4.1 Descriptive statistical analysis of data
The data used in this article are from January 2014 to December 2019. We used the average of each month to fill in the missing data, thus obtaining 72 time series data points. Fig. 1 shows the trend graph of the transaction price of Tianjin carbon emissions trading. Before December 2015, because the Tianjin carbon emissions trading market was in the early stage of development and the rules and regulations were not perfect, the price of carbon trading often fluctuated sharply (Gong, 2019). Most of the carbon allowances in the Tianjin carbon trading market belong to large enterprises (especially power companies). Therefore, carbon trading prices are susceptible to fluctuations due to the performance period of the enterprises. In addition, the Tianjin carbon trading pilot market is dominated by allowance trading, supplemented by CCER trading. The quota trading is mainly concentrated around June each year to complete the transaction and fulfill the contract, while CCER only began to enter the carbon trading market in early 2015, and is subject to various restrictions such as regional restrictions, time restrictions, and technical type restrictions, and is often suspended by exchanges. , Resulting in extremely fragmented CCER trading prices, so the early Tianjin carbon emissions trading prices often fluctuate sharply. At the same time, the Tianjin carbon trading market is mainly based on the primary market and lacks price linkage with the secondary market. The government rather than the market plays a leading role in the Tianjin carbon trading market. Therefore, in different periods, carbon trading prices in the Tianjin market are quite different. After December 2015, the Tianjin carbon emissions trading market has developed more and more perfect in all aspects. Therefore, except for the three periods from May 2016 to September 2016, July 2017 to August 2017, and April 2018 to June 2018, the carbon trading prices in other periods are relatively stable.
The descriptive statistical results of each time series are shown in Table 2. The null hypothesis of the normal distribution is strongly rejected by all-time series through the Jarque-Bera test.
4.2 Test of the model establishment
This paper uses a co-integration test to determine whether there is a long-term equilibrium relationship between carbon market prices and driving factors. First of all, to guarantee the VAR model is effective and avoid the phenomenon of ‘false regression’, we first perform unit root tests on the research problem's relevant data to test its stationarity. As displayed in Table 3, to test the stationarity of all the variables to be studied, the unit root method is used (Carbon, AQI, Industrial, PMI, Coal). The test results show that the sequence is stationary after the first-order difference. When building the VAR model, we use the first-order difference sequence. Therefore, a multiple linear regression model of carbon emission trading price, Industrial, AQI, coal, and PMI can be introduced. The multiple linear regression model is shown below:
where t represents the month t of the research period and ε is the error term.
The Johansen cointegration technique is used to determine whether it is possible to consider the above multiple linear regression model as a long-term balance relationship. The test results are shown in Table 4. The findings show that the price of the carbon market and different driving factors reject the null hypothesis that there is no co-integration relationship at the 5% significance level. The results of the Granger causality test are shown in Table 5. The results revealed that the price of Tianjin carbon emission trading price was not only significantly affected by coal prices, but also by air quality and industrial development status.
In building the VAR model, we focus on selecting the variables with strong correlation and the final lag oder to reflect the variables' influence. Through the above test, it can be understood that each variable has a certain degree of stability. As shown in Table 6, combine the test results of SC, LR, FPE, AIC, and HQ and choose the column's lag order with most asterisks. If the two columns have the same number of asterisks, then select the lag order with the smaller AIC, then the VAR model's optimal lag period can be selected as 1.
Fig. 2 demonstrates the results of the VAR model's AR root test consisting of five variables. The AR root test indicates that the unit circle contains all the characteristic roots, demonstrating that the model has good stability. A VAR model with five variables is therefore established, and the overall model fit is good.
4.3. Impulse response analysis
A variable's impact affects its modifications and affects other related variables, using the VAR model's dynamic structure as a medium. After taking AR roots for testing, the reciprocal of all root moduli of the estimated VAR model was less than 1 (we're located in the unit circle), which indicated that it is stable and verified the validity of the results. This article sets the response time length to 50 days based on VAR stability and analyses the impulse response function with a 95 percent confidence interval, and the results are shown in Fig. 3. In the tiny graph in Fig. 3, the horizontal axis represents the impact action period of hysteresis, and the vertical axis represents the degree of the impulse response. The solid line represents the function of the impulse response which is the response of the price of the Tianjin carbon allowance to its price, Shanghai Stock Exchange Industrial Index, Coal Price Index, AQI, and PMI, and the dotted line represents the deviation band of the positive response and the negative response.
Based on the Tianjin carbon emission trading price's impulse response, it can be seen that the price of carbon emission trading is most affected by itself and PMI. The Shanghai Stock Exchange Industrial Index and AQI have the second-highest impact, and the coal price has the least impact on Tianjin carbon emission trading price. Among them, the Shanghai Stock Exchange Industrial Index and PMI harm the Tianjin carbon emission trading price, and the coal price and AQI have a positive impact on Tianjin carbon emission trading price. As shown in Fig. 3a, the pluse of Tianjin carbon emission trading price had the greatest impact on itself in the current period. It was gradually weakened and reached an equilibrium state in the 43rd period, indicating that Tianjin carbon emission trading price is more sensitive to its impact. The results in Fig. 3b demonstrated that a standard deviation of the Shanghai Stock Exchange Industrial Index will cause carbon emission trading price to fall within 3 days and gradually increase from the 3rd day to the 27th day, reaching equilibrium on 27 days, with a change rate of 0. This shows that industrial development fluctuations will be transmitted to the price of carbon emission trading in Tianjin within a relatively short period. Still, the impact will become smaller and smaller as time goes by, until it disappears. It can be seen from Fig. 3c that a change in the standard deviation of the coal price will cause a slight increase in Tianjin carbon emission trading price, a slight increase in the first three days, a decrease from the third day, and a return to the initial price on the seventh day. It remains unchanged thereafter. This shows that the impact of coal prices on the Tianjin carbon emission trading price is very small and short-lived and can be ignored. As depicted in Fig. 3d, the impact of a standard deviation of air quality will cause a short-term decline in Tianjin carbon emission trading price within one day, with a decrease of 0.15% and then a sharp rise reaching the maximum on the fourth day. The increase was 0.4%, and then began to decline, and fell to 0 within 30 days and remained unchanged. This shows that the Tianjin carbon emission trading price responds very quickly to changes in air quality. Fig. 3e demonstrate the response of the Tianjin carbon emission trading price on the impact of PMI changes. The carbon emission trading price declined rapidly when it was impacted by the change in PMI and continued to decrease from the 2nd to the 9th day. It gradually increased after the 9th day and returned to the initial value on about the 42nd day, indicating that economic fluctuations will immediately be transmitted to the Tianjin carbon emission trading price and have a long-lasting impact on the carbon trading price.
4.4. Variance decomposition
This study examines the influencing factors of the trading price of carbon emissions in Tianjin, so this study only carry out variance decomposition analysis on the Tianjin carbon emission trading price. Based on the analysis of variance decomposition, we explained how each variable affects Tianjin carbon emission trading. We can determine the contribution of each structural impact on endogenous variables by analysing variance decomposition, and then we can evaluate the importance of various structural impacts.
From the results of variance decomposition (Table 7), we can see that with the gradual decrease of variance contribution, the contribution rate of Tianjin carbon emission trading price to its price changes is declining, but the price of Tianjin carbon emission trading is mainly affected by its historical price. In addition to the Tianjin carbon emission trading price itself, the impact of industrial development has contributed the most to changes in Tianjin carbon emission trading price, followed by economic, air, and carbon price impacts. The variance decomposition results are greater than and stabilized since the seventh period.