*5.5. Heterogeneity Analysis*

In order to elucidate the heterogeneity of the relationship between law-based governance and housing prices across city groups, we add the interaction terms, LAWGOV × FIRST, LAWGOV × SECOND, LAWGOV × THIRD, and LAWGOV × FOURTH, in Equation (1). We drop the regional dummy variables to eliminate the possible collinearity between them and the interaction terms. The estimation result is displayed in column (14) of Table 8, suggesting that the association between the rule of law and housing prices in the first- and second-tier cities is significantly greater than that in other cities. Thus, hypothesis 3 is confirmed.

#### *5.6. Robustness Test of the Effect of Rule of Law Quality on Housing Prices*

In China, "comprehensively performing governmen<sup>t</sup> functions by law" is the core of the construction of law-based government. In addition to this critical variable, some other auxiliary variables are also available to measure the quality of the rule of law in the Annual Assessment Report on China's Law-based Government. Each of the auxiliary variables reflects a special aspect of law-based governance. To ensure the trustworthiness of the correlation between the law aspect of governance and housing prices, we construct another variable, MULVAR, to replace LAWGOV. Each indicator score of other auxiliary aspects of law-based governance can be obtained like LAWGOV. Then, we combine these indicators into one indicator to alternatively describe law-based governance, of which the score can be expressed as:

$$\text{MULVAR} = \text{OL} + \text{SC} + \text{AD} + \text{AE} + \text{GI} + \text{SA} + \text{CD} \tag{6}$$

where MULVAR denotes the score of the alternative indicator, OL is the score of "organizational leadership", SC denotes the score of "system construction", AD is the score of "administrative decision", AE denotes the score of "administrative law enforcement", GI is the score of "government information disclosure", SA is the score of "supervision and accountability", and CD denotes the score of "solving social conflicts and administrative disputes". The robustness test results are displayed in Table 9.


**Table 9.** Robustness test of the relationship between law-based governance 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.

Obviously, the coefficient of the alternative indicator of the rule of law is still significantly positive in column (15) of Table 9, and the characteristic of the heterogeneity in column (16) is consistent with that in column (14) of Table 8. Therefore, the relationship between the law aspect of governance and housing prices is robust.

In addition, we construct a 0–1 spatial weight matrix (**W**) to calculate Moran's *I* of housing prices in our sample cities, Moran's *I* is 0.24314 and the *p*-value is less than 2.2e-16, suggesting that there is significant spatial autocorrelation in housing prices. Therefore, we next test whether the relationship between law-based governance and housing prices can still be robust in spatial models after dropping regional dummies. The estimates of the spatial lag model and spatial error model are shown in Table 10.

**Table 10.** Maximum likelihood (ML) estimation of spatial models.


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. To avoid the emergence of cities without neighbors, Urumqi, Kashgar, and Lhasa are dropped.

It can be seen from Table 10 that the estimated coefficients of law-based governance are both significantly positive in the spatial lag model and spatial error model. This implies that our main findings are still supported after taking into consideration spatial autocorrelation.
