## 3 Results and Discussion
### Causality Analysis
#### 3.1.3 Short- and Long-Run Granger Causality (GC) Tests  
This study adopted the Granger causality tests to explore how independent or explanatory variables (e.g., GDP per capita, urban population, FDI inflows, literacy rates,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No. of Co-Integrating** & **Hypothesis** & **Trace** & **Maximum Eigenvalue** \\ \hline \(r=0\) & No CE & 86.47 *** & 32.69 * \\ \(r=1\) & At most 1 CE & 53.77 ** & 27.76 \\ \(r=2\) & At most 2 CE & 26.01 & 15.91 \\ \(r=3\) & At most 3 CE & 10.10 & 9.11 \\ \(r=4\) & At most 4 CE & 0.98 & 0.98 \\ \hline \hline \end{tabular} Note: *, **, and *** illustrate the level of significance at 0.1, 0.05, and 0.01 levels, respectively.  
\end{table}
Table 6: Results of [PERSON]’s test of co-integration for model 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dependent Variable: MSW** & & & \\ \hline \multicolumn{3}{c}{**R-Squared Value: 0.86**} & & \\ \hline
**Explanatory Variable** & **Coefficient** & **Standard Errors** & **_t_-Statistics** \\ \hline Constants & 4.85 & 0.92 & 5.29 \\ GDPPC & 0.0003 & \(8.47\times 10^{-5}\) & 3.09 \\ UPOP & \(5.07\times 10^{-6}\) & \(1.39\times 10^{-6}\) & 3.66 \\ FDI & \(-1.22\times 10^{-10}\) & \(3.91\times 10^{-11}\) & \(-3.12\) \\ LR & -0.096 & 0.08 & \(-1.15\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Co-integrating equation for model 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dependent Variable: ISW** & & & \\ \hline
**R-Squared Value: 0.90** & & & \\ \hline
**Explanatory Variable** & **Coefficient** & **Standard Errors** & **_t_-Statistics** \\ \hline Constants & \(-1.57\) & 2.48 & \(-0.63\) \\ GDPPC & 0.001 & 0.0003 & 3.96 \\ UPOP & \(4.34\times 10^{-6}\) & \(5.2\times 10^{-6}\) & 0.82 \\ FDI & \(1.67\times 10^{-10}\) & \(1.29\times 10^{-10}\) & 1.29 \\ UR & \(-1.18\) & 1.69 & \(-0.69\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Co-integrating equation for model 2.  
and unemployment rates) are contributing to CH\({}_{4}\) emissions from municipal and industrial solid wastes both in the short-run and long-run. One of the advantages of Granger causality tests is that they examine the direction of causality between the dependent and independent variables. F-statistics were used to understand the significance of variables to cause an event in the short-run while _t_-statistics were used for long-run causality tests [41]. Tables 9 and 10 present the results of short- and long-run causality tests for models 1 and 2, respectively.  
The results of the Granger causality test for model 1 showed that GDP per capita, urban population, and FDI inflows had both short- and long-run causal relationships with municipal solid waste emissions and these relationships are significant at 0.001 level (Table 9). In contrast, only GDP per capita had a short- and long-run causal relationship with industrial solid waste emissions (Table 10). The Granger causality test of Model 1 showed that there was a unidirectional short-run causal relationship running from GDP per capita to urban population, FDI inflows, and literacy rate. It also showed that literacy rates caused FDI inflows in the short run. Municipal solid waste emissions had a bi-directional short-run causal relationship with urban population and FDI inflows. This implies that the urban population and FDI inflow cause emissions in the short-run, and vice versa. The results of the Granger causality test for model 2 are presented in Table 10. The results show that GDP per capita had a bidirectional causal relationship with both urban population and FDI inflows in the short run. Results also showed that the unemployment rate has a causal relationship with urban population while there is a causal relationship running from industrial solid waste emissions to FDI inflows. These findings imply that GDP per capita has a strong- and long-run relationship with both municipal and industrial solid waste emissions and the development of a zero-waste economy is crucial for Saudi Arabia to reduce emissions from the solid waste sector.