Digital finance and equitable industrial carbon emissions: an empirical analysis of Chinese cities
Variable construction
Equitable industrial carbon emission (EICE)
According to carbon emission equity theory from Rose et al. (1998), carbon emission allocation method from Song et al. (2017), and variable settings by Shi et al. (2023), this study defines the proxy for EICE as a corrected indicator of industrial carbon emission intensity that accounts for inter-city equity, referred to as equitable industrial carbon emission intensity (EICEI).
$${\sigma }_{i,t}=\frac{{{IGDP}}_{i,t}}{{{ICE}}_{i,t}\times {{POP}}_{i,t}}$$
(1)
$${{EICEI}}_{i,t}=\left(1+\frac{{\sigma }_{i,t}-\min {\sigma }_{t}}{\max {\sigma }_{t}-\min {\sigma }_{t}}\right)\times {{ICE}}_{i,t}$$
(2)
Where \({{IGDP}}_{i,t}\) represents industrial GDP of city \(i\) in year \(t\), \({{ICE}}_{i,t}\) denotes industrial carbon emissions, and \({{POP}}_{i,t}\) is population. \({\sigma }_{i,t}\) signifies the equity distribution index, \(\max {\sigma }_{t}\) and \(\min {\sigma }_{t}\) represent the highest and lowest values of the fairness distribution index in period \(t\). It is important to note that \({EICEI}\) is a negative indicator. A larger value of EICEI suggests that the city bears a higher responsibility for reducing industrial carbon emissions after adjusting for the equity index and thus implies a lower EICE.
Digital finance
The DF indicator in this paper broadly refers to traditional financial institutions and internet companies utilizing digital technology for financing, payments, investments, and other new financial enterprise models (Huang and Huang, 2018). Considering the measurement methods and data limitations of city-level samples (Mao and Wang, 2023), the data source for DF in this paper is the Peking University Digital Financial Inclusion Index of China (PKU_DFIIC), which is co-compiled by the Digital Finance Research Center of Peking University and Ant Financial Enterprise.
Mediating variable
The study identifies four mediating variables: industrial structure transformation (\({Ind}\)), technological advancement (\({Tec}h\)), energy consumption (\({Enc}\)), and marketisation level (\({Mar}\)). The industrial structure (\({Ind}\)) is defined as the ratio of gross output of the tertiary industry to gross output of the secondary industry. The higher the value of \({Ind}\), the larger the proportion of the tertiary sector within the city. Technological advancement is commonly measured by the number of patents in a city, which in this paper is expressed as the logarithm of the number of design patents filed in the year plus one. \({Enc}\) is measured by the total energy consumption of the city. The level of marketisation is defined by the marketisation index provided in the Marketisation Index of China’s Provinces (Wang et al. 2021), which comprehensively reflects the level of marketisation in each city in China from five dimensions: the relationship between the government and the market, the development of the non-state-owned economy, the degree of development of the product market, the degree of development of the factor market, the development of market intermediary organizations, and the legal system environment.
Moderating variable
Referring to the study of Wang et al. (2024), this paper employs the word frequency statistics method to analyse city government work reports. The proportion of four keywords—environmental pollution, synergistic development and environmental co-management, green living, and environmental institution building—relative to the total word count of the reports is used as the indicator of governmental environmental concern (GEC). Inspired by Lu and Wu (2023), this paper captures the search frequency of the keyword ‘industrial pollution’ across various cities from 2011 to 2020 using the Baidu Index search engine. The normalised data are used as a proxy variable for public environmental concern (PEC).
Control variable
As outlined previously, the factors affecting EICE are multidimensional. To minimize the endogeneity problems caused by unobservable factors, this paper introduces economic development (Lngdp), financial development (Fin), government finance (Gov), education investment (Lnedu), and technological investment (Lnsci) as control variables. The economic development is measured by the logarithm of the Gross Domestic Product (GDP), while the financial development is measured by the ratio of the total year-end RMB deposit balances to the total year-end RMB loan balances at financial institutions. Government finance is measured by the ratio of local general public budget revenues to local general public budget expenditures. Education investments and technological investments are represented by the logarithms of local government expenditures on education and technology.
Data sources
This study primarily employs panel data from 276 cities in China, covering the period from 2011 to 2020. The data are mainly obtained from the China Urban Statistical Yearbook, statistical yearbooks of provinces or cities, the Peking University Digital Inclusive Finance Index (2011–2020), and the China Provincial Marketisation Index Report. The GEC and PEC are manually collected from city government reports and Baidu Index. Missing data are filled in with the interpolation method. Descriptive statistics for variables, including definitions, means, and standard deviations, are displayed in Table 1.
Model setting
Baseline regression based on the two-way fixed effects panel model
As a preliminary exploration of the relationship between DF and EICE, this paper constructs a panel regression model incorporating both time-fixed effect and individual fixed effect. The baseline model is set up as shown in Eq. (3).
$${{EICE}I}_{i,t}={\alpha }_{0}+{\alpha }_{1}{{DF}}_{i,t}+{\alpha }_{2}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}$$
(3)
\({{EICEI}}_{i,t}\) denotes the equitable industrial carbon emission intensity for city \(i\) in year \(t\), which is the main dependent variable in this paper. \({{DF}}_{i,t}\) represents the level of digital finance. \({{Control}}_{i,t}\) encompasses a set of control variables. \({\mu }_{i}\) accounts for the city fixed effect, \({\lambda }_{t}\) captures the year fixed effect, and \({\varepsilon }_{i,t}\) represents the random disturbance term. Since EICEI is a negative indicator compared to EICE, a significantly negative coefficient \({\alpha }_{1}\) of DF indicates that an increase in DF effectively reduces EICEI. In other words, DF has a positive impact on EICE, thereby supporting Hypothesis 1. Additionally, the baseline model is also used in two heterogeneity analyses and three robustness tests: substituting the measurement of the explanatory variable DF, winsorizing the data of DF and EICE, and excluding samples from municipalities directly under central government control.
Instrumental variable method with two-stage least squares (IV-2sls) and generalised method of moments (GMM) models
This study focuses on the relationship between DF and EICE, which presents potential endogeneity in Eq. (3). First, the numerous factors affecting EICE imply the control variables selected for this study are limited, which could lead to omitted variable bias. Second, reverse causality may occur if cities with better EICE facilitate the development of DF. To address these concerns, this study employs IV-2sls and GMM models to mitigate the bias in the baseline regression (Song et al. 2021; Fan and Feng, 2022). The models are specified in Eqs. (4)–(6).
$${{DF}}_{i,t}={\tau }_{0}+{\tau }_{1}Z+{\tau }_{2}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}$$
(4)
$${{EICEI}}_{i,t}={\alpha }_{0}+{\alpha }_{1}{\widehat{{DF}}}_{i,t}+{\alpha }_{2}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}$$
(5)
Equations (4) and (5) illustrate the estimation model of the IV-2sls method. The core idea is to eliminate the correlation between DF and the error term by introducing an instrumental variable (IV) that is correlated with DF but uncorrelated with the error term. The predicted \(\widehat{{DF}}\) is substituted as a new explanatory variable into Eq. (5) for the second stage of regression to obtain an unbiased estimator.
$$\begin{array}{l}{{EICEI}}_{i,t}={\omega }_{0}+{\omega }_{1}{{DF}}_{i,t}\\\qquad\qquad\qquad+\,{\omega }_{2}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}\end{array}$$
(6)
The GMM model in Eq. (6) is estimated by constructing a set of moment conditions using multiple instrumental variables. This estimation method mitigates the potential serial correlation and endogeneity issues related to industrial carbon emission inequity among cities and further improves the accuracy and robustness of the estimation (Song et al. 2021).
Mediation model
The mediation model offers deeper insights into the mechanisms through which DF affects EICE, helping to clarify the relationship. Drawing on Wang et al. (2024), this study constructs the following mediation model.
$${{ME}}_{i,t}={\beta }_{0}+{\beta }_{1}{{DF}}_{i,t}+{\beta }_{2}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}$$
(7)
$${{EICEI}}_{i,t}={\gamma }_{0}+{\gamma }_{1}{{DF}}_{i,t}+{\gamma }_{2}{{ME}}_{i,t}+{\gamma }_{3}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}$$
(8)
\({{ME}}_{i,t}\) represents the mediating variable, including industrial structure transformation, technological advancement, energy consumption, and the level of marketisation. All other specifications remain consistent with the baseline regression. If \({\beta }_{1}\) is significant, it indicates that DF effectively influences the mediating variable, establishing the first stage of the mediating effect. Further, if \({\gamma }_{2}\) is also significant, it indicates that the mediating variable influences EICEI, confirming the second stage of the mediating effect. Therefore, if both \({\beta }_{1}\) and \({\gamma }_{2}\) are significant, it proves that this mediating mechanism is valid, and the mediating effect in Hypothesis 2-Hypothesis 4 is supported.
Moderation model
Drawing on Li et al. (2021), the following moderation model is constructed to examine whether environmental concerns from various social parties moderate the relationship between DF and EICE. The corresponding model is shown in Eq. (9).
$$\begin{array}{l}{{EICEI}}_{i,t}={\varphi }_{0}+{\varphi }_{1}{{DF}}_{i,t}+{\varphi }_{2}{{MO}}_{i,t}+{\varphi }_{3}{{DF}}_{i,t}* {{MO}}_{i,t}\\\qquad\qquad\qquad+\,{\varphi }_{4}{{Control}}_{i,t}+{\mu }_{i}+{\lambda }_{t}+{\varepsilon }_{i,t}\end{array}$$
(9)
Where \({{MO}}_{i,t}\) represents the moderating variable, including the governmental environmental concern and public environmental concern. Other variables are specified in the same way as in Eq. (3). If \({\varphi }_{3}\) in Eq. (9) is significant, it suggests that environmental concern significantly moderates the relationship between DF and EICE, thus supporting H6 and H7.
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