Parametric and nonparametric statistical modelling of crop yield: implications for pricing crop insurance contracts

Abstract

This article considers alternative methods to calculate the fair premium rate of crop insurance contracts based on county yields. The premium rate was calculated using parametric and nonparametric approaches to estimate the conditional agricultural yield density. These methods were applied to a data set of county yield provided by the Statistical and Geography Brazilian Institute (IBGE), for the period of 1990 through 2002, for soybean, corn and wheat, in the State of Paraná. In this article, we propose methodological alternatives to pricing crop insurance contracts resulting in more accurate premium rates in a situation of limited data.

Acknowledgements

Ozaki and Shirota are with the University of São Paulo, Brazil. Goodwin is with North Carolina State University. Research support from the North Carolina Agricultural Research Service and CAPES (Brazil) are gratefully acknowledged.

Notes

¹The small number of yield observations, in aggregate level and smaller in the individual level (in several countries) makes any type of statistical analysis a troublesome task.

²Moreover, with small number of observations it is hard to detect structural changes in yields and the occurrence of catastrophic events in the series.

³For the dependent spatial process the CLT the normality assumption is acceptable when the dependence dies off quickly as the distance increase (Guyon, 1995).

⁴Studying the spatial correlation of corn in USA in the three largest producer States.

⁵Information obtained during personal interview with several private insurance companies operating in Brazil.

⁶This subsection was based on the results of Silverman (1986).

⁷We consider neighbour counties not only the contiguous counties to a central county i but all those counties located within a circular area with radius equal to d. Consequently all counties whose centroids were located within this circle were considered neighbours to i.

⁸Rates charged are based only on five years of observations using the empirical rates method.