Exact Eco-Efficiency Measurement in the Yellow River Basin: A New Non-Parametric Approach

Abstract

Frontier-based approaches to eco-efficiency measures have long been controversial because no normative definition is provided. Previous studies have used technical efficiency, environmental efficiency, and other variables as a proxy. To standardize its definition, we propose a formal eco-efficiency indicator, the ratio of actual gross domestic product (GDP) to environmental impact to potential GDP to environmental impact. To quantify it, we develop the biennial meta-frontier non-radial directional distance function (BMNDDF), which addresses the potential threats of technology heterogeneity, the slack variable, and linear programming infeasibility. Using this new indicator, we assess the city-level eco-efficiency in the Yellow River Basin from 2008 to 2017 to identify the harmonious relationship between ecological protection and economic development. The empirical results show a 5.73% increase in eco-efficiency per year, with the technology leadership effect as the main contributor. Because the central region is defined by heavy emissions and many underdeveloped cities, it suffers from more severe conflicts between outputs and emissions than other regions.

1. Introduction

Over the past 60 years, the global economy has grown by 62.7 times, and this crude economic increase has resulted in the transitional exploitation of resources and ecological degradation [1]. Along with the deepening of global sustainable development, determining how to balance economic development and environmental protection has become an important issue of continuous concern for countries around the world.

As the world’s largest and most rapidly developing country, China faces even more difficult environmental problems. In 2019, the Chinese government officially approved the Plan for Ecological Protection and High-Quality Development of the Yellow River Basin as a major national strategy, aiming to address the striking concerns of deteriorating ecological environment and lagging economic development. In response, the Yellow River Basin has elicited extensive scholarly attention, with studies on the patterns of climate change [2,3], air pollution [4,5], watershed ecosystem management [6,7,8], and regional economic development [9], among others. While these papers are useful in assessing the ecological quality and economic benefits of the Yellow River Basin, none has integrated the two to effectively identify a win-win strategy for the basin. First, from the perspective of the research objectives, our paper examines the eco-efficiency of the Yellow River Basin, while the study of Jiang et al. [9] investigates high-quality development. Second, in terms of research methods, it is reasonable to choose an ideal production benchmark technology to measure eco-efficiency using our proposed DEA method, whereas the study is constructed using indicator system, which, to a certain extent, is subjectively. Lastly, from the research content, we identify the underlying mechanisms of eco-efficient growth in the Yellow River Basin from a technology perspective, which is not presented in the study.

The eco-efficiency indicator may be useful for discerning whether the Yellow River Basin can achieve a win-win situation for both ecology and economy because this indicator is defined as the ratio of economic value added to the ecological impact added [10]. Improving eco-efficiency can decouple environmental pressures from economic growth, thus tackling the existing dilemma in the Yellow River Basin. Despite substantial research on eco-efficiency (e.g., Oggioni et al. [11]; Arabi et al. [12]; Wu et al. [13]), this literature fails to offer a normative definition of eco-efficiency. In particular, when measuring eco-efficiency based on frontier analysis, definitions become vague and arbitrary, since they habitually use technical efficiency (e.g., Arabi et al. [12]; Yang et al. [14]; Yu et al. [15]; Huang et al. [16]; Matsumoto and Chen [17]; Wang et al. [18]) and environmental efficiency (e.g., Oggioni et al. [11]; Demiral and Sağlam [19]; Martinsson and Hansson [20]). This lack of clarity may generate highly misleading results.

We exactly follow the concept proposed by Schaltegger and Sturm [21], and provide a normative definition of eco-efficiency based on data envelopment analysis (DEA), defining it as the ratio of actual gross domestic product (GDP) to environmental impact to potential GDP to environmental impact. Furthermore, in addition to the rigid constraints on water resources and pollutant reduction targets, the Yellow River Basin is also burdened with “double carbon” targets [22]; thus, accounting for carbon dioxide (CO₂) emissions in an eco-efficiency indicator is crucial.

Our study proceeds in two stages. First, we standardize the definition of eco-efficiency and use the biennial meta-frontier non-radial directional distance function (BMNDDF) approach to estimate it. The BMNDDF approach we propose addresses the issues of technology heterogeneity [23,24], the slack variable, [25,26,27,28] and linear programming infeasibility [29], and also maintains the previously computed value of eco-efficiency if a new time period is added to the dataset [30]. Second, with the Yellow River Basin as the empirical case, we estimate static and dynamic eco-efficiency at the city level and identify the drivers of eco-efficiency progress from a technology perspective.

Using the panel data of cities in the Yellow River Basin from 2008 to 2017, we measure eco-efficiency growth and its components using the BMNDDF approach. We find that the average city-level eco-efficiency of the Yellow River Basin is 0.637, which implies that the basin is under enormous pressure, both economically and ecologically. We document a 5.73% increase in eco-efficiency per year during the sample period, along with a U-shaped pattern of eco-efficiency from 2012 to 2017. Under the strict water management in the Yellow River Basin since 2012, eco-efficiency declines from 2012 to 2015 and then increases, consistent with the Porter hypothesis [31]. In addition, a heterogeneity analysis suggests that the central region is the least eco-efficient, indicating that the region has sharp economic and ecological conflicts.

The remainder of our paper is structured as follows. Section 2 presents a background information on the Yellow River Basin and literature review from a methodology perspective. Section 3 describes the new eco-efficiency indicator and the BMNDDF approach. Section 4 shows our data and presents descriptive statistics. Section 5 provides our empirical results, including eco-efficiency measure, eco-efficiency growth, and its components. Section 6 discusses the relationship between our results and the Porter hypothesis. Section 7 concludes.

2. Background and Literature Review

2.1. Background of the Yellow River Basin

The Yellow River Basin is located between 96 and 119 degrees east longitude and 32 and 42 degrees north latitude, with a length of about 1900 km from east to west and a width of about 1100 km from south to north. The Yellow River Basin covers an area of 795,000 km². It is widely regarded at home and abroad as an important ecological barrier in China and is a vital water source for northwest and northern China. The river, whose basin area is shown in Figure 1, flows through nine provinces, including Qinghai, Sichuan, and Gansu, finally reaching the Bohai Sea in Shandong Province (since only tributaries of the Yellow River flow through Sichuan Province [32], the province is not covered in this study). In 2019, the Yellow River Basin had a total GDP of CNY 24.6 trillion, supporting nearly one-third of China’s population. Therefore, the Yellow River Basin has a lower real GDP per capita than other regions, especially the coastal areas.

The Yellow River Basin is abundant in energy resources, including coal, oil, natural gas, and non-ferrous metals, but faces serious water shortages, a fragile ecological environment, and other challenges. To tackle the issues affecting this basin, in 2019, the Chinese government proposed, for the first time, an essential discourse on the Plan for Ecological Protection and High-Quality Development of the Yellow River Basin as a major national strategy. In October 2021, the State Council issued the Outline of the Plan for Ecological Protection and High-Quality Development of the Yellow River Basin, emphasizing the promotion of a green, low-carbon transition and overall improvement of the ecological environment (see http://www.gov.cn/zhengce/2021-10/08/content_5641438.htm (accessed on 14 August 2022) (in Chinese)). Therefore, boosting ecological protection and high-quality development in the Yellow River Basin has become a popular area of concern for both scholars and the Chinese government.

In the era of carbon neutrality, the ecological impact of greenhouse gases is self-evident. Therefore, the ecological issues of the Yellow River Basin must include CO₂ emissions in the framework of eco-efficiency. Eco-efficiency is valuable in measuring economic growth and ecological issues, but its application in the energy and environmental field is widely controversial, especially in frontier analysis. Scholars have dealt with the definition of eco-efficiency rather vaguely, and they often use technical efficiency or environmental efficiency to represent this concept. Given this concern, we provide a normative definition of eco-efficiency to correct a long-standing bias in eco-efficiency estimation. Measuring the eco-efficiency of the Yellow River Basin will thus provide an important reference for the top-level design of government policies.

2.2. Literature Review: A Methodology Perspective

The frontier-based methods [33,34,35], planetary boundaries [36], sustainability evaluation approaches [37,38], waste reduction algorithm (WAR) [39], life cycle assessment (LCA) [40], etc. are the most popular measurement tools in the line of eco-efficiency analysis. For example, Vásquez-Ibarra et al. [41] presented a comprehensive and structured literature review based on LCA and DEA methods. Additionally, many studies have adopted planetary boundaries, sustainability evaluation approaches, and WAR to estimate eco-efficiency, as seen in Young et al. [42], and Ducoli et al. [43]. However, some scholars point out that two major drawbacks of the planetary boundaries are the uncertainty of the thresholds and the spatial heterogeneity of environmental problems [44]. The sustainability evaluation approaches, such as the SUI algorithm [37] and the SOFTSCAPES model [38], cannot reflect the substitutability among inputs/outputs. The WAR algorithm was first applied in chemical process analysis, but Young et al. [42] consider energy as an undesirable output, which violates the classical axiom of the production theory [45]. In the production process, however, the relationship among inputs/outputs cannot be ignored, and the measurement of eco-efficiency requires an ideal production benchmark technology; neither of the two issues can be fully addressed by the planetary boundary, the SUI algorithm, the SOFTSCAPES model, or the WAR algorithm.

The frontier-based approaches, including stochastic frontier analysis (SFA) and DEA, can deal with both issues and rule them out [16,46,47]. Du and Mao [48] and Zhang et al. [49] point out that the SFA estimator more easily violates the monotonicity assumptions of inputs/outputs than do those derived by DEA methods. However, the current utilization of DEA methods to estimate eco-efficiency is not normative. Most existing studies (e.g., Arabi et al. [12] and Oggioni et al. [11]) adopt technical efficiency or environmental efficiency to characterize eco-efficiency, which confuses the significant differences among different efficiency concepts. Meanwhile, the existing DEA methods cannot simultaneously address the issues of technology heterogeneity [23], the slack variable [25], and linear programming infeasibility [29], nor maintain the previously computed value of efficiency if a new time period is added to the dataset [30]. Therefore, this paper develops a new methodology, called the BMNDDF method, and offers a normative definition of eco-efficiency, which is the foundation of a convincing eco-efficiency analysis derived from the DEA methods.

Once eco-efficiency is derived, this paper applies this indicator to the Yellow River Basin in China. It is worth noting that the key methodology that motivates this paper is the desire to construct an appropriate method to more precisely derive a general efficiency analysis.

3. Methodology

3.1. Environmental Production Technology

Suppose there are a total of $K$ cities in the Yellow River Basin. Each city uses $N$ inputs jointly to produce $M$ desirable outputs and $J$ undesirable outputs, corresponding to the matrices $\mathit{X}=\left[x_1,x_2,\dots ,x_n\right]\in {\mathit{R}}_{+}^N$, $\mathit{Y}=\left[y_1,y_2,\dots ,y_m\right]\in {\mathit{R}}_{+}^M$, and $\mathit{B}=\left[b_1,b_2,\dots ,b_j\right]\in {\mathit{R}}_{+}^J$, respectively. Therefore, the multi-output environmental technology production set can be expressed as

$$\mathit{T}=\left\{\mathit{X}:\mathit{X} can produce \left(\mathit{Y},\mathit{B}\right)\right\},$$

(1)

where $\mathit{T}$ satisfies the axioms of the production theory [45,47,50], as well as the weak disposability and null-jointness assumptions [51,52].

Subject to the above assumptions, we show the $\mathit{T}$ for $K$ cities exhibiting the constant returns to scale in the non-parametric DEA approach, i.e.,

$$\begin{array}{l}\mathit{T}=\{(\mathit{X},\mathit{Y},\mathit{B}):{\displaystyle {\sum }_{k=1}^K{z}_k{\mathit{X}}_{nk}}\le {\mathit{X}}_n,n=1,2,\dots ,N\\ {\displaystyle \hspace{1em}\hspace{1em}{\sum }_{k=1}^K{z}_k{\mathit{Y}}_{mk}}\ge {\mathit{Y}}_m,m=1,2,\dots ,M\\ {\displaystyle \hspace{1em}\hspace{1em}{\sum }_{k=1}^K{z}_k{\mathit{B}}_{jk}}={\mathit{B}}_j,j=1,2,\dots ,J\\ \hspace{1em}\hspace{1em}{z}_k\ge 0,k=1,2,\dots K\},\end{array}$$

(2)

where $z={\left(z_1,z_2,\dots ,z_k\right)}^T$ is the intensity variable used for connecting the input-output vectors through convex combinations [53,54,55]. When constraint $z_k\ge 0$ holds, $\mathit{T}$ exhibits the characteristic of variable returns to scale [56,57,58].

3.2. Biennial Non-Radial Directional Distance Function

We employ the non-radial directional distance function (NDDF) to illustrate the production possibility set, which allows for the slack variable to address the efficiency overestimation in the directional distance function [25,59,60]. With the environmental constraints and economic targets of the Yellow River Basin, let $\mathit{g}=\left(-g_X,g_Y,-g_B\right)$ be the direction vector. NDDF is defined as

$$\overrightarrow{D}\left(\mathit{X},\mathit{Y},\mathit{B}\right)=\sup \left\{{\mathit{w}}^T\mathit{\beta }:\left(\left(\mathit{X},\mathit{Y},\mathit{B}\right)+\mathit{g}\cdot diag\left(\mathit{\beta }\right)\right)\right\}$$

(3)

This function is to maximize outputs while minimizing inputs and emissions. $\mathit{w}$ is the weight vector, $\mathit{\beta }$ represents the inefficiency value, and $diag(.)$ is the diagonal matrix.

Previous studies have primarily estimated NDDFs using global production technology because that approach addresses the potential linear programming infeasibility [29]. However, when a new time period is added to the dataset, the use of the global production technology forces the re-computation of all previous estimates, resulting in a change in efficiency [30]. To eliminate this concern, we construct a new convex combination ${\mathit{T}}^B=conv\left\{{\mathit{T}}^t,{\mathit{T}}^{t+1}\right\}$ by combining the period $t$ and period $t+1$ production technologies. We then compute all NDDFs via the linear programming approach using the biennial environmental production technology, i.e.,

$$\begin{array}{l}{\overrightarrow{D}}_k^B\left({\mathit{X}}^t,{\mathit{Y}}^t,{\mathit{B}}^t\right)=\sup \left({\displaystyle {\sum }_{n=1}^N{w}_n{\beta }_n}+{\displaystyle {\sum }_{m=1}^M{w}_m{\beta }_m}+{\displaystyle {\sum }_{j=1}^J{w}_j{\beta }_j}\right)\\ \mathit{s}\mathbf{.}\mathit{t}\mathbf{.} {\displaystyle {\sum }_{k=1}^K{z}_k^t{X}_{nk}^t}+{\displaystyle {\sum }_{k=1}^K{z}_k^{t+1}{X}_{nk}^{t+1}}\le X_n^t-{\beta }_{nk}^t{g}_{nk},n=1,2,\dots ,N;\\ {\displaystyle \hspace{1em}\hspace{1em}{\sum }_{k=1}^K{z}_k^t{Y}_{mk}^t}+{\displaystyle {\sum }_{k=1}^K{z}_k^{t+1}{Y}_{mk}^{t+1}}\ge Y_m^t-{\beta }_{mk}^t{g}_{mk},m=1,2,\dots ,M;\\ {\displaystyle \hspace{1em}\hspace{1em}{\sum }_{k=1}^K{z}_k^t{B}_{jk}^t}+{\displaystyle {\sum }_{k=1}^K{z}_k^{t+1}{B}_{jk}^{t+1}}=B_j^t-{\beta }_{jk}^t{g}_{jk},j=1,2,\dots ,J;\\ {\displaystyle \hspace{1em}\hspace{1em}{\sum }_{k=1}^K{z}_k^t}+{\displaystyle {\sum }_{k=1}^K{z}_k^{t+1}}=1;z_k^t,z_k^{t+1}\ge 0;{\beta }_{nk}^t,{\beta }_{mk}^t,{\beta }_{jk}^t\ge 0.\end{array}$$

(4)

In model (4), if ${\overrightarrow{D}}_k^B\left({\mathit{X}}^t,{\mathit{Y}}^t,{\mathit{B}}^t\right)=0$, it implies that the input-output set of the kth city is located on the production frontier.

3.3. Biennial Meta-Frontier Non-Radial Directional Distance Function

Since production technology homogeneity can cause biased estimates, we employ the meta-frontier approach [23,26,52]. Following Oh [23], we divide our sample into $H$ subgroups, each with $K_h$ observations. In this case, we define three types of environmental production technologies. First, we define the biennial benchmark production technology, $T^B=\left\{\mathit{X}:\mathit{X} can production \left(\mathit{Y},\mathit{B}\right)\right\}$, which is constructed using the full sample as the benchmark for the biennial production technology. Second, the biennial benchmark production technology in the hth subgroup is defined as $T_h^B=\left\{{\mathit{X}}^h:{\mathit{X}}^h can production \left({\mathit{Y}}^h,{\mathit{B}}^h\right)\right\}$. Third, we define the contemporary benchmark production technology. This production technology of the hth subgroup is defined as $T_h^t=\left\{{\mathit{X}}^t:{\mathit{X}}^t can production \left({\mathit{Y}}^t,{\mathit{B}}^t\right)\right\}$, which is a production technology set for the period $t$.

The biennial production technology for either the full-sample or the subgroup can be solved directly by the model (4), while the contemporary benchmark production technology is slightly different from them. For the contemporary benchmark production technology, we can solve for NDDFs by the following DEA-type.

$$\begin{array}{l}{\overrightarrow{D}}_k\left({\mathit{X}}^t,{\mathit{Y}}^t,{\mathit{B}}^t\right)=\sup \left({\displaystyle {\sum }_{n=1}^N{w}_n{\beta }_n}+{\displaystyle {\sum }_{m=1}^M{w}_m{\beta }_m}+{\displaystyle {\sum }_{j=1}^J{w}_j{\beta }_j}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathit{s}\mathbf{.}\mathit{t}\mathbf{.} {\displaystyle {\sum }_{k=1}^{K_h}{z}_k^t{X}_{nk}^t}\le X_n^t-{\beta }_{nk}^t{g}_{nk},n=1,2,\dots ,N;\\ {\displaystyle \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\sum }_{k=1}^{K_h}{z}_k^t{Y}_{mk}^t}\ge Y_m^t-{\beta }_{mk}^t{g}_{mk},m=1,2,\dots ,M;\\ {\displaystyle \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\sum }_{k=1}^{K_h}{z}_k^t{B}_{jk}^t}=B_j^t-{\beta }_{jk}^t{g}_{jk},j=1,2,\dots ,J;\\ {\displaystyle \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\sum }_{k=1}^{K_h}{z}_k^t}=1;z_k^t\ge 0;{\beta }_{nk}^t,{\beta }_{mk}^t,{\beta }_{jk}^t\ge 0.\end{array}$$

(5)

3.4. Definition of Eco-Efficiency

Since we have four inputs (labor, capital, energy, and water), one desirable output (GDP), and two undesirable outputs (CO₂ and NO_x), we set the weight vector to $\left(1/12, 1/12, 1/12, 1/12, 1/3, 1/6, 1/6\right)$ [61,62]. To model eco-efficiency in the Yellow River Basin, this paper set the normalized weight vector as (1/3, 1/3, 1/3) for input, desirable output, and undesirable output vectors. This resulting modeling is externally similar to the additive DEA model in the sense that both attempt to identify the potential slacks in the input-output mix as much as possible. This method of setting weights has also been widely used, for example, by Zhou et al. [25], and Zhang and Choi [26]. We exactly follow the concept proposed by Schaltegger and Sturm [21], and provide a normative definition of eco-efficiency based on DEA: the ratio of actual GDP to environmental impact to potential GDP to environmental impact. Assuming that ${\beta }_{gdp}^{*}$, ${\beta }_{C{O}_2}^{*}$, and ${\beta }_{N{O}_x}^{*}$ are optimal solutions corresponding to GDP, CO₂ emissions, and NO_x emissions, the eco-efficiency may be written as

$$\begin{array}{l}eco\_eff=\frac{gdp/\left[1/2\left(C{O}_2+N{O}_x\right)\right]}{\left(gdp+{\beta }_{gdp}^{*}gdp\right)/\left\{1/2\left[\left(C{O}_2-{\beta }_{C{O}_2}^{*}C{O}_2\right)+\left(NOx-{\beta }_{N{O}_x}^{*}N{O}_x\right)\right]\right\}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =\frac{1-1/2\left({\beta }_{C{O}_2}^{*}+{\beta }_{N{O}_x}^{*}\right)}{1+{\beta }_{gdp}^{*}}\end{array}$$

(6)

The eco-efficiency indicator is constructed to measure the maximum possible increase in economy and the minimum possible decrease in emissions. This indicator lies between 0 and 1. The higher the eco-efficiency, the easier it is for the city to achieve a win-win situation of ecological protection and economic growth. If eco-efficiency is equal to 1, the city exhibits the best eco-economic performance at the production frontier.

3.5. Biennial Meta-Frontier Non-Radial Malmquist Index

To investigate the dynamics of eco-efficiency over time, we propose the biennial meta-frontier non-radial Malmquist index (BMNMI), which addresses the issues of technology heterogeneity [23,63], the slack variable [25,26,64], and linear programming infeasibility [29], as well as maintains the previously computed value of eco-efficiency if a new time period is added to the dataset [30]. BMNMI is defined as

$$BMNM{I}_k^{t,t+1}\left(\mathit{X},\mathit{Y},\mathit{B}\right)=\frac{eco\_ef{f}_k^B\left({\mathit{X}}^{t+1},{\mathit{Y}}^{t+1},{\mathit{B}}^{t+1}\right)}{eco\_ef{f}_k^B\left({\mathit{X}}^t,{\mathit{Y}}^t,{\mathit{B}}^t\right)}$$

(7)

where $BMNM{I}_k^{t,t+1}$ is the change rate of eco-efficiency for the kth city from period $t$ to period $t+1$.

Furthermore, to examine the internal drivers of BMNMI, following Choi et al. [65] and Zhang et al. [66], we decompose BMNMI into three important components from a technology perspective,

$$\begin{array}{l}BMNM{I}_k^{t,t+1}(.)=\frac{eco\_ef{f}_k^B\left({.}^{t+1}\right)}{eco\_ef{f}_k^B\left({.}^t\right)}=\frac{eco\_ef{f}_k^{t+1}\left({.}^{t+1}\right)}{eco\_ef{f}_k^t\left({.}^t\right)}\times \left(\frac{\frac{eco\_ef{f}_k^B\left({.}^{t+1}\right)}{eco\_ef{f}_k^{t+1}\left({.}^{t+1}\right)}}{\frac{eco\_ef{f}_k^B\left({.}^t\right)}{eco\_ef{f}_k^t\left({.}^t\right)}}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =\frac{eco\_ef{f}_k^{t+1}\left({.}^{t+1}\right)}{eco\_ef{f}_k^t\left({.}^t\right)}\times \left(\frac{\frac{eco\_ef{f}_k^{Bh}\left({.}^{t+1}\right)}{eco\_ef{f}_k^{t+1}\left({.}^{t+1}\right)}}{\frac{eco\_ef{f}_k^{Bh}\left({.}^t\right)}{eco\_ef{f}_k^{t+1}\left({.}^t\right)}}\right)\times \left(\frac{\frac{eco\_ef{f}_k^B\left({.}^{t+1}\right)}{eco\_ef{f}_k^{Bh}\left({.}^{t+1}\right)}}{\frac{eco\_ef{f}_k^B\left({.}^t\right)}{eco\_ef{f}_k^{Bh}\left({.}^t\right)}}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =E{C}^{t,t+1}\times BP{C}^{t,t+1}\times TG{C}^{t,t+1}\end{array}$$

(8)

where the efficiency change (EC) measures the catch-up effect in ecological protection and economic development from period $t$ to period $t+1$. When EC is greater than 1, it means that efficiency increases; otherwise, efficiency decreases. The best-practice gap change (BPC) portrays the change in biennial environmental production technology for the hth subgroup from period $t$ to period $t+1$, indicating the innovation effect. The technology gap change (TGC) signifies the change in the closeness of the group frontier to the biennial frontier, representing the technology leadership effect.

4. Data

Panel data of 76 cities in 8 provinces of the Yellow River Basin from 2008 to 2017 was collected based on the data availability. The dataset of input-output variables for measuring eco-efficiency was mainly collected from the China City Statistical Yearbook for the period 2009 to 2018. Each city is assumed to produce three outputs (including undesirable outputs), GDP, CO₂ emissions, and NO_x emissions, using the four inputs of labor, fixed assets, energy consumption, and water supply. The burning of fossil fuels produces both greenhouse gases (GHGs) and air pollutants [67]. It is generally accepted that GHGs are dominated by CO₂, which accounts for 77% of GHGs, while SO₂, NOx, and suspended particulates are represented among air pollutants. However, due to the availability of SO₂ and suspended particulates data and the requirement of DEA for a strong balance panel, NOx is chosen as a proxy variable for air pollutants in this paper. Additionally, the primary issue in the Yellow River Basin is the shortage of water resources, and the use of water resources is mainly for agricultural irrigation [68]. Wastewater discharge is insignificant in relation to the total water resource; thus, this variable is ignored in the production process in this paper. We also assume that all CO₂ emissions are from the combustion of fossil fuels. For each city, we estimate CO₂ emissions by multiplying the consumption of each energy type by its carbon emission factor [67,69].

Table 1. Statistical summary for all input-output variables.

Variable	Unit	Mean	Std. Dev.	Min.	Max.
Labor	104 Person	43.95	34.15	4.21	207.55
Capital	CNY 109	129.12	116.58	4.04	777.71
Energy	106 ton	20.16	17.13	0.07	116.24
Water	106 ton	88.62	95.63	3.52	573.96
GDP	CNY 109	170.41	154.39	76.00	1103.73
CO2	106 ton	33.85	19.18	3.72	108.48
NOx	103 ton	81.59	91.32	1.02	924.16

Notes: Our sample covers 76 prefecture-level cities in eight provinces in the Yellow River Basin. City-year sample size: 760 observations. Sample period: 2008–2017. CO₂ emissions are estimated based on Cui et al. [69] and Wei and Zhang [67]. The remaining variables are collected from the China City Statistical Yearbook.

provides the statistical summary of all variables in our sample.

To incorporate regional inequality, we create a grouping of cities in our sample based on technology heterogeneity. Following Zhang and Zhou [34], we divide the cities into eastern, central, and western regions based on their geographical locations. In the Yellow River Basin, the eastern region consists of only Shandong Province, the central region is composed of Henan and Shanxi Provinces, and the western region covers five members: Shannxi, Inner Mongolia, Gansu, Ningxia, and Qinghai Provinces. The eastern, central, and western regions of China are divided based on the level of economic development and geographical location. This division does not refer to the economic level alone, nor is it entirely a division of geographical concepts, but rather it is a mixture of the two. There is a great deal of literature regarding heterogeneity analysis using this division criterion, e.g., Yu and Zhang [70], Zhang et al. [61], and Zhang and Zhou [34]). In

Table 2. Resource, ecological, and economic characteristics for the different regions.

	Eastern Region		Central Region		Western Region
	Mean	Growth	Mean	Growth	Mean	Growth
Labor	65.03	3.50%	48.11	3.79%	28.64	3.58%
Capital	202.82	15.42%	121.51	18.43%	95.58	18.55%
Energy	32.70	5.04%	19.71	3.67%	13.68	11.60%
Water	133.22	3.60%	75.76	1.60%	76.33	3.29%
GDP	307.53	9.41%	148.48	11.23%	115.02	10.89%
CO2	42.92	1.76%	32.03	3.25%	30.51	6.31%
NOx	33.98	20.20%	73.68	45.47%	42.59	35.29%

Notes: The units of variables for each region are exactly the same as in Table 1.

, we find that each group possesses different resource endowments and economic development levels, providing an additional basis for using the meta-frontier approach.

5. Empirical Analysis

5.1. Eco-Efficiency by Regions

The descriptive statistics for eco-efficiency in the Yellow River Basin and its three regions from 2008 to 2017 are reported in Figure 2. Our purpose is to identify the cities that can drive high-quality development while maintaining the stability of the ecosystem. We first provide the “average effect” over our sample period. The eco-efficiency of an average city is 0.637, implying an efficiency loss of close to 40% relative to the production frontier. Hence, a large gap exists both ecologically and economically.

From 2008 to 2012, the eco-efficiency of the Yellow River Basin rose steadily, with an average value of 0.663. This is because the State Council approved the Flood Control Plan for the Yellow River Basin, issued in 2008, which controls flooding and sedimentation (see http://www.gov.cn/zwgk/2008-07/28/content_1057822.htm (accessed on 15 August 2022, in Chinese)). This helped maintain a steady increase in regional GDP while protecting the ecology from damage from natural disasters. In 2012, the State Council implemented a stringent water management system to control regional water consumption (see http://www.gov.cn/gongbao/content/2012/content_2076102.htm (accessed on 15 August 2022, in Chinese)). This system has caused a shortage of inputs in cities, causing a short-term decline in eco-efficiency. With technological advances and productivity gains [71], eco-efficiency rebounded after 2015, consistent with the Porter hypothesis [31,59]. In a nutshell, eco-efficiency shows a U-shaped curve after 2012.

For the three regions, we first measure eco-efficiency based on the group frontier, as shown in

Table 3. Comparison of eco-efficiency under the group frontier.

Region	Obs.	Mean	Std. Dev.	Min	Max
Full sample	760	0.802	0.246	0.199	1
Eastern region	170	0.869	0.192	0.394	1
Central region	280	0.752	0.275	0.199	1
Western region	310	0.811	0.235	0.241	1

. We find that eco-efficiency is highest in the eastern region (0.869) and lowest in the central region (0.752). However, cross-group comparisons are not allowed because different regions do not provide a uniform benchmark technology [52]. Therefore, to address the issue of production technology heterogeneity, we must employ the meta-frontier approach to bring them under a unified benchmark for comparison.

As expected, the eco-efficiency under the meta-frontier is less than under the group frontier. Not surprisingly, the difference between the estimated values of eco-efficiency in the eastern region under the two benchmarks is quite tiny, which indicates that there is a relatively small technology gap in the eastern group. Indeed, in the Yellow River Basin, Shandong Province has a relatively high economic development, and its CO₂ is more strictly regulated. During the 12th Five-Year Plan Period (2011-2015), Shandong Province has a carbon intensity target of 18%, the most stringent carbon regulation in the Yellow River Basin. See http://www.gov.cn/zwgk/2012-01/13/content_2043645.htm (accessed on 15 August 2022, in Chinese). As a result, the group frontier in the eastern regions lies close to the meta-frontier.

Specifically, under the meta-frontier, the eastern region has an eco-efficiency of 0.770, which is 0.260 higher than that of the central region and 0.048 higher than that of the western region. Remarkably, although the eco-efficiency of the eastern region is quite close to that of the western region, the similar results have different causes. In Table 2, we find that the eastern region is characterized by high economic growth (307.53 × CNY 10⁹), as well as high emissions (42.92 × 10⁶ tons of CO₂ and 33.98 × 10³ tons of NO_x), whereas the western region is characterized by the opposite. The central region consists largely of cities with relatively low economic growth, but higher emissions, and it therefore has the lowest eco-efficiency. This finding is also associated with the harsh environment of the central region, which is located on the Loess Plateau. Additionally, the three regions are almost identical to the full sample in terms of trends. An unexpected and logical result is that the eastern region experienced a significant decline in eco-efficiency in 2016. That year, Shandong Province issued the Air Pollution Prevention and Control Regulations of Shandong Province, and these regulations are known as the most stringent local regulations on environmental protection in history; therefore, and cities closed their economies in the short term due to the introduction of capital for abatement.

Although the trends in eco-efficiency in the Yellow River Basin have been described in detail above, our analysis does not allow us to clearly identify which cities are highly efficient. A highly efficient city is a city with unified eco-efficiency. Figure 3 reports the distribution of eco-efficiency for all cities in the Yellow River Basin during our study period. Between 2008 and 2012, we intuitively found that the distribution of eco-efficiency was not altered substantially. It still shows the characteristic highs in the eastern and western regions and lows in the central region. In the eastern region, Qingdao, Weihai, Yantai, Laiwu, Dongying, and Zibo all show a unified eco-efficiency during this period, and are highly efficient cities. In the central region, Zhoukou City is in a highly efficient city. In the western region, Jiayuguan, Dingxi, Zhongwei, and Guyuan are registered as highly efficient cities.

During the period of 2012 to 2017, the central government reinforced the management of the Yellow River Basin, producing a dramatic change in eco-efficiency. We found that all three regions experienced a significant decrease in eco-efficiency in 2016, and the number of highly efficient cities fell. There are two cities in the eastern region, one city in the central region, and 11 cities in the western region. An important reason for more appearances in the western region is that there are more cities and the ecological environment is not as damaged. Subsequently, in 2017, there was a rebound in eco-efficiency, consistent with the findings of the Porter hypothesis described previously.

5.2. BMNMI and Its Components

We examined BMNMI and its components from 2008 to 2017 in Figure 4. Average BMNMI increased by about 5.73% during the study period. This means that an average city in the Yellow River Basin can increase its regional GDP while improving its ecological environment. Specifically, the BMNMI fluctuated slightly from 2008 to 2012, but remained greater than the unity. After 2012, the BMNMI shows a U-shape curve. The eastern region and the central region exhibit similar trends, demonstrating a U-shaped pattern. By contrast, the BMNMI in the western region is more stable and higher than unity in all periods, except for a slight decrease from 2012 to 2013 and from 2014 to 2015.

Regarding efficiency change, the average annual growth rate of efficiency is 1.17%, indicating efficiency gains. Economically, this means that the gap between an average city and the contemporary benchmark production technology narrowed over this period. There are two reasons for the increase in efficiency [23]. First, if the benchmark production technology advances, the catch-up speed of an average city is more rapid than that of the benchmark production technology. Second, if the benchmark production technology regresses, the technical decline speed of an average city is slower than that of the benchmark production technology. Whether the contemporary benchmark production technology has advanced must be investigated further, and this issue will be discussed below. The results of heterogeneity of production technologies show that both the eastern region (1.69%) and the western region (2.05%) are skillful in catching up with frontier technology. By contrast, the central region has an EC less than the unity, indicating that it is moving away from the contemporary benchmark production technology.

The average annual growth rate of technology change, BPC, is 2.05%, implying technological progress. During the sample period, both governments and residents increased their environmental concerns, which appears to have contributed to the advancement of technology. The survey of region-specific BPC reveals that the western region (2.91%) showed the highest technology change from 2008 to 2017, while the eastern region (0.99%) showed the lowest innovation effect, likely related to the high-quality economic development in this region. Here, we also verify the relationship between efficiency gains and technology progress. Technological innovation corresponds to the advancement of the biennial benchmark production technology in a specific subgroup. On this basis, efficiency gains are locked in by the fact that the catch-up speed of an average city is more rapid than that of the benchmark production technology.

The average annual technology gap change rate, TGC, is roughly 6.04%, signifying that the gap between biennial benchmark production technology for the full sample and the specific subgroup is shrinking. While the overall technology advances tend to be in the frontier technology, studies of region-specific TGCs show significant heterogeneity across the regions. Prior to 2016, the eastern region showed lower TGC than the other regions, but after 2016, its TGC increased significantly, far exceeding that of the others. The TGC increase is higher in the central region, implying that the central region’s efforts to advance both energy and environmentally related technologies in recent years are paying off. The western region (2.79%) although relatively static, shows a declining trend, which indicates the potential for technology development in the upper Yellow River Basin.

5.3. The Main Source of Eco-Efficiency Growth

To identify the drivers of eco-efficiency growth in each region, we calculated the contributions of EC, BPC, and TGC in

Table 4. Contribution of EC, BPC, and TGC for each region, 2008–2017.

Period	08–09	09–10	10–11	11–12	12–13	13–14	14–15	15–16	16–17
Panel A: Full sample
EC	0.337	0.318	0.340	0.304	0.329	0.344	0.332	0.330	0.314
BPC	0.327	0.331	0.307	0.343	0.334	0.321	0.329	0.336	0.340
TGC	0.336	0.351	0.353	0.354	0.338	0.335	0.338	0.334	0.345
Source	EC	TGC	TGC	TGC	TGC	EC	TGC	BPC	TGC
Panel B: Eastern region
EC	0.328	0.339	0.349	0.328	0.331	0.336	0.342	0.356	0.298
BPC	0.320	0.331	0.314	0.345	0.344	0.343	0.320	0.346	0.319
TGC	0.352	0.330	0.338	0.327	0.325	0.320	0.338	0.298	0.385
Source	TGC	EC	EC	BPC	BPC	BPC	EC	EC	TGC
Panel C: Central region
EC	0.341	0.296	0.347	0.255	0.330	0.348	0.315	0.315	0.332
BPC	0.322	0.320	0.304	0.333	0.325	0.318	0.347	0.331	0.321
TGC	0.337	0.384	0.349	0.413	0.345	0.334	0.338	0.354	0.347
Source	EC	TGC	TGC	TGC	TGC	EC	BPC	TGC	TGC
Panel D: Western region
EC	0.338	0.327	0.330	0.340	0.326	0.344	0.342	0.331	0.308
BPC	0.336	0.341	0.304	0.351	0.336	0.312	0.319	0.336	0.373
TGC	0.327	0.332	0.365	0.320	0.338	0.344	0.339	0.333	0.319
Source	EC	BPC	TGC	BPC	TGC	EC	EC	BPC	BPC

Notes: The main source of eco-efficiency growth is the maximum value among the contributions of EC, BPC, and TGC.

. Our main finding is that from 2009 to 2013, technology leadership effects contributed to eco-efficiency progress in the Yellow River Basin. This is also evidenced by the fact that the paths of TGC and BMNMI are almost identical in Figure 4. This occurs for several reasons. First, revolutionary eco-technological innovations occurred. Second, during the study period, sufficient technology spillover existed to reduce the technology gap among regions. The impact of TGC on BMNMI declined after 2013, suggesting that the new round of water management inhibited technological innovation in the short term.

Specifically, the eastern region has the largest contribution of EC during the sample period, implying that the eco-efficiency growth mainly comes from the catch-up effect. The central region has the largest share of TGC during the sample period, indicating that the eco-efficiency growth is driven by the technology leadership effect, and the western region is most influenced by the innovation effect. The results of eco-efficiency growth decomposition of the subsamples are consistent with those shown in Figure 4.

Different regions reflect heterogeneity in eco-efficiency progress. For the eastern region, the catch-up effect is the crucial driver for enhancing its eco-efficiency, while the innovation effect and technology leadership effect are the main sources of eco-efficiency growth in the western and central regions, respectively. Figure 5 shows the spatial distribution of EC, BPC, and TGC. We find that the top 5 cities in EC in the Yellow River Basin are located primarily in the richer eastern region and the western region, with better ecology, including Dezhou (12.4%), Wuhai (19.4%), and Hulunbuir (21.8%). The top 5 cities in BPC are all in the western region, including Ulaanchab (21.3%) and Jinzhong (8.4%). The top 5 cities in TGC are all situated in the central region, including Lvliang (30.4%) and Linfen (24.5%). Overall, we reached identical conclusions, both temporally (Table 4) and spatially (Figure 5).

6. Discussion

We discuss the potential implications of the empirical results from the viewpoint of environmental policy. During the 11th Five-Year Plan period (2006–2010), the Chinese government announced a 16% reduction in energy intensity, a 17% decrease in carbon intensity, and a 20% decline in sulfur dioxide emissions over the 2005 figures. Environmental regulation appears to have improved the eco-efficiency of the Yellow River Basin from 2008 to 2010 [52]. In 2012, the central government enacted the most stringent water management system in the Yellow River Basin, which set a goal for total national water use of 700 billion cubic meters by 2030. The most immediate impact is a reduction in water inputs, resulting in resource misallocation and reduced eco-efficiency [72]. Since 2015, we found a significant increase in the technology level in the Yellow River Basin, as BPC is 2.05% and TGC is 6.04%, with both indicating innovation effects.

Temporally, our study shows that the effect of environmental regulations on city-level eco-efficiency is a U-shaped relationship. This suggests that stricter regulations not only increase abatement costs, but also increase the performance level of environmentally friendly production processes. In addition to the U-shaped relationship, many studies suggest that this effect may be a linear, threshold, or inverted U-shaped relationship. In terms of linear relationships, for example, Peng et al. [73] use the difference-in-difference estimator to test the effect of SO₂ emission trading pilots on firm productivity and to verify the linear relationship between environmental regulation and productivity. In threshold relationship studies, for example, Xie et al. [74] use a panel threshold model to study whether environmental regulations have a threshold increase effect on green productivity. Wang and Kang [75] test the inverted U-shaped relationship between environmental regulation and international competitiveness of manufacturing, while Wu et al. [76] and Wu and Lin [77] both provide new evidence for a U-shaped relationship between regulation and environmental performance, validating the Porter hypothesis. Although the Porter hypothesis is controversial in the scientific community, our paper confirms the U-shaped impact of environmental regulation on eco-efficiency in the Yellow River Basin.

From the components of eco-efficiency growth, the trend of eco-efficiency growth in the Yellow River Basin is similar to that of TGC, which implies that the increase in eco-efficiency is primarily driven by the technology leadership effect. For different regions, eco-efficiency varies significantly, with the central region having the lowest eco-efficiency. This is because the central region is characterized by high emissions and low economic growth. It is suggested that the central region should learn from the economic development model of the eastern region and the ecological management of the western region to achieve a win-win strategy.

Of course, there are certain research limitations in this paper. First, we only studied the ecological problem in the Yellow River Basin, a typical region in China, and did not cover the rest of China or other countries around the world. Second, we used only four inputs and three outputs to measure eco-efficiency, and there are potential measurement errors, as well as uncertainties, due to incomplete indicator coverage. Third, the proposed novel DEA method does not possess statistical inference properties, and the future research direction is will provide a sensitivity analysis of eco-efficiency scores using a bootstrapped approach [61,78,79].

7. Conclusions

Like many other ecological reserve areas, the Yellow River Basin faces a stark trade-off between maintaining essential ecological quality and sustaining robust economic growth. This is the first article to propose a normative definition of eco-efficiency based on frontier approaches, and to timely and normatively assess city-level eco-efficiency in the Yellow River Basin.

Combining the concept of eco-efficiency proposed by Schaltegger and Sturm with non-parametric production theory, we propose a novel eco-efficiency indicator based on DEA models, which compensates for the vague definitions in the existing literature. This indicator is estimated by the BMNDDF approach, which addresses the issues of technology heterogeneity, the slack variable, and linear programming infeasibility, while maintaining the previously computed value of eco-efficiency if a new time period is added to the dataset. Using the panel data of cities in the Yellow River Basin from 2008 to 2017, we estimate the average eco-efficiency of the Yellow River Basin to be 0.637. The trend in eco-efficiency has a U-shaped curve.

We also investigated the eco-efficiency growth and its components. The empirical results showed a 5.73% increase in eco-efficiency per year, to which the technology gap change (TGC) is the main contributor. Evidence from heterogeneity analysis suggests that the central region suffers from more severe conflicts between outputs and emissions than other regions because it is defined by severe pollution and underdeveloped economic growth.

Finally, we identify several limitations of our study and discuss future research directions. First, we investigated the drivers of eco-efficiency growth using only technology decomposition, omitting the role of factors. Second, we omitted a few cities in the Yellow River Basin due to missing data issues. Third, the future direction should consider the spatial effects among cities in the Yellow River Basin, as these effects were not considered in this study.