An investigation of the relation between life expectancy & socioeconomic variables using path analysis for Sustainable Development Goals (SDG) in Bangladesh

Abstract

In today’s world, the key variable for measuring population health is life expectancy (LE). The purpose of this research is to find out how life expectancy is related to other factors and develop a model to account for the predictors that contribute to LE. This study is also conducted to investigate and measure the effect of socioeconomic variables on LE in Bangladesh. In this study, the predictor variables are employment rate, gross national income (GNI), population growth rate, unemployment rate, and age dependency ratio. Path analysis disintegrated bivariate analysis and showed that employment rate, GNI, and age dependency ratio are significantly related to life expectancy, although bivariate analysis showed all variables are significantly related to LE. The maximum values of significant factors, GNI and employment rates, are $1930 and 21.32% happened in 2019, which is positively correlated with life expectancy. Also, the maximum value of the age dependency ratio (81.52%) happened in 1991, whereas the maximum value of the dependent variable LE (72.59 years) happened in 2019. It has been observed that LE, GNI, and employment rates all rise with one another. There exists an adverse relationship between LE and age dependency ratio. Based on comparisons with other highly developed nations, Bangladesh’s GNI needs to grow faster than other significant factors to boost life expectancy. We have forecasted variables that were significantly related to LE until 2030 for the purpose of sustainable development goals, especially the 3rd goal.

1 Introduction

Life expectancy is an important summary measure of a population’s health and well-being. Life expectancy reflects a nation’s health, economic, and social conditions, and healthcare infrastructure. Statistically, LE is the average time that an individual or other creature is expected to live from the year of their birth to their current age.

It is widely used as an indicator of a country’s overall development. For one to know one country’s overall condition, the phenomenon of LE plays a vital role, especially in mortality as well as in the economic sector. High-income, developed countries have seen monumental improvements in life expectancy over the 20th and 21st centuries [1, 2]. LE has constantly been the main focus of health science. The health-related predictors of LE were the prevalence of HIV, expenditures on healthcare, mortality rates, resources for healthcare, and outcomes of healthcare. Consumption of pharmaceuticals has a positive effect on LE in advanced and middle-aged people. Vegetable and fruit consumption increased by 30% and tobacco consumption decreased by at least 2 cigarettes per day, which will help to increase LE for a 40-year-old female [3]. Several production functions of health express the technical connection between health inputs and health status, where inputs of health care can be classified into three groups: social factors, natural factors, and economic factors. Many facilities of medical care, such as increasing medical staff and doctors, could reduce mortality and increase LE (life expectancy) [4, 5]. It has been proven that increasing the availability of physicians and decreasing undernourishment and adult illiteracy help to improve LE in a country [6]. Life expectancy (LE) is linked with the mortality rate of infants and a high literacy rate. LE increased with low infant mortality rates and high literacy rates [7]. Economic and demographic factors of life expectancy (LE) were employment rate, gender, gross national income (GNI), education, and age [8–11]. Among these factors, the strongest possible determinant of LE was gross national income. In South Korea, increased GNI had a positive impact on LE [9]. The association between LE and education was significant in Sweden, Finland, Denmark, Norway [12, 13], and other European countries [14]. Similar relationships can also be seen in Brazil [15]. Recent research in Thailand concludes that older people who have higher educational qualifications and better income have greater health satisfaction and better health outcomes [16]. The inconsistency and equality of LE have serious effects on individual and aggregate human behavior because they affect human capital investment, economic growth, fertility behavior, incentives for pension benefit claims, and intergenerational transfers [17, 18].

Although socioeconomic and demographic impacts on life expectancy (LE) have already been shown in many papers [1–18], there is no such research paper found that directly focuses on the relationship between LE and socioeconomic variables, especially for Bangladesh. Therefore, we hope the current study endeavors to complete this. The principal focus of this research is to analyze the relationships between LE and other factors, and develop a model to account for the predictors that contribute to LE. This investigation would be beneficial for Bangladesh to understand which factors have the largest impact on life expectancy.

2 Significance of the method

In real-world data, it is hard to get the total association between variables without any statistical operation. That is why the total association between variables is measured using Pearson correlation coefficients (r). This study aims to explore the relationship of LE with other factors and develop a model to account for the predictors that contribute to LE. Path analysis is used to decompose bivariate analysis and measure several effects by investigating the link between the response variable and more than one predictor variable. With the help of model equations obtained from path analysis, one can easily measure all the magnitudes and relations between variables. After fitting the path analysis model, we have to test the goodness of fit to see how well the data fits into the model. As a result, it will guide the new researcher who wants something new for his study.

3 Objectives of the study

After rigorous study, it is clear that life expectancy plays a vital role in human health and health infrastructure development. The principal purpose of this research is to investigate whether life expectancy is related to socioeconomic variables. This will help us to detect the socio-economic determinants of life expectancy in Bangladesh. We want to estimate several effects of significant factors on LE. This will help us to understand which factors are influencing life expectancy more. After that, we determine the best-fitted model and forecast the future conditions of significant factors for the sustainable development goals of Bangladesh. This will allow us to determine whether life expectancy will increase or decrease in the future as well as how quickly Bangladesh will achieve Sustainable Development Goals, especially the 3^rd goal.

4 Methodology

To make the analysis precise and easy, we used different types of statistical techniques and software, such as R-Studio and SPSS. Both these two statistical programs provide a plethora of basic statistical functions. SPSS and R statistical packages are used to make analyses and predictions [19]. We so used Microsoft Excel for research purposes.

4.1 Data description

The beginning of any meaningful and worthwhile research is its data source. The actual data focuses on real research, which can help to make decisions and plans. We collected data from world development indicators (World Bank) [20]. We initially employed six variables to show the analysis of the data. Variables’ names, identification marks, and sources are given in Table 1.

Table 1. Introductory table.

Variables name	Identification mark	Source
GNI (current US$)	x 1	World Bank
Unemployment rate, total (% of total labor force)	x 2	World Bank
Employment rate (% of total employment)	x 3	World Bank
Population growth rate (annual %)	x 4	World Bank
Age dependency ratio (% of working-age population)	x 5	World Bank
Life expectancy at birth, total (years)	x 6	World Bank

Full-time students, older people, and beggars are excluded from the unemployment rate and included in the age dependency ratio. The employment rate is considered below 60 years.

4.2 Pearson correlation coefficient

The Pearson correlation coefficient is used to estimate the relationship between variables. It is commonly used in linear regression. Its coefficient lies between -1 and 1.

Here,

• 1 is the indicator of a strong positive relationship between variables.

• -1 is the indicator of a strong negative relation between variables.

• 0 is the indicator of no relationship between variables.

The formula for Pearson Correlation Coefficient is,

$$r=\frac{n\left(\sum xy\right)-\left(\sum x\right)\left(\sum y\right)}{\sqrt{\left[n\sum x^2-{\left(\sum x\right)}^2\right][n\sum y^2-{\left(\sum y\right)}^2]}}$$

4.3 Path analysis

A form of multiple regression analysis is Path analysis, which measures several effects models by investigating the link between the response variable and more than one predictor variable.

Fig 1 represents an example of a path diagram. Path models consist of outcome and independent variables graphically with the help of rectangle shape boxes. Variables that are not on other factors are called exogenous variables. Graphically, these variables are located at the outside edges of the model. These variables have only single-headed arrows outgoing from them. Variables that are both dependent and independent are called endogenous variables. Graphically, endogenous variables have both outgoing and ingoing arrows.

Fig 1. Path diagram.

4.4 Stationary and non-stationary time series

The time series whose properties are not dependent on time at which it is observed is called stationary time series. On the other hand, a non-stationary series is one whose properties change over time.

4.5 Augmented Dickey-Fuller test (ADF)

ADF is performed to see the existence of unit roots and find out the order of integration of the variables.

4.6 Autoregressive Integrated Moving Average (ARIMA) process

ARIMA is a model of statistical analysis that utilizes time series data to forecast future conditions. ARIMA is a model that combines the autoregressive model AR(p) with the moving average model MA(q). ARIMA is formed through the lag selection of the autocorrelation function and partial autocorrelation function.

5 Results and discussion

5.1 Univariate analysis

Table 2 shows the maximum value, minimum value, mean, median, standard error of the mean, and standard deviation of study variables during the period 1991–2019. The highest life expectancy in Bangladesh was recorded in 2019 and it was 72.59 years. The maximum value of the factors, GNI, and the employment rate was also discovered in 2019, and these were $1930 and 21.32%, respectively. From the earlier data records, it is clear that gross national income, employment rate, and life expectancy all increased with one another. On the contrary, the highest values for population growth rate (2.33%) and age dependency ratio (81.52%) were recorded in 1991. In 2019, the population growth rate and age dependency ratio were both at their lowest points, while the value of life expectancy was the highest. That means a high life expectancy was associated with the lowest population growth rate and the lowest age dependency ratio. The value of the unemployment rate fluctuated with time, whereas the highest rate of unemployment was 5.00% (2009).

Table 2. Descriptive statistics for predictor and response variables.

	Mean	Median	Max Value	Min Value	Standard Deviation	Standard Error of Mean	1st quartile	3rd quartile
Unemployment rate	3.62	3.91	5.00	2.20	0.83	0.15	2.87	4.30
Employment rate	14.86	13.79	21.32	9.78	3.94	0.73	11.21	18.56
GNI	733	550	1930	320	454	84	420	970
Population growth rate	1.58	1.48	2.33	1.03	0.47	0.09	1.14	2.08
Age dependency	63.88	63.05	81.52	47.92	10.05	1.87	55.83	71.78
Life expectancy	67.10	67.77	72.59	58.89	4.13	0.77	64.25	70.61

5.2 Bivariate analysis

Pearson correlation coefficient is used to examine the strength and direction. It is also used to examine the linear relationship between variables.

From Table 3, it is observed that the dependent variable (life expectancy) is significantly negatively related to the population growth rate, unemployment rate, and age dependency ratio. It is significantly positively related to gross national income and employment rate. Among all major indicators of economic well-being, GNI is significantly positive in relation to employment rate and life expectancy and significantly negative in relation to age dependency ratio. The employment rate is significantly positively associated with gross national income and life expectancy. That means if the employment rate increases, then income and life expectancy will also increase. It is significant that the population growth rate is positively related to the unemployment rate, but it is negatively related to the employment rate and life expectancy. A significant negative correlation between the unemployment rate is found with the employment rate and life expectancy, and a significant positive association is found with the population growth rate. The age dependency ratio has a significant negative correlation with GNI, employment rate, and life expectancy. The age dependency ratio is found to have a positive but non-significant relationship with the population growth rate and unemployment rate. From the Pearson Correlation Coefficient for the total association, we see that all factors had a significant effect on life expectancy.

Table 3. Pearson correlation coefficient between variables.

	x 1	x 2	x 3	x 4	x 5	x 6
Gross national income (x1)	1	-.165	.052**	-.242	-.274**	.436**
Unemployment rate (x2)		1	-.398*	.857**	.037	-.411*
Employment rate (x3)			1	-.386*	-.078*	.558**
Population growth rate (x4)				1	.017	-.443**
Age dependency ratio (x5)					1	-.393*
Life expectancy (x6)						1

p*< 0.05 and p**< 0.01

5.3 Path coefficient analysis

Path coefficient analysis is used here to disintegrate bivariate analysis into total effect, non-causal effect, direct effect, and indirect effect. For Path analysis, we divide our variables into two groups,

1. Exogenous group (x₁ = Gross National Income, x₂ = Unemployment rate, x₃ = Employment rate, x₄ = Population growth rate)

2. Endogenous group (x₅ = Age dependency ratio).

Here x₆ = Life expectancy (LE) is our dependent variable.

Linear equations for the path model are as follows.

$$x_5=Q_{51}{x}_1+Q_{52}{x}_2+Q_{53}{x}_3+Q_{54}{x}_4+Q_{5u}{R}_u$$ (1)

$$x_6=Q_{61}{x}_1+Q_{62}{x}_2+Q_{63}{x}_3+Q_{64}{x}_4+Q_{65}{x}_5+Q_{6v}{R}_v$$ (2)

Here, Path coefficients are denoted by, Q_ij (i = 5,6 and j = 1, 2, 3, 4, 5). Q_5uR_u and Q6_vR_v are disturbances. These disturbances are mutually independent of each other and their predictors. The residual can also be calculated from the regression equation with the help of $\sqrt{1-R^2}$.

Path coefficient analysis of this study explores non-causal effects and total effects by counting direct and indirect effects. Path coefficients (specified in regression Eqs 1 and 2) are the direct effect of factors and are calculated by the least square regression process.

The following path models are derived from Fig 2,

$$x_5=-0.404x_1+0.283x_2-0.205x_3+0.326x_4,$$

$$R_{5.1234}^2=0.43$$ (3)

$$x_6=0.245x_1-0.013x_2+0.386x_3-0.073x_4-0.071x_5,$$

$$R_{6.12345}^2=0.57$$ (4)

Fig 2. Path diagram of factors affecting LE. p* < 0.05 and p**< 0.01.

From path coefficient analysis we obtained direct effects, indirect effects, total effects, non-causal effects and the effects of these factors are given in the following table.

From Table 4, the direct effects of GNI (0.245), employment rate (0.386) and age dependency ratio (-0.071) are significant on life expectancy (Model 4). On the other hand, only the employment rate (-0.205) has a direct significant effect on age dependency ratio (Model 3). The indirect effects of GNI (0.0287) and employment rate (0.0150) are favorable on LE through age dependency ratio, although the effect of age dependency ratio (-0.071) on life expectancy is adverse. The overall effect of employment rate (0.4013) and GNI (0.27371) is favorable on LE, but age dependency ratio (-0.017) has an adverse effect on LE. Among all the determinant predictors, path analysis showed that GNI, employment rate, and age dependency ratio have a significant role in LE. Now we have forecasted all three significant factors for the Sustainable Development Goals (SDG).

Table 4. Effects of independent variables on LE.

Endogenous variable	Exogenous variable	Total effect	Non-causal effect	Indirect effect	Direct effect	Total association
x 5	x 1	-0.404	-0.13	-	-0.404	-.274**
	x 2	0.268	0.231	-	0.268	.037
	x 3	-0.205	-0.127	-	-0.205*	-.078*
	x 4	0.326	0.309	-	0.326	.017
x 6	x 1	0.27371	-0.16229	0.0287	0.245*	.436**
	x 2	-0.0331	0.3779	-0.0201	-0.013	-.411*
	x 3	0.4013	-0.1567	0.0150	0.386*	.558**
	x 4	-0.0961	0.3469	-0.023146	-0.073	-.443**
	x 5	-0.071	0.322	-	0.071*	-.393*

p*< 0.05 and p**< 0.01.

Calculation formula for, Total effect = Indirect effect + Direct effect.

Non-causal effect = Total effect–Total association.

5.4 Univariate time series analysis

At first, we see the comparison graph of significant factors between Bangladesh and other highly developed countries (United States, Canada, Australia, United Kingdom, Norway & Denmark).

From Fig 3, all countries’ employment rates, life expectancy, and age dependency ratios are almost in the same position in 2019, except for GNI. It can be said that if Bangladesh has to increase life expectancy, then GNI should increase faster than other significant factors. If it is possible to do so quickly, Bangladesh can easily increase its SDG ranking.

Fig 3. Comparison graphs of factors between Bangladesh & other highly developed nations.

5.4.1 Checking stationarity of Gross National Income (GNI)

We have to figure out whether the GNI data is non-stationary or stationary.

Fig 4 shows the slightly downward and highly upward pattern of GNI data until 2019 in Bangladesh. This indicates that the data is not stable. The probability value of the ADF test for GNI is 0.99, which is greater than 0.05. Here, the null hypothesis is considered true, or it has a unit root. In other words, the data is non-stationary. In order to make it stationary, we need to take difference in the data.

Fig 4. Time series plot of GNI.

Fig 5 shows the fourth difference time series plot. After taking the fourth difference, we get the probability value of the ADF test is 0.01, which is below 0.05. Therefore, we can accept the alternative hypothesis and say that the data is stationary.

Fig 5. Fourth difference time series plot of GNI.

5.4.2 Selection of appropriate model

The unit root test reveals significant values after taking the fourth difference. So we get the difference value d = 4. Now to choose the best ARIMA model for the data, we need to select lag value through the plot of autocorrelation function (ACF) and partial autocorrelation function (PACF). From the PACF plot, we select lag for the autoregressive model (p), and from the ACF we select lag for the moving average model (q). The PACF and ACF plots after taking the fourth difference are given below.

It can be seen from the PACF (Fig 6) plot that the first and second spikes cross the blue-dotted significant belt. Here, the p term may be the first or second lag. From the ACF plot (Fig 6) of GNI data, lags at order first, second, third, and ninth cross the significant belt, i.e., there are four significant spikes that have crossed the confidence belt.

Fig 6. PACF and ACF plot of stationary GNI.

5.4.3 Checking AIC for different ordered model

Based on the PACF and ACF plots, we select the best-fitted ARIMA model. The model that gives the minimum AIC value will be considered the best ARIMA model.

From above Table 5, it is clear that ARIMA (1,4,2) is the best-fitted model for forecasting GNI data because it gives the minimum AIC value.

Table 5. AIC values of different ordered models for forecasting GNI.

ARIMA (p,d,q) models	Akaike Information Criterion (AIC)
ARIMA (1,4,1)	258.55
ARIMA (1,4,2)	254.18
ARIMA (1,4,3)	255.01
ARIMA (1,4,9)	259.56
ARIMA (2,4,1)	259.33
…	…
ARIMA (2,4,3)	257.97
ARIMA (2,4,4)	259.96

5.4.4 Forecasting future GNI for Bangladesh

We will forecast GNI data till 2030 for the third goal of sustainable development purpose.

Table 6 shows the future predicted values of GNI in Bangladesh. It will be increasing and the highest value will happen in 2030.

Table 6. Forecast value for GNI using ARIMA (1,4,2).

Point	Forecast	Lo 80	Hi 80	Lo 95	Hi 95
2020	2152.891	2118.4	2187.383	2100.141	2205.641
2021	2389.443	2319.276	2459.61	2282.132	2496.754
2022	2651.866	2533.496	2770.237	2470.835	2832.898
2023	2938.309	2760.256	3116.362	2666	3210.618
2024	3251.691	3000.892	3502.491	2868.127	3635.256
2025	3593.314	3255.44	3931.187	3076.581	4110.047
2026	3965.026	3524.09	4405.962	3290.673	4639.379
2027	4368.492	3806.732	4930.253	3509.354	5227.631
2028	4805.44	4103.153	5507.727	3731.384	5879.495
2029	5277.573	4412.995	6142.152	3955.314	6599.832
2030	5786.606	4735.789	6837.423	4179.52	7393.692

The future state of GNI from Table 6 is shown in Fig 7. The blue line indicates the future state of GNI. It will increase in the future. Increasing GNI is good for life expectancy (LE) because they are positively correlated. Path analysis, as well as bivariate analysis, showed that GNI was significantly positively correlated with LE in Bangladesh. From the graph, it is estimated that the LE will also increase in the future. This helps Bangladesh to achieve sustainable development goals. Here, the deep blue shaded region indicates the 80% confidence interval and the light blue shaded region indicates the 95% confidence interval.

Fig 7. Future condition of GNI in Bangladesh.

By adopting the same process, the best-fitted model for employment rate has been selected and it is ARIMA (1,2,1). Based on ARIMA (1,2,1), the estimated future value of the employment rate until 2030 is given in the following table.

Table 7 shows the future predicted values for the employment rate in Bangladesh.

Table 7. Forecast value for employment rate using ARIMA (1,2,1).

Point	Forecast	Lo 80	Hi 80	Lo 95	Hi 95
2020	21.84801	21.54733	22.14869	21.38815	22.30786
2021	22.3353	21.68339	22.9872	21.33829	23.3323
2022	22.85712	21.76548	23.94877	21.18759	24.52665
2023	23.34966	21.75945	24.93986	20.91765	25.78167
2024	23.86703	21.71432	26.01975	20.57474	27.15932
2025	24.36334	21.59922	27.12745	20.13599	28.59069
2026	24.87752	21.44999	28.30504	19.63557	30.11946
2027	25.37654	21.24266	29.51041	19.05432	31.69875
2028	25.88841	21.00346	30.77336	18.41752	33.3593
2029	26.38938	20.71453	32.06423	17.71045	35.06832
2030	26.8996	20.39511	33.4041	16.95183	36.84737

Table 7 values are represented in Fig 8. The blue line gives the future rate of employment for Bangladesh for the period 2020 to 2030. The graph represents an increasing pattern of employment rates in Bangladesh. Both path analysis and bivariate analysis revealed that the employment rate is significantly positively correlated with LE in Bangladesh. That’s why increasing employment rates is good for achieving the third goal of sustainable development.

Fig 8. Future condition of employment rate in Bangladesh.

Again, for the age dependency ratio, the best-fitted model is also ARIMA (1,2,1). From ARIMA (1,2,1) we get the following estimated future value.

Table 8 shows the future value of the age dependency ratio. It will decrease in the future.

Table 8. Future value for age dependency ratio using ARIMA(1,2,1).

Point	Forecast	Lo 80	Hi 80	Lo 95	Hi 95
2020	46.86035	46.72126	46.99945	46.64762	47.07308
2021	45.79149	45.50643	46.07654	45.35553	46.22744
2022	44.71637	44.27042	45.16231	44.03436	45.39837
2023	43.63793	43.01928	44.25658	42.69178	44.58407
2024	42.55773	41.75579	43.35966	41.33128	43.78418
2025	41.4766	40.48136	42.47183	39.95451	42.99868
2026	40.39497	39.19672	41.59321	38.56241	42.22753
2027	39.31307	37.90235	40.7238	37.15555	41.4706
2028	38.23104	36.59858	39.86351	35.7344	40.72769
2029	37.14894	35.2857	39.01218	34.29936	39.99852
2030	36.06679	33.96397	38.16962	32.8508	39.28279

The blue line in Fig 9 indicates the future age dependency ratio status. It will continue to fall until 2030, which is good for LE. This means that the percentage of working-age people will be increasing day by day. Decreasing the age dependency ratio or increasing the percentage of working-aged people is good for LE, which will help Bangladesh to achieve sustainable development goals very quickly.

Fig 9. Future condition of age dependency ratio in Bangladesh.

6 Conclusion

We have analyzed how factors affect life expectancy and determined predictors that could increase our life expectancy (LE). According to the analysis, GNI, employment rate, and age dependency ratio are the top determinants of LE, even though all factors have a role to play. The growth of Gross National Income and employment facilities can contribute to decreasing the age dependency ratio and increasing the LE. Based on previous data records, it has been observed that GNI, employment rate, and LE are on the rise. We checked the future value of GNI, employment rate, and age dependency ratio to see whether LE will increase or decrease. In conclusion, based on the time series analysis, LE is likely to increase in the upcoming days since GNI and employment rates will increase in the future while the age dependency ratio will decrease, which will help Bangladesh to achieve SDG 3^rd goal very quickly.

7 Recommendation

The following recommendations are made to take necessary to enhance life expectancy:

• Employment rate should be increased for LE. Government should target to enhance LE by increasing job facilities in Bangladesh.

• People of this country should be self-dependent. It helps the country to increase national income and reduce the sage dependency ratio. Increasing GNI and reducing the age dependency ratio is essential to enhance average LE.

• Government should take necessary steps to control the unemployment rate, poverty and population growth to increase LE in our country.

Data Availability

Supplementary data associated with this article can be found at https://data.worldbank.org/country/BD.

Funding Statement

The authors received no specific funding for this work.