When Less Is More: On the Use of Historical Yield Data with Application to Rating Area Crop Insurance Contracts

Yong Liu,Alan P Ker

doi:10.1017/aae.2019.40

Abstract

AbstractCrop insurance is the cornerstone program of domestic farm policy in most developed countries. Although most countries’ rating methodology corrects for time-varying movements in the first two moments, it is unclear whether using the entire yield series remains appropriate. We use distributional tests and an out-of-sample retain-cede rating game to answer whether governments/insurers should historically trim yields in estimating their premium rates. Despite small sample sizes and the need to estimate tail probabilities, the historical data appear to be sufficiently different such that trimming is justified.

Highlights

Much of production agriculture in developed countries is produced under heavily subsidized insurance and has been for the past 20–25 years
1We do not impose the spatial and temporal priors on knots used by the Federal Crop Insurance Corporation (FCIC). 2Given any results are dependent on the choice of detrending method, we considered three alternative methodologies to ensure robustness of our results: (1) a linear model estimated by L2, (2) a linear model estimated by L1, and (3) nonparametric local lines using out-of-sample cross validation for the smoothing parameter
Historical yield data have been utilized in many empirical applications in literature, most notably in applications related to crop insurance

Summary

Introduction

Much of production agriculture in developed countries is produced under heavily subsidized insurance and has been for the past 20–25 years. Zhu, Goodwin, and Ghosh (2011), using U.S Department of Agriculture, National Agricultural Statistics Service (USDA-NASS) county-level yield data for corn, soybeans, and cotton, found changes in higher moments through time. Given the need to estimate tail probabilities, the aforementioned results (which are very region-crop specific) do not necessarily suggest that historically trimming yield data will lead to more accurate premium rates; the loss function for each is over very different subsets of the density space. Using county-level NASS yield data for corn, soybeans, and winter wheat, we first, for completeness, consider nonparametric distributional tests to assess if the adjusted yield data may result from different data generating processes. Where λ is the coverage level such that λyT1 is the yield guarantee

Testing the identically distributed assumption

Findings

Conclusions