Tail Dependence is to be Expected Among Crop Yields

Rate setting methods for crop yield and revenue contracts employ methods that presume that correlations are 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. For the government’s book of business, such tail dependence will increase the transactions and political costs of inter-agency reallocation of funds. In this paper we propose a simple model of yields according to interactions between the weather outcome and land limitations as in 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. Yield correlations should be stronger in the left and right tails than in the center, i.e., U shaped state-conditional correlation is hypothesized. Using Risk Management Agency unit level data and a variety of statistics, we find strong evidence in favor of the U shaped tail dependence hypothesis. But the goodness-of-fit test fails to reject the standard Gaussian Copula model, which can be due to power of the tests, sampling error, and/or relatively weak tail dependence over the sample years. We conclude that existing RMA rate-setting methods are deficient.