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Crop rotation systems have played a key role in agricultural production for thousands of years, dating back to the biennial grain-fallow rotations employed by the Ancient Greeks. Fundamentally, rotations are rooted in intertemporal spillover effects between crops, the economic consequences of which depend on relative input and output prices. We contribute to the literature by developing a dynamic, field-level model of crop rotations using a geo-referenced panel dataset that covers 12 years and over 14,000 individual fields. We identify empirical rotations using a Sequence Analysis procedure from the bio-informatics literature, and calibrate a dynamic field-level profit function that satisfies the underlying Euler dynamic first-order conditions using Generalized Maximum Entropy. The resulting model is based entirely on empirical data, and exhibits a stable rotational cycle which responds to changes in expected prices and costs. We illustrate the mechanics of the model with a four-crop rotation of alfalfa, cotton, grain, and fallow, and simulate field-level changes resulting from changes in relative prices.