4.1. Descriptive Statistics Analysis
We have started our analysis with descriptive analysis. The results can be inferred from Table 2. The positive skewness values for all the variables indicate that an increased trend is present in all six-time series. The high mean value for EPF shows that India relies on fossil fuels for a majority of its electricity production followed by renewable sources and nuclear sources. In the next step, we conducted the stationary test to avoid any spurious relationship among them.
[Insert Table 1 Here]
4.2. ADF Unit Root Test
Before performing the Augmented Dickey-Fuller (ADF) unit root tests, the most suitable lag duration was calculated using the Akaike Information Criterion (AIC). The lag length that yielded the best results was determined to be eight. Subsequently, the Augmented Dickey-Fuller (ADF) tests were applied to each of the variables that had been converted using logarithmic functions in a systematic manner. The findings of this study are displayed in Table 2.
[Insert Table 2 Here]
At the level (I(0)), all variables exhibit non-stationarity. This observation is aligned with the common characteristics of economic and environmental time series data, where non-stationarity at the level is frequently observed (Enders, 2014). Upon differencing the variables, they all show strong evidence of stationarity. The presence of non-stationarity at the level and stationarity after the first difference indicates that each of these variables is integrated into order one, denoted as I(1). This attribute is crucial in determining the selection of econometric modelling methods and is consistent with the ideas described in Hamilton (1994). It implies that while the levels of these series exhibit random walks, their changes over time are mean-reverting, making them suitable for analysis using techniques that accommodate integrated variables, such as error correction models or cointegration analysis, as discussed in Engle and Granger (1987), and reinforced by Johansen (1995).
4.3. Johansen Cointegration Test
The Johansen test is pivotal in time series analysis, particularly in the context of multivariate systems where long-term relationships among variables are of interest. It allows for the determination of the number of cointegrating vectors in a non-stationary time series dataset, indicating long-term equilibrium relationships among the variables. The importance of this step is underscored by its ability to discern whether individual non-stationary time series move together over time, a critical aspect in understanding the dynamics of economic and environmental systems (Johansen, 1991; Engle & Granger, 1987).
[Insert Table 3 Here]
[Insert Table 4 Here]
The Trace test results indicate the rejection of the null hypothesis for the presence of no cointegrating equation and suggest two cointegrating equations at the 5% significance level. Similarly, the Max-Eigenvalue test suggests the presence of one cointegrating equation at the 5% significance level. These results are indicative of at least one, possibly two, long-term stable relationships among the variables thus confirming the existence of cointegration among these variables which suggests that any short-term deviations among these variables are corrected over time, bringing the variables back to a long-term equilibrium state.
4.4. Vector Error Correction Model
All variables under consideration became stationary at the first difference. The Johansen cointegration test indicated the presence of cointegrating relationships among these variables. Given these two conditions - stationarity at first differences and cointegration - the Vector Error Correction Model (VECM) becomes an appropriate econometric approach. VECM is specifically designed for use with multiple, cointegrated time series data. It captures both the short-term dynamics and the long-term relationships among the variables. In a VECM framework, the short-term adjustments towards the long-term equilibrium are explicitly modeled through the error correction term (Banerjee et al., 1993). Besides, multivariate causality can easily be inferred.
[Insert Figure 1 Here]
4.4.1. Error Correction Term
The results of the Vector Error Correction Model developed in this study state that the error correction term [ECT(-1)] is -0.27, i.e. it is negative. Besides, the t-statistic also shows that the ECT(-1) is statistically significant at 95% confidence level. This implies a long-run equilibrium relationship among lnCO2, lnTEC, lnEPF, lnEPN, lnEPR and lnGDP.
4.4.2. Long-Run Cointegrating Relationship
The following table shows the coefficients of the variables in the cointegrating equation which is represented as:
[Insert Table 5 Here]
All the coefficients are found to be statistically significant at the 95% confidence level. This indicates that there each variable on the right-hand side of the cointegrating equation has a long-run equilibrium relationship with lnCO2. Moreover, these coefficients represent that a 1% increase in total energy consumption results in a 0.18% rise in CO2 emissions.; a 1% increase in electricity production from fossil fuels results in a 0.71% increase in CO2 emissions; a 1% increase in electricity production from nuclear sources results in a 0.03% decrease in CO2 emissions; a 1% increase in electricity production from renewable sources results in a 0.07% increase in CO2 emissions; and a 1% increase in GDP results in a 0.19% increase in CO2.
4.5. Granger Causality Test
[Insert Table 6 Here]
In our analysis of Granger causality at a 95% significance level, we observed notable insights into the interplay between various economic and potentially environmental variables. Specifically, the results indicated that CO2 levels or environmental factors (LNCO2) do not precede changes in a financial indicator (LNF), suggesting that environmental changes do not have a short-term predictive impact on this particular financial variable. Additionally, fluctuations in a financial variable (LNF) were found not to be predictors of changes in another economic variable (LNN), indicating a lack of immediate influence of financial changes on this economic parameter. Furthermore, our findings revealed that changes in an economic or social variable (LNN) do not lead to short-term impacts on GDP growth (LNGDP), highlighting the complexity in the relationship between social/economic factors and macroeconomic growth. Finally, the analysis showed that GDP growth (LNGDP) does not predict short-term changes in a resource-related or environmental variable (LNR), which could be significant in understanding the lagged effects of economic growth on environmental or resource parameters. These results underscore the multifaceted nature of the relationships between environmental, financial, and economic variables, emphasizing the necessity for long-term planning and comprehensive policy formulation to address the intricate dynamics between these factors.
[Insert Table 7 Here]
In our exploration of the Granger causality relationships at a 90% significance level, we discerned several intriguing dynamics among different economic indicators. Firstly, we found that economic conditions, as indicated by lnTEC, do not have a short-term predictive relationship with CO2 levels or environmental factors represented by lnCO2. This observation suggests a degree of independence in the short-term evolution of these two variables. Intriguingly, CO2 levels or environmental factors (lnCO2) were observed not to be predictors of short-term changes in another economic or social variable (lnEPN), indicating a potential disconnect or lag in their influence on these factors. Additionally, our results showed that GDP growth (lnGDP) has a significant short-term influence on CO2 levels (lnCO2), implying a closer, more immediate relationship between economic growth and environmental changes. The reverse relationship, where economic conditions (lnTEC) predict changes in a financial variable (lnEPF), further highlights the nuanced interplay between broader economic conditions and specific financial indicators. Moreover, the finding that GDP growth (lnGDP) does not predict short-term changes in lnTEC, while lnTEC can predict changes in lnGDP, suggests a complex, bidirectional relationship between overall economic health and GDP growth. These insights are crucial for understanding the immediate impacts and feedback loops within the economic system, particularly in the context of environmental, financial, and broader economic variables, and emphasize the need for policies that consider these intricate relationships in both the short and long term.
4.6. Variance Decomposition Analysis
The above analysis represents the variance decomposition results derived from the Vector Error Correction Model which provides insights into the relative importance of the variables in explaining the forecast error variance of CO2 emissions (lnCO2) over different time horizons. The increasing standard error (S.E.) across periods reflects the diminishing predictability of the model with the extension of the forecast horizon.
[Insert Table 8 Here]
Initially, at period 1, the forecast error variance of lnCO2 is entirely explained by its own shocks, indicating the predominant influence of the variable's immediate past values. This observation aligns with the expectation that in the short run, a variable is largely influenced by its own lags. As the analysis progresses through subsequent periods, a gradual decline in the percentage contribution of lnCO2’s own shocks to its variance is observed. This decline is accompanied by an incremental increase in the contribution of other variables, notably lnTEC (total energy consumption), to the forecast error variance of lnCO2. This shift suggests that as we move further away from the immediate past, the influence of total energy consumption on CO2 emissions becomes more pronounced. Furthermore, the contributions of lnEPF (electricity production from fossil fuels), lnEPN (electricity production from nuclear sources), lnEPR (electricity production from renewable sources), and lnGDP (Gross Domestic Product) to the variance of LNCO2, though relatively modest in comparison to LNEC, are not negligible. These contributions gradually increase over time, highlighting the growing importance of various types of energy consumption and economic activity in explaining long-term CO2 emissions trends.
4.7. Model Diagnostics
The research examines the independence of the residuals by conducting tests for VEC residual serial correlation, VEC residual heteroskedasticity, and VEC residual normality. These tests aim to determine the reliability and strength of the VEC model used in the study. The subsequent tables provide a concise overview of the outcomes of all these examinations. At a 5% level of significance, the absence of serial correlation in the residuals at the given lag of the Breusch-Godfrey test, that is, the null hypothesis, cannot be rejected. Similarly, the null hypothesis that the residuals exhibit a consistent variance, as tested by the Breusch-Pagan-Godfrey test, cannot be rejected at a significance level of 5%. The null hypothesis of the Jarque-Bera test, which asserts that the residuals have a normal distribution, cannot be rejected at a significance level of 5%. The aforementioned results collectively demonstrate the robustness of the created model.