Economic factors affecting life expectancy in G7 countries: a panel data perspective

Introduction: This study aims to examine the relationships between life expectancy at birth (years) and gross domestic product per capita, gross national income per capita, and trade openness via panel data analysis. The focus on G7 countries, recognized as the world’s most developed and leading nations, allows for comparative insights into how macroeconomic factors influence public health outcomes. Understanding these relationships is essential for designing effective economic and health policies.

Methods: For this purpose, the G7 countries were analyzed using the panel data method for the period 1990–2023. A fixed effects model was initially applied; however, deviations from the assumptions of heteroskedasticity, autocorrelation, and interunit correlation were observed. Therefore, a robust panel data analysis using the Driscoll–Kraay robust standard estimator was used to ensure reliable results.

Results: Empirical findings show that per capita gross domestic product and trade openness have positive effects on life expectancy at birth, whereas per capita gross national income exhibits a negative effect. While the effects of per capita gross domestic product and trade openness on life expectancy are statistically significant, the effect of per capita gross national income is insignificant.

Discussion: These results suggest that higher GDP per capita and greater trade openness contribute positively to life expectancy at birth in G7 countries. The study provides comparative evidence from some of the world’s most developed nations and highlights the importance of macroeconomic policies in shaping public health outcomes.

1 Introduction

Panel data typically refer to data containing time-series observations by several individuals. Consequently, there are at least two dimensions involved in the observations in panel data: a time series dimension denoted by subscript t and a cross-sectional dimension denoted by subscript i. Panel data, however, might have a more intricate hierarchical or clustering structure (1, 2).

Life expectancy (LE) is strongly influenced by child mortality rates, which directly affect the average years a population can expect to live (3). Although child mortality is an important determinant, this study focuses on economic indicators. In G7 nations, high GDP per capita (GDPPC) has been associated with increasing LE (4). LE, often considered one of the key indicators of a nation’s economic progress, reflects the average number of years a person can expect to live (5, 6).

Trade openness (TO) affects human health, the environment, and the economy in a variety of ways. TO increases industrial production, which increases economic citizens’ incomes and wellbeing (7). The increased wealth brought about by trade expansion increases living standards, encourages individuals to pursue healthier lifestyles, and helps them preserve their health, all of which increase LE (8, 9). Theoretically, TO and foreign direct investment affect a nation’s welfare in several ways. First, when TO and foreign direct investment promote economic growth, they may improve living and working conditions. Additionally, they improve LE by facilitating better housing, health care, and nutrition, all of which contribute to a significantly longer lifespan. Thus, TO and foreign direct investments improve a household’s literacy and educational attainment, which in turn improves welfare and LE (10, 11).

GDPPC, a core indicator of economic performance, is used to determine the living standards and economic welfare of countries (12). However, since this value is significant in terms of showing the macroeconomic stability policy of the country rather than measuring the welfare of society, it is not included among the income variables that are effective in determining welfare (13). LE is the average length of life a person will live since birth (14, 15). The socioeconomic development of a region or country is highly effective for LE. A study reported that the average life expectancy worldwide was 66.57 years, with women living approximately 4 years longer than men (16). The same study also emphasized that LE was steadily increasing owing to technology, medicine, and international aid. Considering the LE of the world’s population in recent years, according to United Nations world population estimates, the LE for the year 2022 was 71.7 years, and by gender, it was 69.1 years for men and 74.4 years for women worldwide (17). Thus, it is seen that the LE in the world was 66.57 years in 2014 and 71.7 years in 2022. Although an increase was noted in this period (18), there was a stagnation in the average LE in the USA in the last 3 years due to health-related reasons, and the decline, albeit small, continued. In the literature review, the variables affecting LE were specified by Kossis (16) as Carbon Dioxide Emissions (Per Capita (Carbon), GDP Per Worker), Health Expenditures (Per Capita, Health Ex), Average Years of School, National Healthcare System, Percentage of Adults with HIV, Physicians per 1,000 People, and Countries with an Extended Period of Conflict. In the study conducted by Bilas et al. (14), independent variables for LE at birth were GDP growth rate, GDP at market prices based on constant local currency, population growth rate, level of attained education, education enrolment, and GDPPC. In the study conducted by Shah (19), TO was chosen as the independent variable, and a model study was conducted on its relationship with LE in China. The model also examined the relationships between LE, CO₂, and GDP. Ultimately, various studies have been conducted with the variables assumed to affect LE, as presented in the literature examples below. Generally, studies show that economic development (with the exception of CO2 emissions associated with industrialization) leads to an increase in LE. Considering the significance attributed to economic development, it is important to see the effects of the independent variables GDPPC, gross national income per capita (GNIPC), TO which are the subjects of our study for seven countries (G7) that are considered global economic leaders, on the LE of the people living in these countries, in terms of revealing whether the results commonly found in these studies are valid.

1.1 Literature review

A literature review revealed that there are numerous studies on LE. When the studies conducted in recent years are analysed, studies on the relationships between LE and CO₂ emissions, the GDPPC, TO, the education index, and health expenditures are particularly noteworthy. On the other hand, there are not enough studies on the estimation of LE via a model. As a result of the literature review, some case studies are presented below.

In his 1996 study of 84 countries, Barro (20) used LE as the independent variable, and GDPPC as the dependent variable, and a 10% increase in LE was reported to lead to GDPPC growth between 0.52 and 0.62% (21). In the literature review, studies carried out in recent years were considered, and many studies revealed a positive relationship between LE and GDPPC. However, a study conducted by Acemoglu and Johnson (22) concluded that there was no significant relationship between GDPPC and LE. In the study conducted by Kossis (16) to identify the determinants of the LE variable, World Bank data from 117 countries were used (16, 23). The results of the study revealed that increases in education, wages, and health expenses significantly increased average life expectancies and the greatest impact on LE was the percentage of adults infected with HIV.

The data obtained are also intended to inform policymakers on which factors they should strive to improve. In the study conducted by Bilas et al. (14) on the LE of 28 European Union countries; the GDP growth rate, population growth rate, level of education attained, education enrolment, and GDPPC were taken as the determinants of LE, a panel data analysis approach was applied, and it was determined that GDPPC and level of education explained the differences in LE to a great extent. A similar study was conducted by Shafi and Fatima (4). The relationships between countries’ economic growth, population growth, and LE were examined through a regression model, and it was determined that there was an increase in LE in high-income countries. On the other hand, the increase in the elderly population with increasing LE burden on the economy. As a result, positive and strong correlations were found between the GDPPC and LE in all the G7 countries; when the relationships between the GDPPC and the population growth rate and between the growth rate and LE were analysed, a positive relationship was found between these variables only in the UK, whereas a negative relationship was found in all the other G7 countries. In a 2020 study discussing OECD countries, Aydın conducted (24) a panel data analysis to investigate the impacts of economic factors on LE and reported that LE was lower in underdeveloped countries than in developed countries and that studies on the relationships between economic indicators and LE were still insufficient. He stated that in his research, a bidirectional causal relationship emerged between LE and GDPPC. Another study discussing G7 countries was conducted by Cristea et al. (25), and a renewable energy strategy analysis for BRICS, G7, and EU countries in connection with environmental pollution was performed through panel data analysis using a machine learning framework. As a result of the panel data analysis, the gas consumption parameters for the G7 countries, oil consumption for the EU countries, and greenhouse gas emissions for the BRICS countries, which had the highest fea the future importance among the independent variables, emerged as effective in predicting renewable energy generation capacity. The generalized additive model (GAM) estimations for EU countries showed that renewable energy capacity remained relatively constant if gas consumption increased, whereas an increase in oil consumption caused an increase in renewable energy capacity up to a kick point, which was followed by a decrease. The GAM models for the G7 countries revealed that renewable energy production capacity decreases as oil consumption increases and that renewable energy production capacity tends to trend upwards as gas consumption increases. For BRICS countries, it was determined that an increase in gas consumption led to an increase in renewable energy production capacity over time. In the study conducted by Shah et al. (19). TO significantly contributed to LE, and the government should utilize TO as an economic tool not only to increase domestic production but also to improve the health of the population. Therefore, TO increased LE in China. Therefore, TO increased LE in China. Research has shown that TO affects LE in two ways. The first aspect was that the expansion in trade and industrialization mentioned above led to economic activities, increasing the income level of society and therefore improving LE; the other aspect was that industrial expansion increased CO₂ emissions, reducing LE through its negative impact on human health. Mahalik et al. (26) stated that their study was probably the first to examine the effects of CO₂ emissions on LE in 68 low- and middle-income countries, and the research was conducted in two dimensions. The first of these dimensions was expressed as the CO₂ emission sources, and the second was the economic development level of the countries. The results supported the existence of a negative relationship between CO₂ emissions and LE. The study did not consider whether the sources of CO₂ emissions were based on production or consumption. It was suggested that, in these countries, which were selected by their economies, harmful pollutants from both production and consumption caused a reduction in people’s life expectancies. In the study conducted by Aydın et al. (27), the Environmental Kuznets hypothesis was tested for the G7 countries with variables such as nanotechnology, renewable energy consumption, economic growth, and the ecological footprint through panel data analysis with structural breaks. Nanotechnology is expected to decrease environmental degradation by expanding renewable energy consumption and energy savings. The analysis confirmed that all the variables were integrated in the long run. The EKC hypothesis was found to be valid only for the USA. It was determined that, in the USA, nanotechnological innovations had a diminishing impact on environmental degradation, whereas in Italy and the UK, they had a boosting effect on environmental degradation. Dritsaki M. and Dritsaki C. examined the relationships between health expenditures per capita, CO2 emissions per capita, and gross domestic product (GDP) per capita in G7 countries via panel data analysis (28). First, the cross-sectional dependence and slope homogeneity were examined, and then the second-generation unit root test and the Westerlund cointegration test were applied. The preliminary analyses revealed that the variables were cross-section-dependent, heterogeneous, and first-order stationary. As a result of the Westerlund cointegration test, a stable and long-run relationship was detected between the variables. The long-term coefficients were statistically significant and positive for GDP but negative for per capita greenhouse gas emissions. Following the causality test, it was revealed that there was a unilateral causality running from per capita greenhouse gas emissions to per capita health expenditures for all the G7 countries. Another study using data from G7 countries was conducted (29) on the role of renewable energy in LE. This research used the method of moment quantile regression (MMQR). According to the results, renewable energy consumption, health expenditures, and urbanization caused increased LE in all quantiles, whereas higher CO₂ emissions reduced LE in all quantiles. The analysis emphasized that governments should recognize their responsibilities, make tax-related regulations for renewable energy resources, develop policies, and encourage more investments in this area. Chang et al. (30) determined a positive linear relationship between LE and GDPPC through analysis conducted in 13 countries (Bangladesh, China, Egypt, India, Indonesia, Iran, Myanmar, Pakistan, the Philippines, Russia, Thailand, Türkiye, Vietnam) via a linear regression approach. In the study conducted by Tahya (31), a directly proportional correlation was detected between cross-country LE and the GDPPC and the education index. Although they are significant economic indicators, there are almost no studies discussing GNIPC and TO in the literature review, as seen from all these examples, which has an impact on the selection of relevant variables in the present study. Considering the significance of the GDPPC, GNIPC, and TO variables in terms of the economic indicators of countries, the objective is to determine through a model whether these variables have an impact on LE in G7 countries, which are regarded as global economic leaders, and to estimate how much of an increase/decrease in the variables that are found to be significant as a result of the analysis will cause an increase/decrease in LE.

2 Data and method

2.1 Data

This study uses data from G7 countries—Germany, the United States, the United Kingdom (England), Italy, France, Japan, and Canada—covering 1990–2023, obtained from the G7 database (World Bank) (23) and analyzed with Stata 14. LE is the dependent variable, while GDPPC, GNIPC, and TO are independent variables. These indicators, key measures of globalization, are recognized as drivers of productivity growth and economic cycles in developed countries. Although many studies examine their effects on economic outcomes, research on TO’s impact on LE is limited. This study addresses this gap by assessing how GDPPC, GNIPC, and TO influence LE in G7 countries. Countries are treated as cross-sectional units (i) and years as the time dimension (t), enabling the analysis to capture both cross-country and temporal variations.

2.2 Method

Panel data, or longitudinal/cross-sectional time series data, consist of repeated observations of the same units over time, providing both spatial and temporal dimensions (32–34). Using panel data increases the reliability of the estimate by expanding data points, degrees of freedom, and reducing collinearity (35). The study data were analyzed with R version 4.5.1 (R Core Team) (36).

2.3 Panel analysis equation

The panel data methodology was used to handle the large cross-sectional data for the study. By combining N cross-sectional units with T time periods, panel data provide a flexible framework and a range of estimation techniques, making it popular in social science research (37).

The equation describing LE at birth may be (38):

$y_{\mathit{it}}=a_i+{\beta }_1{X}_{1\mathit{it}}+{\beta }_2{X}_{2\mathit{it}}+{\beta }_3{X}_{3\mathit{it}}+{\epsilon }_{\mathit{it}}$

e.g.,

$L{E}_{\mathit{it}}=a_i+{\beta }_1\mathit{\text{gdpp}}{c}_{1\mathit{it}}+{\beta }_2\mathit{\text{gnip}}{c}_{2\mathit{it}}+{\beta }_{3}T{O}_{3\mathit{it}}+{\epsilon }_{\mathit{it}}$

Three common approaches to estimate panel data regression are pooled least squares (PLS), fixed effects (FE), and random effects (RE) models (39).

2.3.1 Common effect model or pooled least squares (PLS)

Since this model ignores time and individual dimensions, it assumes consistent corporate behavior over time and can estimate panel data using ordinary least squares (OLS), with the regression equation having the same form as in OLS., i.e.:

$y_{\mathit{it}}=\alpha +{\beta }_1{X}_{1\mathit{it}}+{\beta }_2{X}_{2\mathit{it}}+\dots +{\beta }_k{X}_{\mathit{kit}}+{\epsilon }_{\mathit{it}}$

e.g.,

$L{E}_{\mathit{it}}=\alpha +{\beta }_1\mathit{\text{gdpp}}{c}_{1\mathit{it}}+{\beta }_2\mathit{\text{gnip}}{c}_{2\mathit{it}}+{\beta }_{3}T{O}_{3\mathit{it}}+{\epsilon }_{\mathit{it}}$

For I = 1, 2, …, N and t = 1, 2, …, T.

Where N is the number of individuals or cross-sections, and T is the number of time periods.

A pooled model assumes homoscedasticity, no autocorrelation, and identical individual behavior, allowing OLS to provide accurate estimates, with assumptions similar to Greene’s (40) simple regression model:

$\mathit{rank}\left(X\right)=\mathit{rank}\left(X^{\prime }X\right)=K$

Where X denotes a factor matrix with k columns and N = nt rows.

Exogeneity:

$E({\epsilon }_{\mathit{it}}\mid X)=0;\mathit{Cor}({\epsilon }_{\mathit{it}},X)=0$

Homoscedasticity:

$\mathit{Var}({\epsilon }_{\mathit{it}}\mid X)=E({\epsilon }_{\mathit{it}}^2\mid X)={\sigma }^2$

There is no cross-sectional or time series correlation:

$cov({\epsilon }_{\mathit{it}},\mid {\epsilon }_{\mathit{js}},\mid X)=E({\epsilon }_{\mathit{it}}{\epsilon }_{\mathit{js}}\mid X)=0$

The disturbance’s normal distribution is

${\epsilon }_{\mathit{it}}.$

2.3.2 Random effects model

In the random effects model, the individual-specific effect is a random variable uncorrelated with explanatory factors (41), with the panel data regression equation as follows (42):

$y_{\mathit{it}}={\alpha }_i+{\beta }_1{X}_{1\mathit{it}}+{\beta }_2{X}_{2\mathit{it}}+\dots +{\beta }_k{X}_{\mathit{kit}}+u_i$

e.g.,

$L{E}_{\mathit{it}}={\alpha }_i+{\beta }_1\mathit{\text{gdpp}}{c}_{1\mathit{it}}+{\beta }_2\mathit{\text{gnip}}{c}_{2\mathit{it}}+{\beta }_{3}T{O}_{3\mathit{it}}+u_i$

Where, $u_i=$ is the individual residual, which is a random characteristic of the i-th unit observation and exists at all times.

2.3.3 The fixed effects model

The individual-specific impact in the fixed effects model is a random variable that can be associated with explanatory factors (41). The panel data regression equation for the fixed effects model is as follows (42):

$y_{\mathit{it}}={\alpha }_i+{\beta }_1{X}_{1\mathit{it}}+{\beta }_2{X}_{2\mathit{it}}+\dots +{\beta }_k{X}_{\mathit{kit}}+{\epsilon }_{\mathit{it}}$

e.g.,

$L{E}_{\mathit{it}}={\alpha }_i+{\beta }_1\mathit{\text{gdpp}}{c}_{1\mathit{it}}+{\beta }_2\mathit{\text{gnip}}{c}_{2\mathit{it}}+{\beta }_{3}T{O}_{3\mathit{it}}+{\epsilon }_{\mathit{it}}$

2.4 Hausman test for differentiating between the fixed effects model and random effects model

In panel data, the model selection must be based on information about the individual components as well as on the exogeneity of the independent variables. Three hypothesis tests are used to select the best model. One is for determining if a fixed or random effects model is acceptable by detecting endogeneity in the explanatory variables: the Hausman test.

The null and alternative hypotheses are defined as follows:

H₀: random effects is the correct model. In the panel data model, there is no association between the error term and the independent variables.

$cov({\alpha }_i,X_{\mathit{it}})=0$

H₁: The proper model is fixed effects.

In the panel data model, the correlation between the error term and the independent variables is statistically significant.

$cov({\alpha }_i,X_{\mathit{it}})\ne 0$

The Hausman statistic is calculated using the following formula:

$H={({\widehat{\beta }}^{\mathit{RE}}-{\widehat{\beta }}^{\mathit{FE}})}^{\prime }{\left[\mathit{Var}\right({\widehat{\beta }}^{\mathit{RE}})-\mathit{Var}({\widehat{\beta }}^{\mathit{FE}}\left)\right]}^{-1}({\widehat{\beta }}^{\mathit{RE}}-{\widehat{\beta }}^{\mathit{FE}})$

Where ${\widehat{\beta }}^{\mathit{RE}}$and ${\widehat{\beta }}^{\mathit{FE}}$ are the coefficient estimate vectors for the random and fixed effects models, respectively. Under the null hypothesis, this statistic has a distribution of ${\chi }^2\left(k\right)$ . The number of factors is equal to the number of degrees of freedom k. The obtained statistic is compared to the critical values for the ${\chi }^2$ distribution with k degrees of freedom. If the Hausman statistic is greater than its critical value, the null hypothesis is rejected (42).

Finally, it is necessary to check for deviations from basic assumptions, as panel data models assume no heteroscedasticity, autocorrelation, or cross-sectional dependence. In the random effects model, heteroscedasticity can be tested with Levene, Brown, and Forsythe tests; autocorrelation with Durbin–Watson and Baltagi–Wu’s locally best invariance (LBI) tests; and cross-sectional dependence with the Pesaran test (43). Because one of the basic assumptions in panel data models is that error terms are unit-independent, it can be observed that errors and cross-sectional units have a contemporaneous association. It precludes the correlation matrix from being a unit matrix in this situation, as it does in autocorrelation and heteroscedasticity. As a result, the Pesaran CSD test, the Friedman CSD test, and the Frees CSD test would all be relevant to the study.

Hypotheses are, therefore,

$H_0={\rho }_{\mathit{ij}}={\rho }_{\mathit{ji}}=\mathit{cor}(u_{\mathit{it}},u_{\mathit{jt}})=0\mathit{\text{for}}i\ne j$

$H_1={\rho }_{\mathit{ij}}={\rho }_{\mathit{ji}}\ne 0\mathit{\text{for}}i\ne j$

Feasible generalized least squares (FGLS) estimation is also possible and will result in more efficient estimators and stronger tests than OLS asymptotically (44). Parks (45) defined this approach originally, and Kmenta (46) popularized it; hence, it is commonly referred to as Parks or Parks–Kmenta.

2.5 Robust panel models

Panel data models face issues such as outliers and heteroskedasticity. Outliers can bias regression slopes but can be down-weighted using M-estimators, while groupwise differences causing heteroskedasticity can be mitigated using group means or, in fixed effects models, a White heteroskedasticity-consistent covariance estimator with OLS (47, 48).

Autocorrelation can occur within panels from one time period to the next. Some difficulties with dynamic panels with residual autocorrelation are solved using a Prais–Winston transformation or a Cochrane–Orcutt transformation, which equates to first partial differencing to eliminate the bias from the autocorrelation. For panel data analysis, Arellano, Bond, and Bover created one and two-step general methods of moment (GMM) estimators. Insofar as they are asymptotically normal, the GMM is usually robust to variations in the underlying data production process as well as violations of heteroskedasticity and normality, although they are not necessarily the most efficient estimators (38).

The equation estimate:

$L{E}_{\mathit{it}}={\alpha }_i+{\beta }_1\mathit{\text{gdpp}}{c}_{1\mathit{it}}+{\beta }_2\mathit{\text{gnip}}{c}_{2\mathit{it}}+{\beta }_{3}T{O}_{3\mathit{it}}+{\mu }_{\mathit{it}}$ is in the form.

3 Results

The findings obtained from the fixed effects model are summarized in Table 1.

Table 1

Table 1. Fixed effects model regression results.

Total sum of squares: 748.3, residual sum of squares: 166.84, R-squared: 0.77705, adj. R-squared: 0.76825, F-statistic: 264.881 on 3 DFs and 228 DFs, p-value: < 2.22e-16.

The relationships in Table 1 were estimated via a fixed effects model. The F-test indicated that the model was overall significant, with an R² of 77.7%. GDPPC, TO, and the constant term were statistically significant (p < 0.001), while GNIPC was not.

After the fixed effects model was estimated, the relationships between the variables were estimated via the random effects model. The random effects model estimation results are presented in Table 2.

Table 2

Table 2. Random effects model.

Total sum of squares: 759.49, residual sum of squares: 193.93, R-squared: 0.74466, adj. R-squared: 0.74139, χ²: 682.424 for 3 DFs, p-value: < 2.22e-16.

The relationships in Table 2 were estimated using a random effects model. The Wald test confirmed the model’s significance, with an R² of 74.47%. GDPPC, TO, and the constant were significant (p < 0.001), while GNIPC was not.

After estimating both fixed effects and random effects models, the Hausman test was conducted to determine the more appropriate estimator. The results of the test (χ² = 345.03, p < 0.001) reject the null hypothesis in favor of the fixed effects specification. This indicates that the fixed effects estimator is both consistent and efficient; therefore, the fixed effects model was preferred over the random effects model.

H₀: The random effects estimator is efficient.

H₁: The fixed effects estimator is efficient.

The Hausman test indicated that the fixed effects model yielded more efficient and consistent results, but assumption checks (heteroskedasticity, autocorrelation, and inter-unit correlation) are necessary. Deviations can bias results, so robust estimators should be used if assumptions are violated.

Heteroscedasticity and autocorrelation in the fixed effects model were examined using the Pesaran CD, Breusch–Pagan, Breusch–Godfrey, and Wooldridge tests. The results of the diagnostic tests indicate several important characteristics of the panel data. The Pesaran CD test (z = 7.597, p = 3.03 × 10⁻¹⁴) suggests the presence of cross-sectional dependence. The Breusch–Pagan test (BP = 16.601, p = 0.00085) indicates heteroskedasticity in the data. Additionally, the Breusch–Godfrey test (χ² = 178.17, p < 2.2 × 10⁻¹⁶) and the Wooldridge test (F = 1279.6, p < 2.2 × 10⁻¹⁶) reveal significant autocorrelation, particularly in the fixed-effects model. These findings highlight the need to account for cross-sectional dependence, heteroskedasticity, and autocorrelation in panel data analysis.

Cross-sectional dependence occurs when the panel units are correlated, affecting standard errors; heteroskedasticity means error variances are unequal, and autocorrelation indicates error terms are time-dependent. The mean residual plot is given in Figure 1.

Figure 1

Figure 1. Mean residual plot.

In Figure 1, the mean residual plot fluctuates around zero over time, which is good. The histogram and QQ plot are presented in Figures 2, 3, respectively.

Figure 2

Figure 2. Histogram of residuals (fixed model).

Figure 3

Figure 3. Normal Q–Q plot.

In Figures 2, 3, the histogram and QQ plot are close to a normal distribution and do not show large deviations.

However, the error variances are not homogeneous by autocorrelation in the panel. In this case, robust standard errors must be used because classical standard errors are not valid. In short, robust panel data analysis is applied. The results of robust panel data analysis, using the Driscoll–Kraay estimator to account for heteroskedasticity and autocorrelation, are as follows. GDPPC has a positive and statistically significant effect on LE (estimate = 0.0000902, robust SE = 0.0000137, t = 6.59, p < 0.001). GNIPC shows a negative but insignificant effect (estimate = −0.0000048, robust SE = 0.0000176, t = −0.27, p = 0.78). TO has a positive and highly significant effect on LE (estimate = 0.10117, robust SE = 0.01229, t = 8.23, p < 0.001). The GDPPC and TO variables have a positive and significant effect on LE. The GNIPC variable is not significant.

Robust standard errors enable reliable inferences even when model assumptions are violated. Using a fixed-effects panel model to control for cross-country differences, autocorrelation, and heteroskedasticity was corrected via the Driscoll–Kraay method. The analysis shows that GDPPC and TO significantly and positively affect LE, while GNIPC is not significant. The model is suitable for panel data and could be extended with dynamic panel models or alternative robust estimators.

The robust estimator model requires the following panel regression model to be created.

$L{E}_{\mathit{it}}=70.88+0.0000902\mathit{\text{gdpp}}{c}_{1\mathit{it}}-0.0000048\mathit{\text{gnip}}{c}_{2\mathit{it}}+0.10117T{O}_{3\mathit{it}}$

The Driscoll–Kraay robust estimates indicate that GDPPC (0.0000902, p < 0.001) and TO (0.10117, p < 0.01) have positive and significant effects on LE, while GNIPC has a negative but insignificant effect. A one-unit increase in GDPPC is associated with a 0.0000902-unit increase in LE, and a one-unit increase in TO corresponds to a 0.10117-unit increase.

The graph showing the effect size of the coefficient estimates (with Driscoll–Kraay) is shown in Figure 4.

Figure 4

Figure 4. Effect sizes of variables in the fixed effects model.

According to Figure 4, the GDPPC coefficient is 0.00009. Controlling for country fixed effects, a $1 increase in GDPPC raises LE by 0.00009 years (~0.03 days), and a $1,000 increase raises it by about 32 days, indicating a small but significant positive effect. The TO coefficient is 0.10044, meaning a 1-point increase (e.g., from 50 to 51%) raises LE by 0.100 years (~36.5 days), and a 10-point increase raises it by approximately 1 year.

4 Discussion

In this study, predictions were made by examining how the GDPPC, GNIPC, and TO variables, which are known to be effective in economic growth, affect LE in the G7 countries, also known as economic leaders, through panel data analysis. Determining a prediction model, especially via robust panel data analysis, constitutes the most significant aspect of the study. The fact that the findings obtained in this study are parallel with those of similar studies supports the validity of the established model. Schnabel and Eilers (49) noted in their study that a country’s wealth had a non-linear effect on the LE of its residents. Oeppen (50) revealed that GDPPC alone was not enough to explain LE, but GDPPC had a very significant effect on LE and even indirectly affected other variables. While Ngangue and Manfred (21) reported a positive relationship between LE and GNIPC in their study, the present research revealed a statistically insignificant correlation. On the other hand, the relationship between GDPPC and LE was investigated in the studies conducted by Shafii and Samren (4), Bilas et al. (14), and Chang et al. (30), and the relationship between TO and LE in the study conducted by Shah et al. (19) yielded parallel results with those of the present study (4, 14, 19, 30). In another study (Kossis) (16), it was determined that the GDPPC variable positively affected the LE variable and was found to be significant. In their model, the variable’s coefficient was close to the result obtained in the present study; it is similar in this respect. In contrast, Azad’s (51) study used panel data analysis to determine the impact of LE on the GDPPC in 182 countries between 1960 and 2015. LE had a significantly positive and strong impact on GDPPC. The dynamic fixed effects model predicted that a 1% increase in LE would lead to a 3.5% increase in GDPPC. In this study, an increase in LE occurred as GDPPC increased, as in the study by Shafi and Fatima (4). On the other hand, as Hermanovski et al. (52) noted in their study, the medium and long-term trends in LE can be determined by variables such as health expenditures, lifestyle, and environmental factors, as well as GDPPC. Poças et al. (53) reported that longevity was positively and significantly impacted by higher levels of education and per capita income, as well as higher health care provisions (measured by prescription expenditures). However, bad habits involving alcohol and tobacco use have significant detrimental effects on health, lowering LE at age 65. Lifespan was negatively impacted by CO₂ emissions and atmospheric pollution.

The effects of official equity market liberalization and capital account openness on real per capita GDP, capital stock, and total factor productivity growth were discussed in the study by Bekaert et al. (54). Per capita GDP, a measure of human capital (secondary school enrollment), the logarithm of LE (health care), TO (exports plus imports divided by GDP), and private credit to GDP (financial development) were among the standard control variables. The authors discovered several important indicators of a crisis in the financial industry. In the capital account specification, higher initial per capita GDP, secondary school enrollment, and LE are all significantly linked to a lower likelihood of a crisis; however, only initial GDP is still significant among these variables in the equity market specification. Jawadi et al. (55) examined the effects of TO on the health outcomes of 12 countries in the Middle East and North Africa (MENA) region: Algeria, Bahrain, Egypt, Jordan, Morocco, Kuwait, Oman, Qatar, Saudi Arabia, Tunisia, Turkey, and the UAE. By using annual data and different panel data regressions, including different proxies for health, it was found that a significant relationship between health and trade openness was found. The positive impact of TO on health is significant only for the G7 countries, which reflects the externalities created by the knowledge and information spillovers from developed countries to the MENA region, according to data that were disaggregated by breaking down trade into trade with the G7 countries and trade with the rest of the world. All the studies that have been and will be conducted on the subject will provide significant contributions to the field and will be an important guide for policymakers.

5 Conclusion

In this study, the relationships between LE and the variables GDPPC, GNIPC, and TO were investigated in G7 countries. Fixed effect and random effect models were used, and the random effect model was preferred. None of the assumptions of heteroskedasticity, autocorrelation, or interunit correlation were met for the random effects model. Therefore, the robust estimation model was examined. As with GDPPC and TO, which were found to be significant as a result of the empirical findings obtained through robust panel data analysis, LE also increased. When the GDPPC increased by 1 unit, the LE increased by 0.0000902 units. For example, if the level of the GDPPC increased by $100,000, LE would increase by 9.02 years. If the TO value increased by $1, the LE value would increase by 0.10107 years, and if the TO value increased by $100, the LE value would increase by approximately 10.107 years. The LE values were positively correlated with GDPPC and TO. While the relationships between LE and GNIPC were insignificant, the relationships between LE and GDPPC and TO were statistically significant (p < 0.001). In conclusion, the estimated results revealed that the explanatory variables representing GDPPC and TO in the 7 developing countries had positive coefficients, which indicated that these variables have a positive relationship with LE. The independent variable, designated GNIPC, was found to have negative coefficients. These results suggest that the “GDPPC” and “TO” variables are important for LE. The increase in the values of economic factors in the G7 countries positively affects people’s LEs. Robust panel data analysis models are useful and applicable methods for examining the impacts of economic variables on people’s LEs.

The fixed-effects panel data model was used to control for cross-country differences. Autocorrelation and heteroskedasticity were identified in the model; therefore, standard errors were corrected via the Driscoll–Kraay method. According to the analysis results, the GDPPC and TO variables have a significant and positive effect on LE. On the other hand, the effect of the GNIPC variable was not statistically significant. The model is suitable for panel data and can be supplemented with dynamic panel models or other robust standard error estimation methods in further analyses.

Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found at: https://data.worldbank.org.

Author contributions

AŞ: Conceptualization, Resources, Supervision, Writing – original draft, Writing – review & editing. ŞÇ: Data curation, Formal analysis, Methodology, Writing – original draft, Writing – review & editing. RŞ: Data curation, Formal analysis, Writing – original draft, Writing – review & editing.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that Generative AI was not used in the creation of this manuscript.

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