Aggregation in area yield insurance:The linear additive model

Earlier analyses of area yield crop insurance schemes used a linear additive model (LAM) to express the relationship between individual and area yield. Although similar to the capital asset pricing model used in finance, the theoretical foundations of the LAM are unknown. A contribution of this paper is the derivation of the precise conditions under which area aggregation results in a LAM, thus establishing a link between micro variables and LAM parameters. The conditions are two-fold. They relate to the interaction of risks in individual technologies and on the extent of aggregation. We show that if systemic and individual risks are additive in individual yields and if the aggregation is such that the law of large numbers hold then the LAM obtains. The paper also shows how departures from these conditions affect the results derived from a LAM analysis.