# Relationship between crop diversification and farm efficiency: Does farm size matter?

Toho Hien

► To cite this version:

Toho Hien. Relationship between crop diversification and farm efficiency: Does farm size matter?. European Review of Agricultural Economics, 2025, 52 (3), pp.334 - 377. 10.1093/erae/jbaf016. hal-05509848

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Special issue article

# Relationship between crop diversification and farm efficiency: Does farm size matter?

**Toho Hien**

Université de Lorraine, Université de Strasbourg, AgroParisTech, CNRS, INRAE, BETA, 54000, Nancy, France

Received 4 June 2024; Final version accepted 18 April 2025

**Abstract**

Crop diversification has gained interest due to its role in climate change adaptation. While previous studies have focused on farm productivity and income variability, this study examines the relationship between crop diversification and farm performance, considering farm size, socio-economic status and location. Using French Farm Accountancy Data Network data from 2010 to 2022, we analyse 19,822 observations from 3,246 crop-focused farms. Results show that small farms benefit from crop diversification, while large farms face income challenges from diversification. Additionally, crop diversification increases the efficiency of larger farms. The results highlight the need for flexible policies to balance economic viability with environmental objectives.

**Keywords:** crop diversification, Shannon Diversity Index, farm performance, stochastic frontier, FADN

**JEL classification:** Q12, D22, C13

**1. Introduction**

Diversification is a practice increasingly adopted by economies worldwide due to its critical role in driving economic structural transformation (Vyas, 1996). The interpretation of this concept varies across disciplines. In marketing, diversification is linked to market concentration, whereas in agriculture, it is viewed as a sequential process encompassing three distinct stages. The first stage is at the crop level and involves moving away from monoculture practices. The second stage involves the integration of multiple enterprises

<footnote>*Corresponding author: E-mail: toho.hien@inrae.fr</footnote>
on farms, allowing for the cultivation of various crops marketed at different
times. The third stage involves mixed farming, characterized by reallocating
resources to a more diverse range of crops or livestock or a combination of
both (Chaplin, 2000; Vyas, 1996). This study focuses on the second and third
stages of agricultural diversification, specifically crop diversification,<fnref n="1" /> defined
as the cultivation of two or more crops using available productive resources.

Diversification is a critical issue in agriculture due to its potential to enhance
resilience, productivity and sustainability. As global agriculture faces increas-
ing pressures from climate change, market volatility and resource constraints,
diversification offers a practical strategy to reduce the risks associated with
monoculture and to improve the adaptability of farming systems. By diver-
sifying crops, farmers can mitigate risks from pests, diseases and extreme
weather, stabilize income and improve food security (Makate et al., 2016;
Singh, 2000). In addition, diversification supports environmental sustainabil-
ity by enhancing biodiversity, improving soil health and reducing dependence
on chemical inputs (Makate et al., 2016). Beyond the farm, diversification can
stimulate the agro-industry, introducing new commodities and technologies,
and potentially leading to more stable incomes and employment opportunities
(Barghouti, Garbus and Umali, 1992).

While the definition of crop diversification is generally agreed upon, the
objectives of its implementation differ between developing and developed
countries. In developing countries, crop diversification aims to improve
income and nutrition for farmers, making it an effective tool in poverty reduc-
tion. Several studies have shown that crop diversification significantly reduces
income variability (Guvele, 2001; Hayatullah, 2017; Mzyece and Ng'ombe,
2020, 2021; Ogundari, 2013). Additionally, it is recognized as a 'climate-
smart' agricultural practice that enhances productivity (Makate et al., 2016;
Mzyece and Ng'ombe, 2021). In contrast, developed countries, particularly in
the European Union (EU), view crop diversification through an environmen-
tal lens, using it as a tool to conserve biodiversity and reduce environmental
harm. The EU Common Agricultural Policy (CAP) promotes diversifica-
tion through subsidies aimed at encouraging environmental-friendly farming
practices (Bureau and Thoyer, 2014). The 2013 CAP reform, for instance,
linked 30 per cent of direct payments to farmers to compliance with agri-
environmental requirements such as crop diversification, the maintenance of
permanent grasslands and the creation of Ecological Focus Areas (EFAs).

Growing interest in crop diversification on the part of agricultural poli-
cies has led to an increasing amount of research on the effectiveness of these
policies and on the relationship between crop diversification and farm produc-
tivity and efficiency. Sauquet (2022) examined the 2013 CAP reform effects in
France, finding a negative correlation between crop diversification and produc-
tion as farmers complied with the measure. Other studies on the relationship

<footnote n="1">1 Livestock and crop-livestock diversifications are not treated in this paper. Livestock diversification is the rearing of two or more livestock types by the farmers given their available resources. Crop-livestock diversification is defined as the production of one or more crops and livestock with the available resources (Asante et al., 2018).</footnote>
between crop diversification and agricultural productivity yield mixed results. For example, some studies indicate a positive correlation between crop diversification, farm yields and profitability (van Rensburg and Mulugeta, 2016; Donfouet et al., 2017; Noack, Riekhof and Di Falco, 2019; Bareille and Dupraz, 2020), while others show negative effects under certain conditions (Kurdyś-Kujawska, Strzelecka and Zawadzka, 2021; Sauquet, 2022). The relationship between crop diversification and efficiency, like its link to production, remains unclear. Studies in developing countries have shown both positive and negative impacts of diversification on efficiency (Coelli and Fleming, 2004; Haji, 2007; Llewelyn and Williams, 1996; Mzyece and Ng'ombe, 2020, 2021; Ogundari, 2013; Rahman, 2009), while research in Europe has largely focused on income diversification rather than crop diversification (Forleo et al., 2021; Lakner et al., 2015). The only notable exception is Kurdyś-Kujawska, Strzelecka and Zawadzka (2021), who found that crop diversification negatively affected the productivity and profitability of small farms in Poland.

These mixed results suggest that the impact of crop diversification on farm productivity and efficiency varies widely depending on regional contexts, farm size and the type of agricultural system in place. Farm size is crucial in determining the efficiency and effectiveness of diversification strategies. Despite extensive research on farm size and its implications for food security, environmental sustainability and social cohesion (Brandth and Haugen, 2011; Redlichová et al., 2023; Ricciardi et al., 2021), few studies have examined the effect of crop diversification on productivity and efficiency with respect to farm size.

This paper aims to fill this gap by investigating the relationship between crop diversification and farm productivity and efficiency with respect to farm size. Understanding this link is essential for developing targeted strategies that optimize both production and efficiency, particularly for smaller farmers who may face resource constraints in response to policy. The focus on farm size in this paper provides new insights into the scalability of diversification strategies and their role in improving agricultural sustainability and resilience.

Staniszewski and Borychowski (2020) highlighted the importance of estimating separate models for different farm sizes to accurately capture the impact of explanatory variables on farm performance. We adopt this approach, estimating separate models for various classes of farm sizes, which differs from the traditional method where farm size is merely a control variable for technical efficiency. To the best of our knowledge, no paper has analysed the relationship between crop diversification and farm productivity and efficiency across farm size classes.

To address these research questions, we use panel data from the French Farm Accountancy Data Network (FADN) for arable farms from 2010 to 2022. These data allow us to estimate crop diversification and examine its impact on farm productivity and efficiency. Our methodology involves a stochastic frontier model that accounts for endogeneity, enabling us to analyse crop diversification's impact on farm yields and efficiency by farm size. We also estimate
a heteroskedastic inefficiency model for each farm size group that considers both economic and area-based measures of size.

The paper is organized as follows. Section 2 outlines the methodology used in this paper. The data and summary statistics are described in Section 3, along with the variables used in the empirical model. Section 4 defines the empirical model and econometric strategies adopted in the study. The econometric results are presented and discussed in Section 5. We check robustness in Section 6 and conclude in Section 7.

## 2. Methodology

The literature offers numerous metrics to estimate diversification over time and space, each with unique strengths and weaknesses. Common indicators include the maximum proportion index, Herfindahl index, Simpson index, Ogive index and the entropy index and its related modifications (Asante et al., 2018). In agricultural systems, diversity is often measured through the richness or evenness of crop species in a given area (Di Falco and Chavas, 2008). This study employs the Shannon Diversity Index (SHDI) (Shannon, 1948) to measure farm-level crop diversity,<fnref n="2" /> a widely used indicator that captures both the richness and evenness of crops cultivated (Bareille and Dupraz, 2020; Bareille and Letort, 2018; Donfouet et al., 2017; Sipiläinen and Huhtala, 2013; van Rensburg and Mulugeta, 2016). It is the unique functional form that allows consistent aggregation across classification levels (Di Falco and Chavas, 2008; Weitzman, 1992). The SHDI for each farm is computed as:

$$SHDI = - \sum_{i=1}^{J} (P_i \times \ln P_i) \qquad (1)$$

where J is the number of crops, Pᵢ denotes the proportion of the area covered by each crop, and ln is the natural logarithm. The SHDI is zero when only one crop is grown, indicating no diversity, and increases as the number of crops and their evenness in land distribution increase. The maximum value for a given number of crops is achieved when crops are grown in equal proportions, i.e. Pᵢ = 1/J. (The farmer is then completely free to choose between the J plots to grow the crop.) In contrast, the index approaches its minimum as the distribution of abundances approaches a monoculture, i.e. one crop has an area share close to one and all others are close to zero. The SHDI has several advantages<fnref n="3" />: it accounts for species richness and evenness, is insensitive to sample size, is well suited to measure habitat diversity and is suited to agricultural data (Bareille and Dupraz, 2020; Mainwaring, 2001; van Rensburg and Mulugeta, 2016).

<footnote n="2">2 Among the indices used to measure diversity, the most similar are the Simpson and Shannon indices, which belong to the Hill family of indices and are generalized formulations of entropy. However, the Simpson index is 'heavily weighted towards the most abundant species in the sample, while being less sensitive to species richness' (Di Falco and Chavas, 2008). The Simpson index is not well suited to the representation of plant diversity in our study.</footnote>

<footnote n="3">3 Despite its advantages, the SHDI has limitations. It places less emphasis on dominant crops, which could impact income or risk management. However, this limitation is not a concern for this study, as we are not focused on direct size comparisons or interpreting absolute SHDI values.</footnote>
These strengths make it an ideal tool for this study, balancing crop richness and evenness while being sensitive to both dominant and rare crops. The SHDI is an appropriate tool to analyse diversification strategies across different farm sizes, offering a comprehensive view of crop diversification by considering the number of crops and their distribution. This is essential for evaluating relationships between farm size, diversification, crop yield and efficiency. Larger farms typically have more available resources (e.g. land, labour and capital), enabling them to accommodate a wider range of crops. This flexibility allows for a higher degree of crop diversification, which leads to a higher Shannon index score. Smaller farms, on the other hand, face constraints due to limited resources and often prioritize staple or cash crops over diversity. This relationship aligns with findings in *Sipiläinen and Huhtala (2013)* and *Ang et al.* (2018), suggesting that larger farms are better positioned to diversify due to economies of scale and resource availability. We therefore assume that larger farms have higher crop diversity, as measured by the Shannon index, compared to smaller farms.

Performance can be measured by several indicators. In this paper, we focus on technical efficiency. Technical efficiency is a measure of farm productivity that relates the farm's outputs to its inputs (Bojnec and Latruffe, 2013). We estimate farm performance using a stochastic production frontier model with technical inefficiency effects. A production frontier is 'the function representing the maximum output that can be obtained from a given quantity of inputs when these inputs are used as efficiently as possible, given the current state of knowledge' (Meeusen and van den Broeck, 1977). Shephard (1953) proposed the distance function as a tool to parametrically examine production technologies involving multiple inputs and outputs. The efficiency score for each farm is calculated using the distance of the farm from the frontier. A farm located on the frontier is fully efficient and has a score of 1. In contrast, inefficient farms have a score of less than 1. The further away from the production frontier (i.e. the less efficient), the lower the score (but still strictly positive).

Recent research has frequently raised the issue of endogeneity when estimating stochastic frontier models. To estimate the relationship between livestock farm profit productivity and biodiversity in Ireland, van Rensburg and Mulugeta (2016) used a stochastic translog production frontier model, with an instrumental variable (IV) to account for the potential endogeneity bias of the diversification indicator. Other authors consider the diversification indicator as an endogenous variable (e.g. Di Falco and Chavas, 2008; Di Falco, Bezabih and Yesuf, 2010; Donfouet et al., 2017). In these studies, where biodiversity indicators were instrumented while other inputs were not, the diversification indicator is considered as a biodiversity indicator and farmers are assumed to optimize crop diversity. Bareille and Dupraz (2020) state that farmers can change input levels in response to input and output prices to the extent that input use depends on farmers' target yields. This dependence can lead to an endogeneity bias, which requires an IV approach. Assuming that farmers maximize their profits (and not the crop diversity) in the very short term, this implies that they only adjust and optimize variable inputs to target yields.
A major source of endogeneity within stochastic frontier analysis is the potential correlation between the frontier determinants and the two-sided error term (Amsler, Prokhorov and Schmidt, 2016; Karakaplan and Kutlu, 2017a; Skevas, 2022). This endogeneity of inputs and/or outputs can lead to inconsistent parameter estimates, resulting in incorrect estimates of inefficiency (Kumbhakar, 2013). Despite increasing concerns about endogeneity problems in stochastic frontier models, the existing literature lacks sufficient research to address this issue. Dealing with endogeneity is more challenging in stochastic frontier models due to the unique characteristics of the error component. Standard IV methods are not applicable, and a clear strategy for dealing with the endogeneity associated with the scaling factors in the one-sided error of a stochastic frontier model has yet to be established in the literature (Hayatullah, 2017). To address this potential endogeneity in the model, we follow the recent work of Karakaplan and Kutlu (2017b) and Karakaplan (2022), who developed an IV estimator based on a general maximum likelihood framework to address the endogeneity problem in stochastic frontier models. Our stochastic frontier panel data model accounting for potential endogenous explanatory variables is (Karakaplan and Kutlu, 2017a):

$$y_{it} = \beta'_{i} x_{yit} + v_{it} - u_{it} \quad (2)$$

$$x_{it} = \delta'_{i} z_{it} + \varepsilon_{it} \quad (3)$$

$$\begin{bmatrix} \tilde{\varepsilon}_{it} \\ v_{it} \end{bmatrix} = \begin{bmatrix} \Omega^{-\frac{1}{2}} \varepsilon_{it} \\ v_{it} \end{bmatrix} \sim N\left(\begin{bmatrix} 0 \\ 0 \end{bmatrix}, \begin{bmatrix} I_p & \sigma_v \rho \\ \sigma_v \rho' & \sigma_v^2 \end{bmatrix}\right) \quad (4)$$

$$u_{it} = h(x'_{u_{it}} \varphi_u) u_i^* \quad (5)$$

where $y_{it}$ is the total production value of the $i^{th}$ farm in period $t$, $\beta$ is a vector of parameters representing the elasticities of production relative to inputs, $x_{yit}$ is a vector of exogenous and endogenous variables; $x_{it}$ is a vector of all endogenous variables (it is part of $x_{yit}$), $z_{it}$ is a vector of both the IVs and other explanatory variables, $v_{it}$ and $\varepsilon_{it}$ are two-sided error terms; $u_{it} \ge 0$ is a one-sided error term capturing the inefficiency, $x_{u_{it}}$ is a vector of exogenous and endogenous variables excluding the constant, $\sigma_{u_{it}} = h(x'_{u_{it}} \varphi_u) > 0$, and $u_i^*$ is a producer-specific random component independent from $v_{it}$ and $\varepsilon_{it}$. Finally, $\Omega$ is the variance-covariance matrix of $\varepsilon_{it}$, $\sigma_v^2$ is the variance of $v_{it}$, and $\rho$ is the vector representing the correlation between $\tilde{\varepsilon}_{it}$ and $v_{it}$. Hence, $u_{it}$ and $v_{it}$ can be correlated with $x_{it}$, yet $u_{it}$ and $v_{it}$ are conditionally independent given $x_{it}$ and $z_{it}$. Similarly, $u_{it}$ and $\varepsilon_{it}$ are conditionally independent given $x_{it}$ and $z_{it}$. Using a Cholesky decomposition of the variance-covariance matrix of $(\tilde{\varepsilon}_{it}, v_{it})'$, we
can represent $(\tilde{\epsilon}'_{it}, v_{it})'$ as follows:

$$ \begin{bmatrix} \tilde{\epsilon}_{it} \\ v_{it} \end{bmatrix} = \begin{bmatrix} I_p & 0 \\ \sigma_v \rho' & \sigma_v \sqrt{1-\rho'\rho} \end{bmatrix} \begin{bmatrix} \tilde{\epsilon}_{it} \\ \tilde{w}_{it} \end{bmatrix} \quad (6) $$

where $\tilde{\epsilon}_{it}$ and $\tilde{w}_{it} \sim N(0,1)$ are independent. The frontier equation can be written as:

$$ y_{it} = \beta'_{i}x_{yit} + \sigma_{v}\rho'\tilde{\epsilon}_{it} + w_{it} - u_{it} \quad (7) $$

$$ y_{it} = \beta'_{i}x_{yit} + (x_{it} - \delta_{i}z_{it})'\eta + e_{it} \quad (8) $$

where

$e_{it} = w_{it} - u_{it}$, $w_{it} = \sigma_v \sqrt{1 - \rho' \rho} \tilde{w}_{it} = \sigma_w \tilde{w}_{it}$ and $\eta = \sigma_w \Omega^{-1/2} \rho / \sqrt{1 - \rho' \rho}$. An important aspect of this setup is that $e_{it}$ is conditionally independent from the regressors given $x_{it}$ and $z_{it}$. The term $(x_{2it} - \delta_i z_{it})' \eta$ in equation (8) serves as a bias correction term. We assume that:

$$ u_i^* \sim N^+(0, 1) \quad (9) $$

$$ h_{it}^2 = \exp(x'_{u_{it}} \varphi_u) \quad (10) $$

where $\sigma_{u_{it}}^2 = h_{it}^2 = \exp(x'_{u_{it}} \varphi_u)$ assuming that the inefficiency term, $u_{it}$, is a function of $x_{u_{it}}$. Let us suppose that we have a vector of observations corresponding to panel i, and $T_i$ is the number of time periods for the panel. Furthermore, suppose that $h_i = (h_1, h_2, \dots, h_{T_i})'$ is a $T_i \times 1$ vector. The log-likelihood function of panel i is given by the following equation:

$$ \ln L_i = \ln L_{i|y|x} + \ln L_{i,x} \quad (11) $$

where

$$ \ln L_{i,y|x} = -\frac{1}{2} \left( T_i \ln(2\pi\sigma_w^2) + \frac{e_i'e_i}{\sigma_w^2} + \left( \frac{\mu_i^2}{\sigma_u^2} - \frac{\mu_{i*}^2}{\sigma_{i*}^2} \right) \right) + \ln \left( \frac{\sigma_{i*} \Phi\left(\frac{\mu_{i*}}{\sigma_{i*}}\right)}{\sigma_u \Phi\left(\frac{\mu}{\sigma_u}\right)} \right) \quad (12) $$

$$ \ln L_{i,x} = -\frac{1}{2} \sum_{t=1}^{T_i} \left( \ln(|2\pi\Omega|) + \varepsilon'_{it}\Omega^{-1}\varepsilon_{it} \right) \quad (13) $$

$$ \mu_{i*} = \frac{\sigma_w^2 \mu - \sigma_u^2 e_i' h_i}{\sigma_u^2 h_i' h_i + \sigma_w^2} \quad (14) $$

$$ \sigma_v^2 = \frac{\sigma_u^2 \sigma_w^2}{\sigma_u^2 h_i' h_i + \sigma_w^2} \quad (15) $$
$$e_{it} = y_{it} - \beta'_{i}x_{yit} - \varepsilon'_{it}\eta \quad (16)$$

$$\varepsilon_{it} = x_{it} - \delta'_{i}z_{it} \quad (17)$$

where $\Phi$ denotes the standard normal cumulative distribution function (CDF). Endogeneity exists if $\eta$ is jointly significant. If $\eta$ is not jointly significant, the correction term is not necessary and efficiency can be estimated using conventional stochastic frontier models.

Note that our model estimates the parameters in a single step, unlike standard control function methods where the estimation is done in two steps. Compared to two-step methods, our model has the advantage of being statistically more efficient and does not require a bootstrap procedure to correct standard errors (Karakaplan and Kutlu, 2017a).

The technical efficiency of a farmer is delineated as the ratio between the average output, considering the inputs $x_{yit}$ and their technical inefficiency effect ($u_{it}$), and the average output that would occur in the absence of technical inefficiency in production ($u_{it} = 0$). The technical efficiency (TE) is predicted as:

$$TE_{it} = \frac{E(y_{it}|u_{it}, x_{yit})}{E(y_{it}|u_{it}=0, x_{yit})} = \exp(-u_{it}) \quad (18)$$

where $E$ represents the expectation operator. The $TE_{it}$ takes a value between 0 and 1. A value of 1 for $TE_{it}$ indicates a farm that is operating at full efficiency, while a value of 0 indicates a farm that is fully inefficient.

# 3. Data description and some statistical tests

## 3.1. Data description

We use an unbalanced sample of individual farm-level data from the French FADN between 2010 and 2022. The dataset consists of farms representing all types of agricultural production across the economic size groups of: 25–50, 50–100, 100–250, 250–500 and more than 500 thousand euros of standard output (SO).<fnref n="4" /> We excluded farms whose main production is livestock, horticulture, fruits or vineyards. The final dataset consists of 19,822 observations and 3,246 farms whose main activity is crop production.

Following the policy of the CAP ‘green payments’, we divided farms into three groups according to the size of their utilized agricultural area (UAA). Indeed, if the UAA is strictly less than 10 ha, the farm is not subject to the crop diversification criterion of the CAP; if it is between 10 and 30 ha, at least two different crops must be grown, with the largest crop accounting for no more than 75 per cent of the arable area; and if it is strictly more than 30 ha, at least three different crops must be grown. We therefore estimate the impact of

<footnote n="4">4 The SO represents the farm-gate value of agricultural products (crops or livestock), reflecting the total value of crops, livestock and related products.</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Distribution of the crop diversification index.</figcaption></figure>

crop diversification on farm performance using these three classes defined by CAP: [0, 10], [10, 30] and [30, +∞] in hectares.

We use farm SO as the output in our study. We define two variable inputs and three fixed inputs. The variable inputs are: (1) intermediate consumption, i.e. materials and operating expenses (seeds, fertilizers, pesticides, energy, gas, water, etc.); and (2) hired labour, expressed in hours. The three fixed inputs are (a) family labour expressed in hours; (b) annual depreciation of buildings and services for capital goods, representing fixed capital; and (c) the UAA in hectares. All monetary variables are measured at constant 2015 prices. Our measure of crop diversification is the SHDI. In our sample, almost all farmers (99.88 per cent) practice crop diversification. Fig. 1 presents the distribution of the crop diversification index.

Research has shown that farms in Less Favoured Areas (LFAs), Environmental Constraint Areas (ECAs) and at high altitudes often underperform due to difficult agro-climatic conditions. We include these three contextual variables to account for the diversity of areas. Both Bojnec and Latruffe (2013) and Kostlivý and Fuksová (2019) found that farms in LFA are less efficient than those outside these areas, highlighting the significant impact of environmental factors. Similarly, Latruffe et al. (2017) confirmed that, all else being equal, an unfavourable environment negatively affects farm output in many countries. Several studies have also shown that the effect of subsidies on farm performance in LFA, ECA and high-altitude areas often differs from their impact on farms outside these regions (Baráth, Fertő and Bojnec, 2018;
Khafagy and Vigani, 2022; Pereira and Navarro, 2015; Pisulewski and Marzec, 2022). Additionally, Ceausu et al. (2015) noted that large areas projected for abandonment were frequently located in or near ECAs. An LFA binary variable takes the value of 0 if most of the farm is not located in an LFA and 1 otherwise. LFAs are regions identified as having natural disadvantages for agricultural production, such as poor soil quality, steep slopes or adverse climate conditions. The ECA variable is equal to 1 if the majority of the UAA is located in a Natura 2000 area and 0 otherwise. Special regulations govern areas with high environmental challenges. The directives of Natura 2000 areas restrict changes in land use and limit the range of activities that can take place there (Gardi, 2017). The last contextual variable, altitude, takes a value of 0 if the altitude is less than 300 meter and 1 otherwise. Altitude affects climate (temperature, precipitation patterns) and, consequently, agriculture. Higher altitudes are often associated with cooler temperatures and shorter growing seasons, which can affect agricultural productivity. The LFA, ECA and altitude<fnref n="5" /> variables are important because they control for heterogeneity and make it possible to estimate the performance of comparable farms. We use a pairwise correlation test to check for multicollinearity (Zhang et al., 2016), and we have found that there is no problem with multicollinearity (Table A.1 in Appendix 1). Descriptive statistics of our final data are presented in Table 1.

Our primary objective is to analyse the relationship between crop diversification and farm efficiency. Sherlund, Barrett and Adesina (2002) highlight that neglecting farm heterogeneity in environmental conditions not only introduces omitted variables bias but also significantly overestimates technical inefficiency. In addition to accounting for area-specific characteristics (LFA, ECA and altitude), following Zhang et al. (2016) and Chen, Huffman and Rozelle (2009), we include socio-economic variables of the farmers, such as gender (coded as 0 for women, 1 for men), age, general education (ranging from no education to higher education) and agricultural education (from no formal education to agricultural higher education). We expect that higher levels of education (general or agricultural) among farmers will lead to more efficient farms. Additionally, we anticipate that women will be more efficient than men and that older farmers will exhibit higher efficiency. Moreover, following Bojnec and Latruffe (2013) and Staniszewski and Borychowski (2020), we control for the potential impacts of subsidies on farm efficiency by including the quantity of subsidies received in our model, assuming they are negatively related to farms' technical efficiency. Finally, Mzyece and Ng'ombe (2021) and Ogundari (2013) highlight the impact of crop diversification on farm efficiency. We use crop diversification as an explanatory variable for efficiency, assuming it has a positive effect on farm efficiency.

<footnote n="5">5 The use of LFA, ECA and altitude as control variables could lead to omitted variable bias, where important factors that influence the outcome of interest are not included in the model. To improve the robustness of the analysis, it would be better to use more precise and disaggregated measures of environmental, climatic and socio-economic conditions and to carefully consider the potential interactions between these factors. However, these disaggregated factors are not available.</footnote>
<table><caption>Table 1. Descriptive statistics of French FADN data from 2010 to 2022 per economic size</caption><thead><tr><th>Variable</th><th>Unit</th><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>All</th></tr></thead><tbody><tr><td>Total output produced</td><td>Euro</td><td>84,924.059</td><td>136,070.92</td><td>264,343.08</td><td>488,832.83</td><td>1,042,780.5</td><td>277,213.2</td></tr><tr><td>Utilized agricultural area (UAA)</td><td>Hectare</td><td>48,581</td><td>80,755</td><td>148,577</td><td>242,996</td><td>319,127</td><td>143,8638</td></tr><tr><td>Intermediate consumption</td><td>Euro</td><td>44,640.509</td><td>68,347.961</td><td>125,853.5</td><td>232,181.2</td><td>486,645.82</td><td>132,801.9</td></tr><tr><td>Hired labour used</td><td>Hour</td><td>265.637</td><td>296.915</td><td>592.126</td><td>1421.655</td><td>6293.863</td><td>796.245</td></tr><tr><td>Family labour used</td><td>Hour</td><td>1730.811</td><td>1779.561</td><td>2108.13</td><td>2648.12</td><td>3235.227</td><td>2116.372</td></tr><tr><td>Capital</td><td>Euro</td><td>11,719.613</td><td>19,689.751</td><td>39,442.382</td><td>66,126.753</td><td>120,843.2</td><td>39,021.85</td></tr><tr><td>Diversification index (SHDI)</td><td></td><td>1.279</td><td>1.435</td><td>1.525</td><td>1.615</td><td>1.57</td><td>1.498</td></tr><tr><td>Less Favoured Area (LFA)</td><td></td><td>0.372</td><td>0.318</td><td>0.236</td><td>0.182</td><td>0.043</td><td>0.253</td></tr><tr><td>Environmental Constraint Area (ECA)</td><td></td><td>0.048</td><td>0.044</td><td>0.03</td><td>0.023</td><td>0.017</td><td>0.033</td></tr><tr><td>Altitude</td><td></td><td>0.10</td><td>0.115</td><td>0.075</td><td>0.06</td><td>0.027</td><td>0.083</td></tr><tr><td>Subsidies</td><td>Euro</td><td>14,791.668</td><td>24,362.095</td><td>43,211.189</td><td>66,231.823</td><td>81,235.107</td><td>41,061.78</td></tr><tr><td>Gender</td><td></td><td>0.838</td><td>0.871</td><td>0.914</td><td>0.934</td><td>0.97</td><td>0.902</td></tr><tr><td>Age</td><td>Year</td><td>52.693</td><td>52.06</td><td>50.691</td><td>50.089</td><td>48,502</td><td>51.026</td></tr><tr><td>General Education</td><td></td><td>1.871</td><td>1.942</td><td>2.048</td><td>2.227</td><td>2.335</td><td>2.044</td></tr><tr><td>Agricultural Education</td><td></td><td>1.863</td><td>2.013</td><td>2.298</td><td>2.56</td><td>2.773</td><td>2.248</td></tr><tr><td>Number of observations</td><td></td><td>1,682</td><td>4,711</td><td>9,737</td><td>3,092</td><td>600</td><td>19,822</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Relationship between farm size and crop diversification.</figcaption></figure>

*Note:* For UAA size, the numbers 1, 2 and 3 correspond to the classes [0, 10], [10, 30] and [30, +∞] (in hectares), respectively. The numbers 6, 7, 8, 9 and 10 correspond to the farm economic size (in EUR 1,000) as follows: [25–50], [50–100], [100–250], [250–500] and >500, respectively.

## 3.2. Statistical tests

We performed statistical tests on the data to verify certain hypotheses and empirical findings. We hypothesize that large farms have more resources to diversify compared to small farms. This assumption is supported by the descriptive statistics for farm economic size. We fitted the SHDI with respect to farm size and found a positive correlation between farm size and the level of crop diversification (Fig. 2).

We also compare crop diversification before and after the 2013 CAP. We found that the 2013 CAP significantly increased the level of crop diversification. These findings align with those from Sauquet (2022), whose econometric analysis of the impact of the 2013 CAP on crop diversification showed that this policy increased crop diversification (see Appendix 2 for more details).

## 4. Empirical model

We model the translog production frontier function, which is flexible and the most frequently used model in empirical work. The translog specification requires the application of a logarithmic transformation to the variables. However, within our empirical dataset, certain variables have observations equal to zero: subsidies (0.52 per cent), capital (0.49 per cent), family labour (0.02 per
cent) and hired labour (61.62 per cent). In order to avoid the loss of data points, the inverse hyperbolic sine (IHS) transformation is applied. This method, as proposed by Bellégo, Benatia and Pape (2022), serves as a remedy for the problem of taking the logarithm of zero. The IHS transformation is very similar to the logarithmic transformation, but preserves observations with zero or negative values without making arbitrary changes to the original variable (Aihounton and Henningsen, 2021; Bellemare, Barrett and Just, 2013; Bellemare and Wichman, 2020). It also allows an interpretation of the regression results similar to that of the logarithmic transformation according to Aihounton and Henningsen (2021). Essentially, this transformation involves adding a specific positive constant to the observations prior to applying the logarithmic transformation as described by Bellégo, Benatia and Pape (2022). It transforms the variable $x_i$ into $\hat{x}_i = \frac{\ln(\theta x_i + \sqrt{\theta^2 x_i + 1})}{\theta}$, with $x_i$ representing any model variable and $\theta$ a scaling parameter. Based on the study by Bellégo, Benatia and Pape (2022), we set $\theta$ equal to 1, which is a common practice in many economic contexts (Aihounton and Henningsen, 2021; Bellemare and Wichman, 2020). In particular, Bellemare and Wichman (2020) have shown that using the IHS-IHS specification (applying the IHS transformation to both sides of the equation) allows the estimated coefficients to be interpreted directly as elasticities.

A reference point is essential for the interpretation of flexible forms such as the translog local approximation (see White, 1980). In this context, the mean of the variables over the studied period (expressed in logarithms) is chosen as the reference point. As a result, all logarithm variables on the right-hand side of the equations are standardized on the basis of their sample mean (referred to as mean scaling). Thus, the elasticity of an explanatory variable depends on its first-order coefficient and the coefficient of its cross-derivative with non-log variables at the sample mean.

For simplicity, we do not use the variable names from Table 1 (data description) when writing the translog model. Since 60 per cent of the sample does not use hired labour, possibly due to technological heterogeneity, we included a dummy variable to capture the effect of the presence or absence of hired labour. The estimated model is:

$$ 
\begin{aligned}
\ln(y_{it}) = \alpha_i + \gamma_i \text{SHDI}_{it} + \omega_{hli} D_{hlit} + \frac{1}{2} \delta_i \text{SHDI}_{it}^2 &+ \sum_{j=1}^{J} \beta_j \ln(x_{jit}) \\
&+ \frac{1}{2} \sum_{k=1}^{K} \sum_{l=1}^{L} \beta_{kl} \ln(x_{kit}) \cdot \ln(x_{lit}) + \tau_i d_{it} + \pi_t T_t + v_{it} - u_{it}
\end{aligned} 
\quad (19) 
$$

where $y_{it}$ is the total output of the farm, $SHDI_{it}$ is the crop diversification index, $x_{it}$ is a vector of inputs (e.g. UAA, intermediate consumption, hired and family labour and capital), $d_{it}$ is a vector of control variables (e.g. LFA, ECA and altitude), along with all other non-logged variables of farm $i$ in period $t$, and time dummies for each farming season of the sample. $D_{hl}$ is a dummy variable, taking a value of 1 if hired labour usage is positive, and 0 otherwise. It accounts for changes in the intercept (Battese, 1997). $\delta_i$, $\gamma_i$, $\omega_{hli}$, $\beta_j$, $\beta_{kl}$, $\tau_i$ and $\pi_t$ are parameters to be estimated. $\alpha_i$ is the estimated constant variable, $v_{it}$ is the error term
and $u_{it}$ is the inefficiency component. Diversifying crops helps mitigate production risk by spreading it across multiple crops. This risk-reduction strategy is particularly important in uncertain environmental conditions, as diversification buffers farms from potential losses due to droughts, pests or fluctuating market prices (Di Falco, Bezabih and Yesuf, 2010; Rao, 2019). For smaller farms, crop diversification may play a critical role in stabilizing income, as they will be less vulnerable to climate variability and market risks. For larger farms, while diversification still offers risk reduction, its relative importance may be diluted by other risk-management strategies (e.g. insurance or contracts). We therefore hypothesize crop diversification reduces production risk, with the effect being more significant for smaller farms. Larger farms may face income losses as they increase their crop diversification.

To account for the endogeneity problems when estimating the distance function, we estimate an output distance function and assume that the input prices and the output are exogenous. Input exogeneity is based on the assertion that producers commonly determine the quantity of inputs to be used and optimize output production accordingly. In addition, certain inputs are either fixed or quasi-fixed and therefore cannot be adjusted immediately in response to a disturbance (Skevas, 2022). In this study, we assume that only hired labour can adjust to a shock and can therefore be endogenous. To address this potential endogeneity, we use two IVs: labour cost and social security cost. Labour cost and social security cost are suitable IVs because they are exogenous to the amount of hired labour in the short term. These costs are largely determined by external factors, such as government regulations, wage-setting policies or macroeconomic conditions, which do not directly depend on individual farms' or firms' decisions regarding labour use. Additionally, labour cost and social security cost are closely linked to the overall cost of hiring, making them relevant instruments. Changes in these costs directly influence firms' demand for hired labour, as firms adjust their labour usage in response to variations in employment costs. The model employs a one-step pooled panel data approach (Karakaplan, 2022; Karakaplan and Kutlu, 2017a). The control function (equation 3) and the distance function (equation 2) are estimated simultaneously.

The assumption that $u_{it} \sim N^+(0, \sigma_{u_{it}}^2)$ allows the estimation of a heteroskedasticity model that captures the effects of a set of explanatory variables on the technical efficiency (Lakner et al., 2018). Following the traditional technical inefficiency effect models in the literature, the variance of the inefficiency error is modelled as a function of farmers' socio-economic variables, subsidies and year dummies (Bojnec and Latruffe, 2013; Lakner et al., 2015; Ogundari, 2013; Rahman, 2009; Todorović et al., 2020). The heteroskedasticity model is defined as:

$$ \sigma_{u_{it}}^2 = \exp \left( \frac{\alpha_0 + \alpha_1 \text{SHDI}_{it} + \alpha_2 \text{Subsidies}_{it} + \alpha_3 \text{Age}_{it} + \alpha_4 \text{Gender}_i + \alpha_5 \text{General\_Education}_{it} + \alpha_6 \text{Agricultural\_Education}_{it} + \alpha_7 \text{LFA}_{it} + \alpha_8 \text{ECA}_{it} + \alpha_9 \text{Altitude}_{it} + \alpha_{10} \text{Dummy}_{\text{Year}}}{\sigma_{u_{it}}} \right) \quad (20) $$
The corresponding variable has a negative (positive) impact on technical efficiency if the estimated parameter $\alpha_i$ is positive (negative). It is important to note that the presence of heteroskedasticity in the inefficiency indicator is considered beneficial in the context of this specified methodology, as it highlights the influence of possible explanatory factors. For example, crop diversification offers various benefits, including improved soil health, pest control and resource optimization, which can enhance farm efficiency. However, the impact on efficiency might vary depending on farm size. Larger farms, though capable of greater diversification, might face diminishing returns or managerial complexity that limits efficiency gains. Smaller farms, by focusing on fewer crops and using traditional, sustainable methods, could potentially achieve higher efficiency per unit of land, as they might be more adaptable and environmentally sustainable (Di Falco and Chavas, 2008). We therefore hypothesize that crop diversification positively impacts efficiency, but the effect is more pronounced on smaller farms due to their ability to optimize resources through traditional methods like crop rotation and organic farming.

# 5. Results and discussion

To test the robustness of our model, we performed a Hausman test to compare the translog to a Cobb-Douglas model. The results indicate that the translog specification is better than the Cobb-Douglas specification (Table A.2 in Appendix 1). Additionally, we checked for potential endogeneity (Karakaplan, 2022) and found that hired labour is indeed endogenous ($\eta \neq 0$) (Table A.3 in Appendix 1). We also empirically controlled for endogeneity using our IVs, finding that there was a significant correlation between the endogenous variable (hired labour) and the two IVs (labour costs and social security costs) and then using the instruments in the analysis (Table A.4 in Appendix 1). To account for time effects, we included years as dummy variables in the model, both in the stochastic frontier and in the heteroskedastic inefficiency. Due to the small sample size in the first UAA size class ([0, 10]) with only 41 observations (representing 0.07 per cent of the sample), it was not possible to estimate the stochastic frontier for this category. Similarly, the largest economic size class (> EUR 500,000), with 600 observations (representing 3.02 per cent of the sample), did not converge, so we excluded its results from our analysis. These excluded categories belong to different farm size classifications (UAA and economic size), which means they do not significantly reduce the number of classes or observations in each farm size group. Consequently, their impact on the overall analysis is minimal. The panel stochastic production frontier and heteroskedastic inefficiency were estimated simultaneously (Karakaplan, 2022).

## 5.1. Impact of crop diversification on farm income

Table 2 presents the results of the output stochastic frontier model accounting for endogeneity.<fnref n="6" /> At the geometric mean, crop diversification (measured by

<footnote n="6">6 The inefficiency components are not included in Table 2, as efficiency is analysed in the next section.</footnote>
the SHDI) has a negative marginal effect<fnref n="7" /> on farm income (Table 3): the more diversified the farm, the lower the income. This outcome might justify the CAP's provision of subsidies to farmers who diversify crops. However, the marginal effect of crop diversification on income varies depending on the farm's economic and UAA size. For farms with a small economic size (< EUR 100,000), crop diversification has a positive marginal effect on income, whereas for larger economic farms (> EUR 100,000), the effect is negative. When considering UAA size, diversification has a positive but insignificant effect on small farms (< 30 ha), while for larger farms, it has a negative and significant impact on income. These findings are in line with Alletto, Vandewalle and Debaeke (2022), who found that, in an 8-year on-farm experiment in south-western France, crop diversification had contrasting effects on farm incomes.

We reject the hypothesis that increased crop diversification positively impacts yields. However, crop diversification remains valuable for optimizing land use, enhancing soil health and reducing the risks associated with relying on a single crop. Diversification allows farmers to better manage resources and lower the chances of soil degradation. Additionally, it mitigates risks from pests, diseases and market fluctuations, contributing to greater production stability and improved overall productivity. For larger farms, however, the management costs associated with diversification can offset these benefits. Managing a wider variety of crops requires more complex planning, increased labour and specialized equipment for planting, harvesting and storage. Each crop may have different needs for irrigation, fertilizers or pest control, adding logistical and operational challenges. As a result, large farms may face higher costs in coordinating these activities efficiently. Moreover, economies of scale—often a key advantage for large farms—may be reduced when resources are spread across different crops, leading to less efficient use

$$y_{it} = e^{\alpha_i + \gamma_i \text{SHDI}_{it} + \frac{1}{2} \delta_i \text{SHDI}_{it}^2 + \omega_{hli} D_{hlit} + \sum_{j=1}^{J} \beta_j \ln(x_{jit}) + \frac{1}{2} \sum_{j=1}^{J} \sum_{k=1}^{K} \beta_{jk} \ln(x_{jit}) \ln(x_{kit}) + \tau_i d_{it} + \pi_t T_t + v_{it} - u_{it}}$$

$$y_{it} = e^{\alpha_i + \gamma_i \text{SHDI}_{it} + \frac{1}{2} \delta_i \text{SHDI}_{it}^2 + \omega_{hli} D_{hlit} + \sum_{j=1}^{J} \beta_j \ln(x_{jit}) + \frac{1}{2} \sum_{j=1}^{J} \sum_{k=1}^{K} \beta_{jk} \ln(x_{jit}) \ln(x_{kit}) + \tau_i d_{it} + \pi_t T_t + v_{it} - u_{it}}$$

The marginal effect of SHDI is:

$$\frac{\partial y_{it}}{\partial \text{SHDI}_{it}} = (\gamma_i + \delta_i \text{SHDI}_{it}) e^{\alpha_i + \gamma_i \text{SHDI}_{it} + \frac{1}{2} \delta_i \text{SHDI}_{it}^2 + \sum_{j=1}^{J} \beta_j \ln(x_{jit}) + \frac{1}{2} \sum_{j=1}^{J} \sum_{k=1}^{K} \beta_{jk} \ln(x_{jit}) \ln(x_{kit}) + v_{it} - u_{it}}$$

At the geometric mean level, the marginal effect of the SHDI is: $\frac{\partial y_{it}}{\partial \text{SHDI}_{it}} = (\gamma_i + \delta_i \text{SHDI}_{it})$. The geometric mean of SHDI is 1.447, and we calculated it for each farm size. Results of marginal effects are presented in Table 3.

<footnote n="7">7 In this paper, the relationship between farm income and diversification is log-linear. Then, the marginal effect of SHDI is the partial derivative of income with respect to SHDI. To show this, we can rewrite equation (19) using an exponential transformation.</footnote>
<table><caption>**Table 2.** Stochastic production frontier model estimates</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All Output</th><th colspan="5">Economic size in EUR 1,000</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><td>D<sub>hl</sub></td><td>0.133<sup>*</sup><br>(0.068)</td><td>0.105<br>(0.259)</td><td>0.247<br>(0.203)</td><td>0.078<br>(0.107)</td><td>0.137<br>(0.156)</td><td>0.33<br>(0.606)</td><td>-0.356<br>(0.521)</td><td>0.107<br>(0.068)</td></tr><tr><td>In(UAA)</td><td>0.334<sup>***</sup><br>(0.007)</td><td>0.214<sup>***</sup><br>(0.053)</td><td>0.164<sup>***</sup><br>(0.024)</td><td>0.293<sup>***</sup><br>(0.01)</td><td>0.27<sup>***</sup><br>(0.027)</td><td>0.223<sup>**</sup><br>(0.11)</td><td>-0.681<br>(0.66)</td><td>0.328<sup>***</sup><br>(0.007)</td></tr><tr><td>In(Intermediate)</td><td>0.526<sup>***</sup><br>(0.005)</td><td>0.48<sup>***</sup><br>(0.046)</td><td>0.522<sup>***</sup><br>(0.019)</td><td>0.438<sup>***</sup><br>(0.009)</td><td>0.384<sup>***</sup><br>(0.032)</td><td>0.553<sup>***</sup><br>(0.112)</td><td>1.065<sup>***</sup><br>(0.222)</td><td>0.525<sup>***</sup><br>(0.006)</td></tr><tr><td>In(Hired_Labour)</td><td>-0.022<sup>*</sup><br>(0.012)</td><td>-0.018<br>(0.049)</td><td>-0.045<br>(0.036)</td><td>-0.012<br>(0.019)</td><td>-0.019<br>(0.027)</td><td>-0.056<br>(0.095)</td><td>0.015<br>(0.1)</td><td>-0.018<br>(0.012)</td></tr><tr><td>In(Family_Labour)</td><td>0.071<sup>***</sup><br>(0.005)</td><td>0.018<br>(0.064)</td><td>0.004<br>(0.022)</td><td>0.083<sup>***</sup><br>(0.007)</td><td>0.067<sup>***</sup><br>(0.021)</td><td>0.12<sup>*</sup><br>(0.067)</td><td>0.296<br>(0.287)</td><td>0.067<sup>***</sup><br>(0.005)</td></tr><tr><td>In(Capital)</td><td>0.063<sup>***</sup><br>(0.002)</td><td>0.086<sup>***</sup><br>(0.016)</td><td>0.069<sup>***</sup><br>(0.006)</td><td>0.05<sup>***</sup><br>(0.003)</td><td>0.065<sup>***</sup><br>(0.012)</td><td>-0.066<br>(0.044)</td><td>0.033<br>(0.103)</td><td>0.062<sup>***</sup><br>(0.002)</td></tr><tr><td>SHDI</td><td>-0.096<sup>***</sup><br>(0.025)</td><td>-0.212<sup>***</sup><br>(0.075)</td><td>-0.079<sup>*</sup><br>(0.045)</td><td>0.052<sup>*</sup><br>(0.032)</td><td>-0.35<sup>***</sup><br>(0.069)</td><td>0.226<br>(0.149)</td><td>0.166<br>(0.133)</td><td>-0.09<sup>**</sup><br>(0.025)</td></tr><tr><td>SHDI×SHDI</td><td>0.031<sup>*</sup><br>(0.017)</td><td>0.176<sup>***</sup><br>(0.06)</td><td>0.072<sup>**</sup><br>(0.033)</td><td>-0.066<sup>***</sup><br>(0.022)</td><td>0.161<sup>***</sup><br>(0.044)</td><td>-0.22<sup>**</sup><br>(0.099)</td><td>-0.163<br>(0.128)</td><td>0.033<sup>*</sup><br>(0.017)</td></tr><tr><td>LFA</td><td>-0.076<sup>***</sup><br>(0.009)</td><td>-0.059<sup>**</sup><br>(0.028)</td><td>-0.036<sup>**</sup><br>(0.015)</td><td>-0.079<sup>***</sup><br>(0.01)</td><td>-0.039<sup>**</sup><br>(0.019)</td><td>-0.121<sup>***</sup><br>(0.045)</td><td>-0.236<sup>***</sup><br>(0.086)</td><td>-0.083<sup>***</sup><br>(0.008)</td></tr><tr><td>ECA</td><td>0.016<br>(0.017)</td><td>0.096<br>(0.081)</td><td>-0.035<br>(0.026)</td><td>0.043<sup>**</sup><br>(0.02)</td><td>0.045<br>(0.043)</td><td>-0.133<sup>**</sup><br>(0.066)</td><td>0.409<sup>**</sup><br>(0.195)</td><td>0.018<br>(0.017)</td></tr></tbody><tfoot><tr><td colspan="9" style="text-align: right;">(continued)</td></tr></tfoot></table>
<table><caption>Table 2. (Continued)</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All Output</th><th colspan="4">Economic size in EUR 1,000</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>> 500</th><th>[10; 30]</th><th>> 30</th></tr></thead><tbody><tr><td>Altitude</td><td>-0.023<sup>*</sup><br>(0.013)</td><td>-0.026<br>(0.04)</td><td>0.027<br>(0.02)</td><td>-0.013<br>(0.014)</td><td>-0.076<sup>***</sup><br>(0.028)</td><td>-0.265<sup>***</sup><br>(0.057)</td><td>0.112<br>(0.111)</td><td>-0.027<sup>**</sup><br>(0.012)</td></tr><tr><td>In(UAA) × In(UAA)</td><td>0.212<sup>***</sup><br>(0.012)</td><td>0.22<sup>***</sup><br>(0.046)</td><td>0.102<sup>***</sup><br>(0.037)</td><td>0.198<sup>***</sup><br>(0.017)</td><td>0.126<sup>***</sup><br>(0.03)</td><td>-0.191<sup>**</sup><br>(0.083)</td><td>-0.341<br>(0.361)</td><td>0.17<sup>***</sup><br>(0.017)</td></tr><tr><td>In(Intermediate) × In(Intermediate)</td><td>0.171<sup>***</sup><br>(0.012)</td><td>0.095<sup>***</sup><br>(0.036)</td><td>0.257<sup>***</sup><br>(0.036)</td><td>0.198<sup>***</sup><br>(0.024)</td><td>0.212<sup>***</sup><br>(0.038)</td><td>0.156<sup>*</sup><br>(0.094)</td><td>0.391<sup>***</sup><br>(0.1)</td><td>0.189<sup>***</sup><br>(0.013)</td></tr><tr><td>In(Hired_Labour) × In(Hired_Labour)</td><td>0.018<sup>***</sup><br>(0.003)</td><td>0.025<sup>*</sup><br>(0.013)</td><td>0.029<sup>***</sup><br>(0.009)</td><td>0.015<sup>***</sup><br>(0.005)</td><td>0.013<sup>***</sup><br>(0.006)</td><td>0.027<br>(0.017)</td><td>0.012<br>(0.021)</td><td>0.017<sup>***</sup><br>(0.003)</td></tr><tr><td>In(Family_Labour) × In(Family_Labour)</td><td>0.014<sup>***</sup><br>(0.002)</td><td>0.029<br>(0.035)</td><td>0.036<sup>***</sup><br>(0.009)</td><td>0.018<sup>***</sup><br>(0.004)</td><td>0.007<br>(0.005)</td><td>0.077<sup>*</sup><br>(0.04)</td><td>0.42<sup>*</sup><br>(0.24)</td><td>0.013<sup>***</sup><br>(0.002)</td></tr><tr><td>In(Capital) × In(Capital)</td><td>0.01<sup>***</sup><br>(0.001)</td><td>0.013<sup>***</sup><br>(0.002)</td><td>0.01<sup>***</sup><br>(0.001)</td><td>0.008<sup>***</sup><br>(0.001)</td><td>0.012<sup>***</sup><br>(0.002)</td><td>0.022<sup>***</sup><br>(0.004)</td><td>0.017<sup>***</sup><br>(0.004)</td><td>0.01<sup>***</sup><br>(0.001)</td></tr><tr><td>In(UAA) × In(Intermediate)</td><td>-0.135<sup>***</sup><br>(0.01)</td><td>-0.125<sup>***</sup><br>(0.032)</td><td>-0.133<sup>***</sup><br>(0.025)</td><td>-0.185<sup>***</sup><br>(0.017)</td><td>-0.116<sup>***</sup><br>(0.03)</td><td>0.0003<br>(0.069)</td><td>0.081<br>(0.138)</td><td>-0.148<sup>***</sup><br>(0.012)</td></tr><tr><td>In(UAA) × In(Hired_Labour)</td><td>-0.014<sup>***</sup><br>(0.001)</td><td>-0.012<sup>***</sup><br>(0.005)</td><td>-0.012<sup>***</sup><br>(0.003)</td><td>-0.015<sup>***</sup><br>(0.002)</td><td>-0.007<sup>***</sup><br>(0.003)</td><td>-0.008<br>(0.009)</td><td>-0.018<br>(0.02)</td><td>-0.014<sup>***</sup><br>(0.001)</td></tr><tr><td>In(UAA) × In(Family_Labour)</td><td>-0.027<sup>***</sup><br>(0.01)</td><td>-0.008<br>(0.043)</td><td>-0.178<sup>***</sup><br>(0.031)</td><td>-0.044<sup>***</sup><br>(0.016)</td><td>-0.016<br>(0.023)</td><td>0.05<br>(0.044)</td><td>0.041<br>(0.175)</td><td>-0.002<br>(0.011)</td></tr><tr><td>In(UAA) × In(Capital)</td><td>-0.000006<br>(0.004)</td><td>-0.006<br>(0.009)</td><td>0.016<sup>**</sup><br>(0.008)</td><td>-0.006<br>(0.007)</td><td>-0.027<sup>*</sup><br>(0.015)</td><td>0.071<sup>**</sup><br>(0.033)</td><td>-0.011<br>(0.058)</td><td>0.004<br>(0.004)</td></tr><tr><td>In(Intermediate) × In(Hired_Labour)</td><td>-0.001<br>(0.001)</td><td>0.0001<br>(0.007)</td><td>0.001<br>(0.003)</td><td>0.001<br>(0.002)</td><td>-0.002<br>(0.003)</td><td>-0.029<sup>***</sup><br>(0.007)</td><td>-0.031<sup>**</sup><br>(0.012)</td><td>0.0004<br>(0.001)</td></tr></tbody></table>
<table><caption>Table 2. (Continued)</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All Output</th><th colspan="5">Economic size in EUR 1,000</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>]10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><td>In(Intermediate) × ln(Family_Labour)</td><td>-0.033<sup>***</sup><br>(0.009)</td><td>-0.104<sup>**</sup><br>(0.046)</td><td>0.011<br>(0.036)</td><td>-0.032<sup>**</sup><br>(0.016)</td><td>-0.035<sup>*</sup><br>(0.021)</td><td>-0.127<sup>***</sup><br>(0.048)</td><td>-0.037<br>(0.1)</td><td>-0.038<sup>***</sup><br>(0.009)</td></tr><tr><td>In(Intermediate) × ln(Capital)</td><td>-0.009<sup>**</sup><br>(0.003)</td><td>0.005<br>(0.009)</td><td>-0.029<sup>***</sup><br>(0.009)</td><td>0.003<br>(0.007)</td><td>0.022<br>(0.015)</td><td>0.011<br>(0.03)</td><td>-0.054<sup>***</sup><br>(0.021)</td><td>-0.011<sup>***</sup><br>(0.004)</td></tr><tr><td>In(Hired_Labour) × ln(Family_Labour)</td><td>0.003<sup>**</sup><br>(0.001)</td><td>0.004<br>(0.008)</td><td>0.002<br>(0.003)</td><td>0.001<br>(0.001)</td><td>0.003<br>(0.002)</td><td>0.008<br>(0.006)</td><td>-0.038<sup>*</sup><br>(0.02)</td><td>0.002<sup>*</sup><br>(0.001)</td></tr><tr><td>In(Hired_Labour) × ln(Capital)</td><td>0.001<sup>***</sup><br>(0.0004)</td><td>0.001<br>(0.002)</td><td>0.004<sup>***</sup><br>(0.001)</td><td>0.001<br>(0.001)</td><td>0.00005<br>(0.001)</td><td>0.015<sup>***</sup><br>(0.004)</td><td>0.006<sup>**</sup><br>(0.003)</td><td>0.002<sup>***</sup><br>(0.0005)</td></tr><tr><td>In(Family_Labour) × ln(Capital)</td><td>0.008<sup>***</sup><br>(0.003)</td><td>0.005<br>(0.006)</td><td>0.003<br>(0.007)</td><td>0.007<br>(0.005)</td><td>0.018<sup>*</sup><br>(0.01)</td><td>-0.024<br>(0.026)</td><td>0.024<br>(0.059)</td><td>0.006<sup>*</sup><br>(0.003)</td></tr><tr><td>Constant</td><td>13.195<sup>***</sup><br>(0.05)</td><td>12.898<sup>***</sup><br>(0.203)</td><td>12.838<sup>***</sup><br>(0.144)</td><td>13.15<sup>***</sup><br>(0.075)</td><td>13.592<sup>***</sup><br>(0.117)</td><td>13.042<sup>***</sup><br>(0.424)</td><td>12.36<sup>***</sup><br>(0.723)</td><td>13.208<sup>***</sup><br>(0.051)</td></tr><tr><td>Observations</td><td>19,822</td><td>1,682</td><td>4,711</td><td>9,737</td><td>3,092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>

Standard errors are in parentheses. *** $P < .01$, ** $P < .05$, * $P < .1$.

Note: SHDI—Shannon Diversity Index; ECA—Environmental Constraint Area; LFA—Less Favoured Area. To simplify matters, the 11-year coefficients are not shown.
<table><caption>**Table 3.** Marginal effect of crop diversification on standard gross output</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All Output</th><th colspan="5">Economic size in EUR 1,000</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>[10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><th>SHDI marginal effect</th><td>-0.0512</td><td>0.0009</td><td>0.0208</td><td>-0.0444</td><td>-0.1646</td><td>-</td><td>0.0150</td><td>-0.0419</td></tr><tr><th>Observations</th><td>19,822</td><td>1,682</td><td>4,711</td><td>9,737</td><td>3,092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>
of machinery and labour. These factors can limit the benefits of diversification for larger farms, making it less profitable despite its environmental and risk-reducing advantages.

We analyse the effect of heterogeneity on farm production using site characteristics. As expected, farms in LFAs and at higher altitudes produce less than others. While this result is consistent across farm sizes in LFA, the impact of high altitude on production varies with farm size. Large farms at high altitudes tend to produce less than those at lower altitudes, due to the compounded challenges of altitude and scale. Larger farms typically require more inputs and resources, and environmental constraints at higher altitudes—such as colder temperatures, shorter growing seasons and poorer soil quality—further limit their productivity. In contrast, smaller farms may adapt better to these conditions through more intensive land use or specialized practices. Thus, altitude has a more significant impact on the production capacity of larger farms compared to smaller ones.

## 5.2. Impact of crop diversification on farm performance

The descriptive statistics of farm efficiency are presented in Table 4. For the whole sample, crop efficiency ranges from 0.188 to 0.996, with a mean of 0.791 and a standard deviation of 0.111. The average efficiency score increases with the economic size of the farm.

The estimates of heteroskedastic inefficiency for farms are presented in Table 5. We found that crop diversification has a positive impact on farm efficiency. This aligns with findings from Rahman (2009) and Coelli and Fleming (2004), who also demonstrated efficiency gains from diversification. However, this contrasts with the results of Llewelyn and Williams (1996) and Haji (2007). To answer our second research question, we analyse the relationship between crop diversification and farm efficiency for each farm size. We find that the effect of crop diversification on farm efficiency depends on both the economic and UAA size of the farms. Crop diversification has a positive and significant impact on the largest farms—those with an economic size of over EUR 100,000 and UAA greater than 30 hectares—while it has no significant effect on the efficiency of smaller farms. These results support our hypothesis that crop diversification improves farm efficiency through better resource allocation, risk reduction and sustainable practices. Large farms—those over EUR 100,000 in economic size and 30 hectares—benefit from diversification. For example, a large farm growing wheat, maize and barley can stagger planting and harvesting, making more efficient use of equipment. In contrast, smaller farms may not experience the same efficiency gains due to limited resources. A small farm, for example, might focus on a few crops and rely on intensive management, like intercropping or precise irrigation, to maximize output. While large farms benefit from economies of scale, smaller farms tend to depend on manual labour and specialized techniques to remain efficient. Therefore, the benefits of diversification are more significant for large farms than for small ones.
<table><caption>**Table 4.** Technical efficiency summary statistics</caption><thead><tr><th></th><th>Size</th><th>Obs.</th><th>Mean</th><th>SD</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>All farms</td><td>All</td><td>19,822</td><td>0.791</td><td>0.111</td><td>0.2</td><td>0.996</td></tr><tr><td rowspan="4">Economic size</td><td>25–50</td><td>1,682</td><td>0.784</td><td>0.114</td><td>0.271</td><td>0.989</td></tr><tr><td>50–100</td><td>4,711</td><td>0.798</td><td>0.113</td><td>0.333</td><td>0.994</td></tr><tr><td>100–250</td><td>9,737</td><td>0.814</td><td>0.104</td><td>0.36</td><td>0.996</td></tr><tr><td>250–500</td><td>3,092</td><td>0.85</td><td>0.087</td><td>0.449</td><td>0.993</td></tr><tr><td rowspan="4">UAA size</td><td>&gt; 500</td><td>600</td><td>0.888</td><td>0.106</td><td>0.454</td><td>1</td></tr><tr><td>[10; 30]</td><td>360</td><td>0.788</td><td>0.146</td><td>0.304</td><td>0.987</td></tr><tr><td>&gt; 30</td><td>19,421</td><td>0.794</td><td>0.111</td><td>0.281</td><td>0.996</td></tr></tbody></table>
<table><caption>**Table 5.** Inefficiency variance estimates</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="5">Economic size in EUR 1,000</th><th rowspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th></tr></thead><tbody><tr><td>SHDI</td><td>-0.198<sup>***</sup><br>(0.063)</td><td>-0.007<br>(0.222)</td><td>0.183<br>(0.127)</td><td>-0.012<br>(0.096)</td><td>-0.624<sup>***</sup><br>(0.225)</td><td>-1.111<sup>**</sup><br>(0.537)</td><td>-0.205<br>(0.564)</td><td>-0.108<sup>*</sup><br>(0.064)</td></tr><tr><td>In(Subsides)</td><td>-0.157<sup>***</sup><br>(0.02)</td><td>-0.059<sup>**</sup><br>(0.029)</td><td>-0.206<sup>***</sup><br>(0.05)</td><td>-0.479<sup>***</sup><br>(0.06)</td><td>-0.265<sup>***</sup><br>(0.101)</td><td>0.193<br>(0.129)</td><td>0.01<br>(0.045)</td><td>-0.397<sup>***</sup><br>(0.038)</td></tr><tr><td>Gender</td><td>0.004<br>(0.045)</td><td>-0.082<br>(0.145)</td><td>0.19<sup>**</sup><br>(0.094)</td><td>0.004<br>(0.067)</td><td>0.233<br>(0.164)</td><td>0.067<br>(0.428)</td><td>-0.16<br>(0.354)</td><td>0.047<br>(0.046)</td></tr><tr><td>Age</td><td>0.002<br>(0.002)</td><td>-0.004<br>(0.008)</td><td>0.001<br>(0.004)</td><td>0.003<br>(0.002)</td><td>-0.0004<br>(0.004)</td><td>0.011<br>(0.011)</td><td>-0.007<br>(0.017)</td><td>0.002<br>(0.002)</td></tr><tr><td>General Education</td><td>0.001<br>(0.027)</td><td>0.007<br>(0.09)</td><td>0.067<br>(0.049)</td><td>-0.057<br>(0.038)</td><td>-0.064<br>(0.063)</td><td>0.072<br>(0.204)</td><td>0.167<br>(0.216)</td><td>0.005<br>(0.027)</td></tr><tr><td>Agricultural Education</td><td>-0.102<sup>***</sup><br>(0.024)</td><td>0.012<br>(0.083)</td><td>-0.115<sup>**</sup><br>(0.046)</td><td>-0.03<br>(0.033)</td><td>0.008<br>(0.053)</td><td>-0.068<br>(0.162)</td><td>-0.067<br>(0.195)</td><td>-0.095<sup>***</sup><br>(0.024)</td></tr><tr><td>LFA</td><td>-0.219<sup>***</sup><br>(0.056)</td><td>0.033<br>(0.219)</td><td>-0.001<br>(0.111)</td><td>-0.23<sup>***</sup><br>(0.076)</td><td>0.062<br>(0.19)</td><td>-1.186<br>(1.085)</td><td>-2.766<br>(2.03)</td><td>-0.256<sup>***</sup><br>(0.056)</td></tr><tr><td>ECA</td><td>0.201<br>(0.145)</td><td>0.671<br>(0.483)</td><td>0.051<br>(0.28)</td><td>0.416<sup>**</sup><br>(0.179)</td><td>0.231<br>(0.482)</td><td>-2.48<br>(3.542)</td><td>1.375<br>(1.354)</td><td>0.236<br>(0.145)</td></tr><tr><td>Altitude</td><td>0.118<br>(0.116)</td><td>-0.051<br>(0.326)</td><td>0.046<br>(0.193)</td><td>0.168<br>(0.154)</td><td>0.164<br>(0.343)</td><td>-36.403<br>(0)</td><td>1.321<br>(2.113)</td><td>0.099<br>(0.115)</td></tr><tr><td>Constant</td><td>-2.277<sup>***</sup><br>(0.162)</td><td>-2.721<sup>***</sup><br>(0.622)</td><td>-3.39<sup>***</sup><br>(0.355)</td><td>-2.761<sup>***</sup><br>(0.234)</td><td>-2.287<sup>***</sup><br>(0.527)</td><td>-23.569<br>(0)</td><td>-2.283<sup>*</sup><br>(1.269)</td><td>-2.454<sup>***</sup><br>(0.166)</td></tr><tr><td>Observations</td><td>19,822</td><td>1,682</td><td>4,711</td><td>9,737</td><td>3,092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>

Standard errors are in parentheses. *** P < .01, ** P < .05, * P < .1.

Note: SHDI—Shannon Diversity Index; ECA—Environmental Constraint Area; LFA—Less Favoured Area. To simplify matters, the 11-year coefficients are not shown.
We also analyse the impact of our control variables on farm efficiency, focusing particularly on subsidies. Our results show that subsidies have a positive effect on the efficiency of the largest UAA farms. Interestingly, unlike the findings of Staniszewski and Borychowski (2020), we observe that subsidies significantly enhance farm efficiency across all economic sizes, not just large farms. This broader impact can be explained by the fact that our study focuses solely on arable farms, which may have more uniform needs and benefit more directly from subsidies than farms in other sectors, such as livestock or mixed farming. For instance, small arable farms can use subsidies to adopt more efficient equipment or precision farming techniques, enhancing productivity even with limited resources. Larger farms, meanwhile, benefit by scaling up and investing in advanced technology. In contrast to mixed or livestock farms, where subsidies may serve diverse purposes, arable farms tend to use them more directly for efficiency improvements. Thus, while previous research suggests that subsidies mainly benefit larger farms, our study highlights that, for arable farms, subsidies can enhance efficiency across all farm sizes, supporting better resource allocation and modernization.

For farmer characteristics, our analysis reveals that general education does not significantly impact farm efficiency, whereas agricultural training does have a positive effect. This suggests that to enhance farm efficiency, policymakers should prioritize improving farmers’ access to specialized agricultural training, which provides practical skills and knowledge directly applicable to farming practices.

In contrast to Baráth, Fertő and Bojnec (2018), who found a small and statistically insignificant difference in efficiency between farms in LFAs and those outside these areas, our study indicates that farms in LFA are more efficient than those in non-LFA. This discrepancy may be attributed to the specific challenges and conditions faced by LFA. Farmers in these areas often adapt by employing tailored processes and technologies that are well-suited to their unique production environments. For example, LFA may require innovative soil management techniques or specialized irrigation systems due to their less favourable conditions. These adaptations can lead to more efficient use of resources and improved productivity.

# 6. Robustness checks

To ensure the robustness of our results, we performed a set of robustness checks highlighted in this section, including verifying regularity conditions, modifying the functional form and combining farm size classes.

## 6.1. Regularity conditions

The production function must satisfy certain regularity conditions such as monotonicity and concavity (Chambers, 1988; Kumbhakar, Wang and Horn-castle, 2015). In this study, we opted for a parametric approach due to its convenience in facilitating statistical comparisons. While advantageous, this method requires the specification of a functional form, which introduces the risk of violating regularity conditions (Ang et al., 2018).
Several factors may contribute to such violations. Firstly, the aggregation of certain inputs, such as intermediate consumption, may obscure the distinct productivity effects of individual inputs. For instance, the combined use of fertilizers and pesticides could generate synergies, leading to non-concave input-output relationships. Secondly, technological advancements and variations in farm management practices may result in non-standard returns to scale, particularly in capital-intensive farms. Lastly, the functional form employed in our estimation may impose unnecessary restrictions on the flexibility of input interactions, limiting its ability to capture the true underlying relationships.

In our analysis, we examined the eigenvalues of the Hessian matrix and found that all were negative. This indicates that the Hessian matrix is negative definite and confirms that the function is concave. Consequently, our model satisfies the regularity conditions, ensuring the robustness of our findings.<fnref n="8" />

## 6.2. Using a different production function

Farm efficiency is closely related to the choice of production function. In the primary analysis, we use the translog production function, as it serves as a second-order Taylor approximation for any unknown function (Coelli et al., 2005) and helps to avoid misspecification of the production function. However, the translog function often results in significant multicollinearity. To address these issues, we applied a Cobb-Douglas production function. The results, presented in Table A.7 in Appendix 3, are consistent with the translog estimates.

## 6.3. Combining farm size classes

In the previous section, estimates for two farm size classes did not converge. The first UAA size class ([0, 10]) has only 41 observations, making it impossible to estimate the stochastic frontier for this group. Additionally, the largest farm economic size (> EUR 500,000) did not converge, so its results could not be interpreted. To include all farms in our estimation, we combined certain size classes. For the economic size of farms (in EUR 1,000), we merged the first two classes and the last two classes, resulting in three categories: [25–100], [100–250] and greater than 250. For UAA size (in hectares), we created three classes: less than 100, [100, 200], and greater than 200. These classifications are arbitrary, but they allow us to confirm or reject our initial findings. The estimates presented in Table A.8 in Appendix 4 are consistent with the translog findings. This confirms that excluding the non-converged farm size classes did not significantly impact the results.

## 7. Conclusion

This study provides valuable insights into the complex relationship between crop diversification, farm productivity and efficiency, with a particular focus

<footnote n="8">8 Many thanks to Mustafa Karakaplan for the fruitful exchanges about regularity conditions in his stochastic panel frontier with endogeneity approach.</footnote>
on farm size. The results show that while crop diversification offers sev-
eral environmental benefits—such as improved soil health, risk reduction and
resilience against market and climate volatility—its impact on farm income
and productivity varies by farm size. Smaller farms tend to benefit from diver-
sification, whereas larger farms often experience income reductions due to
the complexity and cost of managing diverse crops. However, crop diversi-
fication enhances farm efficiency, especially for larger farms. By spreading
resources across different crops, these farms achieve better land use, more
efficient machinery usage and improved risk management. In contrast, smaller
farms do not experience significant efficiency gains, possibly due to their lim-
ited capacity to leverage economies of scale. The analysis also shows that
farms in LFAs tend to be more efficient than those in non-LFA regions, despite
adverse environmental conditions like poorer soils or shorter seasons. Farm-
ers in these areas have adapted through specialized techniques and innovative
land management practices, highlighting the importance of geographic and
environmental factors in determining farm efficiency. Another possible expla-
nation is that the lower productivity potential of LFA regions may create more
challenging conditions for profitability, allowing only the most efficient farms
to remain in the market. Moreover, agricultural subsidies play a crucial role
in enhancing efficiency across all farm sizes, particularly by enabling invest-
ment in advanced technologies, infrastructure and improved farming practices.
Additionally, specialized agricultural training has a significant positive effect
on farm efficiency, with farmers who have such education outperforming those
with general education.

These findings suggest that a ‘one-size-fits-all’ approach to crop diversification may be ineffective. While smaller farms gain income and resilience from diversification, larger farms face potential income reductions. This highlights the need for diverse strategies tailored to farm size. Larger farms do benefit from increased efficiency, and policies promoting diversification could enhance their resource allocation and productivity. Overall, differentiated policy interventions are required to address the varying needs of farm sizes, regions and educational levels, optimizing efficiency and sustainability.

Lastly, the current functional form used in our estimation may impose
unnecessary restrictions on the flexibility of input interactions. Future research
could explore more flexible functional forms or alternative non-parametric
methods to better capture the complexities of agricultural production and
validate these findings.
## Acknowledgements

Access to some confidential data, on which this work is based, has been made possible within a secure environment offered by CASD – Centre d’Accès Sécurisé aux Données (Ref. 10.34724/CASD).

## Funding

This study was supported by the wildE Horizon Europe (GAP- 101081251) projects.

## Appendix 1. Presentation of some test results

<table><caption>**Table A.1.** Pairwise correlation test for multicollinearity of site-specific variables</caption><thead><tr><th>Variables</th><th>LFA</th><th>ECA</th><th>Altitude</th></tr></thead><tbody><tr><td>LFA</td><td>1.000</td><td></td><td></td></tr><tr><td>ECA</td><td>0.136</td><td>1.000</td><td></td></tr><tr><td>Altitude</td><td>0.291</td><td>0.132</td><td>1.000</td></tr></tbody></table>
<table><caption>**Table A.2.** Hausman test to compare Cobb-Douglas and translog estimates</caption><thead><tr><th rowspan="2"></th><th rowspan="2">(b) Translog</th><th colspan="3">Coefficients</th></tr><tr><th>(B) Cobb-Douglas</th><th>(b-B) Difference</th><th>sqrt(diag(V_b-V_B)) Std. Error</th></tr></thead><tbody><tr><td>D<sub>H</sub></td><td>0.1326687</td><td>-0.3085025</td><td>0.4411712</td><td>0.0663863</td></tr><tr><td>In(UAA)</td><td>0.3341515</td><td>0.1905171</td><td>0.1436344</td><td>0.0048655</td></tr><tr><td>In(Intermediate)</td><td>0.5256922</td><td>0.624815</td><td>-0.0991227</td><td>0.0023323</td></tr><tr><td>In(Hired_Labour)</td><td>-0.022769</td><td>0.0546741</td><td>-0.076951</td><td>0.0116038</td></tr><tr><td>In(Family_Labour)</td><td>0.071174</td><td>0.0558798</td><td>0.0152943</td><td>0.0025666</td></tr><tr><td>In(Capital)</td><td>0.0630575</td><td>0.0306318</td><td>0.0324258</td><td>0.0017703</td></tr><tr><td>SHDI</td><td>-0.0958651</td><td>0.107187</td><td>0.0113219</td><td>0.0232063</td></tr><tr><td>LFA</td><td>-0.0758371</td><td>-0.0509206</td><td>-0.0249165</td><td>.</td></tr><tr><td>ECA</td><td>0.0161459</td><td>0.0204565</td><td>0.00366024</td><td>.</td></tr><tr><td>Altitude</td><td>-0.0228384</td><td>0.0419471</td><td>0.0191087</td><td>.</td></tr><tr><td colspan="5">Time variables are excluded.</td></tr><tr><td colspan="5">b = Consistent under H0 and Ha; obtained from xtsfkk.</td></tr><tr><td colspan="5">B = Inconsistent under Ha, efficient under H0; obtained from xtsfkk.</td></tr><tr><td colspan="5">Test of H0: Difference in coefficients not systematic</td></tr><tr><td colspan="5">chi2(22) = (b-B)'[V_b-V_B]A(-1)](b-B) = 1960.86</td></tr><tr><td colspan="5">Prob > chi2 = 0.0000</td></tr><tr><td colspan="5">(V_b-V_B is not positive definite)</td></tr></tbody></table>
<table><caption>**Table A.3.** Endogeneity test for hired labour</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="5">Economic size in thousand euros</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>[10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><th>eta (Hired labour)</th><td>-0.074***<br>(0.013)</td><td>-0.139*<br>(0.072)</td><td>-0.122***<br>(0.043)</td><td>-0.095***<br>(0.02)</td><td>-0.068**<br>(0.031)</td><td>-0.206*<br>(0.11)</td><td>-0.418***<br>(0.151)</td><td>-0.078***<br>(0.013)</td></tr><tr><th>Observations</th><td>19,822</td><td>1,682</td><td>4,711</td><td>9,737</td><td>3,092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>
eta Endogeneity Test

Ho: Correction for endogeneity is not necessary.

Ha: There is endogeneity in the model and correction is needed.

Eta (hired labour) = 0

$$
\chi^2 = 32.71
$$

$$
\text{Prob} > \chi^2 = 0.0000
$$

Result: Reject Ho at 0.1% level.

Following Eq. (16), endogeneity exists if η is jointly significant. If η is not jointly signifi-
cant, the correction term is not necessary and efficiency can be estimated using conventional
stochastic frontier models. For example, the complete endogeneity test for all observations
is presented as follows:
<table><caption>**Table A.4.** Test of instruments</caption><thead><tr><th rowspan="2">Hired labour</th><th rowspan="2">All farms</th><th colspan="6">Economic size in thousand euros</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>]10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><td>Labour cost</td><td>0.226<sup>***</sup><br>(0.004)</td><td>0.396<sup>***</sup><br>(0.014)</td><td>0.289<sup>***</sup><br>(0.008)</td><td>0.164<sup>***</sup><br>(0.005)</td><td>0.224<sup>***</sup><br>(0.009)</td><td>0.076<sup>***</sup><br>(0.012)</td><td>0.57<sup>***</sup><br>(0.025)</td><td>0.222<sup>***</sup><br>(0.004)</td></tr><tr><td>Social security cost</td><td>0.018<sup>***</sup><br>(0.002)</td><td>0.069<sup>***</sup><br>(0.008)</td><td>-0.013<sup>***</sup><br>(0.004)</td><td>0.021<sup>***</sup><br>(0.002)</td><td>0.016<sup>***</sup><br>(0.003)</td><td>0.043<sup>***</sup><br>(0.006)</td><td>-0.026<sup>**</sup><br>(0.012)</td><td>0.017<sup>***</sup><br>(0.002)</td></tr><tr><td>Constant</td><td>-2.644<sup>***</sup><br>(0.021)</td><td>-1.803<sup>***</sup><br>(0.069)</td><td>-2.535<sup>***</sup><br>(0.039)</td><td>-2.879<sup>***</sup><br>(0.03)</td><td>-2.635<sup>***</sup><br>(0.063)</td><td>-3.277<sup>***</sup><br>(0.149)</td><td>-0.614<sup>**</sup><br>(0.292)</td><td>-2.68<sup>***</sup><br>(0.022)</td></tr><tr><td>Observations</td><td>19,822</td><td>1,682</td><td>4,711</td><td>9,737</td><td>3,092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>

Standard errors are in parentheses. ***P < .01, **P < .05, *P < .1.
**Appendix 2. Impact of CAP 2013 policy on crop diversification**

As the 2013 CAP reform came into force in 2015, we compare the level of crop diversification before and after 2015 (Table A.5). There are 49.22 per cent and 50.78 per cent observations before and after 2015, respectively. The average level of crop diversification is 1.45 before 2015 and 1.52 after 2015. The Student's t-test for comparing means shows that farms are more diversified after 2015 than before. This result remains stable according to the economic size of the farm. However, considering the UAA size, small farms ([0, 10 ha])<fnref n="9" /> diversified less than medium ([10 ha; 30 ha]) and large ([30 ha; +∞ ha]) farms after the 2013 CAP. Medium and large farms have diversified more, with a higher proportion of medium farms. These results are consistent with Sauquet (2022), whose econometric analysis of the impact of the 2013 CAP on the crop diversification showed that this policy increased crop diversification.

<footnote n="9">9 This result should be treated with caution as there are only 41 observations with a UAA of 10 ha or less.</footnote>
<table><caption>**Table A.5.** Comparison of the level of crop diversification before and after the 2013 CAP</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="4">Economic size in thousand euros</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>[0; 10]</th><th>[10; 30]</th><th>> 30</th></tr></thead><tbody><tr><td>Before 2015 (A)</td><td>1.469<br>(0.359)</td><td>1.265<br>(0.408)</td><td>1.422<br>(0.359)</td><td>1.499<br>(0.332)</td><td>1.605<br>(0.347)</td><td>1.523<br>(0.310)</td><td>0.905<br>(0.657)</td><td>0.996<br>(0.448)</td><td>1.479<br>(0.349)</td></tr><tr><td>After 2015 (B)</td><td>1.526<br>(0.332)</td><td>1.298<br>(0.335)</td><td>1.451<br>(0.344)</td><td>1.551<br>(0.318)</td><td>1.620<br>(0.323)</td><td>1.593<br>(0.316)</td><td>0.633<br>(0.460)</td><td>1.098<br>(0.359)</td><td>1.535<br>(0.323)</td></tr><tr><td>Difference (A-B)</td><td>-0.057<sup>***</sup></td><td>-0.033<sup>*</sup></td><td>-0.029<sup>***</sup></td><td>-0.052<sup>***</sup></td><td>-0.015<sup>***</sup></td><td>-0.069<sup>***</sup></td><td>0.272<sup>*</sup></td><td>-0.102<sup>***</sup></td><td>-0.056<sup>***</sup></td></tr><tr><td>Observations</td><td>19,808</td><td>1,682</td><td>4,710</td><td>9,727</td><td>3,089</td><td>600</td><td>41</td><td>358</td><td>19,407</td></tr></tbody></table>

Standard deviations are in parentheses. ***$P<.01$, **$P<.05$, *$P<.1$.
It should be noted that we are not analysing the actual implementation of the 2013 CAP. In other words, we are not checking whether diversifying farms are complying with the different land allocations. In fact, the measure sets different requirements for three different farm size categories. Farms with less than 10 ha of arable land are exempt. Farms with 10–30 ha of arable land must grow at least two different crops, with the main crop not exceeding 75 per cent of the total arable area of the farm. Farms with more than 30 ha of arable land must grow at least three different crops, with the main crop covering no more than 75 per cent of the farm’s arable land and the two largest crops together covering no more than 95 per cent of the farm’s arable land.
Appendix 3. Cobb-Douglas estimates

<table><caption>Table A.6. Cobb-Douglas stochastic production frontier model estimates</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="5">Economic size in thousand euros</th><th colspan="2">UAA size in ha</th></tr><tr><th>25-50</th><th>50-100</th><th>100-250</th><th>250-500</th><th>&gt; 500</th><th>[10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><td>D<sub>hl</sub></td><td>-0.309<sup>***</sup><br>(0.013)</td><td>-0.471<sup>***</sup><br>(0.064)</td><td>-0.448<sup>***</sup><br>(0.034)</td><td>-0.281<sup>***</sup><br>(0.017)</td><td>-0.21<sup>***</sup><br>(0.027)</td><td>-0.425<br>(0)</td><td>-0.588<sup>***</sup><br>(0.13)</td><td>-0.309<sup>***</sup><br>(0.013)</td></tr><tr><td>In(UAA)</td><td>0.191<sup>***</sup><br>(0.005)</td><td>0.054<sup>***</sup><br>(0.02)</td><td>0.101<sup>***</sup><br>(0.013)</td><td>0.15<sup>***</sup><br>(0.008)</td><td>0.164<sup>***</sup><br>(0.015)</td><td>0.257<br>(0)</td><td>-0.059<br>(0.066)</td><td>0.257<sup>***</sup><br>(0.006)</td></tr><tr><td>In(Intermediate)</td><td>0.625<sup>***</sup><br>(0.005)</td><td>0.617<sup>***</sup><br>(0.017)</td><td>0.543<sup>***</sup><br>(0.012)</td><td>0.519<sup>***</sup><br>(0.007)</td><td>0.565<sup>***</sup><br>(0.012)</td><td>0.66<br>(0)</td><td>0.624<sup>***</sup><br>(0.028)</td><td>0.606<sup>***</sup><br>(0.005)</td></tr><tr><td>In(Hired_Labour)</td><td>0.055<sup>***</sup><br>(0.002)</td><td>0.103<sup>***</sup><br>(0.009)</td><td>0.083<sup>***</sup><br>(0.005)</td><td>0.049<sup>***</sup><br>(0.002)</td><td>0.037<sup>***</sup><br>(0.004)</td><td>0.052<br>(0)</td><td>0.114<sup>***</sup><br>(0.018)</td><td>0.054<sup>***</sup><br>(0.002)</td></tr><tr><td>In(Family_Labour)</td><td>0.056<sup>***</sup><br>(0.004)</td><td>0.105<sup>***</sup><br>(0.022)</td><td>0.06<sup>***</sup><br>(0.011)</td><td>0.063<sup>***</sup><br>(0.006)</td><td>0.054<sup>***</sup><br>(0.007)</td><td>0.001<br>(0)</td><td>0.208<sup>***</sup><br>(0.056)</td><td>0.048<sup>***</sup><br>(0.004)</td></tr><tr><td>In(Capital)</td><td>0.031<sup>***</sup><br>(0.001)</td><td>0.015<sup>***</sup><br>(0.004)</td><td>0.03<sup>***</sup><br>(0.003)</td><td>0.039<sup>***</sup><br>(0.002)</td><td>0.038<sup>***</sup><br>(0.003)</td><td>0.029<br>(0)</td><td>0.01<br>(0.007)</td><td>0.031<sup>***</sup><br>(0.002)</td></tr><tr><td>SHDI</td><td>-0.107<sup>***</sup><br>(0.009)</td><td>-0.013<br>(0.028)</td><td>0.01<br>(0.016)</td><td>-0.072<sup>***</sup><br>(0.012)</td><td>-0.17<sup>***</sup><br>(0.021)</td><td>-0.378<br>(0)</td><td>0.083<br>(0.075)</td><td>-0.079<sup>***</sup><br>(0.009)</td></tr><tr><td>LFA</td><td>-0.051<sup>***</sup><br>(0.009)</td><td>-0.018<br>(0.034)</td><td>-0.014<br>(0.017)</td><td>-0.074<sup>***</sup><br>(0.01)</td><td>-0.03<br>(0.021)</td><td>-0.024<br>(0)</td><td>-0.159<sup>*</sup><br>(0.081)</td><td>-0.08<sup>***</sup><br>(0.009)</td></tr><tr><td>ECA</td><td>-0.02<br>(0.019)</td><td>0.285<sup>***</sup><br>(0.078)</td><td>-0.093<sup>***</sup><br>(0.026)</td><td>0.039<br>(0.024)</td><td>0.081<br>(0.061)</td><td>-0.206<br>(0)</td><td>0.44<sup>***</sup><br>(0.168)</td><td>-0.016<br>(0.017)</td></tr><tr><td>Altitude</td><td>-0.042<sup>***</sup><br>(0.014)</td><td>-0.068<br>(0.044)</td><td>0.054<sup>***</sup><br>(0.023)</td><td>-0.018<br>(0.015)</td><td>-0.073<sup>**</sup><br>(0.031)</td><td>-0.337<br>(0)</td><td>0.092<br>(0.11)</td><td>-0.053<sup>***</sup><br>(0.012)</td></tr><tr><td>Constant</td><td>13.639<sup>***</sup><br>(0.017)</td><td>13.181<sup>***</sup><br>(0.06)</td><td>13.286<sup>***</sup><br>(0.033)</td><td>13.566<sup>***</sup><br>(0.021)</td><td>13.776<sup>***</sup><br>(0.041)</td><td>14.303<br>(0)</td><td>13.058<sup>***</sup><br>(0.17)</td><td>13.577<sup>***</sup><br>(0.017)</td></tr><tr><td>Observations</td><td>19,822</td><td>1682</td><td>4711</td><td>9737</td><td>3092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>

Standard errors are in parentheses. *p < 0.05, **p < 0.10, ***p < 0.01.
<table><caption>Table A.7. Cobb-Douglas inefficiency variance estimates</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="5">Economic size in thousand euros</th><th colspan="2">UAA size in ha</th></tr><tr><th>25–50</th><th>50–100</th><th>100–250</th><th>250–500</th><th>&gt; 500</th><th>[10; 30]</th><th>&gt; 30</th></tr></thead><tbody><tr><td>SHDI</td><td>-0.458<sup>***</sup><br>(0.054)</td><td>-0.101<br>(0.183)</td><td>0.056<br>(0.123)</td><td>-0.228<sup>**</sup><br>(0.095)</td><td>-1.019<sup>***</sup><br>(0.205)</td><td>-2.692<br>(0)</td><td>0.529<br>(0.476)</td><td>-0.32<sup>***</sup><br>(0.059)</td></tr><tr><td>In(Subsides)</td><td>-0.39<sup>***</sup><br>(0.033)</td><td>-0.067<br>(0.042)</td><td>-0.342<sup>***</sup><br>(0.074)</td><td>-0.626<sup>***</sup><br>(0.054)</td><td>-0.322<sup>***</sup><br>(0.099)</td><td>0.134<br>(0)</td><td>0.029<br>(0.035)</td><td>-0.466<sup>***</sup><br>(0.037)</td></tr><tr><td>Gender</td><td>0.009<br>(0.039)</td><td>-0.18<br>(0.129)</td><td>0.136<br>(0.089)</td><td>0.001<br>(0.063)</td><td>0.129<br>(0.154)</td><td>0.276<br>(0)</td><td>-0.171<br>(0.246)</td><td>0.043<br>(0.042)</td></tr><tr><td>Age</td><td>0.003<sup>*</sup><br>(0.002)</td><td>0.001<br>(0.007)</td><td>0.002<br>(0.004)</td><td>0.002<br>(0.002)</td><td>0.001<br>(0.004)</td><td>-0.003<br>(0)</td><td>0.013<br>(0.014)</td><td>0.002<br>(0.002)</td></tr><tr><td>General Education</td><td>0.004<br>(0.026)</td><td>-0.043<br>(0.085)</td><td>0.05<br>(0.048)</td><td>-0.051<br>(0.038)</td><td>-0.056<br>(0.062)</td><td>0.213<br>(0)</td><td>0.031<br>(0.185)</td><td>0.011<br>(0.026)</td></tr><tr><td>Agricultural Education</td><td>-0.096<sup>***</sup><br>(0.022)</td><td>0.001<br>(0.076)</td><td>-0.106<sup>***</sup><br>(0.045)</td><td>-0.04<br>(0.033)</td><td>0.003<br>(0.052)</td><td>-0.182<br>(0)</td><td>0.006<br>(0.16)</td><td>-0.091<sup>***</sup><br>(0.023)</td></tr><tr><td>LFA</td><td>-0.106<sup>**</sup><br>(0.052)</td><td>0.183<br>(0.22)</td><td>0.052<br>(0.116)</td><td>-0.252<sup>***</sup><br>(0.078)</td><td>-0.074<br>(0.214)</td><td>0.385<br>(0)</td><td>-1.32<br>(0.871)</td><td>-0.24<sup>***</sup><br>(0.054)</td></tr><tr><td>ECA</td><td>-0.014<br>(0.149)</td><td>1.167<sup>***</sup><br>(0.402)</td><td>-0.406<br>(0.292)</td><td>0.41<sup>***</sup><br>(0.193)</td><td>0.469<br>(0.527)</td><td>-2575.239<br>(0)</td><td>0.616<br>(1.178)</td><td>0.013<br>(0.146)</td></tr><tr><td>Altitude</td><td>-0.062<br>(0.113)</td><td>-0.487<br>(0.342)</td><td>0.142<br>(0.197)</td><td>0.073<br>(0.155)</td><td>-0.087<br>(0.363)</td><td>-2.974<br>(0)</td><td>0.681<br>(1.042)</td><td>-0.005<br>(0.114)</td></tr><tr><td>Constant</td><td>-1.545<sup>***</sup><br>(0.146)</td><td>-2.669<sup>***</sup><br>(0.592)</td><td>-3.043<sup>***</sup><br>(0.347)</td><td>-2.133<sup>***</sup><br>(0.226)</td><td>-1.35<sup>***</sup><br>(0.505)</td><td>1.71<br>(0)</td><td>-2.933<sup>***</sup><br>(1.163)</td><td>-1.902<sup>***</sup><br>(0.157)</td></tr><tr><td>Observations</td><td>19,822</td><td>1682</td><td>4711</td><td>9737</td><td>3092</td><td>600</td><td>360</td><td>19,421</td></tr></tbody></table>

Standard errors are in parentheses. ***P<.01, **P<.05, *P<.1.
Appendix 4. Reclassified farm size estimates

<table><caption>Table A.8. Stochastic production frontier model estimates with reclassified farm size</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="3">Economic size in thousand euros</th><th colspan="3">UAA size in ha</th></tr><tr><th>[25-100]</th><th>[100-250]</th><th>&gt; 250</th><th>[0; 100]</th><th>[100; 200]</th><th>&gt; 200</th></tr></thead><tbody><tr><td>D<sub>hl</sub></td><td>0.133<sup>*</sup><br>(0.068)</td><td>0.21<br>(0.163)</td><td>0.078<br>(0.107)</td><td>0.088<br>(0.133)</td><td>0.429<sup>***</sup><br>(0.106)</td><td>0.158<br>(0.108)</td><td>-0.238<sup>*</sup><br>(0.135)</td></tr><tr><td>In(UAA)</td><td>0.334<sup>***</sup><br>(0.007)</td><td>0.241<sup>***</sup><br>(0.021)</td><td>0.293<sup>***</sup><br>(0.01)</td><td>0.256<sup>***</sup><br>(0.025)</td><td>0.354<sup>***</sup><br>(0.029)</td><td>0.339<sup>***</sup><br>(0.033)</td><td>0.674<sup>***</sup><br>(0.072)</td></tr><tr><td>In(Intermediate)</td><td>0.526<sup>***</sup><br>(0.005)</td><td>0.51<sup>***</sup><br>(0.017)</td><td>0.438<sup>***</sup><br>(0.009)</td><td>0.408<sup>***</sup><br>(0.026)</td><td>0.536<sup>***</sup><br>(0.016)</td><td>0.473<sup>***</sup><br>(0.01)</td><td>0.434<sup>***</sup><br>(0.028)</td></tr><tr><td>In(Hired_Labour)</td><td>-0.022<sup>*</sup><br>(0.012)</td><td>-0.039<br>(0.029)</td><td>-0.012<br>(0.019)</td><td>-0.01<br>(0.023)</td><td>-0.086<sup>***</sup><br>(0.019)</td><td>-0.025<br>(0.019)</td><td>0.044<sup>*</sup><br>(0.023)</td></tr><tr><td>In(Family_Labour)</td><td>0.071<sup>***</sup><br>(0.005)</td><td>0.01<br>(0.021)</td><td>0.083<sup>***</sup><br>(0.007)</td><td>0.093<sup>***</sup><br>(0.018)</td><td>0.052<sup>***</sup><br>(0.018)</td><td>0.062<sup>***</sup><br>(0.011)</td><td>0.072<sup>***</sup><br>(0.026)</td></tr><tr><td>In(Capital)</td><td>0.063<sup>***</sup><br>(0.002)</td><td>0.074<sup>***</sup><br>(0.005)</td><td>0.05<sup>***</sup><br>(0.003)</td><td>0.068<sup>***</sup><br>(0.012)</td><td>0.065<sup>***</sup><br>(0.005)</td><td>0.056<sup>***</sup><br>(0.004)</td><td>0.046<sup>***</sup><br>(0.016)</td></tr><tr><td>SHDI</td><td>-0.096<sup>***</sup><br>(0.025)</td><td>-0.114<sup>***</sup><br>(0.04)</td><td>0.052<sup>*</sup><br>(0.032)</td><td>-0.366<sup>***</sup><br>(0.073)</td><td>-0.09<sup>***</sup><br>(0.038)</td><td>-0.116<sup>***</sup><br>(0.041)</td><td>-0.304<sup>***</sup><br>(0.066)</td></tr><tr><td>SHDI × SHDI</td><td>0.031<sup>*</sup><br>(0.017)</td><td>0.097<sup>***</sup><br>(0.029)</td><td>-0.066<sup>***</sup><br>(0.022)</td><td>0.133<sup>***</sup><br>(0.045)</td><td>0.055<sup>**</sup><br>(0.028)</td><td>0.022<br>(0.026)</td><td>0.121<sup>***</sup><br>(0.042)</td></tr><tr><td>LFA</td><td>-0.076<sup>***</sup><br>(0.009)</td><td>-0.057<sup>***</sup><br>(0.014)</td><td>-0.079<sup>***</sup><br>(0.01)</td><td>-0.056<sup>***</sup><br>(0.02)</td><td>-0.085<sup>***</sup><br>(0.015)</td><td>-0.097<sup>***</sup><br>(0.012)</td><td>-0.076<sup>***</sup><br>(0.015)</td></tr><tr><td>ECA</td><td>0.016<br>(0.017)</td><td>-0.019<br>(0.026)</td><td>0.043<sup>**</sup><br>(0.02)</td><td>-0.000<br>(0.037)</td><td>0.091<sup>**</sup><br>(0.041)</td><td>-0.003<br>(0.022)</td><td>-0.016<br>(0.029)</td></tr></tbody><tfoot><tr><td colspan="8" style="text-align: right;">(continued)</td></tr></tfoot></table>
<table><caption>**Table A.8. (Continued)**</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="3">Economic size in thousand euros</th><th colspan="3">UAA size in ha</th></tr><tr><th>[25-100]</th><th>[100-250]</th><th>&gt; 250</th><th>[0; 100]</th><th>[00; 200]</th><th>&gt; 200</th></tr></thead><tbody><tr><td>Altitude</td><td>-0.023<sup>*</sup><br>(0.013)</td><td>0.024<br>(0.02)</td><td>-0.013<br>(0.014)</td><td>-0.117<sup>***</sup><br>(0.028)</td><td>0.012<br>(0.022)</td><td>-0.044<sup>***</sup><br>(0.016)</td><td>-0.074<sup>***</sup><br>(0.024)</td></tr><tr><td>In(UAA) × In(UAA)</td><td>0.212<sup>***</sup><br>(0.012)</td><td>0.175<sup>***</sup><br>(0.025)</td><td>0.198<sup>***</sup><br>(0.017)</td><td>0.117<sup>***</sup><br>(0.027)</td><td>0.235<sup>***</sup><br>(0.029)</td><td>-0.078<br>(0.166)</td><td>-0.268<br>(0.077)</td></tr><tr><td>In(Intermediate) × In(Intermediate)</td><td>0.171<sup>***</sup><br>(0.012)</td><td>0.149<sup>***</sup><br>(0.024)</td><td>0.198<sup>***</sup><br>(0.024)</td><td>0.241<sup>***</sup><br>(0.03)</td><td>0.123<sup>***</sup><br>(0.021)</td><td>0.181<sup>***</sup><br>(0.02)</td><td>0.27<sup>***</sup><br>(0.027)</td></tr><tr><td>In(Hired_Labour) × In(Hired_Labour)</td><td>0.018<sup>***</sup><br>(0.003)</td><td>0.028<sup>***</sup><br>(0.008)</td><td>0.015<sup>***</sup><br>(0.005)</td><td>0.013<sup>***</sup><br>(0.005)</td><td>0.039<sup>***</sup><br>(0.005)</td><td>0.018<sup>***</sup><br>(0.005)</td><td>-0.0004<br>(0.005)</td></tr><tr><td>In(Family_Labour) × In(Family_Labour)</td><td>0.014<sup>***</sup><br>(0.002)</td><td>0.029<sup>***</sup><br>(0.006)</td><td>0.018<sup>***</sup><br>(0.004)</td><td>0.001<br>(0.004)</td><td>0.038<sup>***</sup><br>(0.006)</td><td>0.015<sup>***</sup><br>(0.005)</td><td>0.007<br>(0.005)</td></tr><tr><td>In(Capital) × In(Capital)</td><td>0.01<sup>***</sup><br>(0.001)</td><td>0.011<sup>***</sup><br>(0.001)</td><td>0.008<sup>***</sup><br>(0.001)</td><td>0.012<sup>***</sup><br>(0.002)</td><td>0.01<sup>***</sup><br>(0.001)</td><td>0.008<sup>***</sup><br>(0.001)</td><td>0.014<sup>***</sup><br>(0.002)</td></tr><tr><td>In(UAA) × In(Intermediate)</td><td>-0.135<sup>***</sup><br>(0.01)</td><td>-0.125<sup>***</sup><br>(0.018)</td><td>-0.185<sup>***</sup><br>(0.017)</td><td>-0.049<sup>*</sup><br>(0.024)</td><td>-0.1<sup>***</sup><br>(0.018)</td><td>-0.005<br>(0.036)</td><td>-0.134<sup>***</sup><br>(0.041)</td></tr><tr><td>In(UAA) × In(Hired_Labour)</td><td>-0.014<sup>***</sup><br>(0.001)</td><td>-0.013<sup>***</sup><br>(0.002)</td><td>-0.015<sup>***</sup><br>(0.002)</td><td>-0.006<sup>**</sup><br>(0.003)</td><td>-0.015<sup>***</sup><br>(0.003)</td><td>-0.02<sup>***</sup><br>(0.004)</td><td>-0.005<br>(0.004)</td></tr><tr><td>In(UAA) × In(Family_Labour)</td><td>-0.027<sup>***</sup><br>(0.01)</td><td>-0.074<sup>***</sup><br>(0.023)</td><td>-0.044<sup>***</sup><br>(0.016)</td><td>-0.026<br>(0.02)</td><td>-0.071<sup>***</sup><br>(0.023)</td><td>0.006<br>(0.04)</td><td>-0.004<br>(0.034)</td></tr><tr><td>In(UAA) × In(Capital)</td><td>-0.000006<br>(0.004)</td><td>0.01<sup>***</sup><br>(0.005)</td><td>-0.006<br>(0.007)</td><td>-0.021<br>(0.014)</td><td>-0.005<br>(0.005)</td><td>0.027<sup>*</sup><br>(0.014)</td><td>0.003<br>(0.022)</td></tr><tr><td>In(Intermediate) × In(Hired_Labour)</td><td>-0.001<br>(0.001)</td><td>0.0004<br>(0.003)</td><td>0.001<br>(0.002)</td><td>-0.009<sup>***</sup><br>(0.003)</td><td>-0.006<sup>**</sup><br>(0.003)</td><td>0.001<br>(0.002)</td><td>-0.004<sup>***</sup><br>(0.002)</td></tr><tr><td>In(Intermediate) × In(Family_Labour)</td><td>-0.033<sup>***</sup><br>(0.009)</td><td>-0.07<sup>***</sup><br>(0.025)</td><td>-0.032<sup>**</sup><br>(0.016)</td><td>-0.063<sup>***</sup><br>(0.016)</td><td>-0.046<sup>**</sup><br>(0.019)</td><td>-0.024<br>(0.017)</td><td>-0.052<sup>***</sup><br>(0.016)</td></tr></tbody></table>
<table><caption>Table A.8. (Continued)</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="3">Economic size in thousand euros</th><th colspan="3">UAA size in ha</th></tr><tr><th>[25-100]</th><th>[100-250]</th><th>&gt; 250</th><th>[0; 100]</th><th>[100; 200]</th><th>&gt; 200</th></tr></thead><tbody><tr><td>ln(Intermediate) × ln(Capital)</td><td>-0.009<sup>**</sup><br>(0.003)</td><td>-0.014<sup>**</sup><br>(0.005)</td><td>0.003<br>(0.007)</td><td>0.008<br>(0.012)</td><td>0.0003<br>(0.005)</td><td>-0.031<sup>***</sup><br>(0.006)</td><td>0.02<sup>**</sup><br>(0.01)</td></tr><tr><td>ln(Hired_Labour) × ln(Family_Labour)</td><td>0.003<sup>**</sup><br>(0.001)</td><td>0.006<sup>*</sup><br>(0.003)</td><td>0.001<br>(0.001)</td><td>0.003<sup>*</sup><br>(0.002)</td><td>0.002<br>(0.003)</td><td>0.002<br>(0.002)</td><td>-0.0005<br>(0.002)</td></tr><tr><td>ln(Hired_Labour) × ln(Capital)</td><td>0.001<sup>***</sup><br>(0.0004)</td><td>0.003<sup>***</sup><br>(0.001)</td><td>0.001<br>(0.001)</td><td>0.002<br>(0.001)</td><td>0.002<sup>***</sup><br>(0.001)</td><td>0.002<sup>**</sup><br>(0.001)</td><td>0.0004<br>(0.001)</td></tr><tr><td>ln(Family_Labour) × ln(Capital)</td><td>0.008<sup>***</sup><br>(0.003)</td><td>0.005<br>(0.004)</td><td>0.007<br>(0.005)</td><td>0.02<sup>**</sup><br>(0.009)</td><td>0.005<br>(0.004)</td><td>0.012<sup>**</sup><br>(0.006)</td><td>0.015<sup>*</sup><br>(0.008)</td></tr><tr><td>Constant</td><td>13.195<sup>***</sup><br>(0.05)</td><td>12.919<sup>***</sup><br>(0.119)</td><td>13.15<sup>***</sup><br>(0.075)</td><td>13.672<sup>***</sup><br>(0.109)</td><td>12.88<sup>***</sup><br>(0.08)</td><td>13.244<sup>***</sup><br>(0.081)</td><td>13.625<sup>***</sup><br>(0.113)</td></tr><tr><td>Observations</td><td>19,822</td><td>6,393</td><td>9,737</td><td>3,692</td><td>7,047</td><td>8,554</td><td>4,221</td></tr></tbody></table>

Standard errors are in parentheses. ***P<.01, **P<.05, *P<.1.
<table><caption>Table A.9. Inefficiency variance estimates with reclassified farm size</caption><thead><tr><th rowspan="2"></th><th rowspan="2">All farms</th><th colspan="3">Economic size in thousand euros</th><th colspan="3">UAA size in ha</th></tr><tr><th>[25-100]</th><th>[100-250]</th><th>&gt; 250</th><th>[0; 100]</th><th>[100; 200]</th><th>&gt; 200</th></tr></thead><tbody><tr><td>SHDI</td><td>-0.198<sup>***</sup><br>(0.063)</td><td>0.076<br>(0.1)</td><td>-0.012<br>(0.096)</td><td>-10.17<sup>***</sup><br>(0.195)</td><td>-0.05<br>(0.098)</td><td>-0.434<sup>***</sup><br>(0.097)</td><td>-0.475<sup>***</sup><br>(0.154)</td></tr><tr><td>In(Subsides)</td><td>-0.157<sup>***</sup><br>(0.02)</td><td>-0.101<sup>***</sup><br>(0.021)</td><td>-0.479<sup>***</sup><br>(0.06)</td><td>0.019<br>(0.081)</td><td>-0.073<sup>***</sup><br>(0.021)</td><td>-0.642<sup>***</sup><br>(0.057)</td><td>-0.378<sup>***</sup><br>(0.089)</td></tr><tr><td>Gender</td><td>0.004<br>(0.045)</td><td>-0.034<br>(0.076)</td><td>0.004<br>(0.067)</td><td>0.128<br>(0.147)</td><td>-0.039<br>(0.071)</td><td>0.07<br>(0.071)</td><td>0.016<br>(0.107)</td></tr><tr><td>Age</td><td>0.002<br>(0.002)</td><td>-0.001<br>(0.004)</td><td>0.003<br>(0.002)</td><td>0.0005<br>(0.004)</td><td>0.004<br>(0.004)</td><td>0.005<sup>**</sup><br>(0.002)</td><td>-0.001<br>(0.003)</td></tr><tr><td>General Education</td><td>0.001<br>(0.027)</td><td>0.055<br>(0.045)</td><td>-0.057<br>(0.038)</td><td>-0.054<br>(0.06)</td><td>0.079<sup>*</sup><br>(0.044)</td><td>-0.026<br>(0.042)</td><td>-0.057<br>(0.056)</td></tr><tr><td>Agricultural Education</td><td>-0.102<sup>***</sup><br>(0.024)</td><td>-0.107<sup>***</sup><br>(0.041)</td><td>-0.03<br>(0.033)</td><td>-0.014<br>(0.05)</td><td>-0.123<sup>***</sup><br>(0.04)</td><td>-0.046<br>(0.037)</td><td>-0.109<sup>**</sup><br>(0.046)</td></tr><tr><td>LFA</td><td>-0.219<sup>***</sup><br>(0.056)</td><td>-0.093<br>(0.097)</td><td>-0.23<sup>***</sup><br>(0.076)</td><td>-0.113<br>(0.183)</td><td>-0.216<sup>**</sup><br>(0.097)</td><td>-0.294<sup>***</sup><br>(0.081)</td><td>-0.287<sup>***</sup><br>(0.106)</td></tr><tr><td>ECA</td><td>0.201<br>(0.145)</td><td>0.015<br>(0.245)</td><td>0.416<sup>**</sup><br>(0.179)</td><td>-0.21<br>(0.495)</td><td>0.548<sup>**</sup><br>(0.269)</td><td>0.083<br>(0.202)</td><td>0.084<br>(0.266)</td></tr><tr><td>Altitude</td><td>0.118<br>(0.116)</td><td>0.173<br>(0.169)</td><td>0.168<br>(0.154)</td><td>-0.144<br>(0.354)</td><td>0.239<br>(0.184)</td><td>0.039<br>(0.158)</td><td>-0.112<br>(0.279)</td></tr><tr><td>Constant</td><td>-2.277<sup>***</sup><br>(0.162)</td><td>-2.702<sup>***</sup><br>(0.299)</td><td>-2.761<sup>***</sup><br>(0.234)</td><td>-1.333<sup>***</sup><br>(0.468)</td><td>-2.617<sup>***</sup><br>(0.292)</td><td>-2.158<sup>***</sup><br>(0.251)</td><td>-1.256<sup>***</sup><br>(0.361)</td></tr><tr><td>Observations</td><td>19,822</td><td>6,393</td><td>9,737</td><td>3,692</td><td>7,047</td><td>8,554</td><td>4,221</td></tr></tbody></table>

Standard errors are in parentheses. ***P<.01, **P<.05, *P<.1.
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