Probabilistic Data Fusion for Estimating Production Function Parameters and Modeling Agricultural Supply at Field-Level

Agricultural crop production and its impacts on natural resources often varies strongly in space. As farmers’ responses to climate or price changes may equally differ substantially between locations, spatially explicit knowledge on crop yield, cropping decisions, and their drivers are required to project future crop production and to design effective policy interventions. However, existing agri-economic supply models are incapable of simulating field-level input intensity or yield, mainly because observations for these variables are almost never available for individual fields. Here, we present an approach to estimate the parameters of a structural, field-level crop production model for yield, variable input, and crop choice modeling using widely available data. Our approach evolves around two methodological contributions: First, we conceptually and statistically link variables at different levels of spatial aggregation, specifically observed cropping decisions, biophysical conditions and regional statistics. Second, we show how parameters occurring in multiple structural equations can be simultaneously estimated with Bayesian Probabilistic Programming. We first demonstrate with synthetic data that our approach can recover true model parameters. We then exemplarily apply it for a German federal state and simulate the impacts of an output price increase on expected field-level production quantity changes of wheat, barley, and grain maize.