Crop rotation effects capture the effects of the cropping history of a plot on the current production process of a crop grown on this plot. Actually, the sequence of crops grown on a plot largely impacts pest and weed populations living on this plot, as well as the structure and nutrient content of its soils. Diversified crop sequences significantly impact the production process of any crop grown on this plot through, notably, its effects on chemical input uses (pesticides and fertilizers) and labor and fuel uses (e.g., for tillage and mechanical weeding). They can also impact yield levels directly by, for instance, controlling pest population that cannot be controlled by chemical pesticides. The agronomic effects of crop rotations are exploited by agricultural scientists, extension agents or farmers for designing diversified agricultural production systems aimed to save chemical input uses while maintaining land productivity (e.g., Matson et al, 1997; Tilman et al, 2002; Bowman and Zilberman, 2013).

Investigating and measuring the effects of crop rotations on yield levels and uses of chemical inputs would thus produce essential information for agri-environmental policies. However, despite their usefulness, these effects are poorly documented, notably because farmers' crop sequence acreages and yields are rarely recorded simultaneously, at least in large datasets suitable for statistical analyses. Crop rotation effects on yields and input uses are in fact measured mostly based on experimental data (Hennessy, 2006) and only for a few major crop pairs (e.g., corn-corn versus soybeans-corn in the US and wheat-wheat versus rapeseed-wheat in the EU).

Our aim in this paper is to propose an original approach for estimating crop rotation effects based on existing datasets, namely on large panel datasets of farm accountancy data with cost accounting. Such datasets describe crop yields, acreages and input uses for a large sample of farms over a few years but lack information on farmers' crop sequence acreages. In response to this data issue, our approach relies on three main elements: (i) statistical models of yield and input uses at the crop sequence level, (ii) assumptions related to famers' economic rationality regarding their use of crop rotation effects and (iii) original estimation approaches that allow recovering the unobserved crop sequence acreages while simultaneously estimating the underlying crop rotation effects.

We are interested in first order crop rotation effects, that is to say in the effects of the preceding crops on the yield and input use levels of the current crops. To estimate the effects of crop rotation on yields and input uses, we express the observed yield and input uses of a given crop as a weighted average of the unobserved crop yields and input uses at the crop sequence level, the weights being the shares of each preceding crops in the current crop acreage. Estimating crop rotation effects based on this linear relationship would be straightforward if crop sequence acreages were observed, which is not the case. To overcome this issue, we rely on assumptions related to famers' economic rationality. These assumptions enable us to “reconstruct” famers' crop sequence acreage choices as functions of the crop rotation effects of interest along the estimation process of these effects.

Indeed, recovering the crop sequence acreages chosen by profit maximizing (and forward-looking) farmers from their current and past crop acreages would be a standard linear optimal transport problem if crop rotation effects were known. This allows us to devise a crop sequence acreage share “reconstruction process” based on any candidate estimates of the crop rotation effects. This “reconstruction process” is then combined with standard estimation approaches to define the crop rotation effect estimation problem as a mathematical programming with equilibrium constraints (MPEC) problem (see, e.g., Su and Judd 2012). This estimation problem is closely related to those considered by Berry et al (1995) for estimating differentiated good demand systems or by Rust (1987) for estimating dynamic discrete choice models. We also rely on expert knowledge information obtained from agricultural scientists and extension agents. This information consists of sets of rarely used and/or unwarranted crop sequences or expected ranks of crop rotation effects. It is mostly used for imposing and/or testing constraints on the crop rotation effect estimation problem. The effects of crop rotations on production choices were investigated in a few previous econometric studies. Hennessy (2006) considers crop rotation effects on yields based on the estimation of crop yield models with experimental data and derives their effects on optimal input uses. Other studies focus on the effects of crop rotations on crop acreage choices, following the pioneering work of Tegene et al (1988). These studies rely on dual crop acreage econometric models in which crop rotation effects are aggregated into “fertility stocks” that are managed by farmers (e.g., Ozarem and Miranowski, 1994; Vitale 2009). Thomas specifically (2003) considers the effects of dynamic stock management of nitrogen on yield and input use levels. According to our knowledge, our microeconometric study is the first one aimed at estimating crop rotation effects on yields and input use levels based on farm data while considering their effects on crop sequence acreage choices.

The empirical tractability of our approach is illustrated on an unbalanced panel dataset of 378 French farms specialized in grain production from 2008 to 2014. We consider 8 crops representing more than 90% of farm acreages: wheat, barley, rapeseed, corn, peas, alfalfa, sugar beet and potato. This dataset contains information on crop acreages, crop yields, and input use (quantity of fertilizers and pesticides) for each farm. Our results show that the estimated crop sequence acreage shares are close to what can be observed on average at the plot level in the considered region (average crop sequence acreages in the considered area can be obtained by exploiting administrative data). The estimated crop sequence acreage shares also show that farmers primarily select the “best” crop sequences given their past and current acreage choices. This is consistent with our economic rationality assumption. But, this also implies that crop rotations effects cannot be estimated for the least profitable crop sequences. The estimated crop rotation effects on yield notably show that: i) straw cereals are among the worst preceding crops for straw cereals, ii) cereals are good preceding crop for sugar beet, iii) alfalfa and peas are good preceding crops for wheat.

Our results on crop rotation effects on fertilizer use show that legumes as preceding crop allow reducing the use of fertilizers while cereals as preceding crop tend to increase fertilizer use. All these results conform to agronomic principles. Our results demonstrate little crop rotation effects on pesticide uses. Two explanations can be put forward. First, farmers are reluctant to exploit the effects of crop rotations on pest and weed populations. Second, these effects of crop rotations only appear in the long run due to the resilience of pest and weed populations. This point requires further investigation. The approach that we propose for recovering crop rotation effects from cost accounting data seems to work well in practice. It yields results that are consistent with available data on crop sequence acreages as well as with the opinions of the experts we have consulted. We are currently gathering data on crop sequence acreage share choices to be matched with our dataset. This will allow us to compare our results with “reconstructed” crop sequence acreage shares to results obtained with "observed” crop sequence acreages.