Study on the spatiotemporal evolution characteristics and simulation prediction of urban metabolic efficiency in China’s urban agglomerations

Abstract

Urban metabolic efficiency (ME) links resource-environmental constraints with high-quality urbanization, yet systematic evidence at the urban agglomeration scale remains limited. This study examines 201 prefecture-level cities in 19 national urban agglomerations in China over 2006–2022. A material-flow-based index system is constructed, and a dynamic meta-frontier SBM-DEA model with undesirable outputs is used to measure ME. meta-frontier inefficiency is decomposed into an inter-agglomeration technology gap component and a within-agglomeration residual component. K-means clustering and conventional as well as spatial Markov chains are employed to characterize temporal dynamics and spatial club patterns, while a panel Tobit model is estimated to identify the determinants of ME. Spatial kernel density analysis and several robustness checks complement the baseline results. The findings show that ME in Chinese urban agglomerations is at a medium level overall, with pronounced stratification across agglomerations and a polarized distribution within them, where high- and low-efficiency cities coexist and medium-efficiency cities are relatively scarce. In several cases, core cities exhibit lower ME than their surrounding cities. The meta-frontier decomposition indicates that inter-agglomeration technology and regime gaps account for a larger share of overall inefficiency than within-agglomeration dispersion, although some developed agglomerations display notable internal residual inefficiency. Markov and spatial Markov analysis reveal strong path dependence and club convergence: low- and high-efficiency clubs are relatively stable, while medium-efficiency cities are easily squeezed between them. Spatial dependence is stratified and more pronounced within specific efficiency ranges than at the global level. The Tobit estimates further identify a U-shaped “metabolic efficiency Kuznets curve” with respect to per capita GDP, and show that digitalization and education expenditure significantly improve ME, whereas openness, fiscal decentralization, industrial upgrading and financial development exert less robust effects. These results highlight the need for differentiated policies across agglomeration types that simultaneously narrow cross-agglomeration technology and structural gaps and strengthen within-agglomeration coordination between economic and environmental objectives.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-41959-5.

Introduction

Chinese urbanization and industrialization have increased rapidly since the beginning of the 21 st century. The urbanization rate has risen at an average annual pace of about 1.04%. In spite of this, rapid development is associated with a growing contradiction between economic growth and environmental protection¹. Consequently, urban agglomerations are severely constrained by resource pressures and ecological concerns². A growing body of research evidence suggests that promoting metabolic efficiency in urban agglomerations is crucial to curing urban diseases^3,4. From the perspective of metabolism, the process of urban agglomeration development is essentially the process of urban agglomeration metabolism⁵, which entails a large amount of resources and energy being collected, absorbed, converted, produced and discharged within the urban agglomeration system⁶. In this process, it is the metabolic efficiency of the urban agglomeration that is determined by the output value of each unit of input, including resources, energy, services, and environmental inputs. Ultimately, the imbalance between economic development and environmental protection is a consequence of the disorderly metabolic function of urban agglomerations⁷, as well as the inefficiency of urban agglomeration metabolism, which leads to an excess of resources and environmental inputs without sufficient outputs⁸. Moreover, as a form of urban agglomeration and the focus of China’s regional development policy^9–12, it is important to analyze and evaluate each urban agglomeration and its urban metabolic efficiency to promote high-quality regional economic development, an important perspective to study regional sustainability, and an important reference to improve the sustainable development of the economic system^13–15.

Conceptually, metabolism encompasses various forms, such as urban metabolism, social metabolism, industrial metabolism, household metabolism, etc.^16–20. Urban metabolism is the process of importing materials and energy into the city and exporting products and wastes out of the city^21–23. There is a difference between social metabolism and urban metabolism^24–26, as Fisher-Kowalski M defines it as the process of exchanging material and energy between human society and the natural environment²⁷. Industrial metabolism encompasses the transformation of raw materials, energy, and labor into products and wastes under the umbrella of an individual, an organization, or an industry^28–30. Household metabolism refers to the pattern of resource inputs and outputs within a household³¹, Kissinger et al. combine an analysis of specific household metabolic components (food, electricity, and transportation-related materials) with a nationwide approach to explore ways to improve sustainability in the Israeli household sector^32,33. Defining metabolism and connoting it in academic circles demonstrate a trend of diversification^34,35. In this paper, the conceptual scale of urban metabolism is used to analyze and predict the spatial and temporal evolution of metabolic efficiency at the level of urban agglomerations in China by analyzing and modeling the urban metabolic systems of 201 prefecture-level cities in 19 urban agglomerations. Material flow analysis, energy flow analysis, ecological network analysis, and geospatial analysis are among the methods commonly used in this field^35–37. By tracking the movement path and scale of some substances or elements in the metabolic system, material flow analysis investigates the operating characteristics and metabolic efficiency of a system³⁸. Material flow analysis is intuitive and user-friendly, but it ignores energy’s role in the urban metabolism system^39,40. One aspect of material flow analysis is the analysis of energy flows; energy flows analysis examines the metabolic scale and conversion efficiency of the system from the perspective of energy flow^41,42. The main advantage of this method is that it can standardize a variety of substances and energies into solar energy; however, the method remains ambiguous regarding the determination of its accounting parameters^43,44. By simulating the flow of matter and energy within a network, metabolic network analyses can be used to examine metabolic behavior, structure and function of an ecosystem^45,46. In this method, compartments, pathways and networks are used, but several controversies exist regarding the methodology and dynamic analyses pose a number of difficulties^47,48. In the field of metabolic efficiency measurement, DEA is suitable for evaluating complex economic efficiency due to its ability to combine the action of multiple elements and their substitution effects without requiring the specification of a specific production function^35,44,49. Due to this, this paper utilizes the dynamic meta-frontier SBM-DEA model combined with the material flow method, which has the advantage of being user-friendly, intuitive and able to decompose the inefficient sources of metabolic efficiency further. In terms of research scale, currently, most research focuses on national, provincial and urban case studies^{23,24,50–55}. There are relatively few studies investigating urban agglomerations^56,57. Urban agglomerations are commonly studied as individual entities^9,58. However, few studies have systematically examined metabolic efficiency across all 19 national urban agglomerations in China within a single analytical framework.

Overall, existing studies have concentrated mainly on national and provincial scales, focusing on changes in metabolic scale, total resource use and environmental pressure, and thus primarily addressing questions such as how much a country or region consumes and emits. At the other end of the spectrum, city level or park level case studies usually focus on the material flow paths and metabolic performance of individual cities or specific sectors. These two strands of research enrich our understanding of urban metabolism from macro and micro perspectives, but they leave a clear gap at the meso level of urban agglomerations, especially when metabolism is viewed in terms of efficiency rather than scale. On the one hand, metabolic performance is often loosely linked to the level of economic development, and the logically distinct dimensions of metabolic scale and metabolic efficiency are easily conflated in empirical work. On the other hand, relatively little attention has been paid to the relationship between core and satellite cities in terms of metabolic efficiency, to within agglomeration efficiency stratification, and to possible nonlinear relationships between metabolic efficiency and economic development at different stages. In other words, we still lack a clear picture of how Chinese urban agglomerations are structured and evolving in terms of metabolic efficiency, both internally and in comparison with one another.

Against this background, this paper seeks to make several marginal contributions to the literature. First, on the methodological side, we introduce a dynamic meta-frontier SBM–DEA model with undesirable outputs to measure urban metabolic efficiency. Cities are grouped into 19 national urban agglomerations as distinct technology groups. Within the unified framework of a common frontier and group frontiers, we calculate metabolic efficiency scores and use the technology gap ratio and the decomposition of metabolic inefficiency to separate efficiency differences into a between agglomeration technical gap component and a within agglomeration management related component. This provides a coherent efficiency based approach to distinguishing where agglomerations differ from one another and where cities differ within the same agglomeration. Second, in terms of research object and perspective, we take China’s national urban agglomerations and their internal cities as the units of analysis. We examine not only the stratified structure and temporal evolution of metabolic efficiency across agglomerations, but also the spatial configuration of efficiency within agglomerations, including centre–satellite and single core versus dual core structures. This allows us to identify the “misalignment” between economic development and metabolic efficiency, as well as the squeezed position of medium efficiency cities in some agglomerations, and to interpret these patterns from the viewpoint of metabolic efficiency frontiers and intra agglomeration diffusion mechanisms. Third, regarding dynamic evolution and underlying mechanisms, we combine conventional and spatial Markov chains to characterise path dependence and spatial club convergence in metabolic efficiency, and then estimate a panel Tobit model to test for the existence of a “metabolic efficiency Kuznets curve” from the perspectives of development stage and institutional environment. The Tobit results also identify robust positive effects of digitalisation and education expenditure on metabolic efficiency. In this way, the paper links structural descriptions of metabolic efficiency with the statistical identification of its drivers along spatial, temporal and mechanistic dimensions, and provides empirical evidence and an analytical framework for understanding how urban agglomerations can pursue high quality development under resource and environmental constraints.

Study design

Theory

As a matter of material flow, urban metabolism refers to the process of distributing, absorbing, converting, producing, and discharging different substances within a city³⁵. In urban agglomerations or regions, metabolic processes also involve the transit and exchange of various substances between cities. Urban metabolic processes are rich in connotations. Food from farmland, pastures, fisheries, and other sites is pre-processed or reprocessed to feed the urban population. Water sources such as groundwater, lake water, and river water are filtered and treated and then transported through pipes to various buildings for the city population to drink. Materials such as steel, cement, and plastics are transported to factories as raw materials for production. Oil, coal, and natural gas are burned to supply energy for various activities in the city. Materials are transferred and moved through a well-developed transportation system, including road, rail, water and air transport. Urban government departments are responsible for building public services and urban planning. Businessmen and entrepreneurs promote the circulation of various goods in the market. In this process, the economy is developed, public services are built, and the needs of urban residents are met. In addition to the desired outputs of economic development and public service construction, there are also many undesired outputs in the process of urban system operation. The urban population generates a series of domestic waste in the process of living, a series of by-products in the process of production, and a series of pollution in the process of energy combustion and transformation. The process of urban agglomeration metabolism is similar to urban metabolism; however, it places a heightened emphasis on the interaction between urban subsystems. A dual metabolic relationship exists between and within cities. An urban agglomeration, for instance, has a center-periphery structure, with the population, material, and other resources concentrated in the central city, where metabolic processes are strongest. After the central city reaches its optimal size, it will disperse its resources to drive the development of the surrounding cities, forming a metabolic linkage process. Urban agglomerations or cities achieve their metabolism during this entire process.

Index system

Due to the richness and complexity of metabolic processes and the availability of data, the choice of metrics in material flow analysis is therefore generally not well defined⁴⁰. In the calculation of urban metabolic efficiency, renewable resources, nonrenewable resources, and imports are usually considered as inputs^9,59,60, and economic growth, social welfare growth, and export as outputs^61,62, whereas environmental pollution is considered as an undesirable output^24,52. Wang⁴⁰ provides the following theoretical framework for material flow analysis (Fig. S1).

In summary, this paper constructs the urban metabolic efficiency measurement index system from renewable resource input, non-renewable resource input, urban import and export, economic output, social welfare, and undesirable environmental pollution dimensions. Biomass inputs derived from agricultural production in the urban hinterland, proxied by city-level production of grain, vegetables, meat and dairy products, together with total urban water supply, are taken as renewable resource inputs. In biophysical terms, food production relies on a set of biomass-related ecological inputs, and food production requires biomass inputs such as soil fertility, soil organic matter, water availability and nutrient cycling. These underlying ecological stocks and processes are not directly observed in official statistics, so we approximate the associated biomass inputs by city-level agricultural production of grain, vegetables, meat and dairy products. This setting follows sociometabolic studies that treat harvested biomass and water flows as the main renewable resource flows supporting the basic material requirements of the urban population for daily survival and production. Energy consumption is selected to represent the input of non-renewable resources and to capture the basic energy requirements of various activities in the city. Because comprehensive city-level statistics on total final energy use are not consistently reported, we approximate non-renewable energy inputs by aggregating electricity, liquefied petroleum gas, coal gas and natural gas consumption and converting them into 10,000 tons of standard coal using official energy conversion coefficients. These multiple energy carriers are then summarised into a single energy input index through principal component analysis.Economic growth output is represented by the mean value of regional nighttime light intensity to reflect the most fundamental production output. Social welfare indicators were extracted using principal component analysis to reflect the improvement of inputs to basic public services. Regional imports and exports were used as metabolic inputs and outputs to illustrate the metabolic interactions between cities. Waste generation and environmental pollution are used as undesirable outputs in the metabolic process to reflect the impact of waste generation on metabolism. In order to retain information on the metabolic efficiency of urban agglomerations, cities are the basic units used in measuring efficiency. The metabolic efficiency of a city agglomeration is obtained by averaging the metabolic efficiency of its contained cities. The specific treatment of each indicator is shown in Table 1.

Table 1.

Indicator system.

Indicator category	Variable name	Variable description
Input	Biomass input	Principal factors were extracted using principal component analysis for production of grains, vegetables, meat, dairy, etc. Composite index of biotic resource inputs associated with agricultural production, obtained by principal component analysis of city-level production of grain, vegetables, meat and dairy products
Input	Water consumption	Total water supply
Input	Energy consumption	Electricity, liquefied petroleum gas, gas, natural gas standardized to 10,000 tons of standard coal
Input	Import	Regional imports
Output	Economic growth	Average nighttime light intensity within the administrative area
Output	Social welfare	Composite index obtained by principal component analysis of total wages, number of students in school, number of hospital beds and number of patents granted
Output	Export	Regional export value
Undesirable outputs	Environmental pollution	Composite index obtained by principal component analysis of industrial wastewater, industrial waste gas, industrial solid waste and CO₂ emissions

Additionally, urban agglomerations are abbreviated to conserve space. A cross-reference table of urban agglomerations abbreviations and full names (Table S1) and a map of the study area (Fig. S2) are detailed in the supporting information.

Methods

Dynamic cluster SBM-DEA

While the DEA method has great advantages in measuring total factor efficiency, it also has some limitations. On the one hand, the traditional DEA model is usually static; on the other hand, it assumes that all producers share the same technology. To overcome these shortcomings, we adopt a dynamic DEA framework and combine it with the common frontier (meta-frontier) approach proposed by O’Donnell et al., and build a dynamic slacks-based measure (SBM) model with undesirable outputs under both a common frontier and group (cluster) frontiers. The meta-frontier efficiency and cluster-frontier efficiency are calculated as follows.

Let there be G groups (urban agglomerations), with group g containing cities. The study period is (). For a city o, denote inputs by (), desirable outputs by (), and undesirable outputs by () in period t. The corresponding quantities for city (j) in group g are denoted by , , and . Let be the time weights with .

1. Common frontier (meta-frontier)

   The dynamic common-frontier efficiency of city o is given by the optimal value of the following program.

   Objective:

   1

   where the period-t SBM efficiency is defined as:

   Period-t efficiency:

   2

   subject to, for all ():

   Input constraints:

   3
   Desirable output constraints :

   4
   Undesirable output constraints :

   5
   Convexity constraint:

   6
   Non-negativity constraints:

   7

   The optimal value represents the dynamic common-frontier (meta-frontier) metabolic efficiency of city o.

2. Cluster frontier (group frontier)

   Let () denote the group (urban agglomeration) to which city o belongs. The cluster-frontier efficiency is obtained by restricting the reference set to cities within group . The optimal value of the following program gives the dynamic cluster-frontier efficiency of city o.

   Objective:

   8

   where the period-t cluster-frontier efficiency is:

   Period-t efficiency :

   9

   subject to, for all ():

   Input constraints within group :

   10
   Desirable output constraints within group :

   11
   Undesirable output constraints within group :

   12
   Convexity constraint:

   13
   Non-negativity constraints:

   14

   Based on the common-frontier efficiency and the cluster-frontier efficiency , we further construct the technology gap ratio and decompose metabolic inefficiency into technical gap inefficiency and management inefficiency in Sect. 2.3.3.

K-means clustering method

The clustering method is an unsupervised learning method, which aggregates data into several groups according to similarity through cluster analysis. It does not require labelled samples and can reduce unstable subjective factors. The k-means clustering algorithm has the advantages of fast computation and good interpretability.

Let there be n observations of d-dimensional data:

15

Given the number of clusters (K), the initial cluster centers are denoted by

16

At iteration t, the samples assigned to cluster c form the set , defined by the nearest-center rule:

17

The cluster centers are then updated as the mean of the samples in each cluster. Let () be the number of samples in cluster c at iteration t. The update rule is

18

The algorithm iterates between the assignment step (17) and the update step (18) until the cluster memberships no longer change, i.e.

19

Inefficient decomposition

(1) Technology gap ratio (TGR).

Since the common frontier (meta-frontier) envelops all group frontiers, the common-frontier technical efficiency (MFTE) of any city is no greater than its group-frontier technical efficiency (GFTE) within its own urban agglomeration (group g). For each city we define the technology gap ratio (TGR) as:

20

As indicated in Eq. (20), for a given city, TGR measures how close the technology set effectively available in its own urban agglomeration is to the national meta-frontier. A value of TGR closer to 1 indicates that the group frontier faced by that city lies close to the meta-frontier, whereas a smaller TGR indicates a larger technology gap between its group frontier and the meta-frontier. When TGR is averaged across all cities in an agglomeration, it provides a summary indicator of how far that agglomeration’s frontier, as a whole, is from the national best-practice frontier.

(2) Metabolic inefficiency (IE) decomposition.

To further analyse the sources of differences in metabolic performance among cities, we decompose each city’s common-frontier metabolic inefficiency into two components. Let IE be defined as:

21

Using the relationship between the meta-frontier and the group frontier, IE can be written as:

22

where

23

In this meta-frontier framework, TIE (technical gap inefficiency) captures, at the city level, the part of common-frontier inefficiency that is attributable to the gap between the group frontier and the meta-frontier, i.e. differences in technology regimes, industrial structures and resource–environmental constraints between the city’s agglomeration and the national best-practice frontier. MIE (management-related inefficiency) measures the residual inefficiency of a city relative to the best-practice frontier within its own agglomeration, reflecting within-agglomeration dispersion that may be associated with city-level management, institutional arrangements and micro-structural factors.

It should be emphasised that “technical” and “management-related” inefficiency are statistical labels for these two components of IE arising from the meta-frontier decomposition. They do not imply that we observe pure engineering technology or managerial quality directly. Rather, the decomposition provides a convenient way to separate between-agglomeration frontier gaps from within-agglomeration residual differences when interpreting the sources of metabolic inefficiency.

Spatial Markov chain

The Markov chain is a prediction method that enables the transition of a state from one state to another through its transition probability transition matrix, which is used to describe the state transition probability distribution of socioeconomic phenomena in the region under study. In addition, it can be considered that the state of urban metabolism in one period is only related to the state of the city in the previous period, so the state of urban metabolic efficiency can be viewed as a Markov process.

In traditional Markov chain, the distribution of a type at the moment is represented by the state probability vector of, while the whole process of state transfer of the thing can be represented by the Markov probability transfer matrix with probability value of .

24

In formula (24), denotes the sum of the number of spatial units of type at moment transformed to type at moment ; denotes the sum of the number of spatial units of type at all moments in the study period.

In spatial Markov chains, spatial correlation is taken into account. The spatial Markov chain transfer probability matrix can be decomposed into k conditional transfer matrices. denotes the spatial transfer probability value conditional on the spatial lag type of the spatial unit at moment , which is transformed to type at moment . The spatial lag type of a spatial unit is determined by its spatial lag value, which is the spatially weighted average of the attribute values of the neighboring regions of the spatial unit.

25

In formula (25): is the attribute value of the spatial unit; is the element of the row and column of the spatial weight matrix , which is the relationship matrix between the spatial unit and its neighboring regions.In this study, W is specified as an economic-geographic matrix based on city-level GDP and great-circle distances between city centroids within each urban agglomeration.

Panel Tobit model

To explore the determinants of urban metabolic efficiency (ME), this study estimates a panel Tobit model. Since ME is a bounded efficiency index within the interval ([0,1]) and may exhibit censoring at the lower or upper limits, directly applying ordinary least squares could yield biased and inconsistent estimates. The Tobit model assumes an unobserved latent variable () that is linearly related to a set of covariates, while the observed () is generated through a censoring mechanism. The baseline specification is written as:

26

where and denote city and year, respectively; is the vector of explanatory variables; and capture urban agglomeration fixed effects and year fixed effects. The observed metabolic efficiency is defined as a two-sided censored variable:

27

Following Table 2, the explanatory variables are selected to capture several channels through which cities may improve metabolic efficiency under resource and environmental constraints. Digitalization (DIG, measured by 5G base station density) is introduced to proxy the extent of information infrastructure and digital technology diffusion, which may affect resource allocation efficiency, production coordination, and environmental governance capacity. Economic development is represented by the logarithm of per capita GDP (PGDP); to allow for a possible “metabolic efficiency Kuznets curve” between development level and metabolic performance, we additionally include the squared term (PGDP²). This quadratic specification is used to test whether the relationship between metabolic efficiency and economic development is monotonic or instead exhibits a U-shaped pattern consistent with a Kuznets-type curve. In this framework, a negative coefficient on PGDP combined with a positive coefficient on PGDP² would be consistent with such a U-shaped “metabolic efficiency Kuznets curve”, and the implied income turning point can be obtained in the usual way from the estimated coefficients (−β1/2β2). Openness (OPEN) is included to reflect external linkages that may influence technology spillovers as well as pollution transfer. The share of education expenditure (EDU) is used to proxy human capital accumulation and public service investment, which may strengthen innovation capacity and managerial quality. Fiscal decentralization (FD) is incorporated to account for differences in local government incentives and environmental governance intensity. Industrial structure upgrading (IND) is used to characterize structural transformation toward higher value-added and potentially cleaner sectors. Financial development (FIN) is added to reflect the availability and allocation efficiency of capital, which may facilitate technological upgrading and green investment. To assess the sensitivity of the empirical results to special periods, atypical administrative units, and extreme observations, we also implement a set of robustness designs, including re-estimation after excluding the COVID-19 period, excluding the four centrally administered municipalities (Beijing, Shanghai, Tianjin, and Chongqing), and winsorizing continuous variables at the 5% level.

Table 2.

Descriptive statistics of variables.

Variable	Obs	Mean	Std. Dev.	Min	Median	Max
ME	3420	0.594	0.348	0	0.53	1
DIG	3420	0.363	1.182	0	0	16.729
PGDP	3420	10.659	0.823	7.922	10.641	13.185
PGDP²	3420	114.291	17.645	62.759	113.227	173.846
OPEN	3420	0.003	0.003	0	0.002	0.019
EDU	3420	0.18	0.041	0.044	0.177	0.366
FD	3420	0.514	0.226	0.069	0.49	1.541
IND	3420	2.304	0.147	1.913	2.298	2.836
FIN	3420	2.459	1.297	0.56	2.086	21.301

Data sources

In this paper, 19 urban agglomerations and 201 cities in China are selected for the study. The data in this paper are mainly obtained through the following means.

Remote sensing data. 2006–2022 nighttime light intensity index with a resolution of 1 km×1 km, measured by DMSP/OLS and VIIRS NPP global nighttime light data, obtained from the Resource and Environmental Science and Data Center of the Chinese Academy of Sciences, (http://www.resdc.cn).

Scientific data. The carbon emission data in the paper are based on information published by the Center for Global Environmental Research⁶³. The city-scale carbon emissions data in this paper were obtained from the information published by the Center for Global Environmental Research through the statistics of municipal administrative divisions.

Statistical data. The social, economic and environmental statistics in this paper are obtained from the China Urban Statistical Yearbook 2007–2023, the China Regional Economic Statistical Yearbook 2007–2023, the provincial statistical yearbooks and the statistical bulletins on national economic and social development of each prefecture-level city. Some missing values are completed by interpolation.

It is worth noting that, in line with the index system described in Sect. 2.2, city-level production of grain, vegetables, meat and dairy is used to approximate biomass-related resource inputs into the urban metabolic system. Moreover, because comprehensive statistics on total final energy consumption are not consistently reported at the prefecture level, non-renewable energy inputs are approximated by aggregating electricity, liquefied petroleum gas, coal gas and natural gas consumption and converting them into 10,000 tons of standard coal using official energy conversion coefficients. These biomass and energy indicators, together with water supply, social welfare and environmental pollution variables, are then, where appropriate, transformed into composite indices by principal component analysis.

Results

The results are divided into two main parts. In the first part (3.1–3.3), as part of an analysis of urban agglomeration metabolic efficiency, a perspective of urban agglomerations, in general, is taken, followed by a qualitative assessment of the spatial and temporal evolution of urban agglomeration metabolic efficiency from the perspective of urban agglomeration internal structure. Furthermore, the sources of metabolic inefficiency are identified using plots of parallel axes. In the second part (3.4), the metabolic efficiency of urban agglomerations is dynamically simulated using traditional Markov chains and spatial Markov chains, respectively.

Analysis of the overall metabolic efficiency of urban agglomerations

Using MaxDea 8, this study measures urban metabolic efficiency for 19 national urban agglomerations and their 201 prefecture level cities over 2006–2022 with the dynamic meta-frontier SBM–DEA model including undesirable outputs. At the agglomeration scale, we adopt common frontier (meta-frontier) efficiencies to ensure comparability across groups, and construct a time–agglomeration matrix of metabolic efficiency on this basis. The resulting 3D surface plots visualise the spatiotemporal evolution of metabolic efficiency for each agglomeration, while supplementary ridge plots are reported in Fig. S3.

Figure 1 shows that metabolic efficiency displays a stepped pattern over time. Most urban agglomerations remain at a relatively stable medium efficiency level during 2006–2022, indicating that the position of the national frontier has not shifted dramatically. At the same time, clear gaps between the “surfaces” of different agglomerations reveal a stratified structure of metabolic efficiency: rather than converging to a single frontier, Chinese urban agglomerations cluster around several frontiers at different levels.

Fig. 1.

Metabolic efficiency 3 d surface mapping of urban agglomerations.

Table 3 reports the ranking of the 19 urban agglomerations by common frontier metabolic efficiency and groups them into broad efficiency bands. This ranking does not fully coincide with the usual ranking by economic development. Several highly developed agglomerations such as BTH, YRD and PRD do not occupy the top positions in terms of metabolic efficiency, whereas economically less developed agglomerations such as NSTM and HBOY lie at the upper end of the efficiency distribution. This “misalignment” between development level and metabolic efficiency underlines the distinction between metabolic scale and metabolic efficiency: the former reflects the absolute size of economic and population agglomeration, while the latter captures the combination of desirable and undesirable outputs per unit of metabolic input. High input, high output and high environmental pressure may therefore reduce relative metabolic efficiency even in agglomerations with high absolute output.

Table 3.

Metabolic efficiency ranking of urban agglomerations.

Abbreviations	Rank	Abbreviations	Rank	Abbreviations	Rank	Abbreviations	Rank
NSTM	1	YRD	6	CP	11	MRYR	16
HBOY	2	SC	7	SP	12	LX	17
GC	3	GP	8	BTH	13	NG	18
PRD	4	HC	9	CC	14	LCS	19
CGFZ	5	YC	10	NAYR	15

Within this overall stable and stratified pattern, individual agglomerations still show notable deviations. For example, the LCS agglomeration experiences a marked decline in metabolic efficiency around 2016, whereas the GC agglomeration exhibits an upward tendency that broadly coincides with its recent development of the big data industry and digital economy. These cases suggest that, against a relatively stable national background, some agglomerations can still move up or down the common frontier through adjustments in metabolic structure and development paths.

Analysis of metabolic efficiency of cities within urban agglomerations

To depict the spatial pattern and evolution of metabolic efficiency within urban agglomerations, this study visualises the efficiency scores of 201 cities using ArcGIS 10.8 (Esri, Redlands, CA, USA; https://www.esri.com). This map is based on the standard map (Review No. GS(2019)1825) from the Standard Map Service website of the Ministry of Natural Resources of China (http://bzdt.ch.mnr.gov.cn), and the base map boundaries have not been modified. Taking the year in which each national urban agglomeration was formally proposed as a strategic concept as the starting point, we select one observation every five years and obtain four cross sections for 2006, 2011, 2016 and 2022. Based on the efficiency values in the most recent year (2022), cities are classified into three categories using an equal interval scheme, namely high, medium and low metabolic efficiency. In addition, Table S2, Table S3 and Fig. S4 provide complementary evidence on the distribution of efficiency levels and their trends within each agglomeration.

Figure 2 shows that, in terms of metabolic efficiency, there is no obvious overall spatial bias in the distribution of cities at the national scale. On the one hand, within most urban agglomerations, high, medium and low efficiency cities are interspersed, and simple monocentric ring structures are rare. High efficiency cities do not necessarily form tight clusters around a small number of core nodes. On the other hand, along the time dimension, the efficiency classes of many cities exhibit a clear “oscillating” pattern. Cities frequently move up and down between the three classes, and there is no uniform monotonic upward or downward trend. Under given metabolic inputs and environmental constraints, the spatiotemporal evolution of metabolic efficiency within urban agglomerations thus resembles a multi polar differentiation process rather than one way convergence or linear diffusion.

Fig. 2.

Spatial and temporal evolution of urban metabolic efficiency in urban agglomerations. (a) 2006, (b) 2011, (c) 2016, (d) 2022.

From the perspective of the centre-satellite structure of urban agglomerations, metabolic efficiency does not follow the simple expectation of “absolute dominance of the core city”. In general, the metabolic efficiency of core cities is higher than that of most satellite cities in the same agglomeration, even if the core city itself has not yet reached the efficiency frontier. This is consistent with their relative advantages in industrial structure, infrastructure and factor agglomeration. However, among the 27 core cities in the sample, 7 have clearly lower metabolic efficiency than several satellite cities in their respective agglomerations. For example, in the NG agglomeration, Nanning, and in the NAYR agglomeration, Yinchuan, both show rising efficiency over time but still lag behind some satellite cities in overall level. In the YC and LCS agglomerations, Kunming and Shenyang experience declining metabolic efficiency during the sample period, while several satellite cities perform better. In the HC, HBOY and LX agglomerations, Changchun, Hohhot and Lanzhou are also overtaken by their satellite cities in some years. As shown in Table S2 and Fig. S4, the relative ranking of these core cities within their agglomerations is far from stable, indicating that core cities have not fully transformed their advantages in the concentration of metabolic factors into superior performance in metabolic efficiency.

In agglomerations with dual cores, the internal differentiation of metabolic efficiency is also pronounced. In the HC agglomeration, Harbin substantially outperforms Changchun; in the BTH agglomeration, Beijing scores slightly higher than Tianjin; in the LCS agglomeration, Dalian significantly exceeds Shenyang; in the SP agglomeration, Qingdao performs slightly better than Jinan; and in the CGFZ agglomeration, Xiamen generally outperforms several coastal cities in Guangdong. These examples suggest that even under a nominal “dual core” framework, the two core cities may differ markedly in metabolic input structure, functional specialisation and environmental constraints, which leads to asymmetric gradients of metabolic efficiency.

Taken together, at least 12 of the 27 core cities can be regarded as having some type of “metabolic problem”, either because they rank relatively low within their agglomerations or because they exhibit persistent or pronounced declines over time. Rather than attributing this simply to poor management at the city level, it is more appropriate to see it as evidence that some core cities have not yet found a configuration of metabolic inputs, industrial structure and spatial layout that reconciles their agglomeration functions with higher metabolic efficiency under given environmental constraints. In contrast, some satellite cities, while maintaining a relatively small metabolic scale, achieve higher efficiency in terms of the combination of desirable and undesirable outputs per unit of metabolic input.

Analysis of sources of metabolic inefficiency in Chinese urban agglomerations

To identify the sources of metabolic inefficiency in Chinese urban agglomerations in a more intuitive way, this study builds on the dynamic meta-frontier SBM-DEA results and constructs parallel coordinate plots using year, urban agglomeration, group-frontier metabolic efficiency, common-frontier metabolic efficiency, the metabolic efficiency technology gap ratio (TGR), common-frontier metabolic inefficiency (IE), metabolic efficiency technical gap inefficiency (TIE) and metabolic efficiency management-related inefficiency (MIE) (see Fig. 3).

Fig. 3.

Parallel axes of urban metabolic efficiency in urban agglomerations.

Within the meta-frontier framework of this study, the three key metabolic efficiency indicators can be interpreted as follows. First, the metabolic efficiency technology gap ratio TGR describes the “height” of the group-frontier metabolic efficiency for each urban agglomeration. When the group frontier of an agglomeration is very close to the national common frontier, its TGR approaches 1; when the gap is large, TGR is relatively small. Second, the metabolic efficiency technical gap inefficiency TIE corresponds to the part of common-frontier metabolic inefficiency that is attributable to the relatively low position of the group-frontier metabolic efficiency, and thus reflects systematic differences across urban agglomerations in metabolic technology regimes, industrial structures and resource environmental constraints. Third, the metabolic efficiency management-related inefficiency MIE captures the residual dispersion of cities around the group-frontier metabolic efficiency, that is, the extent to which individual cities fall short of the best metabolic efficiency practice within a given agglomeration, conditional on sharing similar technological and structural conditions.

On this basis, the patterns in Fig. 3 can be interpreted more clearly. The metabolic efficiency technology gap ratio TGR spans the entire interval [0,1], but the lines are much more densely concentrated in the range from 0 to 0.5. This indicates that the group-frontier metabolic efficiency of many urban agglomerations is still markedly below the national common frontier. The set of Chinese urban agglomerations does not revolve around a single unified metabolic efficiency frontier; instead, it forms several “layers” of metabolic efficiency frontiers at different heights. From a metabolic efficiency perspective, this suggests relatively stable regional differences in metabolic structures, infrastructure conditions and ecological constraints, and that different urban agglomerations have developed heterogeneous metabolic efficiency regimes along their own development paths.

The decomposition of common-frontier metabolic inefficiency further clarifies where most of the differences arise. Figure 3 shows that metabolic efficiency technical gap inefficiency TIE is largely concentrated between 0.5 and 1.0, whereas metabolic efficiency management-related inefficiency MIE is generally much closer to zero. In more intuitive terms, a larger share of common-frontier metabolic inefficiency is associated with the fact that different urban agglomerations stand on group frontiers located at very different levels; structural differences across agglomerations in development stages, technological paths and resource environmental conditions account for a sizable part of the variation. A smaller, although non-negligible, share of metabolic inefficiency is due to the dispersion of cities around their own group-frontier metabolic efficiency. Put differently, within the meta-frontier framework of this study, the primary variation in metabolic performance is reflected in which metabolic efficiency frontier an urban agglomeration stands on, whereas within a given agglomeration cities tend to share broadly similar metabolic technology and structural conditions and differ mainly in how close they are to that common frontier.

It is important to note that within-agglomeration differences in metabolic efficiency are not negligible. Figure 3 also shows that in agglomerations such as CGFZ, BTH, YRD and MRYR there are many lines on the MIE axis crossing above 0.5, indicating that a subset of cities inside these relatively developed agglomerations still lie far from the best metabolic efficiency practice within their own group. In these cases, the group-frontier metabolic efficiency is already close to the national common frontier, yet not all member cities converge towards the group frontier. Empirically, this suggests that outward shifts of the group-frontier metabolic efficiency can be accompanied by renewed heterogeneity within the agglomeration. On the one hand, the agglomeration as a whole benefits from more favourable technological and structural conditions; on the other hand, there remain pronounced differences in how individual cities translate these conditions into improved metabolic efficiency and in how effectively they absorb advanced production and environmental governance practices.

It should be emphasised that TIE and MIE are statistical components obtained from the meta-frontier decomposition of metabolic inefficiency. Their labels “technical gap” and “management-related” do not imply that we directly observe narrowly defined engineering technology levels or managerial quality. In this paper, metabolic efficiency technical gap inefficiency TIE is interpreted as a composite measure of differences in the position of agglomeration-level metabolic efficiency frontiers, while metabolic efficiency management-related inefficiency MIE is interpreted as the remaining city-level room for improvement under a given frontier. Taken together, the patterns in Fig. 3 yield a metabolic efficiency oriented empirical observation: the current spatial differentiation of metabolic efficiency in China is primarily manifested in the stratification of urban agglomerations across different metabolic efficiency frontiers, and only secondarily in the speed of convergence and diffusion within individual agglomerations. Understanding differences in metabolic performance therefore requires attention both to the long term structural divergence of metabolic efficiency frontiers across agglomerations and to those cities within developed agglomerations that remain markedly behind their own group-frontier metabolic efficiency.

Markov-chain simulation of urban agglomeration metabolic efficiency and spatial club patterns

Building on the preceding static efficiency analysis, this study further employs conventional Markov chains and spatial Markov chains to depict the dynamic evolution of metabolic efficiency in Chinese urban agglomerations. City level metabolic efficiency is divided into three states using an equal interval classification, namely low efficiency (Q1), medium efficiency (Q2), and high efficiency (Q3). On this basis, a unified national transition matrix is constructed, and spatial lags of neighboring cities’ metabolic efficiency are then introduced to estimate conditional transition probabilities under different neighborhood environments, thereby identifying potential spatial club patterns (see Fig. 4 and Fig. S5). All Markov and spatial Markov results reported in this section are based on the economic–geographic spatial weight matrix described in Sect. 2.3.4.

Fig. 4.

Traditional and spatial Markov transfer probability matrix of urban agglomerations. (a) NSTM, (b) HBOY, (c) GC, (d) PRD, (e) CGFZ, (f) YRD, (g) SC, (h) GP, (i) HC, (j) YC, (k) CP, (l) SP, (m) BTH, (n) CC, (o) NAYR, (p) MRYR, (q) LX, (r) NG, (s) LCS, (t) NATION.

National level temporal dynamics

At the national level, the conventional aspatial Markov transition matrix reveals pronounced path dependence and state inertia in urban metabolic efficiency. Low efficiency cities (Q1) remain in the low efficiency state in the next period with a probability of approximately 0.84, medium efficiency cities (Q2) maintain their status with a probability of about 0.69, and high efficiency cities (Q3) remain high efficiency with a probability of about 0.92.

By comparison, leapfrog transitions across efficiency tiers are rare. The probability that a low efficiency city jumps directly to the high efficiency state within one period is only around 0.01, and the probability that a high efficiency city falls directly to low efficiency is of a similar magnitude. Incremental transitions between adjacent tiers are much more common. The probability of a low efficiency city upgrading to medium efficiency is roughly 0.15, and that of a medium efficiency city upgrading to high efficiency is about 0.11, while the probability of a medium efficiency city downgrading to low efficiency is around 0.21.

These patterns indicate a notable degree of rank persistence and club convergence. High efficiency cities tend to circulate within a high efficiency club, low efficiency cities tend to remain trapped in a low efficiency club, and medium efficiency cities occupy a relatively unstable middle layer that is more vulnerable to both upward and downward shifts.

Neighborhood environment and spatial Markov transitions

After introducing spatial lags, the spatial Markov chain further reveals how neighborhood conditions shape the evolution of metabolic efficiency (see Fig. S5).

For low efficiency cities, higher efficiency neighbors clearly enhance the chances of upgrading. When surrounding cities are predominantly low efficiency (Lag Q1), the probability that a low efficiency city remains low efficiency in the next period is about 0.89, and the probability of upgrading to medium efficiency is about 0.11. When neighboring cities are predominantly high efficiency (Lag Q3), the probability of remaining low efficiency falls to around 0.76, while the probability of upgrading to medium efficiency rises to approximately 0.23. This suggests a discernible pulling effect from high efficiency neighborhoods that weakens the lock in of low efficiency states. However, this effect mainly manifests as incremental upgrading from low to medium efficiency, rather than direct jumps from low to high efficiency.

The position of medium efficiency cities in the spatial structure is more nuanced. When neighboring cities are predominantly medium efficiency (Lag Q2), a medium efficiency city maintains its status with a probability of about 0.67, and the probability of upgrading to high efficiency is around 0.14, which indicates a like with like synergistic effect. In high efficiency neighborhoods (Lag Q3), the probability of remaining medium efficiency rises further to about 0.73, while the probability of upgrading to high efficiency declines to roughly 0.09. Thus, in highly developed high efficiency environments, medium efficiency cities tend to be stabilized in place, and the channels for them to enter the high efficiency club are not substantially widened.

For high efficiency cities, the spatial lock in of the high efficiency club is particularly pronounced. Regardless of whether the neighborhood is low, medium, or high efficiency, the probability that a high efficiency city remains high efficiency in the next period always exceeds 0.91, and reaches roughly 0.94 when surrounded by high efficiency cities. Once a cluster of high efficiency cities forms, it tends to reinforce itself both temporally and spatially.

Spatial heterogeneity at the urban agglomeration scale

At the scale of individual urban agglomerations, the spatial Markov results exhibit clear regional heterogeneity. These patterns can be broadly summarized into three typical modes, each of which can be illustrated by representative cases (see Fig. 4 and Fig. S5).

First, some urban agglomerations are characterized by predominantly positive spatial synergy. In these regions, high efficiency cities are strongly stable, while low and medium efficiency cities have relatively greater room for upward mobility in high efficiency neighborhoods. The overall evolution is close to a pattern of gradient diffusion and coordinated regional upgrading. For example, in the BTH urban agglomeration, the probabilities that low, medium, and high efficiency cities remain in their respective states without conditioning on neighborhood are approximately 0.89, 0.77, and 0.93. Under high efficiency neighborhood conditions, the probability that a high efficiency city remains high efficiency increases to around 0.95, and the probability that a medium efficiency city remains medium efficiency reaches about 0.82. Similarly, in the PRD and SP urban agglomerations, low efficiency cities maintain low efficiency with probabilities around 0.90, medium efficiency cities remain medium efficiency with probabilities near 0.80, high efficiency cities maintain high efficiency with probabilities of roughly 0.89 and 0.91, and the probability that a medium efficiency city upgrades to high efficiency can reach around 0.12. In these regions, core high efficiency cities not only maintain their advantageous positions but also generate spillovers that gradually improve the metabolic performance of some low and medium efficiency cities.

Second, a considerable number of urban agglomerations exhibit a pattern in which medium efficiency cities are squeezed. This pattern is evident in the CP, LX, GP, CC, NAYR, LCS, MRYR, and several western inland urban agglomerations. In this group, medium efficiency cities often occupy an awkward middle position. In low efficiency neighborhoods they tend to be dragged downward, while in significantly more efficient neighborhoods they may be crowded out by dominant core cities, which makes it difficult to transition into the high efficiency club.

The LX urban agglomeration provides a representative example. Without conditioning on neighborhood, the probability that a medium efficiency city downgrades to low efficiency is as high as about 0.57, while the probability of upgrading to high efficiency is essentially zero. When surrounding cities are predominantly high efficiency, all medium efficiency cities in LX are observed to fall into the low efficiency state in the next period, with virtually no upward transitions. Similar behavior is observed in parts of the CP, GP, and MRYR urban agglomerations, where medium efficiency cities in high efficiency neighborhoods display limited resilience and face simultaneous pressures of potential downgrading and constrained upgrading. If such a structure persists over time, it may generate new forms of polarization within urban agglomerations. Core high efficiency cities further consolidate their positions, while medium efficiency cities face a growing risk of marginalization.

Third, a small number of urban agglomerations exhibit more extreme spatial club structures. One configuration combines strong high efficiency lock in with pronounced tier segmentation. This is observed in the NAYR, NG, and CGFZ urban agglomerations. In NAYR, high efficiency cities remain high efficiency with probability 1 under all neighborhood conditions, whereas the probability that medium or low efficiency cities upgrade to high efficiency is very low. Even in high efficiency neighborhoods, the probability of medium efficiency cities entering the high efficiency state is close to zero. In NG and CGFZ, high efficiency cities in high efficiency neighborhoods also maintain high efficiency with probabilities close to or equal to 1, while low efficiency cities, even when adjacent to high efficiency cities, experience only limited improvements in their upgrading probabilities. This points to restricted cross club mobility between efficiency tiers.

Another configuration corresponds to seemingly high efficiency but internally unbalanced structures, as in the NSTM urban agglomeration. Over the sample period, NSTM is dominated almost entirely by high efficiency states, with the probability of a high efficiency city remaining high efficiency approaching 1. Although static indicators suggest excellent metabolic efficiency, the near absence of medium and low efficiency cities implies extreme internal heterogeneity rather than balanced development. By contrast, the YRD urban agglomeration combines stable high efficiency with a certain core siphoning effect. In high efficiency neighborhoods, the probability that a high efficiency city remains high efficiency exceeds 0.95, whereas the upgrading probabilities of medium and low efficiency cities are noticeably lower than in medium efficiency neighborhoods. This suggests that in highly developed regions such as YRD, core cities absorb a disproportionate share of high quality factors of production, while positive metabolic spillovers to surrounding cities remain incomplete.

To further verify the robustness of the above findings, this paper conducts spatial kernel density analysis for all 19 urban agglomerations (see Fig. S5–S7). In the unconditional static kernel density plots, the main probability mass is concentrated near the 45°line, indicating a high probability that cities remain in the same efficiency interval across periods, which is consistent with the state persistence and club convergence revealed by the Markov chain analysis. Under the spatial static condition, when metabolic efficiency is plotted against its spatial lag, the probability contours no longer align strictly along the 45°line, suggesting that, when metabolic efficiency is treated as a continuous variable, global spatial positive correlation is not particularly pronounced. Combined with the Markov results based on efficiency classes, this implies that spatial dependence in metabolic efficiency is more stratified and conditional, manifesting more clearly within specific efficiency intervals or clubs rather than uniformly across the entire distribution. The spatial dynamic kernel density plots show that, after introducing a three-period lag, the location and shape of the main probability mass change little, indicating that time-lagged spatial effects are relatively weak. Overall, these results suggest that the spatial correlation of metabolic efficiency has a pronounced stratified character and is more likely to emerge within particular efficiency ranges than to appear as a strong and homogeneous spatial dependence over the whole distribution.

Further analysis: verification of the metabolic efficiency Kuznets curve and metabolic efficiency determinants

To further uncover the driving mechanisms behind urban agglomeration metabolic efficiency in China, this study estimates a panel Tobit model with metabolic efficiency (ME) as the dependent variable, given its censored nature within the ([0,1]) interval. Region fixed effects and year fixed effects are introduced to control for unobserved spatial heterogeneity and common time shocks. The core explanatory variables include the level of digitalization (DIG), the logarithm of per capita GDP (PGDP) and its squared term (PGDP²), the degree of openness (OPEN), the share of education expenditure (EDU), fiscal decentralization (FD), industrial structure upgrading (IND), and the level of financial development (FIN). The estimation results are reported in Table 4. (DIG represents digitalization level measured by 5G base station density; PGDP is the logarithm of per capita GDP; OPEN denotes the level of opening-up; EDU refers to education expenditure proportion; FD stands for fiscal decentralization; IND indicates industrial structure upgrading; FIN means financial development level. Robust standard errors clustered at the city level are reported in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.)

Table 4.

Tobit regression results of metabolic efficiency determinants.

Explanatory variables	Base Tobit regression		Excluding COVID-19 period (2020–2022)		Excluding municipalities		Winsorized at 5th and 95th percentiles
	Model (a)	Model (b)	Model (a)	Model (b)	Model (a)	Model (b)	Model (a)	Model (b)
DIG	0.037**	0.031**	0.044***	0.035***	0.035**	0.030**	0.064**	0.053**
	(0.015)	(0.014)	(0.013)	(0.013)	(0.015)	(0.014)	(0.028)	(0.027)
PGDP	0.151*	− 2.068***	0.143	− 2.187***	0.145*	− 2.025***	0.165*	− 2.060**
	(0.087)	(0.646)	(0.095)	(0.668)	(0.087)	(0.646)	(0.085)	(0.822)
PGDP²		0.102***		0.108***		9.328***		0.103***
		(0.029)		(0.030)		(3.611)		(0.037)
OPEN	− 0.113	2.510	1.872	3.903	0.045	2.610	− 1.804	0.557
	(9.242)	(9.200)	(9.358)	(9.214)	(9.303)	(9.249)	(11.010)	(10.979)
EDU	1.687**	1.263*	1.489*	1.090	1.663**	1.257*	1.944**	1.640**
	(0.741)	(0.750)	(0.768)	(0.766)	(0.742)	(0.749)	(0.795)	(0.797)
FD	0.081	0.174	0.164	0.258	0.102	0.188	0.091	0.161
	(0.264)	(0.255)	(0.283)	(0.271)	(0.264)	(0.255)	(0.265)	(0.261)
IND	0.568	0.643	0.399	0.443	0.514	0.597	0.518	0.604
	(0.404)	(0.398)	(0.409)	(0.402)	(0.409)	(0.404)	(0.423)	(0.423)
FIN	0.030	0.016	0.037	0.026	0.027	0.015	0.049	0.034
	(0.030)	(0.028)	(0.031)	(0.030)	(0.029)	(0.028)	(0.040)	(0.039)
Constant	− 2.296**	9.445***	− 1.899*	10.384***	− 2.129**	0.100***	− 2.428**	9.337**
	(0.964)	(3.614)	(1.049)	(3.739)	(0.985)	(0.029)	(0.971)	(4.550)
Observations	3420	3420	2814	2814	3403	3403	3420	3420
Pseudo R²	0.129	0.144	0.140	0.157	0.125	0.139	0.134	0.142
Region FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes

With respect to the existence of a metabolic efficiency Kuznets curve, Model (b) shows that the coefficient of PGDP is significantly negative, while the coefficient of PGDP² is significantly positive at the 1% level. This pattern indicates a pronounced non-linear relationship between metabolic efficiency and the level of economic development. Specifically, in the early stages of economic development, increases in per capita GDP are associated with a decline in metabolic efficiency; once income surpasses a certain threshold, further economic growth contributes to improvements in metabolic efficiency. In other words, ME follows a U-shaped trajectory with respect to economic development, which can be interpreted as a “metabolic efficiency Kuznets curve”: urban agglomerations initially rely on high-input, high-consumption and high-pollution growth, but at more advanced stages, technological progress, industrial restructuring, and stricter environmental regulation jointly promote a rebound in metabolic efficiency.

Regarding digitalization, the coefficient of DIG is positive and statistically significant at the 5% level in both Model (a) and Model (b), suggesting that the expansion of digital infrastructure and the diffusion of information technologies significantly enhance metabolic efficiency in Chinese urban agglomerations. On the one hand, digitalization optimizes the spatial and sectoral allocation of resources and energy by reducing information and transaction frictions; on the other hand, digital technologies strengthen monitoring, management and coordination of energy use and pollutant emissions, thereby increasing output per unit of resource and environmental input under existing constraints.

In terms of human capital and public services, the share of education expenditure (EDU) exerts a consistently positive impact on metabolic efficiency, with coefficients that are significant at the 5% level in Model (a) and at the 10% level in Model (b). This finding implies that higher educational spending not only raises labor quality and absorptive capacity for advanced technologies, but also facilitates the diffusion of green technologies and innovative management practices. As a result, both technical efficiency and managerial efficiency can be improved, which is consistent with the earlier decomposition results indicating that technological and managerial dimensions jointly shape urban metabolic performance.

By contrast, the coefficients of openness (OPEN), fiscal decentralization (FD), industrial structure upgrading (IND) and financial development (FIN) do not show stable statistical significance across specifications, although their estimated signs are generally in line with theoretical expectations. This may reflect substantial heterogeneity in the openness patterns, fiscal arrangements, upgrading paths and financial resource allocation across different urban agglomerations. It also suggests that, at the current stage, “quantity-oriented” expansion or marginal institutional adjustments have not yet translated into clear and robust gains in metabolic efficiency, whereas “quality-oriented” factors such as digital transformation and education investment play a more direct and prominent role.

Overall, the Tobit regression results confirm that metabolic efficiency in Chinese urban agglomerations exhibits a typical U-shaped “metabolic efficiency Kuznets curve” along the path of economic development. Digitalization and education emerge as key positive drivers of metabolic efficiency, while the effects of openness, fiscal decentralization, industrial upgrading and financial development are less pronounced in this dimension. These findings are highly consistent with the preceding evidence that inter-group technical inefficiency and intra-group managerial inefficiency are the main sources of metabolic gaps, and they provide further empirical support for understanding how urban agglomerations can improve metabolic performance under binding resource and environmental constraints.

In addition, a series of robustness checks were conducted to verify the stability of the baseline results (Table 4). First, we excluded the special period of the COVID-19 pandemic and re-estimated the models using the subsample for 2006–2019. Second, to avoid the potential influence of the four centrally administered municipalities with atypical administrative and economic status, we removed Beijing, Shanghai, Tianjin and Chongqing from the sample. Third, all continuous variables were winsorized at the 5% level to mitigate the impact of extreme observations. Across these alternative specifications, the signs and statistical significance of the key coefficients—particularly those on digitalization, per capita GDP and its squared term, and education expenditure—remain largely unchanged, confirming that the main conclusions of this paper are robust.

Discussion

Internal structure of metabolic efficiency and club convergence

The metabolic efficiency of Chinese urban agglomerations is relatively stable over time, but displays a persistent stratified pattern in space. This combination of “limited temporal volatility and strong spatial stratification” indicates that, under the joint influence of industrial structure, infrastructure and ecological constraints, each agglomeration forms a relatively stable metabolic configuration and occupies a specific tier in the efficiency distribution^56,64. In the meta-frontier decomposition, metabolic inefficiency is found to arise mainly from differences between agglomerations rather than within them. Long-term choices of industrial paths, technological trajectories and resource–environment conditions tend to lock agglomerations onto frontiers at different heights, while cities within the same agglomeration make comparatively limited adjustments around their group frontier^2,64. Even so, reallocation and adjustment within agglomerations remain necessary.

Against this structural background, the Markov and spatial Markov results show how these frontier tiers are reinforced through path dependence. The conventional Markov transition matrix indicates that high-efficiency and low-efficiency states are both highly persistent, whereas the medium-efficiency state is fragile. The spatial Markov analysis further reveals the role of neighbourhoods: low-efficiency and high-efficiency clusters tend to be both spatially concentrated and temporally stable. Medium-efficiency cities are frequently squeezed between the two ends of the distribution; they either move up into high-efficiency clubs or slip down into low-efficiency clubs, and it is difficult for them to remain in the middle tier for long⁶⁵. For cities in this group, appropriate policies and favourable economic conditions may raise metabolic efficiency, but external shocks may also push them into low-efficiency states. Overall, their resilience is weaker than that of cities in persistently high- or low-efficiency groups.

The discovery of the metabolic efficiency Kuznets curve

The Tobit model shows a relatively robust U-shaped relationship between per capita GDP and metabolic efficiency. Different urban agglomerations are located at different points on the same curve. Agglomerations on the left-hand side of the curve rely more on resource-intensive and pollution-intensive growth patterns, and rising income is accompanied by declining metabolic efficiency. Once development moves into the middle- and high-income range, technological progress, industrial restructuring and environmental regulation begin to play a greater role, and further growth is increasingly associated with higher metabolic efficiency. The analysis of determinants indicates that digitalisation and education expenditure emerge as two robust promoting factors. By contrast, traditional development variables such as openness, fiscal decentralisation, industrial upgrading and financial development do not show robust positive effects in this study. For cities within urban agglomerations, the growth momentum generated by the application of new technologies, together with government investment in education and other basic supporting factors, may become key elements in improving metabolic efficiency.

The metabolic efficiency Kuznets curve also helps to interpret the high efficiency scores observed for the Northern Slope of Tian Mountains agglomeration. Its metabolic efficiency remains close to 1 throughout the sample period and would conventionally be regarded as “best performing”, but this judgement needs to be treated with caution once metabolic scale and development level are taken into account. On the one hand, the resource and pollution intensities of this agglomeration are significantly lower than those of highly urbanised eastern coastal agglomerations. Under a unified input–output–environment indicator system, it is closer to a low-input, low-output and low-emission metabolic bundle, and it is therefore easier for it to form a local frontier in the SBM–DEA framework. On the other hand, the efficiency indicator used in this paper focuses on the relative relationship between desired and undesired outputs per unit of metabolic input. A high efficiency score mainly reflects the degree of resource and environmental saving at a given metabolic scale⁹. Placed on the metabolic efficiency Kuznets curve, the Northern Slope of Tian Mountains is closer to the “low-income, high-efficiency” segment on the left-hand side. Its high efficiency is to a greater extent a relative advantage under conditions of low metabolic scale, rather than a sign that a high-quality development stage has already been achieved. This example suggests that the interpretation of extreme efficiency values needs to take metabolic scale, development stage and indicator meaning into account at the same time. Describing urban agglomeration differences in terms of “what level of efficiency is achieved at what development stage and with what metabolic scale” is more in line with the logic of metabolic efficiency analysis than simply attaching labels of “good” or “poor” performance.

In addition, the metabolic efficiency Kuznets curve contextualizes the Northern Slope of Tian Mountains’ high efficiency scores (near 1). While conventionally deemed “best performing,” this judgement requires caution regarding metabolic scale and development level. Specifically, compared to highly urbanized coastal agglomerations, its significantly lower resource-pollution intensities constitute a low-input, low-output, and low-emission bundle, facilitating the formation of a local frontier in the SBM–DEA framework. Placed in the curve’s “low-income, high-efficiency” segment, this score reflects the indicator’s focus on relative savings at a given scale—signifying a relative advantage of low metabolic scale rather than high-quality development. Consequently, interpreting extreme values necessitates integrating scale, stage, and indicator meaning, favoring a logic of “efficiency-at-specific-stage” over simple “good/poor” labels.

Policy implications and conclusion

Policy implications

Establish a dynamic monitoring system to detect the misalignment between “Metabolic Scale” and “Metabolic Efficiency.” A high economic scale does not equate to high metabolic efficiency. Policy focus must shift from static GDP accounting to dynamic efficiency monitoring. Utilizing the digitalization drivers identified in this study, a real-time warning mechanism should be built to identify cities—especially core cities—that exhibit “high growth but low efficiency,” enabling early intervention against path dependence on resource-intensive development.

Bridge inter-agglomeration technology gaps via digital empowerment and human capital accumulation. Since the inter-agglomeration technology gap (TIE) dominates overall inefficiency, replicating management models is insufficient for lagging regions. Strategies must focus on elevating the regional technology frontier. Leveraging the verified positive effects of digitalization and education, underdeveloped agglomerations should prioritize digital infrastructure and human capital investment to enhance their absorptive capacity for green technologies, accelerating their transition across the inflection point of the “Metabolic Efficiency Kuznets Curve.”

Address the “Center-Low, Periphery-High” paradox by differentiating internal governance strategies. Contrary to the assumption that core cities always lead in efficiency, this study finds they often suffer from agglomeration diseconomies (high input/pollution intensity). Therefore, core cities must prioritize “decoupling”—optimizing industrial structure to reduce resource intensity rather than merely expanding scale. Peripheral cities, often retaining higher efficiency due to lower environmental loads, should be protected from becoming “pollution havens.” Governance should focus on preventing the transfer of inefficient industries from the core to the periphery, ensuring the latter functions as an ecological barrier rather than a waste sink.

Provide resilience support for “Medium-Efficiency” cities to prevent polarization. The Markov chain analysis reveals that medium-efficiency cities are in a precarious “squeezed” state. To prevent them from sliding into low-efficiency clubs, policies should avoid “one-size-fits-all” measures. Instead, differentiated fiscal and industrial policies should support these cities in identifying niche comparative advantages, avoiding homogeneous competition with core cities while securing their upward mobility in the efficiency hierarchy.

Conclusion

This study establishes a unified analytical framework, integrating a dynamic meta-frontier SBM-DEA model, spatial Markov chains, and a panel Tobit model, to systematically examine the spatiotemporal evolution and driving mechanisms of metabolic efficiency in 19 Chinese urban agglomerations from 2006 to 2022. The main contributions of this study are threefold:

First, this paper reveals that the metabolic efficiency of Chinese urban agglomerations exhibits a stable characteristic of “structural stratification” rather than “overall convergence.” The meta-frontier decomposition confirms that the inter-agglomeration technology gap contributes significantly more to inefficiency than the intra-agglomeration management gap, correcting previous biases that overly focused on micro-management factors while neglecting macro-structural differences. Second, the study uncovers the risk of a “middle-efficiency trap” in the green transition process; specifically, both high-efficiency and low-efficiency clubs demonstrate strong self-locking effects, whereas medium-efficiency cities face severe polarization pressures and are prone to regression influenced by their surrounding environment. Finally, empirical results validate the existence of the “Metabolic Efficiency Kuznets Curve” and confirm that digitalization levels and education investment are key drivers enabling urban agglomerations to cross the efficiency inflection point and break path dependence. In summary, this study advocates for a paradigm shift in urban agglomeration governance from focusing on the growth of “metabolic scale” to the improvement of “metabolic efficiency,” supported by long-term monitoring mechanisms and differentiated regional policies.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Author Contributions: Conceptualization, W.W, and H.L; methodology, W.W, and H.L; software, W.W; validation, W.W, and H.L; formal analysis, W.W, and H.L; investigation, W.W, and H.L; resources, W.W; data gathering, H.L; writ-ing—original draft preparation, W.W, and H.L; writing—review and editing, W.W, and H.L; visualization, H.L; supervi-sion, W.W; project administration, H.L; funding acquisition, H.L, and W.W. All authors have read and agreed to the published ver-sion of the manuscript.

Funding

Youth Project of the National Social Science Fund of China“Data Factor–Driven Spatial Production and Rescaling of Mobile Cities”, (Grant number: 25CGL167);

Guangxi Philosophy and Social Sciences Youth Research Project”Mechanisms and Pathways of the Border–Coastal Linkage Urban Belt in Optimizing Guangxi’s Marine-Oriented Economic Development Pattern”,(Grant number:25JYB153).

Data availability

The datasets generated and/or analysed during the current study are not publicly available due the data used in this study are all public statistical data, and no new data was generated.but are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.