We also have information on the number of days the child was alive (before dying) if he/she is dead at the time of the survey or the age of the child, in days, at the time of the survey. So an alternative way to model mortality would be to use a hazard model represented by a log hazard of duration equation. We use a proportional hazard model with covariates and unobserved heterogeneity shifting the baseline hazard. The log hazard of mortality for a child at time t is given by:
( )
0 1( )
2lnh t = +γ γ T t +γ Zc+ +η εc c (2)
where once again Z is a vector of individual (including health inputs provided), c parental/household and other characteristics that can potentially affect child health and child mortality; η captures mother level unobserved heterogeneity that affects the c health of all children born to the same woman and all other residual variation is captured by ε where c εc~ IIDN
( )
0,1 . The set of variables included in Z are the c same as those included in the probit estimation of child mortality. T t is a spline in( )
time beginning with the time the child enters the risk of dying (in this case the moment the child is born). Denote the time at which the child enters the risk of dying by t and 0 subdivide the duration t−t0 into K discrete periods. Then the baseline log hazard function is defined as a spline or a piecewise linear function and the log hazard of the event will have different slopes over the duration. The baseline hazard function can be written as:
The baseline hazard function is therefore the sum of the effects of the various sources of time dependence within the period of risk for an individual and the resulting log hazard equation is piecewise linear in time since the individual enters the risk of the event. The conditional likelihood of child mortality is given by:
%
( ) ( ( ) )
Remember that the sample is censored if the child is alive at the time of the survey and is uncensored if the child is dead at the time of the survey.
As before when early childbirth
(
EARLY , hospital delivery) (
HOSPDEL and child)
vaccination
(
VACCN are treated as endogenous in the child mortality hazard)
regression, the joint marginal likelihood function can be written as:
( ) ( ) ( )
°( ) (
, , ,)
The FIML estimates of equation (7) for the child mortality hazard regressions are presented in Table 10. The results that we present therefore correspond to the specification where EARLY , HOSPDEL and VACCN are all regarded as endogenous in the child mortality regressions (the complete specification 5). The results for the early childbirth (probit), hospital delivery (probit) and child vaccination (probit) are available on request, as are the hazard estimates for child mortality when EARLY, HOSPDEL and VACCN are assumed to be exogenous (with and without unobserved heterogeneity).
A negative coefficient estimate implies that the relevant variable reduces the hazard of child mortality (and increases the duration the child was alive) while a positive coefficient estimate implies that the relevant variable increases the hazard of child mortality (and decreases the duration the child was alive). The baseline hazard model is estimated as a piece-wise constant log hazard model with one node at 6 months i.e., there are two intervals (0, 6) and (6+). The slope of the log hazard is assumed to be constant within each interval but may vary between the intervals. The configuration of
signs of DUR06 and DUR6+ indicate that the hazard of child mortality is increasing in the first 6 months following childbirth but is decreasing thereafter.
Effects of early childbirth and use of health inputs seem to be similar to those obtained from the child mortality probit equation (Specification 5, Table 5) – early childbirth reduces the hazard of child mortality (significant only at 10% level), as does hospital delivery (though it is not statistically significant) and child vaccination (significant at 1% level). Taken together, these selectivity corrected estimates tend to suggest that the adverse effects of early childbirth on child mortality could be mitigated significantly if couples are encouraged to make use of available health inputs.
5. Conclusion
Though adolescent child bearing is widely prevalent in many low- income regions with high child mortality, there is very little systematic investigation of the relationship between mother’s age and child mortality in these regions. This paper examines the relationship between early childbearing and child mortality in Bangladesh, a country where adolescent childbearing is of growing concern. In doing so it specifically focuses on the role of available health inputs on child health (and child mortality), addresses the implicit problems of endogeneity and self-selection and identifies convenient policy instruments.
However, mother’s age at birth as well as use of various health inputs, e.g., hospital delivery, child vaccination, are chosen by the couple in question i.e., are potentially endogenous. Failure to account of the potential endogeneity could result in biased
estimates. In an attempt to reduce this bias we jointly estimate child mortality, mother’s age at birth, and demand for health inputs, allowing for the cross-correlation between the unobserved components of the residual terms in these equations. These estimates suggest that there are significant correlations between these equations so that these correlated estimates are an improvement over the uncorrected estimates of child mortality.
There is evidence of significant self- selection in our sample in that women having early childbirth tend to use health inputs differently from all other women. While uncorrected estimates of child mortality emphasize the adverse effects of early childbirth on child mortality, this effect tends to be much less pronounced, once we take account of the possible endogeneity of early childbirth and use of health inputs on child mortality. More interestingly, these estimates suggest that use of health inputs is one possible way of mitigating the adverse effects of early childbirth. In particular, there is strong evidence that children delivered in hospitals as well as vaccinated against major childhood diseases have better chances of survival.
From a policy point of view this is an extremely important issue. Both researchers and policy makers agree that increasing the stock of human capital is essential to increase the rate of growth of any economy. Good health is now regarded as a basic pre-requisite for human capital formation, which in turn help increasing the income levels in a country. Poor child health therefore has long-term implications in the form of poor adult health and low levels human capital formation. The finding that the adverse effect of adolescent childbirth on child survival is correlated with the use of health
input like hospital delivery implies that one has in principle identified a convenient policy instrument of encouraging use of health inputs among young mothers rather than inducing social change to delay age at marriage.
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Table 1: Effect of Age of Mother at Time of Birth on Child Mortality
Age of the Mother at the Time of Birth
Number of children dead Total number of children born
Probability that the child is dead
Less than 15 17 121 0.14
15 – 19 251 2803 0.09
20 – 24 168 2792 0.06
25 – 29 56 929 0.06
30 or Higher 14 187 0.07
Table 2A: Regional Differences in Child Mortality Rates.
Early Born and First Born
Region All Children
All Home delivery No tetanus Injection
Table 2B. Regional differences in the provision of public services
Division Adul t
Source: Sen and Ali (2003); Institute of Policy Studies (2001); Ranna-Eliya and Somanathan (2003)
Table 3: Selected Parental Characteristics
Adolescent birth Non-adolescent birth
Muslim 0.9152 Mother has primary or higher
schooling
0.5162 (0.499)
0.5703 (0.50) Father has primary or higher
schooling
0.5297 (0.4)
0.6310 (0.48) Mother’s education in single years 2.54
(3.1)
Table 4: Structure of Unobserved Heterogeneity Child Mortality estimated using a Probit model
Early Childbirth Hospital Delivery Child Vaccination Child Mortality 1.4139 ***
Early
Childbirth( )ηm (0.0585)
-0.2985 *** 2.0171 ***
Hospital Delivery
( )ηh (0.0418) (0.1688)
0.0153 -0.1016 * 0.8035 ***
Child Vaccination
( )ηv (0.0383) (0.0528) (0.0548)
0.2699 ** 0.3592 *** 0.6741 *** 1.1241 ***
Child Mortality
( )ηc (0.1193) (0.1367) (0.1120) (0.1678)
Notes:
Standard errors in parentheses.
Diagonal Elements are Standard Deviations. Off-diagonal Elements are Correlation Coefficients.
Significance: '*'=10%; '**'=5%; '***'=1%.
Estimates of the Heterogeneity Structure correspond to the “full” specification.
Table 5: Probit Estimates of Child Mortality
than Primary School (0.0813) (0.1196) (0.1199) (0.1262) (0.1269)
-0.2072 ** -0.2903 ** -0.2544 ** -0.3390 ** -0.2992 **
Education of Mother More
than Primary School (0.0822) (0.1226) (0.1222) (0.1323) (0.1315)
0.0108 0.0114 0.0148 -0.0078 -0.0024
Education of Father Less
than Primary School (0.0739) (0.1083) (0.1078) (0.1154) (0.1145)
-0.1093 -0.1682 -0.2221 * -0.0672 -0.1124
Education of Father More
than Primary School (0.0844) (0.1226) (0.1234) (0.1316) (0.1321)
Muslim -0.0671 -0.0570 -0.0100 -0.1137 -0.0737
Vaccination (0.0879) (0.1263) (0.1253) (0.1338) (0.1329)
0.1557 *** 0.1742 ** -0.3008 0.1973 ** -0.2491
Log Likelihood -12038.78 -11638.02 -5498.59 -7314.88 -11591.61
NOTE: Asymptotic standard errors in parentheses;
Significance: '*'=10%; '**'=5%; '***'=1%.
Table 6: Effect of Early Child birth on Use of Health Inputs
Early Child birth Exogenous (No
Unobserved Heterogeneity)
Early Childbirth Exogenous (With
Unobserved Heterogeneity)
Early Childbirth Endogenous
Hospital Delivery
Early Child Birth -0.3925 *** -0.7314 *** -0.1321
(0.0550) (0.1245) (0.2512)
Child Vaccination
Early Child Birth 0.0465 0.0661 0.2268 **
(0.0325) (0.0444) (0.0995)
NOTE: Asymptotic standard errors in parentheses;
Significance: '*'=10%; '**'=5%; '***'=1%.
Table 7: Probit Estimates for Early Childbirth
Estimates obtained from Full Specification
Constant -0.8120 ***
(0.1583)
Education of Mother Less than Primary School 0.4000 ***
(0.0892)
Education of Mother More than Primary School 0.3100 ***
(0.0865)
Education of Father Less than Primary School 0.0162
(0.0820)
Education of Father More than Primary School -0.4177 ***
(0.0895)
Age Difference between Mother and Father 0.0003 *
(0.0002)
Contraceptive Use -0.1922 **
(0.0763)
Muslim 0.4832 ***
(0.0939)
Asset Index -0.2023 ***
(0.0404)
If Father is Unskilled Labourer 0.1466 **
(0.0724)
Rural Residence 0.2134 ***
(0.0715)
Resident Of Barisal -0.0864
(0.1282)
Resident of Chittagong -0.1730 *
(0.1043)
Resident of Dhaka -0.1938 *
(0.1006)
Resident of Rajsahi 0.1407
(0.1067)
Resident of Sylhet -0.3009 **
(0.1195) NOTE: Asymptotic standard errors in parentheses;
Significance: '*'=10%; '**'=5%; '***'=1%.
Table 8: Probit Estimates for Hospital Delivery
Estimates obtained from Full Specification
Constant -2.2482 ***
(0.3368)
Oldest Child 0.9819 ***
(0.2528)
Youngest Child 0.6395 ***
(0.2162)
Only Child 1.5198 ***
(0.2586)
Education of Mother Less than Primary School -0.0720
(0.1986)
Education of Mother More than Primary School 0.5237 ***
(0.1888)
Education of Father Less than Primary School -0.1218
(0.1890)
Education of Father More than Primary School 0.6432 ***
(0.1849)
Muslim -0.8268 ***
(0.1843)
Asset Index 0.7361 ***
(0.0849)
Rural Residence -1.8279 ***
(0.1746)
If Woman has say on Female Health Care 0.3550 ***
(0.1224)
Resident Of Barisal -1.3259 ***
(0.2626)
Resident of Chittagong -1.1171 ***
(0.2076)
Resident of Dhaka -0.7047 ***
(0.1833)
Resident of Rajsahi -0.4339 **
(0.1873)
Resident of Sylhet -0.4589 *
(0.2432) NOTE: Asymptotic standard errors in parentheses;
Significance: '*'=10%; '**'=5%; '***'=1%.
Table 9: Probit Estimates for Child Vaccination
Estimates obtained from Full Specification
Constant 0.0435
(0.1103)
Oldest Child -0.0501
(0.1044)
First Born Male -0.1426
(0.1276)
Youngest Child -0.2260 ***
(0.0554)
Only Child -0.3752 ***
(0.0692)
Education of Mother Less than Primary School -0.0721
(0.0614)
Education of Mother More than Primary School -0.2572 ***
(0.0623)
Education of Father Less than Primary School 0.0170
(0.0560)
Education of Father More than Primary School 0.1957 ***
(0.0634)
Muslim 0.0556
(0.0661)
Asset Index 0.0025
(0.0271)
Rural Residence 0.2254 ***
(0.0500)
If Woman has say on Child Health Care 0.1269 ***
(0.0424)
Resident Of Barisal 0.0201
(0.0871)
Resident of Chittagong 0.1525 **
(0.0700)
Resident of Dhaka 0.1872 ***
(0.0688)
Resident of Rajsahi 0.0944
(0.0716)
Resident of Sylhet -0.1704 **
(0.0800) NOTE: Asymptotic standard errors in parentheses;
Significance: '*'=10%; '**'=5%; '***'=1%.
Table 10: Hazard Estimates of Child Mortality
Youngest Child -1.2421 ***
(0.2059)
Only Child -0.7516 ***
(0.2474)
Education of Mother Less than Primary School -0.1413
(0.1746)
Education of Mother More than Primary School -0.3730 **
(0.1781)
Education of Father Less than Primary School 0.0696
(0.1555)
Education of Father More than Primary School -0.1237
(0.1837)
Mother Ever had Tetanus Vaccination -0.5465 ***
(0.1872)
Early Child Birth (EARLY) -0.5185 *
(0.2787)
Hospital Delivery (HOSPDEL) -0.4941
(0.3763)
Child Vaccination (VACCN) -7.5757 ***
(0.8432)
Resident of Barisal 0.5236 *
(0.2754)
Resident of Chittagong 0.5206 **
(0.2342)
Resident of Dhaka 0.8939 ***
(0.2249)
Resident of Rajsahi 0.7295 ***
(0.2364)
Resident of Sylhet 0.7713 ***
(0.2357)
Log Likelihood -12285.41
NOTE: Asymptotic standard errors in parentheses;
Significance: '*'=10%; '**'=5%; '***'=1%.
Table A1: Explanatory Variables Used
Education of Mother Less than Primary School
X X X X
Education of Mother More than Primary School
X X X X
Education of Father Less than Primary School
X X X X
Education of Father More than Primary School
X X X X
Muslim X X X X
Asset Index X X X X
Rural Resident X X X X
Mother Ever had Tetanus Vaccination X
Early Child Birth (EARLY) X
Hospital Delivery (HOSPDEL) X
Child Vaccination (VACCN) X
If Woman has say on Female Health Care X
If Woman has say on Child Health Care X
Age Difference between Mother and Father
X If Father is Unskilled Labourer X
Contraceptive Use X
Province Dummies X X X X