*5.2. Endogeneity Test*

If the rule of law has potential endogeneity issues, it can lead to biased estimates. To decrease the inaccuracy of the coefficients to be estimated, we first perform a weak instrument test and Durbin–Wu–Hausman test [71,72], and the results are shown in Table 4.


**Table 4.** Endogeneity test.

Note: \*, \*\*, and \*\*\* indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are in parentheses. The control variables are the same as in Table 3.

In Table 4, the F value of the weak instrument test for columns (4) using OLS and (5) using 2SLS is significantly greater than 10, indicating that the weighted geographical distance is not a weak instrument [73]. Additionally, the F value of the Durbin–Wu– Hausman test for these two columns is not statistically significant, implying that the law aspect of governance may be exogenous. Therefore, the endogeneity problem of the rule of law may not be paid special attention in doing so. This may imply that we could estimate our model using OLS.

#### *5.3. Mediating Mechanism Test*

Mediating mechanism analysis can provide a more detailed understanding to figure out how an interested variable affects the dependent variable [74]. We check the mediating roles of financial loans and foreign investment through testing the regression coefficients step by step [63,64]. The relevant test results are shown in Tables 5 and 6.


**Table 5.** Correlation between law-based governance and financial loans, and correlation between law-based governance and foreign investment.

Note: \*, \*\*, and \*\*\* indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are in parentheses. The control variables are the same as in Table 3.

**Table 6.** Correlation between financial loans and housing prices, and correlation between foreign investment and housing prices.


Note: \*, \*\*, and \*\*\* indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are in parentheses. The control variables are the same as in Table 3.

#### 5.3.1. Mediating Role of Financial Loans

First, in Table 3, we show that the law aspect of governance is positively related to housing prices. Second, it is easy to see that the rule of law is significantly positively correlated with financial loans in column (6) of Table 5. Third, we can see in column (8) of Table 6 that both the law aspect of governance and financial loans are significantly positively related to housing prices. Therefore, the mediating role of financial loans is statistically significant according to the step-by-step approach, which implies that improving the quality of the rule of law may enlarge loans and then raise housing prices. Hypothesis 1 is supported.

#### 5.3.2. Mediating Role of Foreign Investment

Similarly, column (7) in Table 5 shows that the law aspect of governance is significantly positively connected with foreign investment. In addition, both the rule of law and foreign investment are significantly positively associated with housing prices in column (9) of Table 6. Based on the results in Table 3 and the step-by-step approach, the positive mediating role of foreign investment is statistically significant, indicating that raising the quality of the law aspect of governance may attract foreign investment and then boost housing prices. Hypothesis 1 is also confirmed.

#### 5.3.3. Robustness Test of Mediating Role of Loans

In order to ensure the credibility of the positive mediating role of loans, we replace financial loans from banks and non-bank financial institutions with loans from housing provident funds to check the robustness. The test results are in Table 7.

**Table 7.** Robustness test of the mediating role of financial loans.


Note: \*, \*\*, and \*\*\* indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are in parentheses. The control variables are the same as in Table 3.

It is shown in column (10) of Table 7 that the rule of law is significantly positively associated with loans from housing provident funds. Additionally, both housing provident fund loans and the law aspect of governance significantly and positively link with housing prices in column (11) of Table 7. In according with the results in Table 3 and the step-bystep approach, the positive mediating role of housing provident fund loans is statistically significant. Therefore, the mediating role of loans in the relationship between the rule of law and housing prices is very robust.
