The impacts of thresholds on risk behavior: What's wrong with index insurance?

Almost universally, implementers of index insurance for low income households have chosen to embed insurance with other interventions designed to improve productivity, with the insurance used almost entirely to make the other interventions possible. A common example is to use the insurance to allow farmers to have access to loans by reducing the probability of weather related defaults. A bundled loan/insurance implementation with overwhelming take-up rates had low insurance take-up rates when researchers unbundled the package, covering the loan default risk, so that the loans could be available without requiring insurance. If low income farmers are highly risk averse, why do they place so little value on risk reducing insurance once their access to productive inputs is secured? In general, why do index insurance implementers targeting the lowest income households nearly universally utilize insurance as a tool to increase productivity instead of using it to reduce variance? We provide a potential explanation driven by optimal risk behavior in the face of income thresholds, illustrating how models of risk aversion may not adequately represent the behavior of those with very low incomes. We show how variance reduction may not be the most important outcome for a low income farmer who lives near the poverty threshold. We show that if a farmer's goal is to avoid falling into a poverty trap, then the lower his income is, the less risk averse he becomes in the mean-variance utility maximization framework regarding the design of index insurance contracts. We begin this paper by introducing a mean-variance utility maximization framework, using a known joint distribution for the index and yield, and then we show how one's risk aversion changes when the mean-variance utility function is switched to a poverty trap avoidance utility function. We argue that one reason farmers don't always seek to minimize variance is that they may be very near a poverty trap threshold, and are therefore less willing to give up additional expected income in exchange for decreased income variance. In this case, it may be best for implementers to utilize insurance to unlock increases in productivity as opposed to variance reduction per se.