Earlier analyses of area yield crop insurance schemes used a reduced form linear relationship between individual and area yield. However, without knowledge of the structural framework, the analysis and design of alternative schemes is problematic. This paper resolves this problem. The paper characterizes the entire class of structural models equivalent to the reduced form. As a result, the beta, the slope coefficient of the reduced form is expressed as a function of structural parameters. Second, the structural model is used to analyze the relation between the aggregation (that determines area yields) and the risk reduction due to area yield insurance. Third, we consider optimal area yield insurance for an important class of structural models not consistent with the reduced form.