|題名: ||The Design of Multiyear Crop Insurance Contracts|
|作者: ||Chen, Ying-erh;Goodwin, Barry K.|
|關鍵詞: ||crop insurance|
|上傳時間: ||2012-10-21 17:06:28 (UTC+8)|
|摘要: ||Agriculture production suffers potential risks because of the yield and price instabilities which result from unpredictable factors. These factors can be caused by natural disasters such as fire, drought, flooding and pest damage. Yield volatility causes price movements and income instability for farmers. In order to help protect farmers from production, price and income risks, the Federal Crop Insurance Program provides various types of insurance. Some insurance is based on the farm level, such as the farm-level yield insurance (Multiple Peril Crop Insurance or MPCI), farm-level revenue index insurance and farm-level revenue insurance with harvest price feature. Other types of insurance are based on area level, such as the area-level yield insurance (Group Risk Plan or GRP), area-level revenue index insurance and area-level revenue index insurance with harvest price feature.
Current multiple peril (MPCI) and group risk (GRP) crop insurance plans are designed to mitigate monetary fluctuations resulting from yield losses for a single year. However, yield realizations (or yield realization tendency) can vary from year to year and may depend on the correlation of yield realizations among years. Indemnities and actuarially-fair rates, which are given by the expected loss divided by liability, for MPCI and GRP are related to yield realizations. If poor yield realizations can be offset by another year’s better yield realizations, the actuarially-fair rate is expected to decrease when current MPCI and GRP are extended to multiple periods. Therefore, in this proposed multiyear MPCI and GRP, insurance terms are extended to more than a year. The premium, liability and indemnity are also determined by a multiyear term. That is, they are calculated based on the aggregated yields for two or three years. To implement the multiyear MPCI and GRP contracts, we need to model the multivariate multiyear yield distribution and understand the correlation of yields among years. Further, the probability of loss, expected loss, liability, actuarially-fair rate, the optimum premium, the optimum time to pay premium during multiple periods will be investigated.
The objectives of this study are to 1) understand the relationship between correlation of yields among years and actuarially-fair rates for multiyear MPCI and GRP crop insurance policies. 2) investigate how to model multiyear corn yield distributions for farm (MPCI) and county level data (GRP) and to estimate correlation of yields across years; 3) investigate how to design an efficient multiyear MPCI and GRP.
We have used simulations to demonstrate that actuarially-fair rates can be reduced if a multiyear insurance plan is considered and the Pearson correlation coefficient of yields between two consecutive years is less than 1. The simulation results showed that actuarially-fair rate for a multiyear insurance plan decreases when the correlation of yields between two consecutive years also decreases. This implies that in practice, if the yields of two consecutive years are not completely correlated, our proposed multiyear insurance program can perform better than current single year insurance program. Therefore, it is important to estimate the correlation of yields using real data to demonstrate the feasibility of our method.
Farm data for ten years in Iowa, Illinois, Ohio and Indiana were obtained from ftp://ftp.rma.usda.gov/pub/Miscellaneous_Files/yield98/. County data from 1928 to 2007 in Iowa, Illinois, Ohio and Indiana were obtained from www.nass.usda.gov. The top ten productive counties in these 4 states were used in the empirical analysis. We calculated Pearson correlation coefficients for farm and county data for 1) each farm in Iowa, Illinois, and Ohio States and; 2) each county in the four States after farm level data are aggregated to county level data; 3) the top ten productive counties in Iowa, Illinois, Ohio and Indiana States. We found that values of Pearson correlation coefficients vary considerably for farm data. However, most of them are not significantly correlated (i.e. p values > 0.05). It is also notable that there is no significant correlation at the significance levels 0.01 and 0.025 in the top ten productive counties in the four States. The empirical results demonstrate that the proposed multiyear insurance plan can be practical.
Other than calculating sample correlation coefficients based on the Pearson correlation coefficient, we also estimated the correlation of yields among years by modeling the joint distribution of yields. There are two methods to modeling yield distributions- parametric methods (such as Weibull, the log-normal, the gamma, the logistic distributions and mixtures of parametric distributions) and nonparametric kernel methods. Since the dependence structure needs to be considered when a multiyear yield distribution is estimated but current parametric methods usually do not have closed forms for multivariate distributions, parametric copula methods (Frank’s Copula and Farlie-Gumbel-Morgenstern copula in the Archimedean Copula Family, Gaussian Copula and t-Copula in the Normal Copula Family) were used to approximate the multiyear yield distribution. The results also agreed with the Pearson correlation coefficients that the correlations of yields between two consecutive years are not strong.
This study focused on how to redesign MPCI and GRP so that they are more attractive to farmers. Here we propose multiyear MPCI and GRP that insurance terms are extended to more than a year. Our simulation results showed that the actuarially-fair rate for a multiyear insurance program was lower than the actuarially-fair rate for a single year insurance program when the correlation of yield distribution among years decreased. Our real data results also showed that the correlations of yields among years are not strong. Therefore, the proposed multiyear insurance program can be practical and will provide more interests for farmers to participate in the MPCI and GRP.
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