The Role of Socio-economic and Female Indicators on Child Mortality Rate in Bangladesh: A Time Series Analysis

Abstract

This study aims to identify the role of socio-economic and female indicators on child mortality in Bangladesh from the data of 1975 – 2019. A number of econometric techniques of time series analysis like Augmented Dickey-Fuller, Autoregressive Distributive Lag bounds and pair-wise Granger causality tests have been applied to ascertain the desired outcomes. The Augmented Dickey-Fuller test has confirmed that neither series is integrated at level two and the Autoregressive Distributive Lag bounds testing approach has shown the cointegration and short-run and long-run relationship between the variables. Total fertility rate and urbanization have a positive effect, and female education, female life expectancy at birth, and economic growth rate have a negative effect on the child mortality rate. The pair-wise Granger causality test has shown the unidirectional and bidirectional causal relationship among the studied variables. All the outcomes are theoretically consistent and the policy recommendations are made based on findings.

Keywords

ARDL model Bangladesh child mortality rate socio-economic and female indicators time series data.

Introduction

The issue of child mortality is one of the most important and burning problems in the developing and underdeveloped world. A higher child mortality rate increases the vulnerability of a country’s economic and health condition. For this reason, the higher child mortality rate becomes a matter of concern for existing policy makers and researchers. To this concern, in 2015, the United Nations announced the Sustainable development goals (SDGs) and urged the reduction of the child mortality rate to fewer than 25 deaths per 1,000 live births per year across all countries by 2030 (Indicator 3.2.1 of SDGs, United Nations Development Program, 2015; World Health Organization, 2015). However, many developing countries still have high birth rates and high child mortality rates which adversely affect economic development and reveal the weakness of specific health sectors of the country. The recent outbreak of COVID-19 has raised global awareness of health issues and brought a stronger focus on the health sector, especially child health. Moreover, to facilitate economic development of a country, child mortality issue must be addressed appropriately by taking proper policy initiatives.

Bangladesh is one of the developing countries in the South Asia. It has a population of 163.05 million people and faces an annual population growth rate of 1.042% (World Development Indicator [WDI], 2020). It experienced a higher child mortality and fertility rate during the earlier period of post-independence of the country. For example, in 1973, the child mortality rate was 219.60 per 1000 live births and total fertility rate per woman was 6.904 (WDI, 2020). Although the rate of child mortality has diminished over the years (tends to 30.80 per 1000 live births in 2019) (WDI, 2020), but it remains a matter of unease for many existing policy makers.

In contemporary literature, a number of experimental works have been found to be related to the socio-economic and female indicators of child mortality (see Chowdhury et al., 2020; Kousar et al., 2020; Mandal & Chouhan, 2020; Rahman et al., 2018; Zakaria et al., 2020, among others). To attain the goal of being a developed country Bangladesh will have to maintain lower child mortality, fertility and improved female health and economic participation, along with planned urbanization. In Bangladesh there are a few papers are available on child mortality, and these do not take into consideration the role of socio-economic and female indicators on the impact of child mortality rate like us. Therefore, in this paper, we have attempted to fill up the existing literature gap. This study will determine the long-run and short-run dynamics and causal relationships among the child mortality rate and a number of socio-economic and female indicators like total fertility rate, female labor force participation rate, female education rate, female life expectancy at birth, urbanization, trade openness, male education rate, and economic growth of Bangladesh.

The rationale for selecting these variables are: (i) total fertility rate may have a positive link with child mortality rate, as care for each child reduces with the increasing number of children; (ii) female education reflects consciousness; iii) female life expectancy reflects health status (iv) labor force participation empowers women and increases wellbeing; (v) economic growth reduces poverty and improves living standards thus reducing child mortality; (vi) urbanization may affect the child mortality rate both positively and negatively; (vii) trade openness also determines the way of external trade conditions enough to affect child mortality; and (viii) male education also influences the child mortality rate, implying that more education increases more consciousness about child health and nutrition which in turn reduces mortality rate. Further justification of variable selection is noted in “Theoretical or Empirical Rationale for Choosing the Explanatory Variables” section.

Our main objectives of this study are as under:

To ascertain the role of socio-economic and female indicators on child mortality in Bangladesh.

To understand the short-run and long-run relationships and dynamics among child mortality, total fertility rate, female education rate, female life expectancy at birth, female labor force participation rate, per capita GDP, urbanization rate, trade openness, and male education rate.

To detect the causal relationship among child mortality, and other explanatory variables.

The main contributions of this paper are: (a) this is the first ever study in Bangladesh, to the best of our knowledge, that considers the essential socio-economic female characteristics only for detecting the causes of child mortality; (b) the identification of short-run and long-run relationship and causal linkages among child mortality, total fertility rate, female education rate, female life expectancy at birth, female labor force participation rate, per capita GDP, urbanization rate, trade openness, and male education rate; (c) this study uses updated and comprehensive available data (1975 – 2019); (d) the estimated robust results of the study will help policy makers, not only in Bangladesh, but also in other developing countries, to make effective policies.

We have arranged our study in the following manner: Following the introduction, “Literature Review” section analyzes the literature reviews; “The Trend of Our Chosen Variables” section delineates the trend of our chosen variables; “Data and Methodology” section explains the data and methodology; “Findings and Analysis” section interprets and analyses the results; and “Conclusion and Policy Implications” section provides the conclusion and policy recommendations.

Literature Review

A study by Yamada (1984) used the time series techniques developed by Granger (1969) and Sims (1980) in the bivariate framework of fertility and mortality, where he found that infant mortality and fertility are not independent but jointly determined. He also showed that a decline in infant mortality that is due to an increase in per capita real income causes a subsequent decline in fertility. However, his study considered only two variables and other related factors were ignored. Many experimental studies, like those of Zakaria et al. (2020), Mandal and Chouhan (2020), Kousar et al. (2020), Ahmed and Muftawu (2018), Soest and Saha (2018), Nilima et al. (2018), among others, have considered the essential socio-economic and female indicators of child mortality. For instance, Zakaria et al. (2020) conducted a study on the socio-economic, macroeconomic, demographic, and environmental variables as determinants of child mortality in South Asia, where they found that the per capita income, immunization, urbanization, trade openness and high life expectancy reduced, while high fertility rate increased child mortality during the period of 1973 – 2015. But in their study they considered only fertility among females as an indicator of child mortality and other important female indicators were not observed. Kousar et al. (2020) obtained that there was a negative relationship between child mortality and education, access to improved water and sanitation facilities, and health expenditure but a positive link with unemployment and income inequality in the context of South Asian countries by employing a panel cointegration test over the period of 1990 – 2017. Dutta et al. (2020) ascertained that the GDP per capita and educational status of females have reduced the infant mortality rate in SAARC countries. Rahman et al. (2018) conducted a study on the nexus between health expenditure and health outcomes taking the panel data of 15 South and South East Asian countries over the period of 1995-2014. The study revealed that an increase in health expenditure reduced the infant mortality rates. However, the outcomes are on the panel countries as a whole; hence it failed to observe the country specific effect on child mortality. Moreover, they did not consider the female key indicators as determinants of child mortality. Ahmed and Muftawu (2018) obtained the positive long-run relationship and unidirectional causality between infant and childhood mortality and fertility rates of women in Ghana from the time series data of 1960 – 2016. Raganathan et al. (2015) conducted a study on child mortality, fertility and economic growth. Using data from around 200 countries over the 50 years and applying Bayesian statistics they identified that the fertility rate decreases when child mortality is low and that female education drives down fertility rates, but evidence on the changes in child mortality is weak. Mandal and Chouhan (2020) got the significantly high influence of maternal education on child mortality in India from the National Health Survey -4 (2015 – 2016) data and applying the logistic regression model. By employing the Cox proportional hazards model, Masuda and Yamauchi (2020) observed that, in the case of Uganda, educated mothers had a lower probability of child mortality. Similarly, from data obtained from Nigeria DHS-2013, Andriano and Monden (2019) found that, in Malawi and Uganda, a mother’s education lowered the probability of children’s deaths. Yaya et al. (2017) also observed that the different levels of education (primary, secondary, and tertiary) of both father and mother, as well as urban impact, reduces childhood mortality in Nigeria. However, in their study they did not consider the other important socio-economic determinants of females on reducing child mortality. In connection with social determinants, Novignon et al. (2018) identified a negative impact of trade openness on the child mortality rate in 42 Sub‐Saharan African (SSA) countries over the period 1995–2013. Similar findings have also been made by Bombardini and Li (2020) for China, and Togo (2020) for Mali. In contrast, Farooq et al. (2019) found that the trade positively and significantly correlated with the infant mortality rate in low income OIC countries. Similar results have also been observed by Huynen et al. (2005) globally, and by Qadir and Majeed (2018) for Pakistan. Amouzou and Hill (2004) found a negative association between urbanization and child mortality in Sub-Saharan Africa. A contrasting viewpoint was expressed by Torres et al. (2019), who discovered the existence of urbanization penalties on increasing child mortality in Scotland during the 1861 – 1910 study periods.

Some empirical experiments relating to the indicators of child mortality also exist in Bangladesh (see Chowdhury et al., 2020; Khan & Awan, 2017; Nilima et al., 2018; Soest & Saha, 2018, among others). Chowdhury et al. (2020) found that children whose mothers had a minimum education had lower under-5 mortality than those whose mothers were illiterate from the urban samples of seven Bangladesh Demographic and Health Surveys of 1994–2014. Based on the data of 1982- 2005 from the Matlab in Chandpur district in Bangladesh, Soest and Saha (2018) found that a brief interval between births reduced the survival chances of infants. Nilima et al. (2018) accessed information from the Bangladesh demographic and health survey (BDHS)-2014 and applied the Cox proportional hazard model. They ascertained that an improvement in the mother’s education, and mothers’ membership of an NGO have lowered the risk of death of infants and children under five in Bangladesh.

Khan and Awan (2017) found the mutual effect of birth order and earlier birth interval length, sex of the child, maternal age at birth, mother’s working status, parental education were the important determinants associated with risk of child mortality from the data of Bangladesh Demographic and Health Surveys (BDHSs) for the year 2007, 2011 and 2014. Chowdhury (2013) observed that education of father, place of residence, region of residence, quantity of children under five years of age, previous death of sibling, age of mother and breastfeeding have significant impact on under-five mortality in case of Bangladesh from the data of Bangladesh demographic and health survey-2007. Gayen and Raeside (2010) also found the women's power as the degree of social linking is essential in combating child mortality in rural Bangladesh.

From the meticulous investigation of the above literature, it has been found that the outcomes did not provide unanimous, convincing, and conclusive pathways on the child mortality rate by considering the important and inclusive socio-economic and female indicators like fertility, female education, female life expectancy, female labor force participation, male education, GDP per capita, urbanization, and trade openness, especially in the case of Bangladesh. This is the main gaps in the literature. Thus, our present study is a comprehensive attempt to fill up the existing literary gap and provide proper guidelines on the policy implications of socio-economic and female indicators in the health sector, especially child health.

The Trend of Our Chosen Variables

Here we show a brief overview of the trend of our chosen variables (Table 1). We can see that the child mortality rate per 1000 live births (CM) in 1975 was 216.6, which was much higher, but this has been decreasing over the years. This may be the result of the improvement of medical facilities as well as the improvement of the various socio-economic and female indicators to take proper steps for the protection of their children.

Table 1.

Trends of Our Selected Variables.

Period	Child mortality rate (under-5) per 1000 live births	Total fertility rate per woman (%)	School enrollment, tertiary, female (% gross)	Female life expectancy at birth in years	Female labor force participation rate (%)	Per capita GDP in current US$	Urban population (% of total population)	Trade (% of GDP)	School enrollment, secondary, male (% gross)
1975–1979	210.22	6.67	0.77	49.77	3.88	185.39	11.70	19.15	27.01
1980–1984	189.04	6.04	1.42	53.38	5.83	222.91	16.11	20.07	28.08
1985–1989	161.68	5.09	1.59	56.20	32.51	257.92	18.40	17.59	27.83
1990–1994	131.92	4.16	1.89	59.77	25.01	298.63	20.59	20.76	32.29
1995–1999	102.82	3.48	3.18	63.86	26.16	388.52	22.44	27.38	44.06
2000–2004	77.28	2.97	4.08	67.11	27.32	433.56	24.80	28.98	49.03
2005–2009	57.90	2.53	5.94	69.75	28.47	580.88	28.25	39.03	46.12
2010–2014	43.94	2.23	11.16	72.13	30.85	925.34	32.00	44.83	53.39
2015–2019	34.04	2.06	15.96	73.97	34.69	1553.62	35.86	38.07	65.71

Source: WDI (2020); Index Mundi (2020); Knoema (2020a; 2020b).

The total fertility rate (TFR) per woman has also decreased over time. In 1975, it was 6.82 per woman, but in 2019 it had reduced to 2.01, which is the desired replacement level. In 1975, the female life expectancy at birth was 47.604 years, and this is also improving (74.6 years in 2019). The increase in life expectancy of females at birth denotes their improved health status. The female labor force participation rate in 1975 was only 3.58, but the trend is increasing and in 2019 it reached 36.26. Therefore, more and more females are becoming involved in the workforce and are participating in economic activities, although the rate is much lower than that for men. As more females will be involved in the labor force participation rate, the more economic empowerment they will achieve. Another variable is female education: the female education rate at tertiary level was 0.70 percent in 1975 and it increased to 20.02 percent in 2019. Due to lack of data we could not include the female literacy rate as a variable in this study. As more females are educated, the more they will be conscious of their children’s health. The per capita GDP is also increasing over time; it was US$277.57 in 1975, and it was US$1855.74 in 2019. On the other hand the trends of urbanization, trade openness, and male education rate were 9.84%, 10.99% and 27.71% in 1975, which increased to 37.41%, 36.76%, and 67.09% in 2019.

By analyzing the trends of our studied variables we have understood the negative or downward trends on child mortality rate and total fertility rate through recognizing the positive or upward trends on female labor force participation rate, female education rate, female life expectancy at birth, urbanization rate, trade, male education and per capita GDP.

Data and Methodology

Theoretical or Empirical Rationale for Choosing the Explanatory Variables

The theoretical or empirical rationale for choosing the explanatory variables of our study can be explained by three socio-economic theories: modernization theory, gender stratification theory, and developmental state theory. The supporters of modernization theory assert that modernization decreases child mortality by increasing economic output, and following developments in education, health status etc. (Frey & Cui 2016; Frey & Field, 2000; Rostow, 1960; Shen & Williamson, 1997). For this reason we have taken per capita GDP, urbanization, trade openness, and female life expectancy at birth for our study. The followers of gender stratification theory argue that child mortality drops when the status of women increases by education and employment (Caldwell, 1990, 1993; Frey & Cui, 2016; Frey & Field, 2000; Shen & Williamson, 1997). Therefore we have chosen male and female education rates, and female labor force participation rates. The advocates of developmental state theory claim that child mortality reduces when states allocate and redistribute resources in ways that promote public health and education (Evans, 1979, 1995; Frey & Cui, 2016; Frey & Field, 2000; Shen & Williamson, 1997). For this reason we have selected urbanization, trade openness and total fertility rate of women for our study.

Now, the representation of our selected variables can be displayed as under:

CM: Child mortality rate

TFR: Total fertility rate

FED: Female education rate

FLE: Female life expectancy at birth

FLFP: Female labor force participation rate

PerGDP: Per capita gross domestic product

URB: Urbanization rate

TO: Trade openness

MED: Male education rate

So the functional form of our study can be written as:

CM = f (TFR, FED, FLE, FLFP, PerGDP, URB, TO, MED)

We have converted all variables in natural log form to have the direct elasticity from the estimated coefficient of each variables. Hence the econometric form of the above functional form can be written as follows:

{lnCM}_{t} = α + β_{1} {lnTFR}_{t} + β_{2} {lnFED}_{t} + β_{3} {lnFLE}_{t} + β_{4} {lnFLFP}_{t} + + β_{5} {lnPerGDP}_{t} + β_{6} {lnURB}_{t} + β_{7} {lnTO}_{t} + β_{8} {lnMED}_{t} + u_{t}

(1)

Where, α is intercept, β₁, β₂, β₃, β_4, β₅, β_6, β_7, β_8, are coefficients and u_t is error term.

Variables and Data

We have considered the child mortality rate as our dependent variable which can be defined as the mortality of children whose age is below five. According to the World Bank, the under-five mortality rate is the likelihood per 1,000 that a neonatal baby will die before reaching age five, if subject to age-specific mortality rates of the specified year (WDI, 2020). The total fertility rate, female education rate, female life expectancy at birth, female labor force participation rate, urbanization rate, trade openness, male education rate, and per capita gross domestic product are our independent or explanatory variables. We can define the total fertility rate which represents the number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with age-specific fertility rates of the specified year (WDI, 2020). The enrollment at the tertiary level of females (as % gross) is accounted as the proxy of female education rate. The female life expectancy at birth is our proxy variable of the health status of females. This shows the number of years a girl child would live at the time of her birth were to stay the same throughout her life (WDI, 2020). The female labor force participation rate is the proportion of the female population aged 15 and older that is economically active. Here all females are taken who supply labor for the production of goods and services during a specified period. The per capita gross domestic product (GDP) is our proxy variable to see the economic development of Bangladesh. The per capita GDP can be defined as the gross domestic product divided by mid-year population. Urbanization rate (% of total population) is considered to be the people living in urban areas. Trade openness (trade as a % of GDP) is measured as the total of exports and imports of goods and services. The school enrollment at the secondary level of males (% gross) is used as the proxy of male education.

In order to conduct our study, the time series open data of the WDI (2020) of the World Bank for the period of 1975 – 2019 data have been used for the whole of child mortality, per capita GDP, female labor force participation rate, urbanization, trade openness, male and female education rates, and female life expectancy (till 2018, whereas the 2019 data is collected from Knoema (2020a) world Atlas data). The data of total fertility rate have been collected from the gender indicators of Index Mundi (2020) online data (till 2017, whereas 2018 and 2019 data are collected from Knoema (2020b) world Atlas data). Some missing values of female and male education rates, and female labor force participation rate are being linearly interpolated by E-views-11 software

Unit Root Test

For the estimation of the time series data of variables it is important not to have the unit root or have the stationarity of them. The presence of the unit root leads to the possibility of receiving spurious results in accordance with the theory of large number and the central limit theorem. In this case the normal statistics (i.e. t-statistic etc.) become invalid as a way to interpret the result. So the detection of unit root is essential for our further estimation. Some variables have no unit root or become stationary at levels or in first or second differences. In accordance with the methodology of Pesaran and Shin (1999) and Pesaran et al. (2001) we used the Auto Regressive Distributive Lag (ARDL) model in case of the variables having no unit root or having stationarity at level I(0), at first difference I(1) or mixed, but not at second difference I(2). In this regard, the study of the Augmented Dickey-Fuller (ADF) unit root testing method will be used to check the stationarity of the data of our studied variables. We use the null hypothesis H₀: the variable has a unit root and alternative hypothesis H₁: H₀ is not. If our null hypothesis is rejected then the variable does not contain any unit root or it becomes stationary and may proceed for further estimation.

Cointegration Test

It is important to perform cointegration tests for finding the long-run equilibrium relationship and short-run and long-run dynamics among the studied variables. For this reason in our study the ARDL bounds test approach will be conducted because: it is flexible, allows I(0), I(1) and mix; it has single equation settings; different lag length of different variables can be applied; allows small sample size, and permits different diagnostic problems to be properly addressed.

In line with Rahman (2017), Shahbaz et al. (2013), and Rahman and Kashem (2017) the ARDL model for bounds testing cointegration can be written as follows:

\begin{array}{l} {Δ \ln CM}_{t} = α + \sum_{i = 1}^{k} β_{i} {Δ \ln CM}_{t - i} + \sum_{i = 0}^{l} γ_{i} {Δ \ln TFR}_{t - i} + \sum_{i = 0}^{m} η_{i} {Δ \ln FED}_{t - i} \\ + \sum_{i = 0}^{n} ϑ_{i} {Δ \ln FLE}_{t - i} + \sum_{i = 0}^{o} θ_{i} {Δ \ln FLFP}_{t - i} + \sum_{i = 0}^{p} Ω_{i} {Δ \ln PerGDP}_{t - i} + \sum_{i = 0}^{q} λ_{i} {Δ \ln URB}_{t - i} \\ + \sum_{i = 0}^{r} Ψ_{i} {Δ \ln TO}_{t - i} + \sum_{i = 0}^{s} ζ_{i} {Δ \ln MED}_{t - i} + δ_{0} \ln {CM}_{t - 1} + δ_{1} \ln {TFR}_{t - 1} + δ_{2} \ln {FED}_{t - 1} \\ + δ_{3} \ln {FLE}_{t - 1} + δ_{4} \ln {FLFP}_{t - 1} + δ_{5} \ln {PerGDP}_{t - 1} + δ_{6} {\ln URB}_{t - 1} + δ_{7} \ln {TO}_{t - 1} \\ + δ_{8} \ln {MED}_{t - 1} + μ_{t 1} \end{array}

(2)

Here, lnCM, lnTFR, lnFLFP, lnFED, lnFLE, lnPerGDP and lnIMM are our selected variables and $μ_{t 1}$ is a random disturbance term; it is considered that it has no serial correlation, no heteroskedasticity, and is normally distributed. This equation (2) is also called the conditional Error correction Model (ECM) by Pesaran et al. (2001). The summations $\sum$ signs of the above equations are called error correction dynamics and $δ_{s}$ show long-run relationships. The values of maximum lags of k, l, m, n, o, p, q, r, and s will be taken from Schwarz Information criterion (SIC).

Here we will take our null and alternative hypothesis as under:

H₀: There is no cointegration

H₁: There is cointegration

Because of the limitations of the F-statistic, Pesaran et al. (2001) developed bounds on finding asymptotic distribution of the F-statistic (Rahman & Kashem, 2017). In the bounds test it is considered that in the lower bound all the variables are I(0) and in the upper bound all the variables are I(1). It is told that if the value of F-statistic falls below the I(0) bound then no cointegration is possible and, if the value remains above I(1) bound, then the cointegration is found. If the F- statistic value lies between I(0) bound and I(1) bound then we may call it inconclusive and have to seek other tests for cointegration.

From the error correction mechanism (ECM) the short-run parameters can be estimated as under:

\begin{array}{l} {Δ \ln CM}_{t} = α + \sum_{i = 1}^{k} β_{i} {Δ \ln CM}_{t - i} + \sum_{i = 0}^{l} γ_{i} {Δ \ln TFR}_{t - i} + \sum_{i = 0}^{m} η_{i} {Δ \ln FED}_{t - i} \\ + \sum_{i = 0}^{n} ϑ_{i} {Δ \ln FLE}_{t - i} + \sum_{i = 0}^{o} θ_{i} {Δ \ln FLFP}_{t - i} + \sum_{i = 0}^{p} Ω_{i} {Δ \ln PerGDP}_{t - i} \\ + \sum_{i = 0}^{q} λ_{i} {Δ \ln URB}_{t - i} + \sum_{i = 0}^{r} Ψ_{i} {Δ \ln TO}_{t - i} + \sum_{i = 0}^{s} ζ_{i} {Δ \ln MED}_{t - i} \\ + φ {ECT}_{t - 1} + μ_{t 2} \end{array}

(3)

We can acquire the speed of short-run adjustment towards long-run equilibrium through the error correction model (ECM). Here we find the negative and significant value of the error correction term (ECT) coefficient $φ$ and short-run causality by the coefficient of other independent variables (Rahman & Kashem, 2017; Rahman & Mamun, 2016; Shahbaz et al., 2013).

Diagnostic Test

For the estimation of our variables through the ARDL bound testing, it is important to check the serial correlation, heteroskestacity and normality of the model. In this case we have used the Breusch-Godfrey (BG) Lagrange Multiplier (LM) test for serial correlation, the Breusch-Pagan-Godfrey (BPG) test for heteroskedasticity and the Jarque-Bera (JB) test for normality. For assessing the stability of our model we may use recursive tests like cumulative sum (CUSUM) and cumulative sum of squares (CUSUM squares).

Granger Causality Test

To check the causality test we have to use the Granger causality method, which shows the causation among variables. The causality can be unidirectional or bidirectional. Granger (1969) noted that the correlation may not always show the relationship among variables because of spuriousness and it does not affirm causation, so a causality check is needed (Rahman & Kashem, 2017).

According to Rahman and Kashem (2017) the test for the absence of Granger causality can be estimated by using the VAR model as under:

Y_{t} = h_{0} + m_{1} Y_{t - 1} + \dots \dots + m_{k} Y_{t - k} + n_{1} X_{t - 1} + \dots \dots n_{k} X_{t - k} + υ_{t}

(4)

X_{t} = j_{0} + w_{1} X_{t - 1} + \dots \dots + w_{l} X_{t - l} + e_{1} Y_{t - 1} + \dots \dots e_{l} Y_{t - l} + Y_{t}

(5)

Here the null hypothesis is Y does not Granger causes X, and the alternative hypothesis is that Y Granger causes X. That means, H₀: n₁ = n₂ = ….= n_k = 0 and H₁: Not H₀. Here the desirable character for Granger causality is to reject the null hypothesis. We can find four possible results of Granger causality: unidirectional Granger causality from Y_t to X; unidirectional Granger causality from X_t to Y; bidirectional causality; and no causality. To observe the causality among our considered variables we will apply the pair-wise Granger causality test (Awe, 2012; Faisal et al., 2017).

Findings and Analysis

Unit Root Test

To detect the unit root in the data series of our studied variables we have conducted a popular method of unit root test named Augmented Dickey-Fuller (ADF) test. The results of the ADF test (Table 2) has shown that lnCM, lnTFR, lnFLE have no unit root or are stationary at level I(0) but lnFED, lnFLFP, lnPerGDP, lnURB, lnTO, and lnMED have no unit root or are stationary at their first difference I(1) and none of them are I(2). Now according to the methodology of Pesaran et al. (2001), we can use the ARDL bounds test approach for our further estimation.

Table 2.

Results of Unit Root Test.

Variables	ADF		Order of integration (I)
	H₀: The variable has a unit root
	Level	1st Diff.
lnCM	−4.66***	−2.34	I(0)
lnTFR	−4.41***	−2.18	I(0)
lnFED	−0.07	−6.47***	I(1)
lnFLE	−3.34**	0.52	I(0)
lnFLFP	−1.93	−5.19***	I(1)
lnPerGDP	1.17	−10.03***	I(1)
lnURB	−0.73	−3.27**	I(1)
lnTO	−2.52	−11.57***	I(1)
lnMED	0.38	−5.93***	I(1)

, ** and *** indicate statistical significance, respectively, at the 10%, 5% and 1% levels.

ARDL Bounds Test

After completing the unit root test we may proceed to the ARDL bounds test to find out the cointegration among our studied variables. We have found the lag order 2 by running the unrestricted vector auto regression (VAR) lag selection criteria. By imposing unrestricted constant and no trend (Case-III) and applying the Schwarz Information criterion (SIC) we have chosen our ARDL(1, 2, 0, 1, 0, 0, 0, 0, 1) model for our estimation. The results of the ARDL bounds test of the model ARDL(1, 2, 0, 1, 0, 0, 0, 0, 1) are provided in Table 3. Here the calculated F-statistic value is 753.2311 which is far above the upper bounds of 1% level of significance that shows the long-run cointegration among our studied variables.

Table 3.

Results of ARDL Bounds Test.

Critical values	F-statistic: 753.2311
Critical values	Lower boundI(0)	Upper boundI(1)
10%	1.95	3.06
5%	2.22	3.39
1%	2.79	4.1

Long-Run and Short-Run Relationships

After performing the ARDL bounds test and finding the long-term cointegration among our studied variables we can now obtain the long-run relationship among our variables in the model of ARDL(1, 2, 0, 1, 0, 0, 0, 0, 1) as given in Table 4:

Table 4.

Results of Long-Run Coefficients.

Variables	Coefficients	Std. error	t-statistic	Probability
lnTFR	0.986947*	0.539447	1.829554	0.0776
lnFED	−0.049391**	0.022730	−2.172943	0.0381
lnFLE	−6.679267**	3.072942	−2.173574	0.0380
lnFLFP	−0.006725	0.012513	−0.537431	0.5951
lnPerGDP	−0.158108**	0.071599	−2.208237	0.0353
lnURB	1.634557***	0.475396	3.438306	0.0018
lnTO	0.057600	0.046989	1.225818	0.2301
lnMED	−0.142537	0.111910	−1.273676	0.2129

, ** and *** indicate, respectively, 10%, 5% and 1% level of statistical significance.

From the above table we can see that the coefficient of total fertility rate is 0.987 which is positive and statistically significant at 10% level, indicating that if the total fertility rate of female increases or decreases by one percent, the child mortality rate will increase or decrease by 0.99 percent. The coefficients of female education rate, female life expectancy at birth, and per capita GDP are −0.049, −6.679, and −0.158, respectively, which are negative and are all statistically significant at 5% level, signifying that if the female education rate, female life expectancy at birth, and economic growth rate increase by one percent then the child mortality rate will decrease by 0.05 percent, 6.68 percent, and 0.16 percent, respectively. The coefficient of urbanization rate is 1.635 which is positive and statistically significant at 1% level and denotes that one percent increase of urbanization leads to the increase of child mortality by 1.64 percent. This is due to the negative penalties of unplanned urbanization (Torres et al., 2019) where more pollution and more health hazards exist (more people living in slums and unhealthy environment). However the coefficients of female labor force participation rate and male education rate are negative, and for trade openness are positive but they are statistically insignificant. All the results noted in Table 4 are rational and theoretically consistent.

After obtaining the long-run relationship among our variables we can now assess the short-run coefficients or dynamism of our variables. From our model ARDL(1, 2, 0, 1, 0, 0, 0, 0, 1) we can achieve the results of short-run coefficients which are provided in Table 5. The short-run coefficient of total fertility and its first difference of the first lag are 0.152 and 0.186, which are statistically significant at 1%. In case of female life expectancy at birth and male education rate, the coefficients are 0.119 and 0.005 which are also positive and both are statistically significant at 1% level. This is due to the short-run adjustment effect of these twin variables sufficiently to abate the child mortality rate.

Table 5.

Results of Short-Run Coefficients (From the ECM).

Variables	Coefficients	Std. error	t-Statistic	Probability
C	0.886641***	0.010077	87.98342	0.0000
D(lnTFR)	0.152261***	0.039559	3.848947	0.0006
D(lnTFR(−1))	0.185824***	0.038973	4.767974	0.0000
D(lnFLE)	0.119385***	0.028918	4.128341	0.0003
D(lnMED)	0.005240**	0.002035	2.574919	0.0154
CointEq(−1)*	−0.034005***	0.000366	−93.00092	0.0000
R-squared: 0.998385 Adjusted R-squared: 0.998166F-statistic: 4573.296*** Durbin-Watson statistic: 2.227248

, ** and *** indicate, respectively, 10%, 5% and 1% level of statistical significance.

The coefficient of the short-run dynamics with long-run relationships of the lagged error correction term (ECT) [CointEq(-1)*] is -0.034005 which is negative and is statistically significant at 1% level. These results indicate that there is a long-run relationship among our variables and every year 3.40% error will be corrected or adjusted towards the long-run equilibrium.

Diagnostic Tests

To see the well-specification of our model we have tested serial correlation, heteroskedasiticty, and normality, and to see the stability of the model we have tested two recursive residual tests: CUSUM and CUSUMSQ.

Table 6 shows that our model has no serial correlation, using the Breusch-Godfrey Serial Correlation Lagrange Multiplier (LM) test, no Heteroskedasticity, using the Breusch-Pagan-Godfrey heteroskedasticity test, and normal using the Jarque-Bera test under both LM-version and F-version.

Table 6.

Results of Diagnostic Test.

Test	LM-version	F-version
Breusch-Godfrey Serial Correlation Lagrange Multiplier (LM) test	1.090349 [0.5797]	F(2,27): 0.351225 [0.7070]
Breusch-Pagan-Godfrey Heteroskedasticity test	9.933093 [0.6994]	F(13,29): 0.670109 [0.7746]
Jarque-Bera test	0.232642 [0.890190]	Not Applicable

Probability values are shown on parentheses “[.]”.

From Figures 1 and 2, we have found that the cumulative sum of recursive residuals, CUSUM, lies within the 5% limit and the cumulative sum of recursive residuals of squares, CUSUMSQ, also lies within the 5% critical limit. Both have shown that there is no structural break in the model.

Figure 1.

Plot of CUSUM Test.

Figure 2.

Plot of CUSUM of Squares Test.

Granger Causality Test

Since we have found the cointegration and the long-run relationship among variables, now we have to see the direction of the causality. For finding Granger causality we have followed the pair-wise Granger (1988) causality test procedure and the results (F- statistic), which are noted in Table 7.

Table 7.

The Results of Pair-Wise Granger Causality.

Null hypothesis:	F-Stat.	Prob.	Decision
lnTFR does not cause lnCM	2.900*	0.067	lnTFR ↔ lnCM (bidirectional causality)
lnCM does not cause lnTFR	2.947*	0.065	lnTFR ↔ lnCM (bidirectional causality)
lnFED does not cause lnCM	0.414	0.664	lnCM → lnFED (unidirectional causality
lnCM does not cause lnFED	4.071**	0.025	lnCM → lnFED (unidirectional causality
lnFLE does not cause lnCM	5.992***	0.005	lnFLE ↔ lnCM (bidirectional causality)
lnCM does not cause lnFLE	3.757**	0.032	lnFLE ↔ lnCM (bidirectional causality)
lnFLFP does not cause lnCM	0.315	0.732	No causality
lnCM does not cause lnFLFP	1.245	0.299	No causality
lnPerGDP does not cause lnCM	0.157	0.855	lnCM → lnPerGDP (unidirectional causality)
lnCM does not cause lnPerGDP	13.150***	0.000	lnCM → lnPerGDP (unidirectional causality)
lnURB does not cause lnCM	1.538	0.228	lnCM → lnURB (unidirectional causality)
lnCM does not cause lnURB	14.008***	0.000	lnCM → lnURB (unidirectional causality)
lnTO does not cause lnCM	0.166	0.848	lnCM → lnTO (unidirectional causality)
lnCM does not cause lnTO	2.958*	0.064	lnCM → lnTO (unidirectional causality)
lnMED does not cause lnCM	6.768***	0.003	lnMED → lnCM (unidirectional causality)
lnCM does not cause lnMED	1.631	0.209	lnMED → lnCM (unidirectional causality)

, ** and *** indicate respectively 10%, 5% and 1% level of statistical significance.

→

indicates direction of causality.

Table 7 confirmed that the child mortality rate Granger causes total fertility rate, female education rate, female life expectancy at birth, per capita GDP, urbanization rate, and trade openness. Conversely, total fertility rate, female life expectancy at birth, and male education rate Granger causes child mortality rate.

Therefore, we have found the unidirectional causality running from child mortality rate to female education rate, per capita GDP, urbanization rate, and trade openness and unidirectional causality from male education rate to child mortality rate. We have also found the bidirectional causality of child mortality rate with total fertility rate and female life expectancy at birth. Figure 3 depicts the directions of causality.

Figure 3.

Granger Causality.

Conclusion and Policy Implications

In this study we have explored the cointegration, short-run and long-run causal relationships among child mortality rate, total fertility rate, female education rate, female life expectancy at birth, female labor force participation rate, per capita GDP, urbanization rate, trade openness, and male education rate of Bangladesh using data of 1975 – 2019. To achieve the desired outcomes of our study we have used different time series econometric techniques like the Augmented Dickey-Fuller (ADF) unit root test, the ARDL bounds test, the Error Correction Mechanism (ECM) and the pair-wise Granger causality test. In the Augmented Dickey-Fuller (ADF) unit root test we found that all of our variables are either I(0) or I(1) and none are I(2), so we have used the ARDL bounds test and found both short-run and long-run relationship among the variables. Our obtained results reveal that the total fertility rate and urbanization rate positively, and female education rate, female life expectancy at birth, and economic growth rate negatively affect the child mortality rate. The pair-wise Granger causality test has also supported our estimation, showing the unidirectional and bidirectional causal relationship among the studied variables. The policy implication of our findings is: the current child mortality trend, which is declining, should be sustained by improving the related socio-economic and female indicators. To ensure the sustenance of the lower child mortality rate, the role of socio-economic and female indicators should be properly evaluated, and hence the following recommendations can be considered:

Ensuring total fertility rate at the replacement level: The total fertility rate should be always kept at the replacement level for controlling population growth to ensure balanced economic development in Bangladesh. In this respect the government, NGOs, village communities, urban communities can play vital roles in creating consciousness among people. If the fertility rate of women becomes lower, then the child mortality rate also is lowered because of the proper care of existing children. The supply of adequate contraceptives, medical immunities and other logistic supports will come from both the government and the non-government level for the people of Bangladesh.

Enhancing female education: The government of Bangladesh should identify female education as the key factor for reducing child mortality rate. In this regard more access to the education of females should be ensured and adequate security should be provided for them. If more females are educated then they will be more conscious about their own health and their children’s health, and will be more likely to take proper steps for reducing child mortality, which in turn will ensure economic development of the country.

More investment on female health: More investment is needed in strengthening the health care system by establishing more hospitals, supplying improved medications, ensuring quality doctors for the general population, especially females and children throughout the country. In this respect both public and private sectors should come forward to solve the existing problems. Child and mother healthcare services should be improved at union, sub centers, upazilla health complexes and satellite clinics in Bangladesh. The government of Bangladesh should allocate an appropriate budget for this task.

Sustainable economic growth: Sustainable economic growth without damaging the environment is essential to ensure a better habitat for the child. More sustainable economic growth will be helpful for expanding infra-structural development, educational development, and health facilities to act as catalysts for reducing child mortality.

Planned urbanization: Planned urbanization by addressing all types of health related hazards and eradicating unhygienic environmental vulnerabilities should be given top priority on ensuring better health for a variety of people, especially children. In this regard, the negative penalties like polluted air, unsafe drinking water, unhygienic living condition in slums, and excess energy consumption, should be replaced with positive actions, for example, ensuring planned infrastructure development, improved educational facilities, more employment opportunities, quality medical facilities, and sufficient technological amenities to reduce child mortality.

Research and development: The continuous research and development on improving maternal health, increasing women’s status, accelerating female employment, expanding female education, along with planned urbanization and enhancing economic development in Bangladesh is essential for reducing child mortality. The joint initiative by the government, private institutions and NGOs can ensure the reduction of child mortality in Bangladesh.

Like many other studies, this research is also not without limitations. We could not include some relevant variables such as access to clean water, access to sanitation, doctor-patient ratio due to lack of data. Future research is recommended to consider these variables as well as providing proper guidelines to policy makers in Bangladesh.

Footnotes

Authors' Contributions:

MMR: Conceptual and methodological development; variable selection; result analysis, writing abstract; polishing and editing, and improving the quality of the manuscript; closely supervising.

KA: Study plan; literature review; data collection; writing main sections of the paper; econometric estimation, and data and result analysis; undertaking the responsibility of corresponding author of this paper.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Khosrul Alam

Author Biographies

Mohammad Mafizur Rahman is an associate professor in Economics at the University of Southern Queensland, Australia. With extensive academic qualifications in Economics such as B.Sc. Honours, Graduate Diploma, M.Sc., M.Ec. and PhD, he has taught various economics-related courses at undergraduate and postgraduate levels in three different universities in Australia and overseas. His field of research interest is Applied Economics, which includes issues in Health Economics, Development Economics, International Economics and Environmental Economics. Dr. Rahman has an wide-ranging publication record of 85 journal papers, 34 conference papers, 1 scholarly book, 1 book chapter, and 4 repots. A significant number of research papers are published in Q1 and Q2 journals, and his Google scholar citations are 1868, h-index is 24 and i10-index is 42. He is a successful supervisor who has supervised postdoctoral research fellows and HDR students in the last five years. He is an editorial team member of three academic journals in the field of Economics and Business, and has reviewed many journal papers and PhD theses. Dr. Rahman has played a number of managerial and administrative roles at the university, including as a Program Coordinator in Business Economics major, and as an Associate Academic Performance Supervisor and Faculty Board member. He is an expert media commentator who very often provides expert interviews on TV and radio on various socio-economic issues.

Khosrul Alam is an assistant professor of Economics at Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, Bangladesh. He completed is BSS (Honors) and MSS in Economics from the University of Dhaka, Bangladesh. Firstly, he joined at the Department of Economics in the Noakhali Science and Technology University, Noakhali, Bangladesh, and later he joined as an Assistant Professor at the same department in the Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, Bangladesh and served as a Chairman in the Department from 2017 to till 2020. His present research interests are in the fields of Development Economics, Population Economics, Health Economics, Public Economics, Environmental Economics, Rural and Urban Economics etc. He is a life member of the Bangladesh Economic Association. He is a co-author of “Women in Rural Economy in the light of Poverty: Bangladesh Perspective” (IOSR-JHSS, 2015); “Development of rural informal sector for eliminating rural poverty in Bangladesh” (Journal of Science & Technology (JST), 2015); “Future Fertiliser Demand and Role of Organic Fertiliser for Sustainable Rice Production in Bangladesh” (Agriculture, Forestry and Fisheries, 2015); “Forecasting the Quantity of Shrimp and Dry Fish Export from Bangladesh” (Journal of Economics and Sustainable Development, 2015); “Performance of exporting shrimps and dry fishes from Bangladesh”- (Journal of the Bangladesh Agricultural University, 2015) etc. Khosrul Alam is the corresponding author and can be contacted at: alam.khosrul@gmail.com

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