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if x strike ⎤ ⎡0 ⎥ ∗λ, indemnity = ⎢ (10) ⎣ strike − x if x ≤ strike⎦ where x is the index value in the individual years and λ stands for liability.
As it could be seen in equation (10), the indemnity function defines a weather-contingent contract as a put option, that would provide an indemnity if the index value falls below a strike level. In this study, the index strike level was defined as the average level of a particular index. To be able to compare the weather-index insurance products with the areayield insurance, in contrast to the studies on weather derivatives (TURVEY, 2001; BERG et al., 2004), liability was set to correspond to the average farm’s wheat yield in this study.
Moreover, all estimations were completed assuming 100 percent insurance coverage12 and in
0.1 tonnes per hectare.
The assessment of fair premium in case of area-yield insurance was conducted by the application of an indemnity function specified as ⎡α µ − y ⎤ µφ i,0⎥, indemnity = max ⎢ i (11) ⎣ αµ i ⎦ where y stands for the realized area yield, αiµ is the critical yield and φi responds the optimal level of coverage for the farm i (MAHUL, 1999; SKEES et al., 1997).
NtRand (Version 2.01) and Matrix.xla.
According to the Anderson-Darling (AD) and Kolmogorov tests area yields in the considered rayon are distributed as a Weibull-distribution. With respect to the weather indices best fit was provided by a Loglogistic distribution in the case of the rainfall index and drought index by Selyaninov (AD and Kolmogorov tests); drought index by Ped is distributed as an Inverse Gauss distribution with respect to Chi-square and AD tests.
These parameters are presented with respect to the considered weather indices in the formulas (4)-(9).
In the case of area yield insurance the optimal level of coverage was applied. To determine the optimal level of coverage the critical β as specified by MIRANDA (1991) was assessed by means of a regression equation.
Raushan Bokusheva Both indemnity functions were additionally employed to assess expected indemnity by means of the "burn rate" method. This method is often applied in actuarial practice and assumes that future losses will be distributed as in the past. In this analysis we assessed these values in addition to fair premium to prove the performance of the considered insurance products in the short-run using the yield and weather data from 1983 to 2002.
Appropriate price To assess the readiness of farmers to purchase insurance, a formula derived by CHAMBERs and QUIGGIN (2004) in the framework of state-contingent approach can be applied. The appropriate price indicates the maximal price that the farmer is ready to pay for one unit of
insurance and is defined as follows:
c s ( w, z ) v* = ∑ as, (9) ps s where cs are marginal costs in state s, ps stands for output price in state s, as represents payout (indemnity) in state s, w is input price, and finally zs is stochastic production in state s.
The formula allows comparing farmer’s activities to manage risk through production decisions as well as an insurance. Thus, an insurance is plausible as far as it is not more then the cost of increasing revenue by one unit in every state of nature.
Applying this formula to our empirical investigation we had to define the farm’s output prices and marginal production costs. This was a challenging task with respect to the data that was available in the framework of the study. Since no price and production data was available from the considered farm, the study employed regional price data over the period from January 2000 to June 2004 and used data on production costs, which were assessed for the current level of technology employed on most large farms in the respective agri-climatic zone of the Akmola-region (SIGAREV, 2003).
To account for the possible presence of natural hedge, different levels13 of correlation between output price and index values were considered. We considered correlation coefficients between output price and index values instead of the correlation between output price and farm yield because only these variables are introduced into the appropriate price formula.
Output prices are introduced directly into the formula and index values are considered indirectly through the parameter as – indemnity, which is subject to the index value in state s.
In case of parametric insurance the farm’s yields are not used for assessing indemnity, but natural hedge could be observed even better on a region-level, in our case the rayon-level.
Thus, considering area-yield insurance it is legitimate to use the correlation between area yield and price. Further, since specific weather events determine farm yields, in case of presence of natural hedge they have to demonstrate a negative correlation with price as well.
Therefore, in case of weather-index insurance we decided to concern this issue by accounting for a negative correlation between a weather-index and price. As the estimation results show, the appropriate price slightly decreases with increasing absolute values of the correlation coefficients between price and index values. This is in accordance with empirical evidence and shows that farmers are less willing to buy insurance when they can compensate their production losses by higher prices.
The empirical estimation of marginal production costs in different states is an object of our further in-depth investigations. For the moment, we decided to assess this value by using the In our analysis we considered the following values of the correlation coefficients: 0, - 0.1, - 0.3, - 0.5.
Crop insurance in transition: a qualitative and quantitative assessment of insurance products 23 average instead of marginal production costs. Additionally, we had to assume a constant technology so as to use the same level of costs over all states of nature. This illustrates that our estimates of appropriate price are rather rough and should be considered just as an approximation. Consequently, a more advanced investigation is required to introduce the concept of appropriate price into empirical research.
Estimation results In Table 3 the estimation results are presented with respect to the individual indices. The actual loss was calculated using the selected farms’ yields and has an expected value of 1.89 tonnes over the period from 1983 to 2002. The fair premium was assessed on the basis of the generated index values. Estimations of the expected indemnity as well as the appropriate price were done using historical weather data in the above-mentioned period.
As the estimation results show there are some differences in the estimated values of the fair premium with respect to the simulation procedures of the index value generation; particularly in the case of the rainfall-based index and drought index 1. That can be explained by different assumptions with respect to the probability distributions. Using the parameters simulation procedure, a multivariate normal distribution was assumed. In the procedure of direct index simulation, Log-logistic distributions were employed to generate the rainfall-based index and drought index 1 (by SELYANINOV) and an Inverse Gauss distribution was applied in case of drought index 2 (by PED).
Considering the estimations of the fair premium and the expected indemnity the lowest differences in their assessment could be found with regard to drought index insurance 2 and area-yield insurance. This indicates that these insurance products provide more precise estimates also in a short-run, and is an important aspect for actuarial practice.
Comparison of expected loss and indemnity estimates shows that there is no insurance scheme which provides a complete coverage of the farm’s crop losses. This was to expect, since weather-based insurance provides protection against only one, usually the most important risk, in this case – drought, and area-yield insurance covers only systemic yield losses (e.g.
idiosyncratic risk remains uninsured). However, all weather-based insurance products minimize the differences between expected indemnity and loss. This fact supports the argument that drought presents the most important natural hazard in the considered region.
Further on, for all insurance products the estimates of appropriate price approach the fair premium values. However, as appropriate price identifies the maximum price that the farmer is ready to pay for an insurance, it must be lower than the insurance premium. With respect to rainfall-based insurance and drought index (1) insurance no clear assessment is possible: The ratio of fair premium to appropriate price varies between 0.95 and 1.01 and 0.96 and 1.11, respectively. Conversely, in the case of three other insurance products the estimates of appropriate price is definitely lower than the fair premium. This indicates good prospects with respect to the farmers’ participation in crop insurance.
By way of summarizing the discussion of the estimation results, the analysis and comparison of the selected insurance products show that two of them, drought index (2) insurance and area-yield insurance, provide a better basis for developing crop insurance in the considered region. However, further investigations are necessary before these insurance products can be recommended for introduction. This concerns both empirical and methodological issues.
5 CONCLUSIONSDue to the slow development of financial markets and the scarce provision of financial services to farmers in many transition economies, crop insurance can present an initial instrument of farmers' income stabilization. The analysis shows that most of the important aspects of insurance markets in developed countries can be applied in a transition economy as well. However, additional issues can arise in establishing crop insurance in this context.
Depending on the extent of these problems, several insurance products could be assessed in terms of their potential and applicability in an individual transition country. The complexity of the problems to be treated in the transition process involves and requires the gradual development of crop insurance markets. This would allow the accumulation of extensive knowledge and experience for the development of a long-term strategy which aims to increase Crop insurance in transition: a qualitative and quantitative assessment of insurance products 25 sustainability of farming. As first estimations show, in the case of Kazakhstan, introducing drought-index insurance or area-yield insurance for large farms in the grain-producing regions seems to have good prospects. Initial preconditions for that are analyzed in this study.
However, in view of the problem’s complexity, further investigations are necessary.
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