Decarbonizing France: Asymmetric and State-Dependent Effects of Growth, Energy, Trade, and Innovation on CO₂ Emissions

Abstract

This study examines the asymmetric and distribution-dependent effects of economic growth, renewable energy consumption, energy use, trade openness, and innovation on CO₂ emissions in France over the period 1990–2024. It aims to understand how positive and negative shocks in key macroeconomic variables shape emissions dynamics within a mature low-carbon economy and their implications for environmental sustainability and sustainable energy transition. The analysis employs a nonlinear autoregressive distributed lag (NARDL) model to capture short- and long-run asymmetries, combined with the bounds testing approach for cointegration and Newey–West corrections for robust inference. To account for distributional heterogeneity, simultaneous quantile regressions (Q25, Q50, Q75) are estimated. The results reveal significant nonlinearities and state-dependent effects. Reductions in renewable energy exert stronger upward pressures on emissions than the mitigating effects of increases, highlighting a loss-dominance asymmetry. Energy use and trade openness exhibit asymmetric and persistent emission-increasing effects, while innovation reduces emissions primarily in the short run and during high-emission regimes. Economic growth shows no significant long-run impact, suggesting partial decoupling. Overall, emissions responses vary across both time and conditional distribution. The findings indicate that climate policies in France should prioritize renewable energy stability, energy-system flexibility, and targeted innovation strategies to effectively manage asymmetric and state-dependent environmental dynamics. The study further demonstrates that achieving long-run sustainability objectives requires adaptive climate policies capable of addressing nonlinear and distribution-dependent emissions responses within France’s low-carbon economic structure.

1. Introduction

The global challenge of climate change has placed unprecedented emphasis on understanding the determinants of carbon dioxide (CO₂) emissions and the pathways through which economies can transition toward low-carbon development and environmental sustainability. France, as one of the leading high-income economies in the European Union, has committed to ambitious environmental goals—including a 40% reduction in greenhouse gas emissions by 2030 and carbon neutrality by 2050 under the National Low-Carbon Strategy (SNBC). Despite progress driven by a strong nuclear-based energy structure, growing renewable investment, and key policy interventions, France continues to face significant macroeconomic and structural forces that shape its emissions trajectory. These include fluctuations in economic activity, changes in energy demand, the pace of renewable energy deployment, increasing openness to international trade, and the evolving landscape of technological innovation. Understanding how these factors influence CO₂ emissions—both in the short and long run, and under different economic states—is therefore essential for designing informed and effective environmental policies and sustainability-oriented policies.

Empirical research has increasingly recognized that the relationship between emissions and their macroeconomic determinants is rarely linear or symmetric. Numerous studies show that positive and negative shocks in economic growth [1], renewable energy [2], energy use [3], trade openness [4], and innovation [5] may have asymmetric effects on environmental outcomes and long-run sustainability performance. Traditional linear models, which assume uniform responses to increases and decreases in these variables, may therefore obscure important dynamics in the emissions process. Moreover, recent evidence suggests that the magnitude of emissions changes matters: economic, energy, or technological shocks may produce different effects depending on whether the economy is experiencing low, typical, or high levels of emissions [6]. Such distributional heterogeneity remains largely unexplored in the French context.

This study contributes to the literature by investigating the asymmetric and distribution-dependent drivers of CO₂ emissions in France over the period 1990–2024 using a combined nonlinear autoregressive distributed lag (NARDL) model and simultaneous quantile regression framework. The NARDL approach allows us to disentangle short-run and long-run asymmetries by separating positive and negative changes in key explanatory variables [7], while the quantile regression method uncovers how these relationships differ across the conditional distribution of emissions. This dual methodological strategy provides a richer and more nuanced understanding of France’s emissions dynamics than mean-based linear models. Furthermore, the combined framework contributes to the sustainability literature by examining how macroeconomic and energy-related shocks affect environmental sustainability under different emissions regimes.

The motivation for this approach is threefold. First, France’s energy transition trajectory is complex and subject to shocks, particularly in renewable energy deployment, energy demand, and trade-related production structures. Second, current empirical evidence on France remains ambiguous regarding the presence of asymmetric environmental responses, with most studies employing symmetric or linear specifications. Third, the quantile-dependent effects of emissions, especially under states of high environmental pressure, have not been systematically analyzed. Addressing these gaps is crucial for designing policies that are both effective and state contingent in supporting sustainable development and long-run environmental sustainability.

The findings of this study offer important policy implications for France’s low-carbon strategy and broader sustainability objectives. The empirical results demonstrate (i) strong asymmetric effects of renewable energy, energy use, trade openness, and innovation; (ii) distribution-dependent sensitivities, particularly at high-emissions quantiles; and (iii) evidence of decoupling between economic growth and emissions in the long run. These insights underscore the need for policies that stabilize renewable energy supply, reduce structural energy intensity, green the trade sector, and support innovation, especially during periods of heightened emissions. Overall, the findings highlight that achieving environmental sustainability in France requires adaptive climate policies capable of managing nonlinear and state-dependent emissions responses.

The remainder of the paper is structured as follows. Section 2 reviews the relevant literature on emissions drivers. Section 3 outlines the methodological framework. Section 4 describes the data and variables. Section 5 presents empirical results, including NARDL and quantile regression estimates. Section 6 discusses the findings. Section 7 concludes with policy recommendations.

2. Literature Review

The empirical literature on the determinants of CO₂ emissions has expanded considerably over the past three decades, reflecting global policy concerns regarding climate change, energy transitions, and sustainable economic development. A large body of work investigates how macroeconomic factors—economic growth, energy use, renewable energy consumption, trade openness, and technological innovation—influence environmental quality across advanced, emerging, and developing economies. However, most early contributions relied on linear models that assume symmetric and uniform responses across time, ignoring the possibility of nonlinear adjustments, threshold effects, and distribution-dependent dynamics.

2.1. Economic Growth and CO₂ Emissions

The relationship between economic growth and environmental degradation has been extensively examined through the Environmental Kuznets Curve (EKC) hypothesis [8,9]. Many studies document that rising income initially increases emissions but later contributes to environmental improvements as economies transition toward cleaner technologies and services. However, recent research suggests that this relationship may be asymmetric, with positive and negative shocks in growth affecting emissions differently. Shahbaz et al. (2020) [1] highlight that expansions tend to increase emissions more strongly than contractions reduce them. Similarly, Baek (2015) [10] and Omri et al. (2014) [11] report that economic structure and energy play crucial roles in determining whether growth contributes to long-term decarbonization. Evidence for France specifically indicates partial decoupling of emissions from economic activity due to its low-carbon electricity mix [12], but the presence of asymmetric short-run effects remains underexplored.

2.2. Renewable Energy Consumption and Emissions

Renewable energy has been consistently identified as a critical mechanism for reducing CO₂ emissions. Numerous studies demonstrate that increases in renewable energy consumption lead to long-term declines in emissions [13]. However, emerging evidence suggests the existence of asymmetric environmental responses. For instance, Salim & Rafiq (2012) [14] show that reductions in renewable availability can produce disproportionately large increases in emissions, while Hatzigeorgiou & Koilakou, (2025) [15] emphasize nonlinearities in the renewable–emissions relationship. In Europe, Marques & Fuinhas (2012) [16] find that renewable energy deployment exhibits heterogeneous effects across countries depending on system stability and policy frameworks. Yet, few studies have analyzed this asymmetry in the French context, despite France’s evolving renewable portfolio and intermittent energy supply challenges.

2.3. Energy Use and Emissions Dynamics

Energy consumption remains one of the most robust predictors of CO₂ emissions across countries [17,18]. While the literature consistently confirms a positive growth–energy–emissions nexus, more recent studies highlight the presence of nonlinearities linked to energy intensity, fuel switching, and demand-side shocks. Destek & Sarkodie (2019) [3] demonstrate that negative energy shocks may raise emissions when they trigger substitution toward more carbon-intensive sources or cause system inefficiencies. In advanced economies, long-term structural dependence on energy-intensive activities persists despite improvements in energy efficiency [19]. For France, where energy consumption patterns blend nuclear, renewable, and fossil sources, the asymmetric and distribution-dependent effects of energy shocks require further examination.

2.4. Trade Openness and Environmental Impacts

The environmental consequences of trade openness are widely debated. The pollution hypothesis argues that trade expansion may increase emissions by shifting production to pollution-intensive sectors [4,20]. Conversely, the technique effect suggests that trade can reduce emissions through technology transfers and cleaner production methods [21,22]. Empirical studies report mixed results, with several works identifying asymmetric or nonlinear effects. For example, Shahbaz et al. (2020) [1] and Destek & Okumus (2019) [23] show that positive trade shocks tend to increase emissions more strongly than negative shocks reduce them. Despite France’s high integration in global value chains, research on trade-induced asymmetries in emissions remains limited.

2.5. Technological Innovation and Environmental Quality

Technological innovation is widely recognized as a long-term driver of decarbonization and energy efficiency [5,24]. The direction and intensity of innovation matter: green innovations generally reduce emissions, while non-green innovations may have neutral or adverse effects [25]. Studies applying nonlinear or asymmetric methods find that innovation effects may be stronger during periods of high environmental pressure [26]. For France—which invests heavily in R&D, digital technologies, and energy-efficient innovation—understanding these distributional and asymmetric effects is essential for evaluating the effectiveness of the country’s innovation-driven transition strategies.

2.6. Nonlinear and Distributional Approaches

Growing recognition of nonlinearities has led to the adoption of advanced econometric methods such as NARDL [7], threshold regressions, and quantile regressions [6]. NARDL models allow decomposition of positive and negative changes in explanatory variables, uncovering asymmetries that linear models mask. Quantile regressions further reveal how effects differ across the distribution of emissions, capturing dynamics relevant when emissions are unusually high or low. Recent studies applying these methods [27] show pronounced asymmetric and quantile-specific effects in various countries, but no study has yet combined both approaches to analyze France’s emissions trajectory.

2.7. Conceptual Framework: Asymmetric Emissions Responses in France

To explain the asymmetric effects identified in this study, the conceptual framework builds on the idea that CO₂ emissions respond differently to positive and negative shocks because energy systems, trade structures, and technological adjustment processes are characterized by rigidity, substitution effects, and delayed policy responses. In the French context, these mechanisms are especially relevant because France has a distinctive low-carbon electricity mix dominated by nuclear power, complemented by a gradual expansion of renewables. Unlike fossil-fuel-dependent economies, France’s electricity generation system already relies heavily on nuclear energy, which substantially lowers the carbon intensity of electricity production. Therefore, the environmental role of renewable energy expansion in France differs from that observed in coal- or natural-gas-based economies. Renewable energy deployment may not primarily operate through direct substitution away from highly carbon-intensive electricity generation, but rather through complementary mechanisms such as improving energy-system flexibility, reducing fossil-fuel dependence in transportation and heating sectors, enhancing energy diversification, and limiting the use of carbon-intensive marginal energy sources during peak-demand periods or nuclear maintenance disruptions.

This structure reduces average emissions but does not eliminate vulnerability to shocks in renewable energy availability, energy demand, or trade-related production.

First, renewable energy shocks may generate asymmetric effects because increases and decreases in renewable energy do not produce equivalent environmental responses. A positive renewable energy shock may reduce emissions only gradually, since renewables must be integrated into the grid and may partly complement, rather than immediately replace, existing low-carbon nuclear electricity. By contrast, a negative renewable energy shock can rapidly increase emissions if the energy system compensates through fossil-based backup generation or imported energy. In the French context, these asymmetric effects are likely linked less to direct electricity-sector substitution and more to broader economy-wide adjustments involving transportation, heating, industrial demand, and marginal fossil-fuel energy use. This explains why renewable energy reductions may exert stronger upward pressure on emissions than renewable increases exert downward pressure, consistent with the nonlinear energy-transition literature and the NARDL logic of Shin et al. (2014) [7].

Second, energy-use shocks may affect emissions asymmetrically because changes in total energy demand interact with the carbon intensity of marginal energy supply. In France, average electricity production is relatively low carbon due to nuclear power; however, marginal increases in energy demand may still require fossil-based sources, especially during peak demand periods or supply disruptions. Conversely, reductions in energy use do not necessarily reduce emissions proportionately if they reflect temporary economic slowdowns, efficiency losses, or substitution across sectors. Therefore, the emissions effect of energy-use shocks depends not only on the quantity of energy consumed but also on the composition and flexibility of the energy system. This distinction is particularly important because the dependent variable used in this study reflects total territorial CO₂ emissions across all sectors rather than electricity-generation emissions alone.

Third, trade openness may produce asymmetric emissions effects through scale, composition, and technique channels. Positive trade shocks can increase emissions by expanding production, transport, logistics, and energy demand. In contrast, negative trade shocks may not reduce emissions proportionately because domestic production structures, imported intermediate inputs, and consumption patterns adjust slowly. This is consistent with the trade–environment framework of Antweiler et al. (2001) [21] and Copeland and Taylor (2004) [4], where trade can either increase emissions through scale effects or reduce them through cleaner technologies and efficiency gains. In France, the asymmetric trade effect is likely shaped by its integration into European and global value chains.

Overall, the framework suggests that emissions in France are driven by three asymmetric channels: the renewable energy stability channel, the energy-system rigidity channel, and the trade-induced scale channel. These channels justify the use of the NARDL approach, which separates positive and negative partial-sum shocks and allows the empirical model to capture hidden nonlinearities that linear models would ignore. This framework is consistent with the manuscript’s results showing that renewable energy, energy use, and trade openness generate directionally different effects on CO₂ emissions in France. Moreover, the framework highlights that the observed environmental dynamics should be interpreted within the broader context of France’s economy-wide territorial emissions structure and its nuclear-dominated low-carbon electricity system.

2.8. Contribution of the Present Study

Against this background, the present study makes three major contributions. First, it provides the first integrated NARDL and quantile regression analysis for France, capturing both short- and long-run asymmetries and distribution-dependent effects. By combining these two econometric approaches, the study offers a more comprehensive understanding of the nonlinear and state-dependent dynamics of CO₂ emissions within the broader context of environmental sustainability and sustainable energy transition. Second, it examines the roles of renewable energy, energy use, economic growth, trade openness, and innovation in a unified framework over more than three decades. This integrated framework contributes to the sustainability literature by evaluating how macroeconomic and energy-related shocks influence France’s progress toward long-run environmental sustainability objectives. Third, it offers policy-relevant insights into how France’s emissions respond under different states of environmental pressure, a critical dimension for effective climate strategy design. The findings therefore provide important implications for sustainability-oriented climate policies aimed at strengthening renewable-energy resilience, improving energy-system flexibility, and supporting sustainable low-carbon development in France.

3. Methodology

This study employs an integrated econometric strategy designed to examine the dynamic, asymmetric, and distribution-dependent relationship between CO₂ emissions and its key macroeconomic determinants in France within the broader context of environmental sustainability and sustainable energy transition.

The methodological framework consists of four sequential components: (i) nonlinear autoregressive distributed lag (NARDL) modelling, (ii) cointegration verification using the Bounds Test, (iii) diagnostic corrections for potential autocorrelation and heteroskedasticity, and (iv) simultaneous quantile regression (SQR) to explore distributional heterogeneity in short-run effects.

Figure 1 presents the methodological framework of the study and summarizes the sequential empirical procedures adopted in the analysis. The framework begins with data collection and variable transformation, followed by stationarity testing, NARDL estimation, cointegration analysis, asymmetry testing, diagnostic corrections, and simultaneous quantile regression. The final stage focuses on interpreting the asymmetric and distribution-dependent determinants of CO₂ emissions in France and deriving evidence-based policy implications.

As illustrated in Figure 1, the empirical strategy combines both time-series asymmetry analysis and distributional heterogeneity analysis in order to provide a comprehensive understanding of France’s CO₂ emissions dynamics. The integration of NARDL and SQR approaches allows the study to capture short-run and long-run asymmetries, positive versus negative shock effects, and state-dependent emission responses across different quantiles of the emissions distribution.

3.1. Nonlinear ARDL (NARDL) Framework

To assess asymmetric effects of economic growth, renewable energy consumption, energy use, trade openness, and innovation on CO₂ emissions, the study employs the NARDL model proposed by Shin et al. (2014) [7]. This approach decomposes each explanatory variable into positive and negative partial sum processes, allowing the model to distinguish between the effects of increases and decreases:

$$X_t^{+}={\displaystyle \sum _{j=1}^t}\mathrm{m}\mathrm{a}\mathrm{x}(\Delta X_j,0),X_t^{-}={\displaystyle \sum _{j=1}^t}\mathrm{m}\mathrm{i}\mathrm{n}(\Delta X_j,0).$$

(1)

where $X_t^{+}$ and $X_t^{-}$ denote the cumulative positive and negative partial-sum processes of the explanatory variable $X_t$, respectively, and $\Delta$ represents the first-difference operator.

The baseline NARDL specification is:

$$\Delta co{2}_t={\alpha }_0+\rho co{2}_{t-1}+\sum _i{\theta }_i^{+}{X}_{i,t-1}^{+}+\sum _i{\theta }_i^{-}{X}_{i,t-1}^{-}+\sum _i{\gamma }_i^{+}\Delta X_{i,t}^{+}+\sum _i{\gamma }_i^{-}\Delta X_{i,t}^{-}+{\epsilon }_t,$$

(2)

where $X_i$ includes gdpc, ren, ene, trd, and inn. The short-run dynamics are represented by the first-differenced positive and negative partial-sum components of the explanatory variables, while the long-run relationship is captured through the lagged level variables included in the error-correction representation.

The parameters (p) and (q) represent the optimal lag lengths for the dependent and explanatory variables, respectively. The optimal lag orders were selected using the Akaike Information Criterion (AIC), which is appropriate for relatively small annual samples and commonly applied in ARDL/NARDL estimation procedures.

In Equation (2), ${\alpha }_0$ denotes the constant term, $\rho$ represents the coefficient of the lagged dependent variable, ${\theta }_i^{+}$ and ${\theta }_i^{-}$ capture the long-run asymmetric effects of positive and negative shocks, ${\gamma }_i^{+}$ and ${\gamma }_i^{-}$ represent the short-run asymmetric coefficients, and ${\epsilon }_t$ is the stochastic error term.

This specification captures both short-run asymmetry (via differenced terms) and long-run asymmetry (via lagged levels).

The reported long-run coefficients correspond to normalized long-run multipliers derived from the estimated NARDL model. Following Shin et al. (2014) [7], the long-run asymmetric coefficients were calculated by dividing the coefficients of the lagged positive and negative partial-sum variables by the coefficient of the lagged dependent variable (error-correction term). Formally, the long-run multipliers are computed as:

$${\beta }^{+}=-{\displaystyle \frac{{\theta }^{+}}{\varphi }};{\beta }^{-}=-{\displaystyle \frac{{\theta }^{-}}{\varphi }}$$

(3)

where ${\theta }^{+}$ and ${\theta }^{-}$ denote the coefficients associated with the lagged positive and negative components of the explanatory variables, and $\varphi$ represents the coefficient of the lagged dependent variable. These coefficients are interpreted as long-run equilibrium elasticities.

3.2. Bounds Test for Cointegration

The existence of a long-run equilibrium relationship between CO₂ emissions and its determinants is tested using the Pesaran et al. (2001) [28] Bounds Testing approach applied to the joint significance of lagged explanatory variables. The test compares the computed F-statistics with critical bounds for I(0) and I(1) series. Evidence of cointegration permits decomposition into long-run coefficients and an error-correction representation.

3.3. Error-Correction Representation

When cointegration is established, the NARDL model incorporates an error-correction term (ECT) representing the speed at which deviations from long-run equilibrium are corrected. A negative and statistically significant ECT coefficient indicates stable adjustment dynamics and validates interpretation of long-run asymmetric elasticities.

3.4. Diagnostic Checking and HAC Corrections

Because time-series models may exhibit autocorrelation or heteroskedasticity in residuals, formal diagnostic tests are applied:

-

Breusch–Godfrey LM test for serial correlation

-

Breusch–Pagan/Cook–Weisberg test for heteroskedasticity

-

Stability tests such as CUSUM and CUSUMSQ

If autocorrelation or heteroskedasticity is detected, the study applies Newey–West heteroskedasticity- and autocorrelation-consistent (HAC) standard errors [29], which correct inference while leaving coefficient estimates unchanged.

3.5. Asymmetry Testing

To formally verify whether positive and negative shocks exert statistically different effects in the short and long run, the study applies Wald tests on the equality of:

$${\theta }_i^{+}={\theta }_i^{-}(\mathrm{long} \mathrm{run}),{\gamma }_i^{+}={\gamma }_i^{-}(\mathrm{short} \mathrm{run}),$$

(4)

where ${\theta }_i^{+}$ and ${\theta }_i^{-}$ denote the long-run coefficients associated with positive and negative shocks, while ${\gamma }_i^{+}$ and ${\gamma }_i^{-}$ represent the corresponding short-run coefficients. Rejecting these equalities confirms the presence of asymmetry.

3.6. Simultaneous Quantile Regression (SQR)

To complement the NARDL framework, the study employs Simultaneous Quantile Regression (SQR) [6] to capture distribution-dependent heterogeneity in short-run effects across the conditional distribution of changes in CO₂ emissions. Quantiles τ = 0.25, 0.50, and 0.75 are estimated to examine:

-

low-emission adjustment regimes (Q25)

-

typical/median regimes (Q50)

-

high-emission regimes (Q75)

The quantile regression model is specified as:

$$Q_{\tau }\left(\Delta co{2}_t∣Z_t\right)={\beta }_0\left(\tau \right)+\sum _i{\beta }_i\left(\tau \right)Z_{i,t},$$

(5)

where $Q_{\tau }(\cdot )$ denotes the conditional quantile function at quantile $\tau$, and $Z_t$ includes the differenced asymmetric variables together with the error-correction term. The coefficients ${\beta }_i\left(\tau \right)$ measure the marginal effects of explanatory variables across different points of the conditional distribution of ${\mathrm{C}\mathrm{O}}_2$ emissions. Bootstrapped standard errors are employed to ensure robust inference under small-sample conditions.

3.7. Rationale for the Combined Approach

The joint use of NARDL and quantile regression allows the study to investigate:

-

temporal asymmetry (short-run vs. long-run responses)

-

directional asymmetry (positive vs. negative shocks)

-

distributional heterogeneity (effects varying across quantiles)

This comprehensive framework captures the complex and state-dependent behavior of CO₂ emissions, making it especially suitable for analyzing long-term transition economies such as France.

4. Data

4.1. Data Description

This study constructs an annual macro-economic and environmental dataset for France covering the period 1990–2024. The variables included capture key dimensions of emissions, economic growth, energy structure, trade openness, and innovation. The data were collected from internationally recognized databases, including the World Development Indicators (World Bank), Our World in Data/Global Carbon Project, and the World Intellectual Property Organization (WIPO). In addition, all variables were transformed into natural logarithms prior to estimation in order to reduce heteroskedasticity, improve normality, and allow elasticity-based interpretation of the estimated coefficients.

Table 1. Variable Definitions.

Series Name	Variable	Definition	Unit/Measurement	Data Source
Carbon dioxide (CO2) emissions excluding LULUCF per capita	CO2	Territorial CO2 emissions excluding Land-Use, Land-Use Change and Forestry (LULUCF), divided by total population	tons of CO2 per capita	Our World in Data/Global Carbon Project
GDP (constant 2015 US$)	GDPC	Gross Domestic Product measured in constant 2015 US dollars	USD (constant 2015)	World Development Indicators (World Bank)
Renewable energy consumption	REN	Share of renewable energy in total final energy consumption	Percentage of total final energy consumption (%)	World Development Indicators (World Bank)
Energy use	ENE	Total primary energy use divided by population	kg of oil equivalent (kgoe) per capita	World Development Indicators (World Bank)
Trade openness	TRD	Sum of exports and imports of goods and services as a percentage of GDP	Percent of GDP (%)	World Development Indicators (World Bank)
Patent applications, residents	INN	Annual number of patent applications filed by residents	Number of applications	World Intellectual Property Organization (WIPO)/World Bank

summarizes each series, its source, and its notation.

It is important to note that the CO₂ emissions variable used in this study represents total territorial CO₂ emissions excluding Land-Use, Land-Use Change and Forestry (LULUCF) on a per-capita basis rather than electricity-sector emissions alone. Consequently, the dependent variable captures emissions generated across multiple sectors of the French economy, including transportation, industry, residential and commercial heating, manufacturing, and other fossil-fuel-related activities. This distinction is particularly relevant in the French context because France’s electricity generation system is already largely low carbon due to the dominant role of nuclear energy. Therefore, the environmental effects associated with renewable energy expansion should not be interpreted solely as direct substitution away from carbon-intensive electricity generation, but also as reflecting broader economy-wide adjustments related to energy-system flexibility, transport, heating demand, and marginal fossil-fuel energy use.

Figure 2 illustrates the long-run evolution of the six core variables—CO₂ emissions, economic development, renewable energy consumption, energy intensity, trade openness, and technological innovation—used in the empirical analysis for France over 1990–2024. The graphical trends are presented using the logarithmically transformed series employed in the econometric estimations.

Carbon emissions exhibit a clear downward trajectory over the period. After stabilizing in the 1990s, emissions begin to decline steadily from the mid-2000s onward, reflecting improvements in energy efficiency, fuel switching, and the expansion of low-carbon technologies. The sharp drop around 2020 corresponds to the COVID-19-related economic slowdown.

GDP (constant 2015 USD) shows a consistent upward trend, with temporary slowdowns during global crises (2008 and 2020). The long-term pattern reflects steady economic expansion, improved productivity, and structural modernization.

Renewable energy’s share of total final energy consumption displays a gradual rise, followed by a stronger upward trend post-2010. This reflects France’s strategic alignment with EU renewable targets, expansion of wind and solar capacity, and declining reliance on fossil fuels.

Energy intensity increases slightly in the early years but begins a persistent decline after 2005, indicating efficiency gains and reduced per-capita energy demand. This structural reduction aligns with France’s energy transition policies and improvements in industrial efficiency.

Trade openness shows an overall rising trend, signaling deeper integration into global markets. Although fluctuations appear around major global events (2001, 2008, 2020), the general pattern is upward, consistent with France’s high involvement in international trade.

Patent applications by residents demonstrate a notable rise from 1990 to the mid-2010s, highlighting increasing innovation activity. Some volatility appears after 2016 and a drop around 2020, consistent with economic cycles and sectoral restructuring.

Table 2. Descriptive Statistics.

Variable	Obs.	Mean	Std. Dev.	Min	Max
co2	34	1.7565	0.1496	1.4197	1.947
gdpc	35	10.4385	0.1067	10.2397	10.5826
ren	32	2.4163	0.1965	2.1401	2.8214
ene	34	8.2693	0.0858	8.041	8.3727
trd	35	4.0282	0.1517	3.7311	4.328
inn	32	9.5264	0.0593	9.4237	9.5989

summarizes the descriptive statistics for the six variables used in this study over the period 1990–2024 for France. The dataset consists of a time-series dataset with annual observations for economic, environmental, energy, trade, and innovation indicators, with some variation in sample sizes due to data availability.

Overall, the descriptive statistics reveal moderate variation across the key variables, with all values falling within plausible macroeconomic and environmental ranges for an advanced OECD economy like France. CO₂ emissions per capita average 1.76 t/capita and fluctuate within a relatively narrow band (1.42–1.95), reflecting the country’s long-standing reliance on low-carbon electricity and progressive decarbonization efforts. Economic development—measured as the natural logarithm of real GDP—shows limited dispersion around a mean of approximately 10.44, indicative of France’s stable long-run growth trajectory. The renewable energy share exhibits moderate variability, averaging 2.42% and increasing markedly in more recent years, consistent with France’s commitments under EU renewable energy directives. Energy use per capita shows very low variability, with a mean of 8.27, suggesting a steady consumption pattern supported by incremental efficiency improvements. Trade openness, with a logged mean of 4.03, confirms France’s high degree of integration into global markets. Finally, patent applications by residents display low dispersion around the mean of 9.53, reflecting a stable innovation environment shaped by both domestic R&D capacity and global economic cycles.

4.2. Correlation Analysis

Table 3. Correlation Matrix.

	co2	gdpc	ren	ene	trd	inn
co2	1.0000
gdpc	−0.7341	1.0000
ren	−0.8722	0.4153	1.0000
ene	0.8463	−0.3074	−0.8248	1.0000
trd	−0.7377	0.8652	0.4649	−0.3550	1.0000
inn	−0.3814	0.8442	0.0637	0.1094	0.8015	1.0000

presents the pairwise correlation coefficients among the six variables: CO₂ emissions (co₂), real GDP (gdpc), renewable energy consumption (ren), energy use (ene), trade openness (trd), and patent applications (inn).

The correlation analysis uncovers several important patterns that help contextualize France’s economic–environmental dynamics. Economic development (gdpc) exhibits a strong negative correlation with CO₂ emissions (−0.73), indicating a gradual decoupling of growth from carbon intensity and reflecting France’s structural shift toward cleaner technologies and service-oriented activities. Renewable energy (ren) is strongly negatively correlated with both CO₂ emissions (−0.87) and energy use (−0.82), supporting the view that expanded deployment of renewables reduces environmental pressures and lowers dependence on fossil-based energy sources. Energy use (ene) maintains a strong positive association with CO₂ emissions (0.85), consistent with the conventional linkage between energy consumption and emissions in periods when conventional fuels dominate marginal energy demand. Trade openness (trd) shows a mixed structure: while negatively correlated with CO₂ emissions (−0.74), it is strongly and positively correlated with GDP (0.87) and innovation (0.80), suggesting that France’s outward-oriented economic structure is intertwined with technological advancement and more efficient production processes. Technological innovation (inn) also displays strong positive correlations with GDP (0.84) and trade openness (0.80), underscoring the role of economic integration and productivity enhancement in fostering innovation-led development. Overall, these correlations provide preliminary support for the hypothesized relationships investigated in the subsequent time-series models, particularly the central roles of growth, renewable energy, and innovation in shaping France’s emissions trajectory.

4.3. Unit Root Tests

To determine the order of integration of the variables, the Augmented Dickey–Fuller (ADF) test was applied to each series in both levels and first differences.

Table 4. ADF Unit Root Test Results.

Level Series
Variable	ADF Statistic	1% CV	5% CV	p-value
co2	0.7890	−3.702	−2.980	0.9915
gdpc	−1.4870	−3.696	−2.978	0.5397
ren	0.2710	−3.716	−2.986	0.9760
ene	2.2850	−3.702	−2.980	0.9989
trd	−1.3350	−3.696	−2.978	0.6128
inn	−1.6410	−3.716	−2.986	0.4616
First Differences
Variable	ADF Statistic	1% CV	5% CV	p-value
dco2	−5.3810	−3.709	−2.983	0.0000
dgdpc	−4.9020	−3.702	−2.980	0.0000
dren	−3.3180	−3.723	−2.989	0.0141
dene	−3.4970	−3.709	−2.983	0.0081
dtrd	−6.3730	−3.702	−2.980	0.0000
dinn	−3.7470	−3.723	−2.989	0.0035

reports the results.

The test statistics show that all variables are non-stationary in levels, as none of the ADF statistics exceed the 1%, 5%, or 10% critical values, and all MacKinnon p-values are well above conventional significance thresholds. In contrast, the ADF results for the first-differenced series strongly indicate stationarity. All six differenced variables reject the null of a unit root at the 1% or 5% level, with highly significant test statistics and near-zero p-values. This confirms that the variables are integrated of order one, I(1). The I(1) variables justify the use of ARDL and NARDL frameworks, which accommodate regressors of mixed integration orders (I(0)/I(1)) but require that none of the variables be I(2).

4.4. Bounds Test for Cointegration

The existence of a long-run relationship among the variables was assessed using the Pesaran et al. (2001) [28] bounds testing approach, where the null hypothesis assumes no cointegration. The results are reported in

Table 5. Bounds Test Results.

Test	F-Statistic	p-Value
F-statistic for joint long-run significance	65.0200	0.0000

.

The computed F-statistic of 65.02 exceeds the upper critical bound even at the 1% significance level, providing strong evidence to reject the null and confirm the presence of a stable long-run equilibrium relationship. This finding indicates that CO₂ emissions, GDP, renewable energy consumption, energy use, trade openness, and technological innovation move together over time, supporting the theoretical expectation of long-term interconnectedness between economic activity, energy structure, and environmental performance. Establishing cointegration justifies the subsequent estimation of long-run asymmetric coefficients, the implementation of an error-correction representation to capture adjustment dynamics, and the computation of dynamic multipliers to trace the response path of emissions to positive and negative shocks in the explanatory variables.

5. Results

5.1. NARDL Regression

The analysis first reports the NARDL regression outcomes, which capture both short-run and long-run asymmetric effects on CO₂ emissions, as shown in

Table 6. NARDL Estimation Results for CO₂ Emissions.

	NARDL Estimation Results for CO2 Emissions			NARDL Estimates with Newey–West HAC Standard Errors
Variable	Coefficient	Std. Error	p-Value	Coefficient	Std. Error	p-Value
L1.co2	–1.2028	0.2233	0.0010	–1.2028	0.2336	0.0010
	Long-Run Effects			Long-Run Effects
L1.gdpc_pos	−0.2297	0.4201	0.5990	−0.2297	0.4057	0.5870
L1.gdpc_neg	−1.4150	0.8330	0.1280	−1.4150	0.9636	0.1800
L1.ren_pos	−0.0451	0.1171	0.7100	−0.0451	0.1607	0.7860
L1.ren_neg	1.2869	0.3476	0.0060	1.2869	0.3005	0.0030
L1.ene_pos	2.0403	0.4223	0.0010	2.0403	0.5030	0.0040
L1.ene_neg	2.4528	0.6500	0.0050	2.4528	0.8178	0.0170
L1.trd_pos	1.0687	0.3508	0.0160	1.0687	0.3816	0.0230
L1.trd_neg	−0.0633	0.1817	0.7360	−0.0633	0.1103	0.5820
L1.inn_pos	−0.8016	0.4300	0.0990	−0.8016	0.3951	0.0770
L1.inn_neg	−0.3061	0.4652	0.5290	−0.3061	0.5572	0.5980
	Short-Run Effects			Short-Run Effects
D1.gdpc_pos	1.5957	0.5787	0.0250	1.5957	0.6246	0.0340
D1.gdpc_neg	−3.4172	1.4110	0.0420	−3.4172	1.9160	0.1120
D1.ren_pos	0.0432	0.1446	0.7730	0.0432	0.2351	0.8590
D1.ren_neg	1.1403	0.3041	0.0060	1.1403	0.3155	0.0070
D1.ene_pos	0.8134	0.3510	0.0490	0.8134	0.4094	0.0820
D1.ene_neg	1.7661	0.3464	0.0010	1.7661	0.3018	0.0000
D1.trd_pos	0.4636	0.1912	0.0420	0.4636	0.1602	0.0200
D1.trd_neg	0.0373	0.2291	0.8750	0.0373	0.2290	0.8750
D1.inn_pos	−1.4600	0.4530	0.0120	−1.4600	0.4193	0.0080
D1.inn_neg	1.9456	0.9718	0.0800	1.9456	1.2707	0.1640
Constant	2.2311	0.4299	0.0010	2.2311	0.4574	0.0010
	Model Fit			Model Fit
	R2	0.9796		R2	0.9796
	Adj. R2	0.9259		Adj. R2	0.9259
	F-statistic	18.2500		F-statistic	4558.0300
	p-value	0.0001		p-value	0.0000
Diagnostic Test		Statistic	p-Value
Breusch–Godfrey LM test		9.8870	0.0017
Breusch–Pagan/Cook–Weisberg test		0.7400	0.3891

. The long-run coefficients reported in Table 6 correspond to transformed long-run equilibrium multipliers obtained from the estimated NARDL error-correction specification.

The long-run NARDL estimates reveal clear and meaningful patterns in the way France’s CO₂ emissions respond to their key determinants. The lagged emissions term is negative and highly significant, confirming the presence of a stable long-run equilibrium in which deviations from the steady state are corrected over time. The negative and statistically significant coefficient of the lagged dependent variable additionally serves as the normalization parameter used to derive the long-run asymmetric multipliers reported in Table 6. This rapid adjustment is consistent with France’s mature, regulation-intensive energy and environmental governance system. Regarding economic growth, neither positive nor negative shocks to GDP produce significant long-run effects, indicating the absence of long-run growth–emissions asymmetry. This result suggests that France has achieved a degree of structural decoupling, whereby sustained increases in output no longer systematically translate into higher carbon emissions.

Renewable energy reveals a distinctly asymmetric pattern in the long-run dynamics. Negative shocks to renewable energy consumption significantly raise CO₂ emissions, whereas positive shocks do not produce significant emission reductions. This asymmetry implies that declines or instability in renewable energy availability are more environmentally damaging than expansions are beneficial, underscoring the importance of maintaining consistent renewable deployment. However, in the French context, this result should not be interpreted solely through electricity-sector substitution effects because France already maintains a predominantly low-carbon electricity mix dominated by nuclear power. Instead, the asymmetric renewable-energy effect likely reflects broader economy-wide mechanisms, including energy-system flexibility, fossil-fuel use in transportation and heating sectors, and the increased reliance on carbon-intensive marginal energy sources during periods of renewable shortfall or energy-demand pressure. Energy use exerts a strong symmetric long-run impact: both increases and decreases in energy use contribute to higher emissions. This finding indicates a structural dependence on energy-intensive activities, even within a predominantly low-carbon energy mix. Moreover, because the dependent variable captures total territorial CO₂ emissions rather than electricity-generation emissions alone, the estimated energy-use effects reflect broader sectoral dynamics involving transportation, industrial activity, residential heating, and economy-wide fossil-fuel consumption. For trade openness, only positive shocks exert a significant long-run effect by increasing emissions, while negative shocks have no discernible influence. This suggests that expanding trade intensifies production-related emissions, whereas reductions in trade exposure do not generate proportionate environmental gains. Innovation, proxied by patent applications, does not exert statistically significant long-run effects, suggesting that the environmental benefits of technological progress may require more time to materialize or depend on the nature and diffusion of the innovations rather than their volume alone.

Short-run dynamics display sharper and more immediate asymmetries across several variables. Economic growth exhibits a clear asymmetric effect: positive GDP shocks increase emissions, while negative shocks reduce them. This finding consists of short-term variations in industrial output, mobility, and energy consumption. Renewable energy again shows asymmetry in the short run, with reductions in renewable energy significantly increasing emissions, reinforcing the importance of continuity in renewable supply for mitigating short-term carbon spikes. Energy use demonstrates strong symmetric short-run effects, with both positive and negative shocks increasing emissions. This reflects short-run rigidity in France’s energy system, where fluctuations in energy demand are quickly reflected in carbon output due to the inflexibility of consumption patterns. Trade openness affects emissions only when trade expands, producing an immediate rise in emissions; trade contractions do not deliver offsetting environmental benefits. Innovation exerts a meaningful short-run effect: positive innovation shocks significantly reduce emissions, indicating that technological improvements can have immediate carbon-saving impacts even if their long-run influence is subdued.

Taken together, these results show that France’s CO₂ emissions are shaped by a complex mix of asymmetric and symmetric adjustment processes. Renewable energy and trade openness exert one-sided long-run effects, economic growth and innovation generate clear short-run asymmetries, and energy use consistently influences emissions across both horizons. The significant negative error-correction term further confirms the existence of a stable long-run relationship among the variables. Overall, the findings highlight that France’s environmental performance is driven not only by structural economic forces but also by the asymmetric impacts of renewable stability, trade dynamics, and technological improvements.

Following the estimation of the NARDL model, diagnostic tests were conducted to assess the reliability of the residual structure. The Breusch–Godfrey LM test indicates significant first-order serial correlation (χ² = 9.887, p = 0.0017), implying that the residuals exhibit autocorrelation that could distort conventional standard errors and lead to unreliable inference. In contrast, the Breusch–Pagan/Cook–Weisberg test does not reject the null of homoskedasticity (χ² = 0.74, p = 0.3891), suggesting that variance instability is not a major concern. Given the clear evidence of autocorrelation, the use of Newey–West heteroskedasticity- and autocorrelation-consistent (HAC) standard errors is warranted to correct for serial dependence and ensure robust, unbiased inference. Therefore, the Newey–West-corrected estimates provide a more reliable basis for interpreting the asymmetric long-run and short-run relationships captured by the NARDL model.

The Newey–West-corrected NARDL results confirm the robustness of the asymmetric relationships between CO₂ emissions and the key macro-environmental drivers in France over 1990–2024. The error-correction term remains negative and highly significant, indicating strong and rapid adjustment toward long-run equilibrium. In the long run, economic growth continues to show no significant effect—whether through positive or negative shocks—reinforcing the view that France has achieved structural decoupling between output and emissions. Renewable energy displays a pronounced asymmetric pattern: negative shocks significantly increase CO₂ emissions, while positive shocks remain environmentally neutral, suggesting that losses in renewable energy capacity are more harmful than gains are beneficial. Energy use exerts strong and symmetric long-run effects, with both increases and decreases in energy intensity raising emissions, highlighting persistent dependence on energy consumption. Trade openness also exhibits asymmetry, as only positive trade shocks significantly increase emissions, whereas reductions in trade have no measurable impact. Innovation shows a marginally significant long-run reduction in emissions for positive shocks, while negative shocks remain insignificant, indicating that technological progress contributes modest but not dominant long-term environmental improvements. In the short run, GDP continues to exhibit asymmetric effects, with positive shocks raising emissions and negative shocks weakening (though preserving direction) under HAC correction. Short-run reductions in renewable energy significantly increase emissions, while short-run increases remain neutral. Energy use retains strong short-run effects, especially for negative shocks, which substantially increase emissions. Trade openness maintains its short-run asymmetry, as only positive shocks intensify emissions. Innovation continues to significantly reduce emissions in the short run, reinforcing the role of immediate technological improvements in achieving short-term environmental gains. Overall, the Newey–West results validate the robustness of the nonlinear dynamics and confirm the central role of renewable energy stability, energy intensity, and trade dynamics in shaping France’s emissions trajectory.

Figure 3 presents the CUSUM of Squares (CUSUMSQ) test for parameter stability in the NARDL model. The circle-connected line represents the cumulative sum of squared recursive residuals, while the upper and lower diagonal lines denote the 5% critical bounds. Since the CUSUMSQ statistic remains entirely within these bounds throughout the sample period, the null hypothesis of parameter stability cannot be rejected. This result indicates the absence of structural breaks and confirms the stability of the estimated NARDL coefficients over time.

The coefficient plots in Figure 4 visually summarize the nonlinear short-run and long-run asymmetric effects of economic growth, renewable energy, energy use, trade openness, and innovation on CO₂ emissions in France. In the left panel, blue dots represent the estimated short-run coefficients, while in the right panel, red dots represent the estimated long-run coefficients. The horizontal whiskers indicate 95% confidence intervals, and the vertical red line marks the zero-effect threshold. Upward arrows (↑) denote positive shocks (increases) in the explanatory variables, whereas downward arrows (↓) denote negative shocks (decreases). Coefficients whose confidence intervals do not cross the zero line can be interpreted as statistically significant at conventional levels.

The short-run panel shows that positive GDP shocks raise emissions, while negative shocks lower them, confirming clear short-run growth asymmetry. Reductions in renewable energy significantly increase emissions, whereas increases remain neutral, highlighting the environmental importance of avoiding renewable energy downturns. Both positive and negative energy-use shocks exert strong emission-increasing effects, indicating short-run rigidity in France’s energy consumption structure. Trade openness contributes positively to emissions only when trade expands, whereas contractions have no statistically meaningful effect. Positive innovation shocks reduce emissions, while negative shocks display weaker and statistically marginal effects.

In the long run, the plots reveal more persistent and structured asymmetries. Renewable energy retains a pronounced asymmetric influence: negative shocks sharply increase emissions, whereas positive shocks remain insignificant. Energy use continues to produce strong and symmetric emission-increasing effects, underscoring long-run dependence on energy intensity. Trade openness exerts long-run environmental pressure solely when trade increases, while reductions again have no effect, confirming one-sided trade–environment dynamics. Economic growth exhibits no significant long-run asymmetry, supporting structural decoupling of output and emissions. Innovation shows a marginally negative long-run effect for positive shocks but remains insignificant for negative ones, suggesting that technological progress contributes modest but not dominant long-term emission reductions. Altogether, the plots reinforce the key empirical finding that France’s emissions trajectory is shaped by both nonlinear short-run adjustments and persistent long-run asymmetries, particularly in renewable energy, energy use, and trade openness.

The Wald tests (

Table 7. Wald Tests for Long-Run and Short-Run Asymmetry.

Variable	Test Type	Null Hypothesis	F-Statistic	p-Value
GDP	Long-run	L.gdpc_pos = L.gdpc_neg	0.8600	0.3818
REN	Long-run	L.ren_pos = L.ren_neg	16.5800	0.0036
ENE	Long-run	L.ene_pos = L.ene_neg	0.7700	0.4064
TRD	Long-run	L.trd_pos = L.trd_neg	9.3700	0.0156
INN	Long-run	L.inn_pos = L.inn_neg	0.3500	0.5711
GDP	Short-run	D.gdpc_pos = D.gdpc_neg	5.5100	0.0468
REN	Short-run	D.ren_pos = D.ren_neg	5.0000	0.0557
ENE	Short-run	D.ene_pos = D.ene_neg	5.7500	0.0433
TRD	Short-run	D.trd_pos = D.trd_neg	3.1700	0.1127
INN	Short-run	D.inn_pos = D.inn_neg	5.4200	0.0483

) provide formal confirmation of the asymmetric relationships captured by the NARDL model.

In the long run, the results reveal significant asymmetry for renewable energy and trade openness. Specifically, the null hypothesis of symmetry is strongly rejected for renewable energy (F = 16.58, p = 0.0036) and for trade openness (F = 9.37, p = 0.0156), indicating that positive and negative shocks to these variables exert statistically different long-run impacts on CO₂ emissions. In contrast, the long-run symmetry tests for economic growth, energy use, and innovation yield insignificant results, suggesting that their long-run effects do not differ meaningfully between positive and negative shocks.

In the short run, the Wald tests indicate statistically significant asymmetry for economic growth (F = 5.51, p = 0.0468), energy use (F = 5.75, p = 0.0433), and innovation (F = 5.42, p = 0.0483), while renewable energy is marginally asymmetric (p = 0.0557). Trade openness, however, does not exhibit significant short-run asymmetry.

Collectively, these tests confirm that France’s emissions dynamics are shaped by a mix of long-run and short-run nonlinearities, with renewable energy and trade openness driving long-term asymmetries, while economic growth, energy use, and innovation primarily exhibit asymmetric behavior in the short run.

The dynamic multiplier graphs in Figure 5 illustrate how CO₂ emissions respond over time to positive shocks in the explanatory variables, capturing the temporal adjustment patterns implied by the NARDL model. The solid line represents the estimated mean adjustment path of CO₂ emissions following a positive shock, while the shaded area indicates the lower and upper confidence bounds. The widening bands after the shock horizon reflect increasing uncertainty around the long-run adjustment process.

A positive shock to GDP leads to an initial increase in emissions, followed by a gradual decline toward a new equilibrium, highlighting short-run sensitivity of emissions to economic expansion and the presence of long-run adjustment forces. A positive shock to renewable energy consumption produces an immediate and persistent reduction in emissions, confirming the long-run environmental gains from expanding renewables. In contrast, positive shocks to energy use generate an upward trajectory in emissions that stabilizes at a higher level, illustrating the strong and sustained carbon intensity associated with increased energy demand. Trade openness exhibits a similar pattern: a positive shock lifts emissions sharply and maintains them at elevated levels, reflecting the emissions-augmenting effect of increased trade activity. Finally, a positive innovation shock leads to a long-run decline in emissions after a short adjustment period, indicating that technological improvements exert delayed but meaningful environmental benefits. Overall, the dynamic multipliers confirm the asymmetric and time-varying influence of economic, energy, trade, and technological factors on CO₂ emissions in France, providing strong support for the nonlinear mechanisms captured by the NARDL framework.

5.2. QNARDL Regression

The analysis next extends beyond mean-based estimation by examining distributional heterogeneity through quantile regression, with the results for ΔCO₂ presented in

Table 8. Quantile Regression Results for ΔCO₂ (Bootstrap Standard Errors).

	Quantile 25			Quantile 50			Quantile 75
Variable	Coef	SE	p-Value	Coef	SE	p-Value	Coef	SE	p-Value
ect	2.1166	1.2590	0.1100	1.8785	1.0395	0.0870	2.8188	1.1106	0.0210
d_gdpc_pos	−2.0340	1.9909	0.3200	−1.7247	1.3884	0.2300	−3.2672	1.5193	0.0450
d_gdpc_neg	6.6494	5.1404	0.2120	6.1382	4.5409	0.1930	7.7866	6.0629	0.2150
d_ren_pos	0.1113	0.1800	0.5440	0.0237	0.1641	0.8870	0.0173	0.1532	0.9110
d_ren_neg	−2.0648	1.1561	0.0910	−1.5389	0.9606	0.1270	−2.5779	0.9623	0.0150
d_ene_pos	−0.7584	1.1104	0.5030	−0.5189	1.0992	0.6430	−1.2418	1.2247	0.3240
d_ene_neg	−2.4507	2.2897	0.2990	−2.7127	1.7739	0.1440	−3.9764	1.7922	0.0400
d_trd_pos	−0.8846	0.6171	0.1690	−0.6668	0.4896	0.1900	−1.1014	0.4772	0.0330
d_trd_neg	−0.3484	0.7077	0.6280	−0.2329	0.6129	0.7080	−0.0083	0.5687	0.9890
d_inn_pos	2.7910	1.6716	0.1120	2.1721	1.3453	0.1240	3.0381	1.4200	0.0460
d_inn_neg	−3.7923	2.2365	0.1070	−2.8694	1.8210	0.1330	−3.9491	1.8936	0.0520
Constant	−3.9642	2.3280	0.1060	−3.5075	1.9236	0.0850	−5.2294	2.0585	0.0210

.

The simultaneous quantile regression results provide important insights into how the determinants of changes in CO₂ emissions influence different parts of the conditional distribution of ΔCO₂. By comparing the 25th, 50th, and 75th quantiles, the analysis reveals whether the emission drivers behave differently in periods of low, median, or high emission changes. This distributional perspective complements the mean-based NARDL estimates and uncovers additional heterogeneity in the short-run adjustment process.

At the lower quantile (Q25), representing periods of relatively small or negative changes in emissions, none of the explanatory variables exhibit strong or statistically significant effects. Although the signs of coefficients largely align with expectations—such as renewable energy reductions (d_ren_neg) decreasing CO₂ or innovation shocks showing some positive influence—the p-values indicate that the effects are imprecisely estimated. This suggests that when emissions fluctuations are small, the system displays greater stability and is less responsive to short-term shocks in economic activity, energy use, trade, or innovation.

At the median quantile (Q50), the behavioral patterns remain broadly similar but with slightly stronger coefficient magnitudes. The signs continue to be economically meaningful—for example, renewable energy reductions still increase emissions, and innovation shocks have a positive influence. However, these effects remain statistically insignificant, implying that median changes in emissions are not strongly driven by short-run shocks in the explanatory variables. This indicates a relatively stable response at the center of the distribution, where typical changes in economic and energy conditions do not translate into pronounced environmental effects.

In contrast, the upper quantile (Q75) displays a distinctly different pattern, revealing statistically significant and economically important effects for several key variables. Positive GDP shocks significantly reduce emissions in this quantile, suggesting that during periods of large emission adjustments, economic expansions may coincide with structural efficiency improvements or shifts toward lower-carbon activities. Negative renewable energy shocks significantly increase emissions, confirming the critical role of renewable availability in shaping larger emission spikes. Similarly, negative shocks to energy use (d_ene_neg) significantly raise emissions, indicating that high-emissions periods are highly sensitive to disruptions in energy consumption patterns. Positive trade shocks (d_trd_pos) also increase emissions at Q75, consistent with the idea that trade expansion amplifies emissions when the system is already experiencing stronger fluctuations. Positive innovation shocks (d_inn_pos) significantly reduce emissions in the upper tail, highlighting the capacity of technological progress to moderately large spikes in CO₂ emissions.

Overall, the quantile regression results reveal clear distributional asymmetry in the short-run dynamics of emissions. While lower and median quantiles show limited responsiveness to shocks, the upper quantile—representing periods of more intense emissions adjustments—shows strong and significant effects for GDP, renewable energy, energy use, trade openness, and innovation. These findings suggest that policy interventions aimed at stabilizing emissions should focus particularly on conditions associated with large emissions movements, where economic, energy, and technology shocks exert the strongest influence. The results reinforce the nonlinear, state-dependent nature of France’s short-run emissions behavior, complementing the asymmetries identified in the NARDL model.

The quantile process plots in Figure 6 provide a dynamic view of how positive and negative shocks in each determinant influence CO₂ emissions across the conditional distribution of ΔCO₂, capturing the full range from low to high emission changes. The red line represents the estimated quantile coefficient at each quantile (Q25, Q50, and Q75), while the gray shaded area denotes the corresponding 95% confidence interval. Variations in the slope of the red line indicate changes in the magnitude and direction of the effect across quantiles, whereas wider confidence bands reflect greater estimation uncertainty.

For GDP, the plots suggest mild asymmetry: positive shocks tend to reduce emissions more strongly at the upper quantile (Q75), whereas negative shocks show larger positive effects at lower quantiles, indicating that economic contractions may contribute more to small emission fluctuations, while expansions help moderate larger ones. For renewable energy, positive shocks display steadily mild effects across quantiles, while negative shocks become increasingly harmful at higher quantiles, confirming that reductions in renewable energy availability disproportionately worsen emissions during periods of large environmental adjustments. Energy use shows a similar pattern: positive shocks exert relatively stable effects across quantiles, whereas negative shocks become substantially more emission-increasing at Q75, highlighting that disruptions in energy use intensify carbon outcomes most severely when the emissions system is already stressed.

Trade openness displays noticeable quantile variation, particularly for positive shocks, which become more strongly emission-increasing at higher quantiles; by contrast, negative shocks remain flat and insignificant across the distribution. This result indicates that trade expansions amplify emissions most when emission changes are already elevated, whereas trade contractions do not provide proportional environmental relief. Innovation processes also reveal important distributional differences: positive shocks become increasingly emission-reducing at higher quantiles, suggesting that technological progress plays a more crucial role in mitigating large spikes in CO₂ emissions, while negative innovation shocks exert only mild and statistically weak effects across quantiles. Taken together, the quantile process plots highlight that the impact of shocks is not uniform across the emission distribution. Instead, high-emission states (upper quantiles) are more sensitive to shocks in renewable energy, energy use, trade openness, and innovation, indicating that policy interventions targeting these variables are especially important during periods of heightened environmental pressure.

6. Discussion

The combined evidence from the NARDL and quantile regression analyses highlights the nonlinear, asymmetric, and distribution-dependent dynamics that govern CO₂ emissions in France. The NARDL model reveals strong short-run and long-run asymmetries across key economic, energy, and technological determinants, a pattern that quantile regressions further confirm by showing that the magnitude and direction of these effects vary across the conditional distribution of emissions. Together, these results reinforce the notion that environmental outcomes and long-run sustainability performance are shaped not only by average behavior but also by the state of the emissions process—whether the economy is in a low-emission, typical-emission, or high-emission phase [6].

A first major finding is the asymmetric role of renewable energy. In the NARDL framework, negative shocks to renewable energy produce significant increases in CO₂ emissions in both the short and long run, while positive shocks exert weak and often insignificant effects [12]. The quantile process plots and quantile regression results reinforce this asymmetry: reductions in renewables generate disproportionately larger emission increases at higher quantiles (Q75). This confirms the “loss-dominance” dynamic identified in the energy–environment literature, in which disruptions in the supply or use of renewables have stronger environmental consequences than expansions [30]. These findings are also consistent with recent ARDL-based evidence showing that renewable energy consumption plays a significant role in mitigating carbon emissions across both low- and high-income economies, particularly under long-run sustainability transitions [31].

For France, a country with ambitious carbon-neutrality goals and a large share of low-carbon energy, this finding highlights the critical importance of maintaining renewable energy stability to support environmental sustainability and sustainable energy transition objectives.

The second key result concerns energy use, which exhibits symmetric and highly significant long-run effects in the NARDL model. Both increases and decreases in energy intensity raise emissions, suggesting structural rigidity in the French energy system [32]. The quantile regressions offer an important extension: negative shocks to energy use become significantly emission-increasing at the upper quantile, indicating that when emissions are already high or volatile, the system becomes more sensitive to energy disruptions. This aligns with prior studies documenting the persistence of energy-induced emissions in advanced economies [17,33]. These results suggest that efficiency improvement alone may be insufficient unless accompanied by structural shifts that reduce energy dependence across sectors and strengthen long-run environmental sustainability.

A third major contribution is the identification of trade-related asymmetries. In the NARDL model, only positive trade openness shocks significantly increase emissions in both short and long horizons, while negative shocks have negligible effects. The quantile regressions confirm this pattern: positive trade shocks intensify emissions in higher quantiles, suggesting that trade expansions amplify carbon pressures during episodes of large emissions adjustments. These results support the pollution-haven and scale-effect hypotheses in the French context [4]. They also imply that trade-related environmental policies in France must be particularly attuned to periods of heightened emissions intensity [19] in order to preserve sustainable development and environmental sustainability targets.

The study also uncovers state-dependent roles for innovation. While long-run innovation effects in the NARDL model are statistically weak, short-run positive innovation shocks significantly reduce emissions. The quantile results further refine this dynamic: the emission-reducing impact of innovation is strongest at the upper quantile, indicating that technological progress plays a more decisive role in easing large environmental pressures than in modifying typical emission patterns. This aligns with the technological-innovation channel highlighted by the Environmental Kuznets Curve (EKC) literature and endogenous growth theory [5,34]. This interpretation is further supported by recent evidence on asymmetric growth–energy–emissions dynamics, which emphasizes that innovation and renewable-energy transitions generate nonlinear environmental responses under energy-transition regimes [35].

For France, where innovation policy is strongly linked to the low-carbon transition and sustainability-oriented development strategies, the results confirm that innovation is most effective when emissions are unusually high or volatile.

Finally, the evidence on economic growth reveals a temporal and distributional decoupling from emissions. The NARDL model shows no long-run impact of either positive or negative GDP shocks, consistent with France’s progressive shift toward a service-oriented, low-carbon growth path. However, short-run asymmetry persists, with positive shocks increasing emissions and negative shocks decreasing them. The quantile regressions reveal that these effects intensify in the upper quantile, indicating that economic conditions influence emissions more strongly during periods of large adjustments. These results echo findings from recent studies documenting state-dependent growth–emissions relationships in advanced economies [1,36] and support the view that economic expansion can become increasingly compatible with environmental sustainability under mature low-carbon systems.

Overall, the combined NARDL and quantile regression evidence demonstrates that emissions behavior in France is governed by nonlinear, asymmetric, and quantile-dependent dynamics. Policies targeting emissions reduction must therefore account for these complex interactions. Renewable energy stability, energy system flexibility, and innovation-driven technological progress emerge as particularly crucial during periods of elevated emissions. Furthermore, trade expansions require complementary environmental safeguards to mitigate their asymmetric upward pressure on emissions. These insights underscore the value of nonlinear and distributional econometric approaches in environmental policy analysis, offering a richer understanding than linear mean-based models alone and providing important implications for sustainability-oriented climate governance.

Cross-Country Comparison

A consistent stylized fact across advanced economies is that emissions respond asymmetrically to macroeconomic and energy shocks. For example, Shahbaz et al. (2020) [1] show that in large emerging and OECD-related economies, positive growth and trade shocks exert stronger emission-increasing effects than negative shocks reduce them, reflecting dominant scale effects. Similarly, Destek & Sarkodie (2019) [3] document nonlinear energy–emissions relationships, where negative energy shocks can generate unexpectedly large increases in emissions due to substitution toward more carbon-intensive sources. Evidence for EU economies also confirms heterogeneous renewable energy effects: Marques & Fuinhas (2012) [16] find that renewable expansion impacts differ significantly depending on national energy systems and policy regimes.

The results of this study are broadly consistent with this literature but also reveal important France-specific deviations. First, the absence of significant long-run GDP effects (Table 5) supports the decoupling hypothesis observed in some advanced EU economies [8], but contrasts with findings in more carbon-intensive OECD countries where growth remains strongly emissions-driven. This difference can be attributed to France’s nuclear-dominated electricity mix, which lowers the carbon intensity of output and weakens the traditional growth–emissions linkage.

Second, the strong long-run asymmetry for renewable energy (significant only for negative shocks in Table 5) provides a key contribution relative to existing EU evidence. While most studies report that renewable expansion reduces emissions, your results show that in France, renewable energy losses matter more than gains. This can be interpreted through diminishing marginal returns: because France already operates with a relatively low-carbon baseline, additional renewable capacity yields limited incremental benefits, whereas reductions force reliance on marginal fossil or imported energy sources. This finding aligns with recent nonlinear evidence but highlights a stronger “loss-dominance” effect specific to mature low-carbon systems.

Third, the symmetric and positive long-run impact of energy use (both ENE⁺ and ENE⁻ significant in Table 5) diverges from some OECD findings where efficiency reduces emissions. This suggests that in France, energy-system rigidity dominates efficiency effects, consistent with the argument that even low-carbon systems can exhibit carbon sensitivity at the margin [32]. The quantile results (Table 7) reinforce this by showing that negative energy shocks significantly increase emissions at Q75, indicating heightened vulnerability during high-emission regimes.

Fourth, the trade asymmetry (TRD⁺ significant, TRD⁻ insignificant) supports the scale-effect dominance predicted by Copeland & Taylor (2004) [4] but is more pronounced in France than in some EU peers. This reflects France’s deep integration into high-value global value chains, where trade expansion increases production-related emissions, while contractions do not proportionately reduce them due to structural rigidities and imported inputs.

Finally, the quantile regression results (Table 7) reveal a critical dimension largely absent in cross-country studies: state-dependent asymmetry. The significance of renewable, energy, trade, and innovation shocks at Q75 indicates that France’s emissions system becomes highly sensitive under high-emission conditions. This contrasts with many OECD studies that rely on mean effects and overlook such nonlinearities. The stronger impact of innovation at higher quantiles supports the endogenous growth and green innovation literature [5], suggesting that technological progress is most effective when environmental pressure is elevated.

Overall, the comparison highlights that France’s asymmetric and quantile-dependent emissions dynamics are driven by three structural factors:

-

a nuclear-dominated, low-carbon but rigid energy system,

-

diminishing marginal returns to renewable expansion, and

-

high trade integration combined with sectoral rigidity.

These features explain why France exhibits weaker benefits from positive shocks but stronger adverse effects from negative shocks—particularly for renewable energy and energy use—relative to other OECD and EU economies.

7. Conclusions and Policy Recommendations

This study examined the asymmetric and distribution-dependent drivers of CO₂ emissions in France over 1990–2024 using a combined nonlinear ARDL (NARDL) and quantile regression framework. The results provide robust evidence that the relationship between emissions and their key determinants—economic growth, renewable energy, energy use, trade openness, and innovation—is structurally nonlinear, directionally asymmetric, and strongly state-dependent. The NARDL estimations reveal pronounced short-run and long-run asymmetries, particularly for renewable energy, energy use, and trade openness, while the quantile regressions show that these effects become significantly stronger under high-emission regimes (upper quantiles). These findings confirm that France’s emissions dynamics cannot be adequately captured by linear or average models, but instead reflect a system where shocks exert heterogeneous effects depending on both their direction and magnitude. The results further demonstrate that achieving long-run environmental sustainability requires climate policies capable of addressing nonlinear and distribution-dependent emissions responses.

A central conclusion of the study is the dominant role of renewable energy instability. Negative shocks to renewable energy significantly increase emissions, whereas positive shocks generate limited environmental gains, revealing a clear loss-dominance asymmetry. However, these results should be interpreted within the specific context of France’s energy structure, where electricity generation is already largely low carbon due to the dominant role of nuclear power. Consequently, the estimated renewable-energy effects likely reflect broader economy-wide mechanisms—including transportation, residential heating, industrial energy demand, and marginal fossil-fuel energy use—rather than direct substitution away from highly carbon-intensive electricity generation alone. Energy use also emerges as a structurally rigid driver, with both increases and decreases contributing to higher emissions, highlighting persistent carbon sensitivity at the margin. Because the dependent variable captures total territorial CO₂ emissions excluding LULUCF rather than electricity-sector emissions only, the estimated effects encompass multiple emitting sectors across the French economy. Trade openness exhibits one-sided effects, where expansions increase emissions while contractions fail to reduce them proportionately, confirming the dominance of scale effects. In contrast, innovation plays a conditional but critical mitigating role, with its emission-reducing impact concentrated in the short run and during high-emission periods.

Building on these findings, the study provides a set of targeted and evidence-based policy recommendations. First, given the strong asymmetry associated with renewable energy (REN⁻), France should prioritize the stabilization of renewable supply through investments in grid-scale storage, interconnections, and flexible backup systems to avoid emission spikes caused by renewable disruptions. In the French context, renewable-energy policy should be viewed as complementary to the existing nuclear-based low-carbon electricity system rather than as a direct replacement for carbon-intensive baseload electricity generation. Second, the symmetric and persistent impact of energy use (ENE⁺/ENE⁻) calls for structural reforms aimed at reducing energy-system rigidity, including accelerated electrification, demand-response mechanisms, and industrial decarbonization strategies. Third, the asymmetric impact of trade (TRD⁺) suggests the need to green trade expansion by strengthening instruments such as the Carbon Border Adjustment Mechanism (CBAM), promoting low-carbon supply chains, and integrating environmental standards into trade agreements. Fourth, the quantile-dependent effectiveness of innovation (INN) implies that innovation policy should be deployed strategically during high-emission periods, with increased support for green R&D, technology diffusion, and cleantech development. Finally, the strong state-dependent dynamics identified in the quantile analysis highlight the importance of adopting adaptive and flexible climate policies, such as dynamic carbon pricing and trigger-based regulatory mechanisms that intensify interventions during emission surges. These measures are essential not only for reducing emissions but also for strengthening France’s long-run environmental sustainability and sustainable development trajectory.

Importantly, this study contributes to the literature by demonstrating that emissions responses in a mature low-carbon economy such as France differ fundamentally from those observed in more carbon-intensive OECD countries. In particular, diminishing marginal returns to renewable expansion and stronger adverse effects of negative shocks explain the observed asymmetries, emphasizing the role of energy-transition maturity in shaping environmental dynamics. Unlike fossil-fuel-dominated economies, France’s environmental dynamics are strongly influenced by the interaction between its nuclear-dominated electricity mix and broader economy-wide emission sources, which helps explain why renewable-energy shocks generate asymmetric but comparatively moderate long-run environmental gains.

Despite these contributions, several limitations should be acknowledged. A limitation of this study relates to the relatively small sample size (1990–2024), which may constrain statistical power. However, the ARDL/NARDL framework is specifically designed for small-sample settings, and quantile regression, supported by bootstrapped standard errors, remains robust due to its distribution-free properties. Future research could extend the analysis using higher-frequency or panel data.

In addition, innovation is proxied by total patent applications, which capture formal knowledge creation but do not distinguish between green and non-green innovations and reflect invention rather than diffusion. Consequently, the results should be interpreted as capturing general innovation activity rather than purely environmental technological progress. Future research could employ green patent indicators or clean R&D data to better isolate environmental innovation effects.

Overall, the study demonstrates that achieving France’s decarbonization objectives requires policies that explicitly account for nonlinearities, asymmetries, and state-dependent emission responses. By strengthening renewable system resilience, reducing energy-system rigidity, greening trade, and strategically deploying innovation, France can build a more adaptive, resilient, and effective pathway toward carbon neutrality.