# Temporal Convolutional Network for Carbon Tax Projection: A Data-Driven Approach
## 4 Results and Discussion
### Feature Importance Analysis  
We conducted a feature importance analysis using permutation importance to understand the relative impact of different input variables on the model's predictions. Table 5 presents the results of this analysis. As shown in Table 5, while historical carbon prices were the most significant predictor (importance score of 0.42), economic indicators such as GDP (0.23) and energy consumption patterns (0.19) also played crucial roles in the model's predictions. This underscores the complex interplay of factors influencing carbon tax prices and highlights the TCN model's ability to capture these multifaceted relationships. The feature importance analysis revealed several key insights: (1) Historical price dependency: The high importance of historical carbon prices (0.42) suggests that past pricing trends are the strongest predictor of future prices. This aligns with the general principle in time series analysis that recent past values are often the best predictors of future values. (2) Economic influence: The significant importance of GDP (0.23) indicates that overall economic conditions play a crucial role in determining carbon tax prices. This could reflect the influence of economic growth on energy demand and carbon emissions, as well as the political feasibility of implementing higher carbon taxes in different economic contexts. (3) Energy sector dynamics: The relatively high importance of energy consumption (0.19) highlights the close relationship between energy use patterns and carbon pricing. Changes in energy consumption, potentially driven by efficiency improvements or structural changes in the economy, appear to have a substantial impact on carbon tax trajectories. (4) Emissions feedback: The moderate importance of CO\({}_{2}\) emissions (0.11) suggests that there is some feedback between actual emission levels and carbon tax rates. This could reflect policymakers' responsiveness to emission trends when setting carbon prices. (5) Renewable energy transition: The lower importance of renewable energy share (0.05) is somewhat surprising. It may indicate that short-term fluctuations in renewable energy adoption have a limited direct impact on carbon tax rates, though the long-term \begin{table}
\begin{tabular}{l c} \hline \hline
**Feature** & **Importance Score** \\ \hline Historical carbon prices & 0.42 \\ GDP & 0.23 \\ Energy consumption & 0.19 \\ CO\({}_{2}\) emissions & 0.11 \\ Renewable energy share & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Feature importance analysis results. trend towards renewables likely influences policymakers' decisions indirectly through other channels. These findings have important implications for policymakers and stakeholders in the carbon pricing domain: (1) Policy stability: The high importance of historical prices suggests that policy stability and predictability in carbon tax rates could lead to more accurate long-term projections, potentially reducing uncertainty for businesses and investors. (2) Economic considerations: The significant role of GDP in price projections underscores the need for policymakers to carefully consider economic conditions when designing and adjusting carbon pricing policies. (3) Energy policy integration: The importance of energy consumption highlights the need for integrated policy approaches that consider both carbon pricing and broader energy policies. (4) Emissions monitoring: While CO\({}_{2}\) emissions are not the most important feature, their moderate influence suggests that accurate and timely emissions data remain crucial for effective carbon pricing. (5) Long-term planning: The relatively low importance of renewable energy share in short-term predictions should not overshadow its potential long-term impact. Policymakers should consider how the evolving energy mix might influence future carbon tax trajectories.