## 2 Literature Review and Research Question Development
### Research Question Development  
Our research aims to contribute to the carbon-energy correlation literature. We develop combinations of market volatility states in carbon-energy markets and differentiate two cross-market channels: fundamental and volatility spillover. Further, we use our proposed dynamic volatility-correlation relationships to examine the intensity and direction of the volatility spillover effect in carbon-energy markets. Our conjectures are explained as follows: First, as defined in the literature, the fundamental channel is based on real and economic links between the paired markets. Researchers point out three effects: aggregated demand effect, substitution effect, and production restrain effect, supporting the fundamental link. Beyond the fundamental channel, recent studies turn their attention to the volatility spillover effect in carbon-energy markets. Two models may explain the volatility spillover effect. The first model is the cross-market rebalancing model proposed by [PERSON] and [PERSON] [26]. They hypothesize that cross-market shocks occur because investors optimally adjust their investment in one market to respond to shocks in another market. The second model is the social learning model proposed by [PERSON] [27]. He hypothesizes that cross-market contagions occur because investors fear a crisis in one market after observing a crisis in the other market. This study addresses two derivative questions regarding the two cross-market channels. The first question is how does one distinguish the impacts of the two channels (i.e., fundamental and volatility spillover) on carbon-energy correlations? The second question is how does one detect the direction of the volatility spillover channel in carbon-energy markets? We argue that the key to answering the two questions is carbon-energy market volatility conditions. Below, we list our conjectures. First, financial crises go along with high market volatility [28; 29; 30; 31]. Accordingly, we argue that the volatility spillover effect will be maximal when carbon-energy markets encounter a high-volatility condition. Moreover, considering the difference between a low-volatility (LV) and a high-volatility (HV) regime for each market, we may develop a four-volatility-state system for carbon-energy markets: i.e., LV-LV, HV-LV, LV-HV, and HV-HV. Next, we conduct two comparative analyses to answer our two research questions on carbon-energy correlation dynamics. The first comparative analysis is based on the LV-LV versus HV-HV state. The HV-HV state reflects extreme economic and/or financial distresses, causing both carbon and energy markets to experience volatile price movements (4.5% of our test sample, see Table 6). By contrast, the LV-LV state presents the situation when both carbon and energy markets live in a common and non-volatile state (64.54% of our test sample, see Table 6). We argue that the impact of the volatility spillover effect on carbon-energy correlations primarily shows up in the HV-HV state. On the other hand, under the LV-LV state, the carbon-energy correlations are mainly driven by the fundamental channel. Accordingly, the comparative analysis between the LV-LV and HV-HV states may offer a test on the intensity of the volatility spillover effect. To examine the direction of the volatility spillover (the second research question in our study), we conduct a comparative analysis between the other two states: HV-LV versus LV-HV. These two volatility states reflect that only one market (carbon or energy) is experiencing an HV condition. If carbon-energy correlations stimulate when the energy market is under an HV state, it shows that the volatility spillover direction is from the energy market to the carbon market. On the other hand, if we observe a higher carbon-energy correlation when the carbon market faces an HV state, the result implies that the volatility spillover path is from the carbon market to the energy market.