Theoretical or empirical justification for the choice of variables

The theoretical rationale for conducting this study is based on various well-known and recognized theories and models, for example Becker’s theory of human capital [68], Grossman’s model of healthcare [69], and Romer’s neoclassical model [70].

The logic behind the choice of our studied variables is based on the availability of data, taken from contemporary and previous literary works. We considered the variables relating to life expectancy at birth, following Rahman et al. [9], Shahbaz et al. [36], Rodrigues and Plotkine [61], among others; mortality rate according to Rahman et al. [9], Hurt et al. [18], Nicolas et al. [23], among others; access to electricity according to Wang [6], Chen et al. [7], Bridge et al. [13], among others; female enrollment rate according to [8], Hurt et al. [18], Keats [19]; public health expenditure according to Rahman et al. [9], Novignon and Lawanson [10], Nicolas et al. [23], among others; vaccination rate after Akinkugbe and Mohanoe [22], Owais et al. [34], Rodrigues and Plotkine [61], among others; urbanization rate in line with Rahman and Alam [8], Wang [39], Amouzou et al. [40], among others; and economic growth corresponding to research undertaken by Rahman and Alam [8], Rahman et al. [9], Wang et al. [25], among others.

Variables and data

For this study, women’s health outcomes are considered to be dependent variables; for this, the life expectancy of women (FLE) at birth and the adult female mortality rate (FAM) per 1,000 adult women (aged 15 to 60) are used as proxy variables. At the same time, access to electricity (AEL), the rate of education of women, the rate of vaccination (IMM), the rate of urbanization (URB), the gross domestic product (GDP) and public expenditure of health (PUH) are taken as independent variables. Access to electricity is the percentage of the population with access to electricity; the female education rate is the enrollment rate of girls at secondary level as a percentage of gross; vaccination rate is the measles vaccination rate expressed as a percentage of children aged 12-23 months; GDP is used to see the reflection of economic growth; urbanization is defined as the urban population referring to people living in urban areas as a percentage of the total population; and public health expenditure is considered national general health expenditure per capita at the current amount of US $ funded by the government.

All data is collected from the World Development Indicator [5] of the World Bank during the years 2002-2018. Some missing data on girls’ secondary school enrollment are linearly interpolated via E-views-11. To perform the estimation, we used two well-known statistical packages, STATA-16 and E-views1.

The models used for the estimation of this study are presented below:

To obtain the direct elasticity of each variable from the coefficients, we transformed all the variables in the equations. (1) and (2) in natural logarithmic form. So the equations. (1) and (2) can be written:

where, is the intercept, and β₁,₂,₃,₄,₅,₆ are coefficients and_t is the error term.

Econometric approach

For the empirical estimation, we used a number of well-known econometric approaches. We performed the mentioned tests as: a cross-dependence test to identify the shock effect; the modified Wald test for group heteroskedasticity and Wooldridge’s test for autocorrelation in panel data to observe heteroskedasticity and autocorrelation, respectively. We used the Panel Corrected Standard Error Model (PCSE) and the Generalized Feasible Squares (FGLS) model to obtain results that will show the robust relationships between the variables; and pairwise Granger causality to determine the direction of causation.

Due to the similarity of geographic, economic, historical, ethnic and political shocks, the transversal dependence of the variables can be observed. In this study, we used four well-known cross-dependence tests: Breusch and Pagan [46] BP LM, Pesaran [47] LM to scale, Pesaran [47] CD, and Baltagi et al. [48] LM to scale with bias correction.

The Breusch and the Pagan [46] The model for examining the cross-sectional dependence between panel data is as follows:

Pesaran [47] developed the LM statistics to address the healing limitations of the above model such as:

If the size of the cross section is larger than the time dimension, Pesaran [47] recommends the test statistic below:

Baltagi et al. [48] developed the simple asymptotic bias correction model, which is:

or ( widehat {{p} _ {ij}} ) specifies a correlation between errors. In this test, the null hypothesis is H₀: denotes no transverse dependence and the alternative hypothesis is H₁: prevalence of cross-dependency.

To make an efficient and robust estimation of the fixed effects model, the model must be homoscedastic without autocorrelation. If the model suffers from heteroskedasticity, the estimate may be consistent but inefficient [49]. To detect heteroskedasticity, the modified Wald test for group heteroskedasticity is performed [50, 71]. Likewise, the presence of autocorrelation is identified using Wooldridge [51] automatic correlation test for panel data [52].

To overcome the complications of estimating panel data due to cross-sectional dependence, heteroskedasticity, and autocorrelation, panel corrected standard error models (PCSEs) and generalized feasible least squares models ( FGLS) are considered the best and most effective. Thus, the difficulty created due to the nature of the data panel, the PCSE, is the path finder [53]. Alternatively, the FGLS model is also able to overcome the autocorrelation, heteroskedasticity and cross-sectional dependence of the estimate. [54]. PCSE and FGLS methods are effective and efficient in dealing with heteroskedasticity, autocorrelation and outliers [55,56,57, 73,74,75,76].

To observe the causality between the variables studied, Granger in pairs [58] stacked test causality (common coefficients) is used, where three outcomes are revealed as unidirectional causation, bidirectional causation, and no causation. The pairwise Granger causal equations for panel data can be written in the form [59, 60].

where, t indicates the temporal dimension of the panel, and i shows the transverse dimension.

The stacked causality test considers that all coefficients are the same in all cross sections as common coefficients [59, 60]. It can be described as:

Therefore, the decision rule is H0: Y is not Granger cause X, and H1: Y Granger cause X.