Modelling joint distribution of crop plant yields and prices with use of a copula function

The paper constitutes an attempt at modelling the joint distribution of crop plant yields and prices in Poland. The main objective of the paper was to examine the usefulness of the copula function for the task and the selection of suitable marginal distributions. The fit of a joint distribution based copula function was compared with multivariate normal distribution. It was revealed that the multivariate normal distribution is outperformed by a Gaussian copula with the following marginal distribution: yields of both crop plants – normal distribution, price of wheat – Burr distribution (type XII) and price of rapeseeds – lognormal distribution. The main advantages of the copula function were: the possibility to use different marginal distributions and ability to model non-elliptical two-dimensional distributions. The practical implications of choosing the right joint distribution is demonstrated by comparing empirical quantiles of income for a given crop structure with theoretical quantiles based on the proposed joint distributions.