Crop yield distributions: fit, efficiency, and performance

Abstract

Purpose – The purpose of this paper is to contribute to the empirical evidence about crop yield distributions that are often used in practical models evaluating crop yield risk and insurance. Additionally, a simulation approach is used to compare the performance of alternative specifications when the underlying form is not known, to identify implications for the choice of parameterization of yield distributions in modeling contexts. Design/methodology/approach – Using a unique high-quality farm-level corn yield data set, commonly used parametric, semi-parametric, and non-parametric distributions are examined against widely used in-sample goodness-of-fit (GOF) measures. Then, a simulation framework is used to assess the out-of-sample characteristics by using known distributions to generate samples that are assessed in an insurance valuation context under alternative specifications of the yield distribution. Findings – Bias and efficiency trade-offs are identified for both in- and out-of-sample contexts, including a simple insurance rating application. Use of GOF measures in small samples can lead to inappropriate selection of candidate distributions that perform poorly in straightforward economic applications. The β distribution consistently overstates rates even when fitted to data generated from a β distribution, while the Weibull consistently understates rates; though small sample features slightly favor Weibull. The TCMN and kernel density estimators are least biased in-sample, but can perform very badly out-of-sample due to overfitting issues. The TCMN performs reasonably well across sample sizes and initial conditions. Practical implications – Economic applications should consider the consequence of bias vs efficiency in the selection of characterizations of yield risk. Parsimonious specifications often outperform more complex characterizations of yield distributions in small sample settings, and in cases where more demanding uses of extreme-event probabilities are required. Originality/value – The study helps provide guidance on the selection of distributions used to characterize yield risk and provides an extensive empirical demonstration of yield risk measures across a high-quality set of actual farm experiences. The out-of-sample examination provides evidence of the impact of sample size, underlying variability, and region of the probability measure used on the performance of candidate distributions.