Dependence Structure in Agricultural Index Insurance Design and Product Development

Index insurance refers to a broad class of insurance products that indemnify the insured based not on verifiable losses, but rather a distinct variable that ideally is highly correlated with losses, a so-called index. Index insurance products based on rainfall, area-yields, regional livestock mortality, remotely-sensed vegetation indices, and other variables have been promoted as cost-effective risk management tools for agricultural producers in developing countries where traditional insurance is likely to fail due to high transactions costs. Index insurance is generally free of moral hazard, is less susceptible to adverse selection, and is less expensive to administer than conventional insurance. Index insurance, however, has been criticized on the grounds that, in practice, available indices are not sufficiently correlated with losses to provide effective protection against common farm or household risks.;In this dissertation, various issues are addressed pertaining to statistical methods used in the development, design, and economic assessment of index insurance products. Of special interest is whether statistical methods commonly used by actuaries and economists to rate and analyze index insurance products can adequately capture the potentially complex dependence structures that might exist among indices and losses, particularly at the tails of the distributions. I propose a novel approach to statistical analysis of index insurance products based on copulas, and the spatial autoregressive model with variant spatial autoregressive parameters. Bivariate copulas are especially well-suited for capturing complex dependencies that exist among bivariate random variables, particularly at the tails, but have been rarely little used to analyze agricultural index insurance. The spatial autoregressive model with variant spatial autoregressive parameters is suited for characterizing tail dependence among multivariate random variables by introducing the effect of distances.;Three distinct applications are proposed. In Chapter 2 copulas and their properties are introduced. In Chapter 3, the degree of bivariate tail dependence that may exist among common indices will be assessed empirically, using bivariate copulas and Iowa county rainfall as a case study. In Chapter 4, how copulas can be used to design optimal index insurance products will be demonstrated, using Henan Province, China as a case study. In Chapter 5, I discuss how to investigate tail dependence among multivariate indices using spatial autoregressive error model.