Crop insurance premium rate impacts of flexible parametric yield distributions: An evaluation of the Johnson family of distributions

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This study evaluated the Johnson family of distributions as a flexible parametric approach to model crop yields. Specifically, its statistical performance was compared to the most common distribution used to model yields in the literature -- the beta distribution. All distributions examined were re-parameterized such that the suitability of the candidate distributions is solely determined by the span of the skewness-kurtosis combinations allowed by a particular distribution. This re-parameterization facilitates comparison of the performance of the distributions. The parameters of each distribution were then estimated using the maximum likelihood technique. Comparison of likelihood values was used to assess the statistical performance of the distributions. Application of the procedure to a sample of Illinois farm-level corn data showed that the Johnson family of distributions seemed to be a highly flexible parametric distribution that best fits the empirical data (as compared to the beta distribution). This may be attributed to the fact that the Johnson family can theoretically account for any possible underlying mean-variance structure and a wide variety of skewness-kurtosis combinations. The economic significance of the findings was assessed by evaluating the effect of yield distribution choice on the estimation of actuarially fair insurance premiums. Results showed that the actual unsubsidized premium rates used by RMA are significantly different from the premiums estimated using the Johnson family of distributions. This is suggestive of adverse selection problems for the sample of Illinois corn farms investigated. However, when the subsidy to the current RMA premium rates were taken into consideration, the magnitude of the difference became smaller. Hence, the subsidies implemented by the government to encourage participation of low-risk producers seem to have the positive side-effect of reducing adverse selection in the program.

Crop yield model, Parametric model, Johnson distributions