The Impact of Stocks on Correlations of Crop Yields and Prices and on Revenue Insurance Premiums using Semiparametric Quantile Regression

Crop yields and harvest prices are often considered to be negatively correlated, thus acting as a natural risk management hedge through stabilizing revenues. Storage theory gives reason to believe that the correlation is an increasing function of stocks carried over from previous years. Stock-conditioned second moments have implications for price movements during shortages and for hedging needs, while spatially varying yield-price correlation structures have implications for who benefits from commodity support policies. In this paper, we propose to use semi-parametric quantile regression (SQR) with penalized B-splines to estimate a stock-conditioned joint distribution of yield and price. The proposed method, validated through a comprehensive simulation study, enables sampling from the true joint distribution using SQR. Then it is applied to approximate stock-conditioned correlation and revenue insurance premium for both corn and soybeans in the United States. For both crops, Cornbelt core regions have more negative correlations than do peripheral regions. We find strong evidence that correlation becomes less negative as stocks increase. We also show that conditioning on stocks is important when calculating actuarially fair revenue insurance premiums. In particular, revenue insurance premiums in the Cornbelt core will be biased upward if the model for calculating premiums does not allow correlation to vary with stocks available. The stock-dependent correlation can be viewed as a form of tail dependence that, if unacknowledged, leads to mispricing of revenue insurance products.