Aggregation in Area‐Yield Crop Insurance: The Linear Additive Model

Previous analyses of area yield crop insurance have used a linear additive model (LAM) to express the relationship between individual and area yield. However, the theoretical foundations of the LAM are unknown. This shortcoming is addressed by establishing two conditions linking microvariables and LAM parameters. The conditions relate to the interaction of risks in individual technologies and the extent of aggregation. If systemic and individual risks are additive in individual yields, and if the law of large numbers hold, then the LAM obtains. This article also shows how departures from these conditions affect the results derived from a LAM analysis. A classic issue in agricultural economics is the design of schemes that would offer insurance against risks in agriculture. The experience with conventional crop insurance has been disappointing, as insurers have struggled to obtain reliable actuarial data on individual yields (Skees, Black, and Barnett). The primary attraction of area-yield insurance schemes is that insurers do not have to contend with the informational problems of moral hazard and adverse selection (Halcrow). These problems can be dismissed because indemnities and premiums are based not on a producer’s individual yield but rather on the aggregate yield of a surrounding geographical area. However, the key question is: How adequate are aggregate yield instruments for reducing the risks faced by producers? To address this question, previous studies have expressed individual yields as a linear stochastic function of area yield (Mahul, Miranda, Vercammen). The approach has been to use the form of a linear regression model where the dependent variable is the yield of an individual producer, the only independent variable is area yield and the additive random error term measures omitted individual-specific factors uncorrelated with area yield. Thus, the model decomposes variations in individual yield in to variations in area yield that represent systemic risk and Bharat Ramaswami is senior economist in the Indian Statistical