Measuring the dependence structure between yield and weather variables

The design and pricing of weather-based crop insurance and weather derivatives is strongly based on an implicit assumption that the dependence structure between yields and weather variables remains unchanged over time. In this paper, we prove this assumption based on empirical time series of weather variables and farm wheat yields from Kazakhstan over the period from 1961 to 2003. By employing two different methods to measure dependence in multivariate distributions – the regression analysis and copula approach – we reveal statistically significant temporal changes in the joint distribution of relevant variables. These empirical results indicate that greater effort is required to capture potential temporal changes in the dependence between yield and weather variables, and subsequently to consider them in the design and rating of weather-based insurance instruments.