Land Resilience and Tail Dependence among Crop Yield Distributions

We propose and empirically test a simple model to shed light on the nature of interactions between weather, land quality, and yield. The conceptual model posits substitution relations between water stress metrics and soil quality, as well as a soil-conditioned threshold water stress level beyond which soil cannot buffer crop yields. The model implies that yield-yield dependence should vary as growing conditions vary. In comparison with intermediate growing conditions, yield-yield dependence should strengthen when growing conditions are either very good or very poor. County yield data strongly support substitution between soil and benign water availability levels, but complementarity between soil and beneficial heat variables. Our estimated model provides qualified support for the hypothesis that better land is more resilient to water stress. We estimate a pseudo-copula that nests the Gaussian copula, finding strong evidence of left tail dependence among yields. Our formal model and empirical findings corroborate others’ concerns about the appropriateness of current USDA rate-setting methodologies, which posit constant state-conditional rank correlations, implicitly assumed by use of the Gaussian copula. An application to aggregate crop yield rate setting suggests that current methods underprice area yield and whole farm premiums. Applying our empirical model to medium-range weather projections under a climate change scenario for the Northern Great Plains, we infer that systemic yield correlations will increase in future years.