Research on carbon emission efficiency measurement can be generally divided into categories: single-factor and multi-factor approaches. In early studies, carbon emission efficiency was usually measured as carbon emissions per unit of energy consumption (Mielnik and Goldemberg, 1999). It is worth noting that, in addition to carbon emissions per unit of energy consumption, other single-factor indicators—such as emissions per unit of GDP and emissions per capita—were also used in early literature (Schipper et al., 2001b; Schipper et al., 2001a; Stretesky and Lynch, 2009; Ang, 1999).

While such single-factor indicators are easy to calculate and interpret, their limitations are also evident. Carbon emission efficiency typically reflects the input–output performance of economic activities (Dong et al., 2013; Li Shuangjie et al., 2022) and should be viewed as the outcome of multiple production factors, including capital and labor. Therefore, a measurement based solely on energy use is insufficient, and a multi-factor approach should be considered to more accurately capture the underlying efficiency dynamics. In response to this, several multi-factor measurement methods have been proposed in the literature, among which Data Envelopment Analysis (DEA) and Slacks-Based Measure (SBM) are the two most mainstream methods.

Carbon emission efficiency with DEA models have been widely studied over the past 2 decades following the foundational work of Charnes et al. (1978). For example, Meng et al. (2016) conducted a comprehensive review of empirical studies on China’s regional energy and carbon emission efficiency from 2006 to 2015, using DEA-type models to evaluate and compare the performance of 30 provinces between 1995 and 2012. Wang and Feng (2021) applied data envelopment analysis and the Malmquist index to assess agricultural carbon emission efficiency in China from both static and dynamic perspectives, revealing significant regional disparities, with the east performing best and the west lagging behind. Han et al. (2018) proposed an improved environmental DEA cross model incorporating information entropy to dynamically calculate weights in the cross evaluation matrix, thereby enhancing the accuracy and objectivity of carbon emission efficiency analysis for China’s industrial sectors. Aside from the original DEA methods, some literature have presented more flexible approaches that combine DEA with other models, such as three-stage DEA-Tobit model (Zhang et al., 2021), SE-DEA model (Dong et al., 2017), Super-SBM DEA approach (Zhou et al., 2019), and others.

Due to the limitations of DEA and DEA-based models—particularly their tendency to overlook undesirable outputs—alternative methods such as the slacks-based measure (SBM) have become increasingly common in recent literature. Teng et al. (2021) incorporated carbon sequestration from afforestation as an exogenous variable in a modified dynamic SBM model, revealing that provinces with significant tree restoration—such as Yunnan, Qinghai, Inner Mongolia, and Guizhou—experienced notable improvements in energy and carbon emissions efficiency. Li et al. (2025) developed an improved three-stage slack-based measure combined with a super-efficiency DEA model to evaluate the environmental efficiency of China’s power generation industry.

After measuring carbon emission efficiency for a given region, the next step is to identify spatio-temporal patterns to gain a better understanding of its evolution and regional disparities. Time-series analysis, spatial analysis, and spatio-temporal analysis are well represented in the literature on carbon emission efficiency across different study areas.

On the basis of time-series analysis, researchers tract the dynamic changes in efficiency over time, identify long-term trends, and assess the policy interventions on caron emissions performance. Lee and Oh (2006) applied the logarithmic mean Divisia decomposition method to analyze CO₂ emissions in APEC countries, finding that energy efficiency and fuel switching emerged as key areas for potential international cooperation. Zhong et al. (2024) proposed a novel composite forecasting method (DCEF) that integrates Empirical Mode Decomposition, ARIMA, and Truncated Singular Value Decomposition to improve the accuracy and efficiency of daily carbon emissions prediction, particularly in the context of complex and non-stationary big data. Tran (2022) used multivariate time series analysis to examine the long-run relationship between green finance, economic growth, renewable energy consumption, energy imports, and CO₂ emissions in Vietnam, confirming cointegration among the variables and finding that renewable energy consumption and green investment Granger-cause reductions in CO₂ emissions.

While pure time-series analysis is effective in detecting dynamic changes in carbon emissions, such methods often overlook spatial variation across regions; therefore, it is vital to identify spatial patterns as well. For example, Liu and Yang (2021) utilize Malmquist-Luenberger index (ML index) and spatial Morans’I index to analyze the dynamic changes and spatial patterns of agricultural carbon emission performance (ACEP) across 30 Chinese provinces, revealing a weakening spatial aggregation effect and a catch-up trend among regions over the period from 2009 to 2019. Cheng et al. (2024) constructed a spatial correlation network to analyze the energy carbon emission efficiency of 282 prefecture-level cities in China, revealing significant regional disparities, a strong spillover effect from eastern cities, and the influence of economic development and government intervention on network formation. Besides, some newly available data are often combined with spatial methods to explore regional disparities, and nighttime light data being one of the most commonly used sources (Fang et al., 2022; Liu et al., 2022; Yang et al., 2020).

Besides identifying spatio-temporal patterns, another key aspect of carbon emission efficiency research is identifying its driving factors and underlying mechanisms. Understanding these can help researchers better evaluate policy impacts, design targeted interventions, and promote region-specific strategies for emission reduction (Dindar, 2025). These studies often use regression models such as multiple linear regression (Chen and He, 2017), spatial lag regression (Fang et al., 2022), spatial error regression (Bai et al., 2022), and spatial Durbin regression (Peng et al., 2020) to examine the factors influencing carbon emission efficiency. With the development of spatial analysis methods and increased attention to spatial variation, techniques like geographically weighted regression (GWR) (Wang et al., 2018) and geographic detectors (Zhang and Xu, 2023) are also increasingly used to identify and explain the driving mechanisms behind regional differences in carbon emission efficiency. In addition, machine learning and deep learning methods have achieved great success in recent years due to their ability to capture non-linear relationships and complex interactions among variables. For example, Xing et al. (2024) employed a non-radial, non-directional SBM-DDF model combined with machine learning algorithms to assess the carbon emission efficiency (CEE) of 284 Chinese cities from 2006 to 2020. Ma et al. (2025) used a deep learning model (the double bidirectional long short-term memory attention Q-network, DBAQN) to accurately predict building energy consumption and carbon emissions.

In addition to methodological advances, diverse categories of driving factors have been discussed in literature. Socioeconomic variables—such as urbanization rate (Sun and Huang, 2020), income level (Wang et al., 2023), and industrial structure—technological progress indicators like R&D investment (Lee et al., 2015), and natural and environmental factors such as climate (Uddin et al., 2015) and topography (Ashiq et al., 2021) are among the most commonly discussed drivers of carbon emission efficiency in the literature.

The existing literature on carbon emission efficiency has made great progress in terms of both methodological development and the identification of driving factors. Existing studies have examined carbon emission efficiency from perspectives such as policy instruments, sectoral efficiency, and spatio-temporal evolution, including analyses of green tax policies, synergistic effects between construction waste and carbon reduction, and spatial correlation networks of economic resilience (Fang et al., 2023; Wang et al., 2025c; Wang et al. 2024; Wang et al. 2025b; Wang Zhengshuang et al., 2025). However, despite these advancements, gaps still exist.

While significant attention has been given to metropolitan regions, the carbon emission efficiency of peri-metropolitan areas remains relatively underexplored. In this paper, we use the peri-metropolitan regions of the Chang-Zhu-Tan metropolitan area as the study area. After measuring carbon emission efficiency using the SBM model, a spatial pattern analysis is conducted to identify spatial clustering and distribution characteristics. Furthermore, a spatial Durbin regression model is employed to examine how the metropolitan core influences the carbon emission efficiency of peri-metropolitan regions, while also accounting for the specific characteristics of these peri-urban areas. This approach aims to fill the research gap by providing empirical evidence on the spatial interactions between metropolitan cores and surrounding peri-metropolitan regions in the context of carbon emission efficiency.

The Chang-Zhu-Tan metropolitan area, consisting of the cities of Changsha, Zhuzhou, and Xiangtan, is one of the most important metropolitan regions in central China (Figure 1). It has achieved notable success in ecological development and industrial transformation, serving as a representative model of development pathways and spatial structure in the region. This study focuses explicitly on the peripheral domain, covering 42 counties and districts over the period 2010–2022. At present, the core and peripheral areas of the Chang-Zhu-Tan metropolitan region perform different functional roles. However, the spatial variation of carbon emission efficiency (CEE) and its driving factors within these peri-metropolitan areas remains insufficiently understood.

This study examines the peripheral counties of the Chang-Zhu-Tan (CZT) metropolitan area using a panel dataset at the county and district levels. The dataset comprises carbon emissions, energy consumption, and other key socio-economic indicators. Carbon emissions data are primarily drawn from the Carbon Emission Accounts & Datasets (CEADs), China Statistical Yearbooks, and local statistical bulletins. Socio-economic variables, including GDP, industrial added value, and population density, are sourced from the Hunan Statistical Yearbook and county-level yearbooks. To enhance spatial completeness and validate county-level CO₂ emission estimates in the peripheral counties of the Chang-Zhu-Tan (CZT) metropolitan area, gridded CO₂ data from the Emissions Database for Global Atmospheric Research (EDGAR), release EDGAR_2024_GHG (1970–2023 October 2024), were incorporated. EDGAR provides annual global emissions at a spatial resolution of 0.1 ° × 0.1 °. County-level values were obtained by spatially intersecting EDGAR grids with CZT county boundaries and proportionally allocating emissions based on area coverage, while harmonizing historical administrative boundary changes. Considering the spatial clustering of industrial and urban activities within CZT, nighttime lights and local energy accounts were additionally used to refine intra-grid emission allocation where appropriate. The downscaled results were compared against CEADs and provincial energy inventories, confirming consistent spatial structure and inter-annual trends. The use of EDGAR data follows official acknowledgment requirements. To ensure data comparability, all variables are standardized to consistent units, log-transformed, and normalized. Only Total Energy Consumption (TEC) has missing data, and the absence occurs exclusively in 2022. To estimate this value, a trend-based interpolation combined with a county-to-municipal ratio extrapolation method was applied. This approach is supported by local energy statistical bulletins and historical records, which indicate that the structural relationship of regional energy consumption remains stable over a short time horizon. Since the missing portion accounts for only 1 year, the impact on overall data quality is negligible. Table 1 shows the variables and data sources used in this study.

Variable selection in this study is guided by the research objectives, methodological framework, and analytical focus. To measure carbon emission efficiency, input–output variables are constructed based on production theory within the SBM-DEA framework. Economic scale and energy input variables are incorporated to capture production capacity and direct energy use, while GDP is treated as a desirable output and CO₂ emissions as an undesired output to represent environmental costs.

To identify spatial driving mechanisms, control variables are incorporated into the spatial econometric model to reflect key structural and developmental factors. Per capita GDP and the industrial structure ratio are used as representative indicators of development level and energy intensity, while the urbanization rate captures agglomeration and land-use effects that are particularly relevant in peri-metropolitan regions. These variables enable a focused yet comprehensive examination of core–periphery interactions and spatial spillover effects without introducing redundancy.

In the process of economic production, the inputs of labor, capital, and energy not only produce industrial products but also generate by-products such as carbon dioxide (CO₂), which are considered undesirable outputs. The Slacks-Based Measure (SBM) model proposed by Tone (2001) effectively incorporates undesirable outputs into the production process, making it more consistent with real-world conditions. Compared with the traditional Data Envelopment Analysis (DEA), the SBM model is a non-radial, non-angular efficiency measure that simultaneously addresses input–output slacks and the presence of undesirable outputs. Thus, it has been widely used in evaluating carbon emission performance, ecological efficiency, and energy efficiency.

Building upon this theoretical framework, this study applies the Super-Efficiency SBM model with undesirable outputs to measure the carbon emission efficiency of counties in the Chang–Zhu–Tan (CZT) peri-metropolitan region. Each decision-making unit (DMU) is defined as a county–year observation in the panel dataset. The input variables include energy consumption, fixed asset investment, and labor force. The desirable output is gross domestic product (GDP), and the undesirable output is CO₂ emissions. The model is estimated under the assumption of variable returns to scale (VRS) to account for technological heterogeneity across counties.

Formally, let x , y g , and y b represent the vectors of inputs, desirable outputs, and undesirable outputs, respectively. The production possibility set is defined as Equation 1: P = x , y g , y b | x ⩾ X λ , y g ⩽ Y g λ , y b ⩾ Y b λ , λ ⩾ 0 (1)

The basic SBM model incorporating undesirable outputs is formulated as Equation 2: ρ = min 1 − 1 m ∑ i = 1 m s i − x i o 1 + 1 s 1 + s 2 ∑ r = 1 s 1 s r g y r o g + ∑ r = 1 s 2 s r b y r o b , s . t . x 0 = X λ + S − y 0 g = Y g λ − S g y 0 b = Y b λ − S b S − ⩾ 0 , S g ⩾ 0 , S b ⩾ 0 , λ ⩾ 0 (2)

Here, S − , S g ,and S b denote the slacks for inputs, desirable outputs, and undesirable outputs, respectively. The efficiency score 0 < ρ ⩽ 1 indicates how efficiently a DMU transforms inputs into desirable outputs while controlling for undesirable outputs. A value of ρ = 1 implies full efficiency with no slacks, while smaller values reflect inefficiency arising from excess input use or excessive CO₂ emissions.

To further discriminate between DMUs that achieve full efficiency ρ = 1 , this study adopts the Super-Efficiency SBM model (Tone, 2002). The super-efficiency SBM allows efficiency scores greater than one ρ * > 1 and is defined as Equation 3: ρ * = min 1 m ∑ i = 1 m x ¯ i x i o 1 S 1 + S 2 ( ∑ r = 1 S 1 y ¯ r g y r o g + ∑ r = 1 S 2 y ¯ r b y r o b ) , s . t . x ¯ ⩾ ∑ j = 1 , ≠ k n θ j x j y ¯ g ⩽ ∑ j = 1 , ≠ k n θ j y j g y ¯ b ⩾ ∑ j = 1 , ≠ k n θ j y j b x ¯ ⩾ x 0 , y ¯ g ⩽ y 0 g , y ¯ b ⩾ y 0 b , y ¯ g ⩾ 0 , θ ⩾ 0 (3)

The super-efficiency score ρ * represents the efficiency of each DMU relative to the frontier, and values above one indicate that a region performs beyond the efficient frontier. This model enhances the discriminatory power of efficiency assessment and ensures robustness of ranking among efficient units.

Applying this model to the CZT peri-metropolitan counties, the results reveal that regions within the metropolitan core generally achieve higher carbon emission efficiency, while peripheral counties exhibit relatively lower efficiency. Employing the super-efficiency SBM framework not only strengthens the discrimination among efficient DMUs but also ensures a theoretically comprehensive and empirically robust evaluation of carbon emission performance across the CZT region.

Here we utilize Global Moran’s I to examine whether carbon emission efficiency in the CZT peripheral regions exhibit spatial clustering. Global Moran’s I is first proposed by Moran (1950) and is used to assess the presence and strength of overall spatial autocorrelation across the study area, indicating whether regions with similar attributes are geographically clustered.

Since one of the goals of this research is to discover the spatial patterns of carbon emission efficiency in peri-metropolitan areas, we apply Global Moran’s I to analyze the peripheral regions across years.

The formula for Global Moran’s I is as follows Equation 4: I = n ∑ i ∑ j ω i j · ∑ i ∑ j ω i j x i − x ¯ x j − x ¯ ∑ i x i − x ¯ 2 (4) where x i and x j represent the values of carbon emission efficiency in region i and j , respectively; ω i j is the spatial weight based on the adjacency between region i and j , n represents the number of regions; x ¯ denotes the mean value of the carbon emission efficiency across all regions. In this study, we adopt the Queen contiguity criterion, under which two regions are considered adjacent if they share either a common border or a common vertex. Compared with the Rook criterion, Queen captures a broader set of spatial linkages, making it more suitable for county-level analysis where both edge and corner connections may reflect real socioeconomic and environmental interactions. The spatial weight matrix is constructed as symmetric and row-standardized, ensuring that the weights in each row sum to one and that spatial lags can be interpreted as local averages. To highlight the interaction between the metropolitan core and its surrounding periphery, the county-level units within the core Chang-Zhu-Tan (CZT) metropolitan area were merged into a single research unit, resulting in a total of 24 county-level units in the peripheral regions. Each unit has between 1 and 9 neighbors, with an average of 3.92 and a median of 3.50, indicating a balanced spatial adjacency structure. The sparsity threshold of “at least one neighbor” avoids isolated units that lack spatial interaction, ensuring the validity of spatial correlation analysis. Overall, only 16.32% of the potential adjacency relationships are non-zero, confirming that the weight matrix is sufficiently sparse while still capturing meaningful spatial dependence. For the global Moran’s I, we report both the statistic and its permutation-based significance level. Significance is evaluated using 999 random permutations, which generate an empirical reference distribution entirely based on randomization rather than normality assumptions. A significance level of 0.05 is adopted for inference, ensuring robust statistical testing even when the underlying distribution deviates from normality. For the local Moran’s I cluster maps, multiple testing is explicitly accounted for: Bonferroni and FDR adjustments yield a more stringent significance level of 0.00119. Together, the sign and significance of Moran’s I over time provide robust evidence of the spatial distribution and clustering dynamics of carbon emission efficiency across the study area. Importantly,the sign and significance of Moran’s I over time reveal the spatial distribution and clustering trends of carbon emission efficiency in the study area.

To further understand the local variation of carbon emission efficiency across the CZT peripheral regions, we utilize the local Moran’s I to identify spatial clusters and detect potential local spatial autocorrelation.

The formula for local Moran’s I is defined as follows Equation 5: I i = x i − X ¯ S i 2 ∑ j = 1 , j ≠ i n w i , j x j − X ¯ (5) where x i and x j represent the values of carbon emission efficiency in region i and j , respectively; ω i j is the spatial weight based on adjacency between region i and j ; x ¯ denotes the mean value of the carbon emission efficiency across all regions; S i 2 defined as follows Equation 6: S i 2 = ∑ j = 1 , j ≠ i n x j − X ¯ 2 n − 1 (6)

Cluster Maps are a key part of the results for Local Moran’s I and are often used to show spatial distribution of local clusters and outliers. Importantly, the high-high and low-low clusters represent areas where a region with high (or low) carbon emission efficiency is surrounded by nearby regions with similar values, while high-low and low-high clusters indicate that the values of nearby regions differ significantly from values of the target region. In addition, changes in local clusters can reveal underlying dynamics in regional carbon emission efficiency across time.

In the final part of this study, we aim to explore the driving mechanisms and influencing factors of carbon emission efficiency (CEE) through regression analysis. Considering the potential spatial dependence among regions, we adopt the Spatial Durbin Model (SDM), which allows us to capture both direct and indirect spatial effects.

More specifically, the SDM captures both the influence of explanatory variables within each region (the periphery of the CZT metropolitan area) and their effects on neighboring regions through spatial interactions. Therefore, a spatial regression model is employed instead of a traditional panel regression model.

The general form of the SDM is Equation 7: y = ρ W y + X β + W X θ + ε (7) where y denotes carbon emission efficiency, X is the matrix of explanatory variables (e.g., economic development, industrial structure, urbanization rate), W is the spatial weight matrix, ρ is the spatial lag coefficient, θ represents coefficients of spatially lagged independent variables, and ε is the error term. The SDM captures both direct effects (local impact of independent variables) and indirect effects (spatial spillovers).

In Spatial Durbin Models, the coefficients do not represent partial effects because feedback loops arise through spatial multiplies processes. Following LeSage and Pace (2009), we therefore compute the average direct, indirect, and total effects for each explanatory variable based on partial derivatives. Effects are obtained using 1,000 Monte Carlo simulations implemented through the impacts() function in the splm package in R. This procedure provides simulated standard errors and 95% confidence intervals.

The effects quantify (a) the influence of each variable on the region itself (direct), (b) spatial spillover impacts transmitted to neighboring regions (indirect), and (v) their sum (total). These quantities are central for policy interpretation and allow us to evaluate whether core–periphery economic linkages exert stronger local or spillover effects.

The SDM is estimated using two-way fixed effects, controlling for both county-level time-invariant heterogeneity and year-specific shocks. Fixed effects are implemented using the within transformation in the splm package, which mitigates the incidental-parameters problem associated with fixed-effects estimation in nonlinear spatial models.

Including two-way fixed effects ensures that estimated spatial spillovers reflect cross-sectional dependence rather than unobserved region- or time-specific confounders.

Overall, both the Moran’s I analysis and the spatial maps show that CEE values are becoming more geographically concentrated, with the central urban region improving more steadily than its surrounding areas.

The Moran’s I scatterplots for the years 2010, 2015, and 2022 (Figure 2) illustrate a progressive increase in spatial autocorrelation of Carbon Emission Efficiency (CEE) across the study area. Specifically, Moran’s I values rose from 0.105 (p = 0.054) in 2010 to 0.242 (p = 0.008) in 2015, and further to 0.449 (p = 0.001) in 2022. This indicates an increasingly strong spatial clustering of similar CEE values, suggesting that regions with high (or low) carbon emission efficiency have become more geographically concentrated over time.

The geographically concentrated CEE trend is further supported by Figure 3. These maps show that the Chang-Zhu-Tan metropolitan area (outlined in purple) has experienced a clear and consistent improvement in CEE. This suggests strong progress in carbon efficiency within the urban center, likely due to better infrastructure, targeted policies, or more sustainable development practices. However, the spatial-temporal patterns of Carbon Emission Efficiency (CEE) from 2010 to 2022 reveal notable regional disparities in Figure 3. As shown in the three sub-images, different trends are also revealed in the maps. While some peri-metropolitan regions show improvements in CEE over time, others exhibit declines or no significant change. This uneven pattern suggests that progress in carbon efficiency has not been equal across all areas, possibly due to variations in industrial structure, local development strategies, or access to cleaner technologies.

To better understand how CEE patterns have changed across space and time, we used Local Moran’s I to identify local clusters in 2010, 2015, and 2022. The local spatial autocorrelation of Carbon Emission Efficiency (CEE) was further analyzed through Local Moran’s I cluster maps for the years 2010, 2015, and 2022 (Figure 4). These maps show statistically significant local clusters and spatial outliers, offering a more detailed interpretation of spatial heterogeneity in CEE that complements the global Moran’s I results.

In 2010, pronounced High-High clusters (areas characterized by high CEE values surrounded by similarly high-performing neighbors) were concentrated in the northeastern part of the study area. In contrast, Low-Low clusters (low-efficiency zones bordered by other low-efficiency units) were mainly located within the central peri-metropolitan belt, adjacent to the urban core.

By 2015, the spatial clustering pattern evolved. New Low-Low clusters emerged in the southwestern region, indicating an expansion of inefficient zones, while High-Low outliers appeared in the northeast, suggesting localized disparities where high-efficiency units were surrounded by lower-performing neighbors.

In 2022, a marked intensification of Low-Low clustering was observed, particularly throughout the southwestern and southern periphery, signifying a persistent and spatially contiguous decline in CEE across multiple peri-metropolitan subregions. Meanwhile, the Chang-Zhu-Tan metropolitan core continued to exhibit a stable High-High pattern, demonstrating its position as a spatially coherent zone of sustained high carbon emission efficiency.

These findings show increasing spatial differences in environmental performance. The metropolitan center has steadily improved its CEE, while many surrounding regions have not improved or have even declined. This spatial fragmentation suggests the need for further analysis to identify the underlying factors driving these divergent trends.

To further investigate the driving factors affecting carbon emission efficiency in peri-metropolitan regions, here we use a Spatial Durbin Regression Model to account for both direct effects (local variables) and indirect effects (spatial spillover from nearby regions). The local variables include industrial structure (X₁), urbanization rate (X₂), population density (X₃), GDP growth rate (X₄), and the GDP level of the metropolitan core (X₅). In addition, we introduce an interaction term (X₆) between core city GDP and local GDP per capita to examine how local and core region economic capacities jointly influence carbon emission efficiency.

Before conducting the Spatial Durbin Regression analysis, a Variance Inflation Factor (VIF) diagnostic was first applied to detect and control for potential multicollinearity among the explanatory variables, in order to avoid bias in the regression results (Table 2). Following guidelines from existing literature, a VIF value below 5 is generally considered to indicate that no serious multicollinearity exists between a given variable and the others. Therefore, the subsequent regression analysis can be appropriately conducted.

Since there is no standard or universal accepted goodness-of-ft index for spatial regression models such as Spatial Durbin Model (SDM), Spatial Error Model (SEM), and Spatial Lag Model (SLM), we additionally employ Rao’s score (LM) tests using the 2010 cross-section. The results strongly reject the OLS specification in favor of spatial models (LM-error = 4.06, p = 0.044; adjusted LM-error = 7.68, p = 0.006; SARMA = 8.48, p = 0.014). These diagnostics indicate that both spatial lag and spatial error dependence are present, thereby supporting the SDM as the most appropriate and encompassing specification. Table 3 shows the results of the Spatial Durbin Model.

As shown in Table 3, the spatial autoregressive coefficient (ρ) is negative but not statistically significant (Estimate = −0.185, p = 0.167). Although ρ is insignificant, the presence of spatially lagged covariates in the SDM captures the spatial spillover structure more effectively than non-spatial models, and the LM/Rao’s score diagnostics confirm that a spatial specification is required. This indicates that carbon emission efficiency (CEE) across peri-urban regions exhibits spatial interaction through covariates rather than through the dependent variable itself.

Among the local variables, GDP per capita (log_X1) shows a strong and statistically significant negative association with CEE (Estimate = −6.820, p < 0.001). This suggests that regions with higher income levels may still rely on energy-intensive production structures or transitional industrial upgrading, resulting in lower CEE. By contrast, population density (log_X4) has a statistically significant positive effect on CEE (Estimate = 0.249, p < 0.001), implying that more densely populated peri-urban areas may benefit from agglomeration economies, improved energy-use efficiency, or more efficient public infrastructure. GDP growth rate (X5) also shows a significant negative association with CEE (Estimate = −0.0219, p < 0.001), which aligns with the notion that rapid expansion in peri-urban zones is often driven by energy-intensive investment cycles, industrial relocation, or construction booms, all of which may temporarily suppress efficiency.

A key finding concerns the role of the metropolitan core. Metropolitan Core GDP (metro_dev) exerts a strong and highly significant negative effect on CEE in peri-urban regions (Estimate = −9.561, p < 0.001). This result suggests that growth in the core city may initially crowd out or pressure peripheral regions—possibly through industrial transfer, increased commuting, or energy-intensive development spillovers.

However, the interaction term between core GDP and local GDP per capita is positive and strongly significant (Estimate = 0.596, p < 0.001). This indicates that peri-urban regions with stronger local economic capacity can better absorb or transform the development momentum of the core city into improved emission efficiency. In other words, richer peri-urban regions benefit more from core–periphery economic linkage, while less-developed peri-urban regions may face increased environmental pressure from core-city expansion.

In contrast, industrial structure (X2) and urbanization rate (X3) remain statistically insignificant in the SDM. Their weak direct significance may indicate that their effects are overshadowed by stronger economic and demographic forces or captured indirectly through spatial spillovers, rather than through local coefficients alone.

A further step of interpretation requires moving beyond raw SDM coefficients, because they do not directly reflect marginal impacts in the presence of spatial feedback loops. Therefore, we compute the average direct, indirect, and total effects following the LeSage–Pace partial-derivative approach. The results are presented in Table 4. The direct effects capture the impact of each covariate on a region’s own CEE, while the indirect effects quantify spillovers transmitted to neighboring regions through the spatial network. As shown in Table 4, GDP per capita (log_X1) exhibits a positive direct effect (0.112, 95% CI [0.035, 0.186]) but a negative spillover effect (−0.235, 95% CI [–0.501, −0.087]), implying that higher-income peri-urban regions benefit internally but exert negative externalities on their neighbors. In contrast, GDP growth rate (X5) shows a small negative direct effect (−0.017) but a positive and statistically meaningful spillover effect (0.067, 95% CI [0.010, 0.157]), suggesting that efficiency gains may diffuse outward even when local growth is carbon-intensive. Population density (log_X4) and industrial structure (X2) show relatively small effects, while the indirect effect of population density (0.009) also indicates mild spatial diffusion.

Overall, Table 4 demonstrates that the spatial spillover component is substantial for several key variables, underscoring the importance of using an SDM rather than a non-spatial specification.

This study investigates the spatio-temporal evolution and determinants of carbon emission efficiency (CEE) in the peripheral regions of the Chang-Zhu-Tan (CZT) urban agglomeration from 2010 to 2022. A Slack-Based Measure (SBM) model was first applied to quantify CEE, followed by global and local Moran’s I statistics to detect spatial dependence and clustering patterns. The results show that, despite an overall improvement in CEE, significant core–periphery disparities and pronounced intra-periphery heterogeneity persist. While the metropolitan core demonstrates sustained efficiency improvements, many surrounding peri-urban regions lag behind, and pockets of low-efficiency clusters persist throughout the study period.

To further explore the drivers behind these patterns, a Spatial Durbin Model (SDM) was estimated, allowing for both local effects and spatial spillovers. The SDM results indicate that GDP growth rate, population density, metropolitan core GDP, and the interaction between core GDP and local GDP per capita are all significant determinants of CEE. In contrast, industrial structure and urbanization rate show no statistically significant direct associations with CEE. The insignificant spatial lag coefficient and the significant spatial error dependence from the SEM benchmark highlight that spatial dependence arises primarily through spatially lagged covariates and unobserved spatial factors rather than through the dependent variable itself.

Moreover, the LeSage–Pace effects decomposition reveals asymmetric spillover patterns: GDP per capita exerts positive local effects but negative spillover effects, whereas GDP growth rate shows a negative direct impact but a positive spillover impact. This indicates that peri-urban development processes generate both internal and external environmental consequences.

The above findings reflect the presence of spillover effects, core-periphery disparities and intra-periphery disparities, which is similar with existing literature, particularly in studies focused on rapidly urbanizing countries (Bo et al., 2020; Ren et al., 2023; Ding et al., 2022).

Spatial spillover effects. The SDM and effects estimates demonstrate that CEE improvements diffuse through spatial networks. GDP growth, for instance, exerts a negative direct effect but a positive spillover effect, indicating that while rapid local expansion may impose short-term environmental pressures, technological upgrading and environmental management benefits diffuse to neighboring regions. This underscores the regional interdependence of peri-urban development.

Although the SDM provides robust evidence on the determinants of CEE, potential endogeneity especially between GDP growth and CEE remains a concern. Rapid GDP growth in peri-urban regions is often driven by investment- or energy-intensive activities that temporarily reduce efficiency, while improvements in CEE may arise from structural upgrading or environmental regulation that suppress short-term growth. This bidirectional relationship implies possible reverse causality.

Given the difficulty of obtaining external instruments at the county level, we applied several robustness strategies. First, re-estimating the SDM using Rook spatial weights and removing the interaction term yielded highly consistent results. Second, SAR and SEM benchmarks produced similar coefficient patterns, and the SEM’s significant spatial error term confirmed the presence of spatially structured unobserved factors. Third, the absence of residual spatial autocorrelation in the SDM (Moran’s I = −0.154, p = 0.760) confirms that spatial dependence is adequately accounted for rather than left in the error term. Lastly, the direct–indirect effects decomposition reinforces the structural plausibility of the mechanisms identified.

Although some endogeneity cannot be completely ruled out, the consistency across multiple robustness checks suggests that the principal findings are reliable. Future studies could explore spatial instrumental-variable methods or causal-inference frameworks as richer datasets become available.

While this study provides valuable insights into the spatio-temporal patterns and driving factors of carbon emission efficiency in the CZT peripheral regions, several limitations exist and should be addressed in future research.

Due to data source limitations, some important local variables (such as policy implementation measures and technological innovation indices) were not included in this study.

Future research could incorporate a broader set of local variables, conduct comparative analyses across multiple peri-metropolitan regions, and apply non-linear modeling approaches to further improve robustness.