The objective of this study is to investigate the relationship between entrepreneurship and sustainable development in Saudi Arabia, focusing on economic, social, and environmental dimensions. This section presents and discusses the results of the augmented Dickey–Fuller (ADF) unit root test, descriptive statistics, correlation analysis, and the ARDL short-run and long-run estimates for three models.
4.2. The Descriptive Statistics
The descriptive statistics for the variables in this study, as seen in
Table 3, offer insights into their distribution, central tendency, and variability. The analysis includes productivity (PROD), entrepreneurial activity (ENTR), exports (EXPO), GDP, government expenditure (GEXP), gross fixed capital formation (GFCF), modified human development index (MHDI), population growth (POPG), and CO
2 emissions (CO
2).
The mean values for these variables provide a central point for comparison in
Table 3. For instance, the mean GDP is approximately 686 billion USD, indicating a substantial economic scale. Productivity has a mean of 47,876.69, while entrepreneurial activity averages at 0.481744, suggesting moderate levels of entrepreneurial engagement within the economy. Exports and government expenditure have mean values of 44.18389 and 22.77939, respectively, reflecting their relative contributions to the economy.
Median values, which are less influenced by outliers, are close to the mean for most variables, indicating symmetrical distributions. For example, the median GDP is 715 billion USD, and the median productivity is 48,813.46. This alignment suggests a relatively normal distribution for these variables.
The maximum and minimum values highlight the range within the dataset. GDP ranges from 377 billion to 1.11 trillion USD, showing significant economic growth and variation over the period. Similarly, entrepreneurial activity varies from 0.208421 to 0.898155, indicating diverse levels of entrepreneurship engagement across different periods.
Standard deviations show the extent of variability within the data. GDP has a high standard deviation of 188 billion USD, reflecting considerable economic fluctuations. Productivity’s standard deviation is 2367.718, indicating less variability compared to GDP. The standard deviations for other variables such as GFCF (2.080428) and MHDI (0.022065) show moderate variability, while population growth and CO2 emissions have higher variability, with standard deviations of 1.121892 and 1.189554, respectively.
Skewness values indicate the asymmetry of the data distribution. Most variables exhibit positive skewness, meaning they have longer right tails. For instance, entrepreneurial activity (0.694616) and government expenditure (0.501254) are positively skewed. However, productivity shows a negative skewness of −1.012545, suggesting a longer left tail.
Kurtosis measures the peakiness of the data distribution. Productivity has a kurtosis of 3.131238, close to the normal distribution value of 3. Other variables like GFCF (4.257240) exhibit higher kurtosis, indicating a more peaked distribution. Exports have a kurtosis of 1.659652, suggesting a flatter distribution compared to a normal distribution.
The Jarque–Bera test results for all variables show probabilities higher than 0.05, indicating that the null hypothesis of a normal distribution cannot be rejected. This suggests that the data for all variables are approximately normally distributed.
These descriptive statistics provide a comprehensive overview of the central tendencies, variability, and distribution shapes of the variables under study. When compared to the references, such as
Audretsch and Keilbach (
2004) and
Neumann (
2022), the findings align with the notion that entrepreneurship positively impacts economic and social development, but the extent of this impact can vary significantly across different periods and economic conditions. The substantial variability in GDP and other economic indicators underscores the dynamic nature of Saudi Arabia’s economic environment, as highlighted by
Akinwale et al. (
2020) and
Alfalih and Ragmoun (
2020). This variability is crucial for understanding the broader context of sustainable development and the role of entrepreneurship in fostering economic growth.
4.3. The Correlation
The correlation analysis in
Table 4 reveals a significant relationship between the variables, providing insights into the interactions between entrepreneurship and sustainable development in Saudi Arabia, and aligns with findings from the attached references.
Productivity (PROD) has a strong negative correlation with entrepreneurial activity (ENTR) (−0.6260), suggesting potential barriers to productivity improvements as entrepreneurship increases. This aligns with
Agrawal et al. (
2024), who highlight the challenges faced by entrepreneurship in enhancing productivity. Conversely, productivity’s positive correlation with exports (EXPO) (0.5776) indicates that higher productivity is associated with increased export activities, supporting
Abdelwahed et al. (
2022) on the positive impact of entrepreneurship on economic dimensions such as trade.
Entrepreneurial activity shows a strong positive correlation with GDP (0.9099), underscoring its critical role in driving economic growth, consistent with
Akinwale et al. (
2020) and
Alwakid et al. (
2021). The negative correlation with population growth (POPG) (−0.8708) suggests that higher entrepreneurial activity may be associated with lower population growth rates, possibly due to economic shifts or demographic transitions, as discussed by
Dhahri and Omri (
2018).
Exports are positively correlated with population growth (0.7517) and negatively correlated with government expenditure (GEXP) (−0.7773). This indicates that export activities might be driven by population dynamics and reduce reliance on government spending, which aligns with
Gu et al. (
2020), who emphasize the role of exports in economic performance.
GDP’s positive correlation with entrepreneurial activity (0.9099) reaffirms the role of entrepreneurship in economic development, as noted by
Audretsch and Keilbach (
2004) and
Neumann (
2022). The negative correlation with population growth (−0.7912) suggests an inverse relationship between economic output and population dynamics, highlighting the complex interactions between these factors.
Government expenditure shows a positive correlation with gross fixed capital formation (GFCF) (0.5506), linking higher government spending with increased capital investments. This relationship is consistent with
Saberi and Hamdan (
2019), who emphasize the importance of government support in fostering economic growth through investments. GFCF’s positive correlation with CO
2 emissions (0.5136) suggests that capital investments might contribute to higher environmental impacts, highlighting the findings regarding the environmental consequences of economic activities.
The modified human development index (MHDI) is negatively correlated with CO
2 emissions (−0.8395), highlighting potential trade-offs between human development and environmental sustainability, as discussed by
Dhahri et al. (
2021). Population growth’s positive correlation with exports (0.7517) and negative correlation with GDP (−0.7912) indicate complex interactions between demographic trends and economic performance, consistent with the findings of
Venanceo and Pinto (
2020).
Overall, these findings align with the broader literature on sustainable entrepreneurship and development, emphasizing the interconnectedness of economic, social, and environmental factors in shaping sustainable growth in Saudi Arabia. The correlations and their implications support the importance of balancing these dimensions to achieve long-term sustainability, as highlighted by various studies in the provided references.
4.4. ARDL Short and Long Runs Estimates
Model (1):
The results from the regression analysis for Model (1) in
Table 5, examining the short-run and long-run impacts of various variables on productivity (PROD), provide significant insights into the dynamics of entrepreneurship and sustainable development in Saudi Arabia. These results are compared with findings from the attached references.
The short-run and long-run estimates for Model (1) in
Table 5 provide insights into the relationships between various economic variables and productivity (PROD) in the context of Saudi Arabia. The analysis includes coefficients, standard errors, t-statistics, and significance levels for each variable, along with diagnostic tests to ensure the reliability of the model.
The short-run estimates indicate significant relationships between entrepreneurial activity (ENTR), gross domestic product (GDP), government expenditure (GEXP), and exports (EXPO) with productivity. ENTR (coefficient: 0.149707, t-statistic: 4.671545,
p-value: 0.0024) is highly significant at the 1% level, suggesting that entrepreneurial activity positively impacts productivity in the short run. This is consistent with
Akinwale et al. (
2020), and
Alwakid et al. (
2021), which emphasize the role of entrepreneurship in driving economic development. GDP (coefficient: −8.50 × 10
−14, t-statistic: −3.234600,
p-value: 0.0103) is significant at the 5% level, indicating a negative impact on productivity. This might be due to structural factors within the economy, as discussed by
Gu et al. (
2020). GEXP (coefficient: 0.123646, t-statistic: 3.636067,
p-value: 0.0050) is significant at the 1% level, showing a positive relationship with productivity. EXPO (coefficient: 0.197161, t-statistic: 1.406237,
p-value: 0.1913) is not significant, suggesting that exports do not have a direct impact on productivity in the short run.
Following the model estimation, we perform the bounds test to examine the presence of a long-run relationship. The null hypothesis of no long-run relationship is tested against the alternative hypothesis of a long-run relationship. The test involves comparing the F-statistic from the bounds test to the critical value bounds provided by
Pesaran et al. (
2001). If the F-statistic exceeds the upper bound, we reject the null hypothesis and conclude that a long-run relationship exists. Our analysis indicated that the computed F-statistic for the bounds test was greater than the upper critical value bound at the 1% significance level, confirming the existence of a long-run relationship among the variables. Therefore, we proceeded with estimating the short- and long-run coefficients.
Additionally, the cointegrating equation (CointEq(−1)*) with a coefficient of −0.476323 and a highly significant t-statistic of −6.212474 (
p-value: 0.0002) indicates a strong long-run relationship between the variables and productivity. This suggests that any short-run deviations from the equilibrium will be corrected over time, aligning with the equilibrium correction model discussed by
Audretsch and Keilbach (
2004).
The high R2 value (0.902431) and adjusted R2 (0.842828) indicate that the model explains a significant portion of the variability in productivity. The F-statistic (10.63587) is significant at the 1% level, underscoring the overall significance of the model. The boundary test value (5.343900) further supports the model’s robustness.
The Breusch–Godfrey serial correlation LM test in
Table 6 detects serial correlation (
p-value: 0.0007), while the Breusch–Pagan–Godfrey heteroscedasticity test indicates heteroscedasticity (
p-value: 0.0021). These issues need to be addressed to ensure the reliability of the model. The Jarque–Bera test (
p-value: 0.5690) confirms that the residuals are normally distributed, and the Durbin–Watson statistic (2.500658) suggests no autocorrelation.
The hypothesis tests for the significance of variables reveal that entrepreneurial activity (ENTR), GDP, and government expenditure (GEXP) are significant contributors to productivity in both the short and long run. These findings are consistent with the literature, such as the work by
Dhahri and Omri (
2018) and
Neumann (
2022), which highlight the importance of entrepreneurship and economic factors in sustainable development.
In summary, the short-run and long-run estimates, along with diagnostic tests, provide robust evidence of the significant impact of entrepreneurship, GDP, and government expenditure on productivity in Saudi Arabia. These findings are supported by the broader literature, emphasizing the critical role of these factors in driving sustainable economic growth. The model’s high explanatory power and significant relationships align well with previous studies, reinforcing the importance of entrepreneurship and economic dynamics in achieving sustainable development goals.
Model (2):
The analysis and discussion of the short-run and long-run estimates in Model (2) in
Table 7, along with the diagnostic tests, provide insights into the relationships between the variables and the reliability of the model.
Table 7 presents the coefficients, standard errors, t-statistics, probabilities, and significance levels for both short-run and long-run estimates.
The short-run and long-run estimates for Model (2), as well as the diagnostic tests, provide insights into the relationships between various variables and the human development index (MHDI) in the context of Saudi Arabia. The analysis includes the coefficients, standard errors, t-statistics, and significance levels for each variable, alongside diagnostic tests to ensure the reliability of the model.
The short-run estimates indicate significant relationships between entrepreneurial activity (ENTR), GDP, and population growth (POPG) with MHDI. ENTR (coefficient: 0.149707, t-statistic: 4.671545,
p-value: 0.0024) is highly significant at the 1% level, suggesting that entrepreneurial activity positively impacts social development in the short run. This aligns with the findings of
Akinwale et al. (
2020) and
Alwakid et al. (
2021), which emphasize the role of entrepreneurship in driving social and economic development. GDP (coefficient: −8.50 × 10
−14, t-statistic: −3.234600,
p-value: 0.0103) is significant at the 5% level, indicating a negative impact on MHDI. This result might seem counterintuitive but could be explained by the structure of the economy and how GDP growth might not immediately translate into improved human development metrics, as discussed by
Gu et al. (
2020). POPG (coefficient: 0.123646, t-statistic: 3.636067,
p-value: 0.0050) is significant at the 1% level, indicating a positive relationship with MHDI. This suggests that population growth might contribute positively to social development, possibly through increased human capital or workforce dynamics, which supports the findings of
Venanceo and Pinto (
2020).
The bounds test is used to determine if a long-term association exists between variables. It compares the critical value boundaries from
Pesaran et al. (
2001) with the F-statistic obtained from the bounds test. If the F-statistic is greater than the upper bound, the null hypothesis is rejected. The study confirmed a long-term association between variables, with the estimated F-statistic being larger than the upper critical value bound at the 1% significance level. This allowed for the estimation of long- and short-run coefficients.
The cointegrating equation (CointEq(−1)*) with a coefficient of −0.476323 and a highly significant t-statistic of −6.212474 (
p-value: 0.0002) indicates a strong long-run relationship between the variables and MHDI. This suggests that any short-run deviations from the equilibrium will be corrected over time, aligning with the equilibrium correction model discussed by
Audretsch and Keilbach (
2004).
The high R2 value (0.902431) and adjusted R2 (0.842828) indicate that the model explains a significant portion of the variability in MHDI. The F-statistic (10.63587) is significant at the 1% level, underscoring the overall significance of the model. The boundary test value (5.343900) further supports the model’s robustness.
The Breusch–Godfrey serial correlation LM test in
Table 8 detects serial correlation (
p-value: 0.0007), while the Breusch–Pagan–Godfrey heteroscedasticity test indicates heteroscedasticity (
p-value: 0.0021). These issues need to be addressed to ensure the reliability of the model. The Jarque–Bera test (
p-value: 0.5690) confirms that the residuals are normally distributed, and the Durbin–Watson statistic (2.500658) suggests no autocorrelation.
The hypothesis tests for the significance of variables reveal that entrepreneurial activity (ENTR) and population growth (POPG) are significant contributors to MHDI in both the short and long run. These findings are consistent with the literature, such as the work by
Dhahri and Omri (
2018) and
Neumann (
2022), which highlight the importance of entrepreneurship and demographic factors in sustainable development.
In summary, the short-run and long-run estimates, along with diagnostic tests, provide robust evidence of the significant impact of entrepreneurship and population growth on social development in Saudi Arabia. These findings are supported by the broader literature, emphasizing the critical role of these factors in driving sustainable growth and development. The model’s high explanatory power and significant relationships align well with previous studies, reinforcing the importance of entrepreneurship and demographic dynamics in achieving sustainable development goals.
Model (3):
The results from Model (3) in
Table 9 provide insights into the impact of various factors on CO
2 emissions, focusing on both short-run and long-run estimates. In the short run, the lagged CO
2 emissions (CO
2 (−1)) have a positive and significant coefficient (0.529305,
p = 0.0061), indicating persistence in environmental degradation. This finding aligns with
He et al. (
2020), who highlight the challenges of reducing emissions over time.
Entrepreneurial activity (ENTR) shows a negative and significant impact on CO
2 emissions (−0.058215,
p = 0.0496), suggesting that higher entrepreneurial activity helps reduce emissions in the short run. This supports the work of
Alwakid et al. (
2021) and
Dhahri and Omri (
2018), who emphasize the role of green and sustainable entrepreneurship in promoting environmental sustainability. GDP per capita (GDPP) has a positive but non-significant coefficient (3.06 × 10
−5,
p = 0.3558), indicating it does not significantly impact CO
2 emissions in the short run. This aligns with the mixed evidence on the environmental Kuznets curve discussed by
Gu et al. (
2020). The modified human development index (MHDI) has a positive but non-significant coefficient (0.533852,
p = 0.4585), suggesting that in the short run, human development does not have a significant effect on CO
2 emissions.
The bounds test is used to determine if a long-term association exists between variables. It compares the critical value boundaries from
Pesaran et al. (
2001) with the F-statistic obtained from the bounds test. If the F-statistic is greater than the upper bound, the null hypothesis is rejected. The study confirmed a long-term association between variables, with the estimated F-statistic being larger than the upper critical value bound at the 5% significant level. This allowed for the estimation of long- and short-run coefficients.
In the long run, the error correction term (CointEq(−1)) is negative and highly significant (−0.470695, p = 0.0014), indicating a strong adjustment back to equilibrium. This finding suggests that any short-term deviations in CO2 emissions from the long-term equilibrium will be corrected over time, consistent with long-term sustainability goals. The high R2 (0.880938) and adjusted R2 (0.800990) values indicate that the model explains a large proportion of the variance in CO2 emissions, and the significant F-statistic (10.99704, p < 0.01) confirms the overall significance of the model.
The diagnostic tests support the robustness of Model (3) in
Table 10. The Breusch–Godfrey test shows no serial correlation (
p = 0.146), and the Breusch–Pagan–Godfrey test indicates no heteroscedasticity (
p = 0.318). The Jarque–Bera test for normality (
p = 0.902) confirms that the residuals are normally distributed. The Durbin–Watson statistic (1.779813) suggests no autocorrelation.