Modeling Crop Yield Risk Using Parametric and Nonparametric Methods: Case Study of Wheat and Barley in East Azarbaijan Province

Introduction risk is as an uncertainty that has effects on individual’s welfare, which is often related to the adversities and loss and is defined as the probability of adversity or loss too. Activity in the agriculture sector is different from the other sectors because the producer's incomes are affected by a lot of risks. Agricultural insurance is mentioned always as a good strategy for the risk management of the agricultural sector. In designing and rating a crop insurance contract, the modeling of yield risk is fully analogous to modeling the probability of distribution for the crop yield and significantly depends on the distribution function, thus in appropriate designing of agricultural insurance contracts, the accurate modeling of the crop yield distribution is vital.
Materials and Methods There are three approaches for modeling yield distributions, parametric, non-parametric and semi-parametric methods which parametric and nonparametric approaches are more conventional. In many cases, crop yields show increasing trends over time because of technological change which deviation from this pattern (the error term) is often causes variance heterogeneity and reject the assumption that the yields are independently distributed. Thus A common approach to yield risk modeling is detrending the data and using detrended series for modeling yield risk. This approach is often called a two-step approach. The candidate parameterizations includes beta as the parametric and kernel as the nonparametric distribution. The area under the density to the left of the guaranteed yield presents the probability of loss thus the integral of the curve between zero and the insurer yield guaranteed should be calculated as the probability of loss. The Integral under the kernel density to present the probabilities of loss was numerically estimated using a trapezoid rule. Now the yield insurance is running traditionally by the Agricultural Insurance Fund and is faced with problems of mismatch in received insurance premiums and payment indemnities. Therefore, consideration to diversification of insurance products and using the accurate and conventional methods to calculate the probability of losses and premiums in order to improve the current situation is very important. This study attempts to calculate the probability of loss using the parametric and nonparametric approaches for the area yield crop insurance contract and employs historical county-level yield data for irrigated and dry wheat and barley during the years of 1975 to 2013 for Ahar and Hashtrood counties in East Azarbaijan province published by Agriculture-Jihad Organization.
Results and Discussion The descriptive statistics for the detrended yields for all counties and crops indicates that the yields exhibit negative skewness in more than 63 percent of the cases. Negative skewness suggests fatter right-hand-side tails with yields close to the maximum yield observed more frequently than very low yields. We calculate the probability of loss in different coverage levels (65%, 70%, 75%, 80%, 85% and 90%) and the results indicate that the ranges of their variations are different. The results show that the values of probability of loss in parametric approach (beta distribution) are higher than nonparametric approach (kernel distribution). To compare the parametric and nonparametric distributions, the CDF plots of the kernel, beta and empirical distribution are evaluated and the results showed that the kernel distribution fit the sample data very well and fits the data better than beta CDF. Moreover the results show that except for some coverage levels of dry wheat, in all the cases, the values of probability of loss are higher in rain fed crops than irrigated crops. The results also show that the probability of loss in Hashtrood County is more than Ahar County, indicating that the crop yield risk in Hashtrood County is more than Ahar County, thus the probability of indemnity payments will increase and the higher premiums will be needed for this county.
Conclusions In general, the results indicate that the values of the probability of loss obtained from two approaches are significantly different from each other and the nonparametric approach results are more accurate. Therefore, it is recommended that in estimating the premium rates and yield risk calculation, the characteristics of distribution functions to be considered and the appropriate approach to be selected. Due to the results that show the probability of loss in Hashtrood County is more than Ahar County, it is recommended that in determining the premiums, the smaller divisions than province to be considered to organize the homogeneous risk groups. Moreover since the availability of different coverage levels provide better choice power for producer to manage their farm risks, it is recommended that the premium rates which due to the different probability of loss in different coverage levels are different, present in the variable coverage levels to the insurers.