## 5 Conclusions  
Analysis of the impact of FDI, GDP per capita, renewable energy consumption, and urbanization on \(CO_{2}\) emissions in India revealed the existence of an N-shaped EKC. This complex shape suggests that, as GDP increases, \(CO_{2}\) emissions initially rise, peak, and then decline, before rising again at higher levels of GDP. This behavior reflects India's economic transition from intensive industrialization to the adoption of cleaner energy sources and increased energy efficiency. In the early stages of economic growth, India is experiencing significant increases in \(CO_{2}\) emissions due to intensification of industrial activities and rapid urbanization. This growth is fueled by a significant reliance on fossil fuels, particularly coal, to meet energy demand. However, with the increase in GDP and the development of more sustainable energy policies, a downward trend in emissions is observed, suggesting improved energy efficiency and wider use of renewable energy sources. An important aspect of this study is the role of renewable energy consumption and access to electricity in reducing \(CO_{2}\) emissions. The results show that an increase in renewable  
Figure 3: Plot of CUSUMSQ for coefficients’ stability of ARDL model at 5% level of significance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Diagnostic Test** & \(\mathbf{H_{0}}\) & \begin{tabular}{c} **Decision** \\ **Statistics [_p_-Value]** \\ \end{tabular} \\ \hline \(\chi^{2}\) SERIAL & \
\begin{tabular}{c} There is no serial correlation \\ in the residuals. \\ There is no autoregressive \\ conditional heteroscedasticity. \\ \end{tabular} &
\begin{tabular}{c} Accept \(H_{0}\) \\ 0.01 [0.91] \\ Accept \(H_{0}\) \\ 1.31 [0.51] \\ Accept \(H_{0}\) \\ 1.34 [0.12] \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Diagnostic and stability test results for India’s ARDL model. energy consumption has a significant impact in reducing emissions in the long term. This underscores the importance of investing in renewable energy infrastructure and promoting these sources in India's energy mix. Also, expanding access to electricity, especially in rural areas, helps reduce emissions by replacing traditional energy sources such as wood and kerosene with cleaner and more efficient sources. As for FDI, it has a dual impact on \(CO_{2}\) emissions. In the short term, FDI can help increase emissions by financing energy-intensive sectors. However, in the long run, FDI brings more advanced technologies and more efficient production practices that can reduce emissions. To maximize the benefits of FDI in the context of sustainability, it is essential that policies encourage investment in green technologies and less polluting economic sectors. It is essential to acknowledge the possible limitations of any scientific study. Initially, our investigation concentrates on a particular set of variables. The model does not account for other critical factors, including government policies, technological advancements, or global energy market dynamics, despite their potential to significantly influence \(CO_{2}\) emissions. Future research should expand the current analysis by incorporating additional variables, such as government policies, technological advancements, and global energy price dynamics, which are critical in shaping \(CO_{2}\) emissions trends. Furthermore, examining regional disparities within India (e.g., urban vs. rural areas) can provide insights into how localized energy policies and infrastructure impact emissions differently. Comparative studies with other developing economies, such as Brazil, Indonesia, and China, could offer a broader perspective on how economic growth, energy consumption, and urbanization influence environmental sustainability. An important extension of this study would be to analyze the role of sector-specific FDI and how investments in green technologies or energy-intensive industries influence \(CO_{2}\) emissions over time.