Frontier analysis of eco-efficiency gaps: Evidence from European countries

Gross domestic product (GDP) is the standard measure of economic performance, yet it ignores environmental externalities. By design GDP records only market transactions and omits negative externalities such as greenhouse gas (GHG) emissions. In response to these shortcomings, the concept of eco-efficiency (EE) has been developed to account for both economic output and its associated environmental burdens, integrating environmental costs into the measurement of economic performance. The European Environment Agency (EEA) emphasizes that monitoring EE at the macro level is “necessary in order to make sustainability accountable” (EEA, 1999). Despite this policy relevance, country-level EE studies are scarce, and most do not control for country-specific heterogeneity or analyse the sources of EE gaps. The benchmark effort by Robaina-Alves et al. (2015) ranks 26 European countries up to 2011 but does not analyse the factors that may contribute to EE gaps across countries. Orea and Wall (2017) explicitly called for further research to incorporate the determinants of EE directly into the inefficiency component of stochastic frontier (SF) models—a contribution that this paper addresses. Our paper fills this gap by evaluating EE for 22 European countries from 2000–2018 and identifies some factors that could explain country-level variations in EE.

Consistent with the World Business Council for Sustainable Development’s (WBCSD, 2006) call to “do more with less”—that is, to produce goods and services with minimal environmental impacts—we follow a strand of literature in the field in which EE is defined as the ratio of economic output (GDP) to environmental pressure (e.g., Kuosmanen & Kortelainen, 2005; Orea & Wall, 2017). In this paper, we measure environmental pressure by national-inventory GHG emissions consistent with the study by Robaina-Alves et al., 2015. The frontier country achieves the highest GDP per unit of GHG emissions, and deviations from this benchmark define EE gaps.

In this study, we address three questions. First, how large are Europe’s EE gaps, and how have they evolved between 2000 and 2018? Second, what explains these gaps? To what extent do three factors—green innovation (Relative Advantage in Environment-related Technologies (RAET)), the stringency of environmental regulation (EPS), and national GHG tax rates—explain the cross-country variation in EE gaps? Third, how many tonnes of GHG could be avoided if lagging countries matched the frontier level of EE?

We answer these questions with Greene’s (2005) “true” fixed-effects SF model, estimated on a balanced panel that merges OECD, Eurostat, Penn World Table, and International Energy Agency data covering 2000–2018. The model separates time-invariant heterogeneity from time-varying inefficiency and yields an inefficiency term that captures the gap between each country’s actual GDP-per-GHG ratio and the frontier ratio achievable with best practice. By lengthening the time span and controlling for heterogeneity, we extend Robaina-Alves et al. (2015) and provide the first assessment of how policy and technology factors mentioned above may explain variations in EE across the countries.¹ We also provide a calculation of potential GHG emission reductions, based on our results, if EE gaps are eliminated.

Our findings reveal significant variations in EE gaps across Europe. We find that countries like Sweden, Denmark, Italy, Norway, and Luxembourg consistently operate near the frontier (high GDP per unit of GHG emissions), whereas Poland, Estonia, the Slovak Republic, and the Czech Republic typically lag. Countries with higher environmental policy stringency (EPS) and higher GHG emission tax rates tend to operate significantly closer to the EE frontier (i.e. they have smaller EE gaps), though with diminishing marginal effects at high levels, consistent with the Porter Hypothesis suggesting that stricter environmental regulation can improve resource productivity (Porter & van der Linde, 1995). Using our results, we find that closing the EE gap would yield substantial emissions savings. We calculate that if the inefficient countries were to reach the EE frontier defined by the best performers—that is, achieve comparable GDP per unit of GHG emissions—Europe could reduce GHG emissions by approximately 75 million metric tonnes over the sample period. This saving is equivalent to the annual carbon dioxide emissions of 9.7 million US households, or eight years of energy use for Parisian households. These magnitudes underscore the substantial climate gains that could be realized by closing cross-country EE gaps.

The remainder of this paper is organised as follows. Section "Theoretical Background" introduces the concept of EE and discusses its theoretical underpinnings. Section "Literature Review" reviews the methodological approaches used in previous studies, surveys the relevant literature, and highlights key findings. Section Our SFA Specification presents the model used for the analysis, followed by the description of the data in Section "Data". Section Results reports the empirical results. Finally, Section "Conclusions" concludes.

This section surveys the EE literature from two complementary perspectives: methodology and evidence. Section "Frontier Methods for Measuring EE" outlines the frontier methods most used to measure EE—DEA and SFA. Section "Empirical Evidence on EE" reviews the empirical findings, drawing on early frontier applications, cross-country analyses, and firm and sector-level studies. Finally, it identifies remaining gaps that motivate the present research.

We employ a SFA framework to measure EE, defined as the ratio of economic output to environmental impact. Specifically, GDP per unit of GHG emissions —often referred to as carbon productivity— is used as the dependent variable. This specification follows Robaina-Alves et al. (2015), who interpret the GDP-to-GHG ratio as a direct indicator of EE within a SF framework. A higher GDP-to-GHG ratio implies that an economy generates more output per tonne of emissions, thereby balancing economic performance with environmental impact. Countries operating on the efficiency frontier achieve the maximum feasible output per unit of GHG, while any deviation from that frontier reflects eco-inefficiency, or an “EE gap”.

To model the frontier of GDP per unit of GHG emissions, we specify a log-linear Cobb–Douglas stochastic production frontier with multiple inputs and a composite error term capturing inefficiency. This formulation follows Robaina-Alves et al. (2015), who adopt a similar framework to model EE.³ Formally, let \({Y}_{it}\) denote the GDP-to-GHG ratio—our measure of EE— for country i in year t. The SF is then specified as:where \({X}_{jit}\) represents production inputs, timetrend is a linear time trend, and the composite error term is decomposed into statistical noise \({(v}_{it})\) and inefficiency \({(u}_{it})\). The vector \({X}_{jit}\) includes traditional inputs—labour and capital—as well as disaggregated energy inputs – specifically energy consumption from brown, nuclear, and renewable sources. Disaggregating energy use in this way enables the model to capture how a country’s energy mix influences both output and emissions. In contrast to using broad indicators such as the fossil-fuel share or the manufacturing share of GDP, explicitly including brown, nuclear, and renewable energy inputs provides a more detailed representation of how energy composition affects EE. The country-specific effect \({\mu }_{i}\) captures time-invariant heterogeneity—such as climate, geography, or economic structure—that may influence emissions and output but are not directly modelled. Following Greene’s (2005) “true” fixed-effects panel SFA, this specification controls for unobserved country characteristics, ensuring that cross-country comparisons of EE are not confounded by persistent structural differences beyond national control.

Our SF specification follows standard SFA assumptions. The noise term \(\left({v}_{it}\right)\) is assumed to be independently and identically distributed as \(N\left(0,{\sigma }_{v}^{2}\right)\), capturing random shocks and measurement errors. The inefficiency term \(\left({u}_{it}\right)\) is non-negative—since any deviation from the frontier represents a shortfall in performance—and follows a half-normal distribution, \({N}^{+}\left(0, {\sigma }_{u}^{2}\left({{\varvec{z}}}_{it}\right)\right)\). When a country emits substantial GHG emissions without a proportionate increase in GDP, its \({u}_{it}\) value rises, indicating that it operates below the efficiency frontier. In essence, efficient countries lie on the frontier surface, where GDP is maximised for each combination of inputs and emissions. Less eco-efficient countries produce a lower level of GDP than is theoretically attainable given their input mix and emission levels. Equivalently, such countries could achieve the same level of GDP with fewer emissions if they were operating on the frontier. This interpretation aligns directly with the concept of eco-inefficiency as “waste” —where an inefficient observation either wastes inputs (including capital or labour) or generates avoidable excess emissions, or both.

Given the panel nature of our dataset (19 years across European countries), unobserved heterogeneity is a key concern. Countries differ structurally—in aspects such as institutional quality, climate, and industrial composition—which may shift their production possibilities independently of inefficiency. If not accounted for, these unobserved effects could be confounded with \({u}_{it}\) (inefficiency). To address this, we incorporate country-specific effects \(\left({\mu }_{i}\right)\) following Greene’s (2005) “true” fixed-effects SFA framework. In practice, this involves allowing for a country-specific intercept in the production function to capture time-invariant heterogeneity. For instance, a country that consistently achieve higher output—perhaps due to natural resource endowments or advanced technology not fully captured by input variables—will have a higher intercept but may still be fully efficient if it lies on its own frontier. Complementing this, we model the variance of \({u}_{it}\)—and consequently its mean under truncation—as a function of observed country-year characteristics \({z}_{it}.\) Specifically, we specify \({\sigma }_{u}^{2}\left({{\varvec{z}}}_{it}\right)={\sigma }_{u}^{2} exp\left({\theta }_{0}+{\theta}^{\prime}{{\varvec{z}}}_{it}\right)\), where \({{\varvec{z}}}_{it}\) includes factors such as the adoption of clean technologies, environmental policy stringency, or the presence of GHG emission taxes. This flexible variance specification allows changes in the determinants of eco-inefficiency (e.g. technology or policy) to shift the distribution of inefficiency term. Intuitively, stricter environmental policies or greater adoption of clean technologies should lower expected inefficiency—reducing the EE gap—by decreasing the variance of the half-normal \({u}_{it}\). Modeling \({u}_{it}\) in this way enables us to test how these factors contribute to narrowing the gap between actual performance and the eco-efficient frontier.

We estimate the frontier model in Eq. (1)⁴ using maximum likelihood estimation (MLE), which relies on nonlinear optimization to obtain parameter estimates and the sample’s average level of eco-inefficiency. The estimation uses panel data on inputs, GDP, and GHG emissions for each country-year in the sample. The inclusion of country-specific effects \(\left({\mu }_{i}\right)\) following Greene’s true fixed-effects approach ensures that the estimated parameters \(\left({\beta }_{j}\right)\) are not biased by omitted time-invariant heterogeneity, albeit at the cost of estimating many fixed-effect terms. The coefficients \(\left({\beta }_{j}\right)\) represent the elasticities of the GDP-to-GHG ratio with respect to each input, indicating how changes in labour, capital, or specific energy inputs affect EE. The coefficient of time trend \(\left({\beta }_{t}\right)\) captures common technological progress or other gradual shifts in the production frontier over time, such as general improvements in energy efficiency across countries.

After estimating the model, country-year specific inefficiency estimates \(\left({\widehat{u}}_{it}\right)\) are obtained using standard SFA decomposition techniques —specifically, the conditional expectation of \({u}_{it}\) given the composed error \({v}_{it}-{u}_{it}\). EE scores are then derived using the conditional mean estimator of Jondrow et al. (1982) as \({EE}_{it}\) =exp \(\left(-{\widehat{u}}_{it}\right)\), which ranges between 0 and 1 and represents the proportion of maximum feasible GDP (given each country’s inputs and frontier technology) that country i achieves in year t. An EE score of 1 indicates that the country lies on the efficiency frontier (fully eco-efficient), whereas a score of 0.9 implies that the country produces only 90% of the potential GDP attainable per unit of emissions.

To interpret the influence of specific factors (\({z}_{it}\) variables) on EE, we compute marginal effects following the approach of Kumbhakar et al. (2015). In the half-normal specification, the partial derivative of the expected inefficiency E (\({u}_{it}\)) with respect to a determinant \({z}_{k}\) represents the marginal effect of that factor on the eco-inefficiency gap. For instance, if \({z}_{it}\) includes an environmental policy index, the sign of the corresponding coefficient indicates whether increasing that variable tends to raise or reduce average inefficiency. A negative marginal effect suggests that improving that factor—such as adopting cleaner energy sources or implementing stricter environmental policies—reduces inefficiency, thereby moving a country closer to the frontier and improving its EE. The marginal effects are reported to quantify the impact of policy and technological determinants on countries’ EE.

In sum, our SFA model establishes a benchmark frontier of EE against which countries are evaluated, while rigorously accounting for input use, energy composition, and unobserved heterogeneity across countries. This framework enables the isolation of pure inefficiency in generating GDP from GHG emissions, net of country-specific effects and random shocks. Conceptually, the model builds on the literature on pollution-generating technologies, which emphasises incorporating undesirable outputs—such as emissions—directly into production efficiency analysis. By treating GDP as the desirable output and GHG emissions as an undesirable by-product, our approach aligns with the theoretical foundations developed by Färe et al. (2005), who formalise the joint production of “goods” and “bads” within efficiency measurement.

Our dataset includes GDP, GHG emissions, and production inputs—namely labour, capital, and a disaggregated energy mix. It covers annual observations for 22 European countries⁵ over the period 2000–2018.

GDP is expressed in chain-linked volumes with base year 2017 and measured in million euros. GHG emissions are reported under the national inventory concept rather than the national accounts concept. Whereas the national accounts approach captures emissions associated only with residents’ consumption activities, the national inventory method also includes emissions generated from sales to non-residents (for example, fuel sales to foreign drivers). We adopt the national inventory concept because our objective is to measure EE and assess the impact of policies on GDP per unit of total emissions, not just those attributable to domestic consumption.

The emissions dataset covers carbon dioxide (CO₂), methane (CH₄), nitrous oxide (N₂O), perfluorocarbons (PFCs), hydrofluorocarbons (HFCs), sulphur hexafluoride (SF₆), and nitrogen trifluoride (NF₃). To construct a single indicator, all gases are converted into CO₂-equivalent emissions.⁶ Data on GDP⁷ and GHG emissions are obtained from Eurostat.

The independent variables represent inputs to production: energy (E), capital (K), and labour (L). Energy data are sourced from the International Energy Agency (IEA) World Energy Balances⁸ and disaggregated into three categories according to the energy source: (i) nuclear energy, (ii) renewable energy, and (iii) brown energy. The latter category comprises coal, peat, oil shale, crude, oil products, natural gas, electricity,⁹ and heat. Data on capital and labour are taken from the Penn World Table, measuring capital stock at constant 2017 national prices (in million euros) and total labour force, respectively.

Data on the determinants of EE gaps are drawn from several sources. The Environmental Policy Stringency Index (EPS), developed by the OECD, provides a country-specific and internationally comparable measure of the strictness of environmental policies. The EPS quantifies the extent to which environmental policies impose explicit or implicit costs on environmentally harmful behaviours and pollution. It is constructed from the stringency levels of 13 policy instruments, primarily targeting climate change and air pollution. The index ranges from 0 (least stringency) to 6 (most stringent), offering a comprehensive indicator of environmental policy enforcement across countries.¹⁰

The Relative Advantage in Environment-Related Technologies (RAET) index, developed by the OECD, measures a country’s degree of specialization and competitiveness in environmental innovation relative to the global value. This index captures the extent to which a country leads or lags in the global development of environment-related technologies. It is computed as the ratio of a country’s share of environment-related inventions to its total inventions, relative to the corresponding global ratio. A value of 1 indicates that a country’s share of green innovation matches the global benchmark, whereas a value greater than 1 reflects a relative technological advantage in environment innovation. The RAET covers a wide range of technological domains, including environmental management and climate change mitigation technologies.

Finally, the GHG emissions tax rate is defined as the ratio of energy tax revenue to total GHG emissions. Data on energy tax revenue are obtained from Eurostat. The tax base includes: (i) energy products for transport purposes (e.g. unleaded and leaded petrol, diesel, and other transport fuels such as natural gas and fuel oil), (ii) energy products for stationary purposes (e.g. light and heavy fuel oil, natural gas, coal, coke, biofuel, electricity consumption and production, district heat consumption and production and other energy products for stationary use), and (iii) GHGs (e.g., the carbon content of fuels, emissions of GHGs including proceeds from emission permits recorded as taxes in the National Accounts (see Regulation (EU) No 691/2011 of the European Parliament and of the Council of July 2011 on European environmental economic accounts).

The GHG emissions tax rate serves as a key policy variable for promoting EE. A higher tax rate increases the cost of polluting activities, thereby encouraging the adoption of cleaner technologies and a shift towards less carbon-intensive energy sources. In turn, this can contribute to lower emissions and improved long-term EE performance. The correlation coefficients between EPS index, RAET index, and GHG emission tax rate are reported in Table 1 below. As shown, the correlations among these determinants are relatively low, indicating limited multicollinearity. Table 3 in the Appendix presents the annual average summary statistics for the sample over the period 2000–2018.

This section presents the estimation results for EE scores. Recall that the SF model employed in this study is specified as follows:

In this section, we present results from multiple model specifications that incorporate individual and combined determinants of EE gaps into the eco-inefficiency component. This approach allows us to examine how each variable —on its own and jointly with others—affect variations in EE gaps.

While Gross Domestic Product (GDP) remains the most widely used indicator of economic performance, it does not capture the environmental impacts of production, such as greenhouse gases (GHG) emissions. By focusing on eco-efficiency (EE)—a measure of economic performance that explicitly accounts for GHG emissions—this study assess how 22 European countries balance economic output and environmental costs. Countries that maximise their economic output per unit of GHG emitted are considered eco-efficient, while any deviation from this maximum output represents an EE gap, or eco-inefficiency, which we estimated using Greene's true fixed-effects stochastic frontier model (Greene, 2005).

The results reveal notable variation in EE across countries. Average EE scores over the 2000–2018 period range from 0.91 to 0.99 across the 22 countries analysed. Sweden, Denmark, Italy, Norway, and Luxembourg consistently emerge as the most eco-efficient, while the Slovak Republic, Poland, and the Czech Republic are among the least eco-efficient. Luxembourg’s strong performance likely reflects its service-oriented economic structure, which inherently generates lower emissions; however, this factor is explicitly controlled for in the model through country fixed effects and energy mix variables.

The analysis also explores the determinants of EE gaps. Specifically, countries with higher energy tax revenues or more stringent environmental policies, as captured by the Environmental Policy Stringency (EPS) index, exhibit smaller EE gaps. However, the positive effects of these policy variables diminish at higher levels, suggesting decreasing marginal returns to further tightening of policy measures.

Additionally, we estimate the potential carbon savings—measured in CO₂-equivalent GHG emissions—that could be achieved by closing EE gaps. The largest potential savings are observed in Poland, Germany, and the Czech Republic. Overall, eliminating EE gaps across all countries could reduce total carbon emissions by approximately 75 million metric tonnes.

Finally, in the case of Luxembourg—a predominantly service-based economy—our analysis currently aggregates all sectors. Conducting the analysis at the industry level, with particular attention to services, would provide more targeted insights into the effectiveness of policies aimed at improving EE. As the service sector relies less on emissions-intensive inputs and more on labour and digital infrastructure, the impact of policy measures on EE may differ from that observed in energy-intensive industries such as manufacturing. Future research could therefore focus on sectoral-level efficiency analysis to more accurately reflect Luxembourg’s economic structure and better inform policy design.