Real estate finance innovation means the new financial products, instruments and product flows which emerge in the real estate finance system and financial market, as well as the new organizational forms and systems suitable for products, tools and processes^[1]. The innovations in the real estate financial market will help the corresponding subjects in the real estate market to finance, provide more housing finance products and better services for the public, relieve the economic pressure of buyers and enhance their ability to buy houses, alleviate the regional poverty gap and thus achieve the purpose of increasing social welfare^[2]. In addition, financial derivatives generated in the real estate finance innovation reduce transaction and agency costs and decrease information asymmetry, thus making it possible to reduce risks by increasing risk sharing opportunities^[3]. In 1991, China introduced the housing accumulation fund system, opening the door for real estate finance. In the second half of 1998, China began to stop the system of distributing houses in kind; instead, it gradually carried out the housing market reform, developed housing finance and cultivated and developed the housing transaction market. Real estate finance had entered a rapid development stage, enabling the real estate industry to become one of the important pillar industries of the national economy. In this process, the ratio of the GDP of the real estate industry increased from 2.10% in 1980 to 6.78% in 2021, more than tripled. The year-on-year growth rate of the GDP of the real estate industry was nearly twice than that of the GDP of the State in 2020, despite the COVID-19 (Figure 1). The real estate industry contributed 13.73% to GDP growth in 2020. In 2021, due to the downturn of the real estate market and weak expectations, the contribution to GDP growth was relatively weak. (Figure 2).

From the perspective of the credit scale in the real estate market, as of the end of the 2021, the balance of RMB real estate development loans and personal housing loans combined provided by financial institutions was about 52.17 trillion yuan, while the balance of RMB loans of financial institutions nationwide was about 192.69 trillion yuan in the same period, and the balance of real estate loans accounted for 27.07% of the balance of RMB loans of financial institutions. From the perspective of the internal structure of the real estate loan balance, the balance of personal housing loans accounted for a relatively large proportion. At the end of 2021, the proportion was as high as 73.45%, and the year-on-year growth rate of the personal housing loan balance was higher than that of the real estate loan balance (Figure 3). The securitized products of housing assets were suspended since the US financial crisis erupted in 2007, and the issuance of them were not resumed until 2014. By the end of 2021, a total of 282 RMBs products had been issued, with an issuance amount of nearly 2.32 trillion yuan. The number and total amount of issued RMBs products showed an exponential growth; the average proportion of secondary assets showed a fluctuating increase; the average proportion of secondary assets exceeded 10.48% (Figure 4). There are a total of 110 real estate investment trust funds with a total issuance amount of over 202 billion yuan, but the average proportion of secondary assets exceeded 18.04% (Figure 5). Over the past decades, China's real estate finance innovation has developed so rapidly that it has produced a far-reaching impact on the social economy, however, the existing literatures have not carried out a scientific and systematic quantitative evaluation on the level of the real estate finance innovation in China. The vast majority of researches on real estate finance innovation in the existing literatures is only descriptive, and lacks systematic empirical researches. Therefore, it is urgent to compile a real estate finance innovation index to scientifically and objectively evaluate the innovation level of the real estate finance in China.

Over the past decades, most scholars have focused on the incremental market development in the field of real estate finance. However, under the background of the current supply-side structure reform, China has tightened its policies on the real estate industry, and nearly no IPO case of the real estate enterprises occurred in recent years. At the end of 2020, the People's Bank of China and the China Banking and Insurance Regulatory Commission jointly declared the establishment of a real estate loan concentration management system for financial institutions, aiming to manage the loan proportion of real estate loans in financial institutions by grades. Therefore, the huge real estate loan stock assets of financial institutions need to be innovated and securitized to improve the operational ability and financial liquidity of financial institutions. Compared with the developed countries in Europe and America, China's real estate financial system is still far from perfect, in particular, the relevant supervision is not perfect. However, China is in a period of rapid urbanization, and the potential and general trend of rapid development of real estate industry will not change in the short term, so the support of the real estate financial industry is urgently needed. The real estate finance innovation characterized by scale expansion and simple business innovation is still in the financial innovation stage during the transition from financial repression to financial deepening. Under such circumstance, it will be an inevitable choice for China to intensify the innovation of its real estate finance for a long time. Based on the facts, this paper will construct the real estate finance innovation index from the perspectives of the governments, enterprises and the public, scientifically and objectively depict the innovation situation of the real estate finance in China since the financial crisis, and analyze its temporal-spatial characteristics. The theoretical and practical significance of this work is as follows: First, theoretically, this index provides data support for the related research on the real estate finance innovation. It has solved the shortcoming that most financial service companies have no separate R & D budget and have few financial patents, thus rendering it difficult to measure the real estate finance innovation. It enriches the research on the quantification of real estate financial innovation, and perfects the existing research that only describes real estate finance innovation at the enterprise level (the proportion of real estate loans, the financing channels of real estate enterprises and the scale of individual housing loans) due to the lack of indexes to measure real estate finance innovation. Zhang and Li^[4] had constructed a new financial development level index in China based on four aspects: Financial policy and institutional environment, business environment, banks' financial services and financial market. Li and Lin^[5] compiled a structural index of China's financial innovation by summarizing China's financial innovation events from 1979 to 2015. Second, at the practical level, this index includes the real estate finance innovation indexes of all provinces, municipalities and autonomous regions in China at the quarterly level from 2009 to 2019. The real estate financial innovation index clearly depicts the level of real estate financial innovation in various regions and across the country, which is helpful for the government to scientifically grasp the development of real estate finance, promote real estate financial innovation and effectively manage real estate financial risks. It has important reference for the formulation of relevant strategies for real estate financial risk prevention in various regions. The compilation of the index will help real estate enterprises scientifically and comprehensively understand the current situation of China's real estate financial development in the context of the current real estate financial repression, exploring new development models, and promoting the virtuous circle and healthy development of the real estate industry.

Financial deepening and financial liberalization are the first theories related to financial innovation put forward by Chinese scholars, between which there exist both differences and connections. The financial liberalization is mainly relative to financial repression, aiming at reducing the degree of government administrative intervention and establishing the basic adjustment function of market mechanism, while the financial deepening is based on financial liberalization, which enables the relationship between supply and demand in the financial market to determine the current exchange rate or interest rate level, promotes investment and savings, and thus drives the overall economic growth. Therefore, financial liberalization is taken as the way, while financial deepening serves as the goal^[6]. As for the measurement standards, Edward^[7] and McKinnon^[8] first proposed to use broad money M2/GDP ratio, the ratio of year-end credit balances to GDP and the ratio of bank financial assets to GDP to measure the degree of financial deepening, while Chinese scholars Zhan and Yang^[9] directly used broad money supply to measure the degree of financial deepening. Huang^[10] pointed out that the expansion of total financial assets and the rise of financial structure are important symbols of financial deepening, which has improved the savings rate and the efficiency of resource allocation. Considering the institutional and historical reasons. Li and Ma^[11] respectively used the ratio of broad money to GDP, the ratio of bank credit to GDP and the credit interest rate to measure the degree of financial deepening. Ang and McKibbin^[12] used the ratio of commercial bank assets to the total assets of the central bank and commercial banks, and the ratio of current liabilities to nominal GDP to measure financial deepening. Chen, et al.^[13] and Wu, et al.^[14] used the ratio of total bank loans to GDP in the region where the company is located as a proxy variable for regional financial deepening. In respect of the measurement of financial liberalization, Liu and Shen^[15] selected nine indexes of the degree of interest rate marketization, the demand for foreign exchange reserves, the degree of maintenance of credit autonomy, the degree of freedom of institutional access, the degree of diversification of property rights of commercial financial institutions, the degree of freedom of business scope, the free capital flows, the degree of marketization of social financing and the degree of indirect financial regulation and control; and the principal component analysis method was used to construct China's financial liberalization index system. Kaminsky, et al.^[16] examined financial liberalization from three aspects: Capital account liberalization, domestic financial sector liberalization and securities market liberalization. According to these three aspects, the liberalization is divided into three levels: Complete liberalization, partial liberalization and incompleted liberalization. For the criteria of the measurement of liberalization, most scholars currently divided the samples into two parts according to time: "pre-financial liberalization" and "post-financial liberalization". Corresponding indexes were selected from different fields to set dummy variables with the year of releasing liberalization policies as the demarcation point: 0 represents "the pre-liberalization" and 1 "the post-liberalization"^[17].

Most of the methods for measuring the level of financial innovations in existing literatures are based on financial deepening and financial liberalization theories. Financial deepening indexes such as the ratio of personal credit to total credit, the loan balance of financial institutions and the ratio of broad money to GDP are often used to measure financial innovations^[18]. Abiad and Mody^[19] used financial liberalization index to measure the current situation of financial innovations and study the influencing factors of institutional innovation. Kim, et al.^[20] constructed efficiency indexes, scale indexes and business activity indexes according to the relationship between the ratio of private loans to GDP, the ratio of total banking costs to total assets, the ratio of stock market value to GDP and the ratio of stock market turnover to GDP. According to these three indexes, the general index of financial innovation was constructed. Mu^[21] measured the level of financial innovation based on the related businesses of financial institutions, specifically the innovation of electronic banking, guarantee, money management and financial derivatives instruments. Jin^[22] based on the mechanism of financial innovation on the equilibrium of monetary and commodity markets, believed that the interest rate elasticity of IS-LM curve is greatly affected by financial innovation, thus affecting the "crowding out effect" of monetary policies and fiscal policies; Jin also proposed that financial innovation could be replaced by interest rate elasticity.

The vast majority of existing literatures on real estate financial measurement are confined to the qualitative aspects, lacking of quantitative researches. Veronica and Francis^[23] analyzed the current situation of real estate finance in 61 countries and regions from the perspective of supply and demand and put forward a framework to analyze the real estate finance system, the research results showed that a sound legal system, an in-depth credit information system and a stable financial environment are conducive to the deepening of real estate finance. Tian, et al.^[24] used the per capita living area of urban population, the floor space under construction in real estate projects and the sales volume of houses as the data series of system characteristics; also, they used domestic loans, funds from other sources and self-raised funds as the behavior series of related factors to study the deepening of real estate finance as per the principle of advantage analysis, which provided a new idea for quantitative study of real estate finance. Hu, et al.^[25] studied the relationship between real estate financial structure and economic growth, using sales of real estate property as indexes of the real estate economic growth, and domestic loans sources of real estate development funds, self-financing of enterprises and other sources as structural indexes of real estate finance. Dai and Xiao^[26] proposed to improve the two statistical indicators of real estate finance, namely the LTV (Loan-to-Value) Ratio and the DSTI (Debt Service-to-Income) Ratio, to improve the statistics by financial macro-prudential policies of residents' debt service and debt capability by referring to the financial macro-prudential management framework of the real estate in EU, aiming to lay a solid foundation for monitoring risks in the real estate finance market.

It is crucial to select the weight of each index in the evaluation of the level of innovative development objectively and scientifically. Whether the effectiveness of the evaluation system is reasonable depends largely on the empowerment of the weight of an index. There are now many ways of empowerment in the existing literatures. We can select the corresponding weighting methods based on the characteristics and significance of the selected index data. By summarizing the corresponding literatures, we can divide them roughly into three categories as follows: Objective weighting method (principal component analysis, entropy method, range coefficient method, etc.), subjective weighting method (analytic hierarchy process, Delphi method, binomial coefficient method, etc.) and comprehensive weighting method (the combination of subjective weighting and objective weighting methods). Zhao and Zhen^[27] constructed the evaluation index and comprehensive evaluation index of China's regional independent innovation factors through normal distribution function and two-level equal weight summary, with the calculation formulas as follows: $r_{ij}=100\times \varphi (\frac{s_{ijk}-{\overline{x}}_{ij}}{s_{ij}})$; $R=\frac{1}{8}\sum _{i=1}^8{R}_i=\frac{1}{8}\sum _{i=1}^8\sum _{j=1}^{n_i}{r}_{ij}$, where $i=1,2,\cdots ,8$, representing elements; $j=1,2,\cdots$ representing the indexes under the elements; $n_i$ is the number of indexes under the $i$ element, using 3$\sim$8; $k=1,2,\cdots ,31$, indicating the 31 provinces and regions which participate in the comparison 1; $\varphi (x)$ is the function value for calculating the standardized normal distribution function; $R_i$ and $R$ represent the factor evaluation index and the comprehensive evaluation index respectively. Wang and Yu^[28] studied the "Zhong Guancun Index" index system, which consists of five second-level classification indexes and 15 third-level classification indexes. The five classification indexes include the economic growth index (0.18), economic benefit index (0.21), technological innovation index (0.29), human capital index (0.15) and enterprise development index (0.17). The weights of the second-level classification indexes are in the brackets, and the determination of the index weights is made on the basis of extensive consultation with experts from all walks of life. Li and Lin^[5] constructed the China Financial Innovation Structure Index. By adopting the idea of index classification to determine the weight of each index through expert scoring, and obtain the indexes of all levels through the weighting and summing methods step by step from bottom to top, they have obtained six first-level indexes; namely, institutional innovation index, market innovation index, tool innovation index, system innovation index, management innovation index and technology innovation index; also they have calculated the index system of China's financial innovation structure with the weighting and summing methods. Zhang and Li^[4] constructed China's financial development index from four aspects: Financial institutions and policy environment, business environment, banks' financial services and financial market. The weights of these four main indexes have referred to the World Economic Forum^[29] and are empowered 25% respectively, while the weights of the lower indexes under the upper indexes is determined according to the degree of explanation of the upper indexes. Guo, et al.^[30] adopted a combination of subjective and objective methods in the weighting of China's digital inclusive finance development index. The subjective method is the analytic hierarchy process, while the objective weighting method is the coefficient of variance method.

From the above theoretical analysis, it can be seen that there is little research on the compilation of the innovation index of real estate finance in the existing literatures, so this work is also a brand-new exploration from scratch. There are difficulties in three aspects in studying the compilation of the innovation index of real estate finance: First of all, data indexes such as R & D expenditure or patents are often used by scholars to measure enterprise innovation^[31]. However, a majority of relevant enterprises in the financial industry do not have a separate R & D expenditure budget and the number of financial patents applied for is also very small, so there is a serious lack of data in this area^[32]. We also prove this in the process of collecting relevant data. Secondly, there are various forms of innovation in real estate finance with different attributes. It is necessary to use a systematic framework to include various kinds of innovations and potential innovations, such as those in the innovation products of real estate finance and the innovation supervision in real estate finance. Since the monetization of real estate was introduced in China, it has gone through a process from 0 to 1 and from 1 to $N$. There exist both original innovations and diffusion innovations in real estate finance, the changes which need to be reflected by a systematic dynamic process. Finally, there is nearly no empirical research on the innovation in real estate finance, thus rendering it hugely difficult for us to quantitatively select corresponding reasonable indexes or weights for the reasons that the existing literatures adopt objective empirical research methods of contribution or correlation in the selection of index or weights. For example, Zhang and Li^[4] weighted relevant indexes by the degree of explanation between indexes.

Real estate finance is the general term of both housing finance and real estate finance. Real estate finance is mainly a financing activity centered on land ownership or right of use, while housing finance is the general term of financing activities in the process of production, circulation and consumption of houses that can be used for trading. From the definition, it can be seen that real estate finance involves many stakeholders, but roughly it includes enterprises (concerning financing), governments (concerning affairs of policies and supervision) and the public (concerning consumption).

The existing literatures on enterprise innovation start from the internal factors of enterprises and the external environment of them. The internal factors of enterprises include the personal factors of entrepreneurship and management, the ownership structure and corporate governance factors, the cultivation of talents and the training of employees, etc. Liu and Liu^[33] studied the relationship between the tenure of senior executives of listed enterprises and its R & D investment. The research found that there is a significant positive correlation between the length of the tenure of senior executives and the R & D investment during their tenure. The stability of the management helps to improve the R & D investment of enterprises. In addition, Tang and Zhen^[34], Yu, et al.^[35], Zhao, et al.^[36], and Zhang, et al.^[37] respectively studied the relationship between risk preference of the management, the experience of senior executive inventors and the work experiences and educational background of the management and the efficiency of the R & D investment of enterprises or the output of corporate patents. Luong, et al.^[38] pointed out that the holding of shares by foreign investment institutions can improve the technical level of domestic enterprises through technology spillover effect or strict external supervision mechanism, which in turn improves the operating efficiency of enterprises and enhances the innovation level of enterprises. Wachsen and Blind^[39] studied the impact of labor market elasticity on enterprises' innovation capability based on macro data, finding that the external factors which affect enterprises' innovation include market concern and social resources, business environment, industrial policies and supervision, etc. Ke, et al.^[40], Bai and Jiang^[41], and Pan, et al.^[42] respectively studied the innovation activities of enterprises from the perspectives of the social capital of the research and development personnel in enterprises, the school-enterprise cooperation mode and the legal proceedings of enterprises. Amore, et al.^[43] studied the impact of government regulation on industrial innovation of banking industry, finding that the relaxed government deregulation on the financial industry assists enterprises in innovation. Freeman, et al.^[44] found that external environmental laws and regulations will promote enterprise innovation to a certain extent, but the quality of innovations needs to be improved. To sum up, the researches on the influencing factors of enterprise innovation in existing mainstream journals were mostly carried out from the aspects of business entities, public awareness and policies and regulations, which also provide the way of thinking for us to design the index system of innovation in real estate finance.

In order to make our innovation indexes of real estate finance more scientific and theoretically traceable, we analyze the influential innovation index systems at home and abroad based on the existing literatures. On the basis of the summary of Li and Liu^[45], we have made corresponding improvements as shown in Table 1. By means of summary, we find that the innovation index systems have distinct levels and clear evaluation purposes. When compiling regional innovation indexes, it is necessary to have both horizontal (comparable between regions) and vertical (comparable in different years, quarters or months) comparability. By analyzing the evaluation scope of indexes, we find that all indexes concern the aspects of the governments (innovation environment), enterprises (innovation subjects) and the public (human capital, innovative talents, etc.).

The above relevant literatures summarize the commonness of real estate finance innovation from three aspects: The concept of real estate finance, the influencing factors of innovation and the innovation index system which has great influence at home and abroad. We find that the concept, influencing factors and innovation index system are analyzed from three levels: Government policy, enterprises and the public, which provide us with a very meaningful idea to build the real estate finance innovation index. Therefore, this paper constructs the real estate finance innovation index system from the macro-to-micro logic of the governments, enterprises and the public, establishes three sub-indexes of the government innovation index, enterprise innovation index and public innovation index respectively, and selects scientific and reasonable specific indexes for the three sub-indexes based on the existing theories and available data. Let's see it from the government level. The researches by Yu, et al.^[46] show that the innovation and R & D capabilities of enterprises are greatly affected by industrial policies, and supportive industrial policies play a significant role in promoting the innovation capabilities of them, especially private enterprises. Li, et al.^[47], Wang and Du^[48], Edler, et al.^[49] also studied the impact of policies on innovation from different angles. Therefore, we take policies as the breakthrough point at the government level based on the correlation and rationality of the data scale of samples, and take real estate, finance, interest rate, money and credit as the keywords to search for relevant policies on PKULAW.com, and use them as the relevant data for the policy innovation index. Tian, et al.^[24] believed that the indexes to measure real estate finance should include those reflecting the scale of the real estate market operation at the enterprise level. Therefore, we select one index from the supply and demand level of real estate to measure the operation scale of the real estate market. They are the real estate development investment (at the supply level) and the commercial housing sales (at the demand level). Kim, et al.^[20] used the ratio of stock market value to GDP to measure the level of financial innovation. For such, we use the ratio of stock market value and the financial industry to GDP in the A-share real estate industry as a sub-index of real estate finance innovation at the enterprise level. Guo^[1] adopted the ratio of real estate loans to the total RMB loans of financial institutions, the total amount of actual funds used in the real estate market minus the amount of funds generated by traditional channels and the scale of personal housing loans as proxy variables of real estate finance innovation. But in this paper, the proportion of real estate loans is used to measure the real estate finance innovation at the enterprise level, and the reciprocal of this index is taken to measure the financing channels of enterprise innovation. For innovative products, the scale of the securitized products of assets released by the real estate industry and the financial industry is used for depiction. Finally, we calculated the "Three Red Lines" of real estate enterprises: The debt level of real estate enterprises is measured by the asset-liability ratio, the net debt ratio and the ratio of short-term loans in cash in which the advance receipts have been removed. In this way, the higher the debt level is, the greater the innovation capability will be. A group's concentrated debts are the way of resource agglomeration, where a company unifies external financing through the internal capital market, thus easing financing constraints and expanding innovation investment. Finally, based on the innovation perspective of the public attention, the attention of networks formed by China's huge Internet traffic has become a brand-new resource, which has a far-reaching impact on the innovation of enterprises. Moreover, the rise of network attention can significantly the increase of the number of innovations of enterprises^[50]. By referring to the China financial innovation structure index system compiled by Li and Lin^[5], we selected corresponding keywords from the perspectives of technological innovation, institutional innovation, tool innovation, market innovation and organizational innovation to search its Baidu indexes for depicting the public's attention to real estate finance innovation, finding that the rapid development of science and technology has promoted the transformation of the practice and theoretical research of enterprise innovation to digitalization. In practice, digital technology has exerted a huge impact on enterprise innovation^[51]. The index system of real estate finance innovation is shown in Table 2.

In this paper, the data of enterprise innovation come from iFind and the Wind Database, the data of policy innovation come from PKULAW.com, and the data of public innovation come from Baidu Index. In order to ensure the integrity and stability of annual or quarterly data in most provinces, we only selected the quarterly data from 2009 to 2019. Since there is a serious lack of data about Tibet, Taiwan, Hong Kong and Macao, this paper only includes the innovation indexes of real estate finance of 30 provinces in China. Also, due to the financial crisis in 2008 and the COVID-19 in 2020 and 2021, the data may fluctuate abnormally, thus regarded as not universal. We compile the real estate financial innovation index from 2009 to 2019. For the sub-indexes under the enterprise innovation index, the current quarterly value has been employed in the real estate development investment and commercial housing sales, and logarithmic processing is carried out on them. The asset-liability ratio after excluding advance receipts corresponds to long-term liabilities, with the specific calculation formula as follows: (liabilities$-$advance receipts)/(total assets$-$advance receipts $\times$ 0.6); the net debt ratio corresponds to the overall debt, with the specific calculation formula as follows: (liabilities with interest-monetary fund)/net assets; the cash to short-term debt ratio corresponds to current liabilities, with the specific calculation formula as follows: (monetary funds/current liabilities); ABS is the total amount of securitized products of assets issued by the real estate industry and the financial industry, the date of issuance is defined by the date of issuance announcement, and logarithmic processing is conducted on the total amount of issuance; the ratio of market value to GDP for A-share listed companies in the financial industry and the real estate industry is adopted as the ratio of market value for the listed companies; and the proportion of domestic loans is used as the proportion of domestic loans in the source of funds for real estate development enterprises. This index reflects the traditional financing channels, and we take the reciprocal treatment for it. For the policy innovation, we downloaded relevant policies such as local laws and regulations, local government regulations and local normative documents with the effectiveness of a higher level from PKULAW.com as per keywords, the dates of which were defined by the implementation date instead of the release date, and logarithmic processing is conducted on the number of policies. For the public innovation, we used public attention to reflect the public's awareness of real estate finance innovation, and the selection of keywords follows the following three principles: First, they should be statistically significant, featuring continuity; second, they should be of economic significance, and reflect the economic significance of the main indexes; finally, the volatility of keywords should correspond to the volatility of the main economic indexes. Through these principles, we determined the initial keywords, and finally confirmed them according to the correlation coefficient method. The keywords should have a strong correlation with the innovation of real estate finance. For such, we analyzed the Pearson correlation coefficient between the initial keywords and the scale of individual housing loans, and abandoned the keywords whose absolute value of Pearson correlation coefficient is less than 0.5. Finally we selected 20 keywords and conducted logarithmic processing on the Baidu index of these 20 keywords.

Since there are great differences in index dimensions, we need to normalize them, and the MAX-MIN Method is the commonly-used normalization method; however, some index data have abnormal values so that the maximum value may be abnormally expanded and the minimum value may be abnormally reduced; accordingly, through manual screening of index data, 95% quantile and 5% quantile are used to replace the maximum value and the minimum value of the indexes with abnormal values to eliminate any errors caused thereby. In addition, the indexes should be compiled comparable not only in vertical time, but also in horizontal areas. We referred to the treatment methods of Guo, et al.^[30] to conduct the following treatment: Taking 2009 as the base period, we took 95% quantile of each region in 2009 as the maximum value and 5% quantile as the minimum value; also, we processed the data by winsorization. If the maximum value of the base period (2009) of a region exceeds 95% quantile, then the data is adjusted to 95% quantile, and the similar processing is conducted for the minimum value. Since 2009 is taken as the base year to get the maximum value or minimum value, the normalized results of indexes may be less than 0 or greater than 1 in the following years.

After the indexes are normalized, the weights of different indexes will be determined. Through the above analysis, the methods for determining the weights are divided into subjective weighting method and objective weighting method. Subjective weighting method mainly consists of Delphi method and analytic hierarchy process, in which relevant experts grade the weights according to the importance of indexes, while the objective weighting method mainly refers to the, coefficient of variation method and range coefficient method, which does not rely on the subjective judgment of experts, but assign weights according to the characteristics of data themselves. This paper combines the subjective and objective methods in the assignment of weights. Firstly, the analytic hierarchy process is used to obtain the weight of each specific index to the upper index, among which the weight of each index within the three red lines is obtained through the range coefficient method, and then the range coefficient method is employed to determine the weights of government innovation, enterprise innovation and public innovation; finally, the general index is obtained.

The idea of the range coefficient method is similar to that of the coefficient of variation method, which assigns weights according to the standard deviation of the observed value of each index. First, the standard deviation of each index is obtained, and then the standard deviation of each index is summed up. The ratio of the standard deviation of this index to the aggregate standard deviation means the weight of this index, as shown in Formula (1), where represents the weight of the $k$th index:

AHP (analytic hierarchy process) is a multi-criteria decision-making method proposed by Saaty in [52] which reasonably solves the qualitative problems and carries out the quantitative treatment. The steps of weighting by the analytic hierarchy process are as follows: Firstly, construct a judgment matrix, and after completing the structure of all levels, conduct an comparative analysis on the paired indexes of the same level as per experts' opinions, thus obtaining the degree of importance; then calculate the weight of each index through the judgment matrix; namely, the eigenvector corresponding to the maximum eigenvalue. The last step is to carry out the consistency check and the calculation formula of the consistency index (CI) is shown in Formula (2), where ${\lambda }_{max}$ represents the maximum eigenvalue. For the five indexes of the policy innovation, the criteria concerns the policy's correlation with real estate finance and its legal effect on real estate financial regulation; the more relevant the policies are with real estate finance and the higher the legal effect of the issued policies on real estate finance regulation, the higher the weight. For the six indexes of enterprise innovation, we use the depth of innovation and the correlation degree of enterprise with real estate finance as the judging standards; the deeper the innovation and the more correlative it is with real estate finance, the higher its weight. For the five indexes of the public innovation, we assign weights according to the innovation degree of technology, institution, tool, market and organization. In recent years, the emerging financial technologies based on such technologies as big data, blockchain and digital cash have greatly promoted the innovation of real estate finance, so we have given greater weight to technological innovation. The judgment matrices of policy innovation, enterprise innovation and public innovation are shown in Tables 3, 4 and 5:

where, ${\lambda }_{max}=5.0780$ and the consistency index (CI)$=0.0174$, which passed the consistency test smoothly. Where, ${\lambda }_{max}=6.5309$ and the consistency index (CI)$=0.0843$, which passed the consistency test smoothly. Where, ${\lambda }_{max}=5.0681$ and the consistency index (CI)$=0.0152$, which passed the consistency test smoothly.

After normalizing and weighing the indexes, the next step is to summarize them from bottom to top according to the weights. We used the synthesis model of weighted arithmetic mean, and the model construction process is shown in Formula (3), where RFINDEX represents the real estate finance innovation index, represents the weight of each specific index, represents the value of each evaluation index, and $k$ represents the number of each evaluation index, and we multiply them by 100, so that the values of most indexes fall within the range of 0$\sim$100. When collecting the data of the Three Red Lines and ABS of enterprises, there was a lack of data in some central and western provinces (Qinghai, Ningxia, etc.); hence, we assigned 0 to the weight of the Three Red Lines and ABS indexes of these provinces. The lack of data essentially explains the backwardness of these provinces in respect of these indexes, so it does not affect the comparison between provinces in terms of innovation indexes of real estate finance.

Based on the index compilation method and the innovation index system of real estate finance as described above, we have compiled the innovation indexes of real estate finance of 30 provinces, autonomous regions or the municipalities directly under the central government, which covered the whole country. Whether it is provincial, municipal or national data, the time span is from 2009 to 2019, and the frequency concerns the quarterly data. In the following, we will make some meaningful statistical analysis of the development trend and spatial-temporal characteristics of the indexes.

The innovation indexes of real estate finance of the whole country as well as the provinces, municipalities and autonomous regions from 2009 to 2019 are shown in Tables 6 and 7¹. Due to the limited space, three representative provinces, autonomous regions and the municipalities directly under the central government are selected from the eastern, central and western regions of China respectively to demonstrate the innovation indexes of real estate finance at the provincial level. From the innovation indexes of the national real estate finance, we can see that since 2009, the innovation indexes of China's real estate finance had been in a deepening state, but the growth rate was relatively slow. They reached the peak in 2017, and since then, they were in a slow development, the trend of which coincides with the financial repression environment in China in recent years. At the provincial level, we can see that there was a high degree of real estate finance innovation in the eastern developed areas, followed by the central region and finally the western region. We noticed that Xinjiang's innovation indexes of real estate finance were negative from the third quarter of 2009 to the first quarter of 2010. This is because when constructing the public innovation indexes, we found that the data of Xinjiang from the third quarter of 2009 to the first quarter of 2010 were basically 0. We chose the first quarter of 2009 as the base period when doing normalization, thus there will be a negative value. We leave this situation alone, to a certain extent showing the correctness of indexes in the process.

¹The innovation indexes of real estate finance at the national level are not comparable with those at the provincial level for the reason that the national-level data and provincial-level data have not been compared and normalized in the process of non-dimensioning. However the innovation indexes of real estate finance between provinces are horizontally comparable. Due to the limited space, if you need all the innovation index data of real estate finance, please contact the author by email for them; if quoted, please mark the data source. E-mail: lixiuting@ucas.ac.cn or yinlijun16@mails.ucas.ac.cn.

Now, We analyze the change trend of the innovation indexes of real estate finance along with time. As shown in Figure 6, we depict the change trend of the innovation indexes of real estate finance at the national level and the provincial level respectively, of which the change trend at the provincial level means the average value of each province. As can be seen from Figure 6, the change trend of the average innovation index of real estate finance at the national level and the provincial level is basically consistent, showing obvious characteristics of seasonal fluctuation, once again showing that the index design is reasonable and accurate. From the figure, we can see that real estate finance innovation has developed slowly in recent years, despite that it had developed rapidly from 2009 to 2016 mainly for the reason of rapid development of the real estate market in this period. The balance of RMB loans in the real estate industry has been on the rise from 2009 to 2016. The year-on-year growth of RMB loans in the real estate market peaked at 27%. At the end of 2016, the Central Economic Work Conference made clear for the first time that "Houses are for living, not for speculation." Since then, the real estate market has entered a stage of restrained development. Financial institutions began to tighten credit to the real estate market, and market expectations gradually became rational. The development of real estate finance innovation has slowed down accordingly.

This section will analyze the spatial characteristics of real estate finance innovation from three aspects: Regional convergence, spatial autocorrelation and regional differences.

Real estate finance innovation is more prominent in the more developed provinces in the eastern and central regions of China, while it is relatively slow in the central and western regions in China; however, the differences between regions are also further narrowing over time. From Figures 7 to 10, it can be clearly seen that the characteristics of convergence between regions gradually appear. The difference between regions in 2018 and 2019 is significantly smaller than that between regions in 2009 and 2010. With the development of the real estate market, real estate financial innovation is not limited to the eastern coastal areas, but gradually forms a wider coverage of real estate financial innovation.

From the above charts, we can see the convergence characteristics of inter-regional real estate finance, but further empirical tests are required. We learn from Sala-I-Martin^[53] test methods on economic convergence, and use $\beta$ convergence model for testing. This method was put forward according to the economic convergence theory. The $\beta$-convergence of real estate finance innovation means that in the early development stage of real estate finance innovation, the regions with lower indexes will see more rapid growth, as compared with the regions with higher indexes; that is to say, the growth rate of regional digital inclusive finance is negatively correlated with the level at the beginning of the period. This will lead to the gradual convergence of development among regions. $\beta$ convergence is divided into absolute convergence and conditional convergence. Here we test these two kinds of convergence respectively: $\beta$ absolute convergence means that the real estate finance innovation levels in different regions will gradually converge to a stable state with the passage of time without controlling the influence of external environment. The $\beta$ absolute convergence model is shown in Formula (4). There are two methods to calculate $\beta$ conditional convergence: The first method is to add external environmental influencing factors to the absolute convergence model; that is, to add corresponding controlled variables, while the second method is to abandon the controlled variables and control the calculation method of the model; say, control the fixed effects in different regions and their changing trends along with time. In this paper, the second calculation method is adopted; and the $\beta$ conditional convergence model is shown in Formula (5).

where represents the innovation index of real estate finance of each province in 2009, represents the average annual growth rate of the innovation indexes of real estate finance of $k$ region in $t$ years; $\alpha$ and $\epsilon$ are respectively a constant term and an error term; regression represents the convergence coefficient. If is significantly negative, the real estate finance innovation will have absolute convergence; otherwise, it is the decentralized convergence.

Based on Formula (4) and Formula (5), the regression results of each province are shown in Table 8. We can see that the regression coefficients are negative in both absolute convergence and conditional convergence. In China, the real estate finance innovation features the strong convergence geographically.

The real estate financial innovation index shows convergence characteristics, which to some extent shows that the gap between China's provinces has gradually narrowed in recent years. The policies, regulations and government supervision to promote real estate financial innovation and market-oriented reform have been gradually improved. Intermediary institutions such as guarantee, credit, insurance, mortgage and evaluation in real estate financial innovation have also been gradually improved. However, since 2020, under the dual pressure of COVID-19 and downward market expectations, the gap between the middle east region and the western region may widen further.

This section discusses the spatial correlation of the innovation indexes of real estate finance, and empirically studies whether real estate finance innovation has similar development attributes in the geographically adjacent areas; that is, whether the innovation indexes of real estate finance feature spatial autocorrelation. "Spatial autocorrelation" means that regions with similar or adjacent positions have similar variable values. If high values and high values are gathered together, while low values and low values are clustered, there will be "positive spatial autocorrelation". On the contrary, if high values and low values are adjacent, there will be "negative spatial autocorrelation". If high values and low values are randomly distributed, there will be no spatial autocorrelation. There are three main methods to verify spatial autocorrelation: Moran's I, Geary's $C$ and Getis-Ord General $G$. Among them, Moran's I includes Global Moran's I and Local Moran's I, and the Local Moran's I represents the spatial agglomeration near a certain area $i$. And the formula for calculating the Global Moran's I is as follows:

where $S^2=\frac{\sum _{i=1}^n(x_i-\overline{x}{)}^2}{n}$ represents the sample variance and $x_i$ represents the spatial sequence. In this paper, it represents the innovation index of the real estate finance. $w_{ij}$ is the $(i,j)$ element of the spatial weight matrix (used to measure the distance between region $i$ and region $j$), while $\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}$ is the sum of all spatial weights. If you need to construct a spatial Local Moran's Scatterplot, you need to standardize the spatial weights. At this time, $\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}=n$; and Moran's I is as follows:

The Local Moran's I model is as follows:

The value of Moran's I is between $-1$ and 1. The value that is greater than 0 indicates the positive autocorrelation and that less than 0 the negative autocorrelation. Generally, the positive autocorrelation is more common. If the observed value and its space are drawn into a scatterplot, it is called "Moran scatterplot", and Moran's I refers to the slope of the regression line of the scatterplot.

The Geary's $C$ is also called the Geary's Contiguity Ratio, and its model formula is as follows:

Different from Moran's I, the core component of Geary's $C$ is $(x_i-x_j{)}^2$. The value of Geary's $C$ is between 0 and 2. The value greater than 1 indicates the negative correlation, and that equal to 1 the uncorrelation, and that less than 1 the positive correlation.

Although Moran's I and Geary's $C$ can test the agglomeration between regions, they cannot judge whether a region is a "hot spot" or a "cold spot" region. The so-called "hot spot" refers to the area where high values and high values gather, while the "cold spot" the area where low values and low values cluster. Both "hot spot" and "cold spot" areas show positive autocorrelation. Getis-Ord General $G$ can show this correlation, with the model formula shown as follows:

If $G$ is greater than 1.96, the original hypothesis of no spatial autocorrelation will be rejected at the level of 5%, and it is considered that there exist the spatial positive autocorrelation and hot spots.

First of all, we calculated Moran's I, Geary's $C$ and Getis-Ord General $G$ for the regional clustering of the innovation indexes of real estate finance, with the results shown in Table 9. As can be seen from Table 9, the Moran's I of all provinces in China is significantly positive, and Geary's $C$ is significantly less than 1 and greater than 0; hence, we believe that the innovation indexes of real estate finance have significant spatial agglomeration, and the innovation indexes of real estate finance between adjacent regions have similar attributes. The regions with the high-level innovative development in real estate finance cluster, while those with the low-level innovative development in real estate finance gather together. Although $G$ is significantly positive, its value does not exceed 1.96, so there is no "hot spot" or "cold spot" area.

We draw a Local Moran's I scatterplot, which can more vividly illustrate the spatial agglomeration of the innovation indexes of spatial real estate finance. From Figure 11, we can see that most provinces are distributed in the first and third quadrants. As a new business form of finance, real estate financial innovation still needs to follow the basic law of financial development. Digital finance's development still depends on the real economy and traditional finance (Guo, et al^[54]; Yao and Shi^[55]; Guo and Wang^[56]). The same is true for real estate financial innovation. As a new business form, it will not appear for no reason. Its development and promotion depend on geographical factors and economic development, so it presents the characteristics of spatial autocorrelation. Compared with 2018 and 2019, the scatterplots in 2009 and 2010 featured more significant agglomeration characteristics, and such differences between provinces gradually decreased. This has also verified the above-mentioned characteristic that the innovation indexes of real estate finance tend to converge.

Then we discussed the nature of spatial agglomeration of each sub-index from the levels of the governments, enterprises and the public. Table 10, Table 11 and Table 12 represent Moran's I, Geary's $C$ and Getis-Ord General $G$ in terms of government innovation, enterprise innovation and public innovation respectively, while Figure 12, Figure 13 and Figure 14 are the corresponding Local Moran's I scatterplots.

From Table 10, we can see that Moran's I of the policy innovation index was significantly positive except in 2009 for the reason that the impact of the financial crisis had led to the introduction of emergency management policies in various regions based on the specific conditions of provinces and cities, resulting in anomalies in the agglomeration of regions with innovative policies, and the $G$ index was positive but not significant. In 2009, 2012, 2015, 2016 and 2018, Geary's $C$ was less than 1 and greater than 0, but it has no strong significance. Although Geary's $C$ was stricter than Moran's I in the test of agglomeration, it shows that the spatial agglomeration of policies was not particularly significant. This has been indicated in the above scatterplot.

From Table 11 and Figure 13, we can see that the enterprise innovation index also shows strong spatial agglomeration, without showing up of "hot spots" and "cold spots". The spatial agglomeration was strong in 2009 and 2010, but weak in 2018 and 2019.

In the above charts, we analyze the spatial distribution characteristics of the innovation index of real estate finance, government innovation index, enterprise innovation index and public innovation index, finding that Moran's I and Geary's $C$ of these indexes have both passed the spatial positive autocorrelation test at a relatively significant level. This indicates that there is a significant spatial agglomeration of real estate finance innovation. It is embodied in the combination of high values and high values, and that of low values and low values. The Local Moran's I of most provinces is distributed in the first quadrant and the third quadrant, in which the provinces falling in the first quadrant are mostly located in the eastern coastal areas and are economically developed, and the provinces falling in the third quadrant are the provinces and cities in the central and western regions. Due to the limited space, we did not calculate Moran's I based on the economic distance of the provinces and cities. The $G$ test was not significant in some years and all the $G$ values were not greater than 1.96. There exist no relevant "hot spot" or "cold spot" areas in real estate finance innovation.

In this section, we focus on the regional differences in the innovative development of real estate finance. In order to quantitatively study the regional differences in different provinces. Here we introduced such methods as the Coefficient of Dispersion, cluster analysis and hot spot map to reflect the differences in the innovation of real estate finance in different provinces in China. First of all, we calculated the Coefficient of Dispersion of the innovation indexes of China's real estate finance from 2009 to 2019. The specific calculation formula is, where $i$ represents the year, and represent the standard deviation and mean value respectively of China's real estate finance innovation, and represents the Coefficient of Dispersion of real estate finance innovation in each year. The calculation results are shown in Table 13.

From the above table, we can see that from 2009 to 2013, the Coefficient of Dispersion of real estate finance innovation gradually decreased, along with the decrease of differences among regions. However, the Coefficient of Dispersion of real estate finance innovation rebounded from 2014 to 2016, with the regional differences gradually increasing and afterwards gradually decreasing. This is mainly related to the policies issued in China over the recent years for restraining the real estate industry and discouraging housing speculation. In the next step, we carried out the cluster analysis on the innovation indexes of real estate finance of 30 provinces, autonomous regions and municipalities directly under the central government. Here we used the cluster method of inter-group connection, with the clustering plan being between 4 and 5. According to the tree diagram, we selected four categories. The clustering results are shown in Table 14.

From Table 14, we can see that the most developed areas for real estate finance innovation included Beijing, Shandong, Zhejiang and Guangdong in 2018 and 2019. The vast majority of provinces in China were comparatively developed areas for real estate finance innovation, which were mainly concentrated in the central region, while the western region including Qinghai and Ningxia were less developed areas for real estate finance innovation. For such, according to the division of the eastern, central and western regions in the Seventh Five-year Plan of China², we calculated the average value of the innovation indexes of real estate finance in the eastern, central and western regions respectively, and drawn a line chart as shown in Figure 15, which illustrates the above viewpoint.

²According to the division rules as stated in the Seventh Five-year Plan, the country has been divided into three major economic belts: Eastern, central and western. The eastern belt includes 12 provinces, municipalities and autonomous regions of Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi and Hainan which are taken as developed areas; the central belt includes nine provinces and autonomous regions of Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei and Hunan, which are taken as less developed areas; and the western belt includes 10 provinces and autonomous regions of Sichuan, Guizhou, Chongqing, Yunnan, Tibet, Shaanxi, Gansu, Ningxia, Qinghai and Xinjiang which are taken as underdeveloped areas.

In recent years, although real estate financial innovation shows the characteristics of regional convergence, there are still strong regional differences in its development. The economy of the central and eastern regions is relatively developed. The multi-level real estate financial market system and products are relatively perfect, and the corresponding supervision, laws and regulations are relatively complete. There are much more application scenarios of compliant financial instruments such as real estate stocks, trusts and bonds, which have a relatively solid foundation for real estate financial innovation. The economic strength of the western region is weak and the application of real estate financial innovation products is limited. Therefore, the development of real estate financial innovation is relatively backward.

Based on the existing literatures and relevant theories, this paper constructs the innovative development indexes of China's real estate finance from the levels of the governments, enterprises and the public, which accurately depict the real estate finance innovation levels of 30 provinces in China since 2009 on a quarterly basis. We also analyze the temporal and spatial characteristics of the real estate financial innovation index, which provides theoretical support for the quantitative and empirical research on real estate financial innovation in the future.

Since 2009, China's real estate finance innovation has been in a deepening period, while the growth rate has been relatively slow. This is consistent with China's financial repression environment in recent years. At the end of 2016, the Central Economic Work Conference first clarified the positioning of the real estate industry, declaring that "houses are for living in, not speculation". Since then, the real estate market has entered the stage of restrained development, and the development of real estate financial innovation has slowed down accordingly. In addition, we also analyzed the spatial characteristics of real estate finance innovation from the perspectives of the regional convergence, spatial autocorrelation and regional differences, finding that the development of real estate finance innovation in China features regional convergence. We verified this through the $\beta$ convergence model, which had passed the $\beta$ relative convergence and the $\beta$ absolute convergence. The innovative development of real estate finance has a strong spatial positive autocorrelation, which is illustrated by both Moran's I and Geary's $C$, but there exists no "hot spot" or "cold spot". Finally, we studied the regional differences of real estate finance innovation through the methods of the Coefficient of Dispersion, cluster analysis and hot spots map, with the results showing that there existed significant regional differences in the development of real estate finance innovation: The eastern coastal areas are the most developed, followed by the central areas, and the western areas are the most backward. From this hot spots map, we can see not only the differences among provinces horizontally, but also the gradual deepening process of real estate finance innovation with the change of time vertically.