State-Space Aggregation in Markov Chains and the Modeling of US Crop Patterns

Crop rotation is a cornerstone of agricultural production, and Markov chains provide a powerful framework for modeling rotation practices. This paper examines the implications of state-space aggregation in Markov chain models of crop choices in the US Corn Belt. Using a multinomial logit model and over two decades of field-level data, we show that modeling crop choices with a two-state Markov process, where the states are corn and all other crops, leads to significant information loss compared to a three-state model that treats corn, soybeans, and other crops as separate states. We provide a theoretical statement of two distinct aggregation conditions for Markov chains, and discuss how these conditions can be maintained or tested in a multinomial logit parameterization of Markov transition probabilities. Structural tests strongly reject the parameter restrictions required for state-space aggregation. Relative to the three-state model, a two-state Markov chain model produces systematic differences in estimated covariate effects, Markov transition probabilities, and key crop area patterns. Furthermore, tracking soybeans separately from other crops reveals distinct regional trends in cropping patterns, including the widespread adoption of corn-soybean rotation in the recent expansion of corn cultivation in the western Corn Belt. These findings highlight the importance of state-space representation in Markov models and offer new insights into the dynamics of crop rotations in the Corn Belt.