*3.1. Model Specification*

The econometric model used in this study is expressed as:

$$y\_{it} = a + \sum\_{j=1}^{k} \beta\_j \mathbf{x}\_{ijt} + dummy\_{region} + dummy\_{year} + \varepsilon\_{it} \tag{1}$$

where *yit* is the dependent variable for city *i* in year *t*, *α* is the constant term. *xijt* denotes the *j*th explanatory variable for city *i* in year *t*, which may be the key variable of interest or other control variables. *βj* denotes the coefficient to be estimated for the *j*th explanatory variable. *dummyregion* includes the regional submarket dummy variables, *dummyyear* includes the year dummy variables. *εit* is the random error term for city *i* in year *t*. To increase explanatory power, the regional dummy is introduced into Equation (1) [61]. We control for the general time trend effect by employing a time dummy for each year.

#### *3.2. Instrument for Law-Based Governance*

Although we try to include a considerable number of control variables in Equation (1), it is still possible that we omit some relevant variables, especially those unobservable variables that influence housing prices and law-based governance simultaneously. In this case, law-based governance may be correlated with the residual errors, leading to biased estimates of the coefficient. To alleviate any possible endogeneity bias, previous studies generally resorted to constructing various exogenous instrumental variables.

We construct a weighted geographical distance as an instrument for law-based governance using the distance from local governmen<sup>t</sup> to provincial governmen<sup>t</sup> and the distance from provincial governmen<sup>t</sup> to central government. In China, spatial distance deeply affects the degree and efficiency of top-down supervision and monitoring from higherlevel governmen<sup>t</sup> [62]. According to the top-down governmental managemen<sup>t</sup> system in China, local governmen<sup>t</sup> is directly supervised by provincial government. Thus, the closer the local governmen<sup>t</sup> is to the provincial government, the more likely it is that the local construction of law-based governmen<sup>t</sup> should be regulated. Meanwhile, the supervision of central governmen<sup>t</sup> over provincial governmen<sup>t</sup> may have an indirect impact on the local construction of law-based government. However, this impact should be less than the impact of the supervision of provincial governmen<sup>t</sup> over local government. Therefore, we specify the weight of the distance from local governmen<sup>t</sup> to provincial governmen<sup>t</sup> to be 0.8, and the weight of the distance from provincial governmen<sup>t</sup> to central governmen<sup>t</sup> to be 0.2. Furthermore, the weighted geographical distance should be uncorrelated with the error term.

#### *3.3. Causal Steps Approach*

The methodology classically used to identify the mediating role of an interested variable is testing the regression coefficients step by step (causal steps approach) [63,64]. To conveniently describe the principle of this approach, we use the following simplified models.

$$y = \alpha\_1 + \beta\_1 \mathbf{x} + \varepsilon\_1 \tag{2}$$

$$m = \alpha\_2 + \beta\_2 x + \varepsilon\_2 \tag{3}$$

$$y = \mathfrak{a}\_3 + \beta\_3 \mathfrak{x} + \beta\_4 m + \varepsilon\_3 \tag{4}$$

where *y* is the dependent variable, *α*i (I = 1, 2, 3) is the constant term. *x* denotes the independent variable. *β*j (j = 1, 2, 3, 4) denotes the coefficient to be estimated. *m* is the mediating variable for *x* to influence *y*. *ε*i (I = 1, 2, 3) is the random error term.

To identify the mediating role of *m*, the significance of *β*1 should be tested in the first step. If *β*1 is statistically significant, then *β*2 and *β*4 should be tested. If *β*2 and *β*4 are both statistically significant, then the mediating role of *m* is significant. Further, if *β*3 is not statistically significant, then the mediating effect is in full force.

#### **4. Variables and Data**

In this study, we are interested in how the law aspect of governance of one city is related to housing prices in that city. The housing price indicator uses the average annual price of new residential housing sold in a city, because there are is no reliable price data for second-hand housing unit sales for a large number of cities in China. A reliable measure of law-based governance is crucial for the credibility of the estimation results. While there is a large number of efforts measuring the degree of rule of law globally [9,65], few studies have attempted to assess the rule of law or law-based governance at the city level. In this paper, the data of city-level indicators of the quality of the law aspect of governance are collected from the Annual Assessment Report on China's Law-based Government that issued by the School of Law-based Government, China University of Political Science and Law (CUPL) [66]. Since 2014, the report has been successively released five times with annual assessment results for 100 cities, which include four major municipalities that are under the state's direct administration, twenty-seven provincial capitals, twenty-three large cities (according to the category set by the State Council), and forty-six medium-sized cities. These cities have a good representation of the levels of law-based governance in China. The report's assessment index system has nine first-level indicators, including "comprehensively performing governmen<sup>t</sup> functions by law", "organizational leadership", "system construction", "administrative decision", "administrative law enforcement", "government information disclosure", "supervision and accountability", "solving social conflicts and administrative disputes", and "public satisfaction", of local law-based administration. Due to its professionality and independence, the assessment report has earned a good reputation in Chinese society and is widely cited in the media as well as Chinese academic research [66].

As "comprehensively performing governmen<sup>t</sup> functions by law" has been placed at the most prominent position in the Implementation Outline for Constructing Law-based Government (2015–2020), we use the scores of this indicator in the assessment report to measure the quality of law-based governance. This core indicator is specified to capture the situation of administration by law including aspects of institution setting, leadership design, public services, administrative approval, emergency response, etc. [66]. It has a full score of 100 in the annual assessment report, and the score can be expressed as:

$$\text{LAWGOV} = \text{IS} + \text{LD} + \text{PS} + \text{AA} + \text{ER} \tag{5}$$

where LAWGOV is the score of "comprehensively performing governmen<sup>t</sup> functions by law", IS denotes the score of "institution setting", LD is the score of "leadership design", PS is the score of "public services", AA denotes the score of "administrative approval", and ER is the score of "emergency response". Figure 2 shows the spatial distribution of mean law-based governance quality between 2014 and 2017 across the sample cities. It can be seen that the cities falling into the highest quality category are mainly located in the eastern region of China. To ensure the robustness of our main findings, we also use the sum of the scores of other auxiliary aspects as an alternative indicator of law-based governance. Additionally, the two types of indicators (the core indicator and the mix of auxiliary indicators) enable us to describe the different law-based governance models well.

**Figure 2.** The distribution of law-based governance quality.

In addition to the law aspect of governance, many other factors may also affect citylevel housing prices. Guided by findings of the existing literature, we select a large number of control variables that reflect the characteristics of the economic, humanistic, ecological, and geographic environment of cities. Two indicators are utilized to reflect the economic environment, including per capita disposable income of urban households and the ratio of tertiary industry's output value in GDP. For the humanistic environment, we include eight indicators of traffic, educational, medical, and cultural facilities (details in Table 1). Greenness ratio and the emission ratio of industrial soot and dust are used to reflect the ecological environment. Finally, we apply the distance to the coastline to capture the features of the geographic environment.

In addition, as discussed in Section 2.4, law-based governance affects the housing market through the mediating variables of financial loans and foreign investment. We use per capita personal housing purchase loans from banks and non-bank financial institutions to reflect financial loans. The foreign investment indicator is per capita foreign investment. Additionally, per capita loans from housing provident funds are used as an alternative indicator of financial loans to check the robustness of their mediating role between housing prices and law-based governance. In accordance with the suggestions of [67], to improve the estimation results, we incorporate economic regional submarket dummy variables into OLS equations, which can also alleviate the problem of heteroscedasticity [68]. Meanwhile, to control for the time trend effect, we include the time dummy variables for each year.

The data of housing provident fund loans are collected from housing provident fund managemen<sup>t</sup> centers in each city. The data of the distance to the coastline are calculated by ArcGIS software, which is the shortest straight-line distance from the geometric center of each city to the coastline. The data of city-level housing prices, mediating variables, and control variables are collected from the Bureau of Statistics of each city, the data of the RMB/USD exchange rate come from the People's Bank of China. As the original unit of foreign investment is the dollar, we need to convert dollars to yuan using the exchange rate. The eastern, central, western, and northeastern economic regions are divided by the National Bureau of Statistics of China. The division of first-, second-, third-, fourth-, and fifth-tier cities is based on a research report from Shanghai YiCai Media Co., Ltd. (https://www.yicai.com (accessed on 26 April 2021)). It issues the classification of Chinese cities every year based on the commercial store data of mainstream consumer brands, the user behavior data of internet companies, and urban big data. This type of classification changes the traditional classification of cities based on administrative hierarchy. China's cities are classified according to five dimensional indices: business

resource concentration, urban hub, urban activity, lifestyle diversity, and future plasticity, using expert scoring and principal component analysis. The data used in this study cover all the 100 cities in the report over the period 2014–2017 and take their natural logarithm forms in the analysis, except dummy variables. Table 2 describes details of the variables and shows the descriptive statistics.


**Table 2.** Definitions of variables and descriptive statistics.


**Table 2.** *Cont.*

Note: — indicates that corresponding variable is unitless.

#### **5. Research Findings and Discussions**

The economy is sensitive to housing [69], and fluctuations in housing markets have long been recognized as leading indicators of an economy [70]. This study aims to investigate the correlation between the law aspect of governance and the economy in China using housing prices as a proxy for economic prosperity [24]. On the other hand, the data released by the National Bureau of Statistics show that the average annual growth rate of

housing prices was 8% over the past 20 years in China, and the growth rate of GDP was 9%. The difference between them is not significant. Furthermore, in the sample period, 2014–2017, the average annual growth rate of housing prices was 6% and the growth rate of GDP was 7%. There is still no big difference between the two growth rates. To test whether the hypotheses developed above can be supported, we use Equation (1) to explore the association between law-based governance and housing prices. We first use the method of ordinary least squares (OLS) to perform baseline estimation. Then, in order to avoid possible biased estimates, we test the endogeneity of law-based governance. Thereafter, we discuss the sensitivity, heterogeneity, and robustness of the relationship between the rule of law and housing prices.
