Spatiotemporal Dynamic Evolution of Energy Rebound Effect and Sustainable Path for Energy Conservation–Emission Reduction in Resource-Based Cities of China

Abstract

Improving energy efficiency is critical for promoting energy-saving transitions in resource-based cities. However, the expected benefits of such improvements are often offset by the energy rebound effect. Based on 115 prefecture-level cities in accordance with the “National Sustainable Development Plan for Resource-based Cities” as study units, this study employs the efficiency decomposition method to evaluate the energy rebound effect and applies spatial kernel density estimation and standard deviation ellipse analysis to investigate the spatiotemporal evolution of the rebound effect across Chinese resource-based cities. Furthermore, a matrix-based classification framework is applied to identify stages of energy-saving potential and to propose differentiated transition pathways. The results reveal the following: (1) The rebound effect demonstrates fluctuating temporal patterns and a spatial shift from clustering to more dispersed distributions. (2) Temporal dynamics play a suppressive role on the rebound effect while also shaping spatial spillover interactions among cities. (3) Strategic pathway planning is essential for cities with high potential for energy conservation and emission reduction to curb the regional diffusion of the rebound effect. This study offers an assessment of the rebound effect in China’s resource-based cities, providing actionable insights for rebound risks and supporting low-carbon urban transformation.

1. Introduction

Cities are major centers of economic activity, population aggregation, and energy consumption [1], accounting globally for 60% to 80% of total energy use [2]. In China, this proportion is already 70% and is expected to rise to 83% by 2030 [3]. Resource-based cities, whose economies heavily depend on the extraction and processing of natural resources, often feature high energy intensity and outdated industrial structures, making them critical yet vulnerable nodes in China’s energy transition [4].

Against the backdrop of intensified global climate goals, China faces mounting internal and external pressures to promote green transformation, enhance energy efficiency, and reduce emissions. While energy efficiency improvements are widely regarded as an effective strategy to reduce energy consumption and promote sustainable urban development [5], a growing body of evidence suggests that such improvements may trigger a rebound effect. This effect occurs when gains in efficiency reduce the effective cost of energy services, leading to increased consumption through substitution, income, or output effects [6,7,8]. As a result, the actual energy-saving benefits may be partially or fully offset. Given their high dependence on fossil energy and strong responsiveness to policy and technological changes, resource-based cities are likely to exhibit complex and region-specific rebound effects. However, current studies tend to focus on national-level estimations or sectoral analyses, lacking detailed spatial assessments at the city scale. Without a clear understanding of the spatiotemporal patterns and influencing factors of the rebound effect in resource-based cities, it becomes difficult to identify where energy-saving potentials are truly located or to design tailored policy pathways.

Therefore, this study aims to systematically examine the temporal evolution and spatial distribution of the energy rebound effect in Chinese resource-based cities, identify typical patterns of energy-saving potential, and clarify region-specific energy policy paths. The findings of this study are expected to contribute theoretical insights into the spatial heterogeneity of the energy rebound effect, offer practical guidance for low-carbon transformation in resource-based cities, and support China’s broader goals for sustainable and energy-efficient urban development.

The rebound effect, originally proposed by Khazzoom and Brookes and theoretically extended by Saunders (1992) [9] within a neoclassical growth framework, has become a central concept in energy economics [10,11]. The relevant literature can be reviewed from three major perspectives: conceptual foundations, influencing factors, and methodological approaches.

The formation of the rebound effect is typically explained through technological progress and the associated behavioral and economic responses. Technological advancements improve energy efficiency, but the resulting decline in the cost of energy services may induce behavioral shifts—such as increased consumption—thereby offsetting some of the energy savings. Scholars categorize rebound effects into direct, indirect, and economy-wide effects, depending on the nature of the response and scope of analysis [12]. Macro-level analyses are often considered more effective than household-level studies for capturing the full elasticity of rebound effects, especially in developing contexts where energy saturation has not been reached [13]. In the Chinese context, due to the relatively late development of market-based energy systems and incomplete energy price formation, researchers have adopted alternative modeling techniques to infer the mechanism and magnitude of the rebound effect [14].

A range of factors has been identified as key drivers of the rebound effect. These include macroeconomic structure, sectoral energy consumption behaviors, and the nature of energy efficiency interventions. Galvin (2014) [15] shows that rebound effects tend to be more pronounced in high-income economies due to greater energy demand elasticity. In the Chinese setting, Xu et al. (2021) [16] argue that sector-specific planning and differentiated policies are necessary, as uniform efficiency interventions may yield uneven rebound outcomes across industries. Additionally, Kern et al. (2022) [17] highlight the contested effectiveness of typical policy instruments—such as energy taxes and efficiency standards—in mitigating rebound effects, stressing the need for more adaptive, context-sensitive policy designs.

Empirical estimation of the rebound effect varies widely based on regional data availability and methodological choices. In developed countries, long-term panel data and well-established energy pricing systems enable more direct econometric assessments. For example, Belaid et al. (2018) [18] used French household heating data to quantify direct rebound effects, while Chitnis et al. (2020) [19] explored both direct and indirect effects in the UK by disaggregating household expenditures. In contrast, due to China’s regulated energy pricing, researchers often rely on indirect estimation techniques. Kong et al. (2023) [20] employed a Cobb–Douglas production function and Solow residuals to estimate rebound effects at macro-, industry, and sectoral levels in Beijing. Ouyang et al. (2021) [21] adopted a stochastic frontier model to examine how improved electricity efficiency influenced total consumption, ultimately confirming that substitution and income effects could diminish net energy savings. The choice of method remains largely contingent on the research context and data granularity, a consensus broadly shared across the literature.

Prior studies have provided valuable insights into the rebound effect by investigating its mechanisms, influencing factors, and policy implications across various scales. Most existing research focuses either on the macro-national level or the micro-household level [22,23]. However, resource-based cities, which are the critical nodes in China’s national energy security and industrial structure, have received limited attention in this literature. Despite their high energy intensity and structural dependence on resource extraction and consumption, few studies have examined the rebound effect within this urban typology.

Additionally, much of the existing work emphasizes the identification of influencing factors [24,25], with relatively little exploration of the spatiotemporal dynamics of the rebound effect. Given the geographic and developmental diversities across Chinese cities, particularly among resource-based cities at different stages of transformation, it remains unclear whether the rebound effect exhibits regionally differentiated patterns or temporal persistence. This omission limits our understanding of how local rebound dynamics evolve over time and space.

Furthermore, while many scholars recognize that the rebound effect can offset energy savings and undermine sustainability goals [26], few studies explicitly integrate this phenomenon with empirical estimation of energy conservation potential. This gap restricts a holistic understanding of how the rebound effect interacts with actual energy-saving capacities and policy trajectories at the regional level.

In light of these limitations, this study centers on resource-based cities in China and investigates the energy rebound effect from a spatiotemporal perspective, using panel data and spatial simulation techniques. Specifically, it addresses three core gaps: (1) the lack of empirical research on rebound effects in resource-based cities, (2) the absence of dynamic and spatial pattern analyses, and (3) the insufficient integration between rebound effects and energy-saving potential assessment. By doing so, the study contributes new empirical evidence and methodological tools to support low-carbon transition strategies in resource-intensive urban contexts, aligning with national sustainability and energy security priorities.

To address these gaps, this study examines the energy rebound effect in China’s resource-based cities. It applies spatial kernel density estimation and a standard deviation ellipse to analyze spatiotemporal evolution and employs a matrix classification method to identify energy-saving potential and transformation paths. This integrated approach captures both the dynamic patterns and spatial heterogeneity of rebound effects, offering empirical insights into their impact on low-carbon transition. By linking rebound effect with regional energy-saving assessments, the study provides practical evidence to support differentiated and sustainable policy strategies in resource-intensive urban areas.

2. Methods and Data Description

2.1. Measurement of Energy Rebound Effect and Sensitivity Considerations

Before measuring the energy rebound effect, it is essential to ascertain the total energy consumption of each city. Due to the lack of official data on total energy consumption at the prefecture level in China, this study adopts the approach of Liu et al. (2022) [27], using standard coal conversion coefficients from the China Energy Statistical Yearbook to uniformly estimate city-level energy use. Focusing on natural gas, liquefied petroleum gas, and electricity—given their widespread use and data availability—city-level consumption is multiplied by the respective coefficients and summed to approximate the total energy consumption in standard coal equivalents.

While this approach may omit certain energy sources such as coal and diesel, introducing some degree of measurement error, its key strength lies in ensuring cross-city comparability and methodological consistency. The primary objective of this study is not to precisely quantify absolute energy consumption but to classify urban energy rebound effect types and explore their spatiotemporal evolution. To reinforce the robustness and scientific validity of the findings, this paper incorporates a standard deviation ellipse and spatial kernel density estimation for cross-validation. Furthermore, sensitivity tests based on ±5% variation in conversion coefficients show stable spatial patterns and classifications, suggesting that any estimation bias is unlikely to materially affect the study’s relative conclusions.

$$E=\sum E_i=\sum T_i\ast {\delta }_i$$

(1)

In the equation above, $E$ is the total energy consumption, $T_i$ denotes the consumption of natural gas, LPG, and electricity, respectively, and ${\delta }_i$ is the different energy consumption coefficients of 13.300, 1.714, and 1.229, respectively. On this basis, the energy intensity can be further expressed as:

$$EI={\displaystyle \frac{E}{G}}$$

(2)

In the equation above, $EI$ is the energy intensity, and $G$ represents the gross domestic products.

Firstly, technological progress has contributed to a decrease in energy intensity. Therefore, the reduction in energy consumption resulting from this decrease in energy intensity can be expressed as:

$$S_{t+1}=({EI}_t-{EI}_{t+1})G_{t+1}$$

(3)

In the formula above, $t$ represents different years in the study.

Secondly, the technological progress can drive energy economic growth, which, in turn, generates new demand for energy resources inputs, thereby increasing energy consumption. Therefore, the increase in energy consumption due to technological progress can be expressed as:

$${TE}_{t+1}={\tau }_{t+1}(G_{t+1}-G_t){EI}_{t+1}$$

(4)

In the formula above, ${\tau }_{t+1}$ is the rate of technological progress. Given that energy efficiency represents more of a broad technical progress in terms of integrated productivity, this paper needs to decompose the rate of technical progress from energy efficiency in order to accurately measure the actual effect of technical progress on energy consumption. With reference to the relevant literature [11], this paper uses the DEA-BCC model to estimate energy efficiency and decompose the rate of technical progress from it.

$$\left\{\begin{array}{l}max\alpha \\ s.t.{\displaystyle \sum _{i=1}^n} {\beta }_i{x}_i+s^{-}=x_0,{\beta }_i⩾0,s^{-}⩾0,\\ \\ i=\mathrm{1,2},3\cdots n\\ \\ {\displaystyle \sum _{i=1}^n} {\beta }_i{y}_i-s^{+}=\alpha y_0,s^{+}⩾0\\ \\ {\displaystyle \sum _{i=1}^n} {\beta }_i=1\end{array}\right.$$

(5)

In the formula above, $\alpha$ measures the relative efficiency of each decision-making unit, where higher values indicate greater efficiency. $i$ denotes the year, with $n=19$ total years in this study. ${\beta }_i$ is the weight vector of inputs and outputs for year $i$, where $x_i$ and $y_i$ are the input and output values, and $s^{+}$, $s^{-}$ are their slack variables. $x_0$ and $y_0$ represent the optimal input and output levels. If $\alpha =1$ with zero slacks, the unit is fully DEA efficient. If $\alpha =1$ but slacks exist, it is weakly efficient. If $\alpha <1$, the unit is inefficient

Ultimately, the ratio between the increase in energy consumption due to technological progress and the decrease in energy consumption can be expressed as an energy rebound according to the theory of the rebound effect [28], as follows:

$${RE}_{t+1}={\displaystyle \frac{{\tau }_{t+1}(G_{t+1}-G_t){EI}_{t+1}}{({EI}_t-{EI}_{t+1})G_{t+1}}}\times 100\mathrm{\%}$$

(6)

The rebound effect reflects how much of the expected energy savings from improved energy intensity is offset by increased energy demand, with the classification shown in

Table 1. Classification of rebound effect levels and interpretations.

Range	Level	Interpretation
$RE=0$	no rebound	full energy savings achieved
$0<RE<0.5$	weak rebound	most savings retained
$0.5\le RE<1$	strong rebound	part of savings offset, but net savings remain
$RE=1$	no net savings	all gains offset by increased demand
$RE>1$	backfire effect	energy use increases beyond initial levels

.

2.2. Spatial Kernel Density

Spatial kernel density estimation is employed to reveal the continuous spatial distribution and clustering patterns of the energy rebound effect across cities, enabling intuitive visualization of spatial heterogeneity and dynamic evolution [29]. Based on the ordinary kernel density estimation method, the incorporation of time and space parameters results in a spatial kernel density, which estimates the probability density of a random variable and describes its distribution pattern conditioned on space–time. The joint kernel density function of $x$ and $y$ is denoted by $f\left(x,y\right)$, while the distribution of $y$ given $x$ is represented by $g\left(y|x\right)$. In this study’s spatial kernel density analysis, the bandwidth parameter $h$ controls the smoothness of the estimated density curve, where smaller values of $h$ result in less smooth curves but higher estimation precision. Existing studies commonly set the bandwidth within the interval [0, 1] [30]. Balancing the need for capturing data variability and ensuring estimation accuracy, this study sets $h=0.05$. This value has been validated through multiple simulation to effectively capture the evolutionary characteristics of the energy rebound effect, ensuring both estimation precision and strong capability in identifying distribution patterns.

$$f\left(x,y\right)={\displaystyle \frac{1}{n{h}_x{h}_y}}{\sum }_{i=1}^n{K}_x\left({\displaystyle \frac{X_i-x}{h_x}}\right)K_y\left({\displaystyle \frac{Y_{i-}y}{h_y}}\right)$$

(7)

$$g\left(y|x\right)={\displaystyle \frac{f(x,y)}{f\left(x\right)}}$$

(8)

2.3. Standard Deviation Ellipse

The standard deviation ellipse can be used to analyze the spatial distribution characteristics of geographical elements from a global perspective [31]. In this study, the turning angle and the long semi-axis of the ellipse were used to reflect the spatial dominant direction of the energy rebound effect, while the short semi-axis and the average shape index were used to reflect its equilibrium level. The center of gravity and the moving distance were also used to reflect the distribution and evolution characteristics of the rebound effect. These parameters were extracted from ArcGIS10.8 software.

2.4. Spatial Panel Model Analysis

Given the potential for regional linkage and spatial diffusion mechanisms in the rebound effect across geographic dimensions, it is necessary to introduce spatial panel models to empirically test its spatial dependence and dynamic propagation effects [4]. To this end, this study constructs a spatial autoregressive model and a spatial Durbin model to identify spatial spillover paths and influencing mechanisms of the rebound effect across regions. SAR is used to capture how rebound levels in neighboring cities influence local outcomes, while the SDM further incorporates spatial lags of explanatory variables to assess both direct and spillover effects. The models allow for empirical identification of spatial correlation patterns and heterogeneous responses under different spatial weight matrices, both contiguity and distance based, enhancing our understanding of the rebound effect’s spatiotemporal dynamics.

$$\begin{array}{l}SAR:(Energ{y}_{i,t+1}-Energ{y}_{i,t})\\ =\alpha +\beta (Energ{y}_{i,t})+\rho {\displaystyle \sum _{j-1}^n}{w}_{ij}(Energ{y}_{i,t+1}-Energ{y}_{i,t})+{\mu }_i\\ +{\eta }_t+{\epsilon }_{i,t}\end{array}$$

(9)

$$\begin{array}{l}SDM:(Energ{y}_{i,t+1}-Energ{y}_{i,t})\\ =\alpha +\beta (Energ{y}_{i,t})+\rho {\displaystyle \sum _{j-1}^n}{w}_{ij}(Energ{y}_{i,t+1}-Energ{y}_{i,t})\\ +\gamma {\displaystyle \sum _{j-1}^n}{w}_{ij}\left(Energ{y}_{i,t}\right)+{\mu }_i+{\eta }_t+{\epsilon }_{i,t}\end{array}$$

(10)

2.5. Energy Conservation and Emission Reduction Potential Measurement

To capture the joint inefficiencies in both energy use and environmental impact, this paper, based on Sun and Huang’s (2021) [32] idea and methodology, incorporates slack variables to assess energy conservation potential while also accounting for CO₂ emissions, the primary source of air pollution, as an undesired output in the modeling of reduction potential. The geometric model can be expressed as follows (Figure 1):

Under the basic production model, the unitized equal output curve is ${PP}^{\prime }$, with energy, capital, and human resources being the input factors. Points $B$ and $C$ on the production frontier indicate efficiency, while point $A$, located above the production frontier curve, represents inefficiency, as it requires more resources to achieve the same output. According to Farrell’s (1957) [33] definition of the production function, the efficiency at point $A$ can be geometrically expressed as $O{A}^{\prime }/OA$, while point $B$ is the Pareto optimal point, as at point $A\prime$, the energy input can be further reduced by ${BA}^{\prime }$ to reach the production frontier. At point $A$, inefficiency losses occur due to excessive energy input ${AA}^{″}$, caused by technical inefficiency, and slack variable $A^{\prime }B$, resulting from the misallocation of energy resources. Thus, $A^{″}+A^{\prime }B$ represents the amount of energy adjustment required at inefficient point $A$ to reach the target point $B$.

Based on the analysis above, this paper defines the relative energy efficiency at the outset:

$${ERE}_{it}={\displaystyle \frac{{TEI}_{it}}{E_{it}}}={\displaystyle \frac{E_{it}-{LEI}_{it}}{E_{it}}}$$

(11)

In the equation above, ${TEI}_{it}$ represents the energy input required for optimal production on the frontier in period $t$ for city $i$; $E_{it}$ represents the actual energy input; ${LEI}_{it}$ is the energy over-input relative to the optimal production frontier and can be regarded as the energy conservations achieved or the slack in energy input. Accordingly, the specific energy conservation potential for city $i$ in period $t$ can be derived, defined as follows:

$${PEC}_{it}={\displaystyle \frac{{LEI}_{it}}{E_{it}}}$$

(12)

In the equation, the value of ${PEC}_{it}$ reflects the degree of energy conservation potential in the production process. Similarly, the expression for the reduction potential can be derived as follows:

$${PER}_{it}={\displaystyle \frac{{{AE}_{it}-TEI}_{it}}{A{E}_{it}}}$$

(13)

In the equation above, ${AE}_{it}$ denotes the actual carbon emissions in period $t$ in city $i$, and ${TEI}_{it}$ denotes the pollutant emissions at the target point on the production frontier.

2.6. Data Sources

Due to missing data, this paper now selected 115 prefecture-level cities in accordance with the “National Sustainable Development Plan for Resource-based Cities” as the study units. The input factors of energy efficiency were represented by capital, labor, and energy [34], while the GDP was used to represent the output factor. The capital stock is estimated using the perpetual inventory method, with a capital depreciation rate of 10.96% to reflect capital input [35], the number of employees at the end of the year is used to reflect labor input, and total energy consumption is used to reflect energy input. All indicators were obtained from the China Urban Statistical Yearbook and the socio-economic bulletin of each prefecture-level city, except for the capital stock, which required additional estimation. Additionally, carbon emissions were selected as the primary proxy for air pollution emissions in this study, with the data sourced from published articles in Scientific Data [36].

3. Results

3.1. Description of Basic Factual Features

The energy rebound effect refers to the phenomenon where the energy conservation and emission reduction achieved through energy efficiency improvements are partially or fully offset by the increased demand for products and energy consumption. Therefore, classify Chinese resource-based cities into four stages based on their development plans: growing, mature, declining, and renewable. This study will analyze the trends in energy efficiency and energy consumption in each category and conduct a preliminary investigation into the preconditions for the energy rebound effect, as shown in Figure 2.

In terms of the energy efficiency development trend, except for growing resource-based cities that demonstrated a temporary rise followed by a decline, energy efficiency across Chinese resource-based cities generally exhibited high volatility and stage-specific divergence. This fluctuation coincides with major economic shifts and policy transitions, such as the 2008 stimulus package and the 2013 energy intensity targets, highlighting the sensitivity of efficiency levels to macroeconomic and regulatory changes. Regarding energy consumption, aside from brief deviations in 2009 and 2014, which corresponded to the global financial crisis aftermath and industrial structural adjustments, the overall energy use in resource-based cities has shown a continuous upward trend. Despite differences in the average levels of consumption across city types, the yearly energy consumption curves remain broadly consistent, reflecting the inertia of industrial energy demand.

When comparing energy consumption and energy efficiency, the decoupling becomes apparent: while energy efficiency fluctuates in three-year cycles, likely influenced by policy enforcement lags or investment cycles, energy consumption trends upward steadily, showing limited responsiveness to efficiency gains. This suggests that improvements in energy efficiency have not effectively curbed consumption growth, indicating persistent rebound effects.

These findings imply that despite periodic improvements in energy efficiency, resource-based cities continue to consume more energy due to structural and behavioral inertia. The persistence and expansion of the rebound effect across all stages reveal the limitations of efficiency-driven policies and underscore the need for coordinated interventions that integrate energy efficiency with industrial restructuring and demand-side management.

3.2. Spatiotemporal and Morphological Evolution of the Energy Rebound Effect

3.2.1. Spatiotemporal Evolution Analysis of the Energy Rebound Effect

After confirming the occurrence conditions for the rebound effect, this paper proceeds to classify the rebound effect values of each resource-based city and analyze their evolutionary characteristics at four characteristic time points: 2007, 2011, 2015, and 2019, shown in Figure 3.

In terms of the chronological development, the evolution of China’s resource-based cities has shown a shift from predominantly experiencing backfire effects at the beginning of the study period to a greater control of energy rebound effects in 2015, resulting in an increase in weak rebound cities. However, at the end of the study period, while the number of super-conserved cities increased, the number of cities experiencing backfire effects also increased, leading to a divergent trend in the energy rebound effect in resource-based cities. The most significant decline in the energy rebound effect between 2011 and 2015 can be attributed to the issuance of multiple regulations, including the “Opinions on Accelerating the Merger and Reorganization of Coal Mining Enterprises” and the “Circular on Further Eliminating Backward Coal Mining Capacity and Promoting the Consolidation and Closure of Coal Mines” by the State Council and the National Energy Administration after 2010. These regulations have curbed the substitution effect of energy rebounds in China’s resource-based cities and have led to better realization of expected energy conservation.

In terms of spatial patterns, resource-based cities in the south have shown a lower energy rebound effect than those in the north, and those in the east have shown lower rebound effects than those in the west. Differences in location, resource endowment, and industrial structure can have an impact on the distribution of the energy rebound effect. Among all stages of resource-based cities, renewable resource-based cities have gradually reduced their dependence on energy consumption by optimizing traditional industries and developing non-resource-based industries, leading to the lowest rebound effect at all time points. On the other hand, growing resource-based cities have the highest rebound effect among all stages of resource-based cities, as energy efficiency development is slower than the growth in energy consumption demand due to ongoing resource and industrial developments.

3.2.2. Spatial Morphological Evolution Analysis of the Energy Rebound Effect

Based on the initial observation of the spatiotemporal pattern in previous section, this paper now conducts a detailed analysis of the spatial pattern changes of the rebound effect from an evolutionary perspective. Utilizing the standard deviation ellipse analysis method, this study quantitatively identifies the evolutionary dynamics of the energy rebound effect in Chinese resource-based cities at four time points: 2007, 2011, 2015, and 2019. These results are presented in

Table 2. The standard deviation elliptic parameter of energy rebound effect.

Year	Angle of Rotation/°	Major Axis/km	Short Axis/km	Average Shape Index	Barycentric Coordinates	Moving Distance/km
2007	44.54	1444.95	669.76	0.46	113.56° E, 34.84° N
2011	45.64	1542.65	765.16	0.50	114.06° E, 34.93° N	56.23
2015	63.41	1451.16	1105.71	0.76	111.86° E, 34.65° N	247.40
2019	40.37	1698.88	739.12	0.44	114.94° E, 35.15° N	350.00

.

Regarding the standard deviation ellipse, Chinese resource-based cities’ average shape index gradually increased from 0.46 in 2007 to 0.76 in 2015, maintaining a good elliptical shape. The mean shape index gradually decreased from 0.76 in 2015 to 0.44 in 2019, returning to the level observed in 2007. The elliptical shape also deviates from the perfect circle, suggesting that in Chinese resource cities, the energy rebound effect tends to cluster in the early stages and gradually becomes more decentralized and staggered over time.

Regarding rotation angle, it increased from 44.54° in 2007 to 63.37° in 2015, indicating a shift in the spatial distribution pattern of the energy rebound effect from a north–south direction to a northeast–southwest direction. In 2019, the rotation angle decreased to 40.37°, and the spatial pattern of the energy rebound effect shifted back to a north–south direction.

Regarding the barycentric coordinates and trajectory, the center of gravity of each characteristic point shifts between 111.86 and 114.94° E and 34.65 and 35.15° N. Specifically, at the prefecture level, the center of gravity is mainly located around Sanmenxia and Xinxiang, which did not show a significant shift trajectory in the observed years.

3.3. Spatiotemporal Dynamic Simulation of the Energy Rebound Effect

Building on the previous analysis of energy rebound effect in Chinese resource-based cities, this study now employs the spatial kernel density model to simulate the evolution process and spatial distribution patterns of the energy rebound effect in Chinese resource-based cities.

3.3.1. Unconditional Kernel Density Analysis

Under the unconditional setting, Figure 4a presents the three-dimensional kernel density of the energy rebound effect in resource-based cities. A 3-year lag is adopted in the spatial dynamic kernel density analysis to capture the delayed responses of time effect. This temporal window allows for a more accurate reflection of spatiotemporal evolution patterns [37]. The Z-axis represents the conditional kernel density, which reflects the probability of conditional occurrence at each point in the plane. By rotating the vertical plane, the X- and Y-axes were processed in parallel, and the resulting section plane in Figure 4b illustrates the transfer probability distribution of energy rebound effect from year t to year t + 3.

In terms of the distribution state, the density contour of the rebound effect is mainly distributed below the negative 45-degree diagonal, with the primary peak of kernel density located in this area and several side peaks extending in parallel. This phenomenon indicates that the energy rebound effect in Chinese resource-based cities shifts significantly from year t to year t + 3 without considering spatial factors, showing an overall decreasing trend. In general, the time factor causes the energy rebound effect in Chinese resource-based cities to gradually converge in the range of 0 to 0.5 effect values, resulting in a spatial distribution pattern with the weak rebound effect dominating and super-conserved and strong rebound coming second. Additionally, the density contour is primarily parallel to the X-axis, also indicating that an increase in energy consumption does not necessarily lead to an increase in the energy rebound effect. This highlights the potential for energy conservation and emission reduction in Chinese resource-based cities, which is worth exploring.

3.3.2. Spatial Static Kernel Density Analysis

Building on the analysis of the unconditional situation, this study now investigates the potential spatial effects on energy rebound in Chinese resource-based cities. Figure 5 shows the results of this analysis.

In terms of the distribution state, the density contours are concentrated along the negative 45-degree diagonal, with the main peak of kernel density in the upper left corner, and multiple lateral peaks within the range of 0 to 0.5 rebound effect values. This indicates that under spatial conditions, without the consideration of the time span, areas with backfire effects are spatially correlated and tend to be adjacent to each other. In contrast, cities with weak rebound effects are interspersed with those with high rebound effects and do not exhibit significant spatial correlation. Moreover, the contour of the kernel density from −0.5 to 1 in neighboring regions is parallel to the X-axis, suggesting that the energy rebound effect in the local region usually remains weak even when neighboring regions are experiencing weak to strong rebound effects. This indicates that the spatial spillover effect of neighboring regions does not significantly influence the energy rebound effect in Chinese resource-based cities.

3.3.3. Spatial Dynamic Kernel Density Analysis

Subsequently, this study now further investigates the temporal and spatial correlations of the energy rebound effect in Chinese resource-based cities by analyzing the dynamic kernel density with both temporal and spatial conditions, as illustrated in Figure 6.

In terms of distribution state, the spatial dynamic kernel density exhibits a multi-peaked distribution, with density contours mostly clustered around the negative 45-degree diagonal. This suggests that the neighboring regions’ energy rebound effect in year t has a certain impact on the local region’s energy rebound effect in year t + 3 under a three-year time lag, and resource-based cities in China tend to experience a shift toward lower rebound effect levels. In terms of the direction of distribution, the energy rebound effect is characterized by a double-dominant distribution, with density contours roughly parallel to the x-axis for values below −0.5, indicating that the spatial distribution of the energy rebound in resource-based cities in China is dominated by weak and strong rebounds under both spatial and temporal conditions. Moreover, the level of super-conserved effect in neighboring regions has a lagging effect on the energy rebound in the local region through positive spillover effects. Compared to the spatially static kernel density, the dynamic kernel density, with the addition of a time lag, ranges from 1 to a low effect of 0.5 to 0, indicating that time factors have a significant influence on the spatial interaction of the energy rebound effect between cities.

3.4. Empirical Validation

To further validate the spatial and temporal patterns of the energy rebound effect identified before, this section employs spatial econometric regression models to test their robustness from an empirical perspective. By introducing spatial lag (SAR) and spatial Durbin (SDM) models, this paper aims to assess both the direct and spillover impacts of the energy rebound effect under different spatial adjacency structures, thereby offering empirical evidence for the underlying mechanisms of spatiotemporal evolution, as shown in

Table 3. Spatial econometric analysis of the energy rebound system effect.

Matrix	-	Contiguity Based		Distance Based
Model	OLS	SDM	SAR	SDM	SAR
β	−0.988 *** (0.024)	−0.898 *** (0.028)	−0.894 *** (0.027)	−0.894 *** (0.027)	−0.888 *** (0.027)
ρ		0.082 *** (0.023)	0.053 ** (0.023)	0.497 *** (0.065)	0.375 *** (0.089)
γ		0.083 ** (0.041)		0.406 ** (0.162)
sigma2		0.176 *** (0.007)	0.177 *** (0.007)	0.172 *** (0.008)	0.173 *** (0.007)
Time	YES	YES	YES	YES	YES
Individual	YES	YES	YES	YES	YES
R2	0.520	0.455	0.454	0.454	0.450

. ** and *** represent significance levels of 5% and 1% respectively.

The regression results empirically validate the spatiotemporal evolution trends identified in the previous analysis. First, the core explanatory variable—energy efficiency—shows a significantly negative coefficient across all models, −0.988 in OLS and −0.894 to −0.898 in the SAR model and SDM, all significant at the 1% level, confirming that improvements in energy efficiency effectively suppress the rebound effect. This aligns with the kernel density analysis showing a downward shift of the density peak and convergence toward a weaker rebound. Second, although the spatial lag coefficient ρ under the 0–1 contiguity matrix is positive, the spatial error term γ is only 0.083 and weakly significant, indicating limited static spatial spillover. This supports the static kernel density finding of interspersed weak and strong rebound cities without strong spatial clustering. Lastly, dynamic kernel density analysis revealed a time–space convergence toward lower rebound levels and lagged influence from neighboring cities. This is corroborated by a significantly stronger spatial error term under the distance-based matrix, suggesting growing spatial spillovers over time. Together, the regression findings provide robust empirical support for the observed patterns of temporal convergence, spatial differentiation, and dynamic spillover, reinforcing the credibility and scientific rigor of this study’s conclusions on the spatiotemporal evolution of the energy rebound effect.

3.5. Measurement of Energy Conservation and Emission Reduction Potential

The above studies demonstrate the prevalence of the energy rebound effect at different stages in resource-based cities, resulting in significant energy losses and excessive carbon pollution in China. Therefore, this study aims to quantify the energy-saving and emission-reduction potentials of resource-based cities at different stages, providing a reference for designing efficient energy-saving pathways. Due to space constraints, only four characteristic time points—2007, 2011, 2015, and 2019—are selected to present the results in

Table 4. Change in energy conservation potential of various resource-based cities.

	Energy Amount That Can Be Saved	Conservation Potential	Total Share	Energy Amount That Can Be Saved	Conservation Potential	Total Share
		2007			2011
Growing	133.87	48.91%	3.63%	176.20	36.37%	3.33%
Mature	1556.56	49.66%	42.15%	2286.53	53.88%	43.20%
Declining	1080.91	75.86%	29.27%	1319.33	67.41%	24.92%
Renewable	921.44	45.60%	24.95%	1511.39	48.84%	28.55%
		2015			2019
Growing	335.59	55.54%	5.26%	352.95	35.65%	4.47%
Mature	2825.38	60.06%	44.28%	3836.92	54.41%	48.56%
Declining	1303.55	61.02%	20.43%	1510.93	58.67%	19.12%
Renewable	1915.94	59.62%	30.03%	2200.84	56.80%	27.85%

and

Table 5. Change in emission potential of various resource-based cities.

	Emission Amount That Can Be Saved	Emission Potential	Total Share	Emission Amount That Can Be Saved	Emission Potential	Total Share
		2007			2011
Growing	917.79	49.76%	3.63%	871.81	30.03%	2.99%
Mature	10,054.96	44.36%	39.73%	12,598.68	50.77%	43.14%
Declining	7505.65	75.21%	29.66%	7353.65	64.46%	25.18%
Renewable	6828.38	43.02%	26.98%	8382.57	45.18%	28.70%
		2015			2019
Growing	1414.43	42.11%	4.46%	2199.26	38.68%	4.53%
Mature	13,596.23	51.50%	42.88%	23,651.75	56.43%	48.82%
Declining	6222.25	54.95%	19.63%	8718.36	59.09%	18.00%
Renewable	10,471.10	55.36%	33.03%	13,878.81	61.42%	28.65%

.

In general, the energy-saving potential and emission-reduction potential of resource-based cities are comparable at all stages, indicating homogeneity in energy waste and carbon pollution in real production. Energy-saving and carbon emission-reduction tasks are characterized by consistent objectives. During the study period, the average energy conservations that could be achieved by resource-based cities at each stage amounted to 14,144,500 tons of standard coal, with an energy-saving potential of 56.07%. The average emission reduction achievable amounted to 78,485,600 tons, with an emission reduction potential of 52.05%. This suggests that in the process of economic development, more than half of the energy in China’s resource-based cities is wasted, and excessive carbon emissions exceed 50%, leaving ample room for improvement in the effective allocation of resources and reasonable control of energy rebound.

By stage, growing type resource-based cities are in the rising stage of resource and industrial development, characterized by rapid growth in strategic new industries. These cities exhibit lower energy waste and excessive carbon emissions, with rates of 46.33% and 41.33%, respectively, which are the lowest among all types of resource-based cities. Mature resource-based cities have the largest number among all types of resource-based cities and exhibit a high level of socio-economic development and energy demand, resulting in the largest share of energy conservations (43.97%) and emission reductions (42.96%) among all types of resource-based cities. Declining cities exhibit stagnant economic development due to resource depletion, industrial decline, and slowed technological renewal, leaving the greatest room for improvement in energy conservation (65.67%) and emission reduction (62.19%) among all types of resource-based cities and exerting the greatest pressure on energy conservation and emission reduction. It can be seen that the planning and transformation of mature resource-based cities should be prioritized in the process of energy conservation and emission reduction in China’s resource-based cities. Improving the energy conservation and emission reduction potential in renewable resource-based cities will be a key indicator of effective control of the energy rebound effect and transition to sustainable development in resource-based cities.

3.6. Implementation Path of Energy Conservation and Emission Reduction

At the end, to clarify the focus of energy conservation and emission reduction in China’s resource-based cities at different stages, this paper concludes by constructing a matrix that measures the energy conservation and emission reduction potential of resource-based cities in China and categorizing them using a 0.5 dividing line in order to analyze the path of energy conservation and emission reduction in China’s resource-based cities at different stages (Figure 7).

In general, energy-saving and emission-reducing potentials in Chinese resource-based cities are reciprocal, resulting in their distribution mainly within quadrants A and C of the state matrix. Few cities fall into quadrant B, which has high energy-saving and low emission-reduction potentials, or quadrant D, which has low energy-saving and high emission-reduction potentials. Specifically, 4 growing, 18 mature, 6 declining, and 3 renewable resource-based cities fall into quadrant A, with low energy efficiency and emission reduction potential, indicating high energy usage and pollution levels that will reach the optimal frontier sooner. In contrast, quadrant C has a large number of cities, including 5 growing, 23 mature, 22 declining, and 9 renewable resource-based cities, with high energy conservation and emission reduction potential, indicating significant energy wastage and excessive pollution emissions.

Using different paths, resource-based cities in quadrant C have two options to choose from for their energy-saving and emission-reduction planning: the C-B-A or C-D-A progressive implementation path. These paths allow the cities to quickly move to adjacent quadrants based on their own energy-saving or emission-reduction advantages and eventually transition to the A quadrant. Moreover, cities in quadrant B can implement the B-A unilateral breakthrough energy conservation and emission reduction path, which focuses on improving energy efficiency and controlling energy rebound effects to accelerate the overall progress of energy conservation and emission reduction efforts. These cities have an advantage in emission reduction. In the end, it is also worth noting that quadrant D, which is low in energy conservation and high in emission reduction, only has two cities in the quadrant, highlighting the significant pressure that resource-based cities face in dealing with energy rebound and the urgent need for energy-saving and efficiency improvement work.

4. Conclusions and Policy Implications

This study investigates the spatiotemporal characteristics, driving mechanisms, and transformation pathways of the energy rebound effect in Chinese resource-based cities. By constructing a rebound effect index and employing spatial kernel density analysis, a standard deviation ellipse, and energy-saving potential estimation, we provide empirical evidence to support energy efficiency governance and low-carbon transitions. The key conclusions are as follows:

• The energy rebound effect in resource-based cities demonstrates clear temporal volatility and spatial decentralization. From 2007 to 2015, the rebound effect showed convergence toward weak rebound, while the period from 2015 to 2019 marked a divergence, with increases in both backfire and super-conservation cases. This evolution from spatial clustering to staggered distribution indicates that rebound trends vary across development stages and are sensitive to macroeconomic shifts and policy shocks.
• Time factors suppress the rebound effect and moderate its spatial diffusion. Non-spatial analysis reveals gradual convergence in rebound levels, while spatial constraints show limited spillover effects between neighboring cities. When time and space dimensions are combined, a downward convergence trend emerges, reflecting the growing effectiveness of region-wide energy efficiency improvements and the gradual reduction of rebound intensity.
• Resource-based cities have substantial room for energy conservation (average potential of 56.07%) and emission reduction (52.05%). However, cities at different development stages exhibit distinct energy rebound risks and need-tailored transformation pathways. Quadrant C cities, characterized by low efficiency and high rebound, should be prioritized in policy design, with transition paths such as C-B-A or C-D-A providing phased improvement strategies.

Based on these findings, the following policy recommendations are proposed to mitigate the energy rebound effect and accelerate sustainable transitions:

• Embed rebound effect risk into policy frameworks by city type: Energy efficiency policies must account for rebound risks, especially in growing and mature resource-based cities, where efficiency gains may trigger consumption surges. For high-rebound cities, stricter demand-side management tools, such as progressive energy tariffs, mandatory efficiency audits, and behavioral nudges, should be prioritized. In low-rebound cities, incentives for deeper retrofits and innovation adoption can safely amplify efficiency gains.
• Establish regionally coordinated governance platforms: For cities with spatially dispersed and staggered rebound patterns, especially those in overlapping economic zones, regional coordination mechanisms—such as joint emission-reduction agreements, integrated infrastructure planning, and cross-border pilot zones—should be formalized. Such platforms can facilitate technology spillovers, prevent policy fragmentation, and foster synchronized low-carbon transitions.
• Design stage-specific transformation pathways: Cities should be classified into categories—such as high potential, transitional, and lagging—based on their energy-saving and emission-reduction capacities. High-potential cities (Quadrant A) should pilot advanced decarbonization strategies; transitional cities (Quadrants B and D) require technical and financial support to progress; and lagging cities (Quadrant C) need foundational reforms such as restructuring high-emission industries and improving public service energy efficiency. This study provides a novel framework for assessing energy rebound effects by integrating spatiotemporal analysis with efficiency-based estimation, thereby revealing regionalized patterns and transition pathways in China’s resource-based cities. Nevertheless, future research would benefit from incorporating dynamic energy accounting methods, more granular sectoral or firm-level data, and comparative studies across different city types or regions. In addition, extending the temporal scope beyond 2019 and applying causal inference techniques could help capture emerging trends and policy impacts with greater precision.