Urban shrinkage impedes carbon scale but increases carbon intensity in China

Urban shrinkage impedes carbon scale but increases carbon intensity in China | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Urban shrinkage impedes carbon scale but increases carbon intensity in China Chao Ye, Li Yonghe, Zhuang Liang, Philippe s Ciai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6297437/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The pursuit of carbon neutrality in urban environments constitutes a multifaceted challenge, particularly within the framework of China's Dual Carbon Strategy that mandates coordinated reductions in both total carbon emissions and intensity (carbon emissions per unit of GDP). However, existing research predominantly focuses on the impact of urban shrinkage on carbon scale, often overlooking its association with carbon intensity. This study addresses this research gap by systematically examining the dual impacts of urban shrinkage on emission scale and intensity. Using econometric models, we analyze panel data from 288 prefecture-level and higher-tier cities in China, covering the period from 2005 to 2020. Our findings show that the number of high-carbon-emission cities increased over the study period, with a gradual westward shift toward central and western regions. Shrinking cities exhibited significantly lower carbon scale but notably higher carbon intensity compared to non-shrinking cities. In shrinking cities, each 1% decline in population corresponds to a 0.495% decrease in carbon scale, but a 0.629% increase in carbon intensity. The dual effect of shrinkage was most pronounced in central China and among medium-sized cities, large cities, and supercities. Crucially, we identify energy efficiency as the critical mediating mechanism through which urban shrinkage influences both emission scale and intensity. Social science/Environmental studies Earth and environmental sciences/Environmental social sciences/Climate-change adaptation Urban shrinkage Carbon scale Carbon intensity Spatial dynamics Energy efficiency Figures Figure 1 Figure 2 Figure 3 Introduction At the 75th United Nations General Assembly (2020), China formally pledged to achieve carbon peaking by 2030 and carbon neutrality by 2060. This commitment has drawn sustained global attention, positioning China’s decarbonization trajectory at the center of international climate governance. Meanwhile, China's urban development paradigm has undergone significant transformation. Empirical studies show that between 2010 and 2020, 1,507 Chinese counties—representing 52% of all counties nationwide—experienced population decline. Global projections further suggest that over 36% of cities worldwide could enter sustained population contraction by 2050 1,2 . Unlike growth-oriented cities, shrinking cities (SCs) undergo pronounced demographic attrition, a trend hypothesized to significantly impact regional carbon emissions (CEs) 3-6 . The dynamics of CEs in SCs have become a critical research focus, due to their paradoxical dual effects: achieving aggregate carbon emission mitigation under the national regulatory framework while concurrently lowering emission intensity through systemic structural efficiency optimization 7 . Contemporary scholarship identifies population scale regulation as a key determinant of CEs mitigation but also highlights the environmental Kuznets curve framework, where per capita CEs metrics exhibit nonlinear interdependencies with demographic parameters 8 . Although SCs may experience short-term carbon scale reduction, analyses revealed an underlying U-shaped trajectory marked by metabolic rebound effects during later stages of shrinkage 9 . The gradient of demographic attrition exerts differential impacts on carbon scale, with moderate shrinkage rates (0.5-1% annual population loss) enabling simultaneous economic vitality maintenance and carbon scale reduction through optimized resource reallocation. In contrast, cities experiencing rapid contraction (>1% annual population loss) breach critical agglomeration economy thresholds, triggering compensatory carbon scale increases due to infrastructure underutilization and service delivery inefficiencies 10 . Evolutionary phase typology further differentiates carbon scale patterns: post-industrial SCs undergoing regenerative transitions exhibit metabolic suppression via circular economy integration, while resource-dependent cities in growth/maturity phases experience carbon scale intensification due to industrial transition inertia and sunk cost entrapment 3 . Despite these varied pathways, prevailing urban governance paradigms remain entrenched in growth-oriented ideologies, with public infrastructure planning continuing to exhibit scale lock-in effects. This institutional path dependency leads to systemic maladaptation to shrinkage realities, perpetuating energy infrastructure overcapacity and carbon-intensive spatial mismatches 11 . The decline in population size induces a dual depletion mechanism: diminishing workforce concentration weakens urban productivity thresholds, while simultaneously creating structural surpluses in physical infrastructure, residential vacancies, and abandoned industrial land 12,13 . Research indicated that as of early 2021, 17.4% of the housing inventory in China was unoccupied. The construction and operation of these properties contributed to the emission of 55.81 million tons of carbon dioxide annually, which represented 6.9% of the total CEs from the residential sector in China 14 . These spatial-economic transformations fundamentally reshape urban morphology, leading to systemic declines in energy efficiency across multiple urban subsystems 15-18 . Although demographic contraction may superficially reduce aggregate residential energy demand, the inherent rigidity of urban infrastructure systems sustains fixed operational costs, thereby exponentially increasing per capita energy expenditure 19,20 . Consequently, SCs follow distinct environmental degradation trajectories compared to expanding urban areas, primarily due to the widening spatial disjunction between residual population clusters and optimized resource allocation 21 . This systemic dysfunction has led scholars to identify urban shrinkage as a critical destabilizing factor within urban socio-ecological systems, posing significant challenges to low-carbon transition efforts under conventional urban governance frameworks 22-24 . From a socio-metabolic perspective, urban shrinkage may temporarily reduce aggregate resource throughput and energy intensity, theoretically aligning with lowered carbon scale via urban scaling effects 25 . Paradoxically, critical scholarship highlights countervailing mechanisms wherein population contraction can induce suboptimal spatial configurations and compromised agglomeration efficiencies. These structural inefficiencies may, in turn, elevate carbon intensity, thereby constraining systemic decarbonization potential 26 . Within the framework of China’s dual-carbon policy, this dichotomy necessitates rigorous theoretical interrogation. As chronic urban shrinkage transitions from a localized phenomenon to a global urbanization challenge—particularly in post-industrial Chinese cities—understanding its intricate relationship with CEs dynamics emerges as a critical research imperative. The urgency of this inquiry is underscored by mounting evidence that conventional low-carbon strategies, optimized for growth-centric urbanism, fall short in addressing the unique metabolic paradoxes of contracting urban systems. Urban shrinkage has emerged as a critical governance challenge in contemporary urban studies, with its CEs implications representing a pivotal research frontier. Empirical evidence from China’s northeastern industrial cities highlights this dynamic: Daqing and Anshan exhibited a compounded annual carbon scale reduction rate of 1.47% from 2013 to 2015, directly following pronounced urban shrinkage 10 . Current scholarship predominantly examines the scaling effects of shrinkage on CEs, while systematically under-exploring carbon intensity implications—a critical knowledge gap for Chinese municipalities navigating the dual-carbon paradox 27 . This oversight can be attributed to two main disciplinary limitations: (1) insufficient integration of scale-intensity decoupling analysis into decarbonization pathways, and (2) neglect of SCs’ unique role within evolving urban development paradigms. To address these gaps, our study conducts a dual-perspective investigation (scale-intensity) using panel data from 288 Chinese prefecture-level cities spanning 2005-2020. Our findings reveal a scale-intensity decoupling phenomenon in SCs: each percentage point of population decline results in a 0.495% decrease in carbon scale but simultaneously leads to a 0.629% increase in carbon intensity. Policy-wise, the results offer adaptive infrastructure right-sizing suggestions and circular economy governance models for SCs. Results Characteristics of SCs During the baseline observation period (2000–2005), 65 SCs were identified. The average permanent population of these cities was 4.27 million, with 50.77% having a population of less than 5 million. The average urbanization rate stood at 18.8%, and 67.7% of these cities had an urbanization rate below 50%. The average shrinkage rate was 4.63%, with more than 65% of cities experiencing a shrinkage rate below 5%, and over 98% had a shrinkage rate under 15%, indicating regional disparities in shrinkage intensity. These cities were mainly concentrated in three regions: the northeastern border areas adjacent to the Korean Peninsula, small-to-medium-sized coastal cities in southeastern China (with populations under 500,000 or between 500,000 and 1 million), and urban corridors in northeastern Sichuan Province (Figure 1a). Between 2005 and 2010, the number of SCs increased to 122. The average permanent population of these cities decreased to 3.96 million, with the proportion of cities under 5 million in population rising to 74.6%. The average urbanization rate grew to 39.36%, with 82.8% of cities having an urbanization rate below 50%. The average shrinkage rate also increased to 6.65%, with 56.6% of cities having a shrinkage rate below 5%, and 91.8% having a shrinkage rate below 15%. The spatial extent of contraction expanded notably, forming new clusters in central, southwestern, and northeastern China (Figure 1b). Between 2010 and 2015, the National New Urbanization Plan encouraged infrastructure investments in small and medium-sized cities and promoted rural-to-urban migration, leading to a temporary reduction in urban shrinkage. As a result, the number of SCs dropped sharply to 46. The average permanent population of shrinking cities further decreased to 3.31 million, with 80.43% having populations under 5 million. The average urbanization rate rose to 58.47%, and only 26.09% of cities had an urbanization rate below 50%, while 69.57% had an urbanization rate below 60%. The average shrinkage rate reduced to 3.82%, with 67.39% of cities exhibiting a shrinkage rate under 5%, and 93.47% had a shrinkage rate under 15%. Geographically, SCs during this period were primarily concentrated in northeastern China (Figure 1c). In the most recent period (2015–2020), the number of SCs surged to 163. The average permanent population of these cities was 3.50 million, with 86.5% of them having populations below 5 million. The average urbanization rate was 57.86%, with 31.9% of cities having an urbanization rate below 50% and 62.58% below 60%. The average shrinkage rate increased to 8.89%, with 49% of cities experiencing a shrinkage rate below 5%, and 87.73% had a shrinkage rate below 15%. Geospatially, SCs exhibited a cross-shaped distribution pattern, with concentrations along north-south and west-central axes. High-intensity shrinkage persisted, particularly in northeastern China (Figure 1d). Comparison of the carbon scale and carbon intensity between Non-shrinking cities and SCs In 2005, Shanghai (a Non-shrinking City, NSC) recorded the highest carbon emissions among sample cities (201.91 million tons, 3.07% of total), in stark contrast to Lhasa (a Shrinking City, SC), which had the lowest (0.60 million tons, 0.0091%). The average urban carbon scale was 22.85 million tons, with per capita emissions at 6.86 tons/person. NSCs exhibited a slightly lower average carbon scale (22.50 million tons) than SCs (24.04 million tons), yet their carbon intensity was higher (4.87 vs. 3.95 tons/10⁴ RMB) (Figure 2a). By 2010, Tangshan (NSC) had overtaken Shanghai as the top emitter (334.87 million tons, 3.5%), while Lhasa (NSC) remained the lowest (1.07 million tons, 0.011%). The mean urban carbon scale rose 45.2% to 33.17 million tons, and per capita emissions increased 35.7% to 9.31 tons/person. NSCs showed a more rapid increase in emissions (41.89 million tons) than SCs (21.31 million tons). Although both types reduced carbon intensity, NSCs' efficiency gains (3.12 tons/10⁴ RMB) were less pronounced than those of SCs (2.86 tons/10⁴ RMB) (Figure 2b). In 2015, Shanghai (NSC) once again became the highest emitter (276.77 million tons, 2.45%), while Lhasa (NSC) saw its emissions double (2.24 million tons, 0.0198%). The average urban carbon scale rose by 18.5% to 39.29 million tons, and per capita emissions increased by 24.2% to 11.56 tons/person. NSCs maintained a higher average carbon scale (40.7 million tons) than SCs (31.95 million tons). A reversal in carbon intensity trends emerged: NSCs declined to 2.19 tons/10⁴ RMB, while SCs rose to 3.12 tons/10⁴ RMB (Figure 2c). By 2020, Tangshan (SC) re-emerged as the highest emitter (305.79 million tons, 2.6%), whereas Ziyang (SC) recorded the lowest emissions (3.72 million tons, 0.032%). The average urban carbon scale increased marginally to 40.89 million tons (up 4.1% from 2015), with per capita emissions stabilizing at 11.59 tons/person. NSCs reported higher emissions (50.79 million tons) than SCs (33.3 million tons). Both categories achieved further reductions in carbon intensity, with NSCs reaching 1.64 tons/10⁴ RMB and SCs at 2.26 tons/10⁴ RMB (Figure 2d). The impact of urban shrinkage on carbon emissions Collinearity diagnostics, employing the Variance Inflation Factor (VIF) analysis, confirmed the absence of multicollinearity among the independent variables, with all VIF values remaining well below the critical threshold of 10. To rigorously evaluate the impact of urban shrinkage rate on both the carbon scale and carbon intensity, a two-way fixed effects model was employed, controlling for temporal trends and city-level heterogeneity. Empirical results revealed an asymmetric relationship: a 1% population decline corresponded to a 0.495% reduction in carbon scale (total carbon emissions) ( β = -0.00495, P < 0.1) but induced a 0.629% increase in carbon intensity ( β = 0.00629, P < 0.1) (Figure 3). The impact of the interaction between urban shrinkage rate (USR, only for the convenience of footnotes) and various indicators on CEs was further explored (Supplementary Table 4, ST4). The results from M19 (ST4) show that incorporating the interaction term between urban shrinkage rate and energy efficiency makes the effect of urban shrinkage rate on carbon scale statistically insignificant ( β USR = -0.00351, P > 0.1). In contrast, introducing the interaction term between urban shrinkage rate and park green space per capita (PCG) reveals that | β PCG×USR = -0.00963| > | β USR = -0.00497|, suggesting that increasing park green space per capita in SCs may enhance the carbon reduction benefits associated with urban shrinkage (M20, ST4). Interaction analysis reveals that the urban shrinkage rate alone (| β USR = -0.00541|) exhibits a greater absolute coefficient magnitude than its interaction with built-up green coverage rate (BGR) (| β BGR×USR = -0.000566|; M21, ST4), indicating an attenuated interaction effect and suggesting potential compensatory mechanisms between these variables. Specifically, land abandonment resulting from urban shrinkage often facilitates spontaneous vegetation regeneration in former industrial and commercial zones, artificially inflating green coverage metrics. However, this passive greening, lacking systematic planning, leads to two critical consequences. First, the irregular spatial distribution of these green patches weakens their functional connectivity and ecological utility. Second, maintaining fragmented green infrastructure, such as irrigation and landscape upkeep, is energy-intensive and may paradoxically increase carbon emissions, undermining potential sustainability benefits 25,28 . We further analyzed the heterogeneity across regions and city levels (Supplementary Table 5, ST5). The analysis of regional division outcomes shows that the central region exhibits more significant results compared to the eastern and western regions (M23 and M26, ST5; β central(carbon scale/carbon intensity) =-0.0101***/0.0106**, β Eastern(carbon scale/carbon intensity) =-0.000763/0.00318, β Western(carbon scale/carbon intensity) =-0.00175/0.00546). In terms of city scale, urban shrinkage has the most pronounced impact on carbon scale in medium-sized (population between 500,000 and 1,000,000) and large cities (population ≥ 1 million but < 5 million; M28 and M29, ST5; β medium-sized(carbon scale) =-0.0622*, β large(carbon scale) =-0.00685**), while urban shrinkage has the most pronounced impact on carbon intensity in large cities and supercities (population ≥ 10 million; M33 and M35, ST5; β large(carbon intensity) =- 0.00621**, β super(carbon intensity) =0.0372*). Furthermore, our findings suggest that urban shrinkage may have a causal relationship with the carbon intensity (Supplementary Table 6; β carbon intensity =0.0817***, β carbon scale =0.000896). Mediating mechanism Prior research has established a negative link between SCs and energy efficiency 17,29 . Building on these insights, we select specific energy efficiency indicator and employ a four-step methodology to investigate whether reduced energy efficiency acts as a critical mediating factor in the relationship between urban shrinkage rate and carbon scale (Table 1). In analyzing the mediating mechanism affecting the carbon scale, the estimated coefficient for urban shrinkage rate in M4 (when energy efficiency and urban shrinkage rate indicators are incorporated into the model) is -0.00495, which is statistically significant at the 5% level. This coefficient is both larger in absolute magnitude and more statistically significant than the estimated coefficient in M1 (only the urban shrinkage rate indicator was incorporated into the model; -0.00413, P <0.1), indicating that the decarbonization effect of urban shrinkage rate becomes more pronounced when energy efficiency is incorporated into the analysis. The results from M2 and M3 indicate negative values for both the urban shrinkage rate and energy efficiency, confirming that urban shrinkage rate negatively impacts energy efficiency, which in turn reduces energy efficiency’s potential to mitigate carbon emissions. To further substantiate these findings, both a Sobel test and a Bootstrap sampling test were conducted. The Sobel test Z statistic is 2.028, significant at the 5% level. The Bootstrap test produces a 95% confidence interval for the mediation effect that does not include zero, further validating the mediating role of energy efficiency in the relationship between urban shrinkage rate and carbon scale. Furthermore, we found the estimated impact of urban shrinkage rate in M8 is 0.00629, significant at the 5% level, which is both smaller in magnitude and less significant compared to the estimated value of 0.00792 in M5, significant at the 1% level. This indicates that when energy efficiency is considered, the negative effect of urban shrinkage on carbon intensity is reduced. Further confirmation of the mediating role of energy efficiency comes from the Sobel test, which yields a Z statistic of 2.944, significant at the 1% level. Additionally, the Bootstrap sampling test provides a 95% confidence interval for the mediation effect that does not include zero, validating the robustness of the findings. These results underscore that energy efficiency acts as a mediating factor, dampening the increase in carbon intensity caused by urban shrinkage. Table 1|Test of mediating effect of energy efficiency. M1 M2 M3 M4 M5 M6 M7 M8 Variables Log of carbon scale energy efficiency Log of carbon scale Log of carbon scale Log of carbon intensity energy efficiency Log of carbon intensity Log of carbon intensity urban shrinkage rate -0.00413* (-1.75) -0.317*** (-4.48) -0.00495** (-2.07) 0.00792*** (3.08) -0.317*** (-4.48) 0.00629** (2.44) energy efficiency -0.00230** (-2.03) -0.00257** (-2.24) -0.00563*** (-4.61) -0.00515** (-4.18) Constant 6.910*** 26.85*** 6.949*** 6.979*** 4.284*** 26.85*** 4.462*** 4.422*** (55.89) (7.27) (54.79) (54.91) (31.93) (7.27) (32.73) (32.29) Controls Yes Yes Yes Yes Yes Yes Yes Yes City/Year FE Yes Yes Yes Yes Yes Yes Yes Yes Observations 1,152 1,152 1,152 1,152 1,152 1,152 1,152 1,152 R-squared 0.462 0.119 0.462 0.465 0.517 0.119 0.523 0.526 Sobel-Z 2.028** 2.944*** Bootstrap (1000 times) confidence interval [0.00195, 0.00645] [0.00189, 0.00628] Standardized beta coefficients; t statistics in parentheses. *** P <0.01, ** P <0.05, * P <0.1 Discussion and conclusions This research advances urban decarbonization theory by Quantifying the "shrinkage paradox" – simultaneous carbon scale reduction and carbon intensity escalation. And we identified energy efficiency as critical mediator in SCs' low-carbon transitions. More importantly, we proposed a dual-path governance framework balancing spatial repurposing with institutional innovation. This empirical evidence repositions urban shrinkage as both challenge and catalyst in China's dual carbon agenda, demanding spatially sensitive governance models that transform spatial liabilities into decarbonization opportunities. The relationship between SCs and CEs This study elucidates the role of urban shrinkage in CEs dynamics. Our analysis reveals a phased shift in the carbon emissions trajectories of SCs and NSCs between 2005 and 2020. We found a spatiotemporal reconfiguration of emission geographies. China's evolving regional development paradigm and accelerated urbanization have precipitated a spatial redistribution of high-carbon zones, transitioning from eastern-southern coastal regions toward central-western and northern inland territories. Initial observations (2005) revealed SCs as elevated carbon scale contributors (carbon scale SCs = 24.04 Mt vs carbon scale NSCs = 22.50 Mt), yet post-2010 dynamics demonstrated SCs' progressive decarbonization (2020 carbon scale SCs = 33.30 Mt vs carbon scale NSCs = 50.79 Mt). Conversely, carbon intensity patterns exhibited an inverse trajectory—SCs initially maintained lower intensity (2005–2010 carbon intensity SCs = 3.95 tons/10⁴ RMB vs carbon intensity NSCs = 4.87 tons/10⁴ RMB) before surpassing NSCs levels post-2010 (2020 carbon intensity SCs = 2.26 tons/10⁴ RMB vs carbon intensity NSCs = 1.64 tons/10⁴ RMB). This observed scale-intensity divergence stems from two structural shifts. First, the decline in population in shrinking cities led to a reduction in carbon scale, but later exacerbated carbon intensity due to inefficient infrastructure utilization. Second, NSCs’ expansion induced carbon lock-in through sprawl-driven transportation emissions and embedded energy-intensive development patterns. Furthermore, we found the mechanistic dualism in shrinkage impacts. The benchmark regression analysis framework elucidates the paradoxical implications of urban shrinkage. A 1% decrease in population is associated with a 0.495% reduction in the carbon scale ( β = -0.00495, P < 0.1), which can be attributed to factors such as deindustrialization and a contraction in energy demand. Conversely, the same level of population decline is linked to a 0.629% increase in the carbon intensity ( β = 0.00629, P < 0.1), a phenomenon mediated by the underutilization of infrastructure and the persistence of path-dependent energy systems. China's shrinking cities exhibit pronounced geographical heterogeneity and resource-dependent characteristics, predominantly concentrated in regions with mono-industrial structures and path-dependent development trajectories. From a material cycle perspective, urban shrinkage driven by socioeconomic and other endogenous/exogenous factors operates through a cascading mechanism: industrial base erosion - labor market contraction - population outmigration - aggregate carbon emission reduction. Notably, China's urban shrinkage manifests distinct physical-environmental effects – while demographic and economic indicators decline, infrastructure legacy maintains high-carbon lock-in effects in built environments. Our mediation analysis quantifies this underlying mechanism, revealing that declining energy efficiency accounts for 0.163% of the increased carbon intensity in shrinking cities ( β₁ = 0.00792, P₁ < 0.01; β₂ = 0.00629, P₂ < 0.05). We propose that this phenomenon is driven by two primary mechanisms. The first is technological inertia, characterized by slow adoption rates of new energy technologies. The second is institutional fragmentation, which weakens cross-departmental coordination in climate governance. The spatial analysis reveals insights into China's urban shrinkage-carbon emission nexus, particularly highlighting the central region's vulnerability. From 2005 to 2020, cities in this zone exhibit the highest average shrinkage rate (2.93%), surpassing eastern (1.35%) and western counterparts (2.91%), a phenomenon rooted in two interlocking mechanisms: First, the central region’s heavy dependence on carbon-intensive industries has led to a lock-in effect in its industrial framework, resulting in persistent high carbon emissions. For example, since China's 13th Five-Year Plan, Inner Mongolia's total coal production capacity has reached 1.34 billion tons, accounting for 1/4 of the national total. According to the 2019 China Energy Statistical Yearbook, power and heating in Inner Mongolia account for about 50% of coal consumption. Second, demographic-spatial decoupling, for example, Shandong Province experienced an annual population decline of 1.28% (2010–2020), yet simultaneously saw rural residential land expand by 64,000 hectares (+5.19% total area) 30 . An examination of municipal-level disparities reveals that medium-sized and large cities exhibit greater significance in regression analyses concerning carbon scale, while large cities and supercities show a more pronounced significance in relation to carbon intensity. This phenomenon can be attributed to the fact that medium-sized cities in China often receive limited development support, making them particularly vulnerable to urban shrinkage 31 . The combination of shrinkage and labor loss significantly impacts industrial output, leading to a reduction in carbon scale. Meanwhile, many large cities are heavily reliant on natural resources. As resource depletion coincides with urban shrinkage, carbon scale declines, whereas carbon intensity rises significantly. In the case of supercities, two distinct pathways emerge. First, influenced by consumerism and postmodernism, demographic challenges such as an aging population and declining fertility rates have led some supercities to experience partial shrinkage. Second, this shrinkage has led to the deterioration of public services, which has reduced the efficiency of energy system utilization, resulting in a more pronounced impact on carbon intensity. Low-carbon development paths for SCs This study proposes a dual-pathway decarbonization framework for SCs, integrating material stock optimization with institutional innovation to foster sustainable transitions in the post-shrinkage era. Grounded in resilience theory and circular economy theory, this strategic blueprint comprises the following key components: We advocate for the enhancement of metabolic processes in SCs through the implementation of spatial planning strategies informed by circular economy principles. According to the report “ Analysis of Urban Housing Vacancy in China 2017 ”, housing vacancy rates in China’s urban areas were 18.4%, 19.5%, 20.6%, and 21.4% in 2011, 2013, 2015, and 2017 respectively. These figures present unique opportunities for circular economy transitions. The optimization and repurposing of existing resources can drive the development of a circular economy and improve energy efficiency. Urban shrinkage often leads to underutilized infrastructure, which may require reconfiguration or minor upgrades to existing systems, as well as adjustments to the distribution of public services and goods to accommodate population decline. This process may involve reallocating surplus public resources to nearby areas or redistributing them between urban and rural regions to reduce unnecessary energy consumption. SCs frequently face challenges such as idle land and low utilization rates. To address these issues, it is crucial to promote the repurposing of vacant land and improve spatial efficiency through measures such as ecological restoration, creating parks and green spaces, and transforming vacant or abandoned industrial and residential buildings into modern office spaces, cultural facilities, or hubs for innovation and entrepreneurship. Achieving this may require flexible adjustments to land property rights and the designation of land use. Secondly, advancing urban decarbonization requires the enhancement of governance frameworks. A decline in population density often leads to underutilization of public transportation resources. To address this, big data analytics should be leveraged to optimize public transportation routes more effectively. Additionally, policy incentives are essential for attracting green investments and fostering the growth of green and low-carbon industries, such as the "new three" (new energy vehicles, lithium batteries, and photovoltaic modules). Governments should also lead in establishing a valuation and pricing system for the ecological benefits of natural resources and the environmental costs of greenhouse gas emissions. This system would provide a foundation for setting CEs standards for both corporations and individuals. Furthermore, the development of a carbon trading market is necessary to facilitate the paid transfer of public goods, such as carbon emission rights, enabling the efficient circulation of resources. Through such measures, urban decarbonization can be effectively advanced, ensuring sustainable development in the face of urban shrinkage. Methods Data The dependent variables encompass both carbon scale and carbon intensity. Specifically, the carbon scale is determined by aggregating the direct CEs attributable to agriculture, the service sector, residential activities, transportation, and energy consumption, along with the energy imported from outside the urban area. The CEs from energy are derived by applying energy conversion coefficients to various fossil fuel sources, including coal, oil, and natural gas. The data for these indicators is sourced from the China City Greenhouse Gas Working Group (https://www.cityghg.com/). The carbon intensity indicator consists of per capita CEs and carbon intensity. The population figures utilized for these calculations are derived from census data, while GDP data is obtained from the China City Statistical Yearbook (https://www.stats.gov.cn/zsk/snapshoot?reference) as well as from the statistical yearbooks and economic and social development reports available on the official websites of various cities. The phenomenon of urban shrinkage is primarily characterized by three categories of indicators: the urban shrinkage rate, the urban shrinkage status, and the population density change rate in built-up areas. Given that a notable characteristic of urban shrinkage is the population reduction, we employ the population change rate, which is widely utilized in existing literature, as a metric for assessing the urban shrinkage rate 32-34 . This indicator serves as the principal explanatory variable, while the Green coverage rate of built-up areas indicator is utilized to conduct robustness tests on the findings. Land Use and Cover Change (LUCC) data, with a resolution of 30 meters, were sourced from the Resource and Environmental Science Data Platform of the Chinese Academy of Sciences (https://www.resdc.cn/). The delineation of construction land for each city across various years was achieved using the field extraction functionality of geographic information system (GIS) software. Additionally, spatial distribution raster data (Unconstrained individual countries 2000-2020 UN adjusted ( 1km resolution )) reflecting China’s population density were obtained and adjusted according to estimates from the United Nations Population Division, via the WorldPop demographic platform (https://hub.worldpop.org/geodata). The zoning statistics function was employed to compute the average population density of built-up areas across different cities, subsequently characterizing the indicator through the multi-period change rate of population density within these areas 3 . The urban shrinkage rate indicator is processed through a negative standardization approach, whereby cities that have not experienced shrinkage are assigned a value of 0. The urban shrinkage status indicator is incorporated into the causal relationship model, assigning a value of 1 for cities experiencing shrinkage and a value of 0 for those that are not. For detailed indicator calculation methods and data sources, please see Supplementary Table 1. Measures To examine the effects of urban shrinkage on CEs, a two-way fixed effects model (Two-way FE) was developed, as represented in Formula 1. In this context, the variables i and t denote the city and year, respectively. The term “ Carbon ” encompasses the CEs factor, which includes the carbon scale, per capita CEs, and carbon intensity. The variable urban shrinkage rate indicates the urban shrinkage rate. The term “ Controls ” refers to a set of control variables. Additionally, “ year ” and “ city ” account for annual fixed effects and city-specific fixed effects, respectively. The parameters α, β , and ε represent the constant term, the regression coefficient for the independent variable, and the random error term, respectively. A mediation effect model has been constructed to examine the potential mediating mechanism through which urban shrinkage influences CEs (refer to Equation 2-4). The conventional three-stage mediation mechanism testing approach is limited by inherent endogeneity issues 35 . To address these limitations, we incorporate recent findings and augment the traditional model by integrating a regression model that assesses the mediating variable in relation to the explained variable, thereby establishing a four-stage mediation mechanism testing framework. The robustness and validity of the results are further evaluated using the Sobel test and Bootstrap test, thereby enhancing the comprehensiveness and reliability of the mediation analysis 36,37 . In the presented formula, M serves as the mediating variable, while the other symbols retain their previously defined meanings. When the regression coefficients for both the indirect and direct effects exhibit the same sign, or when the direct effect is less significant or possesses a lower absolute value than the total effect, this indicates that the variable M exerts a facilitative influence. Conversely, if these conditions are not met, it suggests that the variable M has a suppressive effect 38 . Robustness checks The robustness of the findings was evaluated through a series of alternative specifications and adjustments, including employing instrumental variable (IV) approach, substituting the primary explanatory variable, modifying the method of measuring urban shrinkage rate, altering the dependent variables to focus separately on carbon scale and carbon intensity, and incorporating an additional control variable, GDP per capita. We found the estimated values remain consistent with the baseline regression, supporting the validity of the conclusions (Supplementary Table 3). Specially, we use the aging rate and financial development level as IVs to alleviate the endogeneity problem in the carbon scale and carbon intensity models (Supplementary Table 2). Large Language Models (LLMs) Usage Declaration In the preparation of this manuscript, the authors, primarily based in China, employed Deepseek-R1 and ChatGPT-4o for linguistic quality of the manuscript. We declare that the use of LLMs was solely aimed at improving the manuscript’s readability and aligning it with the conventions of academic English writing. Declarations Data availability The carbon emissions data are available at https://www.cityghg.com/ . The Land Use and Cover Change (LUCC) data are available at https://www.resdc.cn/ (ref. 39). The China’s population density raster data are available at https://hub.worldpop.org/geodata (ref. 40). The China's demographic data are available at https://www.stats.gov.cn/sj/pcsj/rkpc/d7c/ . Other economic and social statistical indicators are available at https://www.stats.gov.cn/zs/tjwh/tjkw/tjzl/ . The data that support the findings of this study are available on GitHub at https://github.com/yongheli11/Code-of-Urban-shrinkage-impedes-carbon-scale-but-increases-carbon-intensity-in-China . We are committed to making the fully assembled dataset publicly available in a permanent repository that issues a DOI upon acceptance. Code availability The Python and R code for visualizing Figs. 2 and 3, along with the Stata code for the regressions utilized in this research, are available on GitHub at https://github.com/yongheli11/Code-of-Urban-shrinkage-impedes-carbon-scale-but-increases-carbon-intensity-in-China . References Meng, X. & Long, Y. Shrinking cities in China: evidence from the latest twopopulation censuses 2010-2020. Environ Plan A. 54 , 449-453 (2022). Zhai, W. et al. Satellite monitoring of shrinking cities on the globe and containment solutions. iScience 25 , 104411 (2022). Grossmann, K., Bontje, M., Haase, A. & Mykhnenko, V. Shrinking cities: Notes for the further research agenda. Cities 35, 221-225 (2013). Krayenhoff, E.S., Moustaoui, M., Broadbent, A.M., Gupta, V. & Georgescu, M. Diurnal interaction between urban expansion, climate change and adaptation in US cities. Nat. Clim. Chang. 8 , 1097–1103 (2018). Sun, J. & Zhou, T. 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Pro-growth urban policy implementation vs urban shrinkage: How do actors shift policy implementation in shrinking cities in China? Cities 134 , 104157 (2023). Wu, K. & Li, Y. Research progress of urban land use and its ecosystem services in thecontext of urban shrinkage. J. Nat. Resour. 34 , 1121-1134 (2019). Antonic, B., Djukic, A. & Iop. Environmentally-Friendly Planning for Urban Shrinkage. IOP Conference Series: Earth and Environmental Science, IOP Publishing 410 , 012084 (2020). Hospers, G.J. Policy Responses to Urban Shrinkage: From Growth Thinking to Civic Engagement. Eur. Plan. Stud. 22 , 1507-1523 (2014). Rao, Y., Wu, C. & He, Q. The antagonistic effect of urban growth pattern and shrinking cities on air quality: Based on the empirical analysis of 174 cities in China. Sustain. Cities Soc. 97 , 104752 (2023). Chen, Y. & Zhang, D. Evaluation and driving factors of city sustainability in Northeast China: An analysis based on interaction among multiple indicators. Sustain. Cities Soc. 67 , 102721 (2021). Haase, A., Athanasopoulou, A. & Rink, D. Urban shrinkage as an emerging concern for European policymaking. Eur. Urban Reg. Stud. 23 , 103–107 (2013). Schwarz, K., Berland, A. & Herrmann, D. Green, but not just? Rethinking environmental justice indicators in shrinking cities. Sustain. Cities Soc. 41 , 816-821 (2018). Schilling, J. & Logan, J. Greening the Rust Belt A Green Infrastructure Model for Right Sizing America's Shrinking Cities. J. Am. Plann. Assoc. 74 , 451-466 (2008). Glaeser, E.L. & Kahn, M.E. The greenness of cities: Carbon dioxide emissions and urban development. J. Urban Econ. 67 , 404-418 (2010). Leng, H., Pan, X. & Yuan, Q. Research on carbon emission driving factors of land use in shrinkingcities:Taking Heilongjiang Province as an example. Urban Probl. 82-91 (2024). Strohbach, M.W., Arnold, E. & Haase, D. The carbon footprint of urban green space-A life cycle approach. Landsc. Urban Plan. 104 , 220-229 (2012). Liu, X., Wang, M., Qiang, W., Wu, K. & Wang, X. Urban form, shrinking cities, and residential carbon emissions: Evidence from Chinese city-regions. Appl. Energy. 261 , 114409 (2020). Yanbo, Q., Zhan, L., Jiang, G., Wenqiu, M. & Xiaozhen, D. How to Address “Population Decline and Land Expansion (PDLE)" of rural residential areas in the process of Urbanization:A comparative regional analysis of human-land interaction in Shandong Province. Habitat. Int. 117 , 102441 (2021). Gao, L., Ye, C. & Zhuang, L.J.L. Are Medium-Sized Cities in China Shrinking from 2010 to 2020? An Empirical Analysis with a Multi-Dimensional Model. Land 13 , 1865 (2024). Liu, Z. & Liu, S. Urban shrinkage in a developing context: Rethinking China's present and future trends. Sustain. Cities Soc. 80 , 103779 (2022). Ma, Z. et al. Urban shrinkage in the regional multiscale context: Spatial divergence and interaction. Sustain. Cities Soc. 100 , 105020 (2024). Deng, T., Wang, D., Yang, Y. & Yang, H. Shrinking cities in growing China: Did high speed rail further aggravate urban shrinkage? Cities 86 , 210-219 (2019). Jiang, T. Mediating Effects and Moderating Effects in Causal Inference. China Industrial Economics . 100-120 (2022). Niu, Z., Xu, C. & Wu, Y. Business Environment Optimization, Human Capital Effect and Firm Labor Productivity. Journal of Management World. 39 , 83-100 (2023). Zeng, G., Su, S. & Peng, S. Corporate Leverage and Technological innovation. China Industrial Economics . 155-173 (2023). Wen, Z. & Ye, B. Analyses of Mediating Effects: The Development of Methods and Models. Adv. Psychol. Sci. 22 , 731-745 (2014). Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryMaterials.docx Some necessary figures, tables and discussions to support the manuscript results Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6297437","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":439402468,"identity":"25d06073-3f71-4ee7-a463-9f5a7dba6935","order_by":0,"name":"Chao Ye","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArUlEQVRIiWNgGAWjYPACGx5+/gbStKTJSM44QJqWwzYGDQlEqjU43nxM4uOe8zwGDAcYP3zMIUbLmWNpkjOe3eYxZ25glpy5jRgtN3KMjXkO3OaxbDjAxsxLlJb7b4yN/xw4x2NwIIFYLTd4DB8zHDhAghbJM2mJD3sOJPNIzjjYTJxf+I4fPnDgxwE7e37+5oMfPhKjReEAnMnYQIR6IJAnUt0oGAWjYBSMZAAAsjo5cpFYs+QAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-3920-2286","institution":"East China Normal University","correspondingAuthor":true,"prefix":"","firstName":"Chao","middleName":"","lastName":"Ye","suffix":""},{"id":439402469,"identity":"7560c936-9d4c-4600-bdcf-161703433884","order_by":1,"name":"Li Yonghe","email":"","orcid":"https://orcid.org/0009-0003-3783-704X","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Yonghe","suffix":""},{"id":439402470,"identity":"4dbc7fae-3ee2-43f7-850e-5bd1956de6bc","order_by":2,"name":"Zhuang Liang","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zhuang","middleName":"","lastName":"Liang","suffix":""},{"id":439402471,"identity":"00bf3e25-80e0-4c9e-904e-fc00568256fa","order_by":3,"name":"Philippe s Ciai","email":"","orcid":"","institution":"CEA CNRS UVSQ, Centre d’Etudes Orme des Merisiers","correspondingAuthor":false,"prefix":"","firstName":"Philippe","middleName":"s","lastName":"Ciai","suffix":""}],"badges":[],"createdAt":"2025-03-24 17:06:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6297437/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6297437/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80869353,"identity":"eef96d7d-047b-45ce-9be6-781afcc1fe3c","added_by":"auto","created_at":"2025-04-18 04:40:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":3693917,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of SCs in the study areas.\u003c/strong\u003eThis map is derived from the standard map identified by review number GS (2024) 0650, as provided by the standard map service of the Ministry of Natural Resources. The boundary of the base map remains unaltered.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6297437/v1/a3c79a32626b07d1103a3c88.png"},{"id":80869351,"identity":"fa7b1dca-6627-4801-8525-f016a6d494c0","added_by":"auto","created_at":"2025-04-18 04:40:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":391306,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStatistical analysis of CEs.\u003c/strong\u003eThe dashed lines with blue, red and green colors denote the average carbon intensity of all cities, SCs and NSCs, respectively. The bar width and color represent the carbon scale and per capita CEs of each cities. SCs are marked with red triangles.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6297437/v1/78518f2f2df2a2ca568f1f4c.png"},{"id":80869509,"identity":"b139e1eb-e5bd-44bb-9e49-c9e0fa7c62f1","added_by":"auto","created_at":"2025-04-18 04:48:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":70461,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBenchmark Regression Results.\u003c/strong\u003e The red color is the regression result of carbon intensity (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e=0.465\u003c/em\u003e); the green color is the regression result of carbon scale (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e=0.526\u003c/em\u003e).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6297437/v1/9f0607b935d744999774684d.png"},{"id":84291369,"identity":"e2a674d6-2f59-4b1b-bcb1-b6900c5a8f9f","added_by":"auto","created_at":"2025-06-10 08:47:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3283814,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6297437/v1/1f619f35-0fc4-45b2-8b1a-d96e937ad3d0.pdf"},{"id":80869352,"identity":"ae0b906b-19af-4971-93fe-4771597a5da3","added_by":"auto","created_at":"2025-04-18 04:40:44","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":170466,"visible":true,"origin":"","legend":"Some necessary figures, tables and discussions to support the manuscript results","description":"","filename":"SupplementaryMaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-6297437/v1/2b214554da783a469edb4cea.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Urban shrinkage impedes carbon scale but increases carbon intensity in China","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAt the 75th United Nations General Assembly (2020), China formally pledged to achieve carbon peaking by 2030 and carbon neutrality by 2060. This commitment has drawn sustained global attention, positioning China\u0026rsquo;s decarbonization trajectory at the center of international climate governance. Meanwhile, China\u0026apos;s urban development paradigm has undergone significant transformation. Empirical studies show that between 2010 and 2020, 1,507 Chinese counties\u0026mdash;representing 52% of all counties nationwide\u0026mdash;experienced population decline. Global projections further suggest that over 36% of cities worldwide could enter sustained population contraction by 2050\u003csup\u003e1,2\u003c/sup\u003e. Unlike growth-oriented cities, shrinking cities (SCs) undergo pronounced demographic attrition, a trend hypothesized to significantly impact regional carbon emissions (CEs)\u003csup\u003e3-6\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe dynamics of CEs in SCs have become a critical research focus, due to their paradoxical dual effects: achieving aggregate carbon emission mitigation under the national regulatory framework while concurrently lowering emission intensity through systemic structural efficiency optimization\u003csup\u003e7\u003c/sup\u003e. Contemporary scholarship identifies population scale regulation as a key determinant of CEs mitigation but also highlights the environmental Kuznets curve framework, where per capita CEs metrics exhibit nonlinear interdependencies with demographic parameters\u003csup\u003e8\u003c/sup\u003e. Although SCs may experience short-term carbon scale reduction, analyses revealed an underlying U-shaped trajectory marked by metabolic rebound effects during later stages of shrinkage\u003csup\u003e9\u003c/sup\u003e. The gradient of demographic attrition exerts differential impacts on carbon scale, with moderate shrinkage rates (0.5-1% annual population loss) enabling simultaneous economic vitality maintenance and carbon scale reduction through optimized resource reallocation. In contrast, cities experiencing rapid contraction (\u0026gt;1% annual population loss) breach critical agglomeration economy thresholds, triggering compensatory carbon scale increases due to infrastructure underutilization and service delivery inefficiencies\u003csup\u003e10\u003c/sup\u003e. Evolutionary phase typology further differentiates carbon scale patterns: post-industrial SCs undergoing regenerative transitions exhibit metabolic suppression via circular economy integration, while resource-dependent cities in growth/maturity phases experience carbon scale intensification due to industrial transition inertia and sunk cost entrapment\u003csup\u003e3\u003c/sup\u003e. Despite these varied pathways, prevailing urban governance paradigms remain entrenched in growth-oriented ideologies, with public infrastructure planning continuing to exhibit scale lock-in effects. This institutional path dependency leads to systemic maladaptation to shrinkage realities, perpetuating energy infrastructure overcapacity and carbon-intensive spatial mismatches\u003csup\u003e11\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe decline in population size induces a dual depletion mechanism: diminishing workforce concentration weakens urban productivity thresholds, while simultaneously creating structural surpluses in physical infrastructure, residential vacancies, and abandoned industrial land\u003csup\u003e12,13\u003c/sup\u003e. Research indicated that as of early 2021, 17.4% of the housing inventory in China was unoccupied. The construction and operation of these properties contributed to the emission of 55.81 million tons of carbon dioxide annually, which represented 6.9% of the total CEs from the residential sector in China\u003csup\u003e14\u003c/sup\u003e. These spatial-economic transformations fundamentally reshape urban morphology, leading to systemic declines in energy efficiency across multiple urban subsystems\u003csup\u003e15-18\u003c/sup\u003e. Although demographic contraction may superficially reduce aggregate residential energy demand, the inherent rigidity of urban infrastructure systems sustains fixed operational costs, thereby exponentially increasing per capita energy expenditure\u003csup\u003e19,20\u003c/sup\u003e. Consequently, SCs follow distinct environmental degradation trajectories compared to expanding urban areas, primarily due to the widening spatial disjunction between residual population clusters and optimized resource allocation\u003csup\u003e21\u003c/sup\u003e. This systemic dysfunction has led scholars to identify urban shrinkage as a critical destabilizing factor within urban socio-ecological systems, posing significant challenges to low-carbon transition efforts under conventional urban governance frameworks\u003csup\u003e22-24\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFrom a socio-metabolic perspective, urban shrinkage may temporarily reduce aggregate resource throughput and energy intensity, theoretically aligning with lowered carbon scale via urban scaling effects\u003csup\u003e25\u003c/sup\u003e. Paradoxically, critical scholarship highlights countervailing mechanisms wherein population contraction can induce suboptimal spatial configurations and compromised agglomeration efficiencies. These structural inefficiencies may, in turn, elevate carbon intensity, thereby constraining systemic decarbonization potential\u003csup\u003e26\u003c/sup\u003e. Within the framework of China\u0026rsquo;s dual-carbon policy, this dichotomy necessitates rigorous theoretical interrogation. As chronic urban shrinkage transitions from a localized phenomenon to a global urbanization challenge\u0026mdash;particularly in post-industrial Chinese cities\u0026mdash;understanding its intricate relationship with CEs dynamics emerges as a critical research imperative. The urgency of this inquiry is underscored by mounting evidence that conventional low-carbon strategies, optimized for growth-centric urbanism, fall short in addressing the unique metabolic paradoxes of contracting urban systems.\u003c/p\u003e\n\u003cp\u003eUrban shrinkage has emerged as a critical governance challenge in contemporary urban studies, with its CEs implications representing a pivotal research frontier. Empirical evidence from China\u0026rsquo;s northeastern industrial cities highlights this dynamic: Daqing and Anshan exhibited a compounded annual carbon scale reduction rate of 1.47% from 2013 to 2015, directly following pronounced urban shrinkage\u003csup\u003e10\u003c/sup\u003e. Current scholarship predominantly examines the scaling effects of shrinkage on CEs, while systematically under-exploring carbon intensity implications\u0026mdash;a critical knowledge gap for Chinese municipalities navigating the dual-carbon paradox\u003csup\u003e27\u003c/sup\u003e. This oversight can be attributed to two main disciplinary limitations: (1) insufficient integration of scale-intensity decoupling analysis into decarbonization pathways, and (2) neglect of SCs\u0026rsquo; unique role within evolving urban development paradigms. To address these gaps, our study conducts a dual-perspective investigation (scale-intensity) using panel data from 288 Chinese prefecture-level cities spanning 2005-2020. Our findings reveal a scale-intensity decoupling phenomenon in SCs: each percentage point of population decline results in a 0.495% decrease in carbon scale but simultaneously leads to a 0.629% increase in carbon intensity. Policy-wise, the results offer adaptive infrastructure right-sizing suggestions and circular economy governance models for SCs.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eCharacteristics of SCs\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDuring the baseline observation period (2000\u0026ndash;2005), 65 SCs were identified. The average permanent population of these cities was 4.27 million, with 50.77% having a population of less than 5 million. The average urbanization rate stood at 18.8%, and 67.7% of these cities had an urbanization rate below 50%. The average shrinkage rate was 4.63%, with more than 65% of cities experiencing a shrinkage rate below 5%, and over 98% had a shrinkage rate under 15%, indicating regional disparities in shrinkage intensity. These cities were mainly concentrated in three regions: the northeastern border areas adjacent to the Korean Peninsula, small-to-medium-sized coastal cities in southeastern China (with populations under 500,000 or between 500,000 and 1 million), and urban corridors in northeastern Sichuan Province (Figure 1a).\u003c/p\u003e\n\u003cp\u003eBetween 2005 and 2010, the number of SCs increased to 122. The average permanent population of these cities decreased to 3.96 million, with the proportion of cities under 5 million in population rising to 74.6%. The average urbanization rate grew to 39.36%, with 82.8% of cities having an urbanization rate below 50%. The average shrinkage rate also increased to 6.65%, with 56.6% of cities having a shrinkage rate below 5%, and 91.8% having a shrinkage rate below 15%. The spatial extent of contraction expanded notably, forming new clusters in central, southwestern, and northeastern China (Figure 1b).\u003c/p\u003e\n\u003cp\u003eBetween 2010 and 2015, the National New Urbanization Plan encouraged infrastructure investments in small and medium-sized cities and promoted rural-to-urban migration, leading to a temporary reduction in urban shrinkage. As a result, the number of SCs dropped sharply to 46. The average permanent population of shrinking cities further decreased to 3.31 million, with 80.43% having populations under 5 million. The average urbanization rate rose to 58.47%, and only 26.09% of cities had an urbanization rate below 50%, while 69.57% had an urbanization rate below 60%. The average shrinkage rate reduced to 3.82%, with 67.39% of cities exhibiting a shrinkage rate under 5%, and 93.47% had a shrinkage rate under 15%. Geographically, SCs during this period were primarily concentrated in northeastern China (Figure 1c).\u003c/p\u003e\n\u003cp\u003eIn the most recent period (2015\u0026ndash;2020), the number of SCs surged to 163. The average permanent population of these cities was 3.50 million, with 86.5% of them having populations below 5 million. The average urbanization rate was 57.86%, with 31.9% of cities having an urbanization rate below 50% and 62.58% below 60%. The average shrinkage rate increased to 8.89%, with 49% of cities experiencing a shrinkage rate below 5%, and 87.73% had a shrinkage rate below 15%. Geospatially, SCs exhibited a cross-shaped distribution pattern, with concentrations along north-south and west-central axes. High-intensity shrinkage persisted, particularly in northeastern China (Figure 1d).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eComparison of the carbon scale and carbon intensity between Non-shrinking cities and SCs\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn 2005, Shanghai (a Non-shrinking City, NSC) recorded the highest carbon emissions among sample cities (201.91 million tons, 3.07% of total), in stark contrast to Lhasa (a Shrinking City, SC), which had the lowest (0.60 million tons, 0.0091%). The average urban carbon scale was 22.85 million tons, with per capita emissions at 6.86 tons/person. NSCs exhibited a slightly lower average carbon scale (22.50 million tons) than SCs (24.04 million tons), yet their carbon intensity was higher (4.87 vs. 3.95 tons/10⁴ RMB) (Figure 2a).\u003c/p\u003e\n\u003cp\u003eBy 2010, Tangshan (NSC) had overtaken Shanghai as the top emitter (334.87 million tons, 3.5%), while Lhasa (NSC) remained the lowest (1.07 million tons, 0.011%). The mean urban carbon scale rose 45.2% to 33.17 million tons, and per capita emissions increased 35.7% to 9.31 tons/person. NSCs showed a more rapid increase in emissions (41.89 million tons) than SCs (21.31 million tons). Although both types reduced carbon intensity, NSCs\u0026apos; efficiency gains (3.12 tons/10⁴ RMB) were less pronounced than those of SCs (2.86 tons/10⁴ RMB) (Figure 2b).\u003c/p\u003e\n\u003cp\u003eIn 2015, Shanghai (NSC) once again became the highest emitter (276.77 million tons, 2.45%), while Lhasa (NSC) saw its emissions double (2.24 million tons, 0.0198%). The average urban carbon scale rose by 18.5% to 39.29 million tons, and per capita emissions increased by 24.2% to 11.56 tons/person. NSCs maintained a higher average carbon scale (40.7 million tons) than SCs (31.95 million tons). A reversal in carbon intensity trends emerged: NSCs declined to 2.19 tons/10⁴ RMB, while SCs rose to 3.12 tons/10⁴ RMB (Figure 2c).\u003c/p\u003e\n\u003cp\u003eBy 2020, Tangshan (SC) re-emerged as the highest emitter (305.79 million tons, 2.6%), whereas Ziyang (SC) recorded the lowest emissions (3.72 million tons, 0.032%). The average urban carbon scale increased marginally to 40.89 million tons (up 4.1% from 2015), with per capita emissions stabilizing at 11.59 tons/person. NSCs reported higher emissions (50.79 million tons) than SCs (33.3 million tons). Both categories achieved further reductions in carbon intensity, with NSCs reaching 1.64 tons/10⁴ RMB and SCs at 2.26 tons/10⁴ RMB (Figure 2d).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe impact of urban shrinkage on carbon emissions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCollinearity diagnostics, employing the Variance Inflation Factor (VIF) analysis, confirmed the absence of multicollinearity among the independent variables, with all VIF values remaining well below the critical threshold of 10. To rigorously evaluate the impact of urban shrinkage rate on both the carbon scale and carbon intensity, a two-way fixed effects model was employed, controlling for temporal trends and city-level heterogeneity. Empirical results revealed an asymmetric relationship: a 1% population decline corresponded to a 0.495% reduction in carbon scale (total carbon emissions) (\u003cem\u003e\u0026beta;\u003c/em\u003e = -0.00495,\u003cem\u003e\u0026nbsp;P\u003c/em\u003e \u0026lt; 0.1) but induced a 0.629% increase in carbon intensity (\u003cem\u003e\u0026beta;\u003c/em\u003e = 0.00629, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.1) (Figure 3).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe impact of the interaction between urban shrinkage rate (USR, only for the convenience of footnotes) and various indicators on CEs was further explored (Supplementary Table 4, ST4). The results from M19 (ST4) show that incorporating the interaction term between urban shrinkage rate and energy efficiency makes the effect of urban shrinkage rate on carbon scale statistically insignificant (\u003cem\u003e\u0026beta;\u003csub\u003eUSR\u003c/sub\u003e\u003c/em\u003e = -0.00351, \u003cem\u003eP\u003c/em\u003e \u0026gt; 0.1). In contrast, introducing the interaction term between urban shrinkage rate and park green space per capita (PCG) reveals that |\u003cem\u003e\u0026beta;\u003csub\u003ePCG\u0026times;USR\u003c/sub\u003e\u003c/em\u003e = -0.00963| \u0026gt; |\u003cem\u003e\u0026beta;\u003csub\u003eUSR\u003c/sub\u003e\u003c/em\u003e = -0.00497|, suggesting that increasing park green space per capita in SCs may enhance the carbon reduction benefits associated with urban shrinkage (M20, ST4). Interaction analysis reveals that the urban shrinkage rate alone (|\u003cem\u003e\u0026beta;\u003csub\u003eUSR\u003c/sub\u003e\u003c/em\u003e = -0.00541|) exhibits a greater absolute coefficient magnitude than its interaction with built-up green coverage rate (BGR) (|\u003cem\u003e\u0026beta;\u003csub\u003eBGR\u0026times;USR\u003c/sub\u003e\u003c/em\u003e = -0.000566|; M21, ST4), indicating an attenuated interaction effect and suggesting potential compensatory mechanisms between these variables. Specifically, land abandonment resulting from urban shrinkage often facilitates spontaneous vegetation regeneration in former industrial and commercial zones, artificially inflating green coverage metrics. However, this passive greening, lacking systematic planning, leads to two critical consequences. First, the irregular spatial distribution of these green patches weakens their functional connectivity and ecological utility. Second, maintaining fragmented green infrastructure, such as irrigation and landscape upkeep, is energy-intensive and may paradoxically increase carbon emissions, undermining potential sustainability benefits\u003csup\u003e25,28\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe further analyzed the heterogeneity across regions and city levels (Supplementary Table 5, ST5). The analysis of regional division outcomes shows that the central region exhibits more significant results compared to the eastern and western regions (M23 and M26, ST5; \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003ecentral(carbon scale/carbon intensity)\u003c/sub\u003e\u003c/em\u003e=-0.0101***/0.0106**, \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003eEastern(carbon scale/carbon intensity)\u003c/sub\u003e\u003c/em\u003e=-0.000763/0.00318, \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003eWestern(carbon scale/carbon intensity)\u003c/sub\u003e\u003c/em\u003e=-0.00175/0.00546). In terms of city scale, urban shrinkage has the most pronounced impact on carbon scale in medium-sized (population between 500,000 and 1,000,000) and large cities (population \u0026ge; 1 million but \u0026lt; 5 million; M28 and M29, ST5; \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003emedium-sized(carbon scale)\u003c/sub\u003e\u003c/em\u003e=-0.0622*, \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003elarge(carbon scale)\u003c/sub\u003e\u003c/em\u003e=-0.00685**), while urban shrinkage has the most pronounced impact on carbon intensity in large cities and supercities (population \u0026ge; 10 million; M33 and M35, ST5; \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003elarge(carbon intensity)\u003c/sub\u003e\u003c/em\u003e=- 0.00621**, \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003esuper(carbon intensity)\u003c/sub\u003e\u003c/em\u003e=0.0372*). Furthermore, our findings suggest that urban shrinkage may have a causal relationship with the carbon intensity (Supplementary Table 6; \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003ecarbon intensity\u003c/sub\u003e\u003c/em\u003e=0.0817***, \u003cem\u003e\u0026beta;\u003c/em\u003e\u003cem\u003e\u003csub\u003ecarbon scale\u003c/sub\u003e\u003c/em\u003e=0.000896).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMediating mechanism\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePrior research has established a negative link between SCs and energy efficiency\u003csup\u003e17,29\u003c/sup\u003e. Building on these insights, we select specific energy efficiency indicator and employ a four-step methodology to investigate whether reduced energy efficiency acts as a critical mediating factor in the relationship between urban shrinkage rate and carbon scale (Table 1). In analyzing the mediating mechanism affecting the carbon scale, the estimated coefficient for urban shrinkage rate in M4 (when energy efficiency and urban shrinkage rate indicators are incorporated into the model) is -0.00495, which is statistically significant at the 5% level. This coefficient is both larger in absolute magnitude and more statistically significant than the estimated coefficient in M1 (only the urban shrinkage rate indicator was incorporated into the model; -0.00413, \u003cem\u003eP\u003c/em\u003e\u0026lt;0.1), indicating that the decarbonization effect of urban shrinkage rate becomes more pronounced when energy efficiency is incorporated into the analysis. The results from M2 and M3 indicate negative values for both the urban shrinkage rate and energy efficiency, confirming that urban shrinkage rate negatively impacts energy efficiency, which in turn reduces energy efficiency\u0026rsquo;s potential to mitigate carbon emissions. To further substantiate these findings, both a Sobel test and a Bootstrap sampling test were conducted. The Sobel test Z statistic is 2.028, significant at the 5% level. The Bootstrap test produces a 95% confidence interval for the mediation effect that does not include zero, further validating the mediating role of energy efficiency in the relationship between urban shrinkage rate and carbon scale.\u003c/p\u003e\n\u003cp\u003eFurthermore, we found the estimated impact of urban shrinkage rate in M8 is 0.00629, significant at the 5% level, which is both smaller in magnitude and less significant compared to the estimated value of 0.00792 in M5, significant at the 1% level. This indicates that when energy efficiency is considered, the negative effect of urban shrinkage on carbon intensity is reduced. Further confirmation of the mediating role of energy efficiency comes from the Sobel test, which yields a Z statistic of 2.944, significant at the 1% level. Additionally, the Bootstrap sampling test provides a 95% confidence interval for the mediation effect that does not include zero, validating the robustness of the findings. These results underscore that energy efficiency acts as a mediating factor, dampening the increase in carbon intensity caused by urban shrinkage.\u003c/p\u003e\n\u003cp\u003eTable 1|Test of mediating effect of energy efficiency.\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"101%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003eM1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eM2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eM3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eM4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eM5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003eM6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eM7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eM8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eVariables\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003eLog of carbon scale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eenergy efficiency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eLog of carbon scale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eLog of carbon scale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eLog of carbon intensity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003eenergy efficiency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eLog of carbon intensity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eLog of carbon intensity\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eurban shrinkage rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e-0.00413*\u003c/p\u003e\n \u003cp\u003e(-1.75)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e-0.317***\u003c/p\u003e\n \u003cp\u003e(-4.48)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e-0.00495**\u003c/p\u003e\n \u003cp\u003e(-2.07)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e0.00792***\u003c/p\u003e\n \u003cp\u003e(3.08)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e-0.317***\u003c/p\u003e\n \u003cp\u003e(-4.48)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e0.00629**\u003c/p\u003e\n \u003cp\u003e(2.44)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eenergy efficiency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e-0.00230**\u003c/p\u003e\n \u003cp\u003e(-2.03)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e-0.00257**\u003c/p\u003e\n \u003cp\u003e(-2.24)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.00563***\u003c/p\u003e\n \u003cp\u003e(-4.61)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.00515**\u003c/p\u003e\n \u003cp\u003e(-4.18)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eConstant\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e6.910***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e26.85***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e6.949***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e6.979***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e4.284***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e26.85***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e4.462***\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e4.422***\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e(55.89)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e(7.27)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e(54.79)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e(54.91)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e(31.93)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e(7.27)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e(32.73)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e(32.29)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eControls\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eCity/Year FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eObservations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e1,152\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eR-squared\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11px;\"\u003e\n \u003cp\u003e0.462\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.119\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.462\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003e0.465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e0.517\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9px;\"\u003e\n \u003cp\u003e0.119\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e0.523\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12px;\"\u003e\n \u003cp\u003e0.526\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eSobel-Z\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 44px;\"\u003e\n \u003cp\u003e2.028**\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003e2.944***\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10px;\"\u003e\n \u003cp\u003eBootstrap (1000 times) confidence interval\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 44px;\"\u003e\n \u003cp\u003e[0.00195, 0.00645]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" valign=\"top\" style=\"width: 45px;\"\u003e\n \u003cp\u003e[0.00189, 0.00628]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eStandardized beta coefficients; t statistics in parentheses. *** \u003cem\u003eP\u003c/em\u003e\u0026lt;0.01, ** \u003cem\u003eP\u003c/em\u003e\u0026lt;0.05, * \u003cem\u003eP\u003c/em\u003e\u0026lt;0.1\u0026nbsp;\u003c/p\u003e"},{"header":"Discussion and conclusions","content":"\u003cp\u003eThis research advances urban decarbonization theory by Quantifying the \u0026quot;shrinkage paradox\u0026quot; \u0026ndash; simultaneous carbon scale reduction and carbon intensity escalation. And we identified energy efficiency as critical mediator in SCs\u0026apos; low-carbon transitions. More importantly, we proposed a dual-path governance framework balancing spatial repurposing with institutional innovation. This empirical evidence repositions urban shrinkage as both challenge and catalyst in China\u0026apos;s dual carbon agenda, demanding spatially sensitive governance models that transform spatial liabilities into decarbonization opportunities.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe relationship between SCs and CEs\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study elucidates the role of urban shrinkage in CEs dynamics. Our analysis reveals a phased shift in the carbon emissions trajectories of SCs and NSCs between 2005 and 2020. We found a spatiotemporal reconfiguration of emission geographies. China\u0026apos;s evolving regional development paradigm and accelerated urbanization have precipitated a spatial redistribution of high-carbon zones, transitioning from eastern-southern coastal regions toward central-western and northern inland territories. Initial observations (2005) revealed SCs as elevated carbon scale contributors (carbon scale\u003csub\u003eSCs\u003c/sub\u003e = 24.04 Mt vs carbon scale\u003csub\u003eNSCs\u003c/sub\u003e = 22.50 Mt), yet post-2010 dynamics demonstrated SCs\u0026apos; progressive decarbonization (2020 carbon scale\u003csub\u003eSCs\u003c/sub\u003e = 33.30 Mt vs carbon scale\u003csub\u003eNSCs\u003c/sub\u003e = 50.79 Mt). Conversely, carbon intensity patterns exhibited an inverse trajectory\u0026mdash;SCs initially maintained lower intensity (2005\u0026ndash;2010 carbon intensity\u003csub\u003eSCs\u003c/sub\u003e = 3.95 tons/10⁴ RMB vs carbon intensity\u003csub\u003eNSCs\u003c/sub\u003e = 4.87 tons/10⁴ RMB) before surpassing NSCs levels post-2010 (2020 carbon intensity\u003csub\u003eSCs\u003c/sub\u003e = 2.26 tons/10⁴ RMB vs carbon intensity\u003csub\u003eNSCs\u003c/sub\u003e = 1.64 tons/10⁴ RMB). This observed scale-intensity divergence stems from two structural shifts. First, the decline in population in shrinking cities led to a reduction in carbon scale, but later exacerbated carbon intensity due to inefficient infrastructure utilization. Second, NSCs\u0026rsquo; expansion induced carbon lock-in through sprawl-driven transportation emissions and embedded energy-intensive development patterns. Furthermore, we found the mechanistic dualism in shrinkage impacts. The benchmark regression analysis framework elucidates the paradoxical implications of urban shrinkage. A 1% decrease in population is associated with a 0.495% reduction in the carbon scale (\u003cem\u003e\u0026beta;\u003c/em\u003e = -0.00495, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.1), which can be attributed to factors such as deindustrialization and a contraction in energy demand. Conversely, the same level of population decline is linked to a 0.629% increase in the carbon intensity (\u003cem\u003e\u0026beta;\u003c/em\u003e = 0.00629, \u003cem\u003eP\u003c/em\u003e \u0026lt; 0.1), a phenomenon mediated by the underutilization of infrastructure and the persistence of path-dependent energy systems.\u003c/p\u003e\n\u003cp\u003eChina\u0026apos;s shrinking cities exhibit pronounced geographical heterogeneity and resource-dependent characteristics, predominantly concentrated in regions with mono-industrial structures and path-dependent development trajectories. From a material cycle perspective, urban shrinkage driven by socioeconomic and other endogenous/exogenous factors operates through a cascading mechanism: industrial base erosion - labor market contraction - population outmigration - aggregate carbon emission reduction. Notably, China\u0026apos;s urban shrinkage manifests distinct physical-environmental effects \u0026ndash; while demographic and economic indicators decline, infrastructure legacy maintains high-carbon lock-in effects in built environments. Our mediation analysis quantifies this underlying mechanism, revealing that declining energy efficiency accounts for 0.163% of the increased carbon intensity in shrinking cities (\u003cem\u003e\u0026beta;₁\u003c/em\u003e = 0.00792, \u003cem\u003eP₁\u003c/em\u003e \u0026lt; 0.01; \u003cem\u003e\u0026beta;₂\u003c/em\u003e = 0.00629, \u003cem\u003eP₂\u003c/em\u003e \u0026lt; 0.05). We propose that this phenomenon is driven by two primary mechanisms. The first is technological inertia, characterized by slow adoption rates of new energy technologies. The second is institutional fragmentation, which weakens cross-departmental coordination in climate governance.\u003c/p\u003e\n\u003cp\u003eThe spatial analysis reveals insights into China\u0026apos;s urban shrinkage-carbon emission nexus, particularly highlighting the central region\u0026apos;s vulnerability. From 2005 to 2020, cities in this zone exhibit the highest average shrinkage rate (2.93%), surpassing eastern (1.35%) and western counterparts (2.91%), a phenomenon rooted in two interlocking mechanisms: First, the central region\u0026rsquo;s heavy dependence on carbon-intensive industries has led to a lock-in effect in its industrial framework, resulting in persistent high carbon emissions. For example, since China\u0026apos;s 13th Five-Year Plan, Inner Mongolia\u0026apos;s total coal production capacity has reached 1.34 billion tons, accounting for 1/4 of the national total. According to the 2019 China Energy Statistical Yearbook, power and heating in Inner Mongolia account for about 50% of coal consumption. Second, demographic-spatial decoupling, for example, Shandong Province experienced an annual population decline of 1.28% (2010\u0026ndash;2020), yet simultaneously saw rural residential land expand by 64,000 hectares (+5.19% total area)\u003csup\u003e30\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAn examination of municipal-level disparities reveals that medium-sized and large cities exhibit greater significance in regression analyses concerning carbon scale, while large cities and supercities show a more pronounced significance in relation to carbon intensity. This phenomenon can be attributed to the fact that medium-sized cities in China often receive limited development support, making them particularly vulnerable to urban shrinkage\u003csup\u003e31\u003c/sup\u003e. The combination of shrinkage and labor loss significantly impacts industrial output, leading to a reduction in carbon scale. Meanwhile, many large cities are heavily reliant on natural resources. As resource depletion coincides with urban shrinkage, carbon scale declines, whereas carbon intensity rises significantly. In the case of supercities, two distinct pathways emerge. First, influenced by consumerism and postmodernism, demographic challenges such as an aging population and declining fertility rates have led some supercities to experience partial shrinkage. Second, this shrinkage has led to the deterioration of public services, which has reduced the efficiency of energy system utilization, resulting in a more pronounced impact on carbon intensity.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLow-carbon development paths for SCs\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study proposes a dual-pathway decarbonization framework for SCs, integrating material stock optimization with institutional innovation to foster sustainable transitions in the post-shrinkage era. Grounded in resilience theory and circular economy theory, this strategic blueprint comprises the following key components:\u003c/p\u003e\n\u003cp\u003eWe advocate for the enhancement of metabolic processes in SCs through the implementation of spatial planning strategies informed by circular economy principles. According to the report \u0026ldquo;\u003cem\u003eAnalysis of Urban Housing Vacancy in China 2017\u003c/em\u003e\u0026rdquo;, housing vacancy rates in China\u0026rsquo;s urban areas were 18.4%, 19.5%, 20.6%, and 21.4% in 2011, 2013, 2015, and 2017 respectively. These figures present unique opportunities for circular economy transitions. The optimization and repurposing of existing resources can drive the development of a circular economy and improve energy efficiency. Urban shrinkage often leads to underutilized infrastructure, which may require reconfiguration or minor upgrades to existing systems, as well as adjustments to the distribution of public services and goods to accommodate population decline. This process may involve reallocating surplus public resources to nearby areas or redistributing them between urban and rural regions to reduce unnecessary energy consumption. SCs frequently face challenges such as idle land and low utilization rates. To address these issues, it is crucial to promote the repurposing of vacant land and improve spatial efficiency through measures such as ecological restoration, creating parks and green spaces, and transforming vacant or abandoned industrial and residential buildings into modern office spaces, cultural facilities, or hubs for innovation and entrepreneurship. Achieving this may require flexible adjustments to land property rights and the designation of land use.\u003c/p\u003e\n\u003cp\u003eSecondly, advancing urban decarbonization requires the enhancement of governance frameworks. A decline in population density often leads to underutilization of public transportation resources. To address this, big data analytics should be leveraged to optimize public transportation routes more effectively. Additionally, policy incentives are essential for attracting green investments and fostering the growth of green and low-carbon industries, such as the \u0026quot;new three\u0026quot; (new energy vehicles, lithium batteries, and photovoltaic modules). Governments should also lead in establishing a valuation and pricing system for the ecological benefits of natural resources and the environmental costs of greenhouse gas emissions. This system would provide a foundation for setting CEs standards for both corporations and individuals. Furthermore, the development of a carbon trading market is necessary to facilitate the paid transfer of public goods, such as carbon emission rights, enabling the efficient circulation of resources. Through such measures, urban decarbonization can be effectively advanced, ensuring sustainable development in the face of urban shrinkage.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eData\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe dependent variables encompass both carbon scale and carbon intensity. Specifically, the carbon scale is determined by aggregating the direct CEs attributable to agriculture, the service sector, residential activities, transportation, and energy consumption, along with the energy imported from outside the urban area. The CEs from energy are derived by applying energy conversion coefficients to various fossil fuel sources, including coal, oil, and natural gas. The data for these indicators is sourced from the China City Greenhouse Gas Working Group (https://www.cityghg.com/). The carbon intensity indicator consists of per capita CEs and carbon intensity. The population figures utilized for these calculations are derived from census data, while GDP data is obtained from the China City Statistical Yearbook (https://www.stats.gov.cn/zsk/snapshoot?reference) as well as from the statistical yearbooks and economic and social development reports available on the official websites of various cities.\u003c/p\u003e\n\u003cp\u003eThe phenomenon of urban shrinkage is primarily characterized by three categories of indicators: the urban shrinkage rate, the urban shrinkage status, and the population density change rate in built-up areas. Given that a notable characteristic of urban shrinkage is the population reduction, we employ the population change rate, which is widely utilized in existing literature, as a metric for assessing the urban shrinkage rate\u003csup\u003e32-34\u003c/sup\u003e. This indicator serves as the principal explanatory variable, while the Green coverage rate of built-up areas indicator is utilized to conduct robustness tests on the findings. Land Use and Cover Change (LUCC) data, with a resolution of 30 meters, were sourced from the Resource and Environmental Science Data Platform of the Chinese Academy of Sciences (https://www.resdc.cn/). The delineation of construction land for each city across various years was achieved using the field extraction functionality of geographic information system (GIS) software. Additionally, spatial distribution raster data (Unconstrained individual countries 2000-2020 UN adjusted ( 1km resolution )) reflecting China\u0026rsquo;s population density were obtained and adjusted according to estimates from the United Nations Population Division, via the WorldPop demographic platform (https://hub.worldpop.org/geodata). The zoning statistics function was employed to compute the average population density of built-up areas across different cities, subsequently characterizing the indicator through the multi-period change rate of population density within these areas\u003csup\u003e3\u003c/sup\u003e. The urban shrinkage rate indicator is processed through a negative standardization approach, whereby cities that have not experienced shrinkage are assigned a value of 0. The urban shrinkage status indicator is incorporated into the causal relationship model, assigning a value of 1 for cities experiencing shrinkage and a value of 0 for those that are not. For detailed indicator calculation methods and data sources, please see Supplementary Table 1.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMeasures\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo examine the effects of urban shrinkage on CEs, a two-way fixed effects model (Two-way FE) was developed, as represented in Formula 1.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"815\" height=\"66\"\u003e\u003c/p\u003e\n\u003cp\u003eIn this context, the variables \u003cem\u003ei\u003c/em\u003e and \u003cem\u003et\u003c/em\u003e denote the city and year, respectively. The term \u0026ldquo;\u003cem\u003eCarbon\u003c/em\u003e\u0026rdquo; encompasses the CEs factor, which includes the carbon scale, per capita CEs, and carbon intensity. The variable \u003cem\u003eurban shrinkage rate\u003c/em\u003e indicates the urban shrinkage rate. The term \u0026ldquo;\u003cem\u003eControls\u003c/em\u003e\u0026rdquo; refers to a set of control variables. Additionally, \u0026ldquo;\u003cem\u003eyear\u003c/em\u003e\u0026rdquo; and \u0026ldquo;\u003cem\u003ecity\u003c/em\u003e\u0026rdquo; account for annual fixed effects and city-specific fixed effects, respectively. The parameters \u003cem\u003e\u0026alpha;, \u0026beta;\u003c/em\u003e, and\u003cem\u003e\u0026nbsp;\u0026epsilon;\u003c/em\u003e represent the constant term, the regression coefficient for the independent variable, and the random error term, respectively.\u003c/p\u003e\n\u003cp\u003eA mediation effect model has been constructed to examine the potential mediating mechanism through which urban shrinkage influences CEs (refer to Equation 2-4). The conventional three-stage mediation mechanism testing approach is limited by inherent endogeneity issues\u003csup\u003e35\u003c/sup\u003e. To address these limitations, we incorporate recent findings and augment the traditional model by integrating a regression model that assesses the mediating variable in relation to the explained variable, thereby establishing a four-stage mediation mechanism testing framework. The robustness and validity of the results are further evaluated using the Sobel test and Bootstrap test, thereby enhancing the comprehensiveness and reliability of the mediation analysis\u003csup\u003e36,37\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"831\" height=\"200\"\u003e\u003c/p\u003e\n\u003cp\u003eIn the presented formula, \u003cem\u003eM\u003c/em\u003e serves as the mediating variable, while the other symbols retain their previously defined meanings. When the regression coefficients for both the indirect and direct effects exhibit the same sign, or when the direct effect is less significant or possesses a lower absolute value than the total effect, this indicates that the variable \u003cem\u003eM\u003c/em\u003e exerts a facilitative influence. Conversely, if these conditions are not met, it suggests that the variable \u003cem\u003eM\u003c/em\u003e has a suppressive effect\u003csup\u003e38\u003c/sup\u003e.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRobustness checks\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe robustness of the findings was evaluated through a series of alternative specifications and adjustments, including employing instrumental variable (IV) approach, substituting the primary explanatory variable, modifying the method of measuring urban shrinkage rate, altering the dependent variables to focus separately on carbon scale and carbon intensity, and incorporating an additional control variable, GDP per capita. We found the estimated values remain consistent with the baseline regression, supporting the validity of the conclusions (Supplementary Table 3). Specially, we use the aging rate and financial development level as IVs to alleviate the endogeneity problem in the carbon scale and carbon intensity models (Supplementary Table 2). \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLarge Language Models (LLMs)\u003c/strong\u003e \u003cstrong\u003eUsage Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the preparation of this manuscript, the authors, primarily based in China, employed Deepseek-R1 and ChatGPT-4o for linguistic quality of the manuscript. We declare that the use of LLMs was solely aimed at improving the manuscript\u0026rsquo;s readability and aligning it with the conventions of academic English writing.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eThe carbon emissions data are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.cityghg.com/\u003c/span\u003e\u003cspan address=\"https://www.cityghg.com/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. The Land Use and Cover Change (LUCC) data are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.resdc.cn/\u003c/span\u003e\u003cspan address=\"https://www.resdc.cn/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (ref. 39). The China\u0026rsquo;s population density raster data are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://hub.worldpop.org/geodata\u003c/span\u003e\u003cspan address=\"https://hub.worldpop.org/geodata\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (ref. 40). The China's demographic data are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.stats.gov.cn/sj/pcsj/rkpc/d7c/\u003c/span\u003e\u003cspan address=\"https://www.stats.gov.cn/sj/pcsj/rkpc/d7c/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. Other economic and social statistical indicators are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.stats.gov.cn/zs/tjwh/tjkw/tjzl/\u003c/span\u003e\u003cspan address=\"https://www.stats.gov.cn/zs/tjwh/tjkw/tjzl/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. The data that support the findings of this study are available on GitHub at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/yongheli11/Code-of-Urban-shrinkage-impedes-carbon-scale-but-increases-carbon-intensity-in-China\u003c/span\u003e\u003cspan address=\"https://github.com/yongheli11/Code-of-Urban-shrinkage-impedes-carbon-scale-but-increases-carbon-intensity-in-China\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. We are committed to making the fully assembled dataset publicly available in a permanent repository that issues a DOI upon acceptance.\u003c/p\u003e\u003ch2\u003eCode availability\u003c/h2\u003e \u003cp\u003eThe Python and R code for visualizing Figs.\u0026nbsp;2 and 3, along with the Stata code for the regressions utilized in this research, are available on GitHub at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/yongheli11/Code-of-Urban-shrinkage-impedes-carbon-scale-but-increases-carbon-intensity-in-China\u003c/span\u003e\u003cspan address=\"https://github.com/yongheli11/Code-of-Urban-shrinkage-impedes-carbon-scale-but-increases-carbon-intensity-in-China\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMeng, X. \u0026amp; Long, Y. 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However, existing research predominantly focuses on the impact of urban shrinkage on carbon scale, often overlooking its association with carbon intensity. This study addresses this research gap by systematically examining the dual impacts of urban shrinkage on emission scale and intensity. Using econometric models, we analyze panel data from 288 prefecture-level and higher-tier cities in China, covering the period from 2005 to 2020. Our findings show that the number of high-carbon-emission cities increased over the study period, with a gradual westward shift toward central and western regions. Shrinking cities exhibited significantly lower carbon scale but notably higher carbon intensity compared to non-shrinking cities. In shrinking cities, each 1% decline in population corresponds to a 0.495% decrease in carbon scale, but a 0.629% increase in carbon intensity. The dual effect of shrinkage was most pronounced in central China and among medium-sized cities, large cities, and supercities. Crucially, we identify energy efficiency as the critical mediating mechanism through which urban shrinkage influences both emission scale and intensity.","manuscriptTitle":"Urban shrinkage impedes carbon scale but increases carbon intensity in China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-18 04:40:40","doi":"10.21203/rs.3.rs-6297437/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4f1712aa-8f78-431c-8df6-f28f2c721beb","owner":[],"postedDate":"April 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":46776453,"name":"Social science/Environmental studies"},{"id":46776454,"name":"Earth and environmental sciences/Environmental social sciences/Climate-change adaptation"}],"tags":[],"updatedAt":"2025-06-10T08:39:14+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-18 04:40:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6297437","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6297437","identity":"rs-6297437","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}