## 4 Results
Policymakers could encourage more FDI in green technologies and sustainable industries to amplify this effect. By creating incentives for foreign investors to invest in renewable energy, clean technology, and energy efficiency, India could further leverage FDI to achieve greater reductions in \(CO_{2}\) emissions. The effectiveness of FDI in reducing \(CO_{2}\) emissions also depends on how well it is integrated with domestic environmental policies. For instance, if FDI is supported by strong environmental regulations, incentives for green technologies, and a commitment to sustainable development, its impact on reducing \(CO_{2}\) emissions could be enhanced. From Table 8 one can see that the ECT is highly significant and negative (\(-1.42\)), which confirms that any short-run deviations from the long-run equilibrium are corrected by 142% in the next period. This strong adjustment speed indicates a rapid convergence to the long-run equilibrium when \(CO_{2}\) emissions deviate from their long-run relationship with the explanatory variables. The positive and significant coefficient of D(GPP), 186.36, indicates that, in the short run, increases in GDP lead to higher \(CO_{2}\) emissions. This is consistent with the initial stages of economic growth, where higher production and consumption generally result in greater emissions. The notation D denotes the first differences of the variables included in the ECM-ARDL model. For example, D(\(CO_{2}\)) represents the first difference of the \(CO_{2}\) variable, indicating changes in \(CO_{2}\) emissions relative to the previous period. Similarly, D(GDP), D(GDP2), and D(GDP3) reflect changes in gross domestic product and its higher-order forms (e.g., squared and cubed) to capture the non-linear relationship between economic growth and \(CO_{2}\) emissions (as per the EKC framework). The use of first differences is necessary to ensure the stationarity of time series, which is an important condition in ARDL models. Lagged differences, such as D(\(CO_{2}(-1)\)), D(GDP(\(-1\))), etc., capture the delayed effects of these variables on the short-run outcome. Essentially, these variables, referred to as D variables, represent the rates of change compared to the previous period. The negative coefficients of D(GDP2) and D(GDP2(\(-1\))) imply that, as GDP continues to increase, the rate of increase in \(CO_{2}\) emissions diminishes. This suggests the beginning of a turning point in the EKC. The positive coefficient of D(GDP3) and the significant coefficients on its lags highlight the non-linear relationship between GDP and \(CO_{2}\) emissions. The cubic term reinforces the N-shaped EKC, where, after a certain point, \(CO_{2}\) emissions begin to rise again as GDP continues to increase. The coefficient of D(RENC) is strongly negative (\(-0.86\)) and highly significant, indicating that increases in renewable energy consumption contribute to a reduction in \(CO_{2}\) emissions in the short run. This demonstrates the effectiveness of renewable energy in mitigating emissions. The lags D(RENC(\(-1\))) and D(RENC(\(-2\))) show mixed effects, with a significant negative impact at lag 1 and a slight positive correction at lag 2, possibly reflecting the time it takes for the benefits of renewable energy investments to materialize fully. The short-run coefficient of D(ACEL) is positive, suggesting that an increase in access to electricity initially leads to higher \(CO_{2}\) emissions, likely due to increased energy consumption. The large positive coefficients for D(ACEL(\(-1\))) and D(ACEL(\(-2\))) imply a continued rise in emissions as electricity access improves, indicating that, as more people gain access to electricity, there is a significant increase in energy demand, often met by fossil fuel sources.