Before estimating the model, a thorough empirical examination of the summary statistics of the data series was conducted, as indicated in Table 3. The average values of the variables are displayed in the results, with Gross Capital Formation (GCF) exhibiting the highest mean among them. Regarding the distribution shape characterized by skewness, ECOS, LF, and TI display a right-skewed pattern, while CEC, DEC, and GCF exhibit negative skewness. Furthermore, the kurtosis statistics demonstrate that every variable—aside from CEC—displays a platykurtic distribution, which denotes a distribution with a low kurtosis or a short tail. Additionally, the Jarque-Bera test results demonstrate that the residuals for each variable have a normal distribution.
Table 3
Descriptive statistics
|
ECOS
|
LNCEC
|
LNDEC
|
LNLF
|
LNGCF
|
LNTI
|
Mean
|
-1E-08
|
6.0577
|
7.8357
|
4.0029
|
24.0295
|
20.0318
|
Median
|
0.0692
|
6.137
|
7.8942
|
3.9878
|
24.0499
|
19.6626
|
Maximum
|
1.9595
|
6.4358
|
8.3017
|
4.0802
|
24.8345
|
21.7915
|
Minimum
|
-1.699
|
5.1988
|
7.1915
|
3.9523
|
22.9454
|
18.5876
|
Std. Dev.
|
1
|
0.2482
|
0.3256
|
0.0401
|
0.5271
|
0.977
|
Skewness
|
0.0758
|
-1.3934
|
-0.497
|
0.5001
|
-0.4163
|
0.2209
|
Kurtosis
|
2.2974
|
5.0651
|
2.0812
|
1.7568
|
2.2352
|
1.6189
|
Jarque-Bera
|
1.0333
|
24.0626
|
3.6649
|
5.0914
|
2.5565
|
4.2053
|
Probability
|
0.5965
|
0
|
0.1601
|
0.0784
|
0.2785
|
0.1221
|
Table 3. Statistical description
Moreover, Fig. 4 displays box plots that present a summary of the parameters' statistics. Figure 4 also provides descriptive statistics for Pakistan spanning the years 1985 to 2022. The box and scatter plots visually represent the 10th, 25th, 75th, and 90th percentiles of the data. The whisker cap corresponds to the 1st and 99th percentiles, while dots on the plots signify maximum (min) and minimum (cap) values.
Figure 4. Boxplots of the selected parameters
Furthermore, Fig. 5 illustrates the correlation among the variables. The accompanying figures present details on the Pearson correlation coefficients, histograms, and bivariate scatter plots. In the upper right corner of Fig. 5, the triangular region depicts the bivariate Pearson correlation coefficients ranging between − 1 and + 1. Strong positive or negative correlation is indicated by values that are near to + 1 or -1, respectively. Figure 5 reveals a positive correlation among ECOS, CES, and GCF, whereas ECOS, DEC, LF, and TI exhibit a negative correlation.
The statistical analysis using Pearson's correlation coefficient indicates a significant and robust correlation among all variables in the study. Notably, there is a strong correlation observed between ECOS, CEC, DEC, LF, GCF, and TI. The scatter plot in the lower-left corner of Fig. 5 visually represents the relationship between two variables, and the strength and direction of this correlation are elaborated upon in this section. Specifically, an increase in CEC and GCF is associated with a corresponding increase in ECOS, while the relationship is reversed for DEC, LF, and TI. To further illustrate the distributional properties of these variables, Fig. 5 includes a diagonal plot.
Figure 5. Presentation of the correlation structure graphically
Utilizing various stationarity tests, the stationarity analysis for each variable is shown in Table 4. The results indicate that there is statistical significance for all variables in the first-order difference, which suggests that the variables are not stationary at the second-order integral I(2). These results validate the absence of stationarity at the second-order integration level of the series analyzed in this work. Consequently, the ARDL model can efficiently and reliably employ orders I(0) and I(1) to estimate the relationship between the variables.
Table 4
Variables
|
Augmented Dickey-Fuller (ADF)
|
|
Phillip Perron (PP)
|
|
DF- GLS Residuals
|
I(0)
|
I(1)
|
|
I(0)
|
I(1)
|
|
I(0)
|
I(1)
|
ECOS
|
-2.7508
|
-7.5546
|
|
-2.8401
|
-7.5546
|
|
-2.3948
|
-7.6219
|
|
(0.073/-2.925)
|
(0.000/-2.926)
|
|
(0.061/-2.925)
|
(0.000/-2.926)
|
(-1.947)
|
(-1.947)
|
LnCEC
|
-3.8427
|
-10.7709
|
|
-3.6638
|
-12.7744
|
|
-1.1566
|
-10.8823
|
|
(0.004/-1.925)
|
(0.000/-2.926)
|
|
(0.007/-1.925)
|
(0.000/-2.926)
|
(-1.947)
|
(-1.947)
|
LnDEC
|
-2.1131
|
-5.4707
|
|
-2.1131
|
-5.7073
|
|
0.4571
|
-2.2368
|
|
(0.241/-1.925)
|
(0.000/-2.926)
|
|
(0.241/-1.925)
|
(0.000/-2.926)
|
(-1.947)
|
(-1.947)
|
LnLF
|
-0.4189
|
-4.7764
|
|
-0.0727
|
-4.7757
|
|
0.4463
|
-4.7798
|
|
(0.897/-2.925)
|
(0.000/-2.926)
|
|
(0.946/-2.925)
|
(0.000/-2.926)
|
(-1.947)
|
(-1.947)
|
LnGCF
|
-1.9898
|
-5.1646
|
|
-1.8438
|
-5.2385
|
|
0.3671
|
-5.1438
|
|
(0.290/-2.925)
|
(0.000/-2.926)
|
|
(0.355/-2.925)
|
(0.000/-2.926)
|
(-1.947)
|
(-1.947)
|
LnTI
|
-1.2403
|
-13.4448
|
|
-1.6708
|
-13.6443
|
|
-0.8081
|
-4.0381
|
|
(0.649/-2.925)
|
(0.000/-2.926)
|
|
(0.439/-2.925)
|
(0.000/-2.926)
|
(-1.947)
|
(-1.947)
|
Note: (p-scores/t-stat) |
In the ARDL model, both independent and dependent variables are permitted to have varying lag lengths. As shown in Table 5, some tests were run to find the best lag selection criteria. The best lag duration for our model was determined by applying the Akaike Information Criterion (AIC). When the AIC values were compared, the lowest AIC value was obtained with three lags in time, indicating that it made sense for the model. Thus, a lag time of three is judged suitable for capturing the dynamic changes in the variables in our analysis based on the AIC results. To ensure the reliability and stability of the ARDL coefficient, several post-estimation tests were conducted, and the diagnostic results are presented in Appendix Tables A1 through A3.
Table 5
K
|
|
1%
|
|
|
5%
|
|
|
10%
|
|
|
p-value
|
|
|
I(0)
|
I(1)
|
|
I(0)
|
I(1)
|
|
I(0)
|
I(1)
|
|
I(0)
|
I(1)
|
F
|
5.485
|
3.425
|
5.143
|
|
2.41
|
3.791
|
|
1.982
|
3.212
|
|
0
|
0.002
|
t
|
-4.1
|
-2.68
|
-4.693
|
|
-1.968
|
-3.88
|
|
-1.611
|
-3.475
|
|
0.003
|
0.032
|
Note: Lower and upper bounds are indicated by I(0) and I(1) |
Apart from the static test, the assessment of long-run cointegration was conducted using the bound test, and the outcomes are presented in Table 6. It's crucial to remember that the presence of a cointegrating relationship doesn't necessitate a p-value below 0.05 for the constraints test at a 5% significance level. Considering this, a thorough examination of the long-run relationship would be fitting.
Table 6
Lag
|
LogL
|
LR
|
FPE
|
AIC
|
SC
|
HQ
|
0
|
84.6751
|
|
1.30E-09
|
-3.42E + 00
|
-3.33131
|
-3.18214
|
1
|
347.577
|
525.8
|
6.90E-14
|
-13.286
|
-12.6605
|
-11.6163*
|
2
|
406.277
|
117.4*
|
2.8e-14*
|
-14.2729*
|
-13.1114*
|
-11.1722
|
Table 4. Stationarity test
Table 5. Bound test
Table 6. Model lag selection
To assess the short and long-run relationship, we utilized the dynamic ARDL model proposed by Jordan and Philips (2018). The model outcomes are detailed in Table 7. It reveals that the error correction term is -0.32, displaying a negative and statistically significant value. This suggests that the variables gravitate towards a normal long-term relationship over time, with an adjustment rate of 32%. The coefficients related to CEC exhibit notably favorable outcomes in both the short and long run. Conversely, the study findings imply that the increase in ECOS can be attributed to CEC. Specifically, the study indicates that a 1% increase in CEC corresponds to a 0.78% rise in ECOS in the short term and a 0.89% increase in the long term. A positive relationship between clean energy consumption and economic sustainability has been demonstrated by previous studies conducted by Qing et al (2024) and Khan et al (2024). Because they generate jobs, the development and use of clean energy has a positive effect on economic sustainability (Wali et al., 2023; Yang and Long, 2024), fueling economic growth, enhancing cost-effectiveness, bolstering energy security, driving technological innovation, advocating sustainable development, and mitigating environmental impacts (M. Zhang et al., 2024). It is essential to incorporate clean energy into the energy mix to ensure a sustainable future and build an economy that is stable and emits few emissions (Wang et al., 2024).
Table 7
Parameter
|
Dynamic ARDL
|
Coefficients
|
t-stat
|
p-value
|
Short-run:
|
|
|
|
∆LnCEC
|
0.7869
|
2.52
|
0.016**
|
∆LnDEC
|
0.7621
|
1.4
|
0.122
|
∆LnLF
|
-0.4906
|
-2.67
|
0.011**
|
∆LnGCF
|
0.4599
|
2.52
|
0.016**
|
∆LnTI
|
0.3233
|
2.59
|
0.014**
|
Long-run:
|
|
|
|
LnCEC
|
0.8931
|
2.92
|
0.006***
|
LnDEC
|
-0.3276
|
-2.33
|
0.026**
|
LnLF
|
-0.5282
|
-0.79
|
0.432
|
LnGCF
|
0.4012
|
2.12
|
0.041**
|
LnTI
|
-0.7148
|
-2.2
|
0.034**
|
Cons
|
-0.318
|
-2.92
|
0.006***
|
ECT
|
-0.332
|
-3.04
|
0.004***
|
Adjusted R2
|
0.8195
|
|
|
R2
|
0.8976
|
|
|
RMSE
|
0.6397
|
|
|
Simulation
|
5000
|
|
|
Note: *, **, and *** indicates 10%, 5%, and 1% level of significance |
The Dirty Energy Consumption (DEC) coefficient is positive in the short run but not statistically significant; in the long run, though, it turns negative and becomes statistically significant, showing a significant dynamic relationship. The results demonstrate that over the long term, a 1% increase in DEC is associated with a 0.32% decrease in ECOS. The short-term statistical significance of the relationship between dirty energy consumption (DEC) and economic sustainability is not established, but it shifts with time to become significant in the long term due to its negative effects. While not statistically significant, the short-term impact of filthy energy consumption on economic activity may be favorable. However, in the long run, environmental sustainability concerns make the negative impact of filthy energy consumption on economic sustainability clear. Pollution and resource depletion are two undesirable externalities linked to the use of dirty energy sources (Jiang et al., 2022). It additionally indicates the escalating significance of the shift towards clean energy, propelled by alterations in policies, advancements in technology, and the rising cost competitiveness of clean energy (Das et al., 2022).
In addition, the labor force coefficient has a statistically significant negative influence on ECOS in the short term, although this effect loses importance with time. The short-term detrimental and statistically significant effect of LF indicates that the availability of labor has an adverse effect on economic sustainability. This may be attributed to imbalances in the labor market, skill mismatches, or inefficiencies in the utilization of labor (Achuo et al., 2023). Short-term labor surpluses or shortages have the potential to negatively impact the economy's sustainability. LF does not, however, have a detrimental long-term effect on economic sustainability. A number of variables, including resource availability, legislative changes, and technology improvements, may have an impact on long-term economic sustainability. The positive coefficient of GCF significantly influences ECOS, indicating that, based on empirical findings, a 1% rise in GCF is correlated with increases in short-term and long-term ECOS of 0.45% and 0.40%, respectively. The results of the study align with those of (Ying Li et al., 2023), (F. Chen et al., 2023), and (Subhan et al., 2024), which showed that economic sustainability and gross capital formation were positively correlated in the G20, a group of middle-income nations, and Canada, respectively. Building up capital is essential to promoting economic sustainability. Infrastructure, productivity, technology, and machinery capital investments can all help to increase output and spur economic growth. Capital investment in infrastructure, technology, machinery, and productivity can contribute to the improvement of output and economic growth (Zaman et al., 2021). Businesses grow because they generate employment possibilities, which lowers unemployment and improves people's quality of life overall (Etokakpan et al., 2020). In addition, investing in educational and training programs to develop human capital can increase output and promote economic expansion. Through this investment, people can learn the necessary skills that will increase their employability in higher-paying jobs (Li et al., 2022). A robust capital base facilitates investments in public infrastructure and job creation, thereby fortifying the endurance of economic expansion. Empirical findings indicate that capital exerts a substantial and positive influence on economic sustainability, influencing all sectors and fostering enduring growth and stability.
Furthermore, the study found that the technical innovation coefficient has a statistically significant short-term positive influence on economic sustainability and a statistically significant long-term negative impact. According to the empirical data, economic sustainability levels rise by 0.32% for every 1% increase in the technological innovation index in the short term, while in the long term, economic sustainability declines by 0.71% for every 1% increase in the technological innovation index. Technological innovation can, in the near run, minimize energy prices, improve economic activity, and create jobs in order to support economic growth and productivity. However, conventional energy sources like fossil fuels may experience long-term disruptions, which could have negative consequences including job losses and economic difficulties for the affected areas. Government budgets and the viability of the economy as a whole may suffer as a result of the costs involved in switching to new energy technology (Liu and Lin, 2024). Maintaining long-term economic viability requires weighing the benefits and drawbacks in order to facilitate a seamless and inclusive transition.
Table 7. Dynamic ARDL outcome
Dynamic ARDL simulations were used to evaluate the various effects of labor force participation, capital formation, energy consumption, and technological innovation on economic sustainability. The variables under consideration in these simulations were subjected to 10% positive and negative counterfactual shocks between 2022 and 2062 (a period that coincides with the estimation of economic sustainability). A 10% change in estimated clean energy consumption has an effect on economic sustainability in the second stage, which in turn affects the acceleration of economic sustainability in the next stage, as Fig. 6 shows. Conversely, Fig. 7 shows how a 10% positive or negative shock to the estimated amount of dirty energy consumed could affect the second stage's economic sustainability but ultimately lead to a reduction in that sustainability. Both good and bad 10% shocks could have an impact on labor in the second stage of economic sustainability, as shown in Fig. 8, improving the situation in later phases. Nonetheless, the dynamic ARDL simulation depicted in Fig. 8 indicates that long-term economic sustainability is not considerably impacted by the 10% shocks, both positive and negative, to the anticipated workforce. Figure 9 illustrates how the predicted 10% positive and negative shocks in capital production are expected to affect the second stage of economic sustainability, and the future trajectory is expected to follow the capital formation trend. On the other hand, Fig. 10 shows that economic sustainability is predicted to be impacted in the second stage but to fall in the stages that follow due to the 10% positive and negative shocks to technological innovation.
Figure 6. Change in the prediction of CEC
Figure 7. Change in the prediction of DEC
Figure 8. Change in the prediction of LF
Figure 9. Change in the prediction of GCF
Figure 10. Change in the prediction of TI