism due to doubts about its accuracy in the case of certain developing countries - but also because it does not make any allowance for the disparities in the distribution of food between and within households. Furthermore, the indicator is said to be unsatisfactory if health is measured in terms of infant mortality rate. The argument here is that in most developing countries breast-feeding is widespread in the first year of life [g, p.521. In contrast to the above postulations, we expect a relationship between nutrition and infant mortality partly on the basis of the nutritional status of pregnant and nursing mothers, but also on the basis of foods offered to the infants to supplement breast-feeding. Hence, as stated earlier we expect an inverse relationship between the diet and nutrition composite and infant mortality rate.
160
Food aid
According to the World Bank [41] and UNICEF [42] the food deficit on the African continent was most acute during the sample period. The unavailability of food especially in times of war or drought can be detrimental to health particularly for pregnant women, but also in the case of children who have been taken off the breast. In the light of the above, we assume that food aid can help to compensate for the loss of food. Hence, we envisaged a negative relationship between the named variable and infant mortality. Demographic factors Fertility
It is argued that infant deaths increase with ascending number of births and shorter birth intervals. With shorter birth intervals, less care is given to the children. Furthermore, high fertility may lead to competition for the limited resources available to a household [43]. In a study, Oni [44] found that on the average, child mortality could be lowered by 8% if the number of babies born were limited to three or less. In the light of the above, we posited a positive relationship between a high fertility rate and infant mortality. Density
High population density is deleterious to health insofar as it aggravates problems of sanitation and facilitates disease transmission [45]. On the other hand, it is argued that the effectiveness of health service inputs varies inversely with the dispersion of the population, hence a low population density is not conducive to health. According to Cumper, the net effect of the density variable at the international level is to produce a significant negative correlation with health. High population density such as high urban settlement, may lead to greater availability of social services. This in turn may offset negative features such as disease transmission [8, p.481. Medical factors Physicians, nurses and hospital beds
Three categories of medical inputs have been chosen for the regression analysis, namely: the number of physicians, other health workers, e.g. nurses, and the number of beds, all expressed in per 1000 population. The three variables indicate the degree of medical accessibility, hence a negative relationship is posited between the named variables and infant mortality. For example when the stock of physicians increase and the workload decreases doctors may.spend more time on each patient - in this case pregnant women and newborn babies - than otherwise. A similar argument holds for nurses. An increased number of hospital beds may lead to more admissions in hospitals and thereby the diagnosis and cure - provided there are drugs and equipment in the hospital - of potential killers.
161
Environmentaland political factors Drought and involvement in war Drought and wars are likely to be positively correlated to infant mortality due to their impact on the individual’s purchasing power. In a study on the causes of famine, it was concluded that famine is not due to drought and wars per se but rather to the disruption in the individual’s power to purchase food and other items conducive to health [46]. Low purchasing power with its consequent impact on food intake especially by pregnant women is likely to affect the development of the foetus. As stated earlier, a poorly developed child - at birth - is more liable to disease and death than a well developed one. Hence we argue that infant mortality will be higher in countries which have been subjected either to war or to drought.
3. Data, measurement and statistical methodology Data The data used in the present study are taken from diverse sources and are for the year 1984. Since these data files have been used in many studies in the area, comparability is likely to be the best among the available data sources. However it should be emphasised at the outset that numerous problems regarding data quality still remain. To judge the quality in terms of validity, reliability and precision of such aggregate archival data is difficult. There is therefore enough room for imperfect reliability with regard to crosssection comparisons basically as a result of differential classifications; particularly in the case of health determinants. Furthermore, there is no homogeneity in international data compiling. From the viewpoint of reproducibility of empirical analyses however, we have opted for the current situation i.e. to use the data which is available instead of embarking on earlier practices where individual investigators performed their own ‘massage’ to the data. The cross-sectional analysis includes observation from 28 low- and middle-income African countries. We have chosen these countries because they have similar causes of mortality, similar demographic distribution, small diferences in socio-economic status and above all they are within the same geographical (African) region. Furthermore we have selected countries for which data is complete for the sample period.
Measurement In order to clarify this paper Table 1 reports the operationalised and the data sources used.
variables
Statistical methodology The construction of the empirical model is deduced from the theoretical framework. A number of variables - percentage of the population with
162
Table 1 Dethition of the variables in the empirical model for the determinants of infant mortality Variable
Description
Source
IMR
Infant mortality rate; i.e. deaths under 1 year of age per 1.000 hve births Density: population per square km Degree of urbanization: i.e. urban nonulation & percentage of total population Food aid in metric tons School population (5-19 years) per teacher School population as a percentage of the population 5-19 years Percentaee of the total oonulation with reasonable access (oftkn*not more than 1 km distance) to safe and adequate drinking water supply Fertility rate i.e. the number of children that would be born per woman, if she were to live to the end of her child-bearing years and bears children at each age in accordance with prevailing age-specific fertility rates Physicians per 1000 population Other health workers, e.g. nurses per 1000 population Number of hospital beds per 1000 population Percentage of the population with simple sanitary latrines; safe disposal methods for personal and household wastes Gross national product per capita in US% Calorie supply, i.e. daily per capita calorie supply as percentage of requirement Health care exnenditure ner canita in USS Low birth weight, i.e. children*bom weighing
1101
DEN URBAN FOOD TEA PUPC PWSC
FER
PHY OHW BED PEDC GNP CAL HEXP LBIRTH FLITT HCA
SOCECO
less than 25 000 g Female literacy rate, i.e. percentage of females females aged 15 and over who can read and write Health care access, i.e. percentage of the population that can reach appropriate local health services by the local means of transport in no more than 1 h Socio-economic standing. This represents average ranks for GNP per capita, educational status of the population, and level of health
r::; [10,531 ;::j 1541 [3gJOl
[lo,551
[541 [56,571 [571 UOI
1101
1541
access to health care, low birth weight, socio-economic standing, health care expenditure, nutrition and diet, food aid, drought and involvement in war which we think (intuitively) affects the level of infant mortality but were excluded from Cumper’s models were discussed and tested in our empirical search model. The statistical analysis was carried out as follows. First, we replicated Cumper’s model on a disaggregated African data. Later, we constructed an empirical search model by including variables derived from the analytical framework which minimised the Akaike criterion. The replicated models were later evaluated in relation to our proposed model. Both models are
163
evaluated with respect to theoretical consistency, i.e. in accordance with theoretical considerations and statistical performance. The latter is expressed in terms of the R2 (adjusted (adj.)), the log-likelihood value, the parameter of the t-value and the significance level of the J-test. The J-test is an encompassing test of nonnested models. For a technical discussion of the J-test see Refs. 47 and 48. The test is used to evaluate the best of Cumper’s models but also to evaluate the best of Cumper’s models with our proposed empirical model. This test procedure is necessary in assessing the statistical validity of the quoted statistical significance of parameter estimates. The models are estimated in double logarithmic form. However unlike Cumper, we have not done any other data transformation such as deviations, etc. The regression equations are based on the same data set which renders systematic model comparisions free from uncertainties as to data reliability. The models are also estimated with the same estimators. The problem of heteroscedasticity is not present in any of the estimated models because the estimation procedure includes heteroscedasticity invariant covariance matrix. In the first estimation of the model, ordinary least squares (OLS) is applied. This is the same estimator used by Cumper. The OLS estimation is a standard estimator but is sensitive to autocorrelated residuals. In the second estimation, we used the general least squares (GLS) estimator which includes a moving average component (MA) for the error terms. The coefflcients of the moving average component picks up the behaviour of the residuals [48]. In the statistical analysis, countries that suffered war or drought in the year 1983-1984 are given one whereas those that suffered nothing are assigned zero. The statistical method is based on an international cross-section analysis for the year 1984. We have chosen this year due to data availability.
4. Statistical analysis 4.1. Replication of Cumper’s models 4.1.1. Cumper s first model
Cumper’s main hypothesis [8, p.31 is that a change in the factors which improve health at the individual or local community levels could be generalised to be positively correlated to health at the aggregate level, e.g. improved sanitation may lead to low infant mortality rate. The author noted that due to the high correlation between the independent variables and income per capita measured as GNP, the statistical analysis was carried out not in terms of the original data base but in terms of the deviations of the data in logarithmic form from the regression line relating them to GNP per capita. Accordingly, because of the strong correlation between income and the independent variables, the procedure outlined above, standardised for income but also for the independent variables. Furthermore, due to the lack of observations for some variables, multiple regression analysis could not be
164
applied uniformly on all the variables. Therefore, an approach was adopted where four variables - GNP per capita, hospital beds, physicians and other health professionals per 1000 population - for which data was complete and for which there is a strong causal connection with health both at the macro and micro levels were selected for multiple regression analysis. The transformed data in Cumper’s empirical model are logged in natural logarithmic form and have the following structure: 1nIMR = Bo + BJnTEA + BJnPUPC
+ BJnPWSC + B&DEN +
BJnFER + BdnPHY + B7LnOHW + BsLnBED + B9LnPEDC + e,
(1)
with Bi, B2, B3, Bq, B6, Br, Bs, & c 0 and Bs > 0 and where IMR, infant mortality rate, i.e. deaths under 1 year of age per 1000 live births; TEA, school population (5-19 years) per teacher; PUPC, school population as a percentage of the population 5-19 years of age; PWSC, percentage of the population with reasonable access (often not nore than 1 km distance) to safe and adequate drinking water supply; DEN, population per square km; FER, fertility rate; PHY, physicians per 1000 population; OHW, other health workers per 1000 population, e.g. nurses; BED, number of hospital beds per 1000 population; PEDC, percentage of the population with simple sanitary latrines; safe disposal methods for personal and household wastes. In his regression analysis, Cumper [8] incorporated two educational variables - the total population in educational institutions as a percentage of the under 15 population and the number of teachers per 1000 of school population - without explaining why these two variables should be incorporated simultaneously in the regression equation. Cumper never defined what constituted adequate excreta disposal. Therefore, we do not know whether adequate excreta disposal meant improved disposal of waste products explained in terms of the daily collection of rubbish or whether it meant better toilet facilities. Information which could have increased our knowledge about what constituted adequate excreta disposal is missing. The main findings of the above model are summarised in Table 21 on p. 110 of Cumper’s book. The model is consistent with the hypothesised theories stated earlier. However the level of significance was not reported for the various variables. This makes interpretation of the results difficult. Furthermore the R-square and R-square (adj.) for the nine independent variables were not stated in the multiple regression results reported in his Table 21. 4.1.2. Cumper’s second model Cumper’s second model including the transformed rithm form has the following structure: 1nIMR = Bo + B&GNP
data in natural loga-
+ BJnPHY + BJnOHW + B JnBED + e,
(2)
19 0.45 0.76 0.66 -113.9
2.27 0.18 -0.02 -0.03 0.01 0.31 -0.04 0.03 0.13
;.;+ -0:9 0.7 1.5f
3.7’ 1.5+ -0.4 -0.6
18 0.41 0.78 0.67 -112.9
-0.94
A:: -0.5
-0.28
4.5;
;.;t -0:9 0.6 1.4%
t
2.27 0.18 -0.02 -0.03 0.01 0.31 -0.04 0.03 0.13
B
B
t
GLS
OLS
23 0.46 0.75 0.71 -114.4
-h5 0.06 0.19 -0.14
3.83
B
OLS
Model 2
??
8.9’
-2.1 * 1.9; -;:;*
t
22 0.37 0.80 0.76 -111.2
-0.72
-0.03 0.06 -0.14 0.19
-
3.83
B
GLS
4.3’
-1:7+
-1.0 1.5:. _;.;**
t
R2, the adjusted coefficient of determination;
&nificant at the 0.5% level. Significant at the 2.5% level. tSignificant at the 5% level. ‘Significant at the 10% level. “The OLS and the GLS in both models are estimated with heteroskedasticity consistent covariance matrixes. bPercentage of the population with adequate excreta disposal (PEDC) is excluded from the regression for lack of data. ‘Log(L) is adjusted for functional transformations.
Statistics
:Y& BED GNP RES:MA (1)
Variableb Constant TEA PUPC PWSC DEN FER
Model 1
log-likelihood value.
d,, degrees of freedom; SSE, sum of square error; R*, coefficient of determination;
Replication of Cumper’s models on infant mortality rate on nine independent variables. Multiplicative functional form’
Table 2
Log(L),
166
with Bi B2 B3 B4 < 0 and where IMR, infant mortality rate; GNP, gross national product per capita in US$; PHY, physicians per 1000 population; OHW, other health workers per 1000 population, e.g. nurses; BED, number of hospital beds per 1000 population. The use of variables such as GNP per capita, beds, physicians and other health workers as standardising variables in explaining the effect of other factors on infant mortality rate becomes doubtful when one considers the fact that these variables are highly correlated with GNP per capita. Furthermore, the three last named variables are proxies for medical inputs. Of late however, the role of these inputs in health improvement has been subject to criticism and doubts [49-521. The two models are nonnested because certain variables included in Model 1 are missing in Model 2 and vice-versa. Apart from the inclusion of GNP per capita in Model 2, Model 1 can be seen as a more general model. A plausible question is which of the models is to be preferred from a statistical or a theoretical point of view. 4. I. 3. Results Cumper [8] studied the problem of infant mortality at the aggregate level. Using the same variables as Cumper, we were essentially able to replicate his results on twenty-eight African states. Table 2 summarizes the results of our replication of Cumper’s models on nine independent variables. As evident in Model 1 (OLS), only one variable, the fertility rate (FERT) with a coefficient of 0.31 is significant at the 5% level. Two other variables, school population per teacher (TEA) and number of hospital beds per 1000 population (BEDS) are significant at the 10% level, respectively. The elasticities of the latter variables are 0.18 and 0.13, respectively. The abovenamed variables emerged significant at the 10% level respectively in Model 1 GLS. The other variables incorporated in Model 1 (OLS) and (GLS) namely: school population as a percentage of the population 5- 19 years (PUPC), percentage of the total population with reasonable access (often not more than 1 km distance) to safe and adequate drinking water supply (PWSC), population density per square km (DEN), physicians per 1000 population (PHY) and other health workers, e.g. nurses (OHW) are nonsignificant. Model 1 is theoretically consistent except variables like school population per teacher (TEA), other health workers (OHW) and number of hospital beds per 1000 population (BEDS) which did not carry the expected sign. The R* (adj) for the eight variables included in the ordinary least squares (OLS) regression equation in Model 1 is 66% and 67% for the general least squares (GLS). A re-estimation of Cumper’s Model 2 using the OLS method shows how infant mortality is explained by the number of physicians per 1000 population (PHY), other health workers, e.g. nurses (OHW), number of hospital beds per 1000 population (BEDS) and the gross national product per capita (GNP). The elasticities for the named variables are -0.05, 0.06, 0.19 and -0.14 respectively. As evident above, the reported coeflicients for (BEDS) and (OHW) are positive. A practical explanation may be that the positive
167
signs reported for the variables (BED) and (OHW) could be an artifact indicating increased registration of infant mortality when the number of beds and other health workers, e.g. nurses increase. Furthermore, a theoretical and a statistical explanation may be that the variables in the model are highly correlated and subject to omitted variable bias. It is interesting to note that in Model 2 GLS regression, GNP was the only variable that emerged with any significant negative impact on infant mortality. The number of physicians is nonsignificant in Model 2 GLS. On the other hand, the number of beds per 1000 population (BEDS) and other health workers (OHW) remained positively significant. The reported coefticients for the significant variables in Model 2 GLS regression are similar to those of the OLS. The R2 (adj) for the OLS in Model 2 is 71% and 76% for the GLS. The full model R2 in both regression is 75% and 80%, respectively. We compared Cumper’s Model 1 with his Model 2 and vice-versa. The comparisons were performed using a nonnested hypothesis testing procedure. The results are shown in Table 3 below. Table 3 Comparison of the two models: nomwsted hypothesis testing
Model 21 compared with Model 21
Coefficient
SD
J-test
X:!
0.3999 0.2513
::;
From the results, it is apparent that Cumper’s Model 2 is statistically superior to Model 1 as indicated by the J-test which was significant at the 5% level. We cannot reject the hypothesis that Model 2 encompasses Model 1 but we have rejected the inverse hypothesis. 4.2. The empirical search model 4.2.1. Model construction Having completed the replication we proceed to propose an alternative model to explain the determinants of infant mortality in Africa. The proposed model incorporates variables which were overlooked in Cumper’s models. The empirical search model takes the following expression. 1nIMR = B, + BilnXi + B2lnDi + B,lnMi + BJnEi where IMR, infant mortality rate; Xi, socioeconomic variables; Di, demographic variables; Mi, medical variables; Ei, environmental and political variables. The model is constructed by including variables stepwise in order to minimize the Akaike criterion (AIC)-criterion. The AIC-criterion is a statistical discrimination criterion and not a test procedure from a theoretical point of view. The estimator in detecting the original empirical model is ordinary least squares.
168
In the construction of the empirical model, other variables deduced from the theoretical framework were tested but in accordance with the procedure of minimizing the AIC-criterion’they were excluded from the equation. The following variables - gross national product per capita (GNP), school population as a percentage of the population 5- 19 years of age (PUPC), population density (DEN) and the percentage of the population with access to health care (HCA) - were the only ones that minimised the AIC criterion, hence their inclusion in the empirical model as shown in Table 4 below. The coefficients in the OLS and the GLS regression can be interpreted directly as elasticities. The results indicate that a 1% increase in the gross national product per capita (GNP), school population as a percentage of the population 5- 19 years of age (PUPC) and percentage of the population with access to health care services (HCA), led to a -0.11, -0.26 and -0.13 percent decrease in infant mortality rate, respectively. On the other hand, a 1% increase in the population density led to an 0.06% increase in the dependent variable. The reported coefficients are similar in both the OLS and GLS regressions. The models are rather robust and not so sensitive to the choice of estimators. They are consistent with a priori theoretical considerations and include only significant variables as evident in both the OLS and the GLS equations. The reported R2 (adj.) is 79% for the OLS and 80% for GLS regressions, respectively.
Table 4 Estimation of our model on the determimmts of infant mortality in twenty-eightAfrican states d, degrees of freedom; SSE, sum of square error; R’, coeflticient of determination; t i e adjusted coefftcient of determination; Log(L), log-likelihood value. GLSa
OLY t
B Variable Constant Ft!z DEN HCA RESMA”
6.65 -0.11 -0.26 0.06 -0.13 -
t
B 34.3’ -3.0’ -5.8: -;:;** -
6.65 -0.11 -0.26 0.06 -0.13 -0.33
Statistics
R2 (adj.) Log(L) b
23 0.33 0.82 0.79 -110.1
&nificant at the 0.5% level. Srgnificant at the 2.5% level. ‘Significant at the 5% level. aHeteroscedasticity consistent covariance matrix. bLog(L) is adjusted for functional transformations.
22 0.29 0.84 0.80 -108.3
28.7’ -3.9. -5.7;. -:::t -1.2
R2 (adj.),
169
Variables with a nonsignificant but a priori expected sign were female literacy rate (-), water supply (-), food aid (-), calorie supply (-), fertility rate (+), health care expenditure (-) and degree of urbanization (-). Nonsignificant variables with not expected signs were teachers (+), low birth weight (-), nurses (+) and beds (+). Of all these excluded and nonsignificant variables, calorie supply, urbanization, low birth weight and nurses received statistical t-values between 0 and 1. A surprising finding was that the dummy variable for war was highly nonsignificant. The same holds for the dummy variable for drought. A test of the socio-economic standing variable verified its status as a variable capturing the society’s socio-economic level. When the variable was included in the equation, the relationship between infant mortality and education and between infant mortality and gross national product per capita changed dramatically. Table 5 below compares our GLS to the GLS in the replicated Model 2. The idea is to evaluate the models and compare them with respect to theoretical and statistical performance. As evident in the table, four of our variables - the gross national product per capita (GNP), school population as a percentage of population 5-19 years of age (PUPC), population density (DEN), and the percentage of the population with access to health care (HCA) are significant. This can be
Table 5 A
comparisionof
our GIS with Cumper’s Made1 2 GIS’
d/, degrees of freedom; SSE, sum of square error; R,, coefficient of determination; adjusted coefficient of determination; Log(L), log-likelihood value. Our Model B Variable Constant GNP PUPC DEN HCA PHY OHW BED RES:MAa
Cumper’s Model 2 t
6.65 -0.11 -0.26 0.06 -0.13 -
28.7’ -3.9. -5.7;.
-0.33
-12
-::;t -
B
t 3.83 -0.14 -0.03 0.06 0.19 -0.72
Statistics 22 0.29 0.84 0.80 .108.3 &nificant at the 1% level. Significant at the 5% level. tSigniticant at the 10% level. “Heteroscedasticity consistent. bLog(L) is adjusted for functional transformation.
??
-;::**
22 0.37 0.80 0.76 -111.2
-q :.1** -1:7t
R,, the
170 Table 6
Comparison of our sear& model with Cumper’s models: nonnested hypothesis testing Coefficient
SD
J-test
compared with Cumper’s
0.5
0.1967
2.6
0~;~;1.k21 compared with Cumper’s
0.5
0.2942
1.7
O~r,~;;$l
compared to only three variables, namely, gross national product per capita (GNP), other health workers, e.g. nurses (OI-IW), and the number of hospital beds per 1000 population (BEDS) which were significant in the Cumper GLS regression. The R2, which is the explanatory power of a model, is much higher in our model than the replicated model. The reported R2 (adj.) in our model is 80% as compared to 76% for the replicated model. Table 6 compares our search model with Cumper’s model. Here, the idea is to see if our model encompassed the replicated models. The results indicate that our model encompassed the replicated model 1 and was significant at the 5% level. Our model does not however encompass the replicated Model 2. The J-test for our search model and the replicated Model 2 is significant at the 10% level.
5. Conclusions The main purpose of this study has been to provide a comprehensive analysis of eighteen variables potentially explaining the cross-national differences in infant mortality in Africa. The empirical results from the replicated Model 1 indicates that out of the eight explanatory variables only three, namely, fertility rate (FERT), school population per teacher (TEA), and the number of hospital beds per 1000 population (BEDS) were statistically significant. The reported coefficients in both the OLS and the GLS regressions for the named variables are 0.31, 0.18 and 0.13, respectively. In the replicated Model 2, the following variables, physician per 1000 population (PHY), other health workers, e.g. nurses (OHW), number of hospital beds per 1000 population (BEDS) and the gross national product per capita (GNP) emerged significant in the OLS regression. The physician variable (PI-W) was however insignificant in the GLS regression. The replicated Models 1 and 2 were compared with each other using the J-test. The results indicate that the F-acceptable model containing four variables, i.e. Model 2 is preferable to Model 1. Having replicated Cumper’s models, an alternative model was proposed to explain the determinants of infant mortality. The reported coeflicients both in the OLS and the GLS - in the proposed model indicate that a 1% increase in the gross national product per capita (GNP), school population as a percentage of the population 5- 19 years of age (PUPC) and accessibility to health care (HCA) led to a -0.11, -0.26 and -0.13 percent decrease in
171
infant mortality rate. On the other hand, the infant mortality rate went up by 0.06% whet_ the population density increased by 1%. We used an encompassing test to compare the relative efficiency of our model to the replicated models. The results indicate that our model encompassed the replicated Model 1 and was significant at the 5% level. However, our model does not encompass the replicated Model 2. It appears that the choice of an estimator had great consequences in terms of the results of the statistical analysis in general. The general least squares (GLS) is preferable to the ordinary least squares (OLS) because the former produced more effcient estimates of the parameter variances and more reliable t-statistics. Other variables were found to be of importance and consistent to previous studies but were non-significant. For example, a negative relationship is reported for female literacy rate, water and calorie supplies, degree of urbanization and the infant mortality rate. Health care expenditure and food aid carried the expected sign. Four coefficients, namely, school population per teacher, other health workers, e.g. nurses, low birth weight and hospital beds per 1000 population have ‘wrong’ signs. It is approriate at this point - given the importance of the findings in this study - to conclude with a few problems and remarks. First cross-sectional studies do not show the dynamics of change or issues concerning structural changes, because cross-sectional studies deal with static comparisons. However this problem can be dealt with by pooling the data. A pooled crosssectional time-series has a number of advantages over a pure cross-sectional design. For example it is possible to test for other features in the relationship, such as temporal stability and lags. Furthermore, such a design may lead to an increase in the sample sizes. The small sample size evident in most pure cross-sectional studies constitutes an important limitation in statistical comparisons of different regression models. The GNP per capita appears to be the most important statistical factor in cross-national analysis of infant mortality. However, this variable should be treated with caution because the level of per capita income does not say anything about how the income is distributed. The negative sign reported for female literacy and infant mortality conforms with the results in earlier studies. There are however certain limitations with female literacy. For example child care practices are likely to be related to the mother’s working habits. The educated woman is more likely to work outside the home. Work of any kind may inhibit appropriate feeding, especially breast-feeding, in early life and this may reduce the chances of survival. It would therefore be interesting in future research to test the male literacy rate on mortality levels. The educated male is likely to secure a well paid job. If the husband’s income is high the female is more likely to stay at home and take care of the children and this might have a positive impact on infant and child survival. The health care accessibility variable is significant at the 5% level and carries a negative sign indicating that the level of infant mortality decreases if the population has access to health care services. This finding reinforced the universally accepted view of the World Health Organization [9] that the level of infant mortality is a reflection of the level of health care services and
172
their accessibility. Apparently, pregnant women and those with babies utilize health care services provided they are accessible. The accessibility variable used here should be treated with caution because geographical accessibility says nothing about the individuals’ capacity to pay for health services nor their capacity to communicate with health personnel. Both elements are essential in health care utilization. Both food aid and calorie supply carried a negative sign indicating a decline in infant mortality with improvements in the named variables. The food aid variable is of particular interest. During the sample period, most countries in the African region suffered drought and bush fires. It appears that food aid supplemented domestic food production and this helped to keep infant mortality low. Health care expenditure is negatively correlated to infant mortality. Apart from its effects on infant mortality, an increase in health care expenditure may contribute to economic growth and raise incomes. The two density variables, namely the population per square km and the degree of urbanization, appear to differ in their impact on infant mortality. As is evident in Table 4, infant mortality is positively correlated to population density. On the other hand, the negative sign reported for the urbanization variable implies that the more urbanised a country, the lower the infant mortality rate. It is likely - as argued by Cumper [8] - that a high level of urbanization leads to greater availability of social services and this in turn offsets negative features such as disease transmission. An extension of this study to cover the other geographical regions of the world could help to illuminate the determinants of infant mortality across countries with different ‘endowments’. Therefore, we hope in the future to see more empirically oriented studies including evaluations and comparision of models with policy implications in this field.
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174 37 38 39 40
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
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