Static High-Quality Development Efficiency and Its Dynamic Changes for China: A Non-Radial Directional Distance Function and a Metafrontier Non-Radial Malmquist Model

Abstract

Improving China’s high-quality development efficiency represents a key lever for the development of new productivity and successfully achieving the “dual carbon” goal. Starting from the nonparametric production theory, this paper addresses the issues of infeasible solutions and technical heterogeneity by employing the total-factor non-radial directional distance function and a metafrontier non-radial Malmquist model. The static total-factor high-quality development efficiency index (THEI) and its dynamic metafrontier non-radial Malmquist high-quality development efficiency index (MNMHEI) are measured for 31 provinces in China from 2008 to 2021. Given that high-quality development efficiency is led and driven by talent, we use labor of different ages and levels of education as four inputs instead of single labor for the study of THEI. The MNMHEI is divided into three indices for measuring efficiency change (EC), best-practice gap change (BPC), and technology gap change (TGC). The empirical results demonstrate that labor with higher education is the main lever of static high-quality development efficiency; there is a 5.3% decrease in China’s dynamic high-quality development efficiency as a whole, and a lack of technological innovation remains a significant constraint on its improvement. The results of the heterogeneity analysis, which classified all provincial areas into low-carbon and high-carbon regions, indicate that the former exhibits a higher dynamic high-quality development efficiency than the latter, which still lacks innovation and technology leadership. It is recommended that the Chinese government consider the talent management system, investments in upgrading technologies, energy conservation, and emission reduction for high-carbon regions to improve their high-quality development efficiency.

1. Introduction

Since 2010, China’s economic growth rate has been on the decline, from 10.6% in 2010 to 6.9% in 2015. The primary impetus of China’s sustainable development has switched from the massive expansion of its production factors to greater efficiency and technological innovation, coinciding with the country’s slower rate of economic growth. At the same time, the conventional development paradigm has also led to a number of ingrained inconsistencies and issues with economic development, including imbalanced economic growth and excessive resource and environmental costs. This set of issues calls for a shift in the primary goal of economic development from increasing economic scale to raising the standard of economic growth. The Central Economic Work Conference of 2017 declared that “China’s economic development has entered a new era, and the basic characteristic is that China’s economy has shifted from a stage of high-speed growth to a stage of high-quality development”. At present, China is at a strategic juncture of converting the paradigm of development and the power of growth. It must encourage the transformation of quality, efficiency, and power to support economic development [1].

The pursuit of high quality is fundamental to China’s economic development, and it serves as a foundation for the creation of various development strategies as well as the implementation of macroeconomic regulation and control. “Quality first and efficiency priority” have emerged as the two principles that economic development in China must effectively adhere to during the high-quality development era [2]. However, China’s development process remains inefficient, with a slow increase in desired outputs such as GDP, unsatisfactory emission reductions in non-desired outputs such as carbon dioxide (CO₂), and saving for inputs of production [3]. As a result, China’s development is primarily driven by improving the efficiency of high-quality development [4,5,6].

High-quality development emphasizes putting economic construction at the center, accelerating the building of a modern economic system, and achieving sustainable and healthy economic development by improving high-quality development efficiency. In the context of this era, the study of high-quality development efficiency is of crucial significance in promoting the transformation of economic development from scale and speed to quality and efficiency and from rough growth to intensive growth.

Since 2017, when the notion of high-quality development was proposed, scholars have used various methodologies to measure and research its effectiveness. Sun et al. employed the SFA methodology to evaluate the high-quality development efficiency of cities located in the Yangtze River Economic Belt from 2011 to 2019. They subsequently analyzed the elements that impacted this efficiency. The results suggest that the increase in capital, labor, land, and knowledge all contribute positively to the efficiency of high-quality development [7]. Based on the DEA-Malmquist index model with TFP as the efficiency of high-quality development, Zhang and Zhong measured, decomposed, and analyzed the TFP of high-tech industries in 31 provinces of China from 2011 to 2019. The results show that the TFP of high-tech industries in general maintains a growth trend [8]. Using panel data from 30 Chinese provinces and the SBM-DEA model, which has three stages, Yan et al. assessed the effectiveness of high-quality development in China’s industry. The study discovered that the efficiency of high-quality development in China’s industry is significantly boosted by government backing, information technology adoption, urbanization, and other variables [9].

Since the majority of the research mentioned above gauges high-quality development efficiency using TFP, we discuss the results achieved by scholars studying total factor productivity in recent years.

Wei et al. (2024) applied a DDF-GMLPI methodology to measure and analyze the total factor CO₂ emission efficiency of China’s transportation industry. The results of the study show that CO₂ emission efficiency has improved in twenty-eight provinces and that both efficiency improvements and technological advances have played a driving role [10].

In order to analyze environmental efficiency, Chambers et al. (1996) created the directional distance function (DDF), which Chung et al. (1997) extended [11,12]. The definition of DDF states that it simultaneously reduces undesired outputs and maximizes desired outputs. The idea conveyed by DDF is in line with the goal of our current economic and social development goals, which are to grow the economy while reducing environmental emissions. Nonetheless, because the conventional DDF is a measure of radial efficiency and inefficiency that does not account for slacks, it has the potential to lower inefficiencies while exaggerating the efficiency score when slacks exist [13]. Another limitation of the radial DDF is that it cannot distinguish between the inefficiency values of the different input and output factors because the radial DDF can only give the same rate of inefficiency [14]. The radial DDF presents difficulties in achieving integrated, unified efficiency. For this reason, non-radial efficiency measurements are frequently recommended as a means of overcoming the two constraints described earlier in the unified efficiency assessment process [15]. The non-radial DDF with undesirable outputs is defined formally by Zhou et al., (2012) [16]. Subsequently, after benchmarking unified efficiency within a total factor production framework, Zhang et al., (2013) [17] put forward a total-factor non-radial distance function (TNDDF). The formulas and restraints of the model set separate inefficiency values for the separate input factors, desired output factors, and undesired output factors, from which the efficiency values for each factor, as well as the combined efficiency, can be calculated.

Chen et al. (2023) combined the NDDF model and the Luenberger Hicks Moorsteen model to measure the green TFP of forestry based on panel data from 30 provinces in China. The following are the empirical conclusions: The green TFP for forestry is increasing annually and clearly exhibits spatial clustering. Furthermore, regression analyses demonstrate that the digital economy is positively correlated with green TFP in forestry, and industrial structure upgrading and technological innovation act as mediating factors [18].

The DEA-based Metafrontier Malmquist productivity index was proposed and constructed by Oh and Le (2010) [19]. The centerpiece of the Meta-Frontier DEA framework is the definition of the global technology frontier, contemporaneous technology frontier, and intertemporal technology frontier, respectively, so as to better characterize the heterogeneity of different regions. Considering non-radial slack and group heterogeneity, Zhang et al. combine the non-radial directional distance function by Zhou et al., and the metafrontier Malmquist index by Oh and Lee, into the model that is presented as the metafrontier non-radial Malmquist CO₂ emission performance index (MNMCPI) [20].

In recent years, many researchers have used NDDF and the metafrontier method to examine the TFP in different industries. For example, Meng and Pang (2023) applied these methods to evaluate the generation efficiency (TFGP) of the thermal power industry. This efficiency is a substantial catch to ensure the demand for electricity for economic and social progress. The analysis concludes that enhancing economic development, lowering fuel prices, and tightening environmental control will all benefit TFGP [21]. Cheng and Jin (2022) and Meng and Zhao (2022) also used these methods to measure and regress green TFP in the manufacturing industry. The results of Cheng and Jin show that diversified economy and specialized economy are the common drivers of green TFP but with different roles, with the former playing a greater role [22]. Meng and Zhao’s regression outcomes show that TFP benefits from the digital economy, while global value chains function as a helpful moderator [23]. Wang et al. (2022) applied these methods to research the TFP of the power industry, and the findings indicate that the spatial distribution of TFP in the industry is larger in the west than in the east and larger in the east than in the center, which is strongly associated with the western development strategy implemented by the state. Innovation in science and technology continues to be the primary driver of TFP growth in this industry [24].

In summary, despite valuable studies on high-quality development efficiency, there are still certain shortcomings. First, most studies have adopted TFP as the high-quality development efficiency, studying and decomposing it mainly from a dynamic perspective while ignoring the different contributions of the static efficiency components. Secondly, the existing studies generally believe that technology innovation is the main constraint on high-quality development efficiency [25], while ignoring the fact that technology innovation is ultimately led and driven by talent [26] and that talent should be able to serve high-quality development [27]. As a result, there is a lack of more in-depth research on the role of human capital in enhancing the efficiency of quality development. Finally, in terms of research methodology, there is the problem of ignoring non-radial slack and technological heterogeneity. Furthermore, studies often analyze heterogeneity in three regions of China, namely eastern, central, and western, and the classification approach does not account for the green characteristics of high-quality development [28].

This paper makes three marginal contributions to the existing literature. First, this paper proposes a static high-quality development efficiency index (THEI) and a dynamic metafrontier non-radial Malmquist high-quality development efficiency index (MNMHEI) based on non-parametric production theory, followed by a study of static and dynamic development efficiency and their respective components. Second, this paper classifies labor input indicators by age and degree of education for the study of static high-quality development efficiency so as to empirically test the role of talent in driving high-quality development. Finally, given the importance of high-quality development in achieving the “dual-carbon” aim, this study examines group heterogeneity based on the level of energy consumption and carbon emissions. The decomposition of dynamic high-quality development efficiency seeks to elucidate the dynamic changes in efficiency catch-up, technological innovation, and technological leadership in different regions of China.

The remainder of this paper is organized as follows: Section 2 describes the materials and methods. Section 3 empirically estimates the static total-factor high-quality development efficiency index (THEI) of 31 Chinese provinces, and presents the results and the related discussion; Section 4 empirically estimates the dynamic metafrontier non-radial Malmquist high-quality development efficiency index (MNMHEI) of 31 Chinese provinces and presents the results and the related discussion; and Section 5 concludes and proposes some policy suggestions.

2. Materials and Methods

2.1. Methods

2.1.1. Environmental Production Technology

Suppose that there are N provinces and that each province uses capital (K), labor (L), and energy (E) as inputs to generate GDP (G), a desirable output, and CO₂ emissions (C), an undesirable output. In particular, the labor input vector is divided into four, namely young labor with higher education (YHL), young labor without higher education (YLL), other labor with higher education (NYHL), and other labor without higher education (NYLL), which are also abbreviated as L¹⁻⁴. Then, we can express the multi-output production technology as follows:

$$T=\left\{\left( K; L^{1-4}; E; G; C\right):\left( K; L^{1-4}; E\right) \mathrm{c}\mathrm{a}\mathrm{n} \mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\left(G; C\right)\right\}$$

(1)

where T is usually assumed to satisfy the standard axioms of production economics theory [29].

The nonparametric DEA approach can be used to specify the production technology once the production technology T has been determined.

In accordance with the aforementioned assumption, based on Färe et al. [30] and Zhou et al., we can employ a nonparametric DEA method to formulate T for N provinces as follows:

$$T=\left\{\begin{array}{c}\left( K; L^{1-4}; E; G; C\right):{\displaystyle \sum _{n=1}^N}{z}_n{K}_n\le K,{\displaystyle \sum _{n=1}^N}{z}_n{L}_n^{1-4}\le L^{1-4},\\ {\displaystyle \sum _{n=1}^N}{z}_n{E}_n\le E,{\displaystyle \sum _{n=1}^N}{z}_n{G}_n\ge G,{\displaystyle \sum _{n=1}^N}{z}_n{C}_n=C,z_n\ge 0,n=1,\dots ,N\end{array}\right\}$$

(2)

2.1.2. Total-Factor Non-Radial Directional Distance Function

According to the definition of TNDDF by Zhang et al., the NDDF captures different slacks and inefficiencies for all different factors, provided that all inefficiencies for input factors, desirable output factors, and undesirable output factors are integrated into the functions and constraints. Then, it is applied to measure the integrated, unified efficiency on the basis of each efficiency for each factor. This overcomes the constraint of the radial DDF, which can only give the same rate of inefficiency, and thus the same rate of efficiency.

The idea conveyed by NDDF is in line with the requirements and characteristics of high-quality development, which means green development and sustainable development. High-quality development opposes so-called high-speed growth, which is characterized by high pollution and resource consumption, whereas high-quality development prioritizes energy savings and environmental protection while economic growth, resulting in green growth. Sustainable development requires careful consideration of the carrying capacity of various economic and social resources, conservation of resource inputs, adherence to the scientific concept of development, and living within one’s means to ensure smooth and sustainable economic development.

We can compute the NDDF value for N provinces, represented as $\overrightarrow{D}\left(K,L^{1-4},E,G,C;g\right)$, by figuring out the following DEA model. The inefficiencies of input factors, desired outputs, and non-desired outputs are all included in the model, which allows for the measurement of high-quality development efficiency within a total factor framework.

$$\begin{array}{l}\overrightarrow{D}\left(K,L^{1-4},E,G,C;\mathrm{g}\right)=max{w}_k{\beta }_k+w_{L1}{\beta }_{L1}+w_{L2}{\beta }_{L2}+w_{L3}{\beta }_{L3}+w_{L4}{\beta }_{L4}+w_E{\beta }_E+w_G{\beta }_G+w_C{\beta }_C\\ s.t.{\sum }_{n=1}^N{z}_n{K}_n\le K-{\beta }_K{\mathrm{g}}_K; {\sum }_{n=1}^N{z}_n{L^1}_n\le L^1-{\beta }_{L1}{\mathrm{g}}_{L1}\\ {\sum }_{n=1}^N{z}_n{L^2}_n\le L^2-{\beta }_{L2}{\mathrm{g}}_{L2}; {\sum }_{n=1}^N{z}_n{L^3}_n\le L^3-{\beta }_{L3}{\mathrm{g}}_{L3}\\ {\sum }_{n=1}^N{z}_n{L^4}_n\le L^4-{\beta }_{L4}{\mathrm{g}}_{L4}; {\sum }_{n=1}^N{z}_n{E}_n\le E-{\beta }_E{\mathrm{g}}_E\\ {\sum }_{n=1}^N{z}_n{G}_n\ge G-{\beta }_G{\mathrm{g}}_G; {\sum }_{n=1}^N{z}_n{C}_n=C-{\beta }_C{\mathrm{g}}_C\\ z_n\ge 0,n=1,\dots ,N; {\beta }_K, {\beta }_{L1}, {\beta }_{L2}, {\beta }_{L3}, {\beta }_{L4}, {\beta }_E,{\beta }_G, {\beta }_C\ge 0\end{array}$$

(3)

Because there are six inputs (K, L¹⁻⁴, E), one desirable output (G), and one undesirable output (C), in this study, following Zhou et al., Barros et al., and Zhang et al., inputs, desired outputs, and non-desired outputs are assumed to be equally important, and there is no difference in importance between each input [14]. We specify the weight vector as (1/9, 1/36, 1/36, 1/36, 1/36,1/9, 1/3, 1/3). We chose the observed value as the directional vector, namely, as g =$\left(-K; {-L}^1;{-L}^2;{-L}^3;{-L}^4 ;-E; G;-C\right)$. An evaluated province is at the best practice frontier and operates effectively in the direction of the directional vector if $\overrightarrow{D}=0$. If not, the province being evaluated is inefficient in that direction.

Sueyoshi discussed a DEA approach to measure unified efficiency [31]. Zhang et al. synthesized the methods of Zhou and Sueyoshi, proposed a total-factor non-radial distance function (TNDDF), and defined the unified efficiency index as the average efficiency of each factor. Following the study, we can express the static total-factor high-quality development efficiency index (THEI) for a province as the average efficiency of each factor. Assume that ${\beta }_K^{\ast }{,\beta }_{L1}^{\ast }{,\beta }_{L2}^{\ast }{,\beta }_{L3}^{\ast }{,\beta }_{L4}^{\ast }{,\beta }_E^{\ast }{,\beta }_G^{\ast }{,\beta }_C^{\ast }$, represent the optimal solutions to Equation (3) related to capital, four types of labor, energy, GDP, and CO₂, respectively, which are the inefficiencies of the above variables. Then, the THEI can be formulated as follows:

$$THEI={\displaystyle \frac{1/4\left[\left(1-{\beta }_K^{\ast }\right)+\left(1-{\beta }_L^{\ast }\right)+\left(1-{\beta }_E^{\ast }\right)+\left(1-{\beta }_C^{\ast }\right)\right]}{1+{\beta }_G^{\ast }}}={\displaystyle \frac{1-1/4\left({\beta }_K^{\ast }+{\beta }_L^{\ast }+{\beta }_E^{\ast }+{\beta }_C^{\ast }\right)}{1+{\beta }_G^{\ast }}}$$

(4)

where

$${\beta }_L^{\mathrm{*}}=1/4\left({\beta }_{L1}^{\mathrm{*}}+{\beta }_{L2}^{\mathrm{*}}+{\beta }_{L3}^{\mathrm{*}}+{\beta }_{L4}^{\mathrm{*}}\right)$$

(5)

Then, we can decompose the THEI into several indicators of different factors. First, Zhang et al. defined the static total-factor CO₂ emission performance index (TCPI) as the ratio of potential target carbon intensity to actual carbon intensity (C/G). Based on it, TCPI is expressed as follows:

$$TCPI={\displaystyle \frac{\left(C-{\beta }_C^{\ast }C\right)/\left(G+{\beta }_G^{\ast }G\right)}{C/G}}={\displaystyle \frac{1-{\beta }_C^{\ast }}{1+{\beta }_G^{\ast }}}$$

(6)

Similarly, the static total-factor capital performance index (TKPI), labor performance index (TLPI), and energy performance index (TEPI) are expressed as follows:

$$TKPI={\displaystyle \frac{\left(K-{\beta }_K^{\ast }K\right)/\left(G+{\beta }_G^{\ast }G\right)}{K/G}}={\displaystyle \frac{1-{\beta }_K^{\ast }}{1+{\beta }_G^{\ast }}}$$

(7)

$$TLPI={\displaystyle \frac{\left(L-{\beta }_L^{\ast }L\right)/\left(G+{\beta }_G^{\ast }G\right)}{L/G}}={\displaystyle \frac{1-{\beta }_L^{\ast }}{1+{\beta }_G^{\ast }}}$$

(8)

$$TEPI={\displaystyle \frac{\left(E-{\beta }_E^{\mathrm{*}}E\right)/\left(G+{\beta }_G^{\mathrm{*}}G\right)}{E/G}}={\displaystyle \frac{1-{\beta }_E^{\mathrm{*}}}{1+{\beta }_G^{\mathrm{*}}}}$$

(9)

Thus,

$$THEI=1/4(TKPI+TLPI+TEPI+TCPI)$$

(10)

Especially, TLPI can be decomposed into four indices: TYHLPI, TYLLPI, TNYHLPI, and TNYLLPI. These respectively mean the static total-factor performance index of young labor with higher education; the performance index of young labor without higher education; the performance index of other labor with higher education, and the performance index of other labor without higher education.

$$TYHLPI={\displaystyle \frac{\left(L-{\beta }_{L1}^{\ast }L1\right)/\left(G+{\beta }_G^{\ast }G\right)}{L1/G}}={\displaystyle \frac{1-{\beta }_{L1}^{\ast }}{1+{\beta }_G^{\ast }}}$$

(11)

$$TYLLPI={\displaystyle \frac{\left(L-{\beta }_{L2}^{\ast }L2\right)/\left(G+{\beta }_G^{\ast }G\right)}{L2/G}}={\displaystyle \frac{1-{\beta }_{L2}^{\ast }}{1+{\beta }_G^{\ast }}}$$

(12)

$$TNYHLPI={\displaystyle \frac{\left(L-{\beta }_{L3}^{\ast }L3\right)/\left(G+{\beta }_G^{\ast }G\right)}{L3/G}}={\displaystyle \frac{1-{\beta }_{L3}^{\ast }}{1+{\beta }_G^{\ast }}}$$

(13)

$$TNYLLPI={\displaystyle \frac{\left(L-{\beta }_{L4}^{\ast }L4\right)/\left(G+{\beta }_G^{\ast }G\right)}{L4/G}}={\displaystyle \frac{1-{\beta }_{L4}^{\ast }}{1+{\beta }_G^{\ast }}}$$

(14)

$$\begin{array}{cc}TLPI={\displaystyle \frac{1-{\beta }_L^{\ast }}{1+{\beta }_G^{\ast }}}& ={\displaystyle \frac{1-1/4\left({\beta }_{L1}^{\ast }+{\beta }_{L2}^{\ast }+{\beta }_{L3}^{\ast }+{\beta }_{L4}^{\ast }\right)}{1+{\beta }_G^{\ast }}}={\displaystyle \frac{1/4\left(1-{\beta }_{L1}^{\ast })+(1-{\beta }_{L2}^{\ast })+{(1-\beta }_{L3}^{\ast })+{(1-\beta }_{L4}^{\ast }\right)}{1+{\beta }_G^{\ast }}}\hfill \\ & =1/4\left(TYHLPI+TYLLPI+TNYHLPI+TNYLLPI\right)\hfill \end{array}$$

(15)

2.1.3. Dynamic Metafrontier Non-Radial Malmquist High-Quality Development Efficiency Index (MNMHEI)

Zhang et al. proposed the metafrontier non-radial Malmquist CO₂ emission performance index (MNMCPI) to measure the dynamic changes in CO₂ emission performance over time while accounting for group heterogeneity. The contemporaneous production technology $\left(T^C\right)$, the intertemporal production technology $\left(T^I\right)$, and the global production technology $\left(T^G\right)$ were required to define and decompose the dynamic index.

Based on the MNMCPI proposed by Zhang et al., we propose the metafrontier non-radial Malmquist high-quality development efficiency index (MNMHEI) to examine the dynamic changes in high-quality development efficiency. Here, we define the MNMHEI based on the global environmental production technology set $\left(T^G\right)$ as follows:

$$MNMHEI\left(K^S,L^S,E^S,G^S,C^S\right)={\displaystyle \frac{{THEI}^G\left(K^{t+1},L^{t+1},E^{t+1},G^{t+1},C^{t+1}\right)}{{THEI}^G\left(K^t,L^t,E^t,G^t,C^t\right)}}$$

where $S=t,t+1$

$${THEI}^C\left(K^S,L^S,E^S,G^S,C^S\right)={\left[{\displaystyle \frac{1-1/4\left({\beta }_K^{C\ast }+{\beta }_L^{C\ast }+{\beta }_E^{C\ast }+{\beta }_C^{C\ast }\right)}{1+{\beta }_G^{C\ast }}}\right]}^s={\left({\displaystyle \frac{1-{\beta }^{C\ast }}{1+{\beta }_G^{C\ast }}}\right)}^s$$

$${THEI}^I\left(K^S,L^S,E^S,G^S,C^S\right)={\left[{\displaystyle \frac{1-1/4\left({\beta }_K^{I\ast }+{\beta }_L^{I\ast }+{\beta }_E^{I\ast }+{\beta }_C^{I\ast }\right)}{1+{\beta }_G^{I\ast }}}\right]}^s={\left({\displaystyle \frac{1-{\beta }^{I\ast }}{1+{\beta }_G^{I\ast }}}\right)}^s$$

$${THEI}^G\left(K^S,L^S,E^S,G^S,C^S\right)={\left[{\displaystyle \frac{1-1/4\left({\beta }_K^{G\ast }+{\beta }_L^{G\ast }+{\beta }_E^{G\ast }+{\beta }_C^{G\ast }\right)}{1+{\beta }_G^{G\ast }}}\right]}^s={\left({\displaystyle \frac{1-{\beta }^{I\ast }}{1+{\beta }_G^{G\ast }}}\right)}^s$$

where

$$\begin{array}{l}\left(C,I,G\right)=\left(\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{o}\mathrm{u}\mathrm{s} \mathrm{t}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{n}\mathrm{o}\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{y}, \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{n}\mathrm{o}\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{y},\mathrm{g}\mathrm{l}\mathrm{o}\mathrm{b}\mathrm{a}\mathrm{l} \mathrm{t}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{n}\mathrm{o}\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{y}\right)\\ {\beta }^{C\ast }=1/4\left({\beta }_K^{C\ast }+{\beta }_L^{C\ast }+{\beta }_E^{C\ast }+{\beta }_C^{C\ast }\right)\\ {\beta }^{I\ast }=1/4\left({\beta }_K^{I\ast }+{\beta }_L^{I\ast }+{\beta }_E^{I\ast }+{\beta }_C^{I\ast }\right)\\ {\beta }^{G\ast }=1/4\left({\beta }_K^{G\ast }+{\beta }_L^{G\ast }+{\beta }_E^{G\ast }+{\beta }_C^{G\ast }\right)\end{array}$$

According to Oh and Lee, Zhang et al., MNMHEI can be divided into three indices for measuring a technical efficiency change (EC) of high-quality development, a best-practice gap change (BPC) of high-quality development, and a technology gap change (TGC) of high-quality development. To simplify notations, we replace ${THEI}^d\left(K^S,L^S,E^S,G^S,C^S\right)$ with ${THEI}^d\left({·}^s\right)$ to save space.

The decomposition process is as follows:

$$\begin{array}{l}MNMHEI\left(K^S,L^S,E^S,G^S,C^S\right)={\displaystyle \frac{{THEI}^G\left({·}^{t+1}\right)}{{THEI}^G\left({·}^t\right)}}\\ =\left[{\displaystyle \frac{{THEI}^C\left({·}^{t+1}\right)}{{THEI}^C\left({·}^t\right)}}\right]\times \left[{\displaystyle \frac{{THEI}^I\left({·}^{t+1}\right)/{THEI}^C\left({·}^{t+1}\right)}{{THEI}^I\left({·}^t\right)/{THEI}^C\left({·}^t\right)}}\right]\times \left[{\displaystyle \frac{{THEI}^G\left({·}^{t+1}\right)/{THEI}^I\left({·}^{t+1}\right)}{{THEI}^G\left({·}^t\right)/{THEI}^I\left({·}^t\right)}}\right]\\ =\left\{{\displaystyle \frac{{\left(\frac{1-{\beta }^{C\ast }}{1+{\beta }_G^{C\ast }}\right)}^{t+1}}{{\left(\frac{1-{\beta }^{C\ast }}{1+{\beta }_G^{C\ast }}\right)}^t}}\right\}\times \left\{{\displaystyle \frac{{\left(\frac{1-{\beta }^{I\ast }}{1+{\beta }_G^{I\ast }}\right)}^{t+1}/{\left(\frac{1-{\beta }^{C\ast }}{1+{\beta }_G^{C\ast }}\right)}^{t+1}}{{\left(\frac{1-{\beta }^{I\ast }}{1+{\beta }_G^{I\ast }}\right)}^t/{\left(\frac{1-{\beta }^{C\ast }}{1+{\beta }_G^{C\ast }}\right)}^t}}\right\}\times \left\{{\displaystyle \frac{{\left(\frac{1-{\beta }^{G\ast }}{1+{\beta }_G^{G\ast }}\right)}^{t+1}/{\left(\frac{1-{\beta }^{I\ast }}{1+{\beta }_G^{I\ast }}\right)}^{t+1}}{{\left(\frac{1-{\beta }^{G\ast }}{1+{\beta }_G^{G\ast }}\right)}^t/{\left(\frac{1-{\beta }^{I\ast }}{1+{\beta }_G^{I\ast }}\right)}^t}}\right\}\\ =\left[{\displaystyle \frac{{TE}^{t+1}}{{TE}^t}}\right]\times \left[{\displaystyle \frac{{BPR}^{t+1}}{{BPR}^t}}\right]\times \left[{\displaystyle \frac{{TGR}^{t+1}}{{TGR}^t}}\right]=EC\times BPC\times TGC \end{array}$$

(16)

EC captures the “catchup” effect in terms of technical efficiency changes in high-quality development for a specific group for two time periods. BPC can be considered an innovation effect, as it measures frontier shifts over two periods, and the TGC is a measure of the change in technology leadership of a given group.

2.2. Data

We employ the methods described in the previous subsection to analyze the static high-quality development efficiency and its dynamic changes in 31 Chinese provinces during the 2008–2021 period for balanced panel data.

Our research primarily examines the efficiency of high-quality development. To measure this, in order to obtain the desired output, we select the real GDP that was calculated using the year 2000, which has been commonly used in prior studies. (e.g., Meng, 2023; Zhang, 2014). We select CO₂ emissions as the undesirable output, which is in line with China’s commitment to the “dual-carbon goal” of carbon peaking and carbon neutrality. We use three classical inputs: capital (K), labor (L), and energy (E).

We measure the capital input, the labor input, and the energy input by the capital stock numbers, the number of employees, and the total energy consumption, respectively. The capital stock numbers are estimated using the perpetual inventory method [32]. The employees consist of four types (YHL, YLL, NYHL, NYLL). The aggregate energy consumption, encompassing various energy sources including coal, oil, gas, electricity, etc., is quantified in terms of tons of standard coal equivalent. We measure the desirable output and the undesirable output of each province by the real GDP and CO₂ emissions separately, as in many previous studies [33,34]. The capital, labor, and GDP data are downloaded from the Eps Database, which collects data from the China Statistical Yearbook. The energy data used are from the Eps Database, which collects data from the China Power Yearbook. For Tibet, which does not report energy data, we follow the method of Chen [35] to determine its energy consumption. Based on the Regional energy balance tables, CO₂ emissions from the CEADs Database are estimated using the IPCC Sectoral Approach [36,37,38,39,40]. The descriptive statistics of all 434 observations are presented in

Table 1. Descriptive statistics for variables (2008–2021, n = 31).

Variable	Unit	Group	n	Mean	StDev	Min	Max
K	109 ¥	1	210	53,020.33	41,511.08	1048.582	199,512.5
		2	224	39,108.24	31,683.75	2273.023	190,639.8
		all	434	45,839.9	37,378.94	1048.582	199,512.5
YHL	104 persons	1	210	340.7739	235.0554	5.208753	1196.863
		2	224	199.7824	149.809	25.27871	831.3595
		all	434	268.0041	207.8527	5.208753	1196.863
YLL	104 persons	1	210	861.4928	635.8135	61.62585	2714.873
		2	224	570.9986	425.3988	61.73456	2106.442
		all	434	711.5603	556.2817	61.62585	2714.873
NYHL	104 persons	1	210	495.7831	347.5369	4.92	1817.292
		2	224	288.9589	207.905	27.8726	1113.56
		all	434	389.0351	302.1053	4.92	1817.292
NYLL	104 persons	1	210	2450.566	1580.338	157.001	5654.315
		2	224	1677.389	1171.014	210.1544	5498.109
		all	434	2051.507	1435.736	157.001	5654.315
E	104 tons of standard coal equivalent	1	210	14,135.77	8791.268	235.943	35,759.7
		2	224	14,234.85	9462.246	2279	45,539.92
		all	434	14,186.91	9133.349	235.943	45,539.92
G	109 ¥	1	210	6004.92	3936.803	154.1904	17,193.26
		2	224	3305.232	2619.673	391.297	12,064.97
		all	434	4611.533	3583.226	154.1904	17,193.26
C	104 tons of standard coal equivalent	1	210	28,225.11	18,532.25	243.9063	81,768.02
		2	224	33,743.61	23,901.37	3157.438	94,716.29
		all	434	31,073.37	21,624.29	243.9063	94,716.29

.

In particular, we need to clarify the specific criteria for classifying labor according to age and level of education. With regard to the definition of young labor, there are two ways of defining them based on age ranges: narrow and broad. Firstly, the narrower definition: the National Bureau of Statistics of China (NBS) uses the age range of 16–24 years old for the urban youth unemployment rate, which is the age range set by the Labor Law of the People’s Republic of China, which stipulates that “people over 16 years old can formally join the workforce”. Secondly, for a broader scope, UNESCO defines young people as those aged 14–34. Taking into account the provisions of China’s Labor Law and the comparability of international studies, the age range for the study of young labor was defined as 16–34 years. With regard to the definition of labor with higher education, it means those who have received a university education, including college, undergraduate, and postgraduate education. Firstly, we classify labor by age into young labor and other labor. We then divide young labor into those with and without higher education and divide other labor into those with and without higher education. These data are downloaded from the Eps Database, which collects data from the China Statistical Yearbook.

3. Empirical Results and Discussion for the THEI

3.1. Empirical Results for the THEI

The proposed THEI is applied to 31 regions of China. The static total-factor high-quality development efficiency of the regions is calculated from the TNDDF of Equation (3).

The results are presented in

Table A1. Average THEI and its decomposition at the province level.

Region	THEI	TYHLPI	TYLLPI	TNYHLPI	TNYLLPI	TKPI	TEPI	TCPI
Anhui	0.513	0.705	0.461	0.782	0.347	0.549	0.578	0.351
Beijing	0.967	0.960	0.928	0.987	0.940	1.000	0.964	0.949
Fujian	0.574	0.742	0.480	1.000	0.457	0.546	0.607	0.474
Gansu	0.384	0.518	0.305	0.533	0.247	0.520	0.340	0.278
Guangdong	0.699	0.827	0.465	1.000	0.517	0.747	0.703	0.645
Guangxi	0.449	0.639	0.351	0.762	0.287	0.401	0.499	0.386
Guizhou	0.370	0.456	0.445	0.482	0.344	0.423	0.363	0.264
Hainan	0.561	0.685	0.259	0.948	0.291	0.696	0.585	0.418
Hebei	0.460	0.624	0.631	0.635	0.514	0.469	0.438	0.331
Henan	0.475	0.779	0.369	0.860	0.327	0.414	0.518	0.383
Heilongjiang	0.510	0.851	0.656	0.798	0.458	0.481	0.483	0.385
Hubei	0.507	0.773	0.289	0.894	0.276	0.629	0.478	0.361
Hunan	0.527	0.707	0.290	0.775	0.264	0.660	0.510	0.429
Jilin	0.443	0.851	0.566	0.760	0.426	0.313	0.493	0.315
Jiangsu	0.636	0.827	0.678	1.000	0.576	0.664	0.639	0.471
Jiangxi	0.508	0.651	0.279	0.857	0.254	0.548	0.587	0.387
Liaoning	0.465	0.826	0.775	0.840	0.522	0.443	0.385	0.292
Inner Mongolia	0.267	0.491	0.513	0.490	0.402	0.264	0.207	0.124
Ningxia	0.281	0.419	0.474	0.475	0.435	0.329	0.205	0.139
Qinghai	0.301	0.335	0.443	0.450	0.349	0.296	0.214	0.298
Shandong	0.509	0.783	0.576	0.865	0.486	0.476	0.489	0.392
Shanxi	0.358	0.496	0.515	0.514	0.419	0.471	0.280	0.195
Shaanxi	0.399	0.465	0.396	0.638	0.318	0.429	0.422	0.289
Shanghai	0.837	0.956	0.905	1.000	0.878	0.966	0.769	0.678
Sichuan	0.510	0.690	0.271	0.849	0.255	0.642	0.447	0.433
Tianjin	0.437	0.751	0.526	0.872	0.536	0.421	0.372	0.282
Tibet	0.586	0.594	0.340	0.959	0.368	0.591	0.652	0.536
Xinjiang	0.346	0.407	0.449	0.546	0.387	0.441	0.277	0.219
Yunnan	0.452	0.577	0.359	0.692	0.319	0.456	0.467	0.399
Zhejiang	0.647	0.819	0.515	0.996	0.465	0.777	0.623	0.492
Chongqing	0.488	0.717	0.425	0.747	0.368	0.480	0.482	0.427
Mean	0.499	0.675	0.482	0.774	0.420	0.534	0.486	0.388
Min	0.267	0.335	0.259	0.450	0.247	0.264	0.205	0.124
Max	0.967	0.960	0.928	1.000	0.940	1.000	0.964	0.949

. With regard to the overall average THEI, the results suggest that the majority of Chinese provinces are not effectively engaged in high-quality development. The THEI of the provinces varied from 0.267 to 0.967, with an average value of 0.499. With regard to individual regions, the index was divided into five echelons using the natural break method, and the results are shown in Figure 1. Beijing and Shanghai are in the top tier. Beijing showed the best static high-quality development efficiency among all the provinces, with an average static efficiency score of 0.967. Shanghai ranked second, with an average static efficiency score of 0.837. On the other hand, Inner Mongolia showed the poorest static efficiency score of 0.267.

3.2. Discussion for the THEI

Figure 2 shows the trends in the THEI and its decomposition. First, the THEI shows a downward trend as a whole, with a sharp decline between 2008 and 2010 and a slowdown between 2011 and 2017. Then, the decline becomes smaller and smaller, and from 2018 onwards, it is almost flat, with only a minimal decline.

Prior to 2008, China’s rapid economic growth, achieved mainly by increasing the consumption of material resources, was crude and low-quality. In the short term, the marginal cost of energy efficiency and emission reduction increased due to the environmental regulations included in the 11th Five-Year Plan for Sustainable Development. The stringent low-carbon targets have led to a sharp decline in the THEI over the period 2008–2010. In 2010, the Chinese government announced a goal, included in the 12th Five-Year Plan, for the paradigm shift of economic growth from one based on increasing consumption of material resources to one based on improving high-quality labor and technological innovations. As a long-term result, the effect of stricter environmental regulations on improving efficiency and encouraging innovations gradually offsets the impact of increased marginal costs. During the 2011–2017 period, the rate of decline in the THEI has slowed down. In 2017, the 19th National Congress of the Communist Party of China (CPC) put forward the new expression of high-quality development for the first time, and in 2021, the State Council approved the 14th Five-Year Plan on promoting high-quality development. It appears that the Chinese government’s high-quality development measures have been effective in pushing up THEI because from 2018 to 2021, the THEI has been almost horizontal. Following this trend, we can expect the THEI to increase in the near future, which means that we can produce the same GDP with less capital, less labor, less energy, and less CO₂ emissions.

Given that the THEI is composed of various components, it would be more advantageous to examine the trends of these individual components, including the performance index of young labor with higher education (TYHLPI), the performance index of young labor without higher education (TYLLPI), the performance index of other labor with higher education (TNYHLPI), the performance index of other labor without higher education (TNYLLPI), the static total-factor capital performance index (TKPI), the static total-factor energy performance index (TEPI), and the static total-factor CO₂ emission performance index (TCPI), individually for additional insights into performance trends.

From Figure 2, we find that the TYHLPI and the TNYHLPI have the first and second highest values among all the components, indicating that labor with higher education contributes the most to the THEI. Between them, other labor with higher education is more efficient than young labor with higher education. This is thought to be due to the fact that most of them are engaged in intellectual work and therefore need to cultivate their expertise over an extended period of time. Before 2018, the TYHLPI and the TNYHLPI showed a decreasing trend, but after 2018, it shows a U-shaped trend. It started to increase in 2019–2021. The trend implies that China is increasingly viewing talent as the foremost asset for achieving high-quality development.

On the other hand, the TYLLPI and the TNYLLPI have the third and second lowest values among all the components, respectively, indicating that labor without higher education contributes less to the THEI. Between them, young labor without higher education is more efficient than other labor without higher education. This is most likely because the majority of them do physical work. Prior to 2020, the TYLLPI and the TNYLLPI showed a decreasing trend, but there was a small increase from 2020 to 2021. In short, the static labor performance index has improved over the last few years.

The TKPI ranked third in terms of its contribution to the THEI, except for the years 2016–2018. The gap between the TKPI and the second “TNYHLPI” widened over time. The TEPI has a lesser influence on the THEI, while the TCPI has the smallest contribution to the THEI. Moreover, for all three indices, the TKPI, the TEPI, and the TEPI, their trends are in line with those of the THEI, promoted by various national policies for quality development. The role of capital as a driver of static high-quality development efficiency is diminishing. Continuing to promote energy conservation and emission reduction policies and gradual improvements in energy and carbon performance are the way forward. Emphasizing the significance of high-quality talent as the primary resource is especially crucial. In order to foster China’s high-quality development, it is essential to prioritize human resources and talent work, fully utilize the potential of human capital, and effectively stimulate the innovative abilities of talented individuals.

4. Empirical Results and Discussion for the MNMHEI

4.1. The Descriptive Statistics for the Two Groups

To calculate the MNMHEI, we first characterize groups and identify their members. Studies showed that stricter low-carbon targets lead to a decline in economic indicators [41,42]. On the other hand, advanced technologies for energy consumption and carbon emissions can reduce such losses and enable the sustainable growth of the economic system to be organically linked to carbon emission reductions [43]. As energy consumption is an intermediate input; in most cases, the higher the energy consumption, the higher the carbon emissions [44]. Here, the standard for grouping a province is based on the method of Chen. Following Chen, in order to construct a reasonable indicator for the grouping, this paper chooses two sub-indicators for the grouping of energy intensity (E/G) and carbon dioxide emission intensity (C/G) of each province in 2008–2021 and divides the sub-indicators by their respective averages in order to eliminate the influence of different units so that the mean value of the regularized sub-indicators is a unit. The total indicator for the grouping is obtained by weighting the average of the sub-indicators by their respective regularized sub-indicators, and the weights are determined using the method of natural number weights. Specific groupings can be found in column 3 of

Table A2. Average MNMHEI and its decomposition at the province level.

Region	DMU	Group	MNMHEI	EC	BPC	TGC
Anhui	1	1	0.948	0.962	0.999	1.000
Beijing	2	1	1.001	1.000	1.001	1.000
Fujian	3	1	0.958	1.022	0.952	1.000
Gansu	4	2	0.950	1.028	0.937	0.999
Guangdong	5	1	0.955	0.966	0.998	1.000
Guangxi	6	2	0.942	0.995	0.951	0.998
Guizhou	7	2	0.963	1.025	0.956	0.997
Hainan	8	1	0.951	0.953	1.007	1.000
Hebei	9	2	0.919	0.995	0.955	0.979
Henan	10	1	0.949	1.019	1.006	1.000
Heilongjiang	11	2	0.924	1.001	0.951	0.971
Hubei	12	1	0.968	0.980	0.997	1.000
Hunan	13	1	0.962	0.963	1.004	1.000
Jilin	14	2	0.940	1.016	0.945	0.983
Jiangsu	15	1	0.951	1.011	0.961	1.000
Jiangxi	16	1	0.955	0.965	1.002	1.000
Liaoning	17	2	0.952	1.013	0.980	0.974
Inner Mongolia	18	2	0.926	0.981	0.994	0.958
Ningxia	19	2	0.938	0.992	0.953	0.993
Qinghai	20	2	0.944	0.997	0.952	0.998
Shandong	21	2	0.922	1.000	0.949	0.971
Shanxi	22	2	0.960	1.041	0.943	0.991
Shaanxi	23	2	0.952	1.008	0.950	0.997
Shanghai	24	1	0.984	1.000	0.984	1.000
Sichuan	25	1	0.942	0.946	1.010	1.000
Tianjin	26	2	0.923	1.000	0.982	0.947
Tibet	27	1	0.924	0.930	1.007	1.000
Xinjiang	28	2	0.936	0.992	0.947	0.999
Yunnan	29	2	0.942	1.002	0.959	0.984
Zhejiang	30	1	0.956	0.974	0.995	1.000
Chongqing	31	1	0.933	0.936	1.009	1.000
Mean			0.947	0.991	0.975	0.992
Min			0.919	0.930	0.937	0.947
Max			1.001	1.041	1.010	1.000

in the Appendix A.

We consider two types of Chinese provinces: those with low energy intensity and low carbon emissions intensity (group 1), and those with high energy intensity and high carbon emissions intensity (group 2). The group 1 area includes 15 regions—Beijing, Shanghai, Guangdong, Zhejiang, Fujian, Hainan, Jiangsu, Anhui, Hubei, Hunan, Henan, Jiangxi, Sichuan, Chongqing, and Tibet. The group 2 area includes 16 regions—Heilongjiang, Liaoning, Jilin, Shandong, Tianjin, Hebei, Shanxi, Shaanxi, Yunnan, Guangxi, Gansu, Guizhou, Qinghai, Xinjiang, Ningxia, and Inner Mongolia.

The descriptive statistics for the input and output variables for the two groups are presented in Table 1. Group 1 has higher means and standard deviations in the variables K, YHL, YLL, NYHL, NYLL, and G than Group 2, while the converse can be observed for the variables E and C. This indicates that, on average, Group 1 has more capital, labor, and less energy to emit more GDP and less CO₂ than Group 2. Higher standard deviations indicate that there is more variation in the variables K, YHL, YLL, NYHL, NYLL, and G among the members within Group 1 and more variation in the variables E and C among the members within Group 2.

4.2. Empirical Results for the MNMHEI

Table A2 in the Appendix A displays the empirical results for the average MNMHEI from 2008 to 2021, as well as its decomposition for each region.

For the methodological approach, the data show a reduction in dynamic high-quality development efficiency from 2008 to 2021. On average, the dynamic high-quality development efficiency of China’s provinces declines by around 5.3% under the MNMHEI.

At the provincial level, there is a rise in dynamic high-quality development efficiency in only 1 province, while 30 provinces show a decline. Beijing exhibits the greatest MNMHEI (with a growth rate of 0.1%), while Hebei exhibits the lowest MNMHEI (with a growth rate of −8.1%).

The average efficiency change (EC) index of dynamic high-quality development efficiency is 0.991, indicating an annual efficiency drop of around 0.9%. A total of 13 provinces have an EC score greater than unity, indicating that these regions moved toward the contemporaneous technological frontier during the study period, exhibiting the catch-up effect. For specific regions, Shanxi has the best catch-up performance (growth rate = 4.1%). Gansu ranked second with a 2.8% growth rate, while Tibet has the weakest catch-up performance (growth rate = −7%).

The average best-practice change (BPC) index is at 0.975, indicating a reduction in technological change (TC). This implies a change in the contemporaneous frontier away from the intertemporal one. A total of 23 provinces are in a condition of technical decline, with only 8 showing technological advancement. The average annual technology gap ratio change (TGC) value is 0.992, indicating a change in the gap between the global and intertemporal frontiers. This result indicates that China’s provinces lacked technological leadership over the study period.

4.3. Discussion for the MNMHEI

4.3.1. Trends of the MNMHEI and Its Decomposition

Figure 3 displays the trends in dynamic total-factor high-quality development efficiency and its decomposition. Throughout the study period of 2008–2021, the MNMHEI was less than unity, showing a decrease in high-quality development efficiency. But the index presents an upward trend with fluctuations. The minimum value is 0.865 in 2008, and the maximum value is 0.998 in 2021, which is already close to unity. The EC indicator of high-quality development for 2008–2010 has a score greater than unity, suggesting strong catch-up performance. However, during the 2010–2012 period, the EC score is less than unity, indicating a loss in efficiency. Then, for 2012–2013, 2013–2016, 2016–2018, 2018–2020, and 2020–2021, the EC index alternates between above and below unity. The TC index of high-quality development for the period from 2008 to 2010 is below unity, which suggests a decline in technology during that time, but the TC index for the 2010–2011 period is larger than unity, indicating technological advancement. Then, during 2011–2018, 2018–2019, 2019–2020, and 2020–2021, the TC index alternates between above and below unity.

Changes in high-quality development efficiency accord with EC trends for the 2018–2019 period as well as TC trends for the 2008–2018 and 2019–2021 periods. This shows that the improvement in high-quality development efficiency from 2018 to 2019 was mostly pushed by efficiency changes, as opposed to from 2008 to 2018 and from 2019 to 2021, which were pushed by technological advances.

From 2008 to 2020, the EC index and the TC index show opposite trends; for example, during the period 2008–2010, the EC index rose while the TC index declined. The decline in TC was greater than the rise in EC, so the MNMHEI was more affected by TC and also declined. During the period 2010–2011, the EC index declined while the TC index rose. The rise in TC was greater than the fall in EC, so the MNMHEI was more affected by TC and also rose. In brief, the MNMHEI was more affected by TC during 2008–2020.

However, we can notice a positive phenomenon: the MNMHEI has been growing in waves, and in 2021, the EC index and the TC index are moving in the same direction, both exceeding unity, and so the MNMHEI will also reach unity. As a result, we can anticipate that high-quality development efficiency will continue to increase in the future, with significant potential. This situation results from a paradigm shift in China’s policy, as previously noted. In 2017, high-quality development was advocated; in 2020, carbon peaking and carbon neutrality were proposed as its new pathways.

In the short term, the strong regulations for achieving the goal mentioned above had an adverse effect on efficiency and innovation due to the increased regulatory expenses incurred by the regions. Nevertheless, over the long term, stricter environmental and other regulations result in both increased costs and enhanced productivity and innovation for high-quality development.

4.3.2. Trends in the MNMHEI and Its Decomposition into Two Groups

At the group level, we compare the MNMCPI and its decomposition. The MNMHEI estimate and its decomposition for every group are displayed in

Table 2. Group comparison of the MNMHEI and its decomposition.

Group	MNMHEI	EC	BPC	TGC
Group 1	0.9558	0.9750	0.9955	1.0000
Group 2	0.9395	1.0054	0.9564	0.9836

. Group 1 has a higher MNMHEI. When considering decomposed factors, Group 2 has a larger EC index, suggesting a significant catch-up impact. On the other hand, Group 1 exhibits a higher BPC index, showing technological innovation. The TGC index is equal to unity for Group 1, suggesting a position of technology leadership, whereas the TGC index is less than unity for Group 2, indicating a lack of technology leadership. Because the MNMHEI could provide useful information for both efficiency and innovation, considering the group heterogeneities, this information is conducive to the Chinese government’s proposal of specific ways to achieve high-quality development in accordance with regional and provincial characteristics. This will enable each region to choose a high-quality development path that suits its actual situation, adapts to local conditions, and makes up for its shortcomings.

Trends in the MNMHEI and its decomposition for the two groups are shown in Figure 4. The two groups have comparable MNMHEI patterns, with the exception of the 2018–2019 and 2020–2021 periods, which show an increase. Group 1 has a larger MNMHEI than Group 2, except for the 2020–2021 timeframe. The two groups show similar EC patterns except for the 2008–2009 period and have fierce competition with regard to the EC index as their positions fluctuate each time. By way of illustration, between 2008 and 2009, Group 2 showed a upper EC index, whilst Group 1 exhibited a upper EC index from 2009 to 2010. This pattern continues in subsequent periods. Overall, on average, Group 2 shows a higher EC index. We have obtained separate consequences concerning the TC (BPC) index. With the exception of the periods 2012–2013, 2016–2017, and 2020–2021, Group 1 consistently showed a higher TC score compared to Group 2, which suggests that the regions in Group 1 led innovation. The TGC index of Group 1 is always equal to unity throughout the study period, implying no change in technology leadership, while the TGC index of Group 2 has been fluctuating up and down, with 2011–2012, 2016–2017, and 2019–2020 exceeding unity, indicating that the global frontier and the intertemporal frontier have been closer together in these years. The other years are still less than unity. Thus, overall, Group 2 still lacks technology leadership.

In sum, due to the fact that Group 2 is deficient in both creativity and leadership, the regions that belong to Group 2 are not contributing to high-quality development at the national level. This suggests that the government should facilitate increased innovation and leadership for the provinces in Group 2. On the other hand, Group 1 has a higher degree of innovation than Group 2; however, seven provinces in Group 2 lack innovation, indicating potential for more technological innovation in Group 1.

Finally, we conduct a statistical analysis to see if the indices differ significantly between both groups. To determine whether these two groups differ significantly from one another, we use the Wilcoxon–Mann–Whitney rank-sum test. As seen in

Table 3. Wilcoxon–Mann–Whitney rank-sum test and Kolmogorov–Smirnov test for the Group 1 and Group 2.

Test	Index	Null Hypothesis (H0)	Statistics	p-Value
Wilcoxon–Mann–Whitney	MNMHEI	MNMHEI1 = MNMHEI2	6.412	0.0113
	EC	EC1 = EC2	84.613	0.0001
	BPC	BPC1 = BPC2	43.352	0.0001
	TGC	TGC1 = TGC2	26.761	0.0001
Kolmogorov–Smirnov	MNMHEI	MNMHEI1 = MNMHEI2	0.1606	0.011
	EC	EC1 = EC2	0.5048	0.0000
	BPC	BPC1 = BPC2	0.392	0.0000
	TGC	TGC1 = TGC2	0.649	0.0000

, the null hypothesis was rejected at the 1% level, implying a substantial rating difference. To ensure the robustness of the results, further Kolmogorov–Smirnov tests were performed. The results converged on the former rank-sum test.

To determine whether these two groups differ significantly from one another, we apply the Wilcoxon–Mann–Whitney rank-sum test.

The original hypothesis was rejected at the 1 percent level.

5. Conclusions

As high-quality development is becoming more and more significant for socio-economic advancement, China must evaluate its high-quality development efficiency. In this paper, we propose two composite indicators, THEI and MNMHEI, for the measurement of static and dynamic high-quality development efficiency.

These are the main conclusions derived from the study’s empirical findings: First, the majority of Chinese provinces are experiencing subpar performance in achieving static high-quality development and possess considerable potential for enhancement. We propose that the THEI consists of different components: the TYHLPI, TYLLPI, TNYHLPI, TNYHLPI, TKPI, TEPI, and TCPI. We find that labor with higher education, i.e., talent, contributes the most to the THEI. Second, we apply the MNMHEI to solve group heterogeneity and non-radial slack and decompose the index into the EC, BPC, and TGC indices. The improvement in high-quality development efficiency was mostly pushed by technological advances. Group 2 shows better catch-up performance, whereas Group 1 shows better technological innovation and leadership performance.

These empirical findings have some consequences for China. First, policymakers should place a greater priority on talent training and pushing technological innovation, given that they are essential to China’s high-quality development. Second, a variety of schemes must be adopted to boost China’s high-quality development efficiency. The governance of each province must be modified in accordance with the levels of inputs and outputs.

Due to the limitations of the methodology, we ignored the effect of random errors and could not directly analyze the factors affecting efficiency. There are still some directions for research and improvements in the future: other efficiency models (such as SFA with a stochastic frontier) could be used to measure the efficiency of high-quality development and perform convergence analysis for it. Moreover, further regression analyses could be conducted on the factors affecting high-quality development efficiency as well as efficiency changes and technological progress. Due to the limitations of the data, a comparative analysis of China’s high-quality development with that of other countries is also possible in the future.

One final addition,

Table A3. A list of acronyms for vectors/functions/indices.

Acronyms	Vectors/Functions/Indices
YHL	young labor with higher education
YLL	young labor without higher education
NYHL	other labor with higher education
NYLL	other labor without higher education
NDDF	non-radial directional distance function
TNDDF	a total-factor non-radial distance function
THEI	static total-factor high-quality development efficiency index
TCPI	static total-factor CO2 emission performance index
TKPI	static total-factor capital performance index
TLPI	static total-factor labor performance index
TEPI	static total-factor energy performance index
TYHLPI	performance index of young labor with higher education
TYLLPI	performance index of young labor without higher education
TNYHLPI,	performance index of other labor with higher education
TNYLLPI	performance index of other labor without higher education.
MNMHEI	dynamic metafrontier non-radial Malmquist high-quality development efficiency index
EC	technical efficiency change index
BPC	best-practice gap change index
TGC	technology gap change index

in Appendix A, displays a list of acronyms for vectors, functions, and indices to make reading easier.