Are crop insurance premium-implied yield distributions valid?

Purpose - The purpose of this paper is to develop methods for inferring if crop insurance premiums imply yield distributions that are valid according to standard laws of probability and broadly consistent with observed empirical evidence. The authors also survey current premium-implied distributions both before and after conditioning on the producer’s choice of coverage level. Design/methodology/approach - Under an assumption of actuarial fairness, the authors derive expressions for upper and lower bounds for premium-implied yield cumulative distribution functions (CDFs) at loss thresholds for each coverage level. When observed premiums imply a CDF that exceeds one or is not non-decreasing, the authors conclude that premiums cannot be actuarially fair. The authors additionally specify very weak conditions for premium-implied yield CDFs to be consistent with two possible reasonable parametric distributions. Findings - The authors evaluate premiums for the year 2018 for 19,104 county-crop-type-practice combinations, both before and after conditioning on producer’s choice of coverage level. The authors find problems in roughly one-third of cases. Problems are exhibited for all crops evaluated, and are strongly associated with areas with lower expected yields and higher yield variability. At least 40m acres are currently insured under premium schedules that cannot possibly be consistent with valid probability distributions. Originality/value - The authors make two primary contributions. First, the premium-implied yield CDF bounds the authors derive requires fewer assumptions than previous similar work, while simultaneously placing more stringent conditions on premiums to be consistent with actuarial fairness. Second, the authors show that current US crop insurance premiums cannot possibly be actuarially fair for many cases, reflecting tens of millions of insured acres, which implies sub-optimal producer risk mitigation and inequitable expenditures for producers and taxpayers.