Testing for distributional structural change with unknown breaks: application to pricing crop insurance contracts

Agriculture in developed countries is produced under heavily subsidized insurance. The pricing of these insurance contracts, termed premium rates, directly influences farmers profits, their financial solvency, and indirectly, global food security. Changing climate and technology have likely caused significant shifting of mass in crop yield distributions and, if so, has rendered some of the historical yield data irrelevant for estimating premium rates. Insurance is primarily interested in lower tail probabilities and as such the detection of structural change in tail probabilities or higher moments is of great concern for the efficacy of crop insurance programs. We propose a test for structural change with an unknown break(s) which has power against structural change in any moment and can be tailored to a specific range of the underlying distribution. Simulations demonstrate better finite sample performance relative to existing methods and reasonable performance at identifying the break. The asymptotic distribution is shown to follow the Kolmogorov distribution. Our proposed test finds structural change in most major U.S. field crop yields leading to significant premium rate differences. Results of an out-of-sample premium rating game indicate that incorporating structural change in crop yields leads to more accurate premium rates.