Introduction

The economic development mode characterized by high consumption, high pollution, and high emissions leads to a large number of countries entering resource bottlenecks and ecological deterioration, causing increasingly fierce competition for energy and resources, and severe pressure on environmental protection (Deng et al. 2017; Wang et al. 2017). As an essential representative of emerging economies, China also faces a dilemma in unbalanced resource allocation, large energy consumption, and environmental severe pollution (Dong et al. 2021). Currently, China is the world’s largest energy consumer (BP 2020). According to the data of the National Bureau of Statistics of China in 2021, the energy consumption of China reached the value of 4.98 billion tons of standard coal in 2020 (NBSC 2021). In addition, in terms of the environmental performance index released by Yale University, the environmental pollution of China ranks second in the world (Dong et al. 2020), and the ecological problems caused by the pursuit of economic development are exposed.

The United Nations (UN) Sustainable Development Goals (SDGs) aim to address economic, social, and environmental issues that hinder progress in global sustainable development (Gue et al. 2020). Nowadays, the SDGs are a recognized blueprint for global development by 2030 and are used by businesses, industry, governments, and regional organizations (Belmonte-UreñA et al. 2021). Nevertheless, resource-energy and economic-environmental constraints have become the obvious obstacles to sustainable industrial development in the future (Bai et al. 2017). The current resource and environmental problems faced by China have attracted significant attention, and therefore the government has set out to establish a green, low-carbon cycle economic development system, and launched a series of strategic decisions on “green development”. Moreover, the Fifth Plenary Session of the 19th CPC Central Committee also proposed to focus on improving the ecosystem quality and stability, so as to achieve sustainable and high-quality development. Overall, it is urgent to coordinate economic, resource, and environmental factors to promote green development.

Actually, the concept of green development has become an alternative to sustainable development (Liu et al. 2022), and its key lies in the construction of green development efficiency (GDE) for enhancing economic development quality (Rashidi and Farzipoor Saen 2015). Wang and Huang (2014) found that most studies considered the efficiency of environmental factors as environmental efficiency, while the concept of environmental efficiency was inconsistent. In this context, they proposed the concept of green development efficiency to reflect the efficiency level of increased economic output while reducing environmental pollution emissions with a given input. GDE takes into account both resource, environmental, and economic factors, and thus has been extensively studied. Zhao et al. (2016) applied the SBM model to calculate the GDE in China from 1997 to 2013, indicating that the GDE was generally low and the human capital and industrial structure interaction items had a positive effect. Zhu et al. (2020) adopted the ultra-efficiency SBM model to measure the GDE in China from 1999 to 2017, and analyzed the impact of the carbon trading mechanism on the GDE. They found that the GDE showed a u-shaped trend, and the carbon trading mechanism had a positive effect. Ding et al. (2022) employed a spatial econometric model to investigate the influencing factors of GDE and found that industrial collaborative agglomeration played a positive role in promoting regional green development. Overall, a scientific evaluation of China’s GDE is of practical importance to reveal the current situation and development direction of green development in China.

Data envelopment analysis (DEA) is a non-parametric method proposed by Charnes et al. (1979) to assess the relative effectiveness among decision-making units (DMUs). It can integrate inputs and outputs in different dimensions with objective weights emerging from the data to reflect the input–output efficiency. On this basis, scholars have proposed multiple DEA models for specific problems and have various applications in different performance evaluation problems (Färe et al. 1992; Tone 2001). GDE is a complex system including resource factors, economic factors, and environmental factors. Therefore, the DEA method, as an efficiency evaluation method, is especially suitable for the evaluation problem of complex systems (Ma et al. 2018). Actually, the DEA method has been widely applied in analyzing GDE problems (Yang et al. 2020). However, the complexity of the indicator system makes the DEA method have the following shortcomings in evaluating the complex system. On the one hand, the traditional DEA model is mainly based on sectional data and measures the efficiency of DMUs by constructing different technology frontier surfaces. On the other hand, the traditional DEA model has the defects in the same status of indicators and the inability to distinguish effective DMU. Therefore, applying the traditional DEA model to evaluate GDE will suffer from bias.

In addition, there is significant heterogeneity across Chinese provinces in terms of technology level, resource endowment, and industrial structure, leading to regional variability in their GDE. Wang et al. (2021) applied the DEA-Theil model to measure the regional energy efficiency in China and found that the overall energy efficiency was low, accompanied by significant province differences. Yang et al. (2017) used the directional distance function to calculate the provincial green development efficiency from 2003 to 2012, noting that the southern and eastern areas performed the best, while the central and southwest Yangtze River regions performed relatively poorly. Therefore, it is necessary to accurately and reasonably examine GDE and its influencing factors to identify possible shortcomings.

In summary, the traditional DEA model has some defects in evaluating the complex system evaluation problems, and there are large inter-provincial differences in green development efficiency in China. Therefore, this paper has the following innovations: First, the P-SBM model based on the same technology frontier surface that can be used for dynamic efficiency analysis of panel data is developed to measure the efficiency of all DMUs. Second, the MCSE-DEA (multi-level complex system evaluation) model is proposed to address the problems of the same status of indicators and the inability to distinguish effective DMU of the P-DEA model in evaluating the efficiency of complex systems. Overall, in this paper, we firstly measure the GDE of 30 Chinese provinces from 2010 to 2018 based on the MCSE-DEA model. And then the Tobit model is adopted to investigate the influencing factors of GDE. Overall, an accurate and reasonable evaluation of the current situation and influencing factors of GDE in China can promote economic growth with low resource input and environmental impact, which is meant to promote green development in China.

This article consists of 6 sections. The “Introduction” section presents the introduction. The “Literature review” section presents the literature review of existing research. The “Methodology” section presents the MCSE-DEA model that can solve the shortcomings of the P-DEA model in evaluating the efficiency of complex systems. The “Indicator system and descriptive statistics” section presents the indicator system and descriptive statistics. The “Results and discussion” section presents the current situation of inter-provincial green development in China and the influencing factors. The “Conclusion and policy recommendations” section presents the conclusion and policy recommendations.

Literature review

Green development efficiency, as a critical proxy for green development quality, has been extensively studied from different perspectives, such as the national-level analysis (Rashidi and Farzipoor Saen 2015; Shao et al. 2019; Yang and Ni 2022), regional-level analysis (Chen and Lin 2020; Matsumoto and Chen 2021; Yang and Zhang 2018), city-level analysis (Liu et al. 2020, 2021; Xiao et al. 2021), and industry-level analysis (Shao et al. 2019; Wang et al. 2019; Xing et al 2018). Particularly, research on the efficiency evaluation of green development in China has become an essential topic and has progressed (Liu et al. 2022). For example, Shao et al. (2019) used the dynamic network DEA approach (DNDEA) to assess the two-stage eco-efficiency of the Chinese industry from 2007 to 2015. The study found that eastern China performed best, followed by central and western regions. Shuai and Fan (2020) explored the role of environmental regulations in the efficiency improvement of the regional green economy in China from 2007 to 2018, based on the DEA-Tobit model. The results show that the green economy efficiency level of China was on the rise during the study period, and environmental regulation influence on the efficiency of the green economy presented a “U” shaped curve. Zhao et al. (2022) examined the economic growth and intrinsic drivers of 286 prefecture-level cities in China from 2003 to 2018 based on the Metafrontier-global-SBM super-efficiency method. The empirical results show that green economy growth performed well, and the innovation effect was the main factor driving the growth. It can be seen that the DEA method has been widely used for energy economic and environmental efficiency evaluation.

In terms of GDE measurement methods, there are mainly the stochastic frontier approach (SFA) and DEA method, with the former being a parametric method and the latter being a non-parametric method. For the parametric approach, the SFA method can distinguish the random error term from the inefficiency term, making the measurement results more accurate and reasonable, and thus has been widely used. Song and Chen (2019) estimated China’s food production and eco-efficiency based on the water footprint SFA, finding that GDP per capita and water supply per capita had a positive effect on food production eco-efficiency. Koengkan et al. (2022) measured the performance of economic efficiency in Latin America based on the SFA and DEA approaches, showing that Panama was the most economically efficient country in Latin America, followed by Chile. Haider and Mishra (2021) adopted the Bayesian SFA method to measure the corporate energy efficiency of 82 Indian steel companies from 2003 to 2017, indicating that most companies could reduce their energy consumption by half. It can be seen that the SFA method has a certain application in energy and environmental efficiency evaluation. However, the SFA method needs to assume a production function, which is susceptible to the effects of specifying the form of the production function and in turn causes computational errors.

As for the non-parametric method, the DEA method does not need to set the specific form of the production function in advance, which can effectively avoid the above problems of the SFA method, and thus has great advantages in terms of the efficiency measurement. Zhang and Chen (2022) evaluated energy efficiency in Regional Comprehensive Economic Partnership Agreement (RCEP) countries based on the SBM-DEA model, noting that the overall energy efficiency of RCEP was poor, and optimizing the industrial structure and energy consumption structure can improve energy efficiency. Peiro-Palomino and Picazo-Tadeo (2019) applied the DEA method to analyze GDE in EU countries and found that the main driver of environmental efficiency was economic development. In addition, the 2016 Research Frontiers report released by the Chinese Academy of Sciences also indicates that the DEA method has been the most popular method in energy and environmental efficiency evaluation in recent years. Hence, this paper applies the DEA method to measure the GDE in China.

However, the complexity of the indicator system makes the DEA method have the following shortcomings. First, there are different levels of indicators for the complex multi-level system. To be specific, the indicators used in the traditional DEA model have the same levels, leading to the evaluation results overemphasizing the role of secondary factors and biasing the measurement results. And if the weighted sum method is used to synthesize secondary indicators, it is difficult to detect the improved information on the original indicators. Second, multi-level complex systems can have an efficiency value of 1 for most of the DMUs, which is mainly caused by the high number of evaluation indicators and thus the inability to distinguish effective units (Ma et al. 2018). And the traditional DEA model based on sectional data does not allow for analysis of panel data. Therefore, the efficiency values measured by this model are not comparable.

In terms of the research on the influencing factors of green development efficiency, scholars at home and abroad have achieved fruitful results. Regarding the selection of influencing factors, researchers generally analyze the urbanization (Li et al. 2020), industrial structure (Yang et al. 2022), environmental regulation (Passetti and Tenucci 2016), R&D investment (Zhang et al. 2021), and FDI (Zhang 2020). For example, some studies have shown that environmental regulation and technological progress have a driving effect on industrial green total factor productivity (Wang and Zhao 2021). Lin and Zhou (2022) indicated that urbanization might promote green economic growth, while population size and foreign direct investment might inhibit green economic growth. Zhu et al. (2019) found that industrial structure rationalization and advancement can positively affect green development efficiency.

Therefore, this paper will further carry out the following work given the shortcomings of existing research. First, the MCSE-DEA model proposed to address the problems of the same status of indicators and the inability to distinguish effective DMU of the P-DEA model. Second, this paper measures China’s inter-provincial GDE from 2010 to 2018 based on the MCSE-DEA model and compares the results with the P-DEA model. Finally, we apply the MCSE-DEA-Tobit model to analyze the status of inter-provincial GDE and its influencing factors. In summary, the research framework of this study is illustrated in Fig. 1.

Fig. 1
figure 1

The research framework of GDE measurement based on MCSE-DEA-Tobit model

Full size image

Methodology

DEA model with undesirable outputs

Assuming that there are n DMUs, where \({x}_{j}={\text{(}{x}_{1j},{x}_{2j},...,{x}_{mj})}^{T}\) is the input indicator value for the jth DMU, \({y}_{j}={\text{(}{y}_{1j},{y}_{2j},...,{y}_{sj})}^{T}\) is the desirable output indicator value for the jth DMU, and \({\overline{y} }_{j}={\text{(}{\overline{y} }_{1j},{\overline{y} }_{2j},...,{\overline{y} }_{lj})}^{T}\) is the undesirable output indicator value for the jth DMU, and that the indicator values for each DMU are positive, Korhonen and Luptacik (2004) give the following DEA model considering the undesirable output can be formulated as follows:

$$\left\{\begin{array}{c}max\varphi +\varepsilon (\sum_{i=1}^{m}{s}_{i}^{-}+\sum_{r=1}^{s}{s}_{r}^{+}+\sum_{k=1}^{l}{\overline{s} }_{k}^{+})\\ \begin{array}{cc}\text{s.t.}& \sum_{j=1}^{n}{x}_{j}{\lambda }_{j}+{s}^{-}={x}_{{j}_{0}}\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}{y}_{j}{\lambda }_{j}-{s}^{+}=\varphi {y}_{{j}_{0}}\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}{\overline{y} }_{j}{\lambda }_{j}+{\overline{s} }^{+}={\overline{y} }_{{j}_{0}}\end{array}\\ \begin{array}{cc}& \end{array}\delta \sum_{j=1}^{n}{\lambda }_{j}=\delta \\ \begin{array}{cc}& \end{array}\lambda \ge {0},{s}^{-}\ge {0},{s}^{+}\ge {0},{\overline{s} }^{+}\ge {0}\text{.}\end{array}\right.$$
(1)

P-DEA model used for energy and environmental efficiency evaluation

It is assumed that in the evaluation of GDE, there are n DMU with a total of T periods of data. The selected input indicators are capital stock (CS), total employment (TE), construction land area (CL), water consumption (WC), and energy consumption (EC). Gross domestic product (GDP) as a desirable output indicator, solid waste emissions (SW), domestic garbage removal volume (DG), CO2 emissions (CO), SO2 emissions (SO), NOx emissions (NO), soot and industrial dust emissions (SD), and total waste water emissions (WW) are undesirable output indicators. The input–output indicators for the jth DMU in period t are \({x}_{j}^{t}=\text{(}C{S}_{j}^{t},T{E}_{j}^{t},C{L}_{j}^{t},W{C}_{j}^{t},E{C}_{j}^{t}),{y}_{j}^{t}=GD{P}_{j}^{t},{\widehat{y}}_{j}^{t}=\text{(}S{W}_{j}^{t},D{G}_{j}^{t},C{O}_{j}^{t},S{O}_{j}^{t},N{O}_{j}^{t},S{D}_{j}^{t},W{W}_{j}^{t}),\) and the values of each input and output indicator are positive.

The P-DEA model with undesirable outputs is based on panel data, where the efficiency model of the j0th DMU in period t with respect to period t0 is as follows:

$$\left\{\begin{array}{c}max{\varphi }_{{j}_{0}}^{t}+\varepsilon (\sum_{i=1}^{5}{s}_{i}^{-}+{s}^{+}+\sum_{r=1}^{7}{\overline{s} }_{r}^{+})\\ \begin{array}{cc}\text{s.t.}& \sum_{j=1}^{n}\text{(}C{S}_{j}^{{t}_{0}},T{E}_{j}^{{t}_{0}},C{L}_{j}^{{t}_{0}},W{C}_{j}^{{t}_{0}},E{C}_{j}^{{t}_{0}}){\lambda }_{j}+{s}^{-}=\text{(}C{S}_{{j}_{0}}^{t},T{E}_{{j}_{0}}^{t},C{L}_{{j}_{0}}^{t},W{C}_{{j}_{0}}^{t},E{C}_{{j}_{0}}^{t})\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}GD{P}_{j}^{{t}_{0}}{\lambda }_{j}-{s}^{+}={\varphi }_{{j}_{0}}^{t}GD{P}_{{j}_{0}}^{t}\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}\text{(}S{W}_{j}^{{t}_{0}},D{G}_{j}^{{t}_{0}},C{O}_{j}^{{t}_{0}},S{O}_{j}^{{t}_{0}},N{O}_{j}^{{t}_{0}},S{D}_{j}^{{t}_{0}},W{W}_{j}^{{t}_{0}}){\lambda }_{j}+{\overline{s} }^{+}=\text{(}S{W}_{{j}_{0}}^{t},D{G}_{{j}_{0}}^{t},C{O}_{{j}_{0}}^{t},S{O}_{{j}_{0}}^{t},N{O}_{{j}_{0}}^{t},S{D}_{{j}_{0}}^{t},W{W}_{{j}_{0}}^{t})\end{array}\\ \begin{array}{cc}& \end{array}\delta \sum_{j=1}^{n}{\lambda }_{j}=\delta \\ \begin{array}{cc}& \end{array}\lambda \ge {0},{s}^{-}\ge {0},{s}^{+}\ge 0,{\overline{s} }^{+}\ge {0}\text{.}\end{array}\right.$$
(2)

where \(\lambda =({\lambda }_{1},{\lambda }_{2},...,{\lambda }_{n}),{s}^{-}=({s}_{1}^{-},{s}_{2}^{-},...,{s}_{5}^{-}),\) \({\overline{s} }^{+}=({\overline{s} }_{1}^{+},{\overline{s} }_{2}^{+},...,{\overline{s} }_{7}^{+}),\) \(\varepsilon\) is a non-Archimedean infinitesimal quantity, and \(\varphi\) is the efficiency of the j0th DMU. \(\delta\) is a parameter taking values 0, 1, when \(\delta =0\), the production activity satisfies constant returns to scale (CRS), and \(\varphi\) is the comprehensive efficiency value and measures the resource utilization and resource allocation ability in the green development process; when \(\delta ={1}\), the production activity satisfies variable returns to scale (VRS). \(\varphi\) is the pure technical efficiency value and measures the technical level of converting inputs into outputs.

Assuming that \({\varphi }^{0},{\lambda }^{0},{s}^{-0},{s}^{+0},{\overline{s} }^{+0}\) is the optimal solution of model (2) such that

$$\begin{array}{c}{\widehat{x}}_{{j}_{0}}^{t}=\text{(}C{S}_{{j}_{0}}^{t},T{E}_{{j}_{0}}^{t},C{L}_{{j}_{0}}^{t},W{C}_{{j}_{0}}^{t},E{C}_{{j}_{0}}^{t})-{s}^{-0}{,}{\widehat{y}}_{{j}_{0}}^{t}={\varphi }_{{j}_{0}}^{t}GD{P}_{{j}_{0}}^{t}+{s}^{+0}\\ {\widehat{\overline{y}} }_{{j}_{0}}^{t}=\text{(}S{W}_{{j}_{0}}^{t},D{G}_{{j}_{0}}^{t},C{O}_{{j}_{0}}^{t},S{O}_{{j}_{0}}^{t},N{O}_{{j}_{0}}^{t},S{D}_{{j}_{0}}^{t},W{W}_{{j}_{0}}^{t})-{\overline{s} }^{+0},\end{array}$$
(3)

and call \(({\widehat{x}}_{{j}_{0}}^{t},{\widehat{y}}_{{j}_{0}}^{t},{\widehat{\overline{y}} }_{{j}_{0}}^{t})\) as the projection of the j0th decision unit. Let

$$\Delta {x}_{{j}_{0}}^{t}={x}_{{j}_{0}}^{t}-{\widehat{x}}_{{j}_{0}}^{t},\Delta {y}_{{j}_{0}}^{t}={\widehat{y}}_{{j}_{0}}^{t}-{y}_{{j}_{0}}^{t},\Delta {\overline{y} }_{{j}_{0}}^{t}={\overline{y} }_{{j}_{0}}^{t}-{\widehat{\overline{y}} }_{{j}_{0}}^{t}$$
(4)

then \(\left(\Delta {x}_{j}^{t},\Delta {y}_{j}^{t},\Delta {\overline{y} }_{j}^{t}\right)\) reflects the deficiencies and improvement directions of the production of the j0th decision unit in period t relative to period t0.

MCSE-DEA model

In model (2), it is not reasonable to put GDP and CO2, SO2, and NOx in equal position to measure the efficiency values. Therefore, the following combines construction land area (CL), water consumption (WC), and energy consumption (EC) into one indicator of resource utilization (RU), and the specific synthesis formula is as follows:

$${\overline{RU} }_{j}\text{=}\frac{C{L}_{j}^{t}}{3\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}C{L}_{j}^{t}}+\frac{W{C}_{j}^{t}}{3\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}W{C}_{j}^{t}}+\frac{E{C}_{j}^{t}}{3\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}E{C}_{j}^{t}}={a}_{3}C{L}_{j}^{t}+{a}_{4}W{C}_{j}^{t}+{a}_{5}E{C}_{j}^{t}.$$
(5)

In addition, to eliminate the influence of the magnitude on each index, take

$${\overline{CS} }_{j}^{t}\text{=}\frac{C{S}_{j}^{t}}{\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}C{S}_{j}^{t}}\text{=}{a}_{1}C{S}_{j}^{t}{,}{\overline{TE} }_{j}^{t}\text{=}\frac{T{E}_{j}^{t}}{\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}T{E}_{j}^{t}}\text{=}{a}_{2}T{E}_{j}^{t}{,}{\overline{GDP} }_{j}^{t}\text{=}\frac{GD{P}_{j}^{t}}{\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}GD{P}_{j}^{t}}\text{=}{b}_{0}GD{P}_{j}^{t}.$$
(6)

This way \(\text{(}{\overline{CS} }_{j}^{t},{\overline{TE} }_{j}^{t},{\overline{RU} }_{j}^{t})\) gives a complete picture of the inputs in terms of money, people, and resources.

At the same time, the undesirable output \(\text{(}S{W}_{j}^{t},D{G}_{j}^{t},C{O}_{j}^{t},S{O}_{j}^{t},N{O}_{j}^{t},S{D}_{j}^{t},W{W}_{j}^{t})\) is synthesized into an indicator of the amount of waste output (WO) by the following formula:

$$\begin{array}{c}{\overline{WO} }_{j}^{t}\text{=}\frac{S{W}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}S{W}_{j}^{t}}+\frac{D{G}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}D{G}_{j}^{t}}+\frac{C{O}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}C{O}_{j}^{t}}+\frac{S{O}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}S{O}_{j}^{t}}+\frac{N{O}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}N{O}_{j}^{t}}+\frac{S{D}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}S{D}_{j}^{t}}+\frac{W{W}_{j}^{t}}{7\underset{\begin{array}{c}1\le j\le n\\ 1\le t\le T\end{array}}{\mathrm{max}}W{W}_{j}^{t}}\\ \begin{array}{ccc}& & \text{=}\end{array}{b}_{1}S{W}_{j}^{t}+{b}_{2}D{G}_{j}^{t}+{b}_{3}C{O}_{j}^{t}+{b}_{4}S{O}_{j}^{t}+{b}_{5}N{O}_{j}^{t}+{b}_{6}S{D}_{j}^{t}+{b}_{7}W{W}_{j}^{t},\end{array}$$
(7)

The model can be expressed as follows:

$$\left\{\begin{array}{c}max{\varphi }_{{j}_{0}}^{ct}+\varepsilon (\sum_{i=1}^{3}{s}_{i}^{c}+{s}^{cq}+{s}^{cw})\\ \begin{array}{cc}\text{s.t.}& \sum_{j=1}^{n}\text{(}{\overline{CS} }_{j}^{{t}_{0}},{\overline{TE} }_{j}^{{t}_{0}},{\overline{RU} }_{j}^{{t}_{0}}){\lambda }_{j}+{s}^{c}=\text{(}{\overline{CS} }_{{j}_{0}}^{t},{\overline{TE} }_{{j}_{0}}^{t},{\overline{RU} }_{{j}_{0}}^{t})\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}{\overline{GDP} }_{j}^{{t}_{0}}{\lambda }_{j}-{s}^{cq}={\varphi }_{{j}_{0}}^{ct}{\overline{GDP} }_{{j}_{0}}^{t}\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}{\overline{WO} }_{j}^{{t}_{0}}{\lambda }_{j}+{s}^{cw}={\overline{WO} }_{{j}_{0}}^{t}\end{array}\\ \begin{array}{cc}& \end{array}\delta \sum_{j=1}^{n}{\lambda }_{j}=\delta \\ \begin{array}{cc}& \end{array}\lambda \ge {0},{s}^{c}\ge {0},{s}^{cq}\ge 0,{s}^{cw}\ge {0}\end{array}\right.$$
(8)

Assuming that \({\varphi }^{c0},{\lambda }^{0},{s}^{c0},{s}^{cq0},{s}^{cw0}\) is the optimal solution of model (8), the projection formula for the j0th DMU given by model (8) is as follows:

$${\widetilde{x}}_{j}=\text{(}{\overline{CS} }_{{j}_{0}}^{t},{\overline{TE} }_{{j}_{0}}^{t},{\overline{RU} }_{{j}_{0}}^{t})-{s}^{c0}{,}{\widetilde{y}}_{j}={\varphi }_{{j}_{0}}^{ct0}{\overline{GDP} }_{{j}_{0}}^{t}+{s}^{cq0}{,}{\widetilde{y}}^{w}{}_{j}={\overline{WO} }_{{j}_{0}}^{t}-{s}^{cw0}.$$
(9)

According to Eq. (9), it can be seen that model (8) is difficult to find the improvement information against the original indicators and etc. Therefore, this paper further gives the model that can reflect the improvement information against the original indicators as follows:

$$\left\{\begin{array}{c}max\varphi +\varepsilon ({a}_{1}{s}_{1}^{-}+{a}_{2}{s}_{2}^{-}\text{+}{b}_{0}{s}^{q+}\text{+}\sum_{i=3}^{5}{a}_{i}{s}_{i}^{-}+\sum_{r=1}^{7}{b}_{r}{s}_{r}^{w+})\\ \begin{array}{cc}\text{s.t.}& \sum_{j=1}^{n}\text{(}C{S}_{j}^{{t}_{0}},T{E}_{j}^{{t}_{0}},C{L}_{j}^{{t}_{0}},W{C}_{j}^{{t}_{0}},E{C}_{j}^{{t}_{0}}){\lambda }_{j}+{s}^{-}=\text{(}C{S}_{{j}_{0}}^{t},T{E}_{{j}_{0}}^{t},C{L}_{{j}_{0}}^{t},W{C}_{{j}_{0}}^{t},E{C}_{{j}_{0}}^{t})\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}GD{P}_{j}^{{t}_{0}}{\lambda }_{j}-{s}^{q+}=\varphi GD{P}_{{j}_{0}}^{t}\end{array}\\ \begin{array}{ccc}& & \sum_{j=1}^{n}\text{(}S{W}_{j}^{{t}_{0}},D{G}_{j}^{{t}_{0}},C{O}_{j}^{{t}_{0}},S{O}_{j}^{{t}_{0}},N{O}_{j}^{{t}_{0}},S{D}_{j}^{{t}_{0}},W{W}_{j}^{{t}_{0}}){\lambda }_{j}+{s}^{w+}=\text{(}S{W}_{{j}_{0}}^{t},D{G}_{{j}_{0}}^{t},C{O}_{{j}_{0}}^{t},S{O}_{{j}_{0}}^{t},N{O}_{{j}_{0}}^{t},S{D}_{{j}_{0}}^{t},W{W}_{{j}_{0}}^{t})\end{array}\\ \begin{array}{cc}& \end{array}\delta \sum_{j=1}^{n}{\lambda }_{j}=\delta \\ \begin{array}{cc}& \end{array}\sum_{i=3}^{5}{a}_{i}{s}_{i}^{-}\ge 0,\sum_{r=1}^{7}{b}_{r}{s}_{r}^{w+}\ge 0\\ \begin{array}{cc}& \end{array}\lambda \ge {0},{s}_{1}^{-},{s}_{2}^{-},{s}^{q+}\ge 0\end{array}\right.$$
(10)

Assuming that \(\overline{\varphi },\overline{\lambda },{\overline{s} }^{-},{\overline{s} }^{q+},{\overline{s} }^{w+}\) is the optimal solution to model (10), we define

$$\begin{array}{c}{\overline{x} }_{j}=\text{(}C{S}_{{j}_{0}}^{t},R{K}_{{j}_{0}}^{t},C{L}_{{j}_{0}}^{t},W{C}_{{j}_{0}}^{t},E{C}_{{j}_{0}}^{t})-{\overline{s} }^{-}{,}{\overline{y} }_{j}=\overline{\varphi }GD{P }_{{j}_{0}}^{t}+{\overline{s} }^{q+}\\ {\overline{y} }^{w}{}_{j}=\text{(}S{W}_{{j}_{0}}^{t},D{G}_{{j}_{0}}^{t},C{O}_{{j}_{0}}^{t},S{O}_{{j}_{0}}^{t},N{O}_{{j}_{0}}^{t},S{D}_{{j}_{0}}^{t},W{W}_{{j}_{0}}^{t})-{\overline{s} }^{w+},\end{array}$$
(11)

is the projection of the j0th DMU.

It can be verified by the empirical analysis section that model (10) and model (8) give equal values of the efficiency of the DMU. And Eq. (11) can decompose the projection given by Eq. (9) into the original indicators. Let

$$\Delta {x}_{j}={x}_{j}-{\overline{x} }_{j}{,}\Delta {y}_{j}={\overline{y} }_{j}-{y}_{j}{,}\Delta {y}_{j}^{w}={y}_{j}^{w}-{\overline{y} }_{j}^{w}.$$
(12)

Unlike the projection given in model (1), in Eq. (12), if (or \(\Delta {x}_{ij}\ge 0\Delta {x}_{ij}\le 0\)) indicates that the jth DMU is deficiencies (or more efficient) on the ith input indicator. If (or \(\Delta {y}_{j}^{w}\ge 0\Delta {y}_{j}^{w}\le 0\)) means that the jth DMU is under-input (or more efficient) on the rth undesirable output indicator.

Tobit model

The GDE measured in this paper is greater than 0, which is a “restricted dependent variable,” and the Tobit model can solve the regression problem of “restricted dependent variable” well. Thus, the Tobit model is established to analyze the GDE empirically. The equation of the Tobit model is as follows:

$${Y}_{jt}=\left\{\begin{array}{c}{Y}_{jt}^{*}={\beta }_{0}+\sum_{t=1}^{n}{\beta }_{t}{x}_{jt}+{\varepsilon }_{jt},{Y}_{jt}^{*}>0\\ 0,{Y}_{jt}^{*}\le 0,\end{array}\right.$$
(13)

where Yjt is the dependent variable, xjt is the independent variable, β0 is the constant term, βt is the estimated coefficient vector, εjt is the random error perturbation term, and εjt—(0, σ2).

Based on green development theory and drawing on existing research results (Ding et al. 2022; Xu et al. 2022), this paper selects the following six variables as the influencing factors of GDE (as shown in Table 1) and explores the influence of these factors on GDE.

Table 1 Indicators of influencing factors of green development efficiency
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Indicator system and descriptive statistics

Due to data availability, the DMUs in this paper are the 30 provinces, autonomous regions, and municipalities directly under the central government (referred to as provinces) except Tibet, Hong Kong, Macau, and Taiwan. The relevant data are obtained from the China Statistical Yearbooks (NBSC, 2011–2019), China Environmental Statistical Yearbooks (NBSC, 2011–2019), and China Energy Statistical Yearbooks (NBSC, 2011–2019). The indicators used in this paper are as follows.

  1. (1)

    The input indicators include capital, labor, and natural resources (as shown in Fig. 2). We use the estimation method proposed by Zhang et al. (2004) to calculate the capital stock. The calculation formula is \({K}_{j}^{t}={I}_{j}^{t}+(1-\delta ){K}_{j}^{t-1}\), where Kt j and Kt-1 j represent the capital stock of province j in period t and t − 1, respectively. It j is the total fixed asset investment in period t, and δ is the depreciation rate. We convert the energy consumption in resource inputs into standard coal.

  2. (2)

    Output indicators include desirable output and undesirable output (as shown in Fig. 3), where desirable output is GDP, and undesirable output is waste pollutants. For desirable output, we treat GDP as constant 2000 prices. For undesirable output, we use the IPCC reference method (Paustian et al. 2006) to calculate energy-related CO2 emissions.

Fig. 2
figure 2

Input indicators

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Fig. 3
figure 3

Output indicators

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Descriptive statistics are given in Table 2. It can be seen that the growth rates of construction land area, energy consumption, GDP, solid waste emissions, household refuse, CO2 emissions, soot and industrial dust emissions, and total waste water emissions are 27.43%, 20.05%, 92.47%, 60.21%, 44.07%, 24.50%, 30.46%, and 2.53%, respectively, while SO2 and NOx emissions can be observed a negative growth of − 70.11% and − 26.19%, respectively. This indicates that rapid economic development is accompanied by resource consumption. In terms of pollutant emissions, although some pollution emissions have increased, there are also reductions in emissions like SO2 and NOx, indicating an improvement in green development. In addition, there are significant differences in these indicators, showing that there are large differences among provinces in terms of various inputs, GDP, and pollutant emissions.

Table 2 Descriptive statistics of data used in this study (2010–2018, 30 provinces)
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To better analyze the regional characteristics, we divide the 30 provinces into six regions: northeast, southeast, southwest, northwest, Middle Yangtze River, and Middle Yellow River (Tang et al. 2016). The northeast region includes the provinces of Heilongjiang, Jilin, and Liaoning, which are rich in resources such as coal and oil (Wang and Huang 2014). The southeast region includes Guangdong, Hainan, Fujian, and Guangxi, of which Fujian and Hainan have more developed coastal tourism economies (Yang et al. 2020). The southwest region consists of four provinces (Chongqing, Guizhou, Sichuan, and Yunnan), which are an essential base for developing China’s non-ferrous metal industry and strategic reserves. The northwest region consists of five remote provinces (Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang), which are remote, harsh, and sparsely populated, but rich in resources (e.g., oil, coal, and natural gas) (Dong et al. 2021). The Middle Yangtze River (Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, and Hunan) is an essential base for grain, oil, and cotton production in China. They are also the most water-rich regions in China (Tang et al. 2016). Among them, Shanghai, Jiangsu, and Zhejiang have abundant physical and human capital and are three of the most powerful economic entities in China. The Middle Yellow River (Beijing, Tianjin, Hebei, Henan, Shandong, Shanxi, and Inner Mongolia) is rich in hydro energy, coal, oil, natural gas, and minerals, and occupies an essential position in the country with excellent development potential (Wang and He 2022). Among them, Beijing and Tianjin have a large economic capacity and advanced technology.

Table 3 presents the average values of various indicators for six regions in China from 2010 to 2018. It can be seen that the developed regions (i.e., the Middle Yangtze River and Middle Yellow River regions) have much higher inputs than the less developed regions (i.e., the northwest and southwest regions), suggesting that the developed regions rely on using natural resources as inputs. However, from the perspective of pollution emissions, except for household waste and wastewater emissions, the developed regions do not have significantly higher pollution emissions than the less developed regions, meaning that some progress has been made in emission reduction techniques in the developed regions.

Table 3 Descriptive statistics by region (2010–2018, 30 provinces)
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Results and discussion

Comparison of GDE based on the MCSE-DEA model and the P-DEA model

The P-SBM model is constructed based on the same technology frontier surface to measure the efficiency of all DMUs, and thus has longitudinal comparability and can be used for dynamic efficiency analysis of panel data. The MCSE-DEA model is proposed to address the problems of the same status of indicators and the inability to distinguish effective DMU of the P-DEA model. In this paper, we select the data of 2010 as the reference surface and use the MAXDEA software to measure the GDE in China from 2010 to 2018 based on the MCSE-DEA model and the P-DEA model. We rank them by their efficiency value. Figure 4 compares the efficiency distribution of GDE based on the P-DEA model (Fig. 4a) and the MCSE-DEA model (Fig. 4b) during 2010–2018. There are significant differences in GDE between them. In general, the efficiency score of the MCSE-DEA model is lower than the P-DEA model (as shown in Fig. 5), and the efficiency ranking shows significant changes (as shown in Table 4). In terms of efficiency scores, the efficiency score based on the MCSE-DEA model is 0.93, while the efficiency value measured by the P-DEA model is 1.32. From the efficiency ranking of each province, the highest efficiency score under the MCSE-DEA model is Shanghai, with an efficiency value of 1.43, while Shanghai ranks second under the P-DEA model with an efficiency value of 3.69. We can see that the MCSE-DEA model has the same efficiency value calculated by model 10. The MCSE-DEA model can reflect only improved information on the integrated indicators, while model 10 can reveal improved information on the original indicators. From the efficiency distribution map (as shown in Fig. 4), most eastern provinces show higher efficiency scores, while the western provinces gain lower scores.

Fig. 4
figure 4

Average scores of GDE under the P-DEA model and the MCSE-DEA model, 2010–2018

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Fig. 5
figure 5

GDE trends under the P-DEA model and the MCSE-DEA model (2010–2018, 30 provinces)

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Table 4 GDE scores of different models
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Spatial and temporal analysis of GDE

First, Fig. 6 presents the average trend of GDE from 2010 to 2018 in China, from which it can be seen that GDE experiences an increasing trend. The comprehensive efficiency ranges from 0.78 to 1.10, and the pure technical efficiency ranges from 0.81 to 1.28 in 9 years. The comprehensive efficiency and pure technical efficiency are in the efficiency effective state from 2016 to 2018, reaching the technical frontier level of 2010.

Fig. 6
figure 6

Inter-provincial green development efficiency trends in China, 2010–2018

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Secondly, Fig. 7 illustrates the trend of regional efficiency changes and the results show that the average GDE of six regions exhibits an upward trend. It indicates that the regional efficiency in China has improved significantly during the study period. Figure 8 provides the regional GDE and growth rate status. Among them, the greatest improvements in average efficiency value appear in the Middle Yangtze River and southeast region, with growth rates of 58.67% and 38.80%, respectively. The next region is the Middle Yellow River, with an average efficiency value of 0.96 and a growth rate of 49.60%. The northeast region ranks fourth in terms of efficiency value, with an average efficiency value of 0.90 and a growth rate of 27.75%. In contrast, the northwest region gains the worst average efficiency value and growth rate, with the values of 0.66 and 15.31%, respectively. The southwest region, on the other hand, ranks medium with an efficiency value of 0.84 and a growth rate of 37.54%.

Fig. 7
figure 7

GDE trends by region in China

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Fig. 8
figure 8

GDE and growth rate by region

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Figure 9 illustrates the inter-provincial green development status from 2010 to 2018. In the Middle Yangtze River, Shanghai and Jiangsu have higher efficiency values of 1.43 and 1.20, respectively, while Jiangxi performs worst, with the lowest efficiency value of 0.83. Fujian and Guangdong in the southeast have higher efficiency values of 1.24 and 1.18, respectively, while Guangxi has an efficiency value of only 0.88. In the Middle Yellow River, Tianjin gains the highest efficiency of 1.41, while Shanxi and Inner Mongolia have efficiency scores below 0.70. This may be due to serious energy consumption and environmental problems (Tang et al. 2016). The difference in efficiency values among the three provinces in the northeast is relatively small, with efficiency values ranging from 0.88 to 0.92. In contrast, the northwest region has low-efficiency values, with efficiency values ranging from 0.58 to 0.77. In the southwest region, Sichuan and Chongqing perform better, with average efficiency values above 0.94; however, the efficiency value of Guizhou is only 0.66.

Fig. 9
figure 9

Inter-provincial GDE in China, 2010–2018

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Overall, there are still considerable disparities in efficiency levels within and between regions, which may have a negative impact on the synergistic development of regional economies. It is noticeable that the provinces with higher efficiency values are mainly from three regions: the Middle Yangtze River (Shanghai, Jiangsu, and Zhejiang), the Middle Yellow River (Tianjin and Beijing), and the southeast region (Fujian and Guangdong), which are the economically developed coastal provinces. These provinces have actively adopted advanced technology, equipment, and management experience (Tang et al. 2016). Beijing receives a highly efficient ranking, primarily because of the significant reforms it had previously undergone for the 2008 Summer Olympics. The other provinces, Guizhou, Xinjiang, Shanxi, Qinghai, and Ningxia, gain lower efficiency values, with an average efficiency value of no more than 0.66. Among them, Xinjiang, Qinghai, and Ningxia belong to the northwest region. The lower efficiency values in the less developed western regions can be attributed to their relatively backward technology level, and limited capital investment. From the above analysis, it can be seen that although the GDE has improved significantly, there is still a large efficiency gap between different provinces, and therefore the further research of the inefficient provinces is essential.

Analysis of inefficient provinces

From the above analysis, it can be seen that the GDE of five provinces, namely Guizhou, Xinjiang, Shanxi, Qinghai, and Ningxia, is relatively low, and the average efficiency within 9 years does not exceed 0.66. Therefore, we carry out detailed analysis, including the efficiencies of inputs, desirable outputs, and undesirable outputs, respectively, on these provinces based on model 10, and the relevant results are shown in Fig. 10 ~ Fig. 12.

Fig. 10
figure 10

Improvement strategies for input indicators in inefficient provinces (symbol: CS represents capital stock, TE represents total employment, CL represents construction land area, WC represents water consumption, EC represents energy consumption.)

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Figure 10 demonstrates the average proportion of each input factor that can be improved. A larger ratio indicates greater redundancy for these input indicators. Except for Guizhou, Shanxi, and Qinghai, which have negative improvement ratios in construction land area (CL), the five provinces have extensive redundancy in other input indicators and poorer ability to optimize resource allocation. The five provinces are most problematic in total water consumption (WC), with redundancy levels exceeding 44%. Among them, Xinjiang needs to optimize more than 94% in water consumption, which can be attributed to its large area and harsh natural conditions. Secondly, energy consumption (EC) needs to be optimized by more than 26% in five provinces to be effective, among which, the energy consumption of Ningxia should be optimized by 49%. Ningxia has abundant energy resources such as coal, oil, and natural gas, which provide a strong guarantee for its construction of an energy base. As can be seen, these five provinces have relatively high water and energy consumption due to their resource endowment and industrial structure. Xinjiang and Ningxia also have 10% and 42% redundancy in construction land area (CL), respectively, and thus need to improve land use efficiency. In addition, the five provinces need some improvement in capital stock (CS) and total employment (TE). To be specific, they need to improve the efficiency of personnel work and capital use continuously. Overall, according to the above analysis, except for the construction land area, the five provinces have an enormous redundancy in input indicators for optimization, and further measures should be taken to optimize resource allocation, and improve the quality and efficiency of staff.

Second, regarding the desirable output, Fig. 11 presents the average ratio of desirable output indicator that can be improved. A larger ratio indicates a greater degree of deficiency in that output indicator. It can be observed that five provinces have a large deficit in GDP, and need to improve their average GDP by more than 52% to reach validity. Among them, the GDP of Ningxia needs to be optimized by more than 72% before it can reach validity. All in all, the five provinces mentioned above are generally lagging behind and need to promote their economic development.

Fig. 11
figure 11

Improvement strategies for desirable output indicators in inefficient provinces

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Finally, from the perspective of undesirable output, Fig. 12 reports the proportion of each undesirable output indicator that can be improved, with a smaller ratio indicating that the province has better control over undesirable output. It can be found that except for Xinjiang performing better in total waste water emissions (WW), five provinces have certain deficiencies in the rest of the undesirable output indicators. In particular, the problems in solid waste emissions (SW) and soot and industrial dust emissions (SD) are particularly prominent. In terms of the solid waste emissions, the improvement ratio of the five provinces is higher than 71%, with Ningxia and Shanxi needing to optimize more than 90%. In terms of soot and industrial dust emissions, five provinces need an improvement value greater than 74%, while four provinces, except Guizhou, need an improvement ratio of 84% or more. According to the above analysis, the shortcomings of these inefficient provinces can be identified, and constructive suggestions can be made for the next regulation step.

Fig. 12
figure 12

Improvement strategies for undesirable output indicators in inefficient provinces (symbol: SW represents solid waste emissions, DG represents domestic garbage removal volume, CO represents CO2 emissions, SO represents SO2 emissions, NO represents NOx emissions, SD represents soot and industrial dust emissions, WW represents total waste water emissions.)

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Analysis of the Tobit model regression results

The following is the analysis of the influencing factors (as shown in Table 5), where a positive correlation means that the two phenomena change in the same direction and the dependent variable increases with the independent variable, i.e., there is a facilitative effect. A negative correlation means that the two phenomena change in opposite directions, and the dependent variable decreases with the increase of the independent variable, i.e., there is an inhibitory effect. ① Industrial structure (IS). The influence of the share of secondary industry on GDE is significantly negative. The secondary industry consumes more resources and emits more waste, so the increase in the proportion of the secondary industry will inhibit the improvement of GDE. ② Environmental policy (EP). The percentage of environmental protection expenditure has significantly and positively correlated with GDE. Since the construction of ecological civilization has been proposed, it has effectively reduced the generation and emission of pollutants, and therefore environmental policies have contributed to improving GDE. ③ Urbanization level (UL). There is a negative correlation between the proportion of the urban population and GDE. At the early stage of urbanization, industries with low technology levels and high labor densities develop rapidly, and environmental pollution is serious, resulting in a low GDE. ④ R&D investment (RD). The proportion of R&D investment has positively correlated with GDE, indicating that improving science and technology level is conducive to the improvement in resource utilization rate and pollutant management, thereby contributing to the improvement of GDE. ⑤ The level of economic development (ED). GDP per capita has positively correlated with GDE, noting that the improvement of economic development level is conducive to improving residents’ environmental protection awareness, thereby enhancing the GDE. ⑥ Energy consumption (EC2). Electricity consumption per capita has negatively correlated with GDE, showing that the increase in electricity consumption generates more pollutants. Thus, there is a suppressive effect on the improvement of GDE.

Table 5 The regression results of the Tobit model (symbol: IS represents the industrial structure, EP represents the environmental policy, UL represents urbanization level, RD represents R&D investment, ED represents the level of economic development, EC2 represents energy consumption)
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Conclusion and policy recommendations

The continuous and rapid economic development has brought about excessive resource consumption and environmental pollution. Therefore, it is essential to coordinate economic, resource, and environmental factors to achieve sustainable development. This paper develops the MCSE-DEA model to address the problems of the same status of indicators and the inability to distinguish effective DMU of the traditional P-DEA model. We employ the MCSE-DEA model to measure the inter-provincial green development efficiency (GDE) in China from 2010 to 2018. On this basis, the Tobit model is further applied to investigate the influencing factors of GDE. The results show that the average GDE shows an increasing trend during the study period, but there are significant disparities between and within regions. From a regional perspective, six regions show an upward trend in efficiency values, among which the Middle Yangtze River and the southeast region have the highest efficiency values, while the northwest region has the lowest efficiency values. From an inter-provincial perspective, more economically developed provinces, such as Shanghai, Tianjin, and Fujian, have higher efficiency values, while provinces in less developed regions like Shanxi, Qinghai, and Ningxia are less efficient. The study of the inefficient provinces found significant redundancy in most indicators and a lack of optimal resource allocation. From the perspective of influencing factors, the environmental investment, R&D investment, and economic development level can significantly contribute to the improvement of GDE, while industrial structure, urbanization level, and energy consumption have inhibiting effects.

Based on the results obtained from our study, we propose some suggestions as follows. First, GDE has a large gap between and within regions. Studies on inefficient provinces found that water resource utilization in Xinjiang and energy consumption in Ningxia are large. Accordingly, Xinjiang should make great efforts in adjusting the industrial structure, strengthen the construction of water-saving facilities, and introduce advanced monitoring technology. Ningxia can reduce energy consumption by transforming the existing energy industry, utilizing new technologies, and improving the industrial structure. Second, Ningxia and Shanxi provinces have a large amount of waste production and soot and industrial dust emissions, and a high degree of dependence on natural resources. Therefore, in order to improve the efficiency of green development, there is an urgent need to focus on the optimal allocation of resources and improve the overall allocation of resources. Third, it is essential to change the economic development mode actively, reasonably plan the urban layout, effectively reduce the energy consumption intensity, and gradually increase the environmental protection efforts.