Risk in agriculture : a study of crop yield distributions and crop insurance

Abstract

Agriculture is a business fraught with risk. Crop production depends on climatic, geographical, biological, political, and economic factors, which introduce risks that are quantifiable given the appropriate mathematical and statistical methodologies. Accurate information about the nature of historical crop yields is an important modeling input that helps farmers, agribusinesses, and governmental bodies in managing risk and establishing the proper policies for such things as crop insurance. Explicitly or implicitly, nearly all farm decisions relate in some way to the expectation of crop yield. Historically, crop yields are assumed to be normally distributed for a statistical population and for a sample within a crop year. This thesis examines the assumption of normality of crop yields using data collected from India involving sugarcane and soybeans. The null hypothesis (crop yields are normally distributed) was tested using the Lilliefors method combined with intensive qualitative analysis of the data. Results show that in all cases considered in this thesis, crop yields are not normally distributed.

(cont.) This result has important implications for managing risk involving sugarcane and soybeans grown in India. The last section of this thesis examines the impact of crop yield non normality on various insurance programs, which typically assume that all crop yields are normally distributed and that the probability of crop failure can be calculated given available data.