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County-level yield data are used in applied research and crop insurance policy in place of farmlevel yield data, which are likely sparse, not broadly representative, and subject to selection bias. We exploit the fact that county-level yields are the aggregate of farm-level yields to derive bounds that can be reduced to direct relationships between county- and farm-level yields under certain conditions. Simulation experiments indicate that crop insurance premium estimates derived from this method have the potential for bias in certain conditions but are reasonably precise in other conditions, suggesting that these relationships are a new tool for applied analysts.