Estimating bivariate yield distributions and crop insurance premiums using nonparametric methods

Abstract

Modelling crop yield distribution is crucial in crop insurance premium setting. The correlation between different crop yields due to rotations or systemic risks requires estimation of joint yield distribution for multiple crops. In this article, we apply a nonparametric method to estimate bivariate yield distributions using farm-level yield data of wheat and corn in Shandong Province in China. Then, the simulated yields are used to evaluate the expected indemnity of one traditional and one hypothetical crop insurance programme. Our results reveal that the nonparametric bivariate method is very flexible in shaping the yield probability density functions to estimate local idiosyncrasies and correlation between two crops. It is also feasible to simulate the nonparametric yield distributions at a satisfying level of accuracy. The simulation results show that the hypothetical two-crop insurance contract can be more affordable to farmers than traditional individual crop insurance contracts.

Keywords:

• bivariate
• crop insurance
• nonparametric
• yield distribution

JEL Classification:

• Q14
• Q18

Acknowledgements

We thank the editor and two anonymous referees for constructive comments and suggestions.

Funding

We acknowledge the partial financial support by Chinese National Natural Science Foundation Projects No. [71073102] and No. [71273171].

Notes

¹ After detrending, 10 households in Village 3707 which choose AR(1) as trend specification are removed due to lack of historical data to predict 2006 yield trend.

² In China, the market prices for major grains are around the prices set by the government, because government is still the primary purchaser through the state-owned enterprises. Here, we use the government purchase prices.

³ For the two-crop insurance, after the loss from the first crop is realized, farmers may have more incentive to reduce effort on the second crop so that it will not gain a high yield only to compensate the first crop. This is the moral hazard problem that insurance companies need to be aware.