Optimal Index Insurance and Basis Risk Decomposition: An Application to Kenya

• Agricultural Economics Workshop

Date and Location

Thursday, May 13, 2021, 4:10 PM - 5:30 PM
Online Meeting, Zoom

Abstract

Index insurance is a promising cost-effective tool to reduce the risk faced by farmers, yet is found to have little success in practice. One of the main culprit often cited for this low success is the presence of basis risk, the probability that a farmer experiences a loss yet does not receive any indemnity. Following Elabed and Carter (2015), this basis risk can be decomposed into two sources, the intrinsic lack of homogeneity of a given insurance zone (the zonal risk) and the (lack of) accuracy of the index at summarizing that homogeneity (the design risk). The literature has so far almost exclusively focused on design risk, embarking into a quest to find always better indices. Satellite data has proved very useful in that regard, providing a cost-effective way to design indices over a large scale.

In this paper, we formalize the decomposition of basis risk, and illustrate how this decomposition can be used to measure the relative importance of each source of basis risk using satellite data in Kenya. We first derive the optimal index according to two loss functions, showing that the maximum attainable average correlation between individual fields
and any index is equal to the share of the first eigenvalue of the correlation matrix between fields. This provides us with a clear metric of the zonal risk, giving an upper bound for the elusive quest of the best index for a given zone. This allows us in particular to shift the debate from the mere quest of the best index for a given zone to a discussion of the design of the zones itself, their size and location. We illustrate the merits of this approach using a satellite-derived dataset of yields covering the entire area cropped to maize in Kenya. We simulate an index insurance product, and compare the relative benefits of improving the design of the index versus the design of the zone. Our results indicate a strong local heterogeneity (i.e. a high zonal risk), highlighting the need to take the design of zones into consideration.