Estimating Crop Rotations as Dynamic Cycles using Field Data

Crop rotation systems are an important part of agricultural production for managing pests, diseases, and soil fertility. Recent interest in sustainable agriculture focuses on low input-use practices which require knowledge of the underlying dynamics of production and rotation systems. Polices to limit chemical application depending on proximity to waterways and flood management require field-level data and analysis. Additionally, supply elasticity estimates based on crop production as independent activities omit the dynamic effects of a cyclical rotation. We estimate a dynamic programming model of crop rotation which incorporates yield and cost inter-temporal effects in addition to field-specific factors including salinity and soil quality. Using an Optimal Matching algorithm from the Bioinformatics literature we determine empirically observed rotations using a geo-referenced panel dataset of 14,000 fields over 13 years. We estimate the production parameters which satisfy the Euler Equations of the field-level rotation problem and solve an empirically observed four-crop rotation