Can digital finance reduce carbon emission intensity? A perspective based on factor allocation distortions: evidence from Chinese cities

The world is facing the challenges of climate change and energy structure adjustments. The role of digital finance, a new branch of business that combines digital technology and traditional financial products, in reducing global carbon emissions needs to be studied. This paper uses panel data on 280 cities in China from 2011 to 2019 to empirically examine the efficacy of digital finance for governing carbon emission reductions and the mechanism by which it does so. The results show that (1) digital finance can facilitate carbon emission reductions and help reduce carbon emission intensity within regions; (2) digital finance helps promote the rational allocation of resources and alleviates factor distortions by encouraging firms to rationally use their own factor endowments so as to reduce carbon emission intensity, which holds robustly after considering the endogenous issues such as possibly omitting variables and collinearity; and (3) differences in geographical location, the vitality of regional innovation and entrepreneurship, regional willingness to protect the environment, and environmental protection levels lead to heterogeneity in the effect of digital finance on carbon emission intensity. Therefore, it is necessary to vigorously develop digital finance as a long-term tool for carbon governance.


Introduction
Carbon dioxide emissions and the consequent climate change are some of the most important issues of our time (Ahmed and Le 2021). According to a report by the United Nations Environment Programme, the total greenhouse gas emissions in 2019 hit a record high of 59.1 billion tons of carbon dioxide equivalent. According to statistics from the World Bank (Fig. 1), China has the largest amount of carbon dioxide emissions, and despite a series of emission reduction measures, China is still facing enormous pressure to reduce its carbon emissions (Fig. 2). As an active participant in and supporter of global climate governance, China has committed to peak its carbon emissions by 2030 and is striving to achieve carbon neutrality by 2060.
Existing research has shown that carbon emissions can be reduced through changes to the industrial structure and technological innovation (Cheng et al. 2017;Zhang et al. 2020). In fact, technological innovation can help reduce carbon emissions, facilitate the transition away from extensive growth, and effectively promote high-quality economic development. Financial development can provide more financial resources for investment in projects rich in technological innovation through the rational and effective allocation of such resources (Zhou and Du 2021), thereby reducing energy consumption per unit of GDP and reducing carbon dioxide emissions. As a new form of financial service provision, digital finance is gradually becoming an integral part of China's financial system. This raises several questions. Can the rapid development of digital finance have a significant impact on carbon emissions? Which areas are most affected? What is the impact path? This article explores these issues. The answers to these questions will not only help to clarify the impact of digital finance on China's carbon emissions but also provide useful information for ensuring the highquality development of China's economy and for improving related policies.
Digital finance is deeply integrated with internet technology and is an information-driven industry. Its environmental externalities have largely been ignored by the public. As an important and powerful supplement to the traditional financial system, digital finance has many advantages, such as a wide range of coverage, low costs, and high levels of efficiency, which helps to reduce information asymmetries and transaction costs, improve the availability of financial services, and optimize the allocation of resources in the financial market . In this way, digital finance can help improve the traditional financial environment, promote the development of the generalized system of preferences (GSP) in the financial industry, help relax the financing constraints on technological innovation (Chang et al. 2021), and play a very important role in promoting regional technological innovation . Second, the rapid development of digital payment platforms has greatly reduced the transaction and time costs associated with financial services, and resident consumption is not restricted by any geographical conditions, thus reducing the number of daily  countries, 1978-2018 trips made by residents  In addition, digital finance greatly increases sales of retail goods, thus driving enterprises to expand their production, which in turn generates economies of scale and thereby improves the economic efficiency of the entire city. When this occurs, energy consumption per unit of GDP and carbon dioxide emissions are both reduced.
The theme of this paper is how to ensure green, lowcarbon economic development through the development of digital finance. Using a set of panel data on 280 prefecturelevel cities from 2011 to 2019, this paper both theoretically and empirically clarifies the positive role of digital finance in reducing carbon emission intensity, provides theoretical explanations for carbon emission reductions in China, and provides a theoretical basis for other developing countries to reduce carbon emissions. This study provides information on the development of digital finance. The main marginal contributions of this paper are as follows: first, this paper examines the relation between China's carbon emissions and the development of digital finance. It reveals how digital finance facilitates carbon emission reductions and deepens the relevant research on the environmental benefits of digital finance. The conclusions obtained indicate how digital finance can help promote high-quality economic development. Second, an in-depth analysis from the perspective of factor allocation distortions clarifies the specific path by which the digital economy helps promote carbon emission reductions in a robust way that takes the possible omitting variables, multi-mediating variables in parallel, collinearity between the explanatory variable and the mediating variable, and so on into consideration, which enriches the literature on the ways in which carbon emissions can be reduced. Third, this paper fully examines the heterogeneity in the impact of digital finance on carbon emission intensity by geographical location, the vitality of regional innovation and entrepreneurship, regional willingness to protect the environment, and regional environmental protection level and provides important evidence for the government to direct the implementation of local policies. The research results obtained provide important empirical evidence supporting the promotion of digital financial development in China in order to reduce carbon emissions and ensure green development. This paper innovatively conducts robustness tests for possible endogeneity and collinearity in mechanism tests, avoiding issues that may cause causal inference errors in mechanism tests such as overestimation of indirect effects due to correlation between mechanism variables and explanatory variables, omission of variables, and so on. Finally, we provide relevant policy recommendations and references for further reducing carbon emission intensity.
The rest of the paper is arranged as follows: the "Literature review" section presents a literature review, the "Theoretical analysis" section presents a theoretical analysis, and the "Materials and methods" section presents our research design, including the baseline model setting, variables, and data descriptions. The "Empirical results" section presents the results of the empirical analysis, and the "Discussion" section describes the research design and additional analyses, including the heterogeneity analysis and mechanism analysis. The "Conclusions and policy implications" section provides the conclusion and policy recommendations.

Digital finance and carbon emissions
Scholars have long identified links between financial development and environmental performance (Claessens and Feijen 2007;Grossman and Krueger 1995;Shahbaz et al. 2022;Tamazian et al. 2009), and they have argued that developed financial markets can provide better financial support for environmental projects with lower financing costs. For example, Tamazian et al. (2009) found that since many environmental protection projects are considered to be public sector activities, financial development is more important for environmental governance by the government than by enterprises.
In recent years, the focus in the environmental research field has shifted to the analysis of the determinants of carbon dioxide emissions. Scholars have used time series data to conduct country-specific carbon emission research and have found that economic growth (Sadorsky 2010), trade openness (Jalil and Feridun 2011), and financial development (Sadorsky 2010) are all important determinants of carbon dioxide emissions. With the increasing prominence of environmental issues and the popularization of the concept of green development, an in-depth discussion of whether digital finance has any environmental effects and whether it can promote the green transformation of the Chinese economy is needed. According to the literature, in theory, financial development can attract inflows of foreign capital, promote corporate investment, help raise environmental awareness and promote technological innovation (Sha et al. 2022), serve as a mechanism for long-term growth, and enhance the effect of environmental policies. Regulations also improve the environmental performance of developing countries in many ways (Yuxiang and Chen 2011), thereby reducing carbon emissions. Does digital finance have the same impact on carbon emissions?
In contrast with traditional finance, digital finance can reduce information asymmetries, lower search and matching costs and financial service thresholds, and expand the effective frontier of financial services , thereby promoting the upgrading of regional industry . Digital finance is inclusive and precise, and these characteristics increase the availability of financial services in small and medium-sized cities, thus strengthening the industrial carrying capacity of such cities and promoting the transformation of energy-intensive industries into low-carbon industries with high profit margins and high added value . Second, by relying on information technology, digital finance can broaden the sources used in risk assessments, tap into the potential needs of users, and improve the efficiency of risk pricing, thereby increasing the availability of financial services and effectively relaxing the financing constraints faced by small, medium, and microenterprises (Lu et al. 2021). In so doing, digital finance improves the overall economic efficiency of the region and thus reduces its carbon intensity. In addition, digital finance makes consumption more convenient, actively promotes consumption upgrades, and encourages consumer demand Song et al. 2020), thus further promoting the development of a green consumption ecosystem. In the long run, digital finance facilitates household consumption, prompting enterprises to expand their production and thereby producing agglomeration effects and reducing carbon emission intensity. Finally, digital finance can be used to provide financing for technological innovation to enterprises , especially those enterprises in the tail of the financial risk distribution who have been discriminated against by funding providers for a long time, such as small and microenterprises, innovative and entrepreneurial entities, and members of other vulnerable groups. Digital finance not only provides sufficient funds for enterprise R&D but also provides innovative financing methods and can drive the development of new business models and service formats. As a result, digital finance can stimulate regional innovation and development, and it plays an important role in improving regional ecological environments.
Based on the above analysis, this paper proposes: Hypothesis 1: Digital finance helps build up capital stock, accelerates technological innovation and adjustments to the industrial structure, and directly reduces carbon emission intensity.

Digital finance mitigates the effect of distorted factor allocations on carbon emission reductions
The marketization reform of China's factor market is obviously lagging behind (Tan et al. 2019;Zhujun et al. 2020), and the degree to which marketization drives prices for certain basic factors is significantly less than that in the commodity markets. Institutional constraints such as the household registration and land systems and government intervention and control have resulted in the artificial segmentation of the market, making it impossible for factors to be effectively allocated in accordance with market laws, which is not conducive to the regional specialization of labor, knowledge spillovers, or effective competition and which hinders the high-quality sustainable development of China's economy (Foster et al. 2008;Ji 2020;Tan et al. 2019). Therefore, mitigating factor allocation distortions and promoting factor redistribution are indispensable for China's economic growth (Foster et al. 2008;Kuznets 1973). As research has progressed, some scholars have found that there is a close relationship between factor allocation distortions and environmental pollutant emissions (Ji 2020;Yin et al. 2018). The low prices caused by factor distortions lead to the excessive consumption of production factors and high emissions (Liu and Lin 2017) according to empirical evidence from China (Yin et al. 2018). Compared with efficient factor allocations, factor distortions make it easier for inefficient producers to obtain scarce resources without motivating them to engage in innovation or upgrade their production processes Sandleris and Wright 2013). This results in environmental pollution and low ecological quality. Due to the mismatch between human and physical capital in developing countries (Acemoglu and Robinson 2001), even if advanced foreign technology is introduced, it does not have the same effect as in developed countries in terms of improving industrial processes or environmental conditions. In addition, under China's unique system of fiscal decentralization, local officials have few incentives to focus on environmental pollution, especially increases in carbon emissions, and their economic incentives are such that they are more likely to intervene in factor markets and thus increase environmental pollution (Que et al. 2018). Therefore, factor allocation distortions may lead to higher pollutant emissions, lower environmental efficiency, and more intense pollution. How to alleviate these factor distortions to reduce environmental pollution is a problem worthy of attention.
The low efficiency in the capital allocations and the imbalance in the capacity to supply capital caused by the traditional dual financial structure and the monopolized financial system are important sources of the distortions in factor allocations. In a closed economy, a country can reduce the distortions in its factor markets and improve the efficiency of its resource allocations by reducing financial frictions (Midrigan and Xu 2014) and labor market frictions (Hsieh and Klenow 2008). Existing research shows that the popularization of the internet and the development of financial technology have helped to release the flow of production factors such as knowledge, technology, and data in the market by reducing the information asymmetry between supply and demand (Nigam et al. 2020) and improving the quality of the matches between traditional production factors such as labor and capital in market transactions (Borch and Madsen 2007;Kuhn and Skuterud 2004). Specifically, there are two ways in which digital finance alleviates the distortions in factor allocations, thereby impacting carbon emission intensity.
In terms of capital, first, with the help of internet platforms and big data analysis, digital finance can help eliminate the information asymmetries existing in the economic system and reduce the moral hazard and adverse selection present in investment and financing, thus reducing the mismatch in the allocation of capital and effectively alleviating the financing constraints faced by enterprises seeking to invest in projects to upgrade their technology (Boyreau-Debray 2003;Love 2003). In addition, digital finance helps increase enterprise investment in green technology, thereby reducing carbon emission intensity. Second, digital finance is both low cost and highly efficient, which increases the innovation efforts especially of those small and mediumsized enterprises in the tail of the risk distribution. Digital finance can improve the flow and turnover of innovative capital by enabling mobile payments, online transactions, etc. and thus drive the formation of a process chain that integrates the retrieval of the demand for, communication surrounding, and matching related to financing, thereby reducing financing costs (Shahrokhi 2008). This further increases the financing available to small and mediumsized enterprises and thus their R&D innovation (Kaplan and Zingales 1997). Finally, the most important function of digital finance is to overcome the limitations imposed by time and space and establish a direct point-to-point connection between the supply side and the demand side of the financial product market. Production factors such as labor, capital, and technology can be connected and reorganized across regions in a short period of time, strengthening the allocation of resources and optimizing the allocation of credit funds across industries. In addition, internet platforms for shopping built on the basis of third-party payments and e-commerce have gradually both stimulated and satisfied the demand of residents for consumption goods . The diversification of consumer demand and the optimal allocation of credit funds jointly promote the transformation and upgrading of the industrial structure, which decreases carbon emission intensity (Liu et al. 2007).
Second, in terms of labor, first, the development of digital finance increases the demand for skilled workers and alleviates the inefficient allocation of financial workers. Providing basic banking services electronically not only cuts the costs of banks but also improves the efficiency of their work and effectively reduces the waste of labor resources in the financial sector. Digital finance has increased the demand for talent in the financial industry, which helps ensure good matches between high-quality financial talent and firms and alleviates the misallocation of financial labor. Knowledge spillovers accelerate the development of high-quality innovations in cities (Glaeser and Lu 2018), which in turn reduces carbon emission intensity. In addition, the development of digital finance provides financial support via the extension of credit for the training of high-skilled talent, which facilitates the accumulation of human capital for technological innovation. Digital finance provides information, convenient ways to obtain financing, commerce platforms with which highskilled workers can innovate and start businesses, and support for innovative projects and stimulates the innovation potential of workers (Chen et al. 2015). Moreover, digital finance has significantly improved the social security of residents by providing them with more humanized and convenient services (Omar and Inaba 2020), thereby encouraging residents to be innovative. Finally, the effects of knowledge sharing and knowledge spillovers arising from the use of the internet and information technology enable enterprises to obtain more information and information from geographically distant places. The effects of all this learning accelerate the accumulation of human capital, effectively changing the behavior of enterprises and the organizational structure of the industry, thereby promoting technological innovation of enterprises (Pan et al. 2021), improving energy efficiency and enabling low-carbon development (Zhang et al. 2017). Thus, this paper puts forward the following hypothesis: Hypothesis 2: Digital finance alleviates the distortion of factors, stimulates vigorous innovation, and thus reduces carbon emission intensity.

Theoretical analysis
Suppose there are two types of sectors in a city: energyintensive sectors and low-energy sectors. A city's carbon emissions are determined by both types. Enterprises in energy-intensive sectors are large in scale and monopolistic. The members of the low-energy sector are small-scale enterprises that participate in a perfectly competitive market, and in both sectors, the enterprises exhibit constant returns to scale. The production function for enterprises in the energyintensive sectors is as follows: where Y 0 is the output of energy-intensive enterprises, A is green total factor productivity, K 0 is investment in physical capital not related to energy, L 0 is the total labor measured as the total hours worked by employees of energy-intensive enterprises, and E 0 is the total energy input of the energyintensive enterprises, measured by the carbon dioxide emissions of energy-intensive enterprises. 01 and 02 represent the output elasticity of the physical capital and energy input of the enterprise, respectively, and n is the labor output elasticity, since both types of enterprises exhibit constant returns to scale, which means 01 + 02 + n = 1 , and the cost constraints faced by energy-intensive enterprises are Environmental Science and Pollution Research (2023) 30:38832-38852 C 0 is the enterprise cost constraint, and r 0 is the unit cost of physical capital for the energy-intensive enterprises, that is, the bank's lending rate. is the hourly wage, and f is the cost of energy per unit of carbon dioxide emissions. The energy-intensive sector consists of large-scale enterprises with monopoly power. Therefore, the enterprises in this sector are aimed at minimizing their costs subject to the given output condition. Solve the following Lagrangian equation: Taking the derivative with respect to physical capital, labor, and energy consumption: The optimal input of physical capital for the energy-inten- An n 02 02 r n+ 02 0 , and the optimal amount An n 01 01 f n+ 01 . Similarly, the production function for the low-energy sector is Moreover, 11 + 12 + n = 1 , and the cost constraint faced by the enterprises in the low-energy sector is where r 1 is the unit cost of physical capital for the lowenergy enterprises, and their cost of financing is constrained which is greater than the lending rate in the banking system due to crowding out in the traditional finance sector; that is, r 1 is greater than r 0 .
Under these cost constraints, the low-energy sector is aimed at maximizing its output; then, we can solve for its optimal factor input with the following Lagrangian equation: Taking the derivative with respect to capital, labor, and the energy input, we have The optimal input of physical capital for the low-energy sector is K 1 = C 1 11 r 1 , and the optimal energy input is Therefore, the optimal output for low-energy enterprises is Y 1 = C 1 r 1 −a 11 , where = 11 11 n n 12 12 −n f − 12 . Carbon intensity is the ratio of carbon emissions to output: The development of digital finance has expanded the cost constraints on small and medium-sized enterprises by reducing the cost of borrowing for capital; that is, dC 1 > 0 and dr 1 < 0 .
However, the enterprises in the energy-intensive sector obtain financial services mainly through traditional financial service providers such as banks, so they are not affected by the development of digital finance. As a result, the carbon intensity of the low-energy sector is Therefore, the carbon intensity of the low-energy sector decreases with the decrease in r 1 . The energy input of the lowenergy sector increase with the increase in C 1 and the decrease in r 1 . Therefore, Since Y 1 increases with the increase in C 1 and the decrease in r 1 , , and 1 Y 0 ∕E 1 +Y 1 ∕E 1 decreases because of the lower carbon intensity in low-energy sector and the reduction of energy input (i.e., carbon emissions) in the low-energy sectors. Therefore, the total carbon emissions in the economy Factor distortions refer to the deviation of the market price of a kind of factor from its opportunity cost due to imperfect markets or government regulation. Following Hsieh and Klenow (2008), we construct the factor distortion index as follows: An n 01 01 f n+ 01 Since 0 < 11 + n < 1 , −n 11 +n + 1 − 11 > −n 11 +n + 1 − 11 11 +n = 0 . The factor distortion index DIS Hsieh decreases with the reduction of r 1 ; then, − 11 −n 1− 11 −n < 0 , all else remaining unchanged; carbon intensity ( E∕Y ) decreases as the factor distortion index DIS decreases. Therefore, the development of digital finance reduces carbon intensity by alleviating the distortion of factor prices.

Model construction
We examine the impact of digital finance on carbon dioxide intensity with the following regression equation: where i represents the prefecture-level city, and t represents the year. Tcp it is the explained variable of this study: the carbon emission intensity (CO 2 /GDP) of prefecture-level cities. Dif it is the core explanatory variable of this study: digital finance. Control ijt represents other covariables, i represents the unobservable city effect, t represents the time effect, and it is the random error term.
Formula (1) is the static panel model. Considering the dynamic continuity of carbon dioxide emissions and the impact of economic inertia, there is strong path dependence in the high level of carbon emissions in the industrial structure, and existing production and energy consumption patterns cannot easily be changed in a short period of time (Chow and Li 2014;Jayanthakumaran et al. 2012); therefore, carbon emission intensity in the previous period affects that in the current period. In this paper, the firstorder lag term for carbon emission intensity is added to the model to enable the investigation of dynamic effects on carbon emission intensity due to path dependence: where Tcp i,t−1 represents the carbon dioxide intensity in period t − 1 . Notably, the introduction of lagged carbon dioxide intensity into the regression equation has the following effects: (1) It captures the fact that the emission of carbon dioxide is a dynamic process and that in reality, carbon (2) dioxide emissions are consistent. Thus, it may therefore be more reasonable to use the dynamic model than the static model.
(2) Many factors influence carbon dioxide intensity, and it is impossible to completely control for all of these factors and especially those unobserved when setting the model. The introduction of lagged variables can account for the influence of uncontrollable factors to make the regression results obtained more credible.

Carbon emission intensity (Tcp)
Carbon emission intensity is represented as carbon dioxide emissions per unit of prefectural GDP. Prefectural carbon emissions include not only carbon emissions from the direct consumption of energy, such as coal, gas, and liquefied petroleum gas, but also carbon emissions from the consumption of electricity and thermal energy. The equation for calculating the total carbon dioxide emissions in each city is given by formula (3). The carbon emissions from natural gas, liquefied petroleum gas, electricity, and thermal energy consumption are summed to obtain the total carbon emissions in each city.
where C 1 , C 2 , C 3 , and C 4 are the carbon dioxide emissions caused by the consumption of natural gas, liquefied petroleum gas, electricity, and thermal energy, respectively, throughout society. E 1 is total natural gas consumption, and k is the CO 2 conversion coefficient for natural gas. E 2 indicates the consumption of liquefied petroleum gas, and v is the CO 2 conversion coefficient for liquefied petroleum gas. E 3 is total electricity consumption throughout society, and is the emission factor for the grid at baseline in each region.
Finally, E 4 is the total heat supply, including the total supply of steam heat and hot water heat; is the calorific value coefficient of raw coal; and is the CO 2 conversion coefficient for raw coal. The emission coefficients for the various energy sources are shown in Table 1.

Digital finance (Dif)
This article draws on the digital financial inclusion index compiled by the Institute of Digital Finance of Peking University. The index is based on data provided by Ant Financial Service Group and measures the development of digital finance in the provinces and cities of China (excluding Hong Kong, Macao, and Taiwan). This set of data includes information on three dimensions of digital finance: coverage breadth (Dcb), usage depth (Dud), and digitalization degree (Ddl). In this paper, the digital financial inclusion index for (3) each prefecture-level city, divided by 100, is used as a measure of the development of digital finance.

Factor allocation distortions (DIS)
Following Kong et al. (2021) and Qiao et al. (2021), first, capital distortion index Dis Ki and labor distortion index Dis Li are calculated to measure distortions in the factor market, and then, the Cobb-Douglas production function is used to measure capital output elasticity K and labor output elasticity L . The factor market distortions are thus calculated as follows: Since there are two types of distortions, the under allocation of resources ( Dis > 0) and overallocation of resources ( Dis< 0), to ensure a consistent direction for the regression estimates, this paper utilizes the absolute values of Dis Ki and Dis Li so that the final overall factor market distortion index DIS takes positive values. The larger the index is, the more severely resources have been misallocated. 1

Other covariables
To alleviate the endogeneity caused by omitted variables, the following covariables are introduced, in line with existing research: (1) population density (Den). Expressed as the number of permanent residents per square kilometer, it reflects the impact of the population density in each region on carbon emissions. (2) Foreign direct investment (Fdi). On the one hand, the influx of foreign capital has aggravated the pressure on China's environment, and on the other hand, the technological spillovers from foreign enterprises can effectively improve energy efficiency and alleviate pollution. This paper selects the ratio of total foreign direct investment in each city to regional GDP to measure foreign direct investment, and total foreign direct investment is converted into the RMB yuan using the annual average exchange rate between the USD and RMB. (3) Energy consumption . Energy consumption is expressed as the ratio of the total amount of energy consumed in each region to the regional GDP and reflects the impact of regional energy consumption on carbon emissions. (4) Industrial structure (Ind). The following method is used to calculate how advanced the regional industrial structure is, which is used as a proxy variable for the industrial structure. First, the share of GDP attributable to each industry (primary, secondary, and tertiary) is calculated, and the share of each industry in the total regional GDP is used as a component of a vector in the three-dimensional vector space. Then, the angle between this three-dimensional vector and each of three one-dimensional vectors of each industry is calculated, and the three angles are arranged from the smallest to largest. The development level of the industrial structure is the sum of the three angles. (5) Environmental regulation (Ers). Three individual indicators for the discharge of industrial wastewater, industrial sulfur dioxide, and industrial smoke/powder/dust were selected, and an environmental regulation index was synthesized following the comprehensive index method to create a proxy variable for environmental regulation. (6) Technological progress (Tec). This paper selects the number of patents granted in each prefecture-level city as an indicator for the level of scientific and technological development. (7) Government intervention (Gov). Government intervention can significantly affect the relation between the allocation of factor market resources and energy efficiency. This paper measures government intervention with the share of fiscal expenditure in GDP for each city. (8) Financial development (Fi). The ratio of total RMB deposits and loans in financial banking institutions in each city to the GDP of each city over time is selected to measure regional financial development levels.

Data sources and descriptive statistics
The sample period used in this study runs from 2011 to 2019, and data are mainly drawn from the China City Statistical Yearbook, China Statistical Yearbook for Regional Economy, National Bureau of Statistics website, EPS data platform, and corresponding statistical yearbooks for each province and city for each year. Due to limited data availability and to ensure the integrity of the survey data, this paper excludes data from Tibet. Ultimately, 280 prefecture-level cities are selected for the baseline sample. The digital financial inclusion index is the "Peking University Digital Financial Inclusion Index (2011-2020)" released by the Internet Finance Research Center of Peking University. Table 2 presents the descriptive statistics for the main variables. As Table 2 shows, the statistical results show that there are large differences in carbon emission intensity in different cities. The minimum value for carbon emission intensity is 0.0000, the maximum value is 9.6120, and the average value is 0.5385, which indicates that carbon emission intensity is geographically imbalanced. The minimum value for the factor market distortion index is 0.0000, the maximum value is 1.2711, and the average value is 0.3293, which indicates that in most areas, the degree to which factors are misallocated is relatively severe. Table 3 reports the static panel regression results for the impact of digital finance on carbon emission intensity The results indicate that the effect of digital finance in terms of reducing carbon emission intensity is significant at the 1% level whether the covariables are included in the regression equation or not. The dynamic panel regression results, i.e., the model adding the first-order lag term for carbon emission intensity to the regression (L.Tcp), are presented in columns (3) and (4), and the estimation results for this model show that the overall impact of digital finance on carbon emission intensity is significantly negative at the 1% level, indicating that the development of digital finance within a region can help reduce carbon emission intensity. On the one hand, the rapid development of digital finance has enabled financial resources to be more rationally allocated in the domestic market, thus meeting the needs of enterprises to obtain financing for technological innovations; on the other hand, as a new type of internet-based product, digital finance is conducive to ensuring the continuous provision of financial services. This expansion can effectively facilitate the upgrading of regional industries. The regression results also show that the coefficient on the first-order lag term for carbon emission intensity is highly significant at the 1% significance level, indicating that current carbon emissions are affected by previous carbon emissions due to economic inertia and that carbon emissions are path dependent.

Replace the explained variable
To further test the robustness of the estimated results, referring to Chen et al. (2020), we replace the method of carbon emission measurement based on energy consumption with regional carbon emission data estimated by nighttime light. Carbon emissions estimated based on NPP-VIIRS nighttime light data have been widely used in economic studies in recent years (Meng et al. 2017;Zhang et al. 2019). The more economically active a city is at night, the higher its economic development level and the greater its energy consumption. Since these data  (1) and (2) of Table 4. The impact of digital finance on carbon emission intensity is significantly negative, indicating that the regional development of digital finance can help reduce carbon emission intensity.

Elimination of certain special observations
1. Exclude cities that provide centralized heating in winter. 2 Centralized heating in winter consumes a large amount of coal energy. Compared with areas that do not provide centralized winter heat, those prefecture-level cities that do provide centralized heating produce more carbon emissions each year and have a stronger impact on the atmospheric greenhouse effect. In the baseline regression, 280 cities from across China, including both the southern and northern regions, are included in the study sample.
To exclude possible interference from the centralized winter heating in northern districts on the impact of digital finance on carbon emissions, northern cities that provide winter heating are excluded from the sample to obtain more accurate estimation results.
Columns (3) and (4) in Table 4 present the results estimated with those particular cities excluded. These results also support the conclusion that digital finance reduces carbon emission intensity. 2. Eliminate policy interference. It is possible that cities acting as a low-carbon pilot city policy may bias the results of this paper. Specific policies for which cities may have been pilots include the "National Low-Carbon Provinces and Low-Carbon Cities Pilot Work Notice" issued by the National Development and Reform Commission in 2010 and "On Launching the Second Batch of Pilot Projects" issued in 2012. A total of 42 pilot provinces and cities were involved in the two rounds of the "The National Low-Carbon Provinces and Low-Carbon Cities Pilot Work Notice" program.
As an emission reduction policy, this policy should directly affect total carbon emissions. To further improve the robustness of the conclusions of this paper, some provinces and cities were removed from the sample, and the model was then re-estimated. The estimation results are shown in columns (5) and (6) of Table 4. After removing the pilot cities from the sample, the regression results are still significant, which further proves the credibility of the findings.

Exogenous shock test
The development of digital finance in a city often depends on the size of the local market, the level of financial technology development, and the level of financial inclusion, and these factors profoundly affect the quality of development. Therefore, to more robustly evaluate whether digital finance reduces carbon emission intensity within cities, the "Promoting the Development Plan for Inclusive Finance (2016-2020)" policy is adopted as an exogenous policy shock, and the potential interference of this policy is estimated through a difference-in-difference (DID) test. China's prefecture-level cities in 2015 are divided into two groups, those with developed digital finance and those with undeveloped digital finance. The median level of digital finance development is used as the criterion for categorization, and the two groups are classified as the control group and the experimental group. If the development of digital finance in a city in 2015 is greater than the median for all prefecture-level cities in that year, then the city is included in the experimental group, and Treat is taken as 1; otherwise, it is valued at 0. The DID model is as follows: Coefficient captures the impact of the policy. If is significantly negative, reductions in carbon emission intensity are stronger in areas affected by the policy; that is, digital finance significantly reduces the carbon emission intensity of the area. Column (1) of Table 5 reports the DID estimation results, which show that the coefficient on Treat it × Post it is significantly negative to at least at the 1% level, as expected. To ensure the robustness of this finding and the unbiasedness of the estimator, a parallel trend test is conducted, and the results prove that the parallel trend assumption is satisfied.

Instrumental variable analysis
When examining the impact of digital finance on carbon emission intensity, there are inevitably some unobservable confounding factors that affect both the independent and dependent variables, resulting in problems of endogeneity. The 2SLS using the instrumental variable approach is a classic means of solving endogenous problems, as it can identify the causal relationship between digital finance and carbon emission intensity if the appropriate instrumental variables are selected. The number of households with internet access is used as the instrumental variable for the development of digital finance. On the one hand, the number of households with access to the internet, the infrastructure for digital finance, is closely related to changes in digital finance; on the other hand, after controlling for variables related to carbon emission intensity, the number of such households is not closely related to carbon emission intensity. There is no direct path of influence between them. Therefore, the number of households with internet access can be used as the instrumental variable for the development of digital finance. The result is shown in column (1) of Table 6. The measurement results show that the absolute value of the estimated coefficients of digital finance is much larger, and all of the coefficient estimates pass their corresponding significance test. The regression is also tested for endogeneity, and the null hypothesis of exogeneity is rejected, which indicates that 2SLS is more efficient than OLS. This shows that an improvement in the development of digital finance does indeed reduce the carbon emission intensity of a region.

GMM dynamic panel analysis
Carbon dioxide emissions are continuous over time; that is, they exhibit serial correlation. To solve this problem, following (5) Zhao et al. (2022), this study further uses a dynamic GMM panel regression to test the robustness of the previous findings. Table 6 also reports the results. The result of the Sargan test shows that the selected instrumental variable is generally valid. The regression results in columns (2) and (3) of Table 6 show that the coefficients on Dif are significantly negative at the 1% level for both sets of regressions, which indicates that after controlling for the serial correlation of carbon emissions (controlling for L.Tcp and its resulting endogeneity), the conclusion that digital finance reduces regional carbon emission intensity holds robustly. Thus, the previous findings are valid.

Heterogeneity analysis
Geographical heterogeneity Due to regional differences in economic development, there are regional differences in the development of digital finance. Due to differences in geographical locations and resource endowments, the economic development and marketization of the eastern, central, and western regions differ greatly. Therefore, to examine the influence of these regional differences, the cities are divided into subsamples from seven locations: North China, Northeast China, Southeast China, Central China, Southwest China, Northwest China, and South China, following the standard regional division. Table 7 reports the results of the test for regional heterogeneity in the effect of digital finance on carbon emission intensity. The table shows that after adding the lag term for carbon emission intensity as an explanatory variable, carbon emissions and digital finance are negatively correlated with a significance level of 5% in North China and Southeast China and a significance level of 10% level in South China. There are first-tier megacities in North China, Southeast China, and South China, and digital finance is also relatively well developed in those areas. In the surrounding first-tier cities, the tertiary industry represents the largest component of the industrial structure, and digital finance is more developed, so digital finance reduces carbon emission intensity. The effect is very clear. In the northwestern region, where digital finance is the least developed, digital finance has increased carbon emission intensity. In addition, the effect of digital finance on carbon intensity is not significant in Central China, Southwest China, or Northeast China. A possible reason for these results is the difference in the technology levels between the different regions. In theory, digital finance can overcome geographical limitations and provide inclusive and accurate financial services for underdeveloped and marginal areas. However, in reality, the development of digital finance often requires big data and digital technologies such as blockchain, which tend to be more widely available in large cities. Most major large cities in China are located in North China, Southeast China, and South China. These areas have high levels of technology and relatively highly developed digital finance. In areas with low levels of technology, the financial integration problems related to regional economic development cannot be solved effectively, and digital finance has not yet affected the local industries.

The impact of the intensity of entrepreneurial innovation
As a productive service industry, digital finance relies on the vitality of development within the manufacturing industry. Existing research has demonstrated that entrepreneurial and innovative activities are foundational for the development of the financial industry (Ayyagari et al. 2011), and a developed financial system also improves the innovative and entrepreneurial vitality of a region (Amore et al. 2013). Therefore, digital finance in regions with different levels of innovation and entrepreneurship is developed to different degrees. This paper measures the quality of city-level innovation and entrepreneurship with the Langrun Longxin Innovation and Entrepreneurship Index, which is based on data from more than 50 million records contained in the registered industrial and commercial enterprise database, the patent and trademark database, etc. It was jointly compiled by Xin Data Research Institute and Enterprise Research Data. The specific indicators chosen are shown in Table 8.
In this paper, the average value of the innovation and entrepreneurship vitality index from 2011 to 2019 is calculated for each city. Table 8 reports indicators of the index. If the average index value for a city is greater than the median average index value, the city is classified as a city with a high level of innovation and entrepreneurship vitality. If the average value is less than the 25th percentile of all average values, the city is classified as having a low level of innovation and entrepreneurship. In addition, any city whose average index value is greater than the 75th percentile of average index values is classified as a city with a high level of innovation and entrepreneurship vitality. All other cities are classified as having a medium level of innovation and entrepreneurial vitality; thus, three subsamples are formed. Table 9 reports the results of the test for heterogeneity based on innovation and entrepreneurial vitality in the effect of digital finance on carbon emission intensity. The table shows that digital finance significantly reduces carbon emission intensity at the 5% level in cities with a high level of innovation and entrepreneurial vitality and in cities with a moderate level of innovation and entrepreneurial vitality, while cities with a low level of innovation and entrepreneurial vitality present underdeveloped industrial structures, poor productivity, and higher energy consumption. The development of digital finance increases carbon emission intensity. Compared with cities with medium levels of innovation and entrepreneurial vitality, in cities with high levels of innovation and entrepreneurial vitality, digital finance has a weaker inhibitory effect on carbon emission intensity. One likely reason is that more of the economic activities found in highly innovative and entrepreneurial cities are concentrated in low-carbon industries, and thus, carbon emission intensity is reduced to a lesser degree.

The impact of differences in willingness to protect the environment and environmental protection levels
Due to differences in the willingness to protect the environment and environmental protection levels within different regions (Yang et al. 2022), the role of digital finance in reducing carbon emissions differs among cities. Following Chen et al. (2018), this paper uses the ratio of sentences included in government work reports with environmental protection-related word frequencies above a certain threshold to measure local willingness to protect the environment. In addition, we refer to Peng and Wang (2019) in constructing green total factor productivity to measure regional environmental protection levels. The cities are divided into four groups: high willingness to protection the environment and high environmental protection levels, low willingness to protect the environment and high environmental protection levels, high willingness to protect the environment and low environmental protection levels, and low willingness to protect the environment and low environmental protection levels. Table 10 reports the results of the test on the effect of the heterogeneity in the willingness to protect the environment and environmental protection behavior on the relation between digital finance and carbon emission intensity. The table shows that after adding the lagged carbon emission   intensity term as an explanatory variable, digital finance is significantly and negatively correlated with carbon emission intensity in cities with a high willingness to protect the environment. The coefficient is negative but not significant in the low environmental protection level group. In areas with a strong willingness to protect the environment, the willingness to use new approaches and new technologies to reduce pollution levels is stronger than in other areas, so the effect in terms of reducing carbon emissions is also stronger. Moreover, compared to regions with the same willingness to protect the environment, the effect of digital finance on carbon emissions is weaker in regions with higher environmental protection levels, which may be because making progress in regions with lower environmental protection levels is relatively easy.

Mechanism analysis
Digital finance is a new type of financial model in which the traditional financial industry uses digital technology to facilitate financing, investment, and payment. Under the context of peak carbon emissions and achieving carbon neutrality, the development of digital finance provides new momentum for energy conservation and emission reductions. This paper has also empirically proved that digital finance reduces regional carbon emission intensity. In addition, in our literature review, it is noted that one of the most important mediating mechanisms through which digital finance reduces carbon emission intensity is the distortion of factor allocations. As shown in Fig. 3, digital finance mainly alleviates the distortion of factor allocations through three channels and in turn reduces carbon emission intensity. First, digital finance providers have pioneered the establishment of various financial platforms, such as Alipay and Yu'ebao, to create a new type of financial account for the public, enabling their clients to conveniently collect idle funds and convert more change into small deposits. In addition, investment and wealth management products have increased the amount of social capital in circulation and have laid a capital-based foundation for economic development. The emergence of agglomeration economies is expected to alleviate the distortion of factor allocations; second, compared to traditional financial services, digital finance relies on cloud computing and artificial intelligence; conducts the real-time and intelligent collection and analysis of basic information recorded in the big data of financial institutions and nonfinancial enterprises, as well as supporting decision-making based on those data; and can greatly reduce the cost of collecting market information on small and medium-sized enterprises, optimize the allocation of credit funds, and effectively ensure that small and medium-sized enterprises receive financing. The demand for financing and personal loans has promoted the diversification and upgrading of consumer demand, the industrial structure has been optimized and adjusted, and the distortion of factor allocations has been reduced. Finally, digital finance providers have cooperated with enterprises in other sectors to build a corporate credit system at a lower cost, enabling providers to customize precise financial services for entrepreneurial entities and to effectively identify highly innovative entrepreneurial entities, enabling more financial resources to be invested in enterprises engaged in extensive technological innovation projects, resulting in the accumulation of human capital, and further promoting innovation and entrepreneurial behavior through knowledge externalities, which is conducive to mitigating factor allocation distortions.
To further examine the role of digital finance in reducing carbon intensity by mitigating factor distortions, we follow Baron and Kenny (1986). Also, considering the probably existing collinearity, omitting variables that may bias the estimation results, construct the following model: First, if 1 is significantly less than 0, it can be assumed that digital finance significantly mitigates factor distortions. Second, if 1 is significantly greater than 0, factor distortions are significantly negatively correlated with carbon emission intensity. At the same time, to avoid possibly existing omitting variables that may bias the estimation result in the false casual inference of mediating and dependent variables, we add the lag term of the explained variable to the equation shown in formula (8) to eliminate estimation bias caused by omitting variables, especially unobserved variables, as well as other likely existing mediating mechanisms to some degree. However, we cannot conclude that digital finance reduces carbon emission intensity partly through mitigating factors distortions, because Eqs. (6), (7), and (8) can only confirm the correlation between factor distortions and two variables rather than the mechanism through which digital finance affects carbon emission intensity via factor distortions. Thus, we then add the explanatory variable to Eq. (8), which is shown in formula (9), where if 2 is significantly less than 0 and 3 is significantly greater than 0, the effect of digital finance in terms of reducing carbon emission intensity holds robustly after considering the collinearity of digital finance and factor distortions, and the positive correlation between factor distortions and carbon emission intensity also holds robustly after considering the collinearity of digital finance and factor distortions. If the absolute value of 2 is  Fig. 3 Analysis of the mechanism underlying the effect of digital finance on carbon emission intensity less than 2 , the partial effect of digital finance in terms of reducing carbon emission intensity is suppressed by factor distortions. Given the significant correlation between factor distortions and carbon emission intensity, we can conclude that digital finance reduces carbon emission intensity partially through mitigating factor distortions after considering possibly existing omitting variables and collinearity that may cause false casual inferences of the mechanism analysis. Further, to verify the robustness of the mediating effect, this paper also conducts a moderating effect test (Baron and Kenny 1986), and the model is set as follows: If 4 is significantly less than zero, the effect of digital finance in terms of reducing carbon emission intensity is greater as the mitigation of factor distortions. Due to the negative correlation between digital finance and factor distortions, it can also be assumed that digital finance reduces carbon emission intensity partly through the mitigation of factor distortions. Table 11 reports the regression results of the digital financial inclusion index on factor distortions, where column (1) shows the panel data two-way fixed effect regression of digital finance on factor distortions, showing that digital finance significantly reduces factor distortions at the 5% level. Column (2) presents the regression results of the instrumental variables estimated by the digital financial inclusion index on the factor distortion index and indicates that after taking possibly endogenous issues into consideration, the mitigating effect of digital finance on factor distortions is still robust. Specifically, digital finance mitigates capital distortions at the 1% significance level, which is shown in column (4), but the effect on labor distortions shown in column (3) is not significant. Table 12 reports empirical results showing that digital finance affects carbon emission intensity by mitigating factor distortions. According to column (1) of the table, there is a positive relationship between factor distortions and carbon emission intensity, which is significant at the 5% level. Further, we add the lagged term of the explanatory variable to the regression equation in column (1), and the result is reported in column (2), indicating that after considering the possibly issue of omitting variables, the positive correlation between factor distortions and carbon emission intensity is still significant. Further, upon adding the explained variable to the regression equation in column (2), the result shown in column (3) indicates that (1) the correlation between factor distortions and carbon emission intensity is still significantly negatively correlated after considering the correlation between digital finance and factor distortions. At the same time, digital finance significantly reduces factor distortion, so it can be assumed that digital finance reduces carbon intensity by mitigating factor distortions. (2) The (10) absolute value of the estimated regression coefficient of digital finance on carbon intensity is less than the value in the baseline regression after adding the mediating variable to the regression equation, and the coefficient is still significant, which also verifies the robustness of the baseline regression showing that digital finance significantly reduces the carbon emission intensity. At the same time, the effect of digital finance on carbon intensity reduction is weakened after considering the mitigation of factor distortions; i.e., the effect of digital finance on carbon intensity indeed partially occurs through mitigating factor distortions. (3) To prevent the possible existence of other mediating mechanisms that may bias the casual inference of factor distortions and carbon emission intensity, the lags of the explanatory variables are added to the regression equation to control for the possible omission of variables. (4) Carbon emission intensity cannot in turn affect factor allocations, and we only explore the pathway through mitigating factor distortions which excludes the possible interactive influence of multi-mechanism and reverse causality, and the mechanism results obtained can be considered weakly endogenous since the lag term of explained variable has been added to the equation. Finally, to verify the robustness of our conclusion, we also add the interaction term of the digital financial inclusion index and factor distortion index to the equation in column (3), and the result shown in column (4) indicates that (1) the negative correlations between the digital financial inclusion index and factor distortions as well as between the digital financial inclusion index and carbon emission intensity are still significant, verifying the robustness of the above conclusion.
(2) The regression result of the interaction term between the digital financial inclusion index and factor distortion index on carbon emission intensity is less than 0 at the 10% significance level, which indicates that the effect of digital finance in terms of reducing carbon emission intensity is enhanced by the alleviation of factor distortions, and digital finance significantly reduces factor distortions, which also verifies the conclusion that digital finance reduces carbon intensity by alleviating factor distortions. To analyze the path by which digital finance affects carbon emission intensity through factor allocation distortions, this study further considers the sub-indicators for the digital finance index, namely, coverage breadth (Dcb), depth of use (Dud), and degree of digitization (Ddl), and conducts a group test. Table 13 shows the results of regressions that take each of the subdivision indicators as the core explanatory variable. The results show that the depth of use of digital finance and the degree of digitization have a significant negative impact on carbon emission intensity, while the coverage of digital finance has a positive impact on carbon emission intensity. In terms of the breadth of digital finance coverage, due to the availability of digital payment methods and digital financial platforms, an increasing number of enterprises and individuals have begun to accept and use digital finance. The development of green technology will take a long time. Therefore, currently, a wide breadth of digital finance does not reduce carbon emission intensity. This shows that the negative effect of digital finance on carbon emission intensity cannot be driven by the large-scale coverage of an area. In-depth exploration is also required for enterprises to have a continual impetus for innovation. In addition, digital technology must be vigorously developed and digital finance improved. Application efficiency stimulates the innovative and entrepreneurial potential of the whole society and reflects the comprehensiveness of the development of digital finance.

Conclusions and policy implications
Based on a realistic background and literature review, this paper constructs econometric models to analyze the impact of the development of digital finance on carbon emission intensity with data on 280 Chinese cities from 2011 to 2019. Taking the distortion of factor allocation as its entry point, this paper discusses the path by which the development of digital finance affects carbon emission intensity and the impact of heterogeneity on the vitality of innovation and entrepreneurship, environmental awareness, and environmental protection levels in different regions. The main conclusions of this study are as follows:  To accelerate the realization of China's strategic goals of peak carbon by 2030 and carbon neutrality by 2060, the improvement of the efficiency of resource and energy utilization, and the reduction of carbon emissions to achieve green and robust economic development, the following policy recommendations are proposed. First, we must vigorously develop the long-term mechanism of digital finance as part of carbon governance. It has been effectively demonstrated that the development of digital finance significantly reduces carbon emissions. Therefore, by taking full advantage of the opportunities provided by China's "new infrastructure" development project, actively promoting digital technologies such as big data, artificial intelligence, and cloud computing, the traditional financial industry will have the power to accelerate the digital transformation and upgrading of firms. In addition, the inclusivity and accuracy of digital finance should be utilized, the availability of financing for small and medium-sized cities should be improved, industrial carrying capacity should be increased, and the low-carbon transformation and upgrading of local enterprises should be improved. In addition, in the process of organizing the regional layout of digital finance, it is necessary to pay attention to the heterogeneity in the ability of digital finance to reduce carbon emissions. Thus, the "flexible" supervision of digital finance should be strengthened, and digital financial risks should be completely prevented, especially in the Yangtze River Delta, Pearl River Delta, and other industrial areas undergoing transformations and upgrades. The effort to design regional and city layouts to achieve precise emission reduction should be accelerated. Second, it is necessary to regulate the competition for local resources and alleviate the adverse impact of factor distortions on the development of digital finance and the reduction of carbon emissions. Local governments need to fully consider indicators such as those related to environmental prevention and control and green development to build a diversified performance appraisal system, enabling them to gradually abandon the pursuit of the single goal of economic growth, improve environmental protection awareness, and consolidate responsibility for the environment. A joint prevention and control mechanism should be formed with surrounding areas, thus overcoming regional protectionist barriers and enabling regions to jointly contribute to carbon emission reductions. Finally, it is necessary to strengthen the ability of digital finance to allocate financial resources; to guide the flow of financial resources to enterprises with high added value, low energy consumption, and high efficiency; and to achieve regional green transformations so as to control carbon emissions from the source. At present, regions and enterprises with low levels of environmental protection have greater potential for carbon emission reductions. It is necessary to make full use of the development opportunities provided by digital finance to effectively solve the dilemma of urgent and expensive financing to transform and upgrade small and microenterprises and to stimulate the vitality of their market entities. Creativity can improve the quality and efficiency of small and microenterprises as their regional industries transform and upgrade, which can effectively reduce carbon emissions.
where Cmd Ki and Lmd Li are the absolute distortion coefficients for the factor prices and indicate the addition of resources when there is relatively little distortion. In the actual calculation, the relative price distortion coefficient can be used instead: where s i = p i y i Y indicates region i 's share y i , K = ∑ N i s i Ki represents the output of the economy as a whole, and Y represents the output-weighted contribution of capital.
K i K represents the actual ratio of the capital used by region i to the total capital but s i Ki K is the theoretical ratio of the capital used by region i when capital is allocated efficiently. The ratio between the two reflects the degree of the deviation between the actual amount of capital used and the efficient allocation, that is, the degree of the capital mismatch in regioni . If the ratio is greater than 1, then the cost of capital in region i is low relative to that in the entire economy, leading an excessive amount of capital to be allocated to the region; in contrast, if the ratio is less than 1, it means that the actual allocation of capital in the region is lower than the efficient allocation. Relative to the theoretically optimal level, the amount of capital allocated is insufficient. As policymakers and implementers, local government officials, both politicians and economists, to achieve specific economic development goals, intervene in the capital market, affecting the normal allocations in the factor market and generating capital mismatches. Next, a Cobb-Douglas production function is used to measure the output elasticity of capital K and that of labor L . The specific form for the production function is as follows: Taking the natural logarithm of both sides at the same time, we can obtain The whole sample of panel data can be analyzed in a pooled regression, or it can be analyzed by year or by city in order to select the best regression equation for estimating the sum of Kit and Lit . Since the production function for each city is the same over time, estimating the regression by city is more in line with reality. Therefore, the regression is estimated by city with the linear prediction (LP) estimation method. After estimating the factor output elasticity for each province, we calculate the capital mismatch index Dis Ki and the labor mismatch index Dis Li for each city according to formulas (11) and (12).
The output variable ( Y it ). Output is expressed as the GDP of each city. Setting 2003 as the base period, the GDP of the other years is converted into real GDP in constant 2003 prices with the GDP deflator.
Labor input ( L it ). This study uses annual average employment in each city, that is, the arithmetic mean of employment at the beginning of the year (or, equivalently, employment at the end of the previous year) and employment at the end of the current year.
Capital investment ( K it ). Capital investment is expressed as the fixed capital stock in each city. Following Berlemann and Wesselhöft (2014)and Du and Lin (2015), it is calculated using the perpetual inventory method; the formula is as follows: where K t is the current stock of fixed capital, I t is the current total flow of fixed capital in nominal terms, P t is the price index for investment in fixed assets, t indicates the depreciation rate, and K t−1 represents the stock of fixed capital in the previous period.
The energy input ( E it ). Since the regional energy input and carbon dioxide emissions are directly proportional, this paper uses the carbon dioxide emissions of each city to represent the input of energy.
Finally, the factor market distortions are calculated as follows: Since there are two possible types of distortion, the underallocation of resources ( Dis > 0) and the overallocation of resources ( Dis < 0), to ensure a consistent direction for the regression estimates, this paper follows the practice of Shuhan et al. (2016)  and Dis Li so that the overall factor market distortion DIS is positive. The larger the value of DIS is, the more severe the resource allocation.
Funding This work was supported by the National Social Science Foundation of China (Grant Number 19BJY010).
Data availability Some or all data, models, and/or codes generated or used during the study are available from the corresponding author upon request.

Declarations
Ethics approval Not applicable.

Competing interests
The authors declare no competing interests.