Energy efficiency measurement in agriculture with imprecise energycontent information

Stéphane Blancard, Elsa Martin n

AgroSup Dijon, CESAER, France

H I G H L I G H T S

� We develop a method to measure energy efficiency of farms.� We decompose energy efficiency to design accurate energy policies.� We take into account uncertainty on energy content of inputs.� We calculate the bounds of efficiency measurement to produce robust results.� Efficiency is not a fixed value and should be considered with caution.

a r t i c l e i n f o

Article history:Received 13 August 2013Received in revised form28 October 2013Accepted 29 October 2013

Keywords:Data Envelopment AnalysisEnergy efficiencyUncertainty

a b s t r a c t

Measuring energy efficiency is crucial when planning energy reduction policies. However, decision makers areunderstandably reluctant to act in the absence of solid data and results supporting a policy position. This paperproposes a methodology to measure the energy efficiency of farms based on the Data Envelopment Analysis(DEA) approach. In a manner similar to the cost framework, we decompose energy efficiency measurementsinto technical and allocative efficiencies in energy contents of inputs. In this study, we replace input prices usedin traditional economic efficiency measurements by their energy content. We use the energy efficiency modelto explore the optimal input-mix that produces the current outputs at minimum energy-consumption. Wedemonstrate that this decomposition can help policy makers design accurate energy policies. However, theuncertainty of the data and, more particularly, the energy content of the inputs leads us to recommend usingthe methodologies to calculate the bounds of efficiency to obtain more plausible and robust results. Based onour analysis, energy efficiency is not a fixed value, and policy-makers should consider it with caution. We use a2007 database of French farms specialised in field crops for empirical illustration.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In the context of energy consumption reduction, since 2002, theEuropean Union (EU) has adopted a series of measures that led to theNational Energy Efficiency Action Plans (NEEAP), proposed in 2007/2008, and the Energy Efficiency Plan (EEP) (COM, 2011, 109),proposed in March 2011. For France, energy reduction is strategicbecause France is second only to Germany with respect to primaryenergy consumption in the EU-271. Among all French productivesectors, agriculture accounts for 3% of the country's total energyconsumption. While one can consider this proportion to be low, theFrench agricultural sector is notably vulnerable to the cost of energy

(Garnier, 2012). For this reason, after its NEEAP (French Authority,2008), in 2009, the French Agricultural Ministry launched an EEPdedicated to the agricultural sector (Ministère de l’agriculture, 2009).The main objective of this EEP was to measure the energy efficiencyof farms. This measurement should highlight the potential savings offarms and help reduce the energy dependence of agriculture.

The common measurement of energy efficiency is given by theratio between outputs in physical units or converted to energy andinputs converted to energy (Patterson, 1996). For instance, in theagricultural sector, one can measure energy efficiency as the amountof energy required per quintal of product. Among other regulatorybodies, the French Environment and Energy Management Agency(ADEME) uses this measurement within the framework of the EEP tosubsidise agricultural equipment that confers energy savings. Thismeasurement requires not only information on outputs and inputs butalso information on the energy content of inputs.

Our work proposes an alternative method that takes into accountthe uncertainty of the energy content of inputs to measure the energyefficiency of farms and to decompose it into technical and allocative

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/enpol

Energy Policy

0301-4215/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enpol.2013.10.071

n Correspondence to: AGROSUP Dijon, CESAER (UMR 1041 of INRA), 26 BoulevardDr Petitjean, BP 87999, 21079 Dijon, France. Tel.: þ33 3 80 77 26 91;fax: þ33 3 80 77 25 71.

E-mail address: elsa.martin@dijon.inra.fr (E. Martin).1 See http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Consumption

_of_energy

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎

efficiency in energy contents. This alternative method relies on DataEnvelopment Analysis (DEA), a nonparametric method that is espe-cially powerful in evaluating the relative performance of decision-making units with multiple inputs and outputs. As stated by Zhou andAng (2008) and Zhou et al. (2008), DEA has gained in popularity inenergy efficiency analysis. Based on Farrell (1957), Charnes et al. (1978)developed the DEA model under the constant return to scale (CRS)assumption, and Banker et al. (1984) extended it under the variablereturns to scale (VRS) assumption. DEA involves the use of linearprograms to construct nonparametric production frontiers. The bestpractices located on the frontier form the benchmark against whichone can calculate the potential energy savings for those that are not onthe CRS or VRS frontier. Therefore, one can interpret this alternativeenergy efficiency measurement as the ability of farms to produce agiven output level using a minimum amount of energy. Concretely, foreach unit, this measurement equals the ratio of the minimum amountof energy to produce a given output level to the actual amount ofenergy consumed.

In agriculture, various papers have dealt with energy efficiencyusing the basic DEA framework. Among them Chauhan et al.(2006) measured farmers' efficiencies with regard to energyconsumption in rice production in India. More recently, for theIranian agricultural sector, a series of studies, including Nassiri andSingh (2009, 2010), Houshyar et al. (2010), Mousavi-Avval et al.(2011), Fadavi et al. (2012), Heidari et al. (2012) and Rahbari et al.(2013), determined the amount and efficiency of energy consump-tion of agricultural production types by using the DEA method.Several of these studies decomposed technical efficiency (TE) intopure technical and scale efficiencies from CCR (Charnes et al.,1978) and BCC (Banker et al., 1984) models to identify the sourcesof inefficiencies. Overall, these studies help to assess the wastefulconsumption of energy by inefficient farmers and to suggestreasonable savings in energy consumption. Despite similaritieswith these series of papers, our work differs in several ways.

Previous studies used information about the energy content ofinputs solely to convert into joules either the technical and scaleinefficiency scores or the original input data before performing theCCR and BCC models. In our case, we further exploit the energycontent of inputs to reveal another source of inefficiency: an input-mix usage that is inconsistent with the energy content of inputs.Based on the cost framework developed by Färe et al. (1985), wedecompose energy efficiency into (i) technical efficiency (TE), as inprevious studies, and (ii) allocative efficiency (AE) in energycontent. TE measures farms' ability to use the best practices givenexisting technologies. AE measures farms' ability to make optimaldecisions with respect to resource allocation, decisions that areconsistent with the energy content of inputs in place of theirprices. This decomposition allows us to determine where to focusour efforts and to consider other ways of energy savings thansimply eliminating technical inefficiency. Indeed, additional sav-ings are possible if resource waste is due to the managerial failuresof farmers and are still possible if input misallocation exists.

For OECD countries Hoang and Prasada Rao (2010) were the first topropose an energy efficiency decomposition to explore the optimalinput-mix that produces the current outputs at minimum energyconsumption.2 However, contrary to Hoang and Prasada Rao 2010, andmore generally than the previous studies, we also consider a short-runsetting where some inputs are held quasi-fixed to take into accountthe nature of agricultural inputs such as land or family labour. In along-run setting, all inputs are variable. Furthermore, by focusing oninput reduction to diminish energy consumption, we can reasonably

assume that policy-makers will exclude some inputs from the list(such as land or family labour).

Like the common energy efficiency indicator, our alternativemeasurement requires information regarding the energy content ofinputs. Several techniques exist to assess these energy contents but, tothe best of our knowledge, no single best source exists. For instance,ADEME chooses the Life Cycle Assessment (LCA) perspective. Unfortu-nately, due to the large number of parameters to be entered in thismodel, the energy contents of inputs may include uncertainty(see Huijbregts, 1998 for further details). Zegada-Lizarazu et al.(2010) showed that the range of reasonable values for energy contentsis large. For some inputs, the minimum and maximum energycontents can differ by a factor of six. The complex process involvedin their elaboration or the confidentiality stated by manufacturersconcerning pesticides may explain this variability. As stated by Zegada-Lizarazu et al. (2010), these large intervals are a source of confusion,misleading conclusions and, sometimes, discomfort to policy-makers.Therefore, the question is how to take this uncertainty or incompleteinformation into account when measuring the energy efficiency offarms. A final contribution of our paper is that it considers theuncertainty in the energy content of inputs. By addressing thisuncertainty, we also expect to provide robust and plausible energyefficiency measurements. Robust analysis is important for evidence-based policy-making. Indeed, decision makers will understandably bereluctant to act without solid data and results supporting a policyposition. In the same sense, several scenarios should be considered forthe energy efficiency values to help policy-makers avoid choosing asingle scenario that may lead to inadequate policies (for instance, toostringent or insufficiently stringent). Over the years, the DEA literaturehas grown to include papers dealing with this topic. Among otherauthors Kuosmanen and Post (2001, 2003), Camanho and Dyson(2005) and Mostafaee and Saljooghi (2010) showed that modified DEAmodels can provide robust efficiency measurement under priceuncertainty. In the last two cases, to address uncertain price problems,weight restrictions are incorporated in the DEA model in the mannerof Thompson et al. (1986), Thompson et al. (1990), and Charnes et al.(1990).3 Clearly, the use of such restrictions does not solely concernprices, and we can extend them to any other pertinent units, such asthe energy content of inputs.

In summary, in this paper, we propose an extended DEA-basedmeasurement of energy efficiency and its components – technical andallocative in energy contents – with an uncertain energy content ofinputs partly based on Camanho and Dyson (2005) andMostafaee andSaljooghi (2010). The applicationwas conducted on a sample of Frenchfarms specialised in field crops (cereals and oilseeds), which areconsidered a major agricultural production with respect to thecultivated area, number of farms and energy use. Farms are preciselylocated in the “Region Centre”, which is the largest producer of fieldcrops among the European regions (Gabrysiak and Rodier, 2012).

The structure of the paper is as follows. In the next section, wedescribe the methodology to assess energy efficiency and itscomponents. Section 3 provides a description of data and retainedvariables. Section 4 presents the results, while Section 5 is devotedto their discussion and policy implications. Finally, conclusions aredrawn in Section 6.

2. Methodology for an alternative energy efficiencymeasurement

In the next section, we present our model based on the DEAapproach to measure energy efficiency (EE). In Section 2.2, we also

2 Another method is using a set of weighted non-radial DEA models developedby Zhu (1996) to construct a preference structure over the proportions by whichthe current input levels can be changed.

3 For further details about weight-restricted DEA models, see Allen et al. (1997)or Pedraja-Chaparro et al. (1997).

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎2

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

present the weight-restricted DEA methodology for measuring EEwhen the energy content of the inputs is uncertain or bounded.

2.1. Energy efficiency and its decomposition

Fig. 1 illustrates the concepts of input-oriented energy andtechnical and allocative efficiency in energy contents. We assumeseven DMUs (A–G) that produce y with two inputs x1 and x2. Thesegments linking DMUs A, B, C and D form the technically efficientfrontier. We use DMU F to illustrate the efficiency concepts. Theratio 0f/0F gives the technical efficiency. This means that it ispossible to find another DMU or to build a composite DMU (f inour case) that produces the same output level with the leastinput level.

Let us introduce information on the energy content of inputs(w1 and w2) and assume that we perfectly know these contents.Consider EC ¼wx1þw2x2 as the iso-energy line, that is, the lineshowing all combinations of inputs with the same energy con-sumption. For instance, the iso-energy line of F is ECF ¼w1xF1w2xF2:Technical efficiency is equivalent to the ratio between the iso-energy line ECTand that of observed plan ECF.

Now, let us assume that DMU F has eliminated its technicalinefficiency by moving to point f (linear combination of A and B).This point is not energy efficient when we compare it with DMU Clocated at the tangency point between the iso-cost line and theisoquant. DMU C is the least energy-intensive production plan.Thus, given the energy content of inputs, the composite DMU f andF appears allocatively inefficient in energy contents, contrary to C.The ratio 0f′/0f gives the allocative inefficiency in energy contents,which measures the extent to which a technically efficient pointfalls short of achieving the minimum energy content because itfails to make the substitution (or reallocation) involved in movingfrom f’ to C. We can also express the allocative efficiency in theenergy content measurement as a ratio between the minimumenergy at point C and the used energy at the technically efficientpoint f: ECmin=ECT . Finally, we have the relationship:

0f′=0F¼ ð0f=0FÞð0f′=0fÞor

Energy efficiency¼ Technical efficiency�Allocative efficiency in energy contents ð1Þ

In the previous discussion, for simplicity we did not considerthe fact that some inputs may be quasi-fixed. However, in the

short-term or following decision-makers' preferences, input adjust-ment is not possible or desirable for all inputs. In such situations, weconsider the quasi-fixed inputs as a parameter. With this distinc-tion, the decision-maker or policy-maker is able to determine whatto achieve in a relatively short time.4 For readers interested inmethodological issues, Appendix A.1 details the theory and DEAmodels we implement to compute the energy, allocative in energycontents and technical efficiency scores. We use Färe et al.'s (1985)model to compute energy efficiency and the CCR model to computetechnical efficiency. We finally calculate the residually allocativeefficiency in energy contents. Our constant return to scale specifica-tion allows us to treat all farms equally by using the mostproductive scale size as a common benchmark. Furthermore, wecapture the maximum energy savings even if a scale change isnecessary for the farms being scale inefficient. Finally, one whowants to refer to the BCC model could easily rewrite our specifica-tion for variable returns to scale.

2.2. Extended DEA models to account for imprecision in the energycontent of inputs

Our efficiency measurements are not meaningful in the case wherethe energy content of inputs is uncertain or imprecise. The literaturehas developed additional analyses to achieve results that are morerobust in cases of uncertain data. The bootstrap procedure proposedby Simar andWilson (1998, 2008) could help. One could also considerapproaches such as robust alternatives to DEA models (Cazals et al.,2002; Daraio and Simar, 2006). Here, we expect the main uncertain-ties to come from the energy content of inputs. For this reason, it isdesirable to develop a framework for energy efficiency measurementadapted to this topic. To compute input cost efficiency when knowl-edge of the exact price does not exist, it is possible to introduceconstraints with lower and upper bounds on the admissible values ofprices. In the same way, we use the knowledge of upper and lowerbounds whose relative energy content we expect to vary. To exploitthis information, one can use the Assurance Region (AR) approachintroduced by Thompson et al. (1986) and redefined by Thompsonet al. (1990) or the Cone Ratio approach proposed by Charnes et al.(1990). Usually expressed in the form of lower and upper bounds, theassurance region or Cone Ratio methods put constraints on the ratio ofinput (output) weights or multipliers. Several authors have proposedstudies built on these methods (see for instance Camanho and Dyson,2005). In the same vein as these authors, we adopt two perspectives(or scenarios), viz., optimistic and pessimistic, and thus assess twoenergy efficiency scores: one with the most favourable energy contentscenario (the energy content is minimal) and one other with the leastfavourable energy content (the energy content is maximal). Note herethat optimistic and pessimistic notions are relative to each unit. Forinstance, a pessimistic situation for an evaluated unit is not necessarilyso for another unit.

Fig. 2 illustrates these notions (for methodological details, seeAppendix A.2.). We consider the case where only the maximal andthe minimal energy contents for all DMUs can be identified, e.g., fortwo inputs 1 and 2, we havewmin

1 ; wmin2 ; wmax

1 and wmax2 The energy

content (or weight) ratios underlying the energy efficiency evalua-

tion would be restricted to the following range: wmin1

wmax2

rv1v2rwmax

1wmin

2:

The slope of the iso-energy line underlying the evaluation of CE

could vary between the slope of EβEβ′; i:e:; �wmax1

wmin2

and the slope

of EαEα′; i:e:; �wmin1

wmax2

The optimistic EE measurement assesses each

DMU by comparison with the most favourable iso-energy line.

Fig. 1. Energy, allocative in energy contents and technical efficiency measurementsin the input space.

4 In fact, we will have an equivalent of the short-run cost-minimisationproblem (Färe et al., 1985).

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

In Fig. 2, the optimistic EE frontier corresponds to the segmentslinking Eβ; B; C and Eα′ (the energy content ratio of the iso-energyline is as close as possible to the marginal rate of substitutionbetween the inputs). Conversely, the pessimistic frontier measure-ment assesses each DMU by comparison with the least favourableenergy content scenario; it corresponds to the segment linkingEα; ω and Eβ′ for the pessimistic frontier. In the case of DMU F, theoptimistic EE is measured by 0f″/0F, whereas pessimistic EE ismeasured by 0f′/0F. Intuitively, F, which has adopted a more x2 �intensive input mix, is seen as a farm with a more significantenergy reduction potential if wmin

1 and wmax2 are retained rather

than wmax1 and wmin

2 .

3. Data and variables

Our work is based on data from farms specialised in field crops,namely, cereals (wheat, barley, sorghum, triticale) and oilseeds(rapeseed, sunflower), observed in 2007 and located in the French“Region Centre”. At least three factors motivated the selection ofthese data. First, according to the 2010 French agricultural census,field crop production is the largest agricultural production of thecountry. These crops are cultivated by two-thirds of farms andinvolve more than half of French agricultural lands. Second, thisproduction also consumes the most energy. Third, the “RegionCentre” is a good case to study because it is the largest producer offield crops among European regions (Gabrysiak and Rodier, 2012).

SOLAGRO, a French non-profit organisation promoting sustain-able energy and agriculture and respect for the environmentprovided the dataset. With the financial support of ADEME,SOLAGRO and other partners proposed a tool named PLANETE(Pour L’A Nalyse EnergéTique de l’Exploitation agricole) to analysethe farms' energy efficiency and to help them to improve thisefficiency. Within this framework, the energy efficiency measure-ment is the common measurement described in the introductionand expressed as the ratio between outputs and inputs convertedto common energy units (the joule). PLANETE is a free5 spread-sheet programme that automatically computes the commonenergy efficiency measurement of the farm surveyed based onits inputs and outputs. Data were collected and analysed byagricultural organisations applying the PLANETE tool. For thepurpose of this study, these data are assumed to have high quality

and reliability. To further ensure the reliability of data used forDEA estimation, we used the Wilson (1993, 2010) procedureincluded in the software package FEAR proposed by Wilson(2008) to detect and remove potential outlying observations. Thefinal dataset includes 135 farms (instead of 143 farms initially). Weselected the sample in collaboration with SOLAGRO to havehomogeneous characteristics of farms: (i) the same specialisation(field crops), (ii) quasi similar pedo-climatic conditions by all beinglocated in the same geographical area (the French “Region Centre”)and (iii) an identical production system (conventional). Becausethe PLANETE approach relies on voluntary farms, this samplecannot be representative. However, the results can help explorethe different approaches, based on the decomposition of energyefficiency, a policy-maker can use to reduce energy consumption.The results can also encourage policy-makers to use caution beforemaking decisions.

Concerning agricultural outputs, we retain field crops expressed intons for cereals and oilseeds. Other productions (e.g., protein crops orindustrial crops such as sugar beet or potatoes) are of little importancebecause they represent less than 2% of the total area. Concerningagricultural inputs, it is possible to distinguish between their directand indirect energy consumption. Direct energy consumption is theenergy content of an input (the MJ content of diesel oil, for instance),whereas indirect energy consumption corresponds to the energyconsumed to produce and transport an input (e.g., fertiliser, pesti-cides). Chemical fertilisers, pesticides, petroleum, land, labour andmachinery are the inputs we selected. Fertilisers and petroleum arethe major inputs contributing to the total energy requirements of theproduction of field crops (Bochu, 2002). Note that fertiliser, whichencompasses nitrogen, phosphorus and potassium, represents 49% ofthe total energy consumption. Petroleum, which means petroleum-based fuels such as diesel, gasoline and liquefied petroleum gas,represents 21% of total energy consumption. In our work, we firstrestricted ourselves to nitrogen-based fertiliser because 90% of theenergy consumed in fertiliser is due to this input, according to ourpreliminary calculations on the original database.6 However, we thenextended the analysis to diesel fuel, which is mainly consumed forland preparation, other operations of crops production (seeding,weeding, fertilisation, spraying, harvesting and threshing) and trans-portation.7 We also decided to focus on non-renewable energy and toinvestigate its potential reduction. Therefore, we will assume that thereduction of land, labour and machinery is not a priority, in contrast tothe most energy consuming inputs. We consider these three inputsas fixed. It also becomes unnecessary to convert them into energy,except for machinery.8 Table 1 provides descriptive statistics of thesevariables.

In the first step, we converted nitrogen, petroleum and pesti-cides from physical to energy units by using the energy content ofinputs provided by ADEME (2011).9 A national group of expertsthat applied the Life Cycle Assessment methods to French agri-culture, mainly based on the Ecoinvent dataset (see Frischknechtet al., 2005), has established these energy contents. To account forthe uncertainty, we also use minimum and maximum reasonablevalues of these energy contents to compute the upper and lowerbounds for energy efficiency. We use the energy content informa-tion reported in the literature (Dalgaard et al., 2001 and Zegada-Lizarazu et al., 2010) to compute the upper and lower bounds.Table 2 lists the various values of the energy contents we used andtheir respective references.

Fig. 2. Optimistic and pessimistic energy efficiency measurements in the input space.

5 SOLAGRO provides it freely as long as users give them the data in return.

6 For instance, Houshyar et al. (2010) also have more than 90% of the energyconsumed in fertilizer due to nitrogen for wheat production.

7 We did not retain seeds in this study. Generally, seeds represent aninsignificant part of energy expenditure.

8 SOLAGRO directly provided this aggregated variable.9 For further details about the data, see Bochu (2002).

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎4

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

4. Results

Section 4.1 presents the results in the deterministic setting andSection 4.2 the results in the uncertain case.

4.1. Alternative energy efficiency measurement and decompositionin the deterministic case

To examine energy efficiency and its components (technicaland allocative efficiency in energy contents) in the deterministiccase (i.e., when one knows the energy content), we run the input-oriented linear programming models [P1] and [P2a]10 presented inAppendix A.1. At this stage, we use the energy content of inputsprovided by ADEME (2011) presented in Table 2. Table 3 providesthe scores with these equivalents.

Energy efficiency (EE) varies across farms from 0.305 to 1. Theaverage overall EE is 0.721, indicating that, on average, the farmscould reduce all the inputs and thus minimise their energyconsumption by 27.9%. The DEA-based energy efficiency scores(alternatively called the energy efficiency score in the introduction)are higher than those computed by ADEME11 (called the commonenergy efficiency score in the introduction) because ADEME doesnot consider fixed inputs such as land and labour. With respect tothe single ratio proposed by ADEME, one of our contributions is topropose a decomposition of energy efficiency into technical andallocative efficiency in energy contents based on the energy contentof the inputs. According to Table 3, we can identify two sources ofinefficiency. Technical efficiency ranged from 0.254 to 1 with anaverage score of 0.809. Thus, if each farm were technically efficient,the energy use could potentially decrease by 19.1%. Even aftereliminating the mismanagement of resources, most farms have asecond means by which to reduce their energy consumption thatconsists in reallocating inputs or changing the input-mix. Indeed,the allocative efficiency in energy contents ranged from 0.505 to1 with an average efficiency of 0.892. More precisely, through inputreallocation, farms can still reduce their energy consumption to10.8% relative to their costs on the production frontier.

As stated above, this methodology allows us to identify the bestperformers. Forty-four farms are technically efficient but only 24 areboth technically and allocatively efficient. Table A1 of Appendix 3explores some key characteristics of the energy efficient farms and ofthe 25% least efficient farms.12 Energy efficient farms have highercereal yields than the 25% least efficient farms. They also use lesslabour and machinery, and they use cultivation practices that arebased on few pesticide treatments and more bare ground area.This result suggests that farmers have different practices that allowthem to be more efficient but not necessarily environmentallyfriendly. Indeed, reduced bare ground area is an environmentallyfriendly technique because of the link between bare ground anderosion rates (see, for instance, Dale and Polasky, 2007). For the othervariables tested, there are no statistically significant differencesbetween the two groups.

To illustrate the insights gained from a decomposition of theenergy efficiency scores into technical and allocative efficiency inenergy contents scores, we propose the cases of three farms: one isfully energy efficient (farm 88), one is technically efficient but notenergy efficient (farm 44), and one is not efficient in any compo-nent (farm 1). Note that in our sample we do not find the case offarms that only suffer from input mismanagement (i.e., TEo1 andAE¼1). Table 4 lists their input and output levels, whereas Table 5provides the potential reduction of energy used on each compo-nent of these three farms.

Farm 1 suffers both from input mismanagement and input mis-allocation: it can reduce its energy spent by two means, viz., byeliminating technical and allocative inefficiency. Its total potentialenergy saving is equal to 296 487 MJ. Compared with farm 1, farm 44can benefit from energy saving by eliminating only allocative ineffi-ciency in energy contents that corresponds to 36.2% of the energyobserved, i.e., 409 050 MJ. Farm 88 cannot benefit from energy saving.

A first result emerges: the sole consideration of energy effi-ciency can hide the existing disparities in each component(technical and allocative in energy contents).

Table 1Descriptive statistics of inputs and outputs for the 135 farms.

Mean Standarddeviation

Min Max

Variable inputsNitrogen (kg) 26,691 18,171 1992 91,919Petroleum (l) 17,218 13,261 2193 91,279Pesticides (kg of activeingredient)

646 514 16 3500

Fixed inputsLand (ha) 187 110 19 561Labour (unit) 1.65 1.10 0.50 6.50Machinery (MJ) 7297 6343 125 33,949

OutputsCereals (q) 8867 5919 432 33,529Oilseeds (q) 1439 1108 0 4561

Table 2Energy content of inputs (in MJ/unit).

Inputs ADEME Min Max

Nitrogen (kg) 55.57a 32.2b 78.2b

Petroleum (l) 46.4a 35.9b 51.5b

Pesticides (kg of a.i.) 282a 76c 455c

a.i.: Active ingredient.a Source: ADEME.b Source: Zegada-Lizarazu et al. (2010).c Source: Dalgaard et al. (2001).

Table 3Input-oriented DEA scores of energy, technical and allocative efficiency in energycontents.

Mean Standarddeviation

Min Max Number ofefficient farms

Energy efficiency 0.721 0.177 0.305 1 24Technical efficiency 0.809 0.187 0.254 1 44Allocative efficiency inenergy contents

0.892 0.105 0.505 1 24

ADEME score 0.579 0.123 0.277 1 1

10 We implemented the programs by using GAMS software.11 Recall that the score currently used by ADEME is obtained by dividing

the sum of the energy consumed (through variable input use) in megajoules bythe output in quintals. We then normalised the minimum to one (representingthe efficient farm) to obtain an efficiency score that can be compared with theDEA score.

12 Other characteristics, such as socio-economic characteristics (age, agricul-tural education or farming experience), and factors such as crop rotation and theage of agricultural tractors, their combustion efficiency or driving techniques, couldalso be relevant but are unfortunately unavailable.

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 5

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

4.2. Extension to energy content uncertainty

To extend the previous analysis to a framework in which theenergy content of inputs is uncertain, the programming models [P3]and [P4] detailed in Appendix A.2 are performed. We obtainoptimistic and pessimistic AE scores by calculating the optimisticand pessimistic EE/TE, respectively. In the uncertain case, only AEand EE varied, whereas TE was unchanged (i.e., 0.809). Table 6summarises the results. We also recall some results from thedeterministic case to facilitate comparisons with the uncertain case.

A first and direct implication is that the AE and EE scores in thedeterministic case are upper and lower bounded, respectively, by theoptimistic and pessimistic scores. Even in the optimistic scenario,inefficiency persists. Four energy efficient farms in the optimistic casebecome inefficient in the pessimistic case. Therefore, our extendedDEA model allows us to produce robust results through consideringimprecision in the energy content of the inputs. Table 7 illustratesthis point. The table relates the specific results for our three

illustrative farms that also represent the diversity of the situationswe obtain when we consider uncertainty.

In Table 7, we note that the potential reduction in energy offarm 1 increases by 24.6 % from the optimistic case to thepessimistic case. This is different for farm 44, for whom itincreases from 31.8% to 41.4%. Furthermore, we see that for farm44 the uncertainty depends only on the effect of input reallocation,in contrast to farm 1, which can also reduce the inputs used thanksto better management. Finally, farm 88 is among those that stayenergy efficient in all cases and, therefore, constitutes an ideal (i.e.,well-identified) target for the others.

5. Discussion and policy implications

Section 5.1 will be dedicated to a discussion of the results andpolicy implications in the deterministic setting, and Section 5.2will be devoted to a discussion in the uncertain case. In Section 5.3,we clarify the relationship between economic efficiency andenergy efficiency for implementation purposes.

5.1. The alternative energy efficiency measurementand decomposition in the deterministic case

From a policy perspective, an energy policy based on commonenergy efficiency scores will consist in helping farms with lowscores to moderate energy-consuming input. In other words,energy efficiency improving policies may need to target the mostenergy inefficient farms. As illustrated by Table 5, the decomposi-tion we proposed helps improve the design of an energy policy.

For instance, a more precise energy policy designed for farm 44would consist in giving it incentives to reallocate its inputs in away corresponding more to the allocation chosen by energy-extensive farms. The aim of such a policy is to induce an evolutionof farms towards more energy-extensive systems. Consequently,our methodology helps to identify both farms characterised by anenergy-extensive system (like farm 88) and farms characterised byan energy-intensive system (like farms 1 and 44). Studying thedifferences between both will help the policy-maker design anappropriate energy policy.

Precise information about the cultivation practices of the bestperformers is unavailable. However, one can cite examples ofpractices that could allow the inefficient farmers to achieve energyefficiency by changing the input mix so it is consistent with theirenergy contents. First, one can cite the direct seeding (or zerotillage) practice, which refers to the sowing of seeds directly intothe soil. This practice does not require soil preparation andconsequently requires less petroleum, but more pesticides, thantillage (see Talpin, 2010). Inversely, the tillage practice requiresmore petroleum but less pesticide than direct seeding. Second, onecan cite the implantation of intermediate crops (cover crops ornitrogen-fixing crops), which allows farmers to fight weeds andconserve the nitrogen for the following crop. However, thispractice requires more fuel, mainly for land preparation, thanthe practice without cover crops. Third, one can cite the stale

Table 5Input-oriented DEA results of energy efficiency decomposition and potentialreduction of energy in MJ for illustrative farms.

Farm 1 Farm 44 Farm 88

Energy efficiency 0.728 0.639 1Potential reduction in energy 296,487 409,450 0

Technical efficiency 0.865 1 1Potential reduction in energy 146,441 0 0

Allocative Efficiency in energy contents 0.841 0.638 1Potential reduction in energy 150,046 409,450 0

Table 6Input-oriented DEA efficiency scores with and without uncertainty

Mean Standarddeviation

Min Max Number ofefficient farms

Optimistic EE 0.761 0.165 0.369 1 24Optimistic AE 0.941 0.082 0.611 1 35Pessimistic EE 0.640 0.209 0.231 1 20Pessimistic AE 0.792 0.152 0.368 1 20Deterministic EE 0.721 0.177 0.305 1 24Deterministic AE 0.892 0.105 0.505 1 24

Table 7Input-oriented DEA efficiency results for illustrative farms under uncertainty.

Farm 1 Farm 44 Farm 88

EE Optimistic 0.797 0.682 1TE 0.865 1 1AE Optimistic 0.921 0.682 1EE Pessimistic 0.551 0.586 1TE 0.865 1 1AE Pessimistic 0.637 0.586 1

Table 4Input and output data for three illustrative farms.

Farm 1 Farm 44 Farm 88

Variable inputsNitrogen (kg) 10,511 13,432 22,686Petroleum (litre) 9562 7835 29,648Pesticides (kg of active ingredient) 216 84 321

Fixed inputsLand (ha) 127 83 164Labour (unit) 1 1 1Machinery (MJ) 4590 2098 6883

Energy consumption (MJ) 1,088,685 1,113,648 2,726,850

OutputsCereals (q) 4304 4504 13,650Oilseeds (q) 880 455 800

Note: We obtain energy consumption by summing the variable input convertedinto energy with the energy equivalents proposed by ADEME.

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎6

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

seedbed practice, which is a method of soil preparation withoutsowing. The objective is to let weeds germinate to kill them whileminimising soil disturbance that would bring new weed seeds.This technique requires more fuel but less herbicides andpesticides.

An energy policy designed for farm 1 would be more complexthan one designed for farm 44 because it would consist of bothgiving incentives to reallocating inputs, such as for energy-extensive farms, and reduce the use of inputs. The interestingpoint here is that this reduction will generate some gains for thefarm because it will allow it to produce the same amount of outputwith less input, hence, at a lower cost. Consequently, a policyspecifically designed to induce this reduction will not have to gothrough the price system but rather through agricultural consult-ing and advice (in the French agricultural sector, consultants fromtechnical and professional institutes give advice to help farmersmake production choices, such as which fertiliser to use, when,and in which amount).

Within the framework of our sample, no farm suffers solelyfrom input mismanagement (i.e., TEo1 and AE¼1). This meansthat it is important for a policy-maker to direct funding policiesaimed at increasing allocative performance scores in energycontents, i.e., policies based on incentives rather than on advice.

5.2. Extension to energy content uncertainty

By dissociating the energy efficiency scores into each compo-nent and, thus, by pinpointing inefficiency sources, policy-makerscan better target their energy policies towards farmers. However,this decomposition may be of limited help because it assumesexact knowledge of energy contents. For this reason, our extensionconsiders the imprecise knowledge of energy content.

The findings obtained from Table 6 confirm and justify theinterest of potential policy intervention. Furthermore, from theperspective of reducing energy consumption, these findingsunderline that some caution must be taken. We see in Table 6that four energy efficient farms in the optimistic case becomeinefficient in the pessimistic case. To avoid errors and controversy,an energy policy should designate the twenty farms efficient inboth cases as energy-saving target units.

Another policy implication is noteworthy. When one considersthe energy content of inputs as uncertain, but the minimal andmaximal admissible values are available, policy-makers cannotbase their policies solely on average or specific values. Thederivation of upper and lower bounds for the energy efficiencyand allocative efficiency in energy contents through the incorpora-tion of weight restrictions allows the possibility of relying on thebound values with full knowledge of the consequences. Policy-makers can thus design their energy policies according to theirrisk preferences. A risk-neutral policy-maker will base his energypolicy on the results obtained from an average or specific value ofenergy input content. A risk-averse policy-maker will prefer thepessimistic results because they represent the least favourablescenario in an uncertain context. A risk-lover will use the opti-mistic results because they represent the most favourable scenarioin an uncertain context.

5.3. Energy efficiency and economic efficiency

The reduction of energy consumption through simple policiesis not an easy matter. To be acceptable, energy policies musteconomically satisfy the producers who undertake them. Farmerscannot afford to jeopardise their year's income in an attempt torefine the energy efficiency of their practices. Policy-makersshould make a comparison between cost minimisation and energyconsumption minimisation to check the cost of the policies they

want to implement. Cost minimisation is an important considera-tion for farmers. This methodology can be modified to substituteprices for energy content if required. Within the dataset for thisstudy, price data were not available and were unnecessary in astudy focusing on energy efficiency.

More specifically, once a policy-maker has identified targetunits, the question that arises is how to make the farms convergetowards these targets. In other words, how can we eliminatetechnical and allocative inefficiency to achieve energy efficiency?

Reducing technical inefficiency does not require an input mixchange and constitutes a win–win strategy for both the farmersand society (represented by a policy-maker). Indeed, this strategysimultaneously reduces energy consumption and input expendi-tures. By contrast, allocative efficiency in energy content improve-ment can be necessary to achieve energy efficiency but can beinefficient from the farmer's viewpoint due to reorganisationcosts. This modification can lead to deviations relative to the costminimisation objective. Hence, changing the input mix requires apolicy intervention that may consist in modifying the price system.More specifically, the slope of iso-cost lines may be different fromthe slope of the iso-energy lines because the price ratio has noreason to be identical to the ratio of the energy content of inputs.The tangency point between the iso-cost line and the isoquantgives the equilibrium a cost-efficient farm will spontaneouslychoose without an energy policy. Therefore, a policy-maker mustdesign an energy policy aimed at reducing the energy consump-tion of cost-efficient farms to encourage the farmers to choose theequilibrium corresponding to lower energy consumption thantheir cost-efficient point. From an operational viewpoint, such anenergy policy will consist in subsidising or taxing the mostenergy-consuming inputs in such a way that the slope of theiso-cost lines coincides with the slope of the iso-energy lines.

6. Conclusion

In this paper, we highlighted how one can use the DataEnvelopment Analysis (DEA) approach to design more accurateenergy policies in the agricultural sector than the policies designedwith the current indicators. First, DEA methods provide informa-tion on the energy efficiency of farms that can help policy-makerstarget energy policies for specific farms. Second, the resultsindicate that energy inefficiency in the agricultural sector can bedriven either by the mismanagement of input or by misallocationof the input mix. DEA methods allow policy-makers to designpolicies differently depending on the types of inefficiencies thatcharacterise a farm. If a farm is technically inefficient, the energypolicy will consist in giving farms advice to reduce the input levelsused given the output levels. If the farm is allocatively inefficientin energy contents, it will be helpful to study energy-extensiveagricultural systems in greater detail and to compare them withenergy-intensive agricultural systems to implement the mostaccurate energy policy. Third, an extended DEA approach allowsus to carry out a robust sensitivity analysis of the basic resultsgiven the uncertainty of the energy content of inputs and, thus, totest the need for policy intervention in different contexts.

Within the framework of our sample, on average, a policydesigned to encourage farms to be less energy-intensive will saveup to 37% of energy. In this case, we consider the specific value ofthe energy content of inputs retained by ADEME. Nevertheless, thedata used to develop the technology are sometimes uncertain. Inthis paper, we also proposed tackling the problem of imprecisedata by combining several procedures to derive both upper andlower bounds for energy efficiency by considering low and highvalues for certain energy contents. Hence, energy savings between34% and 46% can be included. These findings help justify the

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 7

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

interest of policy intervention because potential savings exist evenin an optimistic case.

In the energy analysis process, the measurement of efficiency isthe first step. To refine the results and further explain key factorsof energy efficiency, a deeper analysis with enhanced data wouldbe desirable. This would allow us to distinguish more precisely theinefficiency due to the exogenous factors beyond the farmers'control (pedo-climatic conditions, structural conditions) from theinefficiency reasonably solvable by better management (cultiva-tion practices, production choices). The dataset we used in ourwork does not contain information on the factors beyond thefarmers' control. Attaining reliable survey data of these factors expost would be difficult. It is consequently suggested that furtherdevelopment of this method be explored with respect to agricul-ture by implementing a survey that includes these data require-ments, enabling deeper analysis in subsequent work.

Acknowledgements

The authors thank Bernadette Risoud from Agrosup Dijon fordiscussions concerning PLANETE and Jean-Luc Bochu and Char-lotte Bordet from Solagro for providing the dataset. Two anon-ymous referees are also acknowledged for their comments, whichconsiderably helped us to improve our work.

Appendix A. A.1. Energy, allocative in energy contentsand technical efficiency models

Let us consider K DMUs and denote K¼ f1;…;Kg by the associatedindex set. We assume that DMUs face a production process with Moutputs, N energy inputs and Z non-energy or fixed inputs where thevector of outputs is y¼ ðy1;…; yMÞARM

þ , x¼ ðx1;…; xNÞARNþ is the

vector of energy inputs and r¼ ðr1;…; rZÞARZþ is the vector of fixed

inputs. We also define the respective index sets of outputs and inputsas M¼ f1;…;Mg; N¼ f1;…;Ng and ℨ¼ f1;…; Zg: Following Färeet al. (1985), under constant returns to scale assumption, convexityand strong disposability on input and output assumptions, we definethe model with the production possibility set T:

T ¼ ðx; r; yÞ : yr ∑k AK

λkykm 8m AM; xZ ∑k AK

λkxkn 8n AN

(;

rZ ∑k AK

λkrkz 8z Aℨ; λkZ0 8k A K

)ð2Þ

where λ is an intensity vector that ensures that all convex combina-tions of the observed inputs and outputs belong to the productiontechnology set T, which can be equivalently defined using thecorresponding input requirement set that represents the set of allvariable inputs required to produce a specific output level y for a givenlevel of quasi-fixed input r. That is:

VðyjrÞ ¼ x : yr ∑k AK

λkykm 8 m AM; xZ ∑k AK

λkxkn 8 n AN;

(

rZ ∑k AK

λkrkz 8z Aℨ; λkZ0 8k A K

)ð3Þ

To measure and decompose energy efficiency, we need a functionalrepresentation of the production technology. We use an input distancefunction introduced by Shephard (1953) for this purpose. We definethe input distance function on the input set VðyjrÞ as:Dnðx; r; yÞ ¼ min fθ : θxAVðyjrÞg ð4Þ

Now, suppose that one converts variable inputs into energy thanksto energy equivalents w¼ ðw1;…;wNÞARN

þ and that policy-makersseek to minimise the energy consumption of each DMU. We can then

define the energy function as:

ECðx; r;wÞ ¼ min fwx : ðx; r; yÞA Tg ð5Þ

We interpret the energy function as the minimal energyconsumption given an output vector (y), fixed input vector (r)and an energy equivalent vector (w) attributed to input variables.

From these operational definitions of the production set (2) andenergy function (5), we compute the energy efficiency for a DMU jwith a production plan ðxj; rj; yjÞ under the assumption of constantreturns to scale (Charnes et al., 1978) via the following linearprogramme [P1]:

ECn ¼ min ∑nAN

wjnxn

s:t: ∑kAKλkykmZyjm 8mAM

∑kAK

λkxknrxn 8nAN ½P1�

∑kAK

λkrkzrrjz 8zAℨ

λkZ0 8kAK

where the weight (here, the energy content) of variable input nfaced by DMU j is wj

n. The non-zero elements of λ identify thereference set of DMU j: Due to the possible existence of positiveslack variables to the optimum, some reductions in fixed inputs arepossible even if there are no variables to optimise. xn Correspondsto each variable input n determined by the model that allows theproduction of each y for DMUj: Therefore, ECn corresponds to theminimum energy consumption required to produce output vectory at a fixed input and variable input weight w.

If we denote ECj as the total energy content of the current inputlevels of DMU j, then we measure its energy efficiency as the ratioof minimum energy consumption to the current energy:

ECn

ECj¼

∑n A N

wjnxn

∑n A N

wjnx

jn

ð6Þ

in which “*” indicates the optimality. The percentage of the totalwasted energy is ½ð1�energy efficiencyÞ100�.

In the same spirit of cost efficiency developed by Färe et al.(1985), the energy efficiency (EE) incorporates two sources ofinefficiency, viz., technical efficiency (TE) and allocative efficiency(AE) in energy contents. Technical inefficiency reflects managerialfailures or a form of wasteful use of inputs that can be reduced, forinstance, by better nutrient and fertiliser management, whereasallocative inefficiency in energy contents reflects input misallo-cation or an inappropriate input mix. Consequently, a DMU willonly be energy efficient if it is both technically and allocativelyefficient.

To obtain a decomposition of energy efficiency, we start fromoperational definitions of the production set (3) and input distancefunction (4). Thus, we measure technical efficiency by the basicinput-oriented DEA model [P2a]. This model does not require an apriori specification of input and output weights. Hence, the multi-pliers may take on unreasonable values (Schaffnit et al., 1997).Fortunately, as we will see below, one can easily bound themultipliers by using the dual programming problems (calledmultiplier models). When the multipliers solely involve input(output) multipliers, it is called an input (output) cone. [P2b] gives

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎8

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

the dual programme for the envelopment models.13 Finally, wehave:

Djiðx; r; yÞ ¼ min θ max ∑

m AMumy

jm� ∑

z Aℨzzr

jz

s:t: ∑kAK

λkykmZyjm 8mAM s:t: ∑m AM

umykm ∑n AN

vnxkn ∑z Aℨ

zzrkzr0 8kAK

∑kAK

λkxknrθxn 8nAN ½P2a� ∑z AN

vzxjz ¼ 1 ½P2b�

∑kAK

λkrkzrrjz 8zAℨ umZε 8 mAM

λkZ0 8kAK vnZε 8nAN

zzZε 8zAℨ

ð7Þ

where ε is a small positive number.In model [P2b], constraints (7) guarantee that such a set of

weights yield efficiency scores less than or equal to one for allDMUs. As suggested by Cooper et al. (1996) and in Schaffnit et al.(1997) in the cost context, we can also demonstrate that one canalternatively obtain the measurement of energy efficiency with theinclusion of weight restrictions in the multiplier DEA model [P2b].More precisely, the restrictions imposed on the weights underlyingthe assessment are the relative values of the energy input contentobserved at each DMU, such that: vna

vnb¼ wna

wnb; na;nb ¼ 1;…;N where

a and b are, for example, two inputs among the set N:

Following decomposition (1) , we can now compute theallocative efficiency in energy contents as the ratio between

energy efficiency ∑n A N

wjnxn= ∑

n A N

wjnx

jn and technical efficiency

Djnðx; r; yÞ: Formally, we have:

Allocative efficiency¼∑

n A Nwj

nxn

Djnðx; r; yÞ ∑

n A Nwj

nxjn

ð8Þ

A.2. Optimistic and pessimistic energy efficiency models

As mentioned above, for the optimistic EE model, we focus ourattention on the most favourable energy content scenario. We canwrite an optimistic EE model as follows:

max ∑m AM

umyjm� ∑

zAℨzzr

jz

s:t: ∑m AM

umykm� ∑n AN

vnykn ∑z Aℨ

zzrkzr0 8kAK

∑n AN

vnxjn ¼ 1 ½P3�

wminna

wmaxnb

rvna

vnbrwmax

na

wminnb

naonb;na;nb ¼ 1;…;NumZε 8 mAM; zzZε 8zAℨ ð9Þ

The constraintswmin

na

wmaxnb

rvnavnb

rwmaxna

wminnb

denoted in (9) provide bounds forvariable input multipliers. They follow the Cone Ratio/AssuranceRegion approach first developed in Thompson et al. (1986) anddefined more precisely in Thompson et al. (1990). They specify thecone ratio/assurance region as a set of homogenous inequalitiesthat define an acceptable input weight to underline the efficiencyassessment. Programme [P3] is nonlinear due to constraints (9).Fortunately, to obtain an optimistic EE linear model, one can easilyrewrite constraints (9) in linear form, given by following con-straints:

vna �wmaxna

wminnb

vnb r0

vna �wminna

wmaxnb

vnb Z0

8>><>>: ð10Þ

Because we base the DMU's evaluation on n inputs, there are CN2

different ratios between two inputs, which give a total of 2� CN2

linear inequality constraints.To obtain the EE model under a pessimistic perspective,

Camanho and Dyson (2005) also propose a method. However, asstated by the authors themselves, their model is computationallyexpensive and may not be feasible (p. 441). Therefore, we proposeanother algorithm for the estimation of pessimistic CE that tends

Table A1Characteristics of the energy efficient and 25% least efficient farms.

Variables Median Bilateral Mann–Whitney Wilcoxon test

Efficient farms (n¼24) 25% Least efficient farms (n¼34) p-Value Significance

YieldsCereals (q/ha) 75 55 0.0001 nnn

Oilseeds (q/ha) 29 28 0.6328

InputsLand (ha) 136 162 0.7543Labour (Unit) 1 1 0.0300 nn

Machinery (MJ/ha) 21 40 0.0011 nnn

Nitrogen (kg/ha) 140 137 0.6929Petroleum (l/ha) 86 92 0.3582Pesticides (kg of a.i/ha) 2.9 3.8 0.0455 nn

Cultivation practices and miscellaneousTillage area (%) 28.9 8.3 0.3915Bare ground (% of area) 6.7 0.0 0.0611 n

Wheat (% of area) 33.5 38.3 0.4426Set-aside area (% of area) 3.9 5.4 0.3283Crop diversity (# of crops) 3 4 0.5830Number of treatments 0 8 0.0839 n

n Differences between samples are statistically significant 10% level.nn Differences between samples are statistically significant at the 5% level.nnn Differences between samples are statistically significant at the 1% level.

13 Banker and Morey (1986) initially proposed the dual programme withvariable and fixed input in the form of a linear fractional programme.

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 9

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

towards the Mostafaee and Saljooghi (2010) method.14 In contrastto Mostafaee and Saljooghi (2010), we confine our attention to thedual programme and, hence, propose to solve for each DMU thefollowing two-level programme:

min max ∑m AM

u yjm� ∑z Aℨ

zzrjz

(

s:t: ∑m AM umykm� ∑n AN

vnxkn∑rkzr0 8kAK ½P4�

∑n AN

vnxjn ¼ 1

vna

vnbAF; na ¼ 1 and nb ¼ 2;…; N

umZε 8 mAM; Zε 8 zAℨ� ð11Þ

where F is a family of 2N sets that are composed of ðN�1Þ relativeinput energy contents obtained from the extreme pointswmin

n and wmaxn , where n¼ 1;…;N:

For instance, let us consider two inputs a and b and their upper andlower bounds of the energy content, i.e., wmin

na ; wminnb ; wmax

na ; wmaxnb :

We now have a family of four singleton sets that can be written

formally: F¼ wminna

wmaxnb

� �;

wmaxna

wminnb

� �;

wminna

wminnb

� �;

wmaxna

wmaxnb

� �� �.

One can perform the inner programme, i.e., the second-levelprogramme, for each set of the family F: This approach allows usto obtain cost efficiency measurements for each set. The outerprogramme determines the set of relative energy input contentsthat produces the lowest cost efficiency measurement for eachDMU. Hence, we adopt for the estimation the least favourablescenario within the range of the energy input content considered.

Let us finish by noting that programme [P4] is nonlinear likeprogramme [P3]. In the same manner, we rewrite constraints (11)in linear form.

A.3. Characteristics of the energy efficient farms and of the 25%least efficient farms

See Table A1.

References

ADEME, 2011. Guide des valeurs Dia’terre. Version du référentiel 1.13, 187 pp.Allen, R., Athanassopoulos, A., Dyson, R.G., Thanassoulis, E., 1997. Weights restric-

tions and value judgments in data envelopment analysis: evolution, develop-ment and future directions. Ann. Operations Res. 73 (0), 13–34.

Banker, R., Charnes, A., Cooper, W.W., 1984. Some models for estimating technicaland scale inefficiencies in data envelopment analysis. Manag. Sci. 30 (9),1078–1092.

Banker, R.D., Morey, R.C., 1986. Efficiency analysis for exogenously fixed inputs andoutputs. Operations Res. 34 (4), 513–521.

Bochu, J.-L., 2002. PLANETE: méthode pour l’analyse énergétique de l’exploitationagricole et l'évaluation des émissions de gaz à effet de serre. Mimeo availableonline from: ⟨http://www.solagro.org/site/im_user/0286_$_014planeteooct02.pdf⟩.

Camanho, A.S., Dyson, R.G., 2005. Cost performance measurement with priceuncertainty: a DEA application to bank branch assessments. Eur. J. OperationalRes. 161 (2), 432–446.

Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric frontier estimation: a robustapproach. J. Econom. 106 (1), 1–25.

Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the performance of decisionmaking units. Eur. J. Operational Res. 2 (6), 429–444.

Charnes, A., Cooper, W.W., Sun, D.B., Huang, Z.M., 1990. Polyhedral cone-ratio DEAmodels with an illustrative application to large commercial banks. J. Econom.46 (1-2), 73–91.

Chauhan, N.S., Mohapatra, P.K.J., Pandey, K.P., 2006. Improving energy productivityin paddy production through benchmarking – an application of data envelop-ment analysis. Energy Convers. Manag. 47 (9–10), 1063–1085.

COM, 2011. 109, Communication from the commission to the European Parliament,the Council, The European Economic and Social Committee and the Committeeof the Regions on Energy Efficiency Plan 2011, Brussels COM (2011) 109 final.

Cooper, W.W., Thompson, R.G., Thrall, R.M., 1996. Introduction: extensions and newdevelopments in DEA. Ann. Operations Res. 66 (1), 1–45.

Dale, V.H., Polasky, S., 2007. Measures of the effects of agricultural practices onecosystem services. Ecol. Econ. 64 (2), 286–296.

Dalgaard, T., Halberg, N., Porter, J.R., 2001. A model for fossil energy use in Danishagriculture used to compare organic and conventional farming. Agric., Ecosyst.Environ. 87 (1), 51–65.

Daraio, C., Simar, L., 2006. A robust nonparametric approach to evaluate and explainthe performance of mutual funds. Eur. J. Operational Res. 175 (1), 516–542.

Fadavi, R., Samavatean, N., Keyhani, A., Mohtasebi, S.S., 2012. An analysis ofimproving energy use with data envelopment analysis in apple orchard. AsianJ. Agric. Rural Dev. 2 (2), 277–286.

Fang, L., Li, H., 2012. A comment on “cost efficiency in data envelopment analysiswith data uncertainty”. Eur. J. Operational Res. 220 (2), 588–590.

Färe, R., Grosskopf, S., Lovell, C.A.K., 1985. The Measurement of Performance ofProduction. Kluwer-Nijhoff, Boston.

Farrell, M.J., 1957. The measurement of productive performance. J. R. Stat. Soc.,Series A 120 (3), 253–282.

French Authority, 2008. Energy Efficiency Plan for France, 37 pp., available onlinefrom: ⟨http://ec.europa.eu/energy/demand/legislation/doc/neeap/france_en.pdf⟩.

Frischknecht, R., Jungbluth, N., Althaus, H.J., Doka, G., Dones, R., Heck, T., Hellweg, S.,Hischier, R., Nemecek, T., Rebitzer, G., Spielmann, M., 2005. The ecoinventdatabase: overview and methodological framework. Int. J. Life Cycle Assess. 10(1), 3–9.

Gabrysiak, J., Rodier, D., 2012. Exploitations de grandes cultures en Francemétropolitaine. Agreste Primeur 283, 8. (pages).

Garnier, C., 2012. Analyse économique de la dépendance de l’agriculture à l’énergie.Evaluation, analyse rétrospective depuis 1990, Scénarios d’évolution à 2020,ADEME Report, 86 pp.

Heidari, M.D., Omid, M., Mohammadi, A., 2012. Measuring productive efficiency ofhorticultural greenhouses in Iran: a data envelopment analysis approach.Expert Syst. Appl. 39 (1), 1040–1045.

Hoang, V.N., Prasada Rao, D.S., 2010. Measuring and decomposing sustainableperformance in agricultural production: a cumulative exergy balance approach.Ecol. Econ. 69 (9), 1765–1776.

Houshyar, E., Sheikh Davoodi, M.J., Nassiri, S.M., 2010. Energy performance forwheat production using data envelopment analysis (DEA) technique. J. Agric.Technol. 6 (4), 663–672.

Huijbregts, M.A.J., 1998. A general framework for the analysis of uncertainty andvariability in life cycle assessment. Int. J. Life Cycle Assess. 3 (5), 273–280.

Kuosmanen, T., Post, T., 2001. Measuring economic efficiency with incomplete priceinformation: with an application to European commercial banks. Eur. J.Operational Res. 134 (1), 43–58.

Kuosmanen, T., Post, T., 2003. Measuring economic efficiency with incomplete priceinformation. Eur. J. Operational Res. 144 (2), 454–457.

Ministère de l’agriculture, 2009. Plan performance énergétique des exploitationsagricoles 2009–2013, available online from: ⟨http://agriculture.gouv.fr/IMG/pdf/plan_PPE.pdf⟩.

Mostafaee, A., Saljooghi, F.H., 2010. Cost efficiency measures in data envelopmentanalysis with data uncertainty. Eur. J. Operational Res. 202 (2), 595–603.

Mousavi-Avval, S.H., Rafiee, S., Jafari, A., Mohammadi, A., 2011. Optimization ofenergy consumption for soybean production using Data Envelopment Analysis(DEA) approach. Appl. Energy 88, 3765–3772.

Nassiri, S.M., Singh, S., 2009. Study on energy use performance for paddy crop usingdata envelopment analysis (DEA) technique. Appl. Energy 86 (7-8), 1320–1325.

Nassiri, S.M., Singh, S., 2010. Energy efficiency for wheat production using dataenvelopment analysis (DEA) technique. Appl. Energy 6 (7-8), 1320–1325.

Patterson, M.G., 1996. What is energy efficiency? Concepts, indicators and meth-odological issues. Energy Policy 24 (5), 377–390.

Pedraja-Chaparro, F., Salinas-Jimenez, J., Smith, P., 1997. On the role of weightrestrictions in data envelopment analysis. J. Product. Anal. 8 (2), 215–230.

Rahbari, H., Mahmoudi, A., Ajabshirchi, Y.A., 2013. Improving energy use efficiencyof greenhouse tomato production using data envelopment analysis (DEA)technique. Int. J. Agric.: Res. Rev. 3 (3), 559–568.

Schaffnit, C., Rosen, D., Paradi, J.C., 1997. Best practice analysis of bank branches: anapplication of DEA in a large Canadian bank. Eur. J. Operational Res. 98 (2),269–289.

Shephard, R.W., 1953. Cost and Production Functions. Princeton University Press,Princeton.

Simar, L., Wilson, P., 1998. Sensitivity analysis of performance scores. How tobootstrap in nonparametric frontier models. Manag. Sci. 44 (1), 49–61.

Simar, L., Wilson, P., 2008. Statistical inference in nonparametric frontier models:recent developments and perspectives. In: Fried, H.O., Lovell, C.A.K., Schmidt, S.S. (Eds.), The Measurement of Productive Performance and ProductivityGrowth. Oxford University Press, Oxford, pp. 421–521.

Talpin, J. (2010). Économies d’énergie sur l’exploitation agricole. Editions FranceAgricole.

Thompson, R.G., Langemeier, L.N., Lee, C., Lee, E., Thrall, R.M., 1990. The role ofmultiplier bounds in performance analysis with application to Kansas farming.J. Econom. 46 (1-2), 93–108.

14 In a recent paper about Mostafaee and Saljooghi's (2010) methodology. Fangand Li (2012) demonstrated that only the lower bound of the cost efficiencyobtained for extreme points is correct. This demonstration partly explains ourchoice to combine methodologies (Camanho and Dyson, 2005 and Mostafaee andSaljooghi, 2010) rather than use one methodology exclusively.

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎10

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i

Thompson, R.G., Singleton Jr., F.D., Thrall, R.M., Smith, B.A., 1986. Comparative siteevaluations for locating a high-energy physics lab in Texas. Interfaces 16 (6),35–49.

Wilson, P.W., 1993. Detecting outliers in deterministic nonparametric frontiermodels with multiple outputs. J. Business Econ. Statistics 11 (3), 319–323.

Wilson, P.W., 2008. FEAR: A software package for frontier efficiency analysis with R.Socio-Economic Planning Sci. 42 (4), 247–254.

Wilson, P.W., 2010. Detecting Outliers in Deterministic Nonparametric FrontierModels with Multiple Outputs: Correction. Working paper. Department ofEconomics. Clemson University p. 5.

Zegada-Lizarazu, W., Matteucci, D., Monti, A., 2010. Critical review on energybalance of agricultural systems. Biofuels, Bioproducts Biorefining 4 (4),423–446.

Zhou, P., Ang, B.W., 2008. Linear programming models for measuring economy-wide energy efficiency performance. Energy Policy 36 (8), 2911–2916.

Zhou, P., Ang, B.W., Poh, K.L., 2008. A survey of data envelopment analysis in energyand environmental studies. Eur. J. Operational Res. 189 (1), 1–18.

Zhu, J., 1996. Data envelopment analysis with preference structure. J. OperationalRes. Soc. 47 (1), 136–150.

S. Blancard, E. Martin / Energy Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 11

Please cite this article as: Blancard, S., Martin, E., Energy efficiency measurement in agriculture with imprecise energycontent information. Energy Policy (2013), http://dx.doi.org/10.1016/j.enpol.2013.10.071i