China is a large import and export economy in global terms, and the carbon dioxide emissions and carbon leakage arising from trade have great significance for China’s foreign trade and its economy. On the basis of trade data for China’s 20 industrial sectors, we first built a panel data model to test the effect of trade on carbon dioxide emissions and the presence of carbon leakage for all industrial sectors. Second, we derived a single-region input–output model for open economies based on the industrial sectors’ diversity and carbon dioxide emissions, and performed an empirical test. We estimated the net carbon intensity embodied in export, which is 0.237tCO2/ten thousand RMB, to divide all sectors (ACSs) into high-carbon sectors (HCSs) and low-carbon sectors (LCSs). The results show that higher trade openness leads to a reduction in the intensity of CO2 emissions and gross emissions and that there are obvious structural differences in different sectors with different carbon emission intensity. The coefficient of trade openness for LCSs is −0.073 and is statistically significant at the 1% level, so higher trade openness for LCSs leads to a reduction in the CO2 emissions intensity. However, the coefficient for HCSs is 0.117 and is statistically significant at the 10% level, indicating that higher trade openness increases the CO2 emissions’ intensity for HCSs. The difference is that higher trade openness in LCSs can help reduce the CO2 emissions’ intensity without the problem of carbon leakage and with the existence of the environmental Kuznets curve (EKC), whereas there is no EKC for HCSs and carbon leakage may happen. We introduced dummy variables and found that a “pollution haven” effect exists in HCSs. The test results in HCSs and LCSs are exactly the opposite of each other, which shows that the carbon leakage of ACSs cannot be determined. The message that can be drawn for policy makers is that China does not need to worry about the adverse impact on the environment of trade opening up and should, in fact, increase the opening up of trade, while becoming acclimatized to environmental regulation of a new trade mode and new standards. This will help amplify the favorable impact of trade opening up on the environment and improve China’s international reputation. The policies related to trade should encourage structural adjustment between the sectors via the formulation of differential policies and impose a restraint on sectors that have high levels of CO2 emissions embodied in export.

Examining the impact of heterogeneous environmental regulations on the carbon emission efficiency of the grain production industry will help to provide a theoretical basis and decision-making reference for achieving the goal of carbon peaking and sustainable agricultural development. Based on the panel data of 30 provinces in China, the DEA-SBM method was used to measure the grain production industry’s carbon emission efficiency from 2011 to 2019. Separating environmental regulations into formal environmental regulations and informal environmental regulations in two parts, then the two-way fixed effect model, threshold effect model, and intermediary effect model are used to test the influence of heterogeneous environmental regulations on the grain production industry’s carbon emission efficiency. The results show that: (1) the grain production industry’s carbon emission efficiency continues to improve but still has space for improvement. (2) the relationship between formal environmental regulations and the grain production industry’s carbon emission efficiency exhibits a “U-shaped” curve; informal environmental regulations have a significantly positive effect on improving the grain production industry’s carbon emission efficiency. The conclusion is still valid after the robustness test. (3) A threshold mechanism test found that there is a single threshold effect between the formal environmental regulations and the grain production industry’s carbon emission efficiency, but it does not cross the “U” inflection point. (4) there is a “U” shaped non-linear mediating effect in the influence of formal environmental regulations on the grain production industry’s carbon emission efficiency; informal environmental regulations also have an intermediary transmission path of production agglomeration of the grain production industry. This study supplies a new perspective for promoting the grain production industry’s carbon emission efficiency.