Threshold Effects of Renewable Energy Investment on the Energy Efficiency–Fossil Fuel Consumption Nexus: Evidence from 71 Countries

Abstract

As global focus on energy transition and carbon reduction grows, energy efficiency and renewable energy investment have become key policy tools. This study explores the nonlinear relationship between energy efficiency and fossil fuel consumption, emphasizing the threshold effect of renewable energy investment. Using panel data from 71 countries and a dynamic panel threshold model, the analysis reveals that at low renewable energy investment levels, energy efficiency improvements may be limited by the rebound effect, failing to significantly reduce fossil fuel consumption. However, once investment surpasses a critical threshold, energy efficiency begins to play a stronger role in reducing fossil fuel use. A heterogeneity analysis further shows that developed countries and those with carbon trading systems are more effective in leveraging energy efficiency for emission reduction. The findings highlight the need for synergistic policies combining renewable energy investment, carbon markets, and environmental regulations to accelerate the energy transition and achieve carbon neutrality.

1. Introduction

Achieving carbon neutrality is a key objective in the global energy transition. However, real-world energy trends do not always align with theoretical expectations. While global energy efficiency has improved significantly, fossil fuel consumption has continued to rise. Some countries and regions have even experienced accelerated growth in fossil fuel use [1]. Between 2000 and 2023, global energy intensity declined by approximately 25%. Yet, fossil fuel consumption increased from 11.6 billion tons of standard coal to 17.2 billion tons, marking a nearly 50% rise. This paradox—where efficiency gains coexist with rising consumption—is particularly evident in emerging economies. For instance, between 2010 and 2020, China’s energy efficiency improved at an annual rate of about 2.5%, yet its fossil fuel consumption surged by nearly 300% [2]. Similar trends are observed in developed economies such as the United States and Germany. Despite continued reductions in energy intensity, these countries have not achieved the expected declines in fossil fuel consumption [3,4]. These patterns challenge conventional energy efficiency policies and suggest that systemic factors may be limiting their effectiveness.

The coexistence of efficiency improvements and growing fossil fuel use has prompted extensive academic discussion. One widely studied explanation is the rebound effect—where lower energy costs encourage higher consumption, partially offsetting efficiency gains [5,6,7]. Other studies highlight the direct suppressive effect, arguing that reducing energy inputs for economic activities can, in some cases, directly lower fossil fuel demand. In addition, the role of clean energy technologies has gained attention [8,9]. Some findings suggest that expanding renewable energy and advancing clean energy technologies are critical to ensuring that efficiency improvements translate into sustained emission reductions [10,11,12].

Despite these insights, existing research has notable gaps. Many studies assume a linear relationship between energy efficiency and fossil fuel consumption, overlooking potential nonlinear effects driven by economic structures, policy environments, and investment levels [13]. Additionally, there is limited empirical analysis of how renewable energy investments shape energy transitions and influence the effectiveness of energy efficiency policies. A key question remains unanswered: How does the level of renewable energy investment determine whether efficiency improvements mitigate or exacerbate the rebound effect? Moreover, much of the research relies on data from single countries or regional case studies, making it difficult to draw generalizable conclusions about global energy transition patterns [2].

To address these gaps, this study integrates threshold effects and technological change theory to examine the nonlinear relationship between energy efficiency and fossil fuel consumption. We propose that this relationship is not uniform across all investment levels. When renewable energy investment is low, efficiency improvements may trigger a rebound effect, leading to increased fossil fuel consumption. However, beyond a certain threshold, widespread adoption of clean energy technologies can alter the energy mix, reducing reliance on fossil fuels. This perspective offers a new explanation for cases where energy efficiency policies fail to deliver expected outcomes. It also provides insights into how energy efficiency strategies can be better aligned with clean energy transitions.

To test this hypothesis, we analyze panel data from 71 countries spanning 2000–2023 using a dynamic panel threshold model. This approach captures nonlinear dynamics and accounts for potential endogeneity through the use of lagged variables, improving the robustness of our findings [14]. Unlike previous studies that focus on individual countries or small regional samples, our research takes a global perspective, covering both developed and emerging economies. This enables us to assess how energy efficiency policies perform across different economic contexts and how renewable energy investment thresholds influence their impact. The findings of this study aim to inform policymakers on designing more effective and targeted energy transition strategies.

This study contributes to the literature in three key ways. Theoretically, it identifies the threshold moderating effect of renewable energy investment on the relationship between energy efficiency and fossil fuel consumption, extending research on nonlinear mechanisms in energy and environmental economics. Methodologically, it innovatively applies a dynamic panel threshold model to address endogeneity bias and dynamic effects, ensuring reliable and robust conclusions. Practically, by identifying the synergistic mechanisms between energy efficiency and renewable energy investment at different threshold levels, this study provides scientific evidence for designing more precise emission reduction policies in diverse economic contexts.

The structure of this paper is as follows: Section 2 reviews the literature and establishes the theoretical framework; Section 3 details the research design, including the construction of the dynamic panel threshold model, variable selection, and data sources; Section 4 presents the empirical findings, robustness tests, and heterogeneity analyses; Section 5 discusses the results; and Section 6 summarizes the conclusions and offers policy recommendations.

2. Theoretical Framework and Literature Review

2.1. Theoretical Framework

Improving energy efficiency is regarded as an important measure to curb fossil fuel consumption. However, existing studies have shown that such improvements do not necessarily produce the expected emissions reduction, with the “rebound effect” playing a critical role [15]. When enhanced energy efficiency leads to a reduction in per-unit usage costs, producers or consumers often increase their demand for energy services, thereby partially or even entirely offsetting the initial energy savings. In high energy-consuming sectors such as industry, transportation, and construction, although improvements in energy efficiency can reduce fossil fuel usage in the short term, without profound structural transformations and policy incentives, the additional demand generated by these efficiency gains will undermine their emissions reduction potential [16]. This clearly indicates that solely relying on energy efficiency policies cannot ensure an actual decline in fossil fuel consumption.

Meanwhile, technological change theory offers a powerful approach to overcoming the rebound effect. Large-scale investments in research and development and equipment typically lead to a significant reduction in the cost of clean energy, enabling it to gradually gain a competitive edge in the market [17,18]. Over the past decade, the continuous decline in the costs of wind and solar power has been closely associated with the rapid growth of global renewable energy investments [19]. However, the effect of such investments in reducing fossil fuel consumption does not manifest in a spontaneous linear fashion; rather, there exists a critical interval. When renewable energy investments are insufficient, clean energy struggles to achieve stable market diffusion and economies of scale, rendering it ineffective at offsetting the additional demand generated by energy efficiency improvements. Only when the scale of investment surpasses a certain threshold does the market penetration of clean energy experience a qualitative leap, thereby significantly weakening the rebound in fossil fuel consumption and further unleashing the emissions reduction potential of improved energy efficiency [20].

Based on this logic, this study regards renewable energy investment as a key moderating variable, focusing on its impact on the relationship between energy efficiency and fossil fuel consumption in a cross-national context, and attempting to explore the nonlinear characteristics of clean energy in the process of substituting for fossil fuels from a threshold effect perspective. This analytical framework not only fully reflects the interactive mechanisms among the rebound effect, technological change, and threshold effect, but also provides a new analytical approach for understanding the multiple challenges and opportunities faced by different countries in the process of energy transition.

2.2. Energy Efficiency, Renewable Energy, and Fossil Fuel Consumption

In existing research, energy efficiency was once considered the primary means of reducing fossil fuel consumption. However, practical experience indicates that this process is influenced by multiple factors, including the rebound effect, economic structure, and policy implementation [21]. Recent studies have also indicated that trade liberalization has an impact on energy efficiency [22]. On the surface, improving energy efficiency means a significant reduction in the energy consumed per unit of GDP—especially in high energy-consuming sectors such as industry, transportation, and construction—where technological upgrades often lead to substantial short-term reductions in energy intensity [23]. Nevertheless, price sensitivity on the demand side and shifts in consumption preferences can result in part of the energy savings being offset by increased demand. Moreover, in some countries, the lack of comprehensive mechanisms for technology dissemination and financial subsidies makes it difficult to absorb the high costs of new energy-saving equipment. In addition, policy enforcement and public awareness are crucial to the effectiveness of energy efficiency measures; without sufficient regulation and incentives, the potential for energy savings often cannot be fully realized [24,25]. Therefore, relying solely on energy efficiency measures is unlikely to achieve a sustained suppression of fossil fuel consumption.

By contrast, renewable energy investment is seen as the “key lever” for fundamentally changing the energy structure. Its role in curbing fossil fuel consumption is not only direct through substitution effects but also synergistic with improvements in energy efficiency [26]. Substantial investment not only accelerates the cost reduction of technologies such as wind and solar power, but also typically accompanies improvements in policy and market environments, enabling clean energy to achieve higher market penetration [27]. Once the scale of investment reaches a certain threshold, the crowding-out effect of clean energy on traditional fossil fuels becomes significantly stronger, leading to a transformation in the overall energy structure [28]. However, significant differences in economic foundations, technological capabilities, and institutional support across countries result in notable heterogeneity in renewable energy investments [29]. Some developed economies, benefiting from robust fiscal support and comprehensive regulatory systems, have achieved rapid expansion of clean energy systems; whereas in emerging economies and resource-dependent regions, the emission reduction effects of investment are often constrained by insufficient funding and supportive policies [30]. Overall, although the existing literature generally affirms the important role of renewable energy investment in substituting for fossil fuels, how it can form a sustained and effective synergy with energy efficiency policies across different stages of development and technological conditions still requires further systematic empirical research.

3. Research Design

3.1. Model Construction

To investigate the nonlinear impact of energy efficiency on fossil fuel consumption and examine the threshold moderating effect of renewable energy investment, this study constructs a dynamic panel threshold model within the theoretical framework of the production function. The model integrates threshold effect theory and dynamic panel methodologies, leveraging their strengths in capturing nonlinear relationships and addressing endogeneity issues.

The production function is a classical model that describes the relationship between production inputs and economic output and has been widely applied in energy economics [31]. The traditional Cobb–Douglas production function assumes that economic output is determined by capital, labor, and energy inputs and is expressed as follows:

$$Y=A{K}^{\alpha }{L}^{\beta }{E}^{\gamma }$$

(1)

where $\mathrm{Y}$ represents total economic output, $\mathrm{A}$ denotes total factor productivity, and $\mathrm{K}$, $\mathrm{L}$, and $\mathrm{E}$ refer to capital, labor, and energy inputs, respectively, with $\mathsf{\alpha }$, $\mathsf{\beta }$, and $\mathsf{\gamma }$ representing their respective output elasticities.

Improvements in energy efficiency imply an increase in the effective utilization of energy, meaning that each unit of energy input can provide more productive services. By introducing the energy efficiency factor ($\mathrm{q}$) into the production function, the total energy service volume can be expressed as $\mathrm{q}\mathrm{E}$, where $\mathrm{q}$ represents energy efficiency. Substituting this into the production function yields the following:

$$Y=A{K}^{\alpha }{L}^{\beta }{(qE)}^{\gamma }$$

(2)

which, after simplification, can be rewritten as follows:

$$Y=A{q}^{\gamma }{K}^{\alpha }{L}^{\beta }{E}^{\gamma }$$

(3)

This formulation indicates that energy efficiency not only directly influences economic output by increasing energy service volume but also interacts with energy input to shape economic activity.

In energy consumption decision-making, total energy consumption can be further decomposed into fossil energy consumption ($\mathrm{F}\mathrm{E}$) and renewable energy consumption ($\mathrm{R}\mathrm{E}$). Renewable energy consumption is closely linked to renewable energy investment, as investment in clean energy drives technological advancements and market expansion, ultimately increasing the share of renewables in the energy mix and optimizing the overall energy structure. Based on this relationship, the demand for fossil energy consumption can be expressed as a function of energy efficiency, renewable energy investment, and other control variables:

$$F{E}_{it}=f(E{E}_{it},IN{V}_{it},Constrol{s}_{it})$$

(4)

Taking into account the dynamic nature of fossil fuel consumption, its current level is not only influenced by contemporaneous energy efficiency and renewable energy investment but is also closely related to its lagged values. Accordingly, the model can be extended as follows:

$$F{E}_{it}=\lambda F{E}_{t-1}+f(E{E}_{it},IN{V}_{it},Control{s}_{it})+{\epsilon }_{it}$$

(5)

where $\mathsf{\lambda }$ represents the path dependence of fossil energy consumption, capturing the persistence of past consumption patterns.

This study incorporates threshold effect theory, hypothesizing that the impact of energy efficiency on fossil fuel consumption varies depending on the level of renewable energy investment. When renewable energy investment is low ($\mathrm{I}\mathrm{N}{\mathrm{V}}_{\mathrm{i}\mathrm{t}}<\mathsf{\tau }$), the capacity for clean energy expansion remains limited, and improvements in energy efficiency may, through the rebound effect, indirectly increase fossil fuel consumption. However, when investment surpasses a certain threshold ($\mathrm{I}\mathrm{N}{\mathrm{V}}_{\mathrm{i}\mathrm{t}}\ge \mathsf{\tau }$), the market penetration of clean energy significantly improves, allowing the energy-saving effects of efficiency gains to become more pronounced. Consequently, this study employs a dynamic panel threshold model to further capture the nonlinear and dynamic relationship between energy efficiency and fossil fuel consumption. The final model is specified as follows:

$$F{E}_{it}=\lambda F{E}_{it-1}+({\alpha }_{1}E{E}_{it}+{\beta }_{1}Control{s}_{it})I(IN{V}_{it}<\tau )+({\alpha }_{2}E{E}_{it}+{\beta }_{2}Control{s}_{it})I(IN{V}_{it}\ge \tau )+{\epsilon }_{it}$$

(6)

where $\mathrm{I}(\cdot )$ is an indicator function identifying whether renewable energy investment exceeds the threshold $\mathsf{\tau }$; ${\mathsf{\alpha }}_1$ and ${\mathsf{\alpha }}_2$ capture the effect of energy efficiency on fossil fuel consumption under low and high investment conditions, respectively; $\mathsf{\beta }$ represents the parameter vector of control variables; and ${\mathsf{ϵ}}_{\mathrm{i}\mathrm{t}}$ is the stochastic error term.

3.2. Variable Selection

In this study, the dependent variable is fossil fuel consumption, the core explanatory variable is energy efficiency, and several control variables are introduced to enhance the explanatory power of the model. The definitions and measurement methods for each variable are detailed below.

Fossil fuel consumption (FE): This study measures fossil fuel consumption using the annual total fossil fuel consumption of each country. This absolute measure directly reflects the scale of a country’s energy use and its trends, allowing for a clearer examination of whether improvements in energy efficiency have actually led to a reduction in fossil fuel use. It is crucial for assessing the energy-saving and emission-reduction effects of energy efficiency policies [32,33].

Energy efficiency (EE): Energy efficiency is measured using an input–output approach. Fixed capital investment, labor, and total energy consumption are considered input indicators, with GDP measured in constant 2015 US dollars as the desired output. Carbon emissions are included as an undesired output to comprehensively reflect both economic and environmental benefits [34].

Renewable energy investment (INV): Due to limitations in statistical definitions and data availability, renewable energy installed capacity is used as a proxy for the investment level. This indicator is usually highly correlated with actual capital input and can better reflect the progress of countries in clean energy technology and infrastructure construction, exhibiting strong cross-country comparability [35].

In order to reduce the interference of omitted variables, this study includes a series of control variables (Controls) covering dimensions such as the economy, population, industry, environment, and technology. The specific definitions are as follows:

Per capita GDP (PGDP): measured in constant 2015 US dollars, per capita GDP assesses a country’s level of economic development and the average standard of living of its residents.

Total population (POP): As a key indicator for measuring the basic scale of a country’s energy demand, population size is usually positively correlated with energy consumption. Especially in the processes of industrialization or urbanization, population growth often drives an increase in fossil fuel consumption.

Industrial value-added ratio (IND): The industrial sector remains a primary source of traditional energy consumption in many countries. By including this variable, the impact of economic structure on changes in energy consumption can be better controlled.

Carbon emissions (CE): carbon emissions are not only a direct result of fossil fuel consumption but also an important indicator of the effectiveness of energy efficiency and related policies.

Technological progress (TECH): Measured by the annual number of patent applications, technological progress reflects a country’s investment in and output from energy technology innovation. Technological progress can not only directly improve energy efficiency but also promote the development and utilization of clean energy, thereby reducing dependence on fossil fuels.

3.3. Data Sources

The data used in this study cover 71 countries over the period from 2000 to 2023. The data are sourced from multiple authoritative institutions to ensure their reliability and international comparability.

Data on fossil fuel consumption and total energy consumption are sourced from the Our World in Data database. Fossil fuel consumption types include coal, crude oil, and natural gas, all uniformly converted into standardized units of TWh (terawatt-hours). Data on renewable energy installed capacity are obtained from the International Renewable Energy Agency (IRENA) database. Data required for calculating energy efficiency—including total fixed capital investment, labor, GDP, and per capita GDP—are sourced from the World Bank database.

Data for the control variables are also obtained from authoritative institutions. Specifically, data on total population and the industrial value-added ratio are sourced from the World Bank database, reflecting the impact of population size and industrial structure on energy consumption. Carbon emissions data, also sourced from the World Bank database, serve as an important indicator of the environmental consequences of fossil fuel use. As a proxy for technological progress, data on the total number of patent applications are sourced from the World Intellectual Property Organization (WIPO) database, which comprehensively reflects the level of technological research and innovation in each country.

To avoid distortions caused by large-scale differences across variables, all variables except energy efficiency ($\mathrm{E}\mathrm{E}$) are log-transformed. Descriptive statistics and multicollinearity test results are presented in

Table 1. Descriptive statistics and multicollinearity tests.

Variables	Obs	Mean	Std. Dev.	Min	Max	VIF
FE	1704	6.120	1.488	2.113	10.563
EE	1704	8.330	2.195	0.693	14.19	8.03
INV	1704	0.971	0.128	0.284	3.287	1.04
PGDP	1704	7.770	1.675	1.749	12.304	2.12
POP	1704	16.872	1.623	12.547	21.08	3.88
IND	1704	3.323	0.302	2.341	4.44	1.43
CE	1704	4.728	1.492	1.049	9.451	8.03
TECH	1704	7.687	2.160	1.792	14.318	4.61

.

4. Results

4.1. Benchmark Regression

The benchmark regression is based on the estimation of Equation (1). In this analysis, we employ ordinary least squares (Model 1), a fixed effects model (Model 2), a random effects model (Model 3), a difference GMM model (Model 4), and a system GMM model (Model 5) to examine the impacts of EE, INV, and other control variables on FE. This multi-model strategy helps to comprehensively evaluate the relationships among the variables and ensures that the results are robust across different estimation methods. The estimation results are presented in

Table 2. Baseline regression results.

Variables	Model (1) (OLS)	Model (2) (FE)	Model (3) (RE)	Model (3) (Dif-GMM)	Model (4) (Sym-GMM)
L.FE	0.933 *** (0.007)	0.519 *** (0.017)	0.901 *** (0.008)	0.840 *** (0.008)	0.848 *** (0.047)
EE	−0.167 *** (0.011)	−0.088 *** (0.01)	−0.157 *** (0.011)	−0.147 *** (0.003)	−0.148 *** (0.046)
INV	−0.008 *** (0.001)	−0.008 *** (0.003)	−0.009 *** (0.001)	−0.011 *** (0.001)	−0.011 *** (0.003)
PGDP	0.003 ** (0.002)	0.041 *** (0.009)	0.004 ** (0.002)	0.006 *** (0.001)	0.005 (0.006)
POP	0.011 *** (0.002)	0.064 ** (0.025)	0.009 *** (0.002)	0.008 *** (0.001)	0.008 *** (0.003)
IND	0.026 *** (0.006)	0.007 (0.014)	0.024 *** (0.007)	0.017 *** (0.004)	0.021 * (0.011)
CE	0.054 *** (0.007)	0.433 *** (0.016)	0.087 *** (0.009)	0.147 *** (0.009)	0.137 *** (0.05)
TECH	0.006 *** (0.001)	0.006 ** (0.003)	0.007 *** (0.002)	0.009 *** (0.001)	0.009 ** (0.005)
_cons	0.043 (0.034)	−0.430 (0.390)	0.107 ** (0.042)	0.226 *** (0.028)	0.201 ** (0.097)
R-squared	0.985	0.993	0.998
AR(1)				−3.64 ***	−3.73 ***
AR(2)				−0.01	−0.02
Hansen test				69.06 ***	69.06 ***
Number of obs	1633	1633	1633	1633	1633
Number of groups	71	71	71	71	71

Note: *, represents the 10% significance level, ** represents the 5% significance level, *** represents the 1% significance level.

.

In Model 1, the OLS results show that EE significantly reduces FE, indicating that, overall, improvements in EE play an important role in directly reducing the energy demand per unit of economic output. Furthermore, INV also significantly reduces FE, reflecting that the expansion of clean energy technology and infrastructure helps to curb the use of traditional fossil fuels.

Model 2 employs a fixed effects model that controls for unobservable, time-invariant characteristics across countries. After accounting for fixed effects, the negative impact of EE is somewhat weakened, suggesting that part of the effect observed in the OLS results may have been driven by unobserved factors. INV continues to have a significant negative effect on FE, demonstrating that its reducing effect remains robust even when country heterogeneity is considered.

Model 3 utilizes a random effects model, assuming that the explanatory variables are uncorrelated with the individual effects. The results reveal that the negative effect of EE is once again strengthened, approaching the OLS outcome, and the coefficient for INV increases slightly. This further supports the stable role of INV as an important tool for emissions reduction.

To address potential endogeneity issues, Model 4 applies the difference GMM method. The results indicate that the lagged term of FE is significantly positive, demonstrating that FE exhibits notable dynamic dependence. Even after controlling for endogeneity, EE still significantly reduces FE, confirming that its emissions reduction effect remains robust even when considering reverse causality. Moreover, the negative effect of INV is further enhanced in the dynamic framework, revealing the long-term influence of clean energy investment in dynamic adjustments.

Model 5 further employs the system GMM approach, which combines both the level equation and the difference equation to comprehensively capture the dynamic relationships among the variables and address endogeneity issues. The coefficient for the lagged term slightly increases to 0.848, indicating that current FE is highly dependent on past consumption levels. The effects of EE and INV are consistent with those in the difference GMM model, further confirming the robust emissions reduction effects of these core variables within a dynamic framework. Additionally, the technological progress variable exhibits a more significant positive impact on FE in the system GMM model, which may reflect the high energy consumption characteristics during the early stages of technology diffusion.

4.2. Threshold Effect Results

Table 3. Threshold effect estimation results.

Variables	Lower Regime	Upper Regime	Overall	Threshold Estimation Test
L.FE	0.198 *** (0.036)	−0.089 * (0.051)	0.186 *** (0.009)	kink	0.070 *** (0.017)
EE	0.074 *** (0.015)	−0.124 *** (0.034)	−0.049 *** (0.008)	Threshold indicator	8.729 *** (0.179)
Controls	Yes			95% Conf.interval	8.37–9.08
_cons	4.355 *** (0.653)

Note: * represents the 10% significance level, *** represents the 1% significance level.

presents the regression results using INV as the threshold variable, differentiating between low investment levels (Lower regime) and high investment levels (Upper regime), along with an overall analysis of the sample. The estimated threshold value is 8.729, and it significantly passes the threshold effect test. This indicates that INV plays a key role in moderating the relationship between EE and FE, exhibiting a clear nonlinear characteristic.

Under low investment levels, the coefficient for EE is significantly positive, suggesting that improvements in EE in this range do not effectively reduce FE and may even trigger a rebound effect due to reduced unit energy costs. However, under high investment levels, the coefficient for EE turns significantly negative, indicating that once INV exceeds the threshold value, the energy-saving potential of EE is fully unleashed, effectively reducing FE.

In the overall sample regression, the coefficient for EE is −0.049, which indicates that, in general, EE contributes to reducing FE. However, its effect is clearly influenced by the threshold value, demonstrating significant heterogeneity. The coefficient for the lagged term is 0.186, revealing a high degree of dynamic dependence in FE. This inertia effect implies that short-term policy interventions may not yield immediate results, and adjustments in FE require a longer time horizon. Additionally, the estimated threshold value is 8.729, with a 95% confidence interval of 8.37–9.08, and it passes the significance test for the threshold effect, thereby confirming the existence of a significant nonlinear moderating mechanism in the relationship between EE and FE.

4.3. Robustness Tests

To control for potential endogeneity issues, this paper selected the Environmental Policy Stringency Index as an instrumental variable and employed the Two-Stage Least Squares (2SLS) method for estimation. The estimation results are presented in

Table 4. Endogeneity test.

	First-Stage	2SLS
EE		−6.331 ** (0.048)
iv	−0.118 ** (0.005)
Constant	1.266 (0.065)	9.221 *** (3.878)
Controls	Yes
R2	0.2003	0.8786
Root MSE	0.037	0.686
First-stage F	11.15 ***
2SLS Wald chi2		9436.83 ***
Robust score chi2	12.816 ***
Robust regression F	13.439 ***

Note: ** represents the 5% significance level, *** represents the 1% significance level.

. The Environmental Policy Stringency Index is closely related to energy efficiency, thereby satisfying the relevance assumption; simultaneously, this variable does not directly affect fossil energy consumption, meeting the exogeneity requirement. The estimation results indicate that although the magnitude of the coefficients varies, they still support the conclusion that energy efficiency can reduce fossil energy consumption. The F-statistic of the first-stage regression is 11.15, which is significantly higher than the critical value of 10, indicating that there is no weak instrument problem. The Hausman test for endogeneity is significant, suggesting that the policy variable indeed exhibits endogeneity; therefore, using 2SLS estimation is more robust and reliable.

To verify the robustness of the research findings, this study conducts dynamic threshold regression tests from three perspectives, as shown in

Table 5. Robustness test results.

	Replace FE		Replace EE		Replace INV
Variables	Lower Regime	Upper Regime	Lower Regime	Upper Regime	Lower Regime	Upper Regime
L.FE	0.316 *** (0.047)	−0.146 * (0.083)	0.172 *** (0.020)	0.013 (0.02)	−0.011 (0.036)	0.045 (0.047)
EE	0.018 *** (0.004)	−0.085 *** (0.011)	1.083 *** (0.068)	−1.075 *** (0.071)	0.698 *** (0.081)	−0.690 *** (0.080)
Controls	Yes		Yes		Yes
_cons	0.948 ** (0.400)		4.038 *** (0.642)		1.456 * (0.800)
Threshold indicator	9.322 *** (0.303)		8.848 *** (0.086)		3.629 *** (0.046)
kink	0.029 *** (0.010)		0.106 *** (0.014)		0.133 *** (0.022)

Note: *, represents the 10% significance level, ** represents the 5% significance level, *** represents the 1% significance level.

. The results indicate that regardless of the substitution method employed, the direction and significance of the regression coefficients remain consistent with those in the benchmark model, further confirming the reliability of the research findings.

In the regression where the dependent variable is replaced, the proportion of FE is used as the dependent variable [36]. The estimated threshold value is 9.322, which passes the threshold effect test significantly. Under low investment levels, the coefficient for EE is 0.018, suggesting that improvements in efficiency might trigger a rebound effect, thereby increasing the proportion of FE. In the high investment regime (Upper regime), the coefficient turns to −0.085, indicating that the expansion of INV can effectively mitigate the rebound effect, enabling EE to achieve energy-saving and emissions-reduction outcomes.

In the regression where the explanatory variable is replaced, energy output per unit of energy consumption is used as a substitute for EE as the explanatory variable [37]. The estimated threshold value is 8.848, which also passes the threshold effect test significantly. The results show that under low investment levels, the coefficient is 1.083, meaning that when INV is insufficient, relying solely on improvements in EE is unlikely to substantially reduce FE. In contrast, under high investment levels, the energy-saving potential of EE policies is fully unleashed.

In the regression where the investment variable is replaced, renewable energy consumption is used in place of INV [27]. The estimated threshold value is 3.629, and the results are similarly significant. Under low investment levels, the coefficient for EE is 0.698, indicating that when renewable energy consumption is insufficient, the energy-saving effect of EE is limited; whereas in the high investment regime, the coefficient for EE turns to –0.690, demonstrating that the expansion of renewable energy consumption significantly promotes the energy-saving effects of EE.

4.4. Heterogeneity Analysis

In the process of energy transition, significant differences exist among countries in terms of economic development, environmental policies, and energy endowments. These differences lead to marked heterogeneity in the impact of EE on fossil fuel usage. Analyzing only the overall sample might overlook the distinctive characteristics of different types of countries, thereby reducing the targeting and effectiveness of policy formulation. To further explore this issue, this study, based on Equation (6), divides the sample into several categories and examines the differences in the impact of EE on fossil fuel usage before and after INV reaches the threshold.

Figure 1 illustrates the impact of EE on fossil fuel usage in developed and developing countries before (Lower regime) and after (Upper regime) INV reaches the threshold.

In the Lower regime, the coefficient for EE is positive in both developed and developing countries, indicating that improvements in EE have not effectively curbed fossil fuel usage; instead, a rebound effect occurs. When INV is insufficient, efficiency enhancements lower the energy cost per unit of output, thereby stimulating overall energy demand and leading to an increase in FE.

In the Upper regime, the impact coefficients in both groups turn negative, indicating that once INV exceeds the threshold, improvements in EE can effectively substitute for a portion of fossil fuel usage. Notably, the absolute value of the negative coefficient is larger in developed countries, suggesting that under high INV conditions—coupled with more mature technology and stricter environmental regulation—FE can be reduced more significantly. Although developing countries also show a negative effect, the magnitude is smaller, reflecting their relatively weak renewable energy technology and infrastructure, and indicating that achieving large-scale fossil fuel substitution will require more time.

Figure 2 presents the impact of EE on FE in carbon trading versus non-carbon trading countries under both regimes.

Specifically, in the Lower regime, the coefficient for EE is positive in both groups, indicating that during the stage of relatively low INV, the cost reductions brought by efficiency improvements stimulate FE. Comparatively, the positive coefficient is more pronounced in non-carbon trading countries, suggesting that in the absence of carbon pricing constraints, improvements in EE are less effective at curbing fossil fuel usage.

In the Upper regime, when INV reaches the threshold, the coefficient for EE turns negative in both groups, signifying that efficiency improvements can effectively reduce fossil fuel demand. However, the absolute value of the negative coefficient is larger in carbon trading countries, demonstrating that the carbon market’s price mechanism further reinforces the emissions reduction effect of EE. In contrast, in countries without a carbon trading mechanism, although a substitution effect is present, its magnitude is relatively limited.

Figure 3 compares the impact of EE on fossil fuel usage in countries rich in fossil fuel resources with those heavily dependent on fossil fuel imports, before and after the INV threshold.

In the Lower regime, the coefficient for EE is positive in both groups, indicating that when INV is insufficient, efficiency improvements can expand overall energy demand and consequently boost fossil fuel usage. For countries heavily dependent on imports, this positive effect is more pronounced, possibly because their lack of an autonomous energy supply means that the economic expansion driven by efficiency improvements further increases the demand for fossil fuel imports.

In the Upper regime, when INV exceeds the threshold, the impact of EE on fossil fuel usage turns negative in both groups. For resource-rich countries, the absolute value of the negative coefficient is larger, meaning that under conditions of high INV, these countries can more quickly implement substitution strategies and reduce FE. In contrast, while countries dependent on energy imports also experience a negative shift, the magnitude is smaller, indicating that they will require more time and resources to achieve a fundamental adjustment in their energy structure.

Figure 4 presents the impact of energy efficiency on fossil fuel consumption in oil-exporting countries and oil import-dependent countries before and after the renewable energy investment threshold is reached. In the low threshold region, the coefficients for the effect of energy efficiency on fossil fuel consumption are positive for both groups, indicating that improvements in energy efficiency may actually promote fossil fuel consumption. When renewable energy investment is sufficient, enhancements in energy efficiency not only fail to increase fossil fuel consumption but instead help reduce it, thereby steering the energy structure toward a cleaner and more sustainable direction.

In the high threshold region, due to adequate renewable energy investment, oil-exporting countries face greater economic transformation pressures and stricter policy regulations; as a result, while improving energy efficiency, the stronger technological substitution and clean energy replacement effects lead to a significant decline in traditional fossil fuel consumption, exhibiting a more pronounced negative inhibiting effect, whereas oil import-dependent countries, with their more diversified economic structures and relatively weaker transformation impetus, show a less marked inhibitory effect.

Figure 5 illustrates the heterogeneity analysis results after grouping the sample countries based on their carbon emission intensity. In this figure, we, first, divided the 71 countries into high and low carbon emission groups according to their average carbon emissions, and then, examined the impact of energy efficiency on fossil fuel consumption under different levels of renewable energy investment. In the low investment threshold range, in both the high and low carbon emission groups, the coefficient of energy efficiency on fossil fuel consumption is positive, indicating that when renewable energy investment is insufficient, an improvement in energy efficiency may trigger a rebound effect that leads to increased fossil fuel consumption.

However, in the high investment threshold range, as renewable energy investment reaches a sufficient level, the impact of energy efficiency on fossil fuel consumption in both groups turns negative, suggesting that at this stage, improvements in energy efficiency help reduce fossil fuel consumption and promote a transition of the energy structure toward a cleaner and more sustainable direction. Notably, the negative effect is more pronounced in the high carbon emission group, which may reflect that these countries face greater market pressure and policy impetus in addressing their dependence on traditional fossil fuels and accelerating technological substitution, thereby enabling renewable energy investment to exert a stronger substitution effect; while the low carbon emission group also exhibits a suppressing effect, its magnitude is relatively moderate. Overall, Figure 5 further supports the core conclusion of this study that, with sufficient support from renewable energy investment, improvements in energy efficiency can effectively reduce fossil fuel consumption, and this policy effect exhibits significant heterogeneity under different carbon emission intensity contexts.

5. Discussion

This paper investigates the nonlinear relationship between EE and FE, applying a dynamic panel threshold model to examine whether INV serves as a threshold that alters this relationship. The research findings indicate that the interaction between EE and INV has a significant nonlinear impact on FE. This discovery not only offers a new perspective on the dynamic mechanisms of various factors during the energy transition but also provides important insights for optimizing energy policies.

The primary contribution of this study lies in proposing and validating the nonlinear relationship between EE and FE, while further clarifying the moderating role of INV as a threshold variable. By testing for threshold effects under different investment levels, this study finds that when INV is at a relatively low level, improvements in EE may lead to an increase in FE due to the rebound effect; however, once INV exceeds a certain threshold, enhancements in EE can significantly curb FE.

Compared with the existing literature, the innovative aspect of this study is its emphasis on the critical moderating role of INV in EE policies. Although previous research has explored the independent effects of EE and INV, few studies have considered INV as a threshold variable to examine its moderating impact on the relationship between EE and FE. Based on this theoretical framework, this paper finds that the synergistic effect of EE and INV is significantly enhanced in the high-investment phase—especially in developed countries and in those implementing carbon emission trading policies—where improvements in EE effectively reduce FE. Additionally, this study verifies that in the low-investment phase, the emissions reduction effect of enhancing EE is relatively weak or may even be constrained by the existing traditional energy structure; this is particularly evident in developing countries.

The heterogeneity analysis in this paper provides profound insights into the differences in the relationship between EE and FE across different countries and regions. By classifying developed and developing countries based on IMF and World Bank standards, this study finds that developed countries can effectively use EE policies to reduce FE under high INV levels, whereas in developing countries, due to factors such as lower technological levels, market mechanisms, and financial investments, improvements in EE do not significantly improve the energy consumption structure. This finding indicates that countries at different stages of economic development face distinct challenges in the energy transition process, with the policy effects in developing countries being significantly constrained under conditions of inadequate financial and technological support [38,39]. Therefore, when implementing EE policies, developing countries must substantially increase investments in renewable energy and technological innovation to effectively achieve a transformation of their energy structures.

This study further verifies the role of the carbon emission trading system in moderating the relationship between EE and FE. The results show that in countries implementing carbon emission trading, improvements in EE significantly suppress FE, especially in the high-investment phase. These countries use market mechanisms to price carbon emissions, thereby promoting low-carbon technological innovation and the diffusion of renewable energy, which in turn optimizes the energy structure and reduces dependence on fossil fuels. Compared with the findings of Hong et al. (2022), this result further broadens the understanding of the important role of INV within carbon emission trading systems [40].

Inspired by the practical implications of our empirical findings, we have further enriched the discussion by incorporating insights from industry reports and real-world implementations. For instance, case studies from countries such as Germany and California reveal that in regions where substantial renewable energy investment has been realized, the promotion of energy efficiency has consistently led to a marked reduction in fossil fuel consumption. Moreover, these real-world examples illustrate that different sectors respond distinctly to renewable energy investments, thereby reinforcing the heterogeneous effects observed in our empirical analysis. Such comparative analyses not only provide additional validation for our conclusions but also offer policymakers a concrete perspective on how various industries are adapting to the twin imperatives of energy efficiency improvement and low-carbon transition.

In addition, it is important to acknowledge the practical challenges that may hinder the implementation of these identified technological opportunities. Financial constraints—especially prevalent in emerging markets—often limit the scale and speed of adopting innovative energy technologies. Policy barriers, including inconsistent regulatory frameworks and insufficient incentive mechanisms, further exacerbate the difficulties of integrating advanced technologies into existing systems. Moreover, technological limitations such as the need for skilled human resources and the challenges associated with upgrading legacy infrastructure also present significant obstacles. Recognizing these challenges is crucial for developing comprehensive strategies; policymakers must not only promote renewable energy investment and energy efficiency improvements but also address these underlying constraints through targeted financial support, robust policy reforms, and capacity-building initiatives.

We recognize that the analysis of the carbon trading system in the current study is primarily based on experiences from developed nations, while emerging markets often face challenges such as inadequate regulatory enforcement and high price volatility under low-INV conditions. To address this, emerging markets may need to adopt phased pilot programs and tailor specific policy adjustments, including enhanced government oversight and price stabilization measures, to establish market mechanisms that align with local conditions. In addition, emerging economies should leverage successful experiences from developed countries and design a multi-level carbon trading framework through inter-agency coordination, the introduction of green finance tools, and capacity building measures. Such comprehensive strategies can not only optimize local energy structures and promote low-carbon technological innovation but also facilitate the effective operation of carbon trading systems even in low-INV contexts, thereby contributing to global emission reduction targets.

However, this study also has certain limitations. Although it employs cross-national panel data and addresses endogeneity issues through a dynamic panel threshold model, data availability constraints mean that some countries’ data are incomplete or missing, which may affect the precision of the results. Moreover, while the selection of variables in this study considers key factors such as EE and INV, other dimensions of energy policy—such as energy subsidies and price regulation—are not explored in depth. Future research could expand the model by incorporating more factors that may affect policy outcomes to improve the comprehensiveness of this study and the specificity of policy recommendations.

In some of the models presented in this study, the TECH variable exhibits a positive coefficient, which is contrary to the expected outcome. We believe this phenomenon may partly reflect the “energy-intensive” nature of early-stage technological innovation. In the initial phases, significant energy is often consumed for testing, prototyping, and production experiments, and such high energy consumption might offset the potential savings from improved energy efficiency in the short run. As technology matures and economies of scale are realized, this effect may change to yield a negative impact on energy consumption, thus enhancing overall energy efficiency. Moreover, the positive coefficient may also be attributable to measurement issues, given that our current patent data might include patents with only a weak connection to clean energy transitions. Future research could refine the technological indicators to focus more specifically on innovations that drive clean energy transformation, thereby more accurately capturing the true impact of technological progress within the energy system.

6. Conclusions and Policy Recommendations

6.1. Conclusions

Through the application of a dynamic panel threshold model, this study has delved into the nonlinear relationship between energy efficiency and fossil fuel consumption and systematically analyzed the moderating role of renewable energy investment in this process. Analyzing panel data from 71 countries worldwide, this study draws the following main conclusions:

First, this study finds that there is a nonlinear relationship between energy efficiency and fossil fuel consumption, with renewable energy investment acting as a key threshold variable that plays an important moderating role in this relationship. In the low renewable energy investment phase, improvements in energy efficiency do not significantly reduce fossil fuel consumption and may even lead to a rebound effect due to fluctuations in energy prices; however, once renewable energy investment reaches a certain level, enhancements in energy efficiency can effectively reduce fossil fuel consumption.

Second, through heterogeneity analysis, this study further explores the differences in the relationship between energy efficiency and fossil fuel consumption across various countries and regions. The results show that developed countries and countries with established carbon emission trading systems can fully leverage energy efficiency policies to reduce fossil fuel consumption under high renewable energy investment levels. These countries, with their strong capabilities in technological innovation, well-developed market mechanisms, and supportive policy environments, are better positioned to promote the synergy between energy efficiency and fossil fuel consumption reduction. In contrast, although developing countries have certain potential for improvements in energy efficiency, constraints related to technology, capital, and infrastructure mean that energy efficiency policies have not significantly reduced fossil fuel consumption. For these countries, renewable energy investment and technological innovation remain key factors in driving the energy transition.

Third, this study underscores the important role of the carbon emission trading system in driving the relationship between energy efficiency and fossil fuel consumption. In countries implementing carbon emission trading, there is a pronounced synergistic effect between improvements in energy efficiency and reductions in fossil fuel consumption. The carbon market, by pricing carbon emissions, promotes the application of low-carbon technologies and the substitution of clean energy, thereby accelerating the transformation of the energy structure. Compared to countries that have not implemented a carbon emission trading system, those that have exhibit a more effective reduction in fossil fuel consumption through improvements in energy efficiency in the high-investment phase.

6.2. Policy Recommendations

Based on the main findings of this study, the following policy recommendations are proposed to guide the formulation of national energy transition strategies, particularly in the areas of energy efficiency, renewable energy investment, and the implementation of carbon emission trading systems.

First, policymakers should prioritize the growth of renewable energy investment. This study indicates that during the low renewable energy investment phase, the emissions reduction effects of energy efficiency improvements are weak and may even be offset by rebound effects. Therefore, especially in developing countries, governments should formulate targeted policies to incentivize renewable energy investment. This approach not only helps to optimize the energy structure and reduce dependence on fossil fuels but also lays the foundation for a low-carbon economy. Governments can encourage investments in the clean energy sector through fiscal subsidies, tax incentives, and green credit schemes.

Second, high-income countries should increase support for the research and development as well as the market application of renewable energy technologies. These countries, with their robust market mechanisms and strong technological innovation capabilities, are better positioned to leverage energy efficiency policies to reduce fossil fuel consumption. Policies should encourage the private sector and technology enterprises to intensify innovation in low-carbon technologies and promote the large-scale deployment of renewable energy sources such as wind and solar power. Additionally, measures should be taken to further relax market entry restrictions for green technologies and provide innovative incentives to support the development and commercialization of energy efficiency-related technologies.

Finally, with regard to energy security—especially for countries heavily dependent on energy imports—it is recommended that domestic investment in clean energy be increased to reduce reliance on external energy supplies. Against the backdrop of increasing volatility in global energy markets, enhancing the autonomy and stability of energy supplies will have profound implications for reducing fossil fuel consumption and optimizing the energy structure. Therefore, governments should promote the diversification of energy sources, with particular emphasis on increasing research and development investments in renewable energy and storage technologies to enhance energy independence and sustainability.