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• WBII is better positioned to avoid moral hazard because of objective nature of parameters that trigger indemnity payments.
Nevertheless, some important issues remain unresolved even by introducing these advanced
• AYCI and WBII do not solve the problem of risk pooling;
• Neither of them provide protection against price risk;
• There exists a danger that risk-averse farmers may change their production patterns in a way that increases systemic risk;
• AYCI can lead to adverse selection since it is based on average yields of a region;
• WBII is attractive for those farmers, who look for insurance against only one, most serious risk – other important risks cannot be insured;
• Risk-averse farmers could prefer farm-level insurance to area products, thus WBII might be more attractive for them compared to AYCI.
With account of these critical issues both schemes have been considered in the quantitative analysis that is presented in the next section.
Crop insurance in transition: a qualitative and quantitative assessment of insurance products 17
4 QUANTITATIVE ASSESSMENT OF INSURANCE PRODUCTS
4.1 Procedure and data
To conduct the quantitative part of the analysis the study employs a procedure which contains
the following steps:
• Index selection and design, estimation of the weights for the parameters included in an index;
• Numerical simulations to assess index distributions;
• Assessment of the expected indemnity and fair premium;
• Calculation of appropriate insurance price to assess the farmer’s readiness to purchase insurance.
The most important steps of the procedure will be discussed in the next subsections.
To evaluate yield dependence on the annual weather conditions, yield data from 12 large grain farms, in the Atbasar-rayon in the Akmola-region were employed. Yield data covers the period from 1983 to 2002. Different functional forms were used to de-trend the farm’s yields to account for technical change4. Since no time trend was found, the further analysis uses the farm yields without detrending5.
Additionally, data from a weather station in the same region has been used in the analysis.
Weather data corresponds to the period from 1974 to 2003 and encloses:
• Daily precipitation (mm),
• Average daily temperature (°C) and
• Productive soil moisture in a one-meter soil horizon on may 18 in respective years.
4.2 Index selection and design
As results of the farm survey indicate, drought presents a major source of production risk over widespread areas in Kazakhstan (HEIDELBACH et al., 2004). In view of the severity of the problem, much research has been done in Kazakhstan on the drought phenomenon, its consequences for agriculture, and instruments to manage its effects on farm. In the literature, drought is defined as a natural phenomenon induced by a continuous and substantial deficit of precipitation, accompanied by high air temperature, which, due to evaporation and transpiration, causes the drainage of productive soil moisture, and thus unfavorable vegetation conditions (SHAMEN, 1997). Three types of drought are distinguished: Atmospheric and soil drought as well as dry wind. To be able to assess its extent, different measures of drought were introduced.
Linear, piecewise-linear, second and third degree polynomial and exponential functions were considered.
Appendix D illustrates the yield development patterns in several (randomly selected) farms in the considered rayon.
Raushan Bokusheva SELYANINOV (1958) (quoted in SHAMEN, 1997) suggested to identify drought by using an index accounting for the effects of two factors: Precipitation and temperature. He introduced
the so-called hydro-meteorological coefficient (HTC):
∑R, HTC = 10 (1) ∑T where ΣR is cumulative precipitation in mm during the period with an average daily temperature ≥ 10 0C; ΣT is the sum of the average daily temperature in degrees Celsius in the same period. SELYANINOV demarcated weak drought when HTC ≥ 2, middle drought when
2.0 HTC 1.0, and strong drought when 1 ≤ HTC ≤ 0.5.
Later on, PED (1975) (quoted in SHAMEN, 1997) suggested to measure drought by means of an
index (Si), which considers, additionally to precipitation and temperature, soil moisture:
∆Ri ∆Qi ∆T Si = + −, (2) σR σQ σT where ∆R, ∆Q and ∆T stand for differences between long-term average and the i-considered period level of precipitation, soil moisture and temperature, respectively; σR, σQ and σT are their long-term coefficient of variation. Ped then defined the drought extent as weak if Si = 1….2, medium if Si = 2.…3 and strong if Si 3.
More recently, another drought index was introduced by BOVA (GREENGOF et al., 1987), who
suggested to assess the extent of drought (K) by using the following formula:
10(W + R) K=, (3) ∑T where W is the productive soil moisture in a one-meter soil horizon in springtime, R is cumulative precipitation from springtime until the moment of index assessment, and T is the sum of the average daily temperature in the period, with an average daily temperature ≥ 0 0C.
In this study, all three presented drought indexes are examined and serve as a basis for the development of a drought-index insurance product.
To prove suitability of the selected indices to reproduce weather conditions in the individual years, their correlation coefficients with wheat yields for every of the 12 farms were calculated. Table 2 represents the minimum, maximum, and average correlation coefficients between the farm yields and annual magnitudes of different weather indexes6. The average correlation coefficients are presented in the last column of the table. The results show that the performance of the indices is varying. The highest degree of dependence is observable in the case of area yield. All drought indices also possess a strong correlation with the yields of several farms. The maximum correlation coefficients reach values 0.81, 0.85, 0.87 in the case of the drought indices by SELYANINOV, PED and BOVA, respectively. It could be supposed that the highest correlation coefficients might be observable in case of the farms which are located in the weather station surrounding area. However, this was not always the case. By introducing data on the farms’ yields power we could find out that the highest correlations are characteristic for the farms in the areas with low soil quality (yield power less than 35 points).
In the farms with higher yield power the correlation between the yields and the selected First, correlation coefficients were calculated for every large farm in the rayon, then the highest and lowest coefficients were selected.
Crop insurance in transition: a qualitative and quantitative assessment of insurance products 19
Area Yield 0.74 0.98 0.79 Note: * Drought indexes were calculated to correspond to the growing period (June 1-August 31).
Source: Own calculation based on data, which was collected during the farm survey.
In our further analysis we used all drought indices and the rainfall-based index in addition to AYI and applied them to a farm with a high correlation between yields and weather indices7.
To improve the performance of the selected indices we modified them by introducing monthly data and fitting them to the farm data. By means of least square regression the effects of the weather parameters (independent variables) on the farm’s wheat-yields (dependent variable) were estimated and the following index structures (shapes/configurations) were identified8.
Rainfall-based index, R2=0.80 0.09(0.03) RMay + 0.09(0.02) R June + 0.08(0.02) R July + 0.1(0.03) R August + 0.03(0.02) RSept − April, (4)
where R is the cumulative rainfall, T – the average daily temperature from June 1 to August 31 and Q is the soil moisture as on May 18.
Since soil moisture is a parameter, which is related to soil cultivation intensity, using soil moisture as a parameter for an insurance product could induce moral hazard problems.
Therefore, we modified the drought index by PED by replacing data on soil moisture through data on cumulative precipitation in the period from September and May.
As it can be seen in (4) to (8) almost all parameters estimates are statistically significant;
except the case of the parameter of cumulative precipitation between September and May in the Selyaninov-index and the same parameter in the rainfall-based index. Moreover, all selected weather-indices explain a substantial portion of annual yield volatility of the selected farm. The R-square measures range between 0.77 in the case of drought index by BOVA and
0.81 for the first modification of the drought index by PED. Correspondingly, the range of correlation between the modified weather indices and the farm’s wheat yields is between 0.87 and 0.90. However, in view of the above-mentioned concern with respect to use of soil moisture as a parameter for insurance pricing, we decided to exclude those drought indices, which enclose soil moisture measures, from an extended analysis.
4.3 Assessment of fair premium and appropriate price
In this section, four insurance products are evaluated with respect to their capacity to present an appropriate base for accurate insurance pricing and a proper instrument of production risk reduction.
• Rainfall-based index insurance;
• Drought index insurance 1 (modification of the Selyaninov-Index);
• Drought index insurance 2 (second modification of the Ped-Index);
• Area-yield crop insurance.
We compared these insurance schemes by considering their ability to provide an actuarially sound insurance pricing and evaluated them with respect to their accuracy in assessing fair premium and its correspondence with the actual yield loss. The actual loss was defined as an expected loss and thus is the expected negative difference between the farm yields in the
individual years and the expected farm yield:
E ( Loss ) = E ( y i − E ( y )), (9) where yi is the yield in the year i (i∈T) and E(y) is expected yield.
Crop insurance in transition: a qualitative and quantitative assessment of insurance products 21 Actual yield loss was calculated by employing the farm yield data corresponding to the period from 1983 to 2002. The insurance products were compared by considering the closeness of the assessed fair premiums to the actual loss.
Distribution estimations and generation of the index values were done by means of @risk and several add-in-programs for MS-Excel9. Two approaches were used to generate large numbers of weather-indices. The first approach employed the following procedure: Using historical weather data as a particular index was calculated, then its historical probability distribution was assessed and after that an index distribution with 10000 sample points was simulated10.
The second approach was based on the generation of a multivariate distribution of the parameters, which are included in the individual indices11; in doing so, the correlations between the individual weather parameters were taken into account. In the first stage mean values, standard deviations of the index parameters as well as covariance matrixes were calculated, after that index parameters were jointly simulated as uniform variables of a multivariate normal distribution, and finally the generated weather parameter sets were used to calculate the index values. With regard to area-yield insurance only the first procedure was employed.
Fair premium We used the generated index values to assess fair premiums and appropriate price of insurance.
To identify the fair premiums an indemnity function was employed (TURVEY, 2001):