# Managing Basis Risk with Multiscale Index Insurance

That’s the title of my article with Ghada Elabed, Michael Carter, and Catherine Guirkinger, which was just published online in *Agricultural Economics*. Here is the abstract:

Agricultural index insurance indemnifies a farmer against losses based on an index that is correlated with, but not identical to, her or his individual outcomes. In practice, the level of correlation may be modest, exposing insured farmers to residual, basis risk. In this article, we study the impact of basis risk on the demand for index insurance under risk and compound risk aversion. We simulate the impact of basis risk on the demand for index insurance by Malian cotton farmers using data from field experiments that reveal the distributions of risk and compound risk aversion.

The analysis shows that compound risk aversion depresses demand for a conventional index insurance contract some 13 percentage points below what would be predicted based on risk aversion alone.We then analyze an innovative multiscale index insurance contract that reduces basis risk relative to conventional, single-scale index insurance contract.Simulations indicate that demand for this multiscale contract would be some 40% higher than the demand for an equivalently priced conventional contract in the population of Malian cotton farmers.Finally, we report and discuss the actual uptake of a multiscale contract introduced in Mali.

The article discusses the index insurance contract my coauthors and I have developed for and sold to cotton producer cooperatives in southern Mali. The rest of this post is more technical, as it goes into the details of the two contributions I’ve highlighted above.

### Two Contributions

Specifically, the article discusses two things. First, it discusses how compound risk aversion explains the demand for insurance much better than the usual concept of risk aversion. To make things simple, suppose I offer you a 50-50 chance of winning or losing $10, or a lottery whose expected monetary value is zero. I can write this “lottery” as [math]0.5\cdot(10)+0.5\cdot(-10)[/math]. Plugging this into your utility function [math]U(\cdot)[/math] would give your expected utility [math]EU=0.5\cdot U(w+10)+0.5\cdot U(w-10)[/math] (where [math]w[/math] denote your wealth level before entering the gamble). This would then allow you to compare this to your alternative to taking the gamble, [math]U(w)[/math]. If [math]EU\geq U(w)[/math], you would take the gamble, and if [math]EU < U(w)[/math], you would decline it.

But suppose I were to make things more complicated. Suppose I were to offer you the following compound lottery: (i) a 50% chance of playing a lottery where you have a 50-50 chance of winning or losing $10 (again, this has an expected monetary value of zero), and (ii) a 50% chance of playing a lottery where you have a 25-75 chance of losing $20 and winning $6.67 (this also has a monetary value of zero). Compound lotteries are thus lotteries composed of two or more lotteries. Both this lottery and the previous one have an expected monetary value of zero, but as it turns out, people are considerably more averse to compound lotteries than they are to simpler lotteries (hence the concept of compound risk aversion), a behavior that is related to ambiguity aversion, or Knightian uncertainty.

Second, the article discusses the use of multiscale contracts, or contracts which rely on more than one index. Micro-insurance contracts typically rely on an index and on whether the index has crossed a certain threshold. For example, an insurance will pay out if rainfall (the index) is less than a predetermined level (the threshold).

Here, we use two indices, each with its own threshold: Our insurance pays out if the average cotton yield in one’s cooperative (which is measured very precisely by the parastatal in charge of running the cotton value chain in Mali) falls below a certain threshold *and* if the average cotton yield in the geographic production zone in which one’s cooperative is located falls below another threshold. By merely introducing this latter threshold, the basis risk to which Malian cotton producers were exposed fell considerably.