This project used historical data on rainfall in Kenya. The economic problem we seek to address is the design of a specific-event weather insurance product that can be embedded into a credit product to provide relief to farm borrowers in time of drought, reduce risk-rationing and increase demand for credit, and provide at least a partial substitute for collateral and reduce financial risk and exposure to lenders, who are reluctant to lend to agriculture because of the very weather risks we seek to insure. To address the phenological problem we develop in what we refer to as a dynamic trigger. This trigger establishes an indemnity if the accumulated rainfall in any 21-day period is below 60% of the historical average rainfall in that same 21-day period for a given year. More on this later, but when we examined the ‘average’ path of overlapping 21-day measures and took the deviation of each year’s equivalent measure we found the distribution of the difference to be non-normal! Indeed we find it to be close to a lognormal distribution with the probability that below-normal rainfall in our study region was approximately 50% more likely than above normal rainfall. The failure of normality suggest also a failure in the Gauss-Markov assumption normally assumed in a first-guess approach to statistical assumption. But this also comes with a possible failure in the independence assumption and Brownian presumption of the historical time-path of our data series – as limited as it is. As Mandelbrot and Wallis (1968) point out the failure to recognize the non-Markov possibilities would greatly underestimate the duration and intensity of the longest drought. Exploring further, we deployed the within-year variance-ratio measure of the Hurst coefficient and found that a) when taken as an average (1983-2017) the within-year Hurst coefficient is approximately H=0.8, b) the within-year Hurst coefficient varies widely from a low of 0.137, a high of 0.687; and c) an average H of 0.466, which with a standard deviation of 0.1369, is not statistically different from H=0.5. Clearly, the Hurst of the average is nowhere near that average Hurst. Combined, these observations should encourage researchers in the field of developing or evaluating the many varieties of weather index insurance models to treat with greater seriousness the combined Noah and Joseph effects. Perhaps this is stating the obvious. However, recognizing that the Noah Effect is essentially dealing with a volume metric of extremes with reference to some measure not considered extreme, it is considered independently of how precipitation is patterned. A weather ‘pattern’ is distinctively non Markovian in the sense that over some measure of scale there is measurable correlation between any time date t, and some other date t-s or t+s. On patterns, the Joseph effect is more important since these correlated patterns can be impactful in the small (within years) or in the large (between and across years). Of course weather patterns come and go, and are mixed in terms of frequency, duration, and intensity, but to assume a priori that H=0.5 is a false-Markov understanding of weather risks and suggests a good chance that the insurance design will fail to accurately reflect the extremities of indemnity.Farm households in Africa must cope with bad conditions as to soil quality, weather and infrastructure. The variability of rainfall causes yields to vary strongly from one year to the next. With yields already low (due to poor soil condition) these variations can be life threatening. Meanwhile, inadequate infrastructure makes it difficult to help the households with access to financial services, insurance and inputs that could stabilize their access to resources, and enhance yields. Solving a single aspect, say bringing inputs to the farm, will not be sufficient as credit is also needed. But credit can only be provided if sufficient likelihood exists that loans will be repaid. Here, insurance can help. If insurance of the loan makes it attractive enough for the lender, a package can be composed of inputs, with credit and insurance, that solves all these problems with one bundle. Yet, the households will remain exposed to some risks as insuring against all is prohibitively expensive. What is the appropriate degree of insurance in such bundles? That is the core question addressed in this research. It aims at supplying inputs to farmers on credit, with insurance, in such a way that a good balance is found between the benefits and risks to the farmers and the profits and risks to the credit provider. We investigate the possibilities for such a balanced approach in Kenya and Ethiopia in collaboration with a large insurance provider and a farmers organisation. Together with them we collect information on the costs, benefits and risks involved in using the inputs, the alternatives open to them, and the costs and benefits involved in providing credit to finance the purchase of inputs, with and without an insurance against crop failure. With all this information, we go and talk to the stakeholders concerned to find out how they would respond if more or less insurance would be provided. Will credit suppliers lower their prices, if repayment of loan is more likely because the crop is insured? Will households decide to take higher yielding (but more risky) crops if part of the downside risk is insured? We establish this for the parties concerned in Kenya and Ethiopia, but also in other African countries. Having established how these stakeholders respond to changes in insurance, we can proceed to derive what the best degree of insurance might be. And this is then finally tested in a field experiment. With this knowledge we can help other suppliers of insurance and credit, and farm organisations to establish similar packages that are adapted to the local conditions for input supply, and financial services.

Historical data on rainfall in Kenya, Africa.