Estimation and comparison of the performance of low-input and conventional agricultural production systems

Abstract

1. Introduction

The need for a more sustainable agriculture is pressing, and the reduction of adverse environmental and health effects of agriculture is on the top of the agenda of food-value chain actors in Europe and globally (Möhring et al. 2020c). The Farm to Fork strategy of the European Union and the Convention for Biological Diversity's Global Biodiversity Framework aim to largely reduce pesticide use and risk and fertilizer use (Schebesta and Candel 2020; Möhring et al. 2023). While current agricultural practices often have deleterious effects on the environment and on biodiversity, there is a need to maintain high production levels for food security (Foley et al. 2005, 2011). Low-input production systems have been proposed as a compromise between environmental and food production concerns as they are scalable and thus applicable for large shares of production practices (Meynard 2008; Fess, Kotcon, and Benedito 2011; Aune 2012; Maitra et al. 2021). They are characterized by the use of adjusted management, e.g. using agronomic principles and new technologies (e.g. new varieties) that substantially reduce the use of synthetic pesticides and/or mineral fertilizers (Meynard and Girardin 1991; Rolland et al. 2003; Bertrand and Doré 2008). A key question is the comparison of low-input and conventional production systems in terms of yield and productivity. Such comparison does not only require appropriate characterization of both production systems but also to account for the potential systematic differences that might exist between low-input and conventional farmers, differences that might affect their yield and input use levels. If not accounted for, such systematic differences lead to bias results and thus taint the comparison between both production systems. These differences between low-input vis-à-vis conventional farmers might also have implications for the efficiency of policies, such as input taxes. However, such systematic differences are rarely totally observed. The comparison between the conventional and low-input production systems is thus hampered by methodological challenges, such as endogeneity in input use and selection biases.¹

This paper seeks to estimate and compare the production function of low-input production systems with conventional, high-input production systems. We propose an endogenous switching approach to test and control for production system selection bias. More specifically, this article considers a non-linear framework while allowing the selection bias to impact the response variable (e.g. farmer's yield) as well as the endogenous covariates (e.g. the variable inputs). The resulting production technology is described both by a production function and input demand equations that are specific to the considered production system. We illustrate the approach using Swiss wheat production, where both conventional high-input and low-input wheat production practices exist in parallel. Arable crops, and especially cereals, represent a large part of the European agricultural crop area and are crucial to reach food security objectives. We here focus especially on wheat, which represents half of all grown European cereals and thus represents a significant share of European pesticide use. Our approach aims to help design efficient policies for the uptake of these extensive production systems while evaluating the impact on pesticide use and yields. Consequently, we choose to (i) use a primal approach with (ii) a damage abatement part for our production functions to quantify the relation between inputs (especially pesticides) and output while accounting for the specific role of pesticides—e.g. protective rather than productive—in low-input and conventional production systems (Lichtenberg and Zilberman 1986).

While organic production systems have been widely compared to conventional production systems in the literature (e.g. Lansink, Pietola, and Bäckman 2002; Acs et al. 2007; Serra, Zilberman, and Gil 2008; Gardebroek, Chavez, and Lansink 2010; Seufert, Ramankutty, and Foley 2012), studies considering low-input production systems are more generally limited. Earlier research on low-input production systems was especially focused on agronomic aspects (e.g. Dawson, Huggins, and Jones 2008; Loyce et al. 2008; Kong et al. 2011; Schrama et al. 2018) or on the determinants of (non-)adoption (e.g. Vanloqueren and Baret 2008; Finger and El Benni 2013; Ricome et al. 2016). Femenia and Letort (2016) are notable exceptions as they rely on two production functions—a conventional and a low-input one—to evaluate the impact of a pesticide tax. Yet, they rely on experimental agronomic data on low-input production systems to estimate the changes from the conventional production technology, thus lacking information on real field conditions. Generally, most data sets used by agricultural production economists do not contain the relevant information needed to distinguish low-input production systems from conventional ones.

When available, a key methodological challenge using observational—instead of experimental—data is selection biases. For example, according to Finger and El Benni (2013), adopters of low-input production systems tend to be ‘smaller’ farmers with already ‘lower’ yields, which may indicate that the opportunity costs of adopting low-input production systems are lower for smaller farms. Additionally, the choice to adopt practices with more uncertain pay-offs might reflect differences in farmers’ behavior. Mzoughi (2011) shows that farmers adopting integrated crop protection tend to value social (here environmental) concerns. Such factors that are affecting both technology choice and other production choices and outcomes, if unobserved, induce endogeneity issues (known in this case as selection bias).² Such self-selection effects and selection biases are well-known when dealing with technology choice. Endogenous regime switching models are standard in production choice models to account for such selection biases (Alene and Manyong 2007; Asfaw et al. 2012; Abdulai and Huffman 2014).

In addition to selection biases, agricultural production functions generally suffer from input endogeneity issues (Marschak and Andrews 1944), especially primal production functions, as they make explicit the relationship between output (e.g. yield) and inputs (e.g. pesticides). Yet, most drivers of input use choice are unobserved by the analyst and might also affect the observed yield. While applied economists have devoted much attention to this endogeneity problem and approaches to solving it (Ackerberg, Caves, and Frazer 2015), there are only a few studies that consider endogenous covariates within an endogenous switching framework (Takeshima and Winter-Nelson 2012; Murtazashvili and Wooldridge 2016). If they allow for correlation between the selection term and the endogenous covariates, none of these studies consider that the selection bias can affect both the endogenous covariates and the response function. Yet, when considering production system choice, few studies consider that such a choice affects the observed yield without impacting farmer's input choice as well. Selection biases thus have to be accounted for when estimating low-input and conventional production functions.

We aim to fill this gap by estimating the production function of low-input wheat production systems and comparing it to conventional production systems. We consider an endogenous switching approach to test for production system selection bias on yield and input use levels. In particular, we use a control function approach to account for input endogeneity (Marschak and Andrews 1944; Ackerberg, Caves, and Frazer 2015) and a corrected inverse Mills ratio to account for production system selection bias on the input demand equation. From our modeling framework, we can derive results in terms of low-input adoption determinants, input demand price elasticity for low-input and conventional producers, and inputs’ role within the low-input and conventional production functions. In particular, we use a case study of Swiss wheat production, whose interest is twofold. First, Switzerland implemented a voluntary integrated production program since 1992, with low-input producers benefiting from a 400 CHF/ha direct payment as well as a price premium (Finger and El Benni 2013).³ By having information on farmers participation, we can directly distinguish between low-input and conventional producers.⁴ Second, we here use data derived from farmers’ field journals with detailed information on output and input use (de Baan, Blom, and Daniel 2020; Gilgen et al. 2023).⁵ In particular, unlike most production economists’ data sets, we have information on each operation conducted in the field and the exact amount—and not only expenses⁶—of each pesticide and fertilizer product used by each farmer to protect its winter wheat crop. Overall, our empirical application uses an unbalanced panel of 148 Swiss winter wheat producers from 2009 to 2015 (N = 575).

We find that, first, variable inputs respond less to price variation in low-input farming systems. Second, our results show that the role of inputs in conventional and low-input production systems differs. For instance, we find fertilizer to be a purely productive input in conventional production systems, while it is an interactive input in low-input production systems. More generally, we find that the role of production conditions, such as temperature and rainfall levels, differs between conventional and low-input production systems. This advocates for a separate estimation of the low-input and conventional production functions. Finally, our results show that selection bias affects Swiss farmers’ input demand and, thus, indirectly, their production functions. This result speaks in favor of accounting for selection bias not only on farmers’ production functions but also on their input demand. Overall, our results advocate for considering separately low-input and conventional producers when implementing and evaluating the impact of pesticide reduction policies. We here provide a methodological approach to do so, which could contribute to tackling future research questions in this field.

The remainder of this article is structured as follows. The next section is dedicated to the presentation of our endogenous regime switching framework with selection on both the output and inputs. Following is the section where we present the Swiss observational data we consider for our empirical application. Then, we describe and compare the Swiss low-input and conventional production systems for wheat. Finally, results will be discussed so that we can draw conclusions from this work.

2. An endogenous regime switching model with endogenous covariates and double selection process

Low-input and conventional are considered as two separate production functions as they represent two different production technologies with different input productivity. With the ultimate goal of estimating the impact of a pesticide reduction policy, we consider primal production functions with a damage-abating part to account for the protective role of pesticides.⁷ Because of the potential self-selection bias associated with the adoption of a low-input farming system, we add a selection model to the set of production functions, resulting in an endogenous regime switching model. We consider an extension of the standard endogenous regime switching framework to account for input endogeneity in the low-input and conventional production functions. Unlike previous extension to the endogenous covariate case, which assumed an undetermined correlation between the endogenous covariate and the selection variable, we consider here that selection also affects the input demand equations. The resulting framework can be described as a ‘double’ endogenous regime switching framework. The following subsections are dedicated to the presentation of this model and its adjoining equations.⁸

2.1. From a standard endogenous switching regime model framework…

Most studies comparing conventional and alternative production systems—in terms of productivity, production risk, or efficiency—consider separate functions, thereby representing different technologies (e.g. Lansink, Pietola, and Bäckman 2002; Gardebroek 2006; Gardebroek, Chavez, and Lansink 2010). Similarly, low-input farming systems may be considered separately from conventional farming systems when estimating production functions. Indeed, low-input farming systems were conceived by agronomists to allow for a reduction in chemical inputs, e.g. pesticides and mineral fertilizers (Meynard 1985; Rolland et al. 2003). To substitute chemical inputs, farmers adopting low-input production systems can benefit from integrated production practices (e.g. soil preparation operations, beneficial management practices, or crop rotations) but also from innovations such as crop breeding (Rolland et al. 2003; Fess, Kotcon, and Benedito 2011; Möhring et al. 2020c). Instead of being at the core of crop protection, pesticides are one element among others that could only be used when there is no other option left in integrated production (Lucas 2007). Consequently, we have two equations corresponding to the production technology of low-input farming systems (denoted as regime |$r = 1$|⁠) and the production technology of conventional ones (⁠|$r = 0$|⁠):

where |$y ^r$|corresponds to observed yield in regimen r,|$\ {f}^r$| are farming system-specific production functions, |${\boldsymbol{x}}$| the vector of input use levels, and |${{\boldsymbol{c}}} $| the vector of control variables that might impact production choices (e.g. topographic and weather conditions). Finally, terms |${{\boldsymbol{\beta }}}^r$| and |$\upsilon ^r$| represent, respectively, the vector of parameters and the error term of the yield model.

If the underlying agronomic principles of low-input and conventional farming systems ask for separate production functions, our economic model should also account for the potential endogenous selection issues in the farming system choice. As aforementioned, farmers might face heterogenous opportunity costs and different utility functions that affect both their decision to adopt low-input farming systems and their production function (Mzoughi 2011; Finger and El Benni 2013). If such selection bias is not accounted for when estimating the low-input and conventional production technologies, it will lead to biased estimates. The most adopted strategy to account for such bias in the agricultural production literature are endogenous regime switching models (Lee 1982). This approach was adopted, for instance, by Alene and Manyong (2007) to evaluate the impact of farmer education on productivity with traditional and improved technology. Endogenous regime switching models were also used by Asfaw et al. (2012) and Abdulai and Huffman (2014) to evaluate the impact of different agricultural technologies adoption, respectively, on (i) rural households’ welfare and (ii) yields and net returns. In line with these previous studies, we consider in this article an endogenous regime switching model. To define such a model, we need a selection equation for farming system choice in addition to Equation (1). Consider a standard linear index model:

where |$r ^*$| is the latent variable for farming system choice and |${r} $| its observable counterpart. |$({\gamma }_0,{{\boldsymbol{\gamma }}}_z)$| and e, respectively, correspond to the vector of parameters and the error term of this dichotomous choice model, and z is used as a vector of instrumental variables for endogenous farming system choice |${r} $|⁠. Among those instrumental variables are the set of control variables |${{\boldsymbol{c}}} $| and variables that are expected to affect the choice of farming system without directly impacting the yield (e.g. age and education).

In the presence of self-selection effects, or more generally selection bias, the covariance between the error terms |$\upsilon ^r$| and e is non-zero. It implies that the expected values of error terms |$\upsilon ^r$| conditional on r are different from zero and that our estimates of |${{\boldsymbol{\beta }}}^r$| are biased. To test and correct for this potential selection bias, the endogenous regime switching model relies on Heckman's (1979) approach. In particular, Lee's (1982) extension of the Heckman selection correction approach gives us that

where |$\omega _{\upsilon e}^r$| corresponds to the covariance between error terms |$\upsilon ^r$| and |${e} $|⁠, and |$\varphi $| and |$\phi $|⁠, respectively, denote the probability and cumulative distribution functions of the standard normal distribution.⁹ The terms |$\frac{{\varphi ( {{\gamma }_0 + \ {{\boldsymbol{\gamma }}}_z{{\boldsymbol{z}}} } )}}{{\phi ( {{\gamma }_0 + \ {{\boldsymbol{\gamma }}}_z{{\boldsymbol{z}}} } )}}$| and |$\frac{{ - \varphi ( {{\gamma }_0 + \ {{\boldsymbol{\gamma }}}_z{{\boldsymbol{z}}} } )}}{{1 - \phi ( {{\gamma }_0 + \ {{\boldsymbol{\gamma }}}_z{{\boldsymbol{z}}} } )}}$| correspond to inverse Mills ratios and are integrated as a covariate in Equation (1) to control for selection bias. If estimates of |$\omega _{\upsilon e}^r$| are significantly different from zero, then selection bias is significant in our model.

2.2. … toward a ‘double’ endogenous switching regime framework with endogenous covariates

Apart from the potential selection bias, our model in Equation (1) might suffer from another estimation problem due to input endogeneity, a long-standing issue that has received much attention in the econometric literature (Ackerberg, Caves, and Frazer 2015). Thus, we need to extend the endogenous regime switching model to the case of endogenous covariates (Takeshima and Winter-Nelson 2012; Murtazashvili and Wooldridge 2016). Takeshima and Winter-Nelson (2012) consider an approach combining a heteroskedastic probit to calculate the inverse Mills ratio coupled to a two-stage least squares (2SLS) approach to estimate the model for the response variable and the endogenous covariate. Murtazashvili and Wooldridge (2016) consider a control function approach to control for the endogenous continuous covariates and a corrected inverse Mills ratio to allow for correlation between discrete and continuous endogenous covariates. The approach we adopt in this article is similar to the one of Murtazashvili and Wooldridge (2016), but (i) considers a non-linear outcome equation¹⁰ and (ii) assumes that the endogenous switching not only affects the response variable but also our endogenous covariates. The resulting model could be considered as an endogenous regime switching model with endogenous covariates and double selection process.

Let us first define farming system-specific input demand functions yield model as

where k corresponds to the index of the variable input considered, |${{\boldsymbol{p}}} $| represents the vector of relevant prices (e.g. crop and input prices), |$( {{\boldsymbol{\alpha }}_{k,p}^r,{\boldsymbol{\alpha }}_{k,c}^r} )$| are the vector of parameters, and |$u_k^r$| is the error term. Input endogeneity implies that the covariances between error terms |$e_k^r$| and |$\varepsilon ^r$| are non-zero and that our estimates of |${{\boldsymbol{\beta }}}^r$| in Equation (1) are still biased. To correct for such bias, we consider a control variable approach (Wooldridge 2015). Assuming that there is only one input k that is endogenous and putting aside the selection bias, we can define the control function as

where terms |$\rho _{\upsilon u}^r$| are to be estimated and represent the intensity of the correlation between error terms |$\upsilon ^r$| and |$u_k^r$|⁠.¹¹

The selection bias and input endogeneity corrections presented in Equations (3) and (5) might be additive, assuming that error terms |$e_k^r$| and |$\mu $| are uncorrelated. Yet, one can reasonably assume that the unobserved factors that are affecting both farming system choice and observed yields are also affecting the input demand. In that case, corrections (3) and (5) are not additive and estimates of |$( {{\boldsymbol{\alpha }}_{k,p}^r,{\boldsymbol{\alpha }}_{k,c}^r} )$| are biased due to uncorrected selection bias. As for Equation (1), we consider a Heckman selection correction for the input demand equations:

where |$\omega _{k,ue}^0$| corresponds to the covariance between error terms |$u_k^r$| and e. The error term of the input demand functions |$u_k^r$| can be decomposed in two parts: the selection correction part as presented in Equation (7) and a random part |$\eta _k^r$|⁠. Thus, setting aside the selection bias, the control function as presented in Equation (5) can be rewritten as

where |${\lambda }^r( {{\gamma }_0 + \ {{\boldsymbol{\gamma }}}_z{{\boldsymbol{z}}} } )$| represents the inverse Mills ratio and |$\rho _{\upsilon u}^r$| represents the intensity of the correlation between error terms |$\upsilon ^r$| and |$u_k^r$|⁠.

The last step to write |$E[\upsilon ^0|\ {\boldsymbol{x}},{\boldsymbol{z}},r = 0]{\boldsymbol{\ }}$|and |$E[\upsilon ^1|\ {\boldsymbol{x}},{\boldsymbol{z}},r = 1]$| is to correct for the existing correlation between the selection correction of Equation (3) and the control function presented in Equation (8). Indeed, the inverse Mills ratio is part of the control function. To account for such correlation, we consider a corrected version of the inverse Mills ratio:¹²

where |$\rho _{eu}^r$| represents the covariance between error terms |$u_k^r$| and e, and |$\psi _{\mu \mu }^r$| is a scale parameter.¹³ Finally, combining Equations (7) and (8), we have:

2.3. A Cobb–Douglas crop production function with damage abatement

In this part, we omit the farming system-specific index r to simplify our notation. To represent the damage-abating role of pesticides in the production process compared with ‘productive’ inputs, we consider a damage abatement function as proposed by Lichtenberg and Zilberman (1986). Hence, the production function |$f( {{\boldsymbol{x}} ,{\boldsymbol{c}} ;{{\boldsymbol \beta }}} )$| is separated into two parts: a potential yield function (noted |$h( \cdot )$|⁠) and a damage-abating function (noted |$d( \cdot )$|⁠). The potential yield function describes how productive inputs contribute to the maximum potential crop yield level, i.e. the yield level that is free of any damage due to weeds, pests, and/or diseases. The damage-abating function gives the share of potential yield that is saved by using pesticides: The range of |$d( \cdot )$| is positive and should not exceed 1. To account for the potential complementary of inputs, we allow inputs to have both a productive and damage-abating role on crop yields (Saha, Shumway, and Havenner 1997). Thus, we have three different sets of inputs: purely productive inputs (noted |${{\boldsymbol{x}}}_{( h )}$|⁠), purely damage-abating inputs (noted |${{\boldsymbol{x}}}_{( i )}$|⁠) and interactive inputs (noted |${{\boldsymbol{x}}}_{( d )}$|⁠). As low-input and conventional farming systems rely on different agronomic principles, we allow the sets of purely productive, purely damage-abating, and interactive inputs to differ across production technologies.

Following Zhengfei et al. (2005, 2006) and Möhring et al. (2020a), our empirical crop yield function models combine Cobb–Douglas potential yield functions:

where |${\rm{exp}}\ ( {{{\boldsymbol{\beta }}}_{( c )}{\boldsymbol{c}}} )$| represents the impact of production conditions and farms’ characteristics on crop yields, and quadratic damage abatement functions:

with |$f( {{\boldsymbol{x}} ,{\boldsymbol{c}} ;\ {{\boldsymbol \beta }}} ) = \ h( {{{\boldsymbol{x}}}_{( h )},{{\boldsymbol{x}}}_{( i )},{\boldsymbol{c}};\ {\boldsymbol{\beta }}} ) \cdot \ d( {{{\boldsymbol{x}}}_{( d )},{{\boldsymbol{x}}}_{( i )};{{\ {\boldsymbol{B}}}}} )$|⁠. In particular, the quadratic damage-abating function is convenient because it ensures the range of |$d( \cdot )$| to be constrained between 0 and 1 without imposing estimation restrictions on the signs of |${\boldsymbol{{{B}}}}$| parameters.¹⁴ We can thus rewrite the farming system-specific yield function from Equation (1) as

with the following decomposition for the error term:

where |$\psi _{\upsilon e}^r\ \lambda _y^r$| and |$\rho _{\upsilon u}^r\ u_k^r$| represent, respectively, the corrections for selection bias and input endogeneity, and |${\mu }^r$| represents the random part of the error term.

2.4. Estimation strategy

The estimation approach considered can be seen as an extension of Heckman's two-step approach for estimating standard endogenous switching regime models in the case of endogenous regressors (Heckman, Tobias, and Vytlacil 2003; Wooldridge 2010, 2015). In particular, our modeling framework relies on two sets of control functions: one to deal with the input use endogeneity issue and the other to deal with sample selection issues.

First, we estimate the probit model for farming system choice—Equation (2)—by maximum likelihood. Estimates of |$({\gamma }_0,{{\boldsymbol{\gamma }}}_z)$| are used to estimate the inverse Mills ratio |${\lambda }^r( {{\gamma }_0 + \ {{\boldsymbol{\gamma }}}_z{{\boldsymbol{z}}} } )$|⁠. Then, we can estimate by least squares the input demand functions—Equation (4)—augmented by the inverse Mills ratio to control for potential selection bias. Essentially, input demand functions are estimated following the standard Heckman two-step procedure. As for the yield function, we can easily estimate the |$u_k^r$| terms with the estimates of |$( {{\boldsymbol{\alpha }}_{k,p}^r,{\boldsymbol{\alpha }}_{k,c}^r} )$| obtained at step 2. The problem comes when considering the estimation of the corrected Mills ratio |$\ \lambda _y^r$|⁠. Equation (8) gives us that

We already have estimates for |$({\gamma }_0,{{\boldsymbol{\gamma }}}_z)$| and |$u_k^r$|⁠. We thus need to get estimates for |$\rho _{eu}^r$| and |$\psi _{ee}^r$|⁠. Devilliers (2021) shows that both terms can be estimated using moment conditions.¹⁵ Once we have estimated the corrected inverse Mills ratio |$\ \lambda _y^r$|⁠, the yield function given in Equation (12) can be estimated with non-linear least squares.

In practice, each estimation step is fairly easy to implement. Yet, computing the asymptotic distribution of the estimators obtained by using the considered multiple-step estimation procedure is not straightforward. We use bootstrap methods to obtain the empirical standard errors of the estimates for the input demand and yield production functions (Efron and Tibshirani 1986; Fess, Kotcon, and Benedito 2011).¹⁶

3. Data

3.1. General characteristics of the data set

To investigate the production technologies of low-input farming systems compared to conventional ones, we consider Swiss data on winter wheat producers. Indeed, since 1992, Swiss farmers have been able to participate in a voluntary integrated production program. With participation, farmers receive a price markup of around 5 CHF/100 kg (reflecting a ca. 10 per cent price markup) and federal per-hectare direct payments of 400 CHF (Möhring and Finger 2022; Mack et al. 2023). These payments are conditional on farmers not using any fungicides, insecticides, plant growth regulators, or chemical-synthetic stimulators of natural resistance.¹⁷ Among eligible crops—cereals, sunflowers, rapeseed peas, and beans—we focus on winter wheat production. This low-input ‘Extenso’ wheat production currently represents more than 50 per cent of the total Swiss wheat production (Finger and El Benni 2013).

The data were obtained from Agroscope, the Swiss center of excellence for agricultural research, and provided by the Swiss Central Evaluation of Agri-Environmental Indicators (de Baan, Blom, and Daniel 2020; Gilgen et al. 2023). It contains information on all management operations performed by the farmers—soil preparation, sowing, fertilization, crop protection operations, and harvest, from 2009 to 2015. Following Möhring et al. (2020), we transform initial data consisting of daily records on crop management and inputs use as follows: We (i) calculate cost-equivalents for used machinery and working time, (ii) convert fertilizer applications into nitrogen equivalents, and (iii) express pesticide use in terms of pesticide load. To this end, we use the Pesticide Load Index as implemented by Möhring et al. (2021), which accounts for differences in standard dosages and the heterogeneous properties of pesticides (Kudsk, Jørgensen, and Ørum 2018; Möhring, Gaba, and Finger 2019).

Overall, our data gathered includes 575 observations from 148 winter wheat farmers from 2009 to 2015. Among those farmers, 107 (resp. 60) implemented low-input (resp. conventional) practices, representing 381 (resp. 194) observations. Switches between low-input and conventional farming systems occurred with nineteen farmers. Among those nineteen farmers, eight switched from conventional to low-input farming, five switched from low-input to conventional farming, and six switched more than one time.¹⁸ Altogether, farmers were observed for an average of 3.56 years in the low-input subsample (resp. 3.23 years in the conventional subsample). Apart from switches and data collection, missing years for farmers could come from (i) crop rotation, as we only consider winter wheat production, (ii) stopping winter wheat production, or (iii) the end of farming activity. In the absence of further information and given that the average number of years observed per farmer is similar in the low-input and conventional subsamples, we consider those missing values to be randomly distributed and not affecting our estimators. The descriptive statistics of the low-input and conventional subsamples can be found in Online Appendix B.

3.2. Variables used for the analysis

Our ‘double’ endogenous switching framework requires us to derive three sets of variables: inputs to build our production functions, instruments to estimate the input demand models, and instruments to estimate the selection model.¹⁹

• Inputs are directly derived from the data transformation we aforementioned: cost equivalents for used machinery and working time (in CHF/ha) with a distinction between mechanical pest control operations and other operations, nitrogen equivalents (in kg/ha), and pesticide load indices for herbicide and fungicide. Insecticides are left apart because their use is very limited in Swiss winter wheat production (see Table B1 in Online Appendix B).  Table 1 provides the observed mean (and standard deviation) of yield and inputs for both low-input and conventional farmers. Except for mechanical pest control, input use significantly differs across those production systems, thus bolstering the use of separate production functions.

• We consider input price ratios²⁰ and the winter wheat price as instrumental variables for the input demand models.²¹ Input price ratios were built using (i) the national representative price indices of herbicide, fungicide, nitrogen, and energy and (ii) the winter wheat price data, all coming from Agristat (2015). While input prices only vary in time, winter wheat prices can also vary across farmers. Indeed, winter wheat prices can differ depending on (i) the chosen variety and (ii) the adoption of the Extenso production system (as farmers benefit from a 5 CHF/100 kg price markup). We keep the different variety prices to control for wheat quality.

• To be able to identify parameters from the selection model, we need to consider an additional set of instruments for the production system's choice. Based on the previous work of Finger and Lehmann (2012), we consider the share of non-agricultural income, the education of the farmer,²² the age of the farm head, the share of rented land, and the labor intensity.

In addition to these three variables’ sets, we consider a set of control variables to account for farm/farmer heterogeneity in all three—selection, input demand, and production function—models. First, we consider standard farm characteristics as farm size (in ha) and the share of winter wheat in the crop area. We also try to control for pedoclimatic conditions. First, we consider a mountainous dummy equal to 1 if the farm is located either in a mountainous or hilly area, and the altitude of the farm (in m) as proxies for the pedologic characteristics of the farm. Second, we consider average annual temperatures in °C and average annual rainfall in 1,000 l |${\rm{m}}^{ - 2}$|⁠, obtained from SwissMeteo, as proxies for climatic conditions (Frei et al. 2006; Frei 2014). We also consider cantonal dummies to try to control for (i) heterogenous soil characteristics and (ii) potential differences in extension services.

4. Results and discussion

4.1. The choice of production systems and specific variable input demand functions

Estimated conditional predicted probabilities of choosing a low-input production system are presented in Table 2. Negative impacts of farm size and of the share of arable surface allocated to winter wheat cropping from our descriptive analysis are confirmed by our probit model. An increase of one percentage point of the share of winter wheat reduces the probability to adopt a low-input production system by 50 per cent among our sample, ceteris paribus. We also find that being in a mountainous region increase by almost 15 per cent the probability to adopt a low-input farming system. It confirms the findings of Finger and El Benni (2013), who find free-rider effects of the ‘Extenso’ low-input program for farms with a lower yield potential.²³ Also, rainy years and/or being in rainier areas decrease the probability of adopting a low-input production system.

As for the variables considered as specific determinants of the choice of production system, our model shows that the adoption of low-input production systems tends to be favored by younger and more educated farmers. Also, greater labor intensity and greater shares of revenue coming from non-agricultural activities increase the probability of adopting such production systems. As for prices, input prices have no significant impact on such choices. However, wheat prices have a quadratic—not linear—effect on low-input production system adoption. Higher wheat prices discourage adoption at first, but at a decreasing rate. It confirms, at least partially, the economic principle underlying the adoption of low-input production systems. Low-input farming systems were designed to reduce production costs in a context where support was increasingly decoupled. Hence, when crop prices are low, the incentive to reduce input costs is more important. On the contrary, high crop prices act as an incentive to maximize yields, i.e. use conventional production systems.

Estimation results from the farming system choice were used to compute the inverse Mills ratio, controlling for the potential selection bias in the input demand equations. Results for the conventional and low-input input demand equations are presented in Tables 3 and 4, respectively. The presence of selection bias is confirmed for herbicide demand. The negative selection bias associated with low-input herbicide demand means that low-input farmers’ unobserved characteristics tend to decrease their herbicide use. The positive selection bias associated with conventional herbicide demand means that conventional farmers’ unobserved characteristics tend to increase their herbicide use.

Among the observed characteristics, few seem to affect variable input demand.²⁴ Globally, variable input demand in conventional production systems decreases with farm size. Yet, nitrogen fertilization demand increases with the share of winter wheat. This might indicate that winter wheat is more intensive in nitrogen fertilization than other crops. Otherwise, we find that conventional herbicide demand responds negatively to rainfall and positively to altitude. In low-input production systems, we show that herbicide demand responds positively to being in a mountainous region. Indeed, mechanical weed control is easier to implement in plains than in sloped areas. At the same time, when controlling for belonging to a mountainous region, altitude negatively affects herbicide demand for low-input farmers. This might indicate a lower level of weed competition at higher altitudes.

We see significant differences between input demand price elasticities across production systems. First, in low-input production systems, variable input demand is not significantly affected by price variables. The only exception is for nitrogen demand, which increases when the herbicide price index ratio increases. Using pesticides in low-input production systems is one strategy among others and should only be used when there is no other option left (Lucas 2007). Given that, and assuming that herbicides are used as parsimoniously as they should in complementing mechanical pest control, the limited response to price variation is not surprising. To understand the impact of the herbicide price index ratio on low-input nitrogen demand, we mobilize the theory of opportunity costs (Schaub et al. 2023). As aforementioned, the economic principle of low-input farming systems relies on cost reduction in the context of relative low crop prices. An increase in the herbicide price index results in lower profitability for low-input production systems and increases the opportunity cost of yield loss. An answer to such a rise in the opportunity cost of yield loss would be to increase the level of fertilizers to try and increase yield and avoid any profitability drop.

In conventional production systems, we show a greater responsiveness of input demand to price variations.²⁵ Both nitrogen fertilizers and fungicide demand are negatively impacted by an increase in fertilizer or fungicide price index ratios. They are positively impacted by an increase in herbicide or energy price index ratios. From an agronomic viewpoint, conventional production systems were designed to achieve high target yield levels with high levels of fertilization and crop protection. If nitrogen fertilizers tend to trigger weed competition, they also tend to increase wheat susceptibility to disease (Henson and Jordan 1982; Boquet and Johnson 1987; Howard, Chambers, and Logan 1994; Lintell-Smith et al. 1992). An increase in the fertilizer price index might encourage farmers to be more parsimonious in their use without impacting too much their yields. The negative impact of the increase in fertilization price index ratio on the conventional fungicide demand is to be explained by both agronomic and economic factors. First, by reducing their fertilization levels, conventional farmers might also reduce wheat susceptibility to disease (Lintell-Smith et al. 1992; Howard, Chambers, and Logan 1994), and hence a lower need for fungicides and a decrease in fungicide demand. Second, even if yield reduction is limited, a decrease in revenue associated with a reduction in nitrogen fertilization might encourage farmers to reduce their costs by reducing fungicide applications. The same reasoning can be applied when considering an increase in the fungicide price index.

Despite triggering weed competition, an increase in the fertilizer price index does not negatively affect herbicide demand. Statistics from Table 1, in particular the similar levels of herbicide use and mechanical pest control across production systems, might indicate that even conventional farmers make parsimonious use of herbicides and use mechanical weed control as a substitute for them. Hence, we find a relative inelasticity of the herbicide demand, even for conventional farmers. Such herbicide inelasticity also permits the understanding of why fungicide and nitrogen demands are positively affected by an increase in herbicide price index ratio. Indeed, such an increase induces a higher opportunity cost of yield loss. As a response, and because of the inelasticity of herbicide demand, farmers may increase their fertilization levels, as well as their fungicide use, to try to increase their yield and absorb this herbicide price increase. The rationale behind the negative impact of a rise in the energy price index is analogous.

4.2. Conventional and low-input production systems specific production functions

Before estimating the production functions specific to each type of production system, we need to determine, for each farming system, the set of purely productive, interactive, and purely damage-abating inputs. As the agronomic principles of conventional and low-input farming systems are different, we allow for these sets of inputs to differ across types of production practices. Herbicides, fungicides, and mechanical pest control are considered as purely damage-abating inputs. Thus, we need to determine among fertilizers, work, and machinery, which are productive inputs, if they belong to the set of purely productive inputs or if they need to be considered as interactive inputs. Based on separability tests (Saha, Shumway, and Havenner 1997), we consider (i) work and machinery as purely productive inputs for both conventional and low-input functions, and (ii) fertilizers as purely productive input for the conventional function and interactive input for the low-input function.²⁶ Then, based on Zhengfei et al. (2006), we perform asymmetry tests to see whether or not it is relevant to consider that inputs have an asymmetric role on crop production or if their role is symmetric (i.e. we only need the productive part with all inputs as covariates). For both low-input and conventional farmers, results from the asymmetry tests confirm the asymmetric role of inputs.²⁷

Table 5 includes the results from the conventional and low-input asymmetric production functions. First, for both conventional and low-input farmers, we notice that the coefficient associated with the corrected inverse Mills ratio is not statistically significant. This might indicate that selection bias only affects farmer yield through its impact on herbicide demand functions.²⁸ Control function coefficients for input endogeneity are only significant in the low-input production function. As for the inputs themselves, their effects on conventional and low-input production functions differ. While productive inputs have no significant impact on conventional yields, work and machinery are found to increase low-input yields. Nitrogen fertilizers impact low-input yields only through their interactive role in the damage-abating part. The herbicide damage-abating role is found to be significant in both conventional and low-input production functions.

Observed characteristics such as farm size and the share of winter wheat surface do not significantly affect conventional or low-input yields. However, being in a mountainous region has a positive impact on low-input yields. This might indicate that low-input production systems are more profitable when cropping conditions are more difficult, as in mountainous regions. Table 5 also shows that conventional yields are sensitive to rainfall, while low-input yields are rather sensitive to temperatures. This result can be interpreted alongside the results of the probability of adopting a low-input production system. Rainfall decreases the probability of adopting low-input practices. Then we might argue that, in the perspective of high yield losses due to excessive rainfall, farmers would rather use fungicides, which means being classified as a ‘conventional’ farmer, to limit their losses.

In Table 6, we compare the marginal effect at the mean of inputs on the yields from three different specifications.²⁹ Model (1) corresponds to the main specification of this article, i.e. the endogenous regime switching model with both selection bias and input endogeneity. Model (3) shows the results from a joint production function with no distinction between the production systems considered. Finally, model (2) is an in-between, as we consider separate production functions for conventional and low-input farmers with neither selection bias nor input endogeneity.

First, notice that contrary to models (1) and (3), there are no significant coefficients associated with input use in model (2). Considering separate conventional and low-input production functions is not enough: Selection bias and input endogeneity should be accounted for. While the comparison with the separate functions with no selection bias nor input endogeneity suffers from the lack of significant coefficients, the joint production function comparison is insightful. Model (3) shows a positive effect of additional work and machinery on yields. Yet, model (1) shows that this positive effect of work and machinery only affects the low-input production function. In the conventional case, we do not find a significant effect of work and machinery on yields. The positive marginal effect at the mean of fungicide on yield from model (3) becomes negative for conventional producers when considering model (1). Models (1) and (3) also give different results in terms of significance. Unlike separate functions, the joint production function shows a significant marginal effect at the mean of mechanical pest control on yields. Model (1) shows a significant (and opposite) marginal effect at the mean of herbicides on conventional and low-input yields. In model (3), the herbicide marginal effect at the mean is not statistically significant.

4.3. General discussion on our modeling framework and results

Our modeling framework mostly ignores the panel dimension of our dataset due to a limited sample size compared to the rather complex modeling framework we consider.³⁰ In particular, such limited sample size prevents us from introducing time or individual fixed effects. To circumvent such issue, first we try to decompose time fixed effects using weather variables and a time trend variable for each model.³¹ Except for the low-input herbicide demand, it seems that there are no time trends in the low-input adoption, input demands, or observed yields. Second, instead of individual fixed effects, we introduce canton dummies to control for the ‘individual’ heterogeneity that is not already captured by the other control variables. It remains that the panel dimension of our data is mostly ignored in our error terms. Despite the flexibility of the Swiss voluntary integrated production program, it remains highly unlikely that the adoption of low-input farming systems is independent across time when adopting the viewpoint of an individual farmer.³² Similarly, the input demands and observed yields of an individual farmer cannot be considered independent across time. Our models might suffer from heteroskedasticity due to autocorrelation of error terms. Heteroskedasticity might also derive from our modeling framework not considering the potential spatial dependency in our data. In particular, the adoption of low-input farming systems can benefit from neighboring effects as well as differences in extension services (Wang, Möhring, and Finger 2023). If we try to capture such effects with control variables, such as canton dummies, the potential spatial dependency of error terms is mostly ignored. Even if not directly accounted for, our consideration of bootstrapped standard errors should provide us with reasonably robust standard errors despite these potential sources of heteroskedasticity.

Another point worth discussing is our consideration of winter wheat crops only.³³ Because of this single-crop approach, we neglect the effects and adaptations introduced using different crop rotations, which is especially important for low-input farming systems. In particular, crop rotations might impact farmers’ input demand, their input productivity, and their yield. In the input demand models, we do not expect the crop rotation system to affect the price ratios or the other considered variables. Hence, even if omitted, the crop rotation system should not result in biased estimates. As for the production functions, the crop rotation system might affect both the yield level and the productivity of inputs, thus creating an endogeneity issue. Yet, we expect the resulting bias to be limited in our application for two reasons. First, our application displays little statistical significance for the coefficients associated with fertilizers and pesticides in both the low-input and conventional production functions. The impact of such bias on our results would thus be limited. Second, crop rotation systems are highly standardized. Hence, the additional heterogeneity associated with the introduction of crop rotations is unlikely to introduce significant differences in our estimates, while introducing an entire crop rotation comes at the cost of estimates that are more computationally intensive.

Overall, our results advocate the consideration of both selection bias and input endogeneity when estimating production functions when farmers are using different production systems. One should not empirically assess the effects of the adoption of low-input practices on input uses and yields without considering selection and input endogeneity issues. This is in line with previous findings from the literature, e.g. Pietola and Lansink (2001), who advocate for an adverse selection issue for agri-environmental programs as adopters have lower yields at the baseline. In particular, our results show that in the Swiss case, low-input production systems are adopted by younger and more educated farmers with smaller farms and more diversified source of revenue, as previously highlighted by Finger and El Benni (2013). Hence, if the Swiss Extenso program is well-diffused among farmers and could be considered successful from the adoption viewpoint, our findings show its impact on pesticide use is limited as it was adopted with farmers with already lower input use levels. Plus, pesticide savings mainly concern fungicides and are very limited when considering herbicides. Yet, herbicides also have a negative impact on the environment. A cost-benefit analysis of the existing Extenso program should be considered. Whereas the question of an herbicide-free Extenso program has already been raised (Böcker and Finger 2018; Böcker, Möhring, and Finger 2019), the question of how to encourage reluctant conventional farmers to adopt low-input production systems remains. In particular, from our descriptive statistics, we find that low-input farmers benefit from similar, if not superior, economic returns. Hence, the need for a more thorough investigation into the factors that explain such a lock-in could help to design policy instruments that would specifically target the ‘laggards’. Recent studies have pointed out that especially farmers preferences and expectations could play an important role in such adoption decisions (Finger and Möhring 2022; Möhring and Finger 2022; Garcia et al. 2023).

5. Conclusion

This paper investigates the production functions of low-input production systems compared to conventional ones. We consider observational data from Swiss wheat producers. To investigate and account for the potential selection bias in production system choice, we consider an endogenous regime switching model combined with control functions that account for input endogeneity. We find selection bias in both conventional and low-input herbicide demand, meaning that unobservables that affect the choice of production systems also affect the level of herbicide demand for farmers. At the same time, we find endogeneity in farmers’ input choices, meaning that unobservables affecting input demands also impact observed yields. Finally, we find that both biases are interlinked, highlighting the need to account for both selection bias and endogeneity in input use when estimating the production functions of conventional and low-input production systems.

Our article also highlights differences across conventional and low-input wheat production systems when accounting for their differences in their estimation. First, the input demands of low-input farmers seem to be rather inelastic to relative input price. Input demands of conventional farmers, particularly nitrogen and fungicide demand, vary as a function of the relative input prices. Second, production functions also display significant differences across conventional and low-input production systems. First, the role of inputs—e.g. productive, damage-abating, or interactive—in the production function varies across production systems. In low-input production systems, nitrogen fertilizers and herbicides have a significant interactive effect on pest control. By triggering weed competition, nitrogen fertilizers affect the efficiency of herbicides. Whereas in conventional systems, this interactive effect does not appear statistically significant. As for the effect of inputs and other factors on yields, our approach highlights differences across production systems. For instance, conventional yields are significantly impacted by rainfall, while low-input yields respond rather to temperature variations. Differences in the conventional and low-input production functions are robust across different specifications.

Such differences in the farmer's input demand and production functions need to be accounted for when designing public policies, for example, for the uptake of low-input production systems. For instance, pesticide taxation policies, especially if targeting herbicide use, might have more harmful effects for low-input farmers than conventional ones. Inelasticity of input demand of low-input farmers to input prices means that a tax would result in an increase in their production costs. Our results suggest that conventional Swiss wheat farmers can better adjust their input demand to input price variations to limit the impact of such taxation policy on their profitability, since a larger range of chemical inputs is available to them. If not differentiated across production systems, a pesticide taxation policy could reduce low-input production systems’ profitability and potentially encourage the adoption of conventional production systems. More globally, because of the differentiated role they play in low-input and conventional yields, we need to separately assess the impacts of policies on variable input use in the two production systems.

Future research could expand our modeling framework in two main directions. First, future research might consider a modeling framework accounting for the potential heteroskedasticity issues we previously mentioned. Indeed, our modeling framework neglects the heteroskedasticity inherent to our dataset by ignoring the panel dimension of our data and the potential spatial dependency mechanisms that affect the adoption of low-input farming systems, the input demand as well as observed yields. If such heteroskedasticity should not affect directly our estimates, an extension of the Carlson generalized two-step Heckman estimator (2022) to our endogenous regime switching model would still be interesting to consider. Indeed, instead of using bootstrapped standard errors, such extensions would allow for autoregressive and spatially dependent error terms to investigate both the time-interdependence and spatial dependency of the low-input adoption decision, as well as farmers’ input demand and yields.

Second, future research could consider crop rotations, not single crops. Considering a multicrop approach would be interesting in order to (i) integrate the effects of crop rotation into our model while (ii) investigating the extensive margin impact of public policies that implement taxes or subsidies on pesticides. Indeed, such policies might impact the intensive margin through the choice of production practices and input uses, but they might also cause the farmer to change the crops s/he is cultivating as well as the share attributed to each culture (Möhring et al. 2020b).

Acknowledgements

We thank Agroscope and MeteoSwiss for access to farm-level and weather data, respectively. We thank Alain Carpentier for helpful comments on the econometric modeling framework. We also thank for comments on earlier versions of the manuscript by Stéphane Auray, Jean-Paul Chavas, and Sabine Duvaleix as well as participants from the XVI EAAE Virtual Congress and from the 2020 CREM-INRA seminar in which this paper was presented. Finally, we thank the two reviewers and the editor for constructive and helpful feedback on an earlier version of this paper. This work being part of my PhD thesis, I, Esther Devilliers, also acknowledge financial support from the ANR Project SoilServ (ANR-16-CE32-0005).

Data availability

The data supporting this study's findings are provided by Agroscope—the Swiss Federal center of excellence for agricultural research. The farm-level data is confidential and thus cannot be made publicly available. Stata code for the analysis performed in the manuscript is available in the online supplementary material.

Footnotes

References