Since carbon price volatility is critical to the risk management of the CO(2)emissions trading market, research has focused on energy prices and macroeconomic drivers which cause changes in carbon prices and make the carbon market more volatile than other markets. However, they have ignored whether the impact of carbon price determinants changes when the carbon price is at different levels. To fill this gap, this paper applies a semiparametric quantile regression model to explore the effects of energy prices and macroeconomic drivers on carbon prices at different quantiles. The model combines the advantages of parameter estimation, nonparametric estimation and quantile regression to describe the nonlinear relationship between carbon price and its fundamentals, which do not need to make any assumptions about the random error. Carbon prices are high-tailed and exhibit higher kurtosis, the traditional models which tend to assume that data are normally distributed can't perform well. Furthermore, the semiparametric model doesn't need to assume that the data are normally distributed. Therefore, the semiparametric model can effectively model the data. Some new evidence from China's emission trading scheme (ETS) pilots shows that energy prices and macroeconomic drivers have different effects on carbon prices at high or low quantiles. First, the negative impact of coal prices on carbon prices was greater at the lower quantile of carbon prices in the Shenzhen ETS pilot. However, the effects of coal prices were positive in the Beijing ETS pilot, which may be attributed to great demand for coal. Second, oil prices had greater negative effects on carbon prices at higher quantiles in Beijing and Hubei ETS pilots. This can be attributed to the fact that businesses use less oil when carbon prices are high. For the Shenzhen ETS pilot, the effects of oil prices were positive. Third, natural gas prices have a stronger effect on carbon prices as quantiles increased in the Beijing and Hubei ETS pilots. Lastly, the effects of macroeconomic drivers on carbon prices at low quantiles were stronger in the Shenzhen ETS pilots and higher at the medium quantiles in Beijing and Hubei ETS pilots. These findings suggest that the impact of determinants on the carbon prices at different levels is not constant. Ignoring this issue will lead to a missed warning about the risks of the carbon market. This study will be of positive significance for China's emission trading scheme (ETS) pilots, in order to accurately monitor the effects of carbon prices determinants and effectively avoid carbon market risks.
