4.3.1. Propensity Score Matching DID (PSM–DID)

DID estimation is most appropriate when the experiment is random. Considering that the assignment of the treated group by TCZ policy in our study may be not random, we should first use the Propensity Score Matching (PSM) approach to find and construct some comparable cities as the untreated group, and then evaluate the average impact of the TCZ policy on green patent applications using the DID model to examine whether our basic empirical results remain robust. PSM uses a logistic regression of the outcome variable that equals 1 if the city is in two control zones and equals 0 if it is not, and the independent variables include characteristics before treatment that would influence the "propensity" of cities in TCZ. Cities are matched to kernel values based on their propensity scores.

Firstly, we examine the results of treated and untreated cities before and after matching using the PSM approach. Figure 2 shows city characteristic bias between treatment and control groups before and after matching, implying that the deviation of all characteristics in both groups dropped to zero significantly after matching. From the perspective of kernel density, Figures 3 and 4 display the kernel density of treatment and control groups before and after matching, respectively. We find that the kernel density of the two groups is much closer. The above results indicate the validity of grouping using the PSM approach.

**Figure 2.** City characteristic bias before and after matching.

**Figure 3.** Kernel density of treated and control groups before matching.

Secondly, the PSM–DID results are shown in Table 3. In column (1) the regression includes no fixed effects, while column (2) only includes control city–fixed effects. Both coefficients in column (1) and (2) are significantly positive. The estimated result is controlled for city–fixed effects and year–fixed effects in column (3). The estimate for TCZ policy is significantly positive (at the 1 percent level), implying that targeted cities have 37% more green patent applications when the TCZ policy is enacted. Thus, the interference of unobservable factors in the selection of the treated and untreated groups on the conclusions of this study can be excluded.



Note: For each regression, the log volume of green patent applications is used as outcome variable. Controls include total population at the end of the year (Pop), annual gross regional product (GDP), investment in fixed assets (Fixedinvest), foreign investment utilized (FDI), the logarithm of number of students in higher education institutions (Students), the logarithm of number of teachers in higher education institutions (Teachers), the logarithm of proportion of employment in the secondary industry (Second), the logarithm of employment at the end of the year (Employment), and the logarithm of the number of new contracts signed in the current year (Contracts). Standard errors in parentheses are clustered at the city–year level. \*\*\* *p* < 0.01.

#### 4.3.2. Test on the Number of Granted Green Patents

Apart from examining the efficacy of the TCZ policy for the number of green patent applications, the further test is analyzing the policy's effect on the number of green patents granted. We put the log of the number of green patents granted into Equation (1) as the outcome variable instead of the number of green patent applications. The results in Table 4 show that all of the coefficients are statistically significant at the 1 percent level. In column (4), we include control variables, city–fixed effects, and year–fixed effects. The key interaction term's coefficient is 0.565 and statistically significant at the 1% level, indicating that the number of green patents granted increases by 56.5% in two control zones, which examines the robustness of the conclusions of this study.


**Table 4.** The effect of TCZ policy on green patents granted.

Note: The dependent variable in each regression is the log of the number of green patents granted. Controls include total population at the end of the year (Pop), annual gross regional product (GDP), investment in fixed assets (Fixedinvest), foreign investment utilized (FDI), the logarithm of number of students in higher education institutions (Students), the logarithm of number of teachers in higher education institutions (Teachers), the logarithm of the proportion of employment in the secondary industry (Second), the logarithm of employment at the end of the year (Employment), and the logarithm of the number of new contracts signed in the current year (Contracts). Standard errors in parentheses are clustered at the city–year level. \*\*\* *p* < 0.01.

#### **5. Further Discussion**
