Theory, model and data
The theoretical rationale of this study lies on Becker’s human capital model Becker [50], where he emphasized that education, along with health is an important impetus for human development (Becker [50], Teixeira [51]. In this line, Grossman [52] developed the health care model where he considered health as a durable capital stock to generate healthy time which depreciates with the age but can be improved through investment (Grossman [52], Galama and Kapteyn [53]). Thus the investment on health status includes different settings as utilizing the fruit of globalization, energy consumption, ICT, financial development, and level of education.
The empirical justification for choosing the variables lies mainly on previous research works. Life expectancy at birth is a well-accepted determinant of measuring health status, and is taken following the works of Shaw et al. [54], Rahman et al. [22], Rahman and Alam [35], and Shahbaz et al. [9]. Globalization is in line with the literature of Shahbaz et al. [9], Guzel et al. [10], and Martín Cervantes et al. [11]; renewable energy consumption is adopted following the studies of Majeed et al. [12], and Rodriguez-Alvarez [13]; non-renewable energy is used following the research of Ibrahim et al. (2021), and Ibrahim and Ajide (2021); ICT is in line of the works of Majeed and Khan [15], Lee and Kim [16], and Aksentijevic [17]; education rate is considered following the studies of Ray and Linden [18], and Mondal and Shitan [19]; financial development is in accordance the works of Alam et al. [20], Shahbaz et al. [9], and Wang et al. [21]; and economic growth rate is in line the studies of Shahbaz et al. [9], and Wang et al. [21].
For empirical estimation this study adopts the below model following Rahman et al. [48], Rahman and Alam [47], Rahman, (2017); and Shahbaz et al. [55]:
$${\mathrm{LEX}}_{\mathrm{t}}=\mathrm{f}\left({\mathrm{GLOB}}_{\mathrm{t}}, {\mathrm{RE}}_{\mathrm{t}}, {\mathrm{NRE}}_{\mathrm{t}}, {\mathrm{ICT}}_{\mathrm{t}}, {\mathrm{GDPC}}_{\mathrm{t}}, {\mathrm{EDU}}_{\mathrm{t}},{\mathrm{FD}}_{\mathrm{t}}\right)$$
(1)
In Eq. (1), LEX is stands for life expectancy at birth and also indicates the proxy for health status; GLOB is globalization as defined by the economic, social and political extent of globalization; RE is renewable energy use determined in exajoules (input-equivalent); NRE is non-renewable energy use, which is the total of oil, gas, and coal use expressed in terms of exajoules; ICT specifies information and communication technology and used as a proxy for individuals using the internet (% of population); GDPC is a per capita gross domestic product; EDU expresses education rate used as a proxy for school enrollment, primary (% gross); and FD indicates financial development, used proxy for stocks traded, total value (% of GDP).
For making comparison through direct elasticity and reducing heteroskedasticity among the variables, the Eq. (1) is transformed into natural logarithmic form (Rahman et al. [48], Rahman and Alam [47], Rahman and Alam [35]), as under:
$${\mathrm{lnLEX}}_{\mathrm{t}}={\mathrm{\alpha }+{\upbeta }_{1}{\mathrm{lnGLOB}}_{\mathrm{t}}+{\upbeta }_{2}\mathrm{ ln}{\mathrm{RE}}_{\mathrm{t}}+{\upbeta }_{3}{\mathrm{lnNRE}}_{\mathrm{t}}+ {\upbeta }_{4}{\mathrm{lnICT}}_{\mathrm{t}}+{\upbeta }_{5}\mathrm{lnGDPC}}_{\mathrm{t}}+{\upbeta }_{6}{\mathrm{lnEDU}}_{\mathrm{t}}+{\upbeta }_{7}{\mathrm{lnFD}}_{\mathrm{t}}+{\Upsilon }_{\mathrm{t}}$$
(2)
where, along with variables, the β1, β2, β3, β4, and β5 express the long-run elasticities of respective variables; \(\Upsilon\) indicates error term, and t shows time.
For empirical estimation, we have used the time series data over the period of 1990–2018. All the data except globalization, renewable and non-renewable energy consumption are collected from the World Development Indicators (WDI [5]) of World Bank database. The globalization data is obtained from the KOF Globalization Index [6] and renewable and non-renewable energy use data are obtained from BP Statistical Review [7].
Test for unit root
The presence of unit root may generate spurious or counterfeit statistical inference and display unpredictable systematic patterns of the time series models. Moreover, the unit root or non-stationarity of the regression model demonstrates the standard assumptions for asymptotic analysis to be invalid. Thus it is imperative for the model to be stationary or absence of unit root which be checked through robust testing method. To diagnose whether there prevails unit root or the series is stationary, this study employs the Dickey-Fuller generalized least square (DF-GLS) unit root testing approach. This is a widely accepted technique as developed by Elliott, Rothenberg and Stock (ERS) by modifying the Dickey-Fuller (DF) test (Elliott et al. [56]. The unit root test provides three types of integrations namely, integration at level I(0), integration at first difference I(1), and integration at second difference I(2). According to the methodologies of Pesaran and Shin [57] and Pesaran et al. [58] the ARDL bounds test can be applied in case of all the variables that are integrated at I(0), I(1), or mixed, but never at I(2) (Shahbaz et al. [55], Rahman and Mamun [59], Rahman and Alam [47], Rahman and Kashem [60]). In this regard, the assumed null hypothesis (H0) is, there is a unit root, and the alternative one is no unit root. If the test rejects the null hypothesis, then assures that there is no unit root in the series or they are stationary.
Test for cointegration
After finding the integration level of the studied variables, the examination of cointegration among those variables is important. To obtain proficient outcomes, this study adopts a powerful econometric tool, named, Autoregressive Distributed Lag Model (ARDL) bounds testing method following the methodology of Pesaran and Shin [57] and Pesaran et al. [58]. This technique is efficient, effective, and robust in determining the cointegration, and assessing the long-run and short-run relationship and dynamics among the variables (Pesaran et al. [58]. Moreover this approach has numerous benefits over other traditional approaches, as: it is consistent in small sample case; it is a single equation model, it deals with integration level of I(0), I(1), or both; it has both short and long run dynamics; and the confirmation of fitness through different diagnostic tests. This study uses the following ARDL bounds test model (Rahman and Alam [47], Rahman and Kashem [60], Rahman and Mamun [59], Zhang et al. [61], Adebayo et al. [62], He et al. [63], and Shahbaz et al. [55]), as:
$${\mathrm{\Delta lnLEX}}_{\mathrm{t}}=\mathrm{\alpha }+\sum_{\mathrm{i}=1}^{\mathrm{k}}{\upbeta }_{\mathrm{i}}{\mathrm{\Delta lnLEX}}_{\mathrm{t}-\mathrm{i}}+ \sum_{\mathrm{i}=0}^{\mathrm{l}}{\upgamma }_{\mathrm{i}}{\mathrm{\Delta lnGLOB}}_{\mathrm{t}-\mathrm{i}} +\sum_{\mathrm{i}=0}^{\mathrm{m}}{\uptheta }_{\mathrm{i}}\mathrm{\Delta ln}{\mathrm{RE}}_{\mathrm{t}-\mathrm{i}}+\sum_{\mathrm{i}=0}^{\mathrm{n}}{\updelta }_{\mathrm{i}}{\mathrm{\Delta lnNRE}}_{\mathrm{t}-\mathrm{i}}+\sum_{\mathrm{i}=0}^{\mathrm{p}}{\Omega }_{\mathrm{i}}{\mathrm{\Delta lnICT}}_{\mathrm{t}-\mathrm{i}}+ \sum_{\mathrm{i}=0}^{\mathrm{q}}{{\uplambda }_{\mathrm{i}}\mathrm{\Delta lnGDPC}}_{\mathrm{t}-\mathrm{i}}+ \sum_{\mathrm{i}=0}^{\mathrm{r}}{{\uppi }_{\mathrm{i}}\mathrm{\Delta lnEDU}}_{\mathrm{t}-\mathrm{i}}+ \sum_{\mathrm{i}=0}^{\mathrm{s}}{{\uprho }_{\mathrm{i}}\mathrm{\Delta lnFD}}_{\mathrm{t}-\mathrm{i}}+ {\mathrm{\varnothing }}_{0}{\mathrm{lnLEX}}_{\mathrm{t}-1}+{\mathrm{\varnothing }}_{1}{\mathrm{lnGLOB}}_{\mathrm{t}-1}+ {\mathrm{\varnothing }}_{2}{\mathrm{lnRE}}_{\mathrm{t}-1}+{\mathrm{\varnothing }}_{3}{\mathrm{lnNRE}}_{\mathrm{t}-1}+{\mathrm{\varnothing }}_{4}{\mathrm{lnICT}}_{\mathrm{t}-1}+{\mathrm{\varnothing }}_{5}{\mathrm{lnGDPC}}_{\mathrm{t}-1}+{\mathrm{\varnothing }}_{6}{\mathrm{lnEDU}}_{\mathrm{t}-1}+{\mathrm{\varnothing }}_{7}{\mathrm{lnFD}}_{\mathrm{t}-1}+{\Upsilon }_{\mathrm{t}1}$$
(3)
In the above Eq. (3), the lnLEX, lnGLOB, lnRE, lnNRE, lnICT, lnGDPC, lnEDU, and lnFD are used as the studied variables. \({\Upsilon }_{\mathrm{t}1}\) is disturbance term which has assumed no serial correlations, heteroskedasticity, and is normally distributed. Equation (3) also specifies the conditional error correction model (ECM). The error correction dynamics is expressed by the summations ∑ signs, and the long-run affiliation is denoted by \(\mathrm{\varnothing }\) s (Peseraran et al., 2001). The lag lengths are chosen based on the Schwarz information criterion (SIC), where the maximum lags are indicated by k, l, m, n, p, q, r, and s. The cointegration under ARDL bounds test assumes the null hypothesis (H0): no cointegration, and the alternative hypothesis (H1): cointegration. The rejection of null hypothesis guarantees the cointegration. For this the asymptotic distribution of F- statistic is used following the methodology of Pesaran et al. (2001) due to its superiority over traditional F-statistic. This has two bounds as lower bound I(0), and upper bound I(1). These bounds exert three cases: if the calculated F-statistic value falls below lower bound, the relationship becomes inconclusive; if it falls between the two, shows no cointegration; finally, if it crosses the upper boundary, confirms cointegration among the studied variables (Rahman and Alam [47], Rahman and Kashem [60]). Beyond F-statistic, the cointegration also be crossed-matched through t-statistic (Rahman and Alam [47], Rahman and Kashem [60], Giles [64]).
From the error correction model (ECM) the short-run parameters can be derived as:
$${\mathrm{\Delta lnLEX}}_{\mathrm{t}}=\mathrm{\alpha }+\sum\nolimits_{\mathrm{i}=1}^{\mathrm{k}}{\upbeta }_{\mathrm{i}}{\mathrm{\Delta lnLEX}}_{\mathrm{t}-\mathrm{i}}+ \sum\nolimits_{\mathrm{i}=0}^{\mathrm{l}}{\upgamma }_{\mathrm{i}}{\mathrm{\Delta lnGLOB}}_{\mathrm{t}-\mathrm{i}} +\sum\nolimits_{\mathrm{i}=0}^{\mathrm{m}}{\uptheta }_{\mathrm{i}}\mathrm{\Delta ln}{\mathrm{RE}}_{\mathrm{t}-\mathrm{i}}+\sum\nolimits_{\mathrm{i}=0}^{\mathrm{n}}{\updelta }_{\mathrm{i}}{\mathrm{\Delta lnNRE}}_{\mathrm{t}-\mathrm{i}}+\sum\nolimits_{\mathrm{i}=0}^{\mathrm{p}}{\Omega }_{\mathrm{i}}{\mathrm{\Delta lnICT}}_{\mathrm{t}-\mathrm{i}}+ \sum\nolimits_{\mathrm{i}=0}^{\mathrm{q}}{{\uplambda }_{\mathrm{i}}\mathrm{\Delta lnGDPC}}_{\mathrm{t}-\mathrm{i}}+ \sum\nolimits_{\mathrm{i}=0}^{\mathrm{r}}{{\uppi }_{\mathrm{i}}\mathrm{\Delta lnEDU}}_{\mathrm{t}-\mathrm{i}}+ \sum\nolimits_{\mathrm{i}=0}^{\mathrm{s}}{{\uprho }_{\mathrm{i}}\mathrm{\Delta lnFD}}_{\mathrm{t}-\mathrm{i}}+\uppsi {\mathrm{ECT}}_{\mathrm{t}-1} +{\Upsilon }_{\mathrm{t}1}$$
(4)
The short-run association and causality is found in Eq. (4). The error correction term (ECT) can also be obtained; negative sign of the coefficient \(\uppsi\) indicates the speed of short-run adjustment towards long-run equilibrium (Rahman and Alam [47], Rahman and Kashem [60], Rahman and Mamun [59], Shahbaz et al. [55]).
Diagnostic test
The diagnostic test is essential to declare the better and well-specified model, particularly the ARDL bounds test approach. If the model suffers from serial correlation, and heteroskedascity, there may produce inappropriate outcomes to take proper policy initiatives. Thus the checking of serial correlation, heteroskedascity, and normality is imperative to derive effective decisions. To accomplish this this study employs Breusch-Godfrey (BG) Lagrange Multiplier (LM) test, Breusch-Pagan-Godfrey (BPG) test, and Jarque–Bera (JB) test to diagnose serial correlation, heteroskedasticity, and normality of the model. Moreover, the stability of the model is also another important issue for better prediction of the outcomes. For this purpose, the cumulative sum (CUSUM) and cumulative sum of squares (CUSUM squares) tests are used following the methodology of Pesaran and Pesaran [65].
Granger causality test
The cointegration alone may not produce enough prediction between the causal associations of the studied variables (Rahman and Kashem [60]). To detect the causal relationship between the variables this study adopts pairwise Granger [66] causality test. This causality demonstrates three important decisions as, bidirectional causality, unidirectional causality, and no causality.
The following Granger [66] causality model is used in this study to predict the causal affiliation (Rahman and Alam [47], Rahman and Alam [35]; Rahman and Kashem [60]) as:
$${\mathrm{Y}}_{\mathrm{t}}= {\mathrm{\varphi }}_{0}+{\upeta }_{1}{\mathrm{Y}}_{\mathrm{t}-1}+\cdots \ldots+ {\upeta }_{\mathrm{k}}{\mathrm{Y}}_{\mathrm{t}-\mathrm{k}}+ {\upsigma }_{1}{\mathrm{X}}_{\mathrm{t}-1}+\cdots \ldots {\upsigma }_{\mathrm{k}}{\mathrm{X}}_{\mathrm{t}-\mathrm{k}}+{\upupsilon }_{\mathrm{t}}$$
(5)
$${\mathrm{X}}_{\mathrm{t}}= {\upomega }_{0}+{\mathrm{\varrho }}_{1}{\mathrm{X}}_{\mathrm{t}-1}+\cdots \ldots + {\mathrm{\varrho }}_{\mathrm{k}}{\mathrm{X}}_{\mathrm{t}-\mathrm{l}}+ {\uptau }_{1}{\mathrm{Y}}_{\mathrm{t}-1}+\cdots \ldots {\uptau }_{\mathrm{k}}{\mathrm{Y}}_{\mathrm{t}-\mathrm{l}}+{\upphi }_{\mathrm{t}}$$
(6)
Equations (5) and (6) are expressing Granger causality equations. The null hypothesis is Y does not Granger causes X, and the alternative hypothesis is Y Granger causes X, indicating H0: \({\upsigma }_{1}\)= \({\upsigma }_{2}\) = ….= \({\upsigma }_{\mathrm{k}}\) = 0 and H1: Not H0. Alternatively, this also be as H0: \({\uptau }_{1}\) = \({\uptau }_{2}\) = ….= \({\uptau }_{\mathrm{k}}\) = 0 and H1: Not H0. The decision rule is to reject null hypothesis to assure causality.