4.3.5. Other Robustness Check

In addition to the above four robustness tests, other robustness tests are discussed to ensure the robustness of the results in this paper.

Control provincial trend. To exclude the impact of the variation of some characteristics of provinces over time trend on the city carbon emission, we add to control the provincial trend. The result is shown in column (1) of Table 5. The Treat\*Post is still significantly negative with the LnCO2.

Eliminate the impact of the financial crisis. A financial crisis affects economic development, which affects the city's carbon emissions. Therefore, we should exclude the 2008 sample, which would eliminate the impact of the 2008 financial crisis on city carbon emissions. The result is shown in column (2) of Table 5. The Treat\*Post is still significantly negative with LnCO2.

Winsorize the data. In baseline regression, some variables may lead to extreme values in the data. Therefore, to alleviate the impact of extreme values on the estimated results in this paper, we process the data with 1% winsorizing. The result is shown in column (3) of Table 5. The Treat\*Post is still significantly negative with LnCO2.

Placebo test of the experimental group. Following Li et al. (2016) [27], we randomly select a city cluster for placebo testing. Figure 3 shows the distribution of the regression coefficients of the "artificial" processing variable Treat\*Post in the simulation. It can be observed that the randomly assigned estimated values are concentrated around zero, while the truly estimated coefficients are on the left side of Figure 3. It verifies that the city cluster policy has significantly reduced the city's carbon emissions.

**Figure 3.** Placebo test of the experimental group.

In a word, the robustness above indicates that the core conclusion still remains when a series of possible and potential interference factors are excluded.

## **5. Further Discussion**

#### *5.1. Economic Channels*

In this section, we will explore the three plausible underlying economic channels by which city cluster policy affects city carbon emissions. The economic channels build on existing theories, and factors such as productivity, technological innovation, and industrial structure optimization are important in reducing city carbon emissions.
