Copula-Based Models of Systemic Risk in U.S. Agriculture: Implications for Crop Insurance and Reinsurance Contracts

The federal crop insurance program has been a major fixture of U.S. agricultural policy since the 1930s, and continues to grow in size and importance. Indeed, it now represents the most prominent farm policy instrument, accounting for more government spending than any other farm commodity program. The 2014 Farm Bill further expanded the crop insurance program and introduced a number of new county-level revenue insurance plans. In 2013, over $123 billion in crop value was insured under the program. Crop revenue insurance, first introduced in the 1990s, now accounts for nearly 70% of the total liability in the program. The available plans cover losses that result from a revenue shortfall that can be triggered by multiple, dependent sources of risk-either low prices, low yields, or a combination of both. The actuarial practices currently applied when rating these plans essentially involve the application of a Gaussian copula model to the pricing of dependent risks. We evaluate the suitability of this assumption by considering a number of alternative copula models. In particular, we use combinations of pair-wise copulas of conditional distributions to model multiple sources of risk. We find that this approach is generally preferred by model-fitting criteria in the applications considered here. We demonstrate that alternative approaches to modeling dependencies in a portfolio of risks may have significant implications for premium rates in crop insurance.