The Impact of Financial Development and Economic Growth on Renewable Energy Supply in South Africa
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4.4. Final Model Interpretation—Long-Run Relationship
Table 6 represents the final model with only the statistically significant explanatory variables with p-values below 0.05. There were several iterations of the model until only significant variables remained. The model depicted below was tested for robustness by applying various model diagnostic tests. The diagnostic test results revealed that the model is free from multicollinearity, autocorrelation, and heteroscedasticity. In addition, it is normally distributed and demonstrates a lack of coefficient unsteadiness.
The null hypothesis of insignificance is tested by means of using the p-value of each beta coefficient and a 95% confidence level is used to reject the null hypothesis. Thus, if the p-value is below 0.05 the null hypothesis of insignificance is rejected. The results presented above reveal that the p-value for financial development in the current period is 0.000, which is below 0.05, resulting in the null hypothesis being rejected. In other words, financial development in the current period significantly impacts renewable energy supply. An increase in financial development in the current period results in a 0.034 percentage increase in renewable energy supply, keeping all else constant. This indicates that financial development in the current period has a positive and significant impact on renewable energy supply in the long run.
The results for financial development two periods back reveal that the p-value is 0.010, which is below 0.05, therefore resulting in the null hypothesis being rejected. In other words, financial development two periods back significantly impacted renewable energy supply. However, unlike the results for financial development in the current period, financial development two periods back had a negative coefficient of −0.012, suggesting that it has a negative impact on renewable energy supply. Therefore, an increase in financial development two periods back results in a 0.012 percentage decline in renewable energy supply, keeping all else constant. This indicates that financial development two periods back had a negative and significant impact on renewable energy supply in the long run.
The p-value for economic growth two periods back is 0.029, which is below 0.05, therefore the null hypothesis is rejected. In other words, economic growth two periods back significantly impacted renewable energy supply. An increase in the production of economic goods and services in South Africa results in a 12.576 percentage increase in renewable energy supply, keeping all else constant. This indicates that economic growth two periods back had a positive and significant impact on renewable energy supply in the long run.
Similar to the results for financial development two periods back, the p-value for coal electricity supply is 0.000, which is below 0.05, resulting in the null hypothesis, that coal electricity supply does not significantly impact renewable energy supply, being rejected. An increase in the coal electricity supply results in a decline in renewable energy supply by a 0.831 percentage change, keeping all else constant. This indicates that coal electricity supply negatively and significantly impacts renewable energy supply in the long run.
The p-value for load shedding levels is 0.003, which is below 0.05, resulting in the null hypothesis that load shedding levels do not significantly impact renewable energy supply being rejected. A GWh increase in the demand deficit of coal electricity supply represented as load shedding in the current period results in a 0.001 percentage change in renewable energy supply, keeping all else constant. This indicates that load shedding levels in the current period positively and significantly impact renewable energy supply in the long run.
The adjusted R-squared of the model is reported at a coefficient of 0.935, which indicates that the explanatory variables in this model explain renewable energy supply at a 93.5% magnitude. These results indicate that the explanatory variables in the model strongly explain renewable energy supply, as only 6.5% is not explained by these variables.
4.5. Diagnostic Tests
The study performs various diagnostic tests on the model that only include statistically significant variables to assess its robustness. The diagnostic tests performed are multicollinearity, autocorrelation, heteroscedasticity, normality, and model parameter stability tests.
4.5.1. Multicollinearity Test
The assumption is that the model for the study has no multicollinearity. Therefore, this diagnostic test intends to confirm this assumption. Whether the correlation is positive or negative, a correlation coefficient of 0.9 or more is considered a high correlation [37]. Presented in Table 7 are the multicollinearity test results that reveal that none of the independent variables employed for this study are highly correlated as they all have a coefficient lower than 0.9.
4.5.2. Autocorrelation Test
Table 8 presents the results of the Breusch–Godfrey serial correlation LM test performed to determine whether a serial correlation exists within the model:
Employing the Breusch–Godfrey LM test, the null hypothesis that the model has no serial correlation is tested. The serial correlation test results reflect that the chi-square’s probability value is greater than 0.05, as it is 0.205. This suggests that the null hypothesis can be accepted, and it can be concluded that the residuals in the model do not possess serial correlation.
4.5.3. Heteroscedasticity Test
Table 9 presents the results of the heteroskedasticity test, performed to determine whether heteroskedasticity exists within the model:
Employing the Breusch–Pagan–Godfrey test, the results of the heteroscedasticity test reflect that the probability value of the chi-square is greater than 0.05, as it is 0.104. This indicates that the null hypothesis that the model is free from heteroscedasticity can be accepted. Therefore, it can be confirmed that the residuals in the model have homoscedasticity.
4.5.4. Normality Test
Table 10 presents the results of the test performed to determine whether the series in the model are normally distributed or not:
The results reveal that the probability value of the Jarque–Bera test is greater than 0.05, as it is 0.805. This indicates that the null hypothesis that the model is normally distributed can be accepted. Therefore, it can be concluded that all series in the model are normally distributed.
4.5.5. Model Parameter Stability Test
Figure 3 below presents the results of the CUSUM and CUSUMSQ tests performed to determine the parameter stability of the model:
The CUSUM and CUSUMSQ statistic distribution is within the 5% significance intervals, crucial ranges for parameter stability. This demonstrates the lack of any coefficient unsteadiness, attesting to the robustness of every coefficient in the model.
4.6. Short-Run Relationship
Table 11 presents the results of the short-run relationship test.
The null hypothesis is that the variables in the model do not explain and impact renewable energy supply in the short run. The null hypothesis is rejected if the p-value is below 0.05, which indicates that the variable explains and has an impact on renewable energy supply in the short run. However, if the p-value is above 0.05, the null hypothesis is accepted that the explanatory variable does not explain and impact renewable energy supply in the short run. The ECM results reveal that none of the variables employed for the study in their current period impact renewable energy supply in the short run.
Renewable energy supply two periods back has a p-value of 0.398. The p-value is above 0.05. Therefore, the null hypothesis is accepted, and it can be concluded that this variable does not have a statistically significant impact on renewable energy supply in the short run. These results are consistent with those revealed in the final model of the long-run relationship, where renewable energy supply was insignificant one and two periods back.
One and two periods back, financial development has a p-value of 0.002 and 0.006, respectively. The p-values are below 0.05. Therefore, the null hypothesis is rejected, and it can be concluded that these variables have a statistically significant impact on renewable energy supply in the short run. An increase in financial development one and two periods back results in an increase in renewable energy supply by 0.027 and 0.013 percentage points, respectively, keeping all else constant. The results reveal that financial development both one and two periods back positively and significantly impacts renewable energy supply in the short run. In contrast, financial development two periods back negatively and significantly impacts renewable energy supply in the long run, while financial development one period back is insignificant.
Economic growth one and two periods back has a p-value of 0.201 and 0.044, respectively. The p-value for economic growth one period back is above 0.05. Therefore, the null hypothesis is accepted. However, economic growth two periods back has a p-value below 0.05, which indicates that the null hypothesis can be rejected. It can be concluded that economic growth one period back does not have a statistically significant impact on renewable energy supply in the short run. However, economic growth two periods back has a positive and statistically significant impact on renewable energy supply. An increase in the production of economic goods and services in South Africa results in a 10.999 percentage increase in renewable energy supply in the short run, keeping all else constant. These results are consistent with those revealed in the final model of the long-run relationship, where economic growth two periods back positively and significantly impacts renewable energy supply.
CO2 emission by coal power generation one and two periods back has p-values of 0.610 and 0.159, respectively. The p-values are above 0.05, therefore the null hypothesis is accepted, and it can be concluded that these variables do not have a statistically significant impact on renewable energy supply in the short run. These results are consistent with those revealed in the final model of the long-run relationship, where CO2 emissions by coal power generation in the current period and both one and two periods back are insignificant.
One and two periods back, coal electricity supply has p-values of 0.000 and 0.245, respectively. The p-value for coal electricity supply one period back is below 0.05. Therefore, the null hypothesis is rejected. However, the coal electricity supply has a p-value above 0.05 two periods back, meaning the null hypothesis can be accepted. It can be concluded that the coal electricity supply one period back has a negative and statistically significant impact on renewable energy supply in the short run. However, the coal electricity supply two periods back has no statistically significant impact on renewable energy supply in the short run. An increase in coal electricity supply one period back results in a −0.625 percentage decline in renewable energy supply in the short run, keeping all else constant. These results are inconsistent with those revealed in the final model of the long-run relationship, where coal electricity supply one and two periods back is insignificant.
Coal price changes one and two periods back have a p-value of 0.126 and 0.006, respectively. The p-value for coal price changes one period back is above 0.05. Therefore, the null hypothesis is accepted. However, coal price changes two periods back have a p-value below 0.05, meaning the null hypothesis can be rejected. It can be concluded that coal price changes one period back do not significantly impact renewable energy supply in the short run. However, coal price changes two periods back have a negative and statistically significant impact on renewable energy supply in the short run. An increase in coal price changes two periods back results in a 0.818 percentage decline in renewable energy supply in the short run, keeping all else constant. These results are inconsistent with those revealed in the final model of the long-run relationship, where coal price change variables in the current period and one and two periods back are insignificant.
Load shedding levels one and two periods back have p-values of 0.005 and 0.169, respectively. The p-value for load shedding levels one period back is below 0.05. Therefore, the null hypothesis is rejected. However, load shedding levels two periods back have a p-value above 0.05, meaning the null hypothesis can be accepted. It can be concluded that load shedding levels one period back have a positive and statistically significant impact on renewable energy supply in the short run. However, load shedding levels two periods back have no statistically significant impact on renewable energy supply in the short run. A GWh increase in the demand deficit of coal electricity supply represented as load shedding one period back results in an increase in renewable energy supply by 0.001 percentage points in the short run, keeping all else constant. These results are inconsistent with those revealed in the final model of the long-run relationship, where load shedding levels one and two periods back are insignificant.
The error correction term is −0.760, with a p-value of 0.000. The error correction term is significant as it has a p-value below 0.05. The negative coefficient of the error correction term indicates that should there be a shock in the model, there is an adjustment back to equilibrium. Therefore, it can be concluded that the model possesses significant adjustments, given short-run deviations due to the negative and significant error correction term. The adjusted R-squared of the model is reported at a coefficient of 0.684, indicating that the explanatory variables in this model explain renewable energy supply at a 68.4% magnitude. The adjusted R-squared in the ECM has decreased compared to the long-run relationship results.
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