4.3.1. Propensity Score Matching DID (PSM-DID)

Of course, the city cluster policy is not a perfect quasi-natural experiment. There is a certain degree of randomness in the selection of the city cluster. Strictly speaking, whether a city can be selected as one of the city clusters is not a completely random selection process. It will be disturbed by economic factors, political factors, and human factors.

These differences will affect the validity of the DID model. In order to reduce the interference caused by these differences in model estimation, we will use the propensity score matching (PSM) method proposed by Heckman et al. (1998) [28] to select comparable treatment and control groups, and then use a DID model to estimate the policy effects [26]. We adopt the 1:1 nearest neighbor matching method. The estimation result is shown in column (1) of Table 4. It can be seen that the Treat\*Post is still significantly negative with the city's carbon emissions (lnCO2), indicating that our core findings remain valid after alleviating the problem of sample selection bias.


**Table 4.** Robustness check of the effect of city cluster policy on CO2 emissions(PSM-DID).

Note: *t* statistics are shown in parentheses; \*\*\*, \*\*, and \* represent significance at the 1%, 5%, and 10% levels, respectively.
