Land Resilience and Tail Dependence among Crop Yield Distributions

Rate setting procedures for United States crop yield and revenue insurance contracts employ methods that presume correlations to be state invariant. Whether this is true matters. If yield-yield correlations strengthen when crops are subject to widespread stress, then diversification opportunities for private insurers weaken when most needed, and an insurer's portfolio of retained business may not be as diversified as standard statistics would suggest. For government outlays, such tail dependence will increase the transactions and political costs of reallocations from the general fund. In this paper we propose a simple model of yield correlations according to interactions between a weather outcome and a land unit's yield resilience to adverse shocks, as might be measured by the United States Soil Conservation Service's land capability classification. Our model shows that yield-yield tail dependence is to be expected and, furthermore, should take a particular form. In better growing regions, yield correlations across units should be stronger in right tails than in left tails, whereas in marginal growing regions the reverse should apply. Using USDA Risk Management Agency unit level data and a variety of statistics, we find strong evidence in favor of this land yield resilience hypothesis. Our findings call into question the appropriateness of current USDA rate-setting methodologies, which posit constant state-conditional ordinal correlations by implicitly assuming that yields can be represented by a Gaussian copula. A goodness-of-fit test rejects the standard Gaussian copula model, implying that existing RMA rate-setting methods are deficient.