<sup>4</sup> Endogenous problem

Additionally, there may exist endogeneity between environmental regulation and urban innovation, as the more innovative a city is, the more likely it is to reduce pollution emissions through innovation, thus rendering it unnecessary for the city to reduce pollution emissions through environmental regulation policies. Thus, a certain reciprocal causality exists. With this in mind, a two-stage least squares analysis of the baseline model was conducted, with air circulation coefficients as instrumental variables. The main considerations for selecting instrumental variables were as follows. First, there exists no theoretical relationship between the air circulation coefficient and the innovation capacity of cities, which satisfies the exogeneity requirement of the instrumental variable. Second, air circulation coefficients correlated to environmental regulation by directly determining the level of air pollution dissipation. Specifically, when at a uniform level of pollution, cities with better air circulation assume that as pollution dissipates quickly, they do not need to adopt stricter environmental regulation policies. However, cities with lower air mobility need to increase their level of environmental regulation to control pollution emissions. Hence, when the air circulation coefficient is higher, the regional environmental regulation policy is theoretically weaker, thus satisfying the exogeneity requirement of instrumental variables. Table 9 presented the endogeneity test with the inclusion of the instrumental variable of air circulation coefficient. The findings of this study remained robust. Moreover, this study conducted a weak instrumental variables test, considering the issue of possible weak instrumental variables between the instrumental variables and environmental regulation. As deduced from the weak instrumental variables test, the F-values (F-weak) in the first stage were all

beyond the empirical value of 10, suggesting the absence of weak instrumental variables. Additionally, the regression results for the instrumental variables indicated the conclusions of the current study remained valid following the endogeneity issue addressed.


**Table 9.** Endogeneity test with the inclusion of the instrumental variable (air circulation coefficient).

Note: \*\*\*, \*\* and \* represent the significance at the 1%, 5% and 10% levels, respectively. The *t*-values are in parentheses.
