Weather index insurance has been attracting much attention from academics and policy makers. When deciding whether and how much insurance to obtain, farmers face a trade-off: while an increasing acre coverage reduces the weather risk, it increases the basis risk. This dissertation investigates the demand for rainfall index insurance in India. Chapter 1 presents the subsidy experiment that was conducted in India and describes the key variables collected. It offers directions for quantitative research using the analyzed dataset. In Chapter 2, I particularly focus on the relationships among basis risk, weather risk, and the risk aversion of potential insurance buyers. Based on the subsidy experiment, I develop a structural model, and estimate the risk aversion parameters. The estimated risk aversion is found to be consistent with the observed inelasticity of demand for many farmers. I also show that a heterogeneity of socio-economic characteristics affects the level of the estimated risk aversion. I find that age, education, and literacy are negatively correlated with the estimated risk aversion. Finally, I derive an aggregate demand and conduct a counterfactual analysis to quantify the effect of basis risk. I find that basis risk is important enough that only farmers within approximately 4km to a weather station can actually reduce the overall risk by purchasing this insurance.