## 4 Empirical Results and Discussion
### The Indirect Effects of Crude Oil Price Shocks  
The result of Section 3.1 is the response value of each price index to crude oil shocks. After a positive shock in crude oil price, not all of the price indices are directly influenced. Since there are transmission relationships among price indices, the crude oil price shocks could further impact more price indices. For example, crude oil price fluctuation can transmit to PPI by influencing the price of industrial raw materials, and due to the supply-demand relations, the fluctuation of the PPI could further impact consumer prices, such as CPI. In this paper, we define that there is an indirect impact from crude oil to CPI. Moreover, since the direct impacts vary over time, the indirect effects also change over time. Thus, we calculate the indirect impact of crude oil price shocks on price indices based on Section 3.2.2. The indirect impacts of the shocks of four kinds of crude oil prices on price indices from the second month to the fifteenth month are shown in Appendix A. To offer more detailed and finer observations on the indirect impacts over time, we abstract the indirect effects from the second month to the sixth month and draw Figure 4. It can be concluded that the evolution trends of the indirect effects are different from those of the direct effects. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Brent** & **WTI** & **Dubai** & **Daqing** \\ \hline MPI & 1.2850 & 1.2756 & 1.3224 & 1.3324 \\ EPI & 2.1980 & — & 2.1220 & 1.9811 \\ CGPI & 0.6007 & — & 0.6339 & 0.5207 \\ PPI & 0.4994 & — & 0.4767 & — \\ PPIRM & 0.6588 & — & 0.6372 & — \\ RPI & 0.2940 & 0.2729 & 0.2885 & 0.2931 \\ CPI & — & — & — & — \\ MAPPI & — & — & — & — \\ \hline \end{tabular} Note: “—” means that the corresponding price index could not be directly impacted by crude oil price shocks.  
\end{table} 
Table 1: The total direct impacts on each price index. For MPI, the indirect impacts of oil price shocks are positive (Figure 4). The indirect impacts of Brent, WTI, Dubai, and Daqing reach a peak of 0.3031, 0.0630, 0.2646, and 0.1348, respectively, in the second month, meaning a positive shock of one standard deviation in the four crude oil prices has an indirect positive impact on MPI in the second month, with values of 0.5469, 0.3875, 0.4772, and 0.4654, respectively. The indirect impact could last for only two months. For EPI, in the second month, the impacts of Brent and Dubai are positive, while the impacts of WTI and Daqing are negative. The indirect impacts of four kinds of crude oil price shocks are positive in the third month with a peak of 0.1981, 0.0409, 0.1729, and 0.0887, respectively. However, the indirect impacts turn negative in the fourth month, after which the impacts die out. For CGPI, only Daqing crude oil price fluctuations could indirectly affect it, and the impacts are too small that they could be ignored. For PPI and PPIRM, Brent and Dubai crude oil price fluctuations could only affect them in the second month with the impact degree exceeding 0.044. Although Daqing could influence them in the long run, the impacts are small. Thus, the duration of the indirect impact of crude oil price shocks on PPI and PPIRM is only one month. Furthermore, the indirect impacts on RPI are the largest in the second month, and the impacts could last until the fourth month. Through analyzing the indirect effects, we find that some price indices that are not directly affected by crude oil price shocks are indirectly impacted, such as CPI and MAPPI. For MAPPI, Brent and Dubai crude oil price fluctuations could only indirectly affect it in the second and third months. Although a positive shock to Daqing oil price could indirectly affect MAPPI for a long period, the impacts are small after the third month and can be ignored. For CPI, the impacts of the shocks of four oil prices are significant only in the second month, with a value of less than 0.0310.