## 4 Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lag** & **Loglog** & **LR** & **FPE** & **AIC** & **SC** & **HQ** \\ \hline
0 & 267.89 & NA & \(1.16\times 10^{-16}\) & \(-\)16.83 & \(-\)19.03 & \(-\)19.22 \\
1 & 547.87 & 415.45 & \(4.24\times 10^{-23}\) & \(-\)31.73 & \(-\)29.30 & \(-\)30.61 \\
2 & 599.05 & 52.83 & \(6.28\times 10^{-23}\) & \(-\)31.87 & \(-\)28.22 & \(-\)30.65 \\
3 & 752.25 & 88.95 * & \(4.85\times 10^{-25}\) * & \(-\)38.59 & \(-\)28.76 * & \(-\)32.32 * \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Lag order selection criteria for the VAR model of India’s economic indicators. From Table 7 it follows that a 1% increase in GDP exerts a 53.64% long-term increase in \(CO_{2}\) for India. As India's economy grows, it experiences a surge in industrial activities, particularly in sectors such as manufacturing, construction, and transportation. These industries are often energy-intensive, relying heavily on fossil fuels like coal, oil, and natural gas for production processes. As industrial output expands to meet both domestic and international demand, \(CO_{2}\) emissions naturally increase due to higher consumption of these energy sources. Economic growth in India is also accompanied by rapid urbanization and infrastructure development. The construction of new cities, roads, bridges, and other infrastructure projects requires significant energy inputs, often derived from fossil fuels, leading to a rise in \(CO_{2}\) emissions. The expansion of cities also leads to increased vehicular traffic and energy demand for residential and commercial buildings, further contributing to emissions. Economic growth drives higher energy consumption across all sectors of the economy. As income levels rise, so does the demand for energy-consuming goods and services, such as automobiles, air conditioning, and electronic appliances. In India, where coal is still a dominant energy source for electricity generation, this increase in energy demand directly correlates with higher \(CO_{2}\) emissions. Despite India's efforts to diversify its energy mix by incorporating more renewable sources, fossil fuels continue to play an important role in meeting the country's growing energy needs. Coal, in particular, remains a major energy source due to its abundance and affordability, but it is also the most carbon-intensive, leading to significant \(CO_{2}\) emissions. Developing economies like India often face challenges in upgrading their energy infrastructure to support large-scale renewable energy deployment. This includes the need for investment in grid modernization, energy storage solutions, and the development of efficient energy markets. Until these systems are fully developed, fossil fuels will continue to be a significant part of the energy mix, contributing to higher emissions as the economy grows. A 1% increase in RENC exerts a long-term 1.04% decrease in \(CO_{2}\) in India. The more-than-proportional decrease in \(CO_{2}\) emissions suggests that renewable energy sources in India are particularly effective in displacing carbon-intensive fossil fuels. For instance, when solar, wind, hydro, or biomass energy is used instead of coal or natural gas, the reduction in \(CO_{2}\) emissions is significant. This is likely because renewable energy sources produce little to no \(CO_{2}\) emissions during operation, whereas fossil fuels emit large amounts of \(CO_{2}\) per unit of energy produced. This strong negative relationship underscores the importance of India's renewable energy initiatives. The government's efforts to increase the share of renewables in the energy mix--through investments, subsidies, and regulatory support--are important for achieving long-term reductions in \(CO_{2}\) emissions. The effectiveness of these policies is reflected in the more-than-proportional decrease in emissions as renewable energy consumption increases. Given this significant impact, there is a clear incentive for policymakers to accelerate the adoption of renewable energy.