In crop insurance it is necessary to understand how underlying risk variability arises from changes in prices, yields, or both. Typically, agricultural risks are not isolated from one another. The underlying risks are dependent in different dimensions, such as time dependence, portfolio dependence, and spatial dependence. Thus, it is important to be able to adequately model dependence with multivariate outcomes. Ignoring dependencies can lead to possibly biased and inefficient estimates of the risk. This study provides a comprehensive and in-depth economic and statistical analysis of various risk in agriculture, especially the dependence structure of agricultural risk. Using both estimation and simulation methods, we analyze the interaction of risk in the presence of time-varying dimension, portfolio dimension and spatial correlation dimension. By modeling and measuring dependence, it is possible to improve risk management instruments that take advantage of dependencies between different products. This will help improve the risk management and will help government, insurance/reinsurance companies, and policy makers to evaluate their contract design and policy making.