Greenhouse Gas Emission Reduction Potentials in Europe by Sector: A Bootstrap-Based Nonparametric Efficiency Analysis

The reduction of greenhouse gas emissions is the key action to limit global warming. An important source of greenhouse gas emissions and pollution is the inefficiency of production processes. We report results from a stochastic nonparametric efficiency analysis using directional distance functions to take account of undesirable outputs like greenhouse gases. With this approach, we are able to provide estimates of the potential emission reductions for 7 main sectors in 16 European countries. A specially adapted bootstrapping approach allows to implement a bias correction of the estimates and to compute confidence intervals. The results show that static efficiency improvements are a quantitatively important element of the emission reductions which are required to achieve the reduction targets of the European Union.


Introduction
The reduction of greenhouse gas (GHG) emissions on a global level is the key measure to counteract the detrimental effects of climate change and global warming. Other approaches to limit global warming, like carbon removal or geoengineering approaches are either infeasible or extremely risky (see Nordhaus (2019Nordhaus ( , p. 1998) for a clear statement). This is largely undisputed in the economic literature (see the survey articles by Myhre et al. (2001), Aldy et al. (2010), Hsiang and Kopp (2018) and Tol (2018), among others) and is the basis for several international agreements. The most prominent agreements are the Kyoto Protocol of 1997 and the Paris Agreement on climate change of 2015 to reduce GHG emissions to reach the 2 • C target, meaning the stabilization of the increase in temperature at "well below 2 • C above pre-industrial levels". 1 The European Union (EU) as a key actor in this area has achieved an agreement among its member countries to reduce GHG emissions by 40% until 2030, 60% until 2040 and 80% until 2050, compared to the levels of 1990 (EU 2011, p. 3). Recently these targets have been tightened to reduce GHG emissions by 55% until 2030, 80% percent until 2040 and to reach climate neutrality by 2050, also accounting for the effects of carbon removal technologies, land use change and forestation (see EU (2020) and especially figure 1 therein).
Efforts to improve the productive efficiency of sectors could be a potentially important building block of an emission reduction strategy. Therefore, it is important to know to which extent GHG emissions could be reduced by achieving productive efficiency while holding the economic inputs and outputs constant. In our companion paper (Krüger and Tarach 2020) we applied nonparametric methods of efficiency analysis in the presence of undesirable outputs derived from a variant of data envelopment analysis (DEA) to give an account of the potential reductions of GHG by country and sector for the period 2008-2016. The main finding there is that efficiency improvements can contribute considerably to emission reduction, albeit the extent to which the measured potentials could be realized in practice remains open. However, the measurement approach used in the companion paper is purely deterministic and prone to biases. Furthermore, no account of the estimation uncertainty is provided there.
In this paper we pick up these issues by combining the nonparametric efficiency measurement approach with a specifically designed bootstrapping procedure to achieve a bias correction and to compute confidence intervals for assessing estimation uncertainty. To our knowledge this is the first time that a nonparametric approach combined with stochastic elements is applied in an environmental efficiency measurement context. We report estimates of aggregate emission reduction potentials for 16 major EU countries and 7 main sectors of the private economy. As emissions we consider a broad GHG aggregate as well as splits to single GHGs ( CO 2 , CH 4 and N 2 O ). The results show that the bias correction leads to larger emission reductions compared to the "raw" measures from our companion paper which are based on the purely deterministic approach. We can show that the potentials for emission reduction are concentrated in certain countries and sectors. In addition, we find that the estimation uncertainty is substantial in these cases.
In contrast to much of the literature on eco-efficiency which is also concerned with emission reduction on a macroeconomic level or the level of major sectors we assess the contribution of potential efficiency improvements to the EU reduction targets by expressing them as potential reductions measured in physical units, i.e. CO 2 equivalents ( CO 2 e ). The usual practice in the literature (see Camarero et al. (2014), Färe et al. (2004), Korhonen and Luptacik (2004), Kortelainen (2008), Kuosmanen and Kortelainen (2005), Rashidi and Farzipoor Saen (2015), Zaim and Taskin (2000), Zhou and Ang (2008) and Zofío and Prieto (2001), among others) is to focus on relative measures instead. More closely related to our analysis are studies such as Domazlicky and Weber (2004) and Krautzberger and Wetzel (2012) which are also based on a methodological setting employing directional distance functions and are also confined to specific industries.

3
The exposition in this paper starts with a description of the data and the country-sector coverage in Sect. 2. This is followed by the description of the nonparametric methodology we use to obtain our estimates of emission reduction potentials in Sect. 3. In this section, the implementation of the bootstrapping approach as well as the computation of the biascorrected measures and the confidence intervals are also outlined. Section 4 contains the discussion of the results from several specifications of the undesirable outputs. The specifications comprise a single total GHG aggregate as well as splits to CO 2 , CH 4 and N 2 O . We also discuss the results of a variant where possible enhancements of the economic output are permitted in addition to the emission reductions. Policy recommendations are provided at the end of the section. The final Sect. 5 concludes with an evaluation of the contribution of the emission reduction by efficiency improvements to the EU emission reduction targets and discusses the feasibility of the potential reductions measured.

Data Description
The data required for the efficiency analysis comprise the inputs, the good (desirable) outputs and the bad (undesirable) outputs, i.e. the emissions of greenhouse gases. In the subsequent measurement of inefficiency and the potential emission reduction derived thereof we always include the two conventional inputs labor and capital as well as value added as the single economic output. The emissions as undesirable outputs are used in different forms. As the description of the methods will show, the inefficiency is measured as the potentially reachable enhancement of the good output and/or the potentially reachable reduction of the emissions. The economic data, meaning the inputs and the good (desirable) output are taken from the EU-KLEMS database. The November 2019 release we use is described by Stehrer et al. (2019) and can be obtained from https:// eukle ms. eu. Labor input is measured in total hours worked by employees (comprising self-employed persons and expressed in full-time equivalents). Capital input is quantified by the real fixed capital stock (at constant 2010 prices). The output variable is gross value added (also at constant 2010 prices). 2 Using this variable is associated with a much more comprehensive data coverage compared to the alternative of using a gross output measure with materials and energy as additional input variables. 3 The emissions data to quantify the bad (undesirable) outputs 4 are taken from two sources. 5 As greenhouse gas (GHG) emissions, we focus on the three main greenhouse gases (GHGs) which are emitted by anthropogenic sources, namely carbon dioxide ( CO 2 ), methane ( CH 4 ) and nitrous oxide ( N 2 O ). The global warming potentials usually differ for each GHG, but they can be converted to CO 2 equivalents (abbreviated CO 2 e and measured in tons, kilotons or megatons). CO 2 emissions are retrieved from the World Input Output Database (WIOD) described in Timmer et al. (2015) and can be downloaded from http:// www. wiod. org. The data for CH 4 and N 2 O emissions are retrieved from the Eurostat Air Emission Accounts (AEA). 6 In the AEA database, CH 4 and N 2 O emissions are already expressed in tons of CO 2 e and so we obtain our measure of total GHG emissions by simply adding them to the CO 2 emissions from the WIOD. There are further GHGs which are of minor quantitative importance and therefore neglected. 7 All three major GHGs have specific anthropogenic sources. CO 2 emissions stem primarily from burning fossil fuels (coal, oil and natural gas), but also from industrial processes such as the manufacturing of cement. In addition, CO 2 is emitted or absorbed by land use, land use change and forestry (LULUCF). Although its global warming potential per ton is less than that of CH 4 or N 2 O , CO 2 is quantitatively the most important GHG. In 2010 CO 2 emissions (without LULUCF) accounted for 82% of total GHG emitted by the EU (Debelke and Vis 2015, p. 96).
CH 4 has an atmospheric lifetime of 12 years, meaning that on average it stays in the atmosphere for only 12 years before it is broken down into CO 2 and water (Hsiang and Kopp 2018, p. 12). It has a global warming potential of 25 CO 2 e (meaning one ton of CH 4 has the global warming potential of 25 tons of CO 2 , Eurostat 2015, p. 105). The two major anthropogenic sources of CH 4 emissions are industrial livestock farming and the exploitation of fossil fuels. Natural gas (largely consisting of CH 4 ) may be leaking when recovered from gas or oil fields or during transport and storage. CH 4 is also contained in coal beds (coal mine methane), especially in deeper coal beds and coals with higher carbon content (i.e. hard coal), and may similarly leak during coal mining (Kholod et al. 2020). In the EU, CH 4 emissions already declined between 1990 and 2010 by 32% (Debelke and Vis 2015, p. 96).
N 2 O is a very potent GHG with the same global warming potential as 298 tons of CO 2 (Eurostat 2015, p. 105) during an atmospheric lifetime of 116 ± 9 years (Tian et al. 2020). In addition, N 2 O has a depleting effect on the stratospheric ozone layer. The major anthropogenic source of N 2 O is the agricultural sector, in particular the large-scale use of nitrogen fertilizers. According to Tian et al. (2020) agricultural emissions accounted for about 70% of anthropogenic N 2 O emissions globally in 2007-2016. Other comparatively smaller anthropogenic sources include the fossil fuel and chemical industry. In contrast to rising or stagnant N 2 O emissions in most other countries globally, European emissions from agriculture declined by 21% between 1990 and 2010 (Tian et al. 2020, p. 254), which the authors attribute to European agricultural policies favoring more efficient fertilizer use. Besides, non-agricultural N 2 O emissions in the EU were reduced even more strongly during that period, mainly due to improved abatement technologies in the chemical industry (Tian et al. 2020, pp. 253-255).
Assessing the data coverage in the database we are able to achieve an almost complete coverage for 16 countries and 7 sectors during the period 2008-2016 on a classification of sectors (industries) according to NACE Rev. 2 (equivalent to ISIC Rev. 4 The emissions data in the AEA database are only available for a sector combining the sectors D and E. So we had to aggregate the economic input-output data of the sectors D and E to a combined sector, henceforth named DE. Cross checking assures that the sums of the values of the sectors D and E are very close to the values of the combined sector DE which is also available in the EU-KLEMS data. 8 Since the sector D is considerably larger than E in most countries we refer to the combined sector DE frequently as "energy" or as "energy and water" in the subsequent discussion. We exclude Estland, Lithuania, Luxembourg and Slovenia from our analysis despite full data coverage. The reason is that these are very small countries and Luxembourg is merely a large city rather than a country. Including those small countries can severely bias the entire efficiency analysis when they determine parts of the frontier function and overstate the potential emission reductions. Growiec (2012) provides further discussion of this issue. In some of these countries we also suspect recording errors in the data for some sectors (e.g. zero emissions in sector G in Slovenia).
The value added and capital stock data are directly expressed in Euro for the majority of the countries (appropriately deflated with base year 2010). In the case of the non-Euro countries Czech Republic, Denmark, Poland, Sweden and the United Kingdom these variables are expressed in the respective national currencies. To convert the data to a common currency we use purchasing power parities (PPPs) from the OECD National Accounts Statistics (OECD 2020). While exchange rates only convert currencies, PPPs also take account of different price levels of the countries. This is important since price levels tend to be systematically higher in high-income countries than in low-income countries. Using exchange rates would therefore overstate the values of the variables in the case of high-income countries and understate them in low-income countries. Instead, PPPs convert expenditures to a 1 3 common price level. This is also important for countries with a common currency (as the Euro) which also can have rather different national price levels. 9 We split these data in two five-year subperiods t 1 = 2008-2012 and t 2 = 2012-2016 and take medians over these subperiods for the subsequent empirical analysis. This eliminates the effects of single or even two outlying observations and makes the efficiency analysis more robust. The way of taking medians to robustify the analysis is in our view preferable to the alternative of outlier detection by methods such as those proposed by Wilson (1993) and subsequent outlier elimination. This procedure also solves the problem with two missing values in sector C of Ireland. 10 Thus, when we refer to the first and second subperiod in the following we always mean the medians of the inputs and outputs (including emissions) over the indicated five-year intervals.
The aggregate GHG emissions over all countries and sectors are 3341 mt of CO 2 e in the first subperiod, declining to 3070 mt in the second subperiod. Figure 1 shows stacked barplots of the three GHG emission variables for both subperiods (the corresponding data are reported in Table 1 in the appendix). The left-hand side of each plot depicts the bars for the sectors, followed by the bars of the countries on the right-hand side (separated by the thick vertical line). This kind of plot gives a succinct summary of the distribution of the aggregate emissions over sectors and countries jointly with an indication of the distribution of the different GHGs ( CO 2 , CH 4 and N 2 O in mt of CO 2 e ). More descriptive information on the data is discussed in the companion paper of Krüger and Tarach (2020).
From Fig. 1 we immediately see that the sectors C and DE are most emission intensive, while A and H also contribute considerably, and the remaining sectors (B, F and G) are of minor importance. CO 2 is the quantitatively most important emission category in all sectors except A where CH 4 and N 2 O emissions are dominating. CO 2 is the main emission category in all countries, including those with large aggregate emissions (Germany, Spain, France, the United Kingdom, Italy and Poland), although the contribution of CH 4 and N 2 O is also visible here. While the overall quantity declines from the first to the second subperiod, the distribution of the emissions across sectors and countries is rather similar in both subperiods.

Nonparametric Efficiency Measurement and Bootstrapping
For the estimation of the potential emission reductions we apply nonparametric methods of efficiency analysis. These methods are an extension of data envelopment analysis (DEA), developed by Charnes et al. (1978) and Banker et al. (1984). The specific modification we rely on is based on the concept of the directional distance function (DDF), introduced by Chambers et al. (1996) and extended to an environmental context by Chung et al. (1997). This approach allows to measure inefficiency as the distance to a piece-wise linear frontier function along a mix of possible reduction of inputs and enhancement of some outputs 9 PPPs are also central for the construction of comparable national accounts provided in the Penn World Table (see Feenstra et al. 2015). 10  (the good, desirable outputs), while other outputs (the bad, undesirable outputs) are supposed to be reduced (see Färe and Grosskopf (2004)). This property of reducing outputs allows to incorporate undesirable outputs like GHG emissions in a consistent way (Zhou et al. 2008b). Like in DEA, here also no price information is required and no functional form assumptions about the underlying technology (e.g. a production function) need to be imposed. These are major advantages of the nonparametric approach.

Technology Set
The nonparametric approach of efficiency analysis is based on the concept of an abstract technology set, comprising the feasible input-output combinations. It can be stated as where x denotes the m-vector of the input quantities, y the s-vector of the quantities of the good (desirable) outputs and u the r-vector of the quantities of the bad (undesirable) outputs. 11 Since we are dealing with sectors within countries it is suitable to suppose that each sector operates with a different technology set. 12 To impose some structure on the technology set it is supposed to be closed and convex (Färe and Primont 1995). Furthermore, it is supposed that standard axioms such as strong disposability of the inputs and the good outputs are satisfied. Two additional axioms are required in the context of an environmental efficiency analysis to incorporate the special role of undesirable outputs in a consistent way. The first is null-jointness, meaning that it is not possible to produce positive quantities of the good outputs without generating emissions (i.e. if (x, y, u) ∈ T and u = 0 then y = 0 ). The second is weak disposability stating that proportional reductions of emissions are always feasible as long as the good outputs are reduced by the same proportion (i.e. if (x, y, u) ∈ T then (x, y, u) ∈ T for ∈ [0, 1] ). For more detailed discussions of these axioms see (Färe and Grosskopf (2004), Färe et al. (2005) and Zhou et al. (2008a)). 13

Directional Distance Functions
The directional distance function (DDF) is defined on the technology set T as proposed by Chambers et al. (1996) and extended to the incorporation of undesirable outputs by Chung et al. (1997). It is a generalization of the (Shephard 1970) distance function to the case of non-proportional changes of the inputs and outputs and can be formally stated as 11 In the subsequent discussion of the results we will frequently simply refer to the outputs when we mean the good outputs and to the emissions when we mean the bad outputs. 12 Here we also include conventional inputs as labor and capital. Related papers such as (Picazo-Tadeo et al. 2012) measure eco-efficiency scores by directional distance functions without using inputs. 13 An alternative to this approach is the so-called by-production approach proposed by Murty et al. (2012) which relies on the availability of abatement options (and requires appropriate data). This approach models the technology set as the intersection of two parts to be estimated separately. One part is related to the production of the good outputs and the other part is related to the production of the bad outputs. This setting avoids the assumptions of weak disposability and null-jointness. Further discussion and critique is provided by Dakpo et al. (2016).
Herein, the inefficiency measure expresses the distance of a particular input-output combination (x, y, u) towards the boundary of the technology set along a particular direction g x ≥ 0 , g y ≥ 0 , g u ≥ 0 . This measure is equal to zero if the input-output combination is a point on the boundary (is on the frontier function) and it is larger than zero if the inputoutput combination is below the boundary (is below the frontier function).
In the following we mostly impose the restriction g x = 0 and g y = 0 , meaning that the inefficiency is measured exclusively as the extent of possible reduction of the bad outputs. In our application the entities under investigation are sectors in different countries. On such a high level of aggregation it is appropriate to assume that no reduction of input usage is intended. Since we are mainly interested in measuring the maximum potential emission reductions, we also exclude the possibility of output enhancement for most of the analysis. In one variant we only impose g x = 0 so that the output enhancement would also be possible.
The data required for the computation of the DDF pertain to n countries in a particular sector. The analysis is performed for each sector separately, so that an additional index to distinguish sectors is not necessary. The data for the m inputs are contained in the m × n matrix X with the ith column x i comprising the input quantities of country i ( i = 1, … , n ). Likewise, the data for the s good outputs are contained in the s × n matrix Y and the data for the r bad outputs are contained in the r × n matrix U , with the ith columns y i and u i comprising the observations pertaining to country i for the good and bad outputs, respectively.
In (2) the direction vectors g y and g u are not specified. A frequent choice in applications is to make the directions proportional to the variables y i and u i which serves to let the inefficiency measure be invariant to units of measurement (see e.g. Chung et al. (1997) and Färe et al. (2007)). Since this is restrictive it would be beneficial to compute the directions endogenously. Hampf and Krüger (2015) propose one possibility to endogenize the direction in an environmental efficiency setting and Färe et al. (2013) provide a related proposal to compute endogenous directions in the case of a slacks-based inefficiency measure. As pointed out by Chen and Delmas (2012), these proposals have the additional advantage of avoiding the problem of dominated (weakly-efficient) reference points on the frontier function.
We follow Hampf and Krüger (2015) and propose the following optimization problem to endogenize the computation of the direction vector where ' ⊙ ' denotes the direct (Hadamard) product. Herein, is a n-vector containing the weight factors to determine the reference point on the frontier function. The direction weights y and u are computed jointly with and with the objective of maximizing the distance towards the frontier function. The identification of is permitted by the additional constraint 1 � y + 1 � u = 1 . In this specification the direction vectors are proportional to y i and u i which lets the inefficiency measure be invariant to the units of measurement.
The optimization problem (3) is nonlinear and therefore difficult so solve. This is caused by and y or u arising multiplicatively. By defining y = y and u = u the problem can be transformed to a well-behaved linear programming problem Taking the constraint 1 � y + 1 � u = 1 from (3) into account we easily see that the value of the objective function is equal to as before. Program (4) can be easily solved by the ordinary simplex algorithm. 14 The solution values for , y and u can be backed out from the solutions for y and u by = 1 � y + 1 � u as well as y = y ∕ and u = u ∕ . For a particular country i the solution values are denoted i , yi , ui , yi , ui and i ( i = 1, … , n). 15 With these solution values we can compute the efficient input-output combination on the frontier function with the coordinates x i = X i , ŷ i = Y i and û i = U i . The potential reductions of the r bad outputs for country i in the sector under consideration can be computed as u i −û i = ui ⊙ u i = i ui ⊙ u i . We see that the potential emission reductions depend on the magnitude of the inefficiency measure i as well as on the optimized direction vector ui of country i. The total emission reduction potential of country i is the sum over all emission categories RP i = 1 � (u i −û i ) with 1 denoting a conformable vector of ones and the prime denoting transposition. The sum can, of course, only be validly computed if the emission variables are denominated in a common unit of measurement. This is indeed the case in our application where greenhouse gas emissions are expressed in CO 2 equivalents. To report the results later on we further aggregate the potential emission reductions across countries and sectors. Potential output enhancement can likewise be computed as

Variable Returns to Scale
The above stated optimization problems compute the inefficiency measures under the assumption of constant returns to scale (CRS). In a cross-country sectoral setting with countries of rather different size and with a rather different sectoral structure CRS seems to be an overly restrictive assumption. So it would be beneficial to get rid of this rather unrealistic assumption and to measure inefficiency under variable returns to scale (VRS).
In nonparametric approaches of efficiency measurement VRS is usually induced by adding the constraint 1 � = 1 to the optimization problems. In the case of environmental efficiency analysis this would violate the weak disposability property. Zhou et al. (2008a) show how to induce VRS in a way which is consistent with weak disposability. This implementation again leads to a linear programming problem with an additional parameter which is bounded in [0, 1]. Details can be found in Zhou et al. (2008a). As before, we obtain the solution values for y , u which allow to back out = 1 � y + 1 � u , y = y ∕ and u = u ∕ and to compute the emission reduction potentials. This problem can again be easily solved by the simplex algorithm. Here also, the solution values are denoted i , yi , ui , yi , ui and i for a particular country i ( i = 1, … , n ). We stick to the VRS assumption throughout this paper.

Bootstrapping
The inefficiency measures and the derived reduction potentials are estimates from a data sample which are subject to measurement error and therefore stochastic in nature. Frontier function estimation is associated with a further peculiarity. Specifically, the empirical implementation of the linear programming problems (4) or (5) is based on the observed input-output combinations in the data. This lets the empirically estimated frontier function provide a closer envelopment of the data than the true (unobserved) frontier function. As a consequence, the empirically determined technology set T DDF underlying the subsequent analysis is a subset of the true technology set T , i.e. T DDF ⊆ T . This leads to downward-biased estimates of the inefficiency measures and the emission reduction potentials. This bias can be substantial and bootstrapping provides a practical way to achieve a correction (see Wilson 2008, 2011).
We resort to a bootstrapping approach to compute bias-corrected estimates of the reduction potentials and to establish confidence intervals for these measures. The specific approach pursued here is analogous to the procedure proposed by Simar and Wilson (1998) adapted to the setting of directional distance functions. Compared to the double-bootstrap algorithm of Simar et al. (2012) the chosen approach is more transparent and easier to communicate. The approach of Simar et al. (2012) uses a complicated orthogonal transformation of the data and two smoothing loops which requires the selection of two critical bandwidth parameters instead of one. This bandwidth choice is particularly problematic in small-sample situations. Moreover, the algorithm seems not to be adapted to the inclusion of bad outputs since the direction vector pertaining to the outputs is restricted to be non-negative.
The smoothed bootstrap algorithm adapted from Simar and Wilson (1998) to the DDF setting starts with some preparatory steps. First, the DDF and the optimal directions are computed from the original data by solving (5) to obtain ̂i as well as the optimal directions yi and ui for all i = 1, … , n . The directions are computed once and kept fixed during the whole procedure. Furthermore, the bandwidth parameter h for the smoothing is chosen as described in Simar and Wilson (2011) where also some R code is provided.
The main part of the bootstrapping algorithm cycles B times through the following steps: • A bootstrap resample is obtained by first drawing with replacement from D = {̂1, … ,̂n, −̂1, … , −̂n} which implements a boundary reflection about zero. The result of this step is denoted ̃i (i = 1, … , n). • The smoothing step is performed by adding h ⋅ i to each draw, where the i are independent standard normal draws, thus obtaining ̃i + h ⋅ i and finally returning * for all i = 1, … , n where ̄ and ̃2 denote the sample mean and variance of ̃i (i = 1, … , n) , respectively. • These resampled inefficiencies are used to construct the bootstrap resample of the reference points by setting By that operation the observation ( y i , u i ) is first projected on the frontier (by +̂i ) and then randomly away from the frontier (by − * i ) along the fixed direction ( yi ⊙ y i and − ui ⊙ u i ). The resulting bootstrap resample consists of Cycling through the preceding steps B times we obtain the bootstrap resamples ( for each country i = 1, … , n in a given sector. Based on the bootstrap resamples the bias correction and percentile confidence intervals can be obtained. Letting z j be the generic notation of either interesting variable (e.g. aggregates of reduction potentials over sectors or countries), we denote the estimate from the original data by ẑ j and the bootstrap resamples by ẑ * j,b for each b = 1, … , B. The bias correction is performed by computing ẑ bc, This measure is only computed for those cases j (countries or sec- The rationale for this rule is that the absolute bias has to be sufficiently large compared to the standard deviation in order to achieve a reduction in the mean squared error from the bias correction (see Simar and Wilson 2008, p. 449f.).
One problem that occasionally arises during the bootstrap resamples is that we obtain reduction potentials which are larger than the actual emission quantities. To deal with this problem we prune out those cases in the spirit of an accept-reject procedure. The bias correction and the confidence intervals are established from this truncated distribution. Since we base the confidence intervals on a large number of bootstrap replications (actually B = 20, 000) 17 there always remains a sufficient number of replications for obtaining reliable estimates of the confidence bounds. The bias correction, which is more concerned with the center of the distribution instead of the tails, is even less affected by the pruning operation anyway.

Results and Discussion
The exposition of the results in this section is structured along four specification variants: (a) with a single emission variable (total GHG emissions in CO 2 e ), (b) with two emission variables ( CO 2 and other (non-CO 2 ) GHG emissions) and (c) with three emission variables ( CO 2 , CH 4 , N 2 O measured in CO 2 e ). Whereas we fix y = 0 in these variants, we pursue an additional variant (d) where we also allow for enhancement of the (good) output. We consider the two subperiods t 1 = 2008-2012 and t 2 = 2012-2016 where all inputs and outputs are computed as medians over the indicated years to achieve greater robustness of the results. 18 Most of the discussion focuses on the second subperiod, since there is not much change in the pattern of results across sectors and countries between both subperiods and the results for the more recent subperiod are of greater relevance for the current discussion about climate change. All variants include the conventional inputs capital K and labor L as well as the single economic output Y as defined in Sect. 2. Finally, in Sect. 4.4 we conclude this section with an extensive discussion of policy implications.

Total Greenhouse Gas Emissions
We start with total GHG emissions as the single emission variable. Figure 2 depicts the results for the first subperiod in the upper panel and for the second subperiod in the lower panel. In each panel we depict the actual emissions (open circles, connected by a dashed line) and the bias-corrected emission reduction potentials (bullet points, connected by a solid line) aggregated for the 7 sectors on the left side and the 16 countries on the right side. The vertical lines extending above and below the bullet points indicate the 95% bootstrap confidence intervals as explained above. The scale on the ordinate reveals that all values are expressed in million tons (mt) of CO 2 e.
The corresponding numerical results are reported in Table 2 in the appendix for reference. There we see that the sum of actual emissions over all sectors and countries amounts to 3341 mt of GHG (in CO 2 e ) in the first subperiod which decrease to 3070 mt in the second subperiod. Total bias-corrected reduction potentials are 1522 mt (with 95% confidence interval [1236,1886]) in the first subperiod and 1448 mt (with 95% confidence interval [1177,1801]) in the second subperiod. These amount to 46% and 47% of the actual emissions in the two subperiods, respectively. Figure 2 shows that the bias-corrected reduction potentials are quite sizable in some sectors and in a number of countries. Notice that the countries are of rather different size economically and this is also reflected in the differences of the actual GHG emissions. The bias correction lets the estimates of the reduction potentials appear much larger compared to their "raw" counterparts discussed at length in the companion paper of Krüger and Tarach (2020). 19 Most of the confidence intervals are quite narrow pointing to rather precise estimates of the potential emission reductions. There are some exceptions, however, where the confidence intervals are wider. These exceptions pertain to sectors or countries with larger actual emissions and larger reduction potentials (e.g. sectors C and DE or Germany).
We first turn to the lower panel with the results for the second subperiod. Regarding the sectors the estimated reduction potentials are particularly large in sector DE (mostly energy) and C (manufacturing) where they amount to 49% and 52% of the actual emissions, respectively. 20 This is followed by sectors A (agriculture) and H (transport) where the reduction potentials are smaller in absolute terms, amounting to 57% and 29% of the actual emissions, respectively. For the remaining sectors the reduction potentials are small to negligible. Germany (DEU) is the country with the largest actual emissions, but its reduction potential is of the same size as that of the United Kingdom (which is considered as an EU 19 The gray line depicts the "raw" reduction potentials (without bias correction) which are throughout smaller than their bias-corrected counterparts and track them quite closely, except in some cases where the actual emissions are particularly large. 20 In sector DE emissions are to a large extent determined by the share of fossil power generation. France and Sweden are very efficient and have shares of nuclear and water power of about 80% (see NEA-OECD (2018, p. 19) and Byman (2016, p. 8), respectively). Thus, the reduction potentials of the other countries implicitly require similar shares of non-fossil power generation which may be realized by either nuclear power, water power or other renewable forms (biomass, solar, wind). member country during the sample period until 2016) which has the second largest actual emissions. Other countries with sizable reduction potentials are Poland, Italy, France and Spain (with decreasing reduction potentials in this order). The reduction potentials amount to 34% of the actual emissions in the case of Germany, 61% for the United Kingdom, 67% for Poland, 48% for Italy, 45% for France and Spain. Reduction potentials of the other 10 countries in our sample are absolutely smaller and thus are not as easily visible. Nonetheless, for both groups of countries reduction potentials are very much in proportion to their actual GHG emissions. During 2012-2016, these 10 smaller countries account for almost one quarter of total GHG emissions in our sample. As can be verified from Table 2, summing the reduction potentials of these countries results in almost one quarter of the total reduction potential as well. Hence, although we primarily focus our discussion here on the results for the largest countries, we want to stress that the joint contribution of the smaller countries to emission reduction is as important as that of the largest countries.
Comparing these results with those for the first subperiod in the upper panel of the figure we find the distributions across sectors and countries to be rather similar in both subperiods. The major difference is the overall magnitude of the actual emissions and the estimated reduction potentials which are both larger in the first compared to the second subperiod. There are exceptions from this rule in the some sectors and countries as can be seen from a closer inspection of Table 2 in the appendix but these are of minor quantitative importance. Combined with the greater relevance of the more recent subperiod for the current debate about climate change, this similarity justifies the focus on the subperiod 2012-2016 in the subsequent discussion of the other variants

CO 2 and other GHG ( CH 4 and N 2 O ) Emissions
In this subsection, we proceed by splitting total GHG emissions into CO 2 and other GHG emissions (which is the sum of CH 4 and N 2 O , or equivalently total GHG minus CO 2 , expressed in CO 2 e ). Bias-corrected estimates of reduction potentials and confidence intervals are calculated for each of the two emission variables as well as for their sum (total GHG emissions). Figure 3 shows actual emissions and reduction potentials for the sectors and countries in the sample, and Table 3 in the appendix permits a closer look at the exact quantities. Aggregated over all sectors and countries we find total GHG reduction potentials of 1642 mt (with 95% confidence interval [1321,2049]), amounting to 53% of the actual emissions.
The lowest panel of the figure reveals that sector A is by far the largest emitter of other GHG, and these emissions also account for the majority of emissions in this sector (about 80%). In addition to sector A, emissions of other GHG are sizable in absolute terms in sector DE, although they amount only to about 10% of the sector's total GHG emissions. In contrast, emissions of other GHG in sector B are small in absolute size, but nonetheless make up 42% of total GHG emissions here. Figure 3 shows that the sectors C and H emit mostly CO 2 . Together with sector DE they account for the majority of CO 2 emissions in our sample. One result of this subsection, which is evident from the middle panel of Fig. 3, is that sector C has almost the same CO 2 reduction potential as sector DE, although it emits clearly less CO 2 , which points to the relevance of the manufacturing sector for saving CO 2 emissions. Another finding is that there is overall higher inefficiency regarding other GHG rather than CO 2 in relative terms. In particular, the share of reduction potentials to actual emissions for other GHG is with 64% (largely concentrated in sector A) considerably above the corresponding value for CO 2 (51%).
Looking at the countries we observe that reduction potentials for other GHG are particularly sizable for the two largest emitters of other GHG, namely France and Germany, where they make up 42% and 26% of the countries' total GHG reduction potentials, respectively. This indicates that it is important also to include the agricultural sector with its CH 4 and N 2 O emissions in the respective emission reduction plans in France and Germany. For some other large countries, the potentially feasible reductions for other GHG are comparably smaller than for CO 2 (at or below 17% of total GHG reduction potentials in the cases of the United Kingdom, Poland, Italy and Spain). Confidence intervals are generally quite narrow for reductions of other GHG for most sectors and countries.
Next, we further split the other GHG emissions into CH 4 and N 2 O emissions. Figure 4 shows the results of this split (see also Table 4). The differences to the results above can be explained by the direction choice where now one further possibility is available. During the second subperiod 2012-2016, our sample countries and sectors emitted a total of 3070 mt CO 2 e , out of which 6% were N 2 O emissions, 12% CH 4 emissions, and 82% CO 2 emissions. As above, the shares of reduction potentials in actual emissions are higher for N 2 O (81%) and CH 4 (57%) than for CO 2 (45%). For total GHG this translates into a share of reduction potentials in actual emissions of 48%, or 1487 mt (with 95% confidence interval [1214,1840]).
Since the use of nitrogen fertilizers is the major source of N 2 O emissions, their reduction potentials are clearly largest in sector A. Here, we find that the lower bound of the confidence interval indicates that reduction potentials below 65% of actual emissions are unlikely at the 95% confidence level. Our results imply that there is the potential for the sample countries to continue the N 2 O reduction path that has already started in Europe during 1990-2010 (see Tian et al. (2020) for regional trends of anthropogenic N 2 O emissions for the period 1980-2016). Sector A also is the major source of CH 4 emissions (mainly from animal livestock) and our results reveal that it has a sizable potential for reducing CH 4 . Our bias-corrected estimate is 69% of actual emissions (144 mt of CO 2 e ) and a reduction potential of less than 50% of actual emissions is unlikely based on the 95% confidence interval. In addition to sector A, Fig. 4 reveals that sector DE contributes substantially to CH 4 emissions with a rather small reduction potential. Finally, for sector B the CH 4 reduction potentials are an order of magnitude smaller than those of sector A, and for the other sectors they are negligible.

Combined Direction with Output Enhancement
In the preceding subsections we have measured inefficiency exclusively in the direction of reducing emissions, holding the good output and the inputs constant. As noted in Sect. 3.2, it is not sensible to measure inefficiency in the direction of reducing the inputs at this high level of aggregation. However, instead of pure emission reductions a combination of emission reductions and output enhancement (i.e. economic growth) is a realistic objective of policy makers. We account for this possibility by permitting more flexible directions y ≥ 0 in the linear program of equation (3). 21 By this, we allow emission reductions to be traded off against output enhancement, so that inefficiency measures reflect a combination of emission reduction and output enhancement.
These estimates are reported (again for the second subperiod) in Fig. 5 and Table 5. For the emission variable we use total GHG, so that reduction potentials can be directly compared with those from Sect. 4.1 for the period 2012-2016. In total, allowing for output enhancement causes reduction potentials to decline from 1448 mt to 1272 mt (with 95% confidence intervals changing from [1177,1801] to [1028,1595]), or equivalently from 47% to 41% of the actual emissions. This decline is rather small, indicating that most inefficiency is due to generating too much emissions instead of producing too less of the economic output. When comparing the upper panel of Fig. 5 with the lower panel of Fig. 2, we notice only slight differences regarding the distribution across sectors. It is visible that reduction potentials for sector C (manufacturing) decline the most (by about 100 mt) from 52% to 40% of actual emissions. For the other sectors the differences are much smaller. This is in line with our estimates for output enhancement potentials, which are low in all sectors except C (see Fig. 5, lower panel). 22 Hence, we find that a great deal of inefficiency in the direction of output enhancement, being large enough to substantially lower the scope for emission reductions, is present only in sector C.
For most countries we find reduction potentials of somewhat smaller size than in Sect. 4.1. Figure 5 (upper panel) reveals a distribution across countries which is very similar to that of Fig. 2 (lower panel). There are three exceptions (Belgium, France and Poland) where we obtain even higher reduction potentials than in Sect. 4.1. This can be attributed to the bias correction applied to the "raw" estimates.

Policy Recommendations
Altogether, the preceding discussion shows that there is a sizable extent of inefficiency in the sectors which could be transformed into emission reductions. Therefore, the question arises how can policy support the realization of the potentials in practice. Policy should aim at inducing firms to improve their productive efficiency (which then improves the efficiency of the sectors we measure here) to move towards the frontier function combined with specific measures to channel this movement in the right direction, i.e. mainly in the direction of emission reduction and less in the direction of output enhancement. In the long-run, effort to generate technological progress to shift the frontier function towards less emission intensive modes of production would also work in the right direction, although this aspect is beyond the scope of the measurement exercise we conduct here. As a theoretical guidepost for structuring the discussion of policy measures we use the macroeconomic model of Stern and Kander (2012). From the first-order condition in equation (15) of that paper one can derive an equation for energy demand as with E denoting the energy input in the underlying CES production function, Y gross output, and p E ∕p the price of energy relative to the price of output. A E is an augmentation factor of the energy input in the production function. This factor increases if a sector in a country improves its energy efficiency. It can be viewed as also comprising the aspect of energy quality as discussed in Stern and Kander (2012) and Stern (2010). Increasing energy quality acts like a further factor (named Q in Stern and Kander (2012)). If we consider E as the input of mostly fossil fuels, changing the energy mix towards renewable energy sources operates analogous to an improvement of energy quality associated with less GHG emissions. The parameter is related to the elasticity of substitution between energy and a capital-labor aggregate by = ( − 1)∕ and E is a further production function parameter related to the energy input.
Various estimates of the parameters are reported in table 1 of Stern and Kander (2012). They can be roughly summarized as E ≈ 0.2 , ≈ 2∕3 and ≈ −1∕2 . Taken at face value we get a calibrated version of the energy demand equation as This shows that the energy demand and therefore GHG emissions (assuming that a substantial part of energy is generated from fossil sources) are linearly related to the level of gross output. Emissions are decreasing with a higher relative price of energy p E ∕p as well as with an improvement of productive efficiency leading to a larger A E . These variables are linked to various policy measures which are discussed in the following. In addition to the direct effect of p E ∕p there is a further, indirect, effect working through A E , i.e. adopting more energy efficient and therefore less emission intensive technologies in the medium to long run when p E ∕p is higher.
To increase the productive efficiency of sectors, a large variety of policy measures can be beneficial. Examples of these measures directed generally towards inefficiency reduction are fostering competition, reducing some regulations, incentivizing research and development and protecting intellectual property. Yet, the effect of these policy measures has to be channeled towards improvements in energy efficiency ( A E ) or energy quality which are associated with emission reductions. There are many diverse policy measures available which could be appropriately combined and coordinated.
This policy mix, of course, has to comprise traditional instruments of environmental policy such as phasing out the most emission-intensive modes of power generation (i.e. coal), abandoning certain modes of travel (e.g. short-distance flights) or setting energy consumption standards for new products (e.g. cars, heating). Incentives or subsidies for behavior modification (i.e. switching to electric cars, more attractive public transport, thermal insulation of buildings) could also direct efficiency improvement in the desired direction.
A well-designed carbon price is a key measure to influence the relative price of fossil-fuel based energy ( p E ∕p ) and thus, by the energy demand relation, also combustion thereof (Sen and Vollebergh 2018;Best et al. 2020). Important for the design here is a broad sector and country coverage (Aldy et al. 2010, p. 928). One finding of our efficiency analysis, in particular from Sect. 4.2, is that emission reduction potentials for the manufacturing sector are substantial, i.e. of similar magnitude as for the energy sector. We also find substantial reduction potentials in the transport sector, although these are smaller in relative terms. Currently, European emission trading still covers only power generation, heavy industry and intra-European aviation (Delreux and Ohler 2019, p. 7). Thus, comprehensive EU-wide carbon tax policies could push manufacturing and transport sectors closer to their frontier in the desired direction of reducing CO 2 emissions. An extension of emission trading to these sectors, if designed effectively (i.e. with a steadily decreasing cap of overall emissions), would also work in the desired direction. However, for the manufacturing sector, we also find in Sect. 4.3 that there is considerable inefficiency in the output direction. Therefore, a uniform carbon price could easily be set too low in order to channel the direction of inefficiency reduction towards CO 2 reduction in those sectors where much efficiency can also be gained by output enhancement instead. Furthermore, innovations are important for decarbonization. Sufficient carbon pricing works in the direction of inducing innovations for technologies with high potential for GHG emission reductions and therefore increases A E (Aghion et al. 2016; van den Bergh and Savin 2021). These include in particular renewable energy technologies (i.e. wind and solar), large-scale and cost-efficient energy storage, and electric cars. Equally important may be all types of innovations which are able to substantially improve the energy efficiency of products or production processes, in particular if the energy used there is still fossil-fuel based. 23 To induce innovative activity, public funding of research and development could be specifically targeted at these areas. As knowledge creation is a public good, there is considerable under-investment in these areas to be expected (Knopf et al. 2013, p. 233). However, it seems generally difficult to anticipate which technologies will be most crucial for the energy system of the future. Thus, with respect to the direction of research and development funding, "policy-makers have to strike a delicate balance between supporting promising developments whilst avoiding the temptation to prematurely pick winners" (Knopf et al. 2013, p. 234).
These policy measures appear to be well adapted to the sectors C, DE and H with a large amount of CO 2 emissions, while sector A (agriculture) is special in its emission mix caused by the use of fertilizers, animal livestock, as well as its essentiality for human nutrition. When comparing our results for N 2 O to other studies, these seem to be quite optimistic. For example, Winiwarter et al. (2018) estimate that if only the lowest-cost N 2 O abatement measures were implemented, global emissions thereof could be reduced by 6.2% compared to a baseline scenario, while if also high-cost abatement measures were implemented, global N 2 O reduction potentials would amount to 26%. Independent of the exact quantity of N 2 O reduction potentials, there are several N 2 O abatement measures available which in the agricultural sector generally comprise any measures that improve the efficiency of nitrogen application to crops (Winiwarter et al. 2018, table 1). There is also evidence that organic farming, in particular biodynamic farming, reduces N 2 O emissions per yield and is associated with a modest uptake of CH 4 (Skinner et al. 2019, p. 4).
The extent of measured inefficiency is, of course, not confined to Europe. In other countries, emerging economies in particular, there are also huge quantities of potential emission reductions to be expected which could be realized by means of efficiency improvements. Thus, strengthening international cooperation and technology transfer from advanced countries towards emerging countries at favorable conditions could tremendously enhance the overall benefit.

Discussion and Conclusion
The bottom line of the results of the above analysis with the stochastic nonparametric approach to environmental efficiency analysis is that the bootstrap bias-corrected estimates of potential reductions of GHG emissions by reducing the inefficiency relative to the most efficient countries in each of seven sectors are quantitatively substantial. Along with the bias-correction also confidence bounds are established which show that the reduction potentials are estimated with great precision in some sectors while being wider in other sectors. The comparison with the results of the companion paper (Krüger and Tarach 2020) shows that the bias correction leads to substantially increased estimates of the potential emission reductions.
To put the magnitudes of the estimated potential emission reductions into perspective we compare them to the emission reduction targets recently tightened by the European Commission (see EU 2020). Therein, an emission target of 45% (meaning a reduction by 55%) compared to the GHG emission levels in 1990 until 2030 is postulated. Since the 16 sample countries of our study overall emitted roughly 5000 mt of GHG in 1990 (retrieved from the EEA greenhouse gas data viewer) this implies a necessary emission reduction of about 2750 mt until 2030. As stated by the European Environmental Agency (EEA 2019), it is highly likely that the target level of a reduction of 20% compared to 1990 is to be achieved or is even slightly outperformed by 2020. Thus, an emission reduction of about 1000 mt is already achieved to date. The remaining 1750 mt until 2030 are not far away from the bias-corrected estimates of the total potential emission reductions aggregated over both countries and sectors (ranging from 1271 mt in variant (d) to 1642 mt in variant (b)) and are well within the confidence intervals. The distribution of the EU reduction targets across sectors also corresponds to the pattern of our estimated reduction potentials. Therefore, becoming more efficient can provide a substantial part of the reductions until 2030, especially in the sectors with large emission volumes.
The distribution of the reduction potentials across countries reflects their (economic) size. Naturally, larger countries tend to have larger manufacturing and transportation sectors which goes along with a need for a larger energy generating sector. These are the sectors with the largest actual emission quantities and also with the largest reduction potentials. Poland seems to be an exception operating with a much higher emission intensity. 24 Agriculture is another sector with large GHG emissions which are here more caused by CH 4 and N 2 O rather than CO 2 . Thus, in addition to conventional environmental policy measures and new technologies which come to mind first, structural change in a direction towards the less emission intensive sectors could contribute to the realization of reduction potentials. Exactly this form of structural change is taking place since several decades in the form of tertiarization (where tertiarization means an increasing share of the less emission intensive service sector at the expense of the primary and secondary sectors; Fourastié 1949).
Of course, it is not realistic to expect that these emission reductions can be fully achieved within the next decade. The reasons for this assessment are manifold. Policy measures become effective with a time lag. Despite structural change going in the right direction it is a rather sluggish process taking place over longer spans of time. Here, the demand side and the slowly changing consumer preferences play a major role. Economic actors also adapt to changing conditions such as prices and also adverse reactions are to be expected (such as "rebound effects"; Greening et al. 2000). Structural change is also impeded by the specific roles of the countries in the context of international specialization which prevents that all countries will reach the same sectoral structure (de Araújo et al. 2020).
On the other hand, the present analysis is purely static (mostly confined to the medians to 2012-2016) and does not take account of the emission reducing effects of technological change. New technologies and in particular less emission intensive forms of energy generation and mobility are crucial for reaching the targets. Since the European countries are only responsible for a small share of global GHG emissions, spillover effects and the transfer of these emission reducing technologies to countries outside Europe is the key factor for new technologies to become effective for large scale emission reduction. This leads to the natural extension of this work towards a dynamic analysis (by projecting the potential emission reductions into the future) or an extension with a global country sample.  Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.