# Environmental and technical efficiency of French sheep farms in less favored areas: off-season production penalizes environmental performance

Jean-Joseph Minviel, Marc Benoit, Laure Latruffe

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Jean-Joseph Minviel, Marc Benoit, Laure Latruffe. Environmental and technical efficiency of French sheep farms in less favored areas: off-season production penalizes environmental performance. Agricultural and Food Economics, 2026, 14 (1), pp.22. 10.1186/s40100-026-00467-w. hal-05535798

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# Environmental and technical efficiency of French sheep farms in less favored areas: off-season production penalizes environmental performance

Jean-Joseph Minviel<fnref n="1" />*, Marc Benoit<fnref n="1" /> and Laure Latruffe<fnref n="2" />

## Abstract

Given the need for farms to reduce their negative environmental impacts while maintaining their productive performance, this study analyzes the technical and environmental efficiency of a sample of sheep farms in France, with a focus on greenhouse gas emissions and nitrogen surplus. To do so, we use a multi-equation stochastic frontier approach that accounts for the physical processes that generate environmental pollution. The results indicate that, on average, the potential technical and environmental efficiency gains for the farms in our sample would be approximately 20% if they could align their practices with best practices observed. The results also show that farms with low environmental efficiency have a high proportion of out-of-season production to meet the sheep industry's demand, which increases their use of concentrates, nitrogen on forage areas, and energy, thereby worsening their environmental performance. Likewise, econometric estimates show that while off-season production could enhance farms' productive efficiency, it is detrimental to their environmental efficiency. A set of production practices was identified as suitable for alleviating this issue by improving both the technical and environmental efficiency of the sheep farms in our sample.

**Keywords:** Environmental efficiency, Technical efficiency, Sheep farming, France, Off-season production

**JEL Classification:** Q12, D24, Q51

## Introduction

Livestock farming is a key economic activity, accounting for almost 40% of French and European agricultural sales (excluding premiums), and is a key component of the rural vitality and landscapes of many territories (Ryschawy et al. 2017; Espagnol et al. 2019). It, however, faces several challenges. Not only do livestock farming systems have to ensure food security, but they are also expected to use fewer polluting inputs (pesticides, fertilizers, and energy) and water, and to lessen their contribution to climate change. Global demand for animal proteins is increasing rapidly and is projected to rise by 21% between 2020 and 2050 (FAO 2023). At the same time, the negative impacts of livestock farming

<footnote>*Correspondence:
jean-joseph.minviel@inrae.fr</footnote>

<footnote n="1">¹ Université Clermont
Auvergne, INRAE, Vetagro Sup,
UMR Herbivores, F-63122,
Saint-Genès-Champanelle,
France</footnote>

<footnote n="2">² INRAE, Univ. Bordeaux, CNRS,
BxSE, UMR 6060, UMR 1441,
F-33600 Pessac, France</footnote>
on the environment are increasingly pointed and include (i) soil and water pollution due to excess nutrients linked to the intensive use of chemical inputs and excess manure and slurry in some areas and (ii) a significant contribution to climate change via greenhouse gas (GHG) emissions that represent around 11.1–19.6% of total anthropogenic emissions in the world estimated at around 50 Gt CO2 eq (Xu et al. 2021; FAO 2023).

Pollutant emissions in agriculture arise from physical laws, in particular, the first law of thermodynamics. This law can be summarized by the material balance principle, which stipulates that material inputs entering a production process are not destroyed but are transformed into desirable outputs and undesirable outputs, the latter being emissions that have the potential to cause pollution (Hoang and Coelli 2011; Førsund 2018). According to the material balance principle, the livestock production process inevitably yields undesirable outputs. For instance, the use of nitrogen fertilizers can increase crop yields (desirable outputs) but can also generate undesirable outputs (e.g., leaching and runoff). Likewise, milk and meat production (desirable outputs) also generate undesirable outputs, such as nitrogen surpluses and GHG emissions (Kumbhakar and Malikov 2018). In this context, to reduce the negative environmental impacts of livestock production systems while meeting global food demand, a strategy is to increase the efficiency with which farm inputs are transformed into output.

A commonly used efficiency measure in agriculture and livestock farming in particular is technical efficiency (Gaspar et al. 2009; Latruffe et al. 2017). A farm is technically efficient if it has perfect command of the technical aspects of a production process, implying that it can generate the maximum possible output from a given level of input, or, symmetrically, that it can use the minimum possible level of input to produce a given level of output, given the technology. Hence, improving the technical efficiency of a farming system could typically enhance the environment. For instance, improving soil fertility and incorporating clover into grasslands can reduce the amount of environmentally damaging inputs, such as nitrogen fertilizers, needed to produce a given amount of forage. This may then reduce total GHG emissions and GHG emission intensity (emissions per unit of output) while maintaining the production of desirable outputs. However, improving technical efficiency can also be associated with environmental damage if the production process relies on environmentally harmful inputs. For instance, in sheep farming, improvements in mortality and weaning rates may increase technical efficiency because more live lambs are weaned per ewe. However, with this strategy, total GHG emissions may remain unchanged or even increase due to increased animal numbers (i.e., more lambs weaned per ewe).

Also, while production intensification per animal and per land unit can increase farm technical efficiency and reduce emission intensity (Monteny et al. 2006), the total emissions may remain unchanged or even increase because production intensification is often associated with higher consumption of polluting inputs, such as fertilizers, concentrate feed, and fuel (Gerber et al. 2011; Mosnier et al. 2017). This may explain why FAO (2020) observes that despite progress in productive efficiency, GHG emissions from livestock production continue to rise. Hence, given the multiplicity of challenges faced by livestock farming, multicriteria efficiency is preferable to the classic technical efficiency, as it can help identify promising practices to address the combined challenges of environmental damage and food security. This can be achieved,
for instance, by jointly estimating technical and environmental efficiency using a pro-
duction frontier approach, in which a production unit is efficient if it lies on the pro-
duction frontier. Because the frontier is constructed using observed best practices, it
can be used to identify potential improvements in the technical and environmental
performance of production systems.

In light of the foregoing, this paper aims to jointly estimate the technical and envi-
ronmental efficiency of French sheep farms in less favored areas (LFAs). In European
terminology, in an LFA, farming practices are constrained by adverse natural conditions.
Ruminant livestock farming is often the main activity in LFAs (Barnes et al. 2023), as
other production systems are not feasible under the prevailing conditions. Sustainable
livestock farming strategies focused on environmental and technical efficiency are there-
fore of crucial importance in LFAs. An important implication of our analysis is therefore
to identify strategies aimed at reducing the emission of pollutants into the environment
without (significant) loss of production.

This paper contributes to the literature in three ways: First, although the technical efficiency of farms located in LFA has been widely studied (Barnes et al. 2023), to our knowledge, only Minviel et al. (2025) have examined their joint technical and environmental efficiency. Minviel et al. (2025) analyzed their environmental efficiency solely in terms of GHG emissions. Here, we go a step further by investigating it in terms of GHG emissions and nitrogen surplus. Second, we contribute to the emerging literature on estimating technical and environmental efficiency using econometric approaches grounded in recent theoretical advances in modeling pollution-generating production technology, namely the by-production approach.

Finally, to the best of our knowledge, we present the first study on the induced effects
of off-season sheep production on technical and environmental efficiency. The season-
ality of sheep reproduction is linked to a South-North gradient. While sheep in tropi-
cal climates are not seasonal or have a low reproductive seasonality, in more northerly
areas (Northern Europe, for example), reproduction is highly seasonal, with animals
being most fertile in September, October, and November, ensuring lambing when pas-
ture availability is optimal, in late winter and spring (Simões et al. 2021). Off-season pro-
duction, therefore, consists of mating ewes during unfavorable sexual periods (anestrus)
using specific practices or genotypes, for example, from April to July, so that lambing
occurs from September to December. In our network of French farms, some breeders
make a special effort to ensure that lambing occurs from July to mid-January in order to
meet the industry's demand (See the Appendix for more details).

However, the least seasonal breeds are also most often the least carcass-shaped, which is
generally the opposite of what the sheep industry expects. As such, hormone treatments
have been developed to artificially desynchronize the production cycles of the most sea-
sonal and conforming breeds to better meet industry expectations. The “rustic” breeds
found in temperate climates continue to be used, particularly in challenging geographic
areas (e.g., mountains), but are often crossbred to improve lamb conformation. There
are, therefore, several possible ways to supply the sheep industry with lambs produced in
the counter-season, thereby providing consumers with lambs of high meat quality year-
round while optimizing slaughterhouse utilization. Nevertheless, the potential adverse
environmental impacts of this counter-seasonal practice, which involves raising animals
in buildings and using concentrates (that are generated from polluting inputs), have been rarely studied (Dowling and Crossley 2004; Benoit et al. 2019).

The rest of the article is organized as follows: Sect. "Theoretical framework" describes the theoretical framework. Sect. "Empirical specification and data used" presents the methodological approach and the data used. The results are presented and discussed in Sect. "Results and discussion", and Sect. "Concluding remarks" provides concluding remarks.

## Theoretical framework

Our theoretical framework is based on the by-production approach developed by Før-sund (1998, 2009, 2018, 2021) and Murty et al. (2012), which provides a formal framework for treating pollution within a multi-equation production system, rooted in Frisch's (1965) work on production theory. Production theory offers two main frameworks for modeling and analyzing pollution-generating production technologies: single-equation and multiple-equation models. Under the single-equation framework, pollution is treated either as inputs (e.g., Hailu 2003; Hailu and Veeman 2001; Mahlberg et al. 2011) or as outputs under the weak disposability and the null-jointness assumptions (Chung et al. 1997; Fare et al., 1989). The single-equation framework has been criticized because it ignores physical realities (Coelli et al. 2007; Murty et al. 2012). For instance, given that the undesirable outputs are by-products of the desirable outputs, it is difficult to conceptualize a production system in which undesirable outputs are used as inputs in the production process that generated them (Minviel et al. 2025). The weak disposability assumption imposes a physical trade-off between the two categories of outputs, so that any reduction of the undesirable output requires some proportional sacrifice of the desirable output. This may be incompatible with the material balance principle (MBP). The MPB is a physical law that explains the generation of pollution in many production processes, as follows: $M \equiv Y+R$; that is, materials in inputs (M) are transformed into desirable outputs (Y) and undesirable outputs (R). As such, in a production process, for a given level of M, a reduction in R implies that more nutrients are transformed into Y. For instance, for a given amount of feed, higher intake is associated with more desirable output and lower methane emissions because it reduces rumen retention time (Ellis et al. 2008; Johnson and Johnson 1995). Similarly, one approach to reducing emissions of reactive N and GHG emissions in dairy cattle farming is to increase milk yields by feeding higher quality forage (Pierer et al. 2016). Against this background, an emerging strand of literature argues that the multi-equation approach is more suitable for modeling pollution-generating production technologies (Apparicio et al. 2020; Førsund 2018, 2021; Dakpo et al. 2017; Murty et al. 2012).

Under the multi-equation framework, the pollution-generating production technology (T) is defined as the intersection of two sub-technologies: $T_1$ that generates the desirable outputs and $T_2$ generating the undesirable outputs. So that:

$$T = T_1 \cap T_2 \qquad (1)$$

where

$$T_1 = \{(x_s, x_m, y, b) | y \le f(x_s, x_m)\} \qquad (2)$$
$$T_2 = \{(x_s, x_m, y, b) | b \ge g(x_m)\} \qquad (3)$$

Accordingly, for econometric estimations of technical and environmental efficiency, Minviel et al. (2025) suggest the following system of equations:

$$y = f(x_s, x_m) - u^y + v^y \qquad (4)$$

$$b = g(x_m) + u^b + v^b \qquad (5)$$

where y denotes the desirable outputs, b stands for the undesirable outputs, $x_m$ is a vector of material inputs (i.e., pollution-generating inputs), and $x_s$ is a vector of non-material inputs (also called service inputs). Note that the function g(.) is defined only on the material input $x_m$ due to the fact that the materials in b can only come from the material inputs (Førsund 2021). In other words, the non-polluting inputs do not have direct impacts on b. The sub-technology in Eq. (5) is a generic representation that includes two sub-technologies $T_2^{b_1}$ and $T_2^{b_2}$, generating GHG emissions and nitrogen surplus, $b_1$ and $b_2$, respectively.

The function f(.) provides the maximum amount of desirable output generated by the production technology, given the quantities of (polluting and non-polluting) inputs. Technical inefficiency, captured by $u^y$, when non-zero, means that less than the maximal amount of the desirable output is produced. Likewise, the function g(.) provides the minimum amount of undesirable output generated by the production technology, given the quantities of polluting inputs. Environmental inefficiency, captured by $u^b$, when non-zero, means that more than the minimal amount of the undesirable output is produced. That is, a given level of polluting input use may generate a minimum level of pollution, but it can also generate greater pollution, depending on the production practices adopted by farmers. The error terms $v^y$ and $v^b$ make the frontiers stochastic and capture random factors that are not under farmers' control but that influence the production levels.

From a theoretical standpoint, the production function of the desirable outputs f(.) is assumed to have the standard properties of positive (but decreasing) marginal productivity of inputs, that is: $f'_{x_s}, f'_{x_m} \ge 0$ and $f''_{x_s}, f''_{x_m} \le 0$. By contrast, the undesirable output function g(.) is assumed to be less conventional: $g'_{x_m} \ge 0$ and $g''_{x_m} \ge 0$ (Førsund 2018, 2021). These properties lead to the following graphical representation of the production technology (Fig. 1).

## Empirical specification and data used

### Empirical specification

To avoid imposing restrictive assumptions about input substitutability, the stochastic multi-equation frontier model is specified using a translog functional form. For a production process i in period t that uses a vector of non-polluting inputs ($x_s \in \mathbb{R}_+^S$) and a vector of polluting inputs ($x_m \in \mathbb{R}_+^M$) to produce a single desirable output ($y \in \mathbb{R}_+$) and generate a vector of undesirable outputs ($b \in \mathbb{R}_+^B$), the translog specification is given by:
<figure><img src="image_3.png" /><figcaption>**Fig. 1** The by-production technology representation. Source: The authors, adapted from Sueyoshi and Goto (2011).</figcaption></figure>

$$ \ln y_{it} = \beta_0^y + \sum_{s=1}^{S} \beta_s^y \ln x_{s,it} + \sum_{m=1}^{M} \beta_m^y \ln x_{m,it} + \frac{1}{2} \sum_{s=1}^{S} \sum_{s'=1}^{S} \beta_{ss'}^y \ln x_{s,it} \ln x_{s',it} \\ + \frac{1}{2} \sum_{m=1}^{M} \sum_{m'=1}^{M} \beta_{mm'}^y \ln x_{m,it} \ln x_{m',it} + \sum_{s=1}^{S} \sum_{m=1}^{M} \beta_{sm}^y \ln x_{s,it} \ln x_{m,it} - u_{it}^y + v_{it}^y \quad (6) $$

$$ \ln b_{it} = \beta_0^b + \sum_{m=1}^{M} \beta_m^b \ln x_{m,it} + \frac{1}{2} \sum_{m=1}^{M} \sum_{m'=1}^{M} \beta_{mm'}^b \ln x_{m,it} \ln x_{m',it} + u_{it}^b + v_{it}^b \quad (7) $$

Where $u^y$ and $u^b$ are non-negative random terms that capture inefficiencies, and $v^y$ and $v^b$ are symmetrical error terms that account for usual statistical noise and measurement errors.

The multi-equation model thus specified is estimated using the info-metrics (generalized maximum entropy, GME) approach developed by Minviel et al. (2025). The advantages of the GME approach for estimating econometric models in general are readily presented in Golan et al. (1996) and Golan (2018). Its advantages in estimating stochastic frontier models in particular have been documented in many papers (e.g., Oude Lansink et al. 2000, 2001; Balasubramanyan et al. 2012; Laureti et al. 2014; Macedo et al. 2014; Minviel et al. 2025). Regarding our multi-equation stochastic frontier model (SFM), this estimator has several desirable properties. First, it makes it easy to estimate all the equations simultaneously. Although the different equations can be estimated separately (Førsund 2018; Kumbhakar et al. 2022; Serra et al. 2014), their simultaneous estimation could yield more precise parameter estimates (Kumbhakar et al. 2022). Second, it addresses both endogeneity and unobserved heterogeneity issues inherent in the production processes. Taking endogeneity into account is particularly important for our multi-equation SFM, as farmers may shift their input mix toward less-polluting inputs to reduce their production of undesirable outputs and increase their production of desirable outputs, leading to endogeneity problems. Third, this approach yields precise estimates of the unknown parameters (Zheng and Gohin 2018), even with small samples and many covariates, and even when the covariates are highly correlated (Golan 2018).
This is also an interesting feature because the consideration of different polluting inputs
implies estimating a large number of parameters from potentially correlated variables.

Fourth, the consistency of GME estimates does not rely on the validity of assump-
tions on the distribution of the error terms. Indeed, under maximum likelihood (ML),
SFM evaluates efficiency by measuring closeness to an “ideal production model” (the
best-practice frontier) based on distributional assumptions about the error terms. If
the error terms of the ML SFM do not conform to these distributional assumptions, the
ideal model identified cannot be used as a benchmark for efficiency evaluation (Balasu-
bramanyan et al. 2012). As such, an essential feature of GME SFM is that it combines the
strengths of both standard SFM and non-parametric approaches (such as Data Envelop-
ment Analysis–DEA) by allowing the estimation of stochastic production frontiers with-
out making assumptions about the distributions of the efficiency components and the
random disturbance terms.

Finally, the GME approach makes it easy to impose theoretical constraints, which is
crucial because pollution-generating technologies may have non-standard properties
(Førsund 2018). Bayesian approaches can also be used to impose some of these con-
straints by specifying prior density functions (Judge et al. 1988). However, the GME
approach provides a relatively more straightforward way to impose restrictions through
the parameter support matrix (Campbell and Hill 2006; Rezek and Campbell 2007). The
maximum entropy approach can also be viewed as a derivation of Bayesian approaches
(Skilling 1989). Nevertheless, unlike Bayesian approaches, the GME approach does not
require prior information on the parameters to be continuous; instead, it uses discrete
support points, which facilitates the imposition of theoretical constraints.

The generalized method of moments (GMM) is another method that can be used
to estimate SFM. Golan (2018) provides an interesting discussion on the relationship
between GMM and info-metrics. One advantage of GMM is that it is readily connected
to behavioral theory: zero-moment conditions can be derived from the first-order con-
ditions of the agents’ optimization process. In info-metric terms, these moment condi-
tions can be viewed as “constraints” that provide information about the parameters of
the model. As such, Golan (2018) shows that, under the duality principle, GMM can
be reformulated within the info-metrics framework. An advantage of the resulting
info-metrics method, as an alternative to the original GMM, is that it can use availa-
ble, observed information more efficiently, thereby producing more efficient estimates
(Golan 2018). In our view, this may be an interesting avenue for estimating SFM in a
single stage while accounting for endogeneity issues through the moment conditions.
Indeed, under the standard GMM paradigm, SFM is estimated using a multi-stage
approach, which may lead to less efficient estimates than a one-step estimator (Bokush-
eva et al. 2023; Minviel et al. 2024). Like ML, GMM has interesting large-sample proper-
ties, and it is not efficient for small samples (Golan 2018).

Early on, GME was often thought to have two potential disadvantages. The first is that
the statistical inference was not well developed, and the second is that the results can be
sensitive to the choice of prior distributions for the parameters and error terms. To over-
come the first potential drawback, asymptotic properties and inference for GME estima-
tors have been developed (see Mittelhammer et al. 2000, 2013; Corral and Terbish 2015;
Corral et al. 2017; Golan 2018). In addition, the empirical properties of GME estimators
can be obtained using bootstrapping techniques (Minviel et al. 2025). Regarding the second potential disadvantage, it is well known that this is not a serious problem if we choose large bounds for the support's values, while ensuring that the parameters have economic meaning (Lence and Miller 1998; Golan 2018). Otherwise, sensitivity analysis about the support values can be carried out. These strategies have been used in many studies (e.g., Rezek and Campbell 2007; Campbell et al. 2008; Macedo and Silva 2010; Laureti et al. 2014; Minviel et al. 2025).

## The GME estimator

In the GME framework (Golan et al. 1996; Golan 2018), instead of directly estimating the regression coefficients, probability distributions are estimated for each coefficient and for the one- and two-sided error terms. In this procedure, a range of feasible values is chosen as support values for the probability distribution; then, the regression coefficients and the error terms are reparametrized in terms of unknown probabilities over the support values. In this setup, the regression coefficients and the one- and two-sided error terms in Eqs. (6) and (7) are recast as follows:

$$ \beta = S^{\beta} p^{\beta} = \begin{bmatrix} S_{1}^{\beta} & 0 & \cdots & 0 \\ 0 & S_{2}^{\beta} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & S_{j}^{\beta} \end{bmatrix} \begin{bmatrix} p_{1}^{\beta} \\ p_{2}^{\beta} \\ \vdots \\ p_{j}^{\beta} \end{bmatrix} \quad (8) $$

$$ u = S^{u} p^{u} = \begin{bmatrix} S_{1}^{u} & 0 & \cdots & 0 \\ 0 & S_{2}^{u} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & S_{j}^{u} \end{bmatrix} \begin{bmatrix} p_{1}^{u} \\ p_{2}^{u} \\ \vdots \\ p_{j}^{u} \end{bmatrix} \quad (9) $$

$$ v = S^{v} p^{v} = \begin{bmatrix} S_{1}^{v} & 0 & \cdots & 0 \\ 0 & S_{2}^{v} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & S_{j}^{v} \end{bmatrix} \begin{bmatrix} p_{1}^{v} \\ p_{2}^{v} \\ \vdots \\ p_{j}^{v} \end{bmatrix} \quad (10) $$

where $S^\beta$ is a vector of support values defined for each regression coefficient $\beta$ and $p^\beta$ is the corresponding probability distribution; $S^u$ is a vector of support values defined for the one-sided error term and $p^u$ is the corresponding probability distribution; and $S^v$ is a vector of support values defined for the two-sided error term and $p^v$ is the corresponding probability distribution. In the estimation procedure, the sum of each of the probability vectors is restricted to unity. All the vectors of support values ($S$) are assumed to be of dimension $J$. Five support values are used for all regression coefficients, as well as the one-sided and two-sided error terms. The support values are defined using parameter estimates, random disturbances, and technical inefficiencies from a standard stochastic frontier model that assumes a truncated-normal distribution (see Minviel et al. 2025, for more details).

The GME estimates of the pollution-generating production technology are obtained by maximizing the joint entropies of the distributions of the coefficients and the error
terms in (11), subject to data consistency constraints defined by the specification of each sub-technology described in (6) and (7) by reparametrizing the regression coefficients and the error terms as in Eqs. (8–10), and subject to proper probability constraints:

$$H(p) = -p^{\beta} \ln(p^{\beta}) - p^{\mu} \ln(p^{\mu}) - p^{\nu} \ln(p^{\nu}), \quad (11)$$

Furthermore, a set of theoretical consistency constraints must be imposed (if necessary) to the production frontier of the desirable outputs f(.) and the one of the undesirable outputs g(.), so that $f'_{x_s}, f'_{x_m} \ge 0$ and $f''_{x_s}, f''_{x_m} \le 0$; and $g'_{x_m} \ge 0$ and $g''_{x_m} \ge 0$ (Førsund 2018, 2021), where $x_m$ is a vector of polluting inputs and $x_s$ is a vector of non-polluting inputs.

Following Battese and Coelli (1995), farm-specific technical efficiency (TE) and environmental efficiency (EE) levels can be estimated as follows for farm i in period t:

$$TE_{it} = \exp(-u_{it}^{y}) = \exp(-\delta z_{it} - \eta_{it}^{y}) \quad (12)$$

$$EE_{it} = \exp(-u_{it}^{b}) = \exp(-\vartheta z_{it} - \eta_{it}^{b}) \quad (13)$$

where $z_{it}$ is a vector of contextual variables that may influence the efficiency of the production units; $\delta$ and $\vartheta$ are unknown parameters to be estimated. The terms $\eta_{it}^y$ and $\eta_{it}^b$ are symmetric random variables, defined so that the inefficiency components are non-negative (Battese and Coelli 1995). We use the estimation procedure described in Minviel et al. (2025) to address endogeneity and unobserved heterogeneity issues. This approach applies bootstrapped techniques to ensure accurate inference for the slope parameters (see Wooldridge 2010; Lin and Wooldridge 2019). However, as indicated in Sect. "Empirical specification", the generalized method of moments (GMM) can be reformulated within the info-metrics framework to account for endogeneity and behavioral theory (Golan 2018).

## Data and descriptive statistics

The dataset used in this study is an unbalanced panel of 410 observations from 50 suckler sheep farms, observed over the period from 2012 to 2017. These data were collected from a network of farms monitored by the French National Research Institute for Agriculture, Food, and the Environment (INRAE) in Central France. Following the recent literature on efficiency analysis based on the by-production framework (e.g., Aparicio et al. 2020; Førsund 2021; Dakpo et al. 2023; Minviel et al. 2025), we have retained four non-polluting inputs (land, labor, non-polluting intermediate inputs, and farm capital), four polluting inputs (herd size, fertilizers, energy, and purchased feed), one desirable output (meat), and two undesirable outputs (GHG and nitrogen surplus) to characterize the suckler sheep farms' production process. Regarding the non-polluting inputs, land corresponds to the utilized agricultural area (UAA) in hectares; labor is defined as family and hired labor measured in annual working units (AWU, i.e., the number of full-time equivalent workers); the non-polluting intermediate inputs include veterinary fees, mortality insurance, and other breeding fees in Euros; and the farm capital consists of the annual depreciation value of farm building and machinery in Euros. As regards
the polluting inputs, herd size is measured in livestock units, fertilizers in kg, energy use (fuel, gas, and electricity) in megajoules, and purchased feed in Euros. Before the analysis, all variables measured in monetary units have been deflated using specific price indexes from the French National Institute of Statistics and Economic Studies (INSEE), with 2012 as the base year. This allows the recovery of their implicit physical quantities, as classically done in efficiency studies (Minviel and De Witte 2017; Sipiläinen and Oude Lansink 2005; Zhu et al. 2011). A time trend variable (t) is also used to accommodate shifts in the production function.

As for the outputs, the desirable output is the quantity of meat production, expressed in kilograms of carcass weight. The two undesirable outputs consist of nitrogen surplus and GHG emissions. Nitrogen surplus reflects the emission of nitrogen excesses into the environment, which may lead to water pollution (eutrophication of surface water by nutrient runoff and groundwater pollution by leaching). It is defined as the difference between the quantity of nitrogen entering the production system and the quantity of nitrogen removed by the system. The quantity of nitrogen entering the system is estimated from the quantities of synthetic and organic fertilizers used, purchased animal feed, purchased animals, and various inputs such as purchased straw, using a set of technical coefficients (Simon et al. 2000; Dalgaard et al. 2012). Likewise, the quantity of nitrogen removed by the system is estimated from the desirable productions (crops, forage, and meat) and animal waste leaving the farm. Nitrogen surplus and its environmental impacts depend, inter alia, on nitrogen use efficiency and farming practices (OECD 2008). It should be noted that there is also the entry of atmospheric nitrogen by the symbiotic fixation of legumes. But because these data are difficult to collect reliably, we use an apparent nitrogen surplus, i.e., one that does not account for atmospheric nitrogen.

The total GHG emissions are expressed in terms of carbon dioxide equivalent by summing three main GHGs generally considered in livestock farming (methane ($CH_4$), nitrous oxide ($N_2O$), and carbon dioxide ($CO_2$)) based on their global warming potential (GWP). We consider net GHG emissions, that is, the difference between gross GHG emissions and carbon sequestration in pasture (Benoit and Dakpo 2012; Dollé et al. 2013). The gross GHG emissions are estimated using life-cycle analysis (LCA), which helps evaluate the environmental impacts associated with products throughout their life cycles (Guinée, 2002; Finnveden et al. 2009). However, as usual in agricultural production, we set the system boundary from the cradle to the farm gate. As such, carbon dioxide emissions from the downstream of the farms are not included in this analysis. Methane is mainly related to enteric fermentation (a process during livestock digestion, where microbes in the digestive system ferment feed consumed by the animal), and a small share of it arises from manure management (manure stocking and spreading). Nitrous oxide results from nitrogen fertilizers, animal excreta, volatilized ammonia, and the production of nitrogenous fertilizers. Carbon dioxide comes from energy used on the farms (tractor fuel) and energy used in the livestock building (heating and electricity), and from fertilizers, purchased feed, etc. (Lewis et al. 1999).

Descriptive statistics on these variables are provided in Table 1. Over the whole 2012–2017 period, farms in the sample operated on average 102 hectares of total agricultural area, of which 87% is allocated to fodder areas and 13% for on-farm feed production. On average, over the period of study, farms in our sample produced around 11 thousand
<table><caption>**Table 1** Definition and descriptive statistics of the main variables used (average 2012–2017)</caption><thead><tr><th>Variable</th><th>Definition</th><th>Mean</th><th>Std. dev</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td colspan="6"><strong>Outputs</strong></td></tr><tr><td>Meat production</td><td>Total meat produced in kg of carcass weight</td><td>10,861.53</td><td>6,909.58</td><td>4,071.20</td><td>30,038.70</td></tr><tr><td>Net GHG emissions</td><td>Net GHG emissions in kg of CO<sub>2</sub> eq</td><td>262,329.80</td><td>162,442.50</td><td>877.23</td><td>1,041,878.90</td></tr><tr><td>Nitrogen surplus (kg)</td><td>Nitrogen balance in kg</td><td>2,398.80</td><td>2,173.83</td><td>6.34</td><td>11,933.49</td></tr><tr><td colspan="6"><strong>Inputs</strong></td></tr><tr><td>Usable agricultural area (ha)</td><td>Total agricultural area used</td><td>102.57</td><td>63.22</td><td>21.65</td><td>299.00</td></tr><tr><td>Labor (full-time equivalent)</td><td>Paid and unpaid labor used (in annual working units)</td><td>1.50</td><td>0.70</td><td>0.40</td><td>3.50</td></tr><tr><td>Non-polluting Intermediate inputs (Euros)</td><td>Expenses in purchased seeds and veterinary fees, mortality insurance, and other breeding fees</td><td>8,813.93</td><td>4,879.95</td><td>1,204.50</td><td>30,765.17</td></tr><tr><td>Capital (Euros)</td><td>Annual depreciation value of buildings and machinery</td><td>82,237.38</td><td>49,611.08</td><td>5,900.75</td><td>349,379.10</td></tr><tr><td>Herd size (Livestock units)</td><td>Reference unit for the aggregation of animals of various ages based on their nutritional requirement</td><td>78.84</td><td>39.79</td><td>13.86</td><td>199.99</td></tr><tr><td>Fertilizer (kg)</td><td>Synthetic fertilizer used in kg</td><td>4,347.82</td><td>3,807.31</td><td>0.00</td><td>26,414.30</td></tr><tr><td>Energy (megajoule)</td><td>Non-renewable energy</td><td>266,904.80</td><td>149,942.90</td><td>27,319.34</td><td>809,739.40</td></tr><tr><td>Purchased feed (Euros)</td><td></td><td>12,789.23</td><td>8,037.59</td><td>10,465.30</td><td>38,457.57</td></tr><tr><td colspan="6"><strong>Contextual and farm characteristics' variables<sup>*</sup></strong></td></tr><tr><td>Off-season lambing index</td><td>Sum [number of lambings per fortnight × Off-season coefficient]/ number of lambings during the calendar year. The off-season coefficient is higher when the mating occurs during an unfavorable period (See the Appendix)</td><td>30.38</td><td>19.60</td><td>0.00</td><td>99.82</td></tr><tr><td>Organic farming</td><td>Dummy = 1 if organic farm, Dummy = 0 if not</td><td>0.25</td><td>0.43</td><td>0</td><td>1</td></tr><tr><td>Green payments</td><td>Public subsidies including grassland subsidy and extensification subsidy. They can be seen as a "pay for performance setting"</td><td>31.13</td><td>32.82</td><td>0</td><td>281.34</td></tr><tr><td>Direct payments</td><td>Public subsidies granted to farmers without connection to the level of production</td><td>168.35</td><td>147.49</td><td>92.21</td><td>753.17</td></tr><tr><td>Lambing rate (%)</td><td>Number of annual lambings (including abortions) × 100/ewes over 12 months old used for mating</td><td></td><td>19.38</td><td>48.71</td><td>160.71</td></tr><tr><td>Prolificacy (%)</td><td>Number of lambs born (dead and alive) × 100/number of lambings (including abortions)</td><td>154.38</td><td>25.69</td><td>112.21</td><td>271.64</td></tr><tr><td>Mortality rate (%)</td><td>Number of dead lambs (up to sale or 1 year of age) × 100/number of lambs born (dead and alive)</td><td>14.91</td><td>6.79</td><td>3.82</td><td>45.71</td></tr><tr><td>Numerical productivity (%)</td><td>Annual number of lambs produced × 100/Number of ewes over 12 months old used for mating</td><td>141.09</td><td>30.48</td><td>40.47</td><td>248.43</td></tr><tr><td>Carcass weight/Ewe</td><td>/</td><td>20.72</td><td>5.81</td><td>5.45</td><td>48.32</td></tr><tr><td>N/Fodder area (kg/ha)</td><td>Nitrogen fertilizer used in fodder production</td><td>17.08</td><td>20.02</td><td>0</td><td>158.65</td></tr><tr><td>Concentrate/Ewe (Kg)</td><td>/</td><td>140.27</td><td>51.36</td><td>3.43</td><td>306.33</td></tr><tr><td>N/Crop area (kg/ha)</td><td>Nitrogen fertilizer used in crop production</td><td>200.13</td><td>465.98</td><td>0</td><td>3,924.53</td></tr><tr><td>Number of observations</td><td></td><td>410</td><td></td><td></td><td></td></tr></tbody></table>

<footnote>* Only a subset of these variables is used as determinants of inefficiency in the multi-equation SF model to ensure stable results</footnote>
kilograms of carcass meat, emitted roughly 262 tons of carbon dioxide equivalent, and had a nitrogen surplus of around 2 tons. The other descriptive statistics in Table 1 can be interpreted similarly.

# Results and discussion

## Production frontier estimates

The estimated parameters for the multi-equation stochastic frontier model are reported in Table 2. Table 2 indicates that the first-order parameters, representing elasticity at the sample mean because the variables were divided by their geometric mean, have expected signs. The estimated first-order parameters indicate that the production function of the desirable output is non-decreasing in all inputs at the geometric mean of the data (Table 2). In the same vein, the production functions of the undesirable outputs are non-decreasing in the environmentally detrimental inputs at the geometric mean of the data (Table 2). Likewise, Figs. 2, 3, and 4 provide similar results when the elasticity is calculated for all sample points using the first- and second-order parameters. These results are in line with Førsund (2018).

## Environmental and technical efficiency estimates

The mean technical efficiency over the sample and the period 2012–2017 is 0.84 (Table 2), meaning that, on average, meat production could have been 16% higher without using more inputs. The average environmental efficiency is around 0.80 and 0.78 for GHG emissions and nitrogen surplus, respectively. This suggests that, on average, the farmers in our sample could reduce their GHG emissions by 20% and their nitrogen surplus by 22% while maintaining their meat output. In short, the potential technical and environmental efficiency gains for the farms in our sample would be about 20% on average if they could align their practices with the best practices observed in the sample. Overall, these results suggest that farms in our sample could reduce their level of pollution and increase their level of desirable output from a given level of inputs. Figure 5 depicts the evolution of the mean efficiency scores over the study period. All three efficiency scores show a similar slightly increasing pattern up to 2016. By contrast, in 2017, while both environmental scores slightly decrease, the technical efficiency increases. Figures 6, 7, and 8 show that behind the average estimates, there are wide variations between farms.

To study the relationship between the different types of efficiency estimated, they are classified into three categories that we call low degree of efficiency (Efficiency < 0.65), moderate degree of efficiency (0.65 ≤ Efficiency < 0.85), and high degree of efficiency (Efficiency ≥ 0.85), based on the quartiles of their distributions. The farms are then classified according to the different possible combinations of efficiency categories. The results are shown in Fig. 9, which suggests that the relationship between the different types of efficiency is rather complex. In other words, there is no clear-cut pattern between the different possible combinations. For example, among the possible combinations, 38% of farms have high levels of technical and environmental efficiency (high TE & high EE). This suggests that, for our sample, relatively few farms succeed in substituting polluting inputs for non-polluting ones in their production
<table><caption>**Table 2** Estimated parameters of the multi-equation stochastic frontier model in 2012–2017</caption><thead><tr><th rowspan="2"></th><th colspan="2">Meat Production</th><th colspan="2">GHG Emission</th><th colspan="2">Nitrogen Surplus</th></tr><tr><th>Estimate</th><th>Std. error</th><th>Estimate</th><th>Std. error</th><th>Estimate</th><th>Std. error</th></tr></thead><tbody><tr><td>lnx<sub>1</sub>(Land)</td><td>0.136***</td><td>0.052</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>2</sub>(Labor)</td><td>0.245***</td><td>0.087</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>3</sub>(Interm. input)</td><td>0.102***</td><td>0.035</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>4</sub>(Capital)</td><td>0.311***</td><td>0.075</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>5</sub>(Herd size)</td><td>0.183***</td><td>0.003</td><td>0.250**</td><td>0.121</td><td>0.248***</td><td>0.029</td></tr><tr><td>lnx<sub>6</sub>(Fertilizer)</td><td>0.024***</td><td>0.021</td><td>0.017***</td><td>0.003</td><td>0.063**</td><td>0.027</td></tr><tr><td>lnx<sub>7</sub>(Energy)</td><td>0.125***</td><td>0.004</td><td>0.366**</td><td>0.038</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>8</sub>(Feed)</td><td>0.155***</td><td>0.005</td><td>0.089***</td><td>0.004</td><td>0.089***</td><td>0.001</td></tr><tr><td>lnx<sub>11</sub></td><td>-0.029**</td><td>0.014</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>22</sub></td><td>-0.059**</td><td>0.025</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>33</sub></td><td>-0.018***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>44</sub></td><td>-0.031***</td><td>0.003</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>55</sub></td><td>-0.022**</td><td>0.011</td><td>0.034***</td><td>0.003</td><td>0.007**</td><td>0.004</td></tr><tr><td>lnx<sub>66</sub></td><td>-0.023**</td><td>0.011</td><td>0.009***</td><td>0.002</td><td>0.002***</td><td>0.001</td></tr><tr><td>lnx<sub>77</sub></td><td>-0.015***</td><td>0.002</td><td>0.08***</td><td>0.005</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>88</sub></td><td>-0.017***</td><td>0.001</td><td>0.027***</td><td>0.002</td><td>0.012***</td><td>0.002</td></tr><tr><td>lnx<sub>12</sub></td><td>-0.003</td><td>0.006</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>13</sub></td><td>-0.001</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>14</sub></td><td>-0.003</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>15</sub></td><td>0.004</td><td>0.005</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>16</sub></td><td>0.002***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>17</sub></td><td>0.002***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>18</sub></td><td>0.004</td><td>0.009</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>23</sub></td><td>-0.004***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>24</sub></td><td>-0.006***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>25</sub></td><td>0.005***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>26</sub></td><td>-0.002***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>27</sub></td><td>-0.002***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>28</sub></td><td>-0.001***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>34</sub></td><td>-0.004**</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>35</sub></td><td>-0.005***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>36</sub></td><td>-0.004***</td><td>0.002</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>37</sub></td><td>-0.006***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>38</sub></td><td>-0.006***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>45</sub></td><td>-0.014</td><td>0.005</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>46</sub></td><td>0.003***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>47</sub></td><td>-0.005***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>48</sub></td><td>-0.003***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>56</sub></td><td>0.002***</td><td>0.001</td><td>0.005***</td><td>0.001</td><td>0.047***</td><td>0.002</td></tr><tr><td>-lnx<sub>57</sub></td><td>-0.014</td><td>0.001</td><td>0.004***</td><td>0.001</td><td>/</td><td>/</td></tr><tr><td>lnx<sub>58</sub></td><td>0.001***</td><td>0.002</td><td>0.006***</td><td>0.001</td><td>0.021***</td><td>0.004</td></tr><tr><td>lnx<sub>67</sub></td><td>0.005***</td><td>0.001</td><td>0.009***</td><td>0.002</td><td>/</td><td>/</td></tr><tr><td>lnx<sub>68</sub></td><td>0.009***</td><td>0.001</td><td>0.008***</td><td>0.001</td><td>0.004</td><td>0.003</td></tr><tr><td>lnx<sub>78</sub></td><td>-0.009***</td><td>0.003</td><td>-0.002</td><td>0.002</td><td>/</td><td>/</td></tr><tr><td>T</td><td>0.004*</td><td>0.001</td><td>0.001**</td><td>0.000</td><td>0.004**</td><td>0.001</td></tr><tr><td>t<sup>2</sup></td><td>-0.002***</td><td>0.001</td><td>-0.005***</td><td>0.001</td><td>-0.006**</td><td>0.003</td></tr><tr><td>lnx<sub>1</sub>t</td><td>-0.004**</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>lnx<sub>2</sub>t</td><td>0.004***</td><td>0.001</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
<table><caption>**Table 2** (continued)</caption><thead><tr><th rowspan="2"></th><th colspan="2">Meat Production</th><th colspan="2">GHG Emission</th><th colspan="2">Nitrogen Surplus</th></tr><tr><th>Estimate</th><th>Std. error</th><th>Estimate</th><th>Std. error</th><th>Estimate</th><th>Std. error</th></tr></thead><tbody><tr><td>lnx<sub>3</sub>t</td><td>0.005***</td><td>0.001</td><td>–</td><td>–</td><td>–</td><td>–</td></tr><tr><td>lnx<sub>4</sub>t</td><td>0.018***</td><td>0.001</td><td>–</td><td>–</td><td>–</td><td>–</td></tr><tr><td>lnx<sub>5</sub>t</td><td>–0.003</td><td>0.05</td><td>0.007</td><td>0.008</td><td>0.006***</td><td>0.002</td></tr><tr><td>lnx<sub>6</sub>t</td><td>–0.008***</td><td>0.001</td><td>0.006***</td><td>0.003</td><td>0.005*</td><td>0.003</td></tr><tr><td>lnx<sub>7</sub>t</td><td>0.008***</td><td>0.001</td><td>0.006***</td><td>0.002</td><td>–</td><td>–</td></tr><tr><td>lnx<sub>8</sub>t</td><td>–0.002***</td><td>0.001</td><td>0.005***</td><td>0.001</td><td>0.004**</td><td>0.001</td></tr><tr><td>Intercept</td><td>0.117**</td><td>0.036</td><td>0.022***</td><td>0.001</td><td>0.025***</td><td>0.001</td></tr><tr><td>Mean Efficiency</td><td>0.84</td><td></td><td>0.80</td><td></td><td>0.78</td><td></td></tr><tr><td>Information index</td><td></td><td></td><td>0.867</td><td></td><td></td><td></td></tr><tr><td>Number of obs</td><td></td><td></td><td>410</td><td></td><td></td><td></td></tr></tbody></table>

The asterisks *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively

<figure><img src="image_4.png" /><figcaption>**Fig. 2** Distribution of the input elasticities for the sub-technology generating the desirable output in 2012–2017. Source: The authors</figcaption></figure>

processes (Graham 2004). The results also indicate that, for our sample, technical efficiency is not a sufficient condition for environmental efficiency. In fact, from Fig. 9, we observe that 15% of observations show that high technical efficiency is associated with low environmental efficiency.

In Fig. 9, the category “Others” includes situations such as high levels of environmental efficiency in terms of GHG emissions, low levels of environmental efficiency in terms of nitrogen surplus, and moderate levels of technical efficiency for a given farm. In other words, the category “Others” consists of situations for which we did not observe any clear-cut pattern between technical and environmental efficiency. As such, the category “Others” suggests that the relationship between technical and environmental efficiency is relatively complex for almost one-third of the observations.
<figure><img src="image_5.png" /><figcaption>**Fig. 3** Distribution of the elasticity for the sub-technology generating the GHG emissions in 2012–2017.
*Source:* The authors</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4** Distribution of the elasticity for the sub-technology generating nitrogen surplus in 2012–2017. *Source:* The authors</figcaption></figure>

## Production characteristics/strategies of the different efficiency groups

Additional information on the farm efficiency groups is presented in Fig. 10. Figure 10 shows that the group of farms with a high level of technical and environmental efficiency (high TE & high EE) has a good level of productivity per ewe (but not the highest level), buys relatively little nitrogen fertilizer, and a good proportion of these farms are organic (no synthetic nitrogen fertilizer purchased and low consumption of concentrates purchased). The farms in this group offer a better compromise between technical and environmental efficiency.
<figure><img src="image_7.png" /><figcaption>**Fig. 5** Evolution of the mean efficiency scores in 2012–2017. Source: The authors</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6** Distribution of technical efficiency in 2012–2017. Source: The authors</figcaption></figure>

The group of farms with low technical and environmental efficiency (low TE & low EE) has the lowest ewe productivity, uses a lot of nitrogen fertilizer, and has a high proportion of off-season lambing, which penalizes them from a technical and environmental perspective. The group of farms with high technical efficiency and low environmental efficiency (low TE & low EE) has the highest productivity per ewe (very productive farms). It uses excessive nitrogen fertilizer, which harms its environmental efficiency. They also have a high proportion of out-of-season lambing to meet demand from the sheep industry, which amplifies concentrate consumption and worsens their environmental outcomes.
<figure><img src="image_9.png" /><figcaption>**Fig. 7** Distribution of environmental efficiency (GHG). Source: The authors.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 8** Distribution of environmental efficiency (excess nitrogen). Source: The authors</figcaption></figure>

Regarding the off-season sheep production, these results can be further discussed as follows: In out-of-season sheep production, lambs are mainly fattened in sheepfolds with concentrates (Dowling and Crossley 2004; Benoit and Laignel 2011). Similarly, Khlil et al. (2017) report that feed supplementation is needed to improve estrus response and increase the fertility of sheep induced to breed out-of-season. Benoit and Laignel (2011) observe that farms that initially fed their animals mainly on grass increased their use of concentrates as the proportion of off-season lambing increased. This can be detrimental to their environmental efficiency. Likewise, in beef production systems in France, Veysset et al. (2015, 2017) report increased use of feed concentrate and decreased farm
<figure><img src="image_11.png" /><figcaption>**Fig. 9** Distribution of farms depending on their relationship between technical efficiency (TE) and environmental efficiency (EE). Source: The authors</figcaption></figure>

performance. In sum, out-of-season production can lead farmers to simplify their feed-
ing practices by distributing more concentrated feed.

Increased use of concentrate feed could also be accompanied by changes in grass
harvesting practices, including the adoption of wrapping, which could substantially
affect farm energy consumption (Veysset et al. 2015). A report by IDELE (the French
technical institute for livestock) shows that breeding practices such as autumn graz-
ing of suckler ewes and finishing lambs on grass can lead, on average, to a reduc-
tion in CO2 emissions, and fossil fuel consumption of 2% and 11%, respectively, while
wrapping can lead to an increase in fossil fuel consumption of 4.6% (Sagot et al. 2019).
On the other hand, another report by two French technical institutes (IDELE and
Interbev) (Béchu et al. 2014) shows that sheep farms have a 40% autonomy in con-
centrate feed. This suggests that a substantial proportion of the concentrates used are
produced on farms, which can lead to additional forms of pollution, such as nutrient
runoff and groundwater contamination from excess nitrogen and pesticide use.

The results also indicate that (Fig. 10) strategies that are likely to provide high level
of technical and environmental efficiency (high TE & high EE) bring together, with
trade-offs, (i) sound level of lambing rate, prolificacy, and management of lamb mor-
tality (key components of the numeric productivity), (ii) a rather low use of nitrogen
fertilizer needed to grow a given quantity of forage, (iii) an optimal off-season lamb-
ing proportion, and (vi) a feed concentrate use as limited as possible. More concretely,
it appears that a combination of a lambing rate of about 100%, a prolificacy rate equal
to or greater than 150%, a mortality rate lower than 10%, a numerical productivity of
at least 140%, an off-season lambing rate of about 20%, about 10 kg of nitrogen per ha
of fodder area, and less than 150 kg of concentrates per ewe per year is likely to pro-
vide a high level of technical and environmental efficiency.
<figure><img src="image_12.png" /><figcaption>**Fig. 10** Technical characteristics of farms in the main efficiency groups. Source: The authors.</figcaption></figure>

<table><caption>**Table 3** Technical and Environmental Inefficiency Determinants</caption><thead><tr><th rowspan="2"></th><th colspan="2">Meat Production</th><th colspan="2">GHG Emission</th><th colspan="2">Nitrogen Surplus</th></tr><tr><th>Estimate</th><th>Std. error</th><th>Estimate</th><th>Std. error</th><th>Estimate</th><th>Std. error</th></tr></thead><tbody><tr><td>Off-season lambing</td><td>-0.073***</td><td>0.007</td><td>0.031***</td><td>0.006</td><td>0.032***</td><td>0.006</td></tr><tr><td>Organic farming</td><td>0.013***</td><td>0.001</td><td>-0.026***</td><td>0.001</td><td>-0.019***</td><td>0.003</td></tr><tr><td>Green payments</td><td>0.003</td><td>0.002</td><td>-0.011</td><td>0.021</td><td>-0.015</td><td>0.017</td></tr><tr><td>Direct payments</td><td>0.014***</td><td>0.003</td><td>-0.022***</td><td>0.005</td><td>-0.022***</td><td>0.003</td></tr><tr><td>Time trend</td><td>-0.006</td><td>0.005</td><td>-0.004</td><td>0.035</td><td>0.001</td><td>0.001</td></tr><tr><td>Intercept</td><td>-0.121</td><td>0.098</td><td>-2.465***</td><td>0.628</td><td>-2.531***</td><td>0.844</td></tr></tbody></table>

The asterisks *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively

## Determinants of environmental and technical efficiency

The GME estimation results of the determinants of environmental and technical inefficiency from the multi-equation SF model are reported in Table 3 and discussed below.
A positive (negative) parameter estimates indicate a positive (negative) association with inefficiency and thus a negative (positive) association with efficiency. The coefficient on the off-season lambing index is statistically significant across the three equations. It has a negative sign in the equation for the desirable output (meat production) and a positive sign in the equations for the undesirable outputs (GHG emissions and Nitrogen surplus). This confirms the descriptive results of Sect. "Production characteristics/strategies of the different efficiency groups" and suggests that while off-season production could enhance farms' productive performance (technical efficiency), it is detrimental to their environmental performance (environmental efficiency). These findings could be explained by the fact that out-of-season lambing is based on productive aims (Menant et al. 2022), with a focus on increasing the number of lambs produced per ewe each year (Barkley et al. 2022), implying that it relies on intensified feeding regimes (Benoit et al. 2019; Voutzourakis et al. 2021). This may yield increased efficiency in the use of labor, land, equipment, and buildings (Barkley et al. 2022) but decreased environmental efficiency due to a higher level of concentrate feed (Benoit et al. 2019; Lal et al. 2022).

The fact that farms use more concentrate feed per kg of meat produced can reduce their concentrate feed use efficiency and their environmental efficiency, as increased concentrate use is also associated with higher GHG emissions. Benoit et al. (2019) found that off-season sheep production negatively affects environmental performance. Likewise, Lal et al. (2022) reported that sheep farming with perennial fodder grasses has minimal environmental impacts. It must be noted that the increase in productive efficiency does not necessarily imply an increase in the overall sheep farm economic performance because out-of-season production is an expensive practice in terms of purchased feed (Pellicer-Rubio et al. 2023). It is worth noting that although off-season production may reduce concentrate feed use efficiency, it is associated with increased overall productive efficiency and decreased environmental efficiency. This result aligns with FAO (2020), which observes that despite progress in productive efficiency, GHG emissions from livestock production continue to rise. As such, an appealing feature of the results presented in Fig. 10 is that they show the levels of off-season production that could lead to increased productive and environmental efficiency.

Organic farming is found to be negatively associated with technical efficiency and positively related to environmental efficiency. The effect on technical efficiency can be explained by the fact that organic farms are less productive than conventional farms, suggesting that they are less technically efficient (Kumbhar et al. 2009). The positive effect on environmental efficiency scores may be related to the fact that organic production is primarily based on a more restricted use of specific inputs, such as synthetic fertilizers (Kumbhakar et al. 2009). The coefficients on direct payments indicate that these public subsidies are negatively associated with technical efficiency and positively related to environmental efficiency. The negative association with technical efficiency suggests that the additional income from decoupled direct payments reduces farmers' managerial effort (Martin and Page 1983; Zhu and Oude Lansink 2010; Minviel and Latruffe 2017; Minviel et al. 2024). The positive nexus of decoupled direct payments with environmental efficiency could be related to cross-compliance measures (e.g., environmental protection standards) required to be eligible for decoupled payments in the CAP, which could reduce the use of polluting inputs such as chemical fertilizers (Jaraite and Kazukauskas
2012; Koundouri et al. 2009). The non-significant effect of the green payments may be related to their low levels (Table 1), which do not provide sufficient incentives for farmers to pursue environmental efficiency goals closely (Minviel et al. 2025).

## Concluding remarks

In this paper, based on recent theoretical developments in modeling pollution-generating production technologies, we use a multi-equation stochastic frontier framework to jointly estimate technical and environmental efficiency for French sheep farms in LFA. The multi-equation stochastic frontier framework is rooted in the material balance principle, which enables the consideration of the physical processes that generate environmental pollution. We find that the average technical efficiency of the sample over the period 2012–2017 is 0.84, and the average environmental efficiency is 0.80 for GHG emissions and 0.78 for nitrogen surplus. This suggests that the farms in our sample could increase their desirable output (meat) by 18%, reduce GHG emissions by 20%, and reduce nitrogen surpluses by 22%. These results indicate that, on average, the farms in our sample could achieve approximately 20% gains in technical and environmental efficiency by aligning their practices with the observed best practices. In this respect, the farms in our sample have some room to reduce their level of inefficiency.

The results also show that farms with low environmental efficiency have a high proportion of out-of-season production to meet the sheep industry's demand. This raises their concentrate consumption and nitrogen use on forage areas to increase winter forage stocks in terms of quality and quantity, with a corresponding increase in energy use, thereby worsening their environmental performance. These results are confirmed by econometric estimates showing that while off-season production could enhance farms' productive performance (technical efficiency), it is detrimental to their environmental performance (environmental efficiency). We also identify a set of production strategies that could enhance both the technical and environmental efficiency of the sheep farms in our sample. More concretely, we find that a combination of a lambing rate of about 100%, a prolificacy rate equal to or greater than 150%, a mortality rate lower than 10%, a numerical productivity of at least 140%, an off-season lambing rate of about 20%, about 10 kg of nitrogen per ha of fodder area, and less than 150 kg of concentrates per ewe per year is likely to generate a high level of technical and environmental efficiency.

These results imply that precise technical information should be made available to farmers to help them choose production and management strategies that improve technical and environmental efficiency. The results also suggest that farmers need additional policy incentives to implement the identified strategies to improve their multicriteria efficiency while refining the requirements of the sheep industry to meet these efficiency targets. Indeed, we find that drivers such as decoupled direct payments are positively associated with environmental efficiency and negatively related to technical efficiency. In contrast, the effect of green direct payments is not statistically significant, possibly because their current levels do not provide sufficient incentive for farmers to pursue environmental efficiency goals. In addition to incentives from sheep industry strategies, consumers' “global” expectations regarding product types, environmental quality, and related factors should also be taken into account.
<table><caption>**Table 4** Sexual season</caption><thead><tr><th colspan="4">Sexual rest: anestrus</th><th colspan="7">Sexual activity: sexual</th></tr><tr><th>F</th><th>M</th><th>A</th><th>M</th><th>J</th><th>J</th><th>A</th><th>S</th><th>O</th><th>N</th><th>D</th><th>J</th></tr></thead></table>

<table><caption>**Table 5** Off-season lambing coefficients (Benoit and Laignel 2006)</caption><thead><tr><th>Lambing season</th><th>July</th><th>01 Aug.-15 Oct</th><th>15 Oct.-01 Nov</th><th>01 Nov.-15 Nov</th><th>15 Nov.-15 Dec</th><th>15 Dec.-15 Jan</th><th>Other seasons</th></tr></thead><tbody><tr><td>Off-season coefficients</td><td>0.8</td><td>1</td><td>0.9</td><td>0.7</td><td>0.6</td><td>0.5</td><td>0</td></tr></tbody></table>

Multicriteria efficiency analysis appears to be a promising approach for addressing the multiple challenges faced by livestock farming. However, the potential for improving multicriteria efficiency may be challenged in some areas. For instance, in a multicriteria efficiency analysis, it may be challenging to increase productive (technical) efficiency in areas where livestock is used for social and financial purposes (i.e., assets for meeting sudden cash needs) rather than for production. As such, further research is needed to more precisely define complementary production strategies. The multicriteria efficiency framework (the by-production stochastic frontier model) used in the current study could also be extended to include social and financial criteria. However, this requires sound theoretical reasoning because the by-production frontier model is based on the material balance principle, which may not be appropriate for integrating certain social criteria.

## Appendix: off-season lambing (this appendix is mainly extracted from Dirand<fnref n="1" /> (2007))

Like goats, sheep in more northerly areas are sexually active only during certain periods of the year. Sheep are therefore classified as a species with seasonal sexual activity. This characteristic derives from their ancestor, the mouflon, which was domesticated more than 10,000 years ago. For wild mouflon, the birthing season is spring, which is the most favorable time for the survival of young animals. Given the 5-month gestation period, mating takes place in the fall.

For sheep, sexual activity happens when the days get shorter, like in late summer and fall. It starts in late July and ends in December or January (see Table 4). This period is called the mating season. It reaches its peak intensity in October–November. Moreover, the lambing rate and prolificacy are highest for matings during these 2 months. Table 5 provides off-season lambing coefficients, which are higher when the mating occurs during an unfavorable sexual period (anestrus).

When the days begin to become longer from winter to late spring, ewes are in sexual rest (anestrus). Bucks also exhibit seasonal breeding patterns, but these are less

<footnote n="1">¹ Dirand, A. (2017). L'élevage du mouton. Educagri éditions, Dijon, France.</footnote>
# pronounced than in ewes. During the off-season, they have lower sperm production and less intense sexual behavior due to reduced testosterone secretion

## Author contributions

JJM: Conceptualization; analyze; writing; and review. MB: Conceptualization; analyze; writing; and review. LL: Conceptualization; analyze; writing; and review.

## Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

## Data availability

The data that support the findings of this study are not publicly available. They are available from INRAE, but access to these data is restricted.

## Declarations

### Ethics approval and consent to participate

This research does not involve human participants and does not include human data, individual persons' data, or human tissue.

### Competing interests

The authors declare no competing interests.

Received: 13 August 2025 Revised: 16 December 2025 Accepted: 17 February 2026

Published online: 04 March 2026

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