Is the “One Province One Rate” premium policy reasonable for Chinese crop insurance? The case in Jilin Province

ZHOU Xian-hua, LIAO Pu, WANG Ke

1 China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, P.R.China

2 Agricultural Information Institute, Chinese Academy of Agricultural Sciences, Beijing 100081, P.R.China

Abstract Crop insurance in China is currently adopting the premium pricing strategy of “One Province One Rate”, which appears to be in line with the systematic risk characteristics within crop insurance. This research aims to investigate the theoretical rationalization of this pricing strategy and its implications using the spatial lag model and the county-level data from the 45 corn plant counties of Jilin Province, China. Results corroborate that: (1) the spatial spillover effect of the corn yield risk is significant in Jilin but decreases rapidly when the risk unit includes more than eight counties; and (2) separating Jilin Province into eight risk zones for corn insurance will significantly reduce the high cross-subsidy phenomenon arising from the “One Province One Rate” strategy and shall benefit poor peasants in the region as well. This paper not only proves the existence of a systematic risk of crop insurance but also reveals that the spatial correlation and systemic features of the crop yield risk do not create a solid foundation for the current pricing strategy of “One Province One Rate”. These conclusions will undoubtedly provide important references and empirical evidence for the role of China’s crop insurance in poverty alleviation.

Keywords: crop insurance, premium, spatial correlation, spatial lag model

1. Introduction

Household poverty and agricultural risk are strongly linked, and larger poverty populations are lived in high risk regions (Rosenzweig and Binswanger 1993; Mosley and Krishnamurthy 1995). This finding provides policy makers an important inspiration that reducing poverty can be achieved by mitigating agricultural risks faced by such areas. Therefore, crop insurance, as an agriculture risk management tool, has been considered a poverty reduction measure in certain regions including the United States, Europe, Canada, Japan (Barnett and Mahul 2007), India, and Kenya (Chantaratet al.2015). Crop insurance program was enacted in China in 2004, and its importance was continuously emphasized in the No.1 Central Document of succeeding years. In 2007, the central government of China began to subsidize the crop insurance premium. Consequently, the Chinese crop insurance program rapidly expanded in the past decade.Additionally, theCrop Insurance Regulations, which established rules for contracts, operations, and the relative laws of crop insurance, was officially issued in 2012.

Policy orientation apparently fuels the development of crop insurance in China. From 2007 to 2016, Chinese crop insurance premium grew briskly with more than 30%increase annually. In 2016, the Chinese crop insurance premium reached 41.7 billion CNY (about 6 billion USD),and the insured value reached 2.1 trillion CNY and covered 283.3 million acres for main crops. Moreover, more than 200 million peasants participated in the crop insurance program in the same year. China has become the secondlargest crop insurance market globally in terms of premium volume. However, the Chinese crop insurance scheme is flawed and faces the challenges of product design,subsidy structures, and the government role (Zhou 2010).Among these problems, the risk zoning and the pricing for Chinese crop insurance was the most prominent one.

Private insurance usually works well to underwrite the risk that distributes independently and subject to the law of large number criteria. However, because crop production is strongly influenced by regional factors such as weather, crop insurance has a highly correlated systemic risk, resulting in insurance market failure (Glauber 2004). Consequently, the actuarial pricing issues of crop insurance have been widely discussed by scholars(Glauber 2004). Tuo and Ding (1994) argued that the“Risk-Premium Consistency Principle” is the key to make an actuarial pricing for the crop insurance program, and risk zoning and premium classification are needed to achieve the goal. Ding (1997) provides the premium calculation methods following two crop yield distribution hypotheses(discrete and continuous). However, previous studies mainly adopt the temporal yield distribution model to price crop insurance and the spatial factors which are one of the inherent features of crop production risk are largely ignored (Yeet al. 2012).

Miranda and Glauber (1997) argued that the spatial autocorrelation and tail dependence are two major sources of the systemic risk in crop insurance and the empirical loss of crop insurance is more spatially correlated compared to that in other business lines of insurance industry such as auto insurance and family property insurance. Hungerford and Goodwin (2014) analyzed the spatial dependence of corn and soybean yields in the states of Iowa, Illinois,and Indiana, and they found that corn and soybean yields have spatial correlations at the 1% significant level. The spatial correlation or dependence of crop yield risk implied that a large region in spatial dimension is needed for a homogeneous risk unit for crop insurance. As a result, Denget al.(2002) and Shi (2011) explored risk zoning problems at the provincial level and provided empirical evidence for the widely implemented premium policy (known as “One Province One Rate” policy1The “One Province One Rate” policy means that the same premium rate is set and charged for the same crop in the entire province.The policy was first proposed in 2007 when Chinese government begins to subsidy the agricultural insurance program, mainly because China has little experience on agricultural insurance at that time and there were few data reflecting agricultural risk except for the data in) for the Chinese crop insurance program. These studies prove that the “One Province One Rate” policy appears to be rational in China. However, the spatial correlations of crop losses among regions exhibit rapid decay in the distance dimension, and the spatial dependence can be ignored when the distance dimension exceeds 570 miles (Wang and Zhang 2003). In addition,the heterogeneity of farmers’ risk could be easily ignored if the risk unit acreage is too large, which will result in the mismatch of “risk” and “premium”, leading to the problem of adverse selection (Makki and Somwaru 2001), and affecting farmers’ land use and crop sowing (Younget al.2001; Lubowskiet al.2006).

Compared with the province-level pricing in China, crop insurance pricing in the United States has been elevated to the county- and farm-levels2. Skees and Reed (1986)investigate the crop insurance premium rate problems and claim that viewing a certain proportion of farm-level yield as the pricing base will partially solve the adverse selection problem. Some literature also confirms that the countylevel data are more appropriated to be used to capture the farmer’s risk and make the rational price for crop insurance because the expected loss does not change while volatility is reduced during data accumulation (Goodwin and Ker 1998;Claassen and Just 2011; Finger 2012). The analysis of the 30-year yield and loss data in the central Corn Belt of the United States by Joshuaet al. (2012) elucidate that corn loss is highly correlated between adjacent counties and that the coverage level, an important factor for loss calculation, also shows a significant positive correlation. Using the spatial lag model, they prove that the premium cross-subsidies among counties caused by spatial dependence rose to 26% of the total premium. Because peasants who live in high-risk regions are likely to be the poor (Dercon 2001; Mosley and Krishnamurthy 1995), theoretically, social welfare will be substantially improved if poor peasants with high risks get substantial subsidies. In practice, insurers also tend to pay the indemnity according to their premium income; that is, a high premium income is likely to result in a high payment3Although doubtful in principle, such argument is true in practice because accurately estimating crop loss is difficult and insurers usually have kinds of elasticity in evaluating the actual yield or yield loss after the farmer makes a claim..Therefore, we can formulate the rational assumption that an appropriate risk zoning wherein peasants pay their premiums according to their risk levels will allow poor peasants in high-risk regions to receive more insurance indemnity, which would be helpful in alleviating their poverty.

In a word, previous literature shows that the “One Province One Rate” policy of the China’s crop insurance program appears to be rational because of the spatial dependence and systemic features of the crop yield risk,but it will results into serious consequences if the policy is not appropriated. Unfortunately, previous literature fails to investigate the rationalization of “One Province One Rate”policy in China’s crop insurance program. Therefore,taking corn insurance in Jilin Province of China as an example, this paper explores the rationalization and the consequences of the “One Province One Rate” policy by analyzing the spatial distribution of crop insurance losses and using the spatial lag model. A spatial clustering analysis method was also proposed to conduct the appropriate risk mapping in Jilin Province. It is found that the spatial spillover effect in Jilin Province is significant but insufficient to support the categorization of Jilin Province as a unit of risk, and the new risk zones based on spatial clustering analysis method will decrease the cross-subsidy rate by 35.3%. The conclusions of this work have important policy implications for the development of crop insurance in China.

Compared with the extant research, this paper presents the following contributions. (1) An applicable method and paradigm for the sub-provincial risk zoning of China’s crop insurance was proposed in this paper; (2) Our paper integrates the average physical loss and spatial distance of administrative units into one system to carry out a systematic clustering (spatial clustering) while the general clustering method in literature does not consider spatial correlation;(3) The spatial econometric methods are adopted in this research rather than the traditional methods of adjacent data weighted average and hierarchical Bayesian modeling to capture the spatial characters more accurately for crop insurance; (4) County-level data are used in this work for analyzing the impact factors and spatial effects of corn insurance empirical loss, which is an extension of previous literature that mostly relies on data in the national and/or provincial level.

The rest of this research is structured as follows. The next section presents the data and method adopted in this paper. The third section provides the empirical results and estimates the effect of risk zoning on poverty reduction.The concluding remarks are offered in the last section of this article.

2. Data and methods

2.1. Data source

The empirical part of this research primarily relies on the example of Jilin’s corn insurance. Jilin, the province in Northeast China, is one of the main corn planting regions.Corn insurance has been implemented in Jilin Province since 2004 and it shares the same characteristics as that in other Chinese regions, such as covering the yield loss risk because of adverse weather, adopting a flat rate for the province, and limiting the insured value to the physical costs of crop planting.

Data in this paper were in county-level and were chiefly obtained from the statistical yearbook of Jilin Province.County-level crop yield data cover the period from 1999 to 2014. In addition, some data were obtained from the Meteorological Bureau of Jilin Province, the industry database of the China Economic Information Network,and the publicly disclosed information from the Ministry of Agriculture and Rural Affairs of China.

2.2. Data preprocessing

Zoning adjustmentAccording to the latest administrative divisions in 2015, Jilin consists of nine prefecture-level divisions (Changchun, Jilin, Siping, Tonghua, Baishan,Liaoyuan, Baicheng, Songyuan, and the Yanbian Korean Autonomous Prefecture), and the two county-level cities(Meihekou and Gongzhuling). The Changbai Mountain Administrative Committee is also within the jurisdiction of Jilin. As the cities typically plant few crops, the municipal districts of the regional cities are merged into a single observation area. For example, Changchun City comprises the following districts: Nanguan, Chaoyang, Lüyuan,Erdao, Shuangyang, Kuancheng and Jiutai. This research merges them into the Changchun Municipal District, but the municipal county remains. Consequently, we obtained 45 county-level regions in Jilin Province.

Preprocessing of policy dataPolicy data, including data of the premium, insured value, insured acreage, and claim data in crop insurance policies, were first sorted and coded according to the 2015 administrative division of Jilin Province. Subsequently, the actual yield losses were estimated by multiplying the claim acre and the loss extent,which is in line with the practice for crop insurance claims in China. Two measures were used in this paper to assess the experienced losses of crop insurance, namely, loss rate per acre (LSi) and unit premium loss rate (LPi). For the sake of data stability, the experienced losses in each region were estimated by averaging theLSiand theLPiloss rate from 2009 to 2014, i.e.,Where,Lijdenotes the insurance indemnity of countyiin yearj,Sijis the coverage area, andPijis the premium income. Summaries of the processed policy data are shown in Table 1.

Preprocessing of yield dataCrop yield will significantly increase in the long term because of the advancements in planting technology and the improvement of crop varieties.Hence, we must distinguish between long-term crop yield trends and short-term crop yield fluctuations when analyzing crop yield risk in each observation district. Accordingly, the Hodrick-Prescott (HP) filter method was used in this work,and then both growth rate of the yield over a long period of time (HPT) and the standard deviation over a short period time (HPC) were calculated.

2.3. Model building

The purpose of this paper is to study the rationalization of the “One Province One Rate” policy by exploring the spatial correlation of experience loss in crop insurance. Although the crop insurance experience loss could be significantly affected by meteorological factors, geographical conditions,biological disasters and the level of planting technology, we are not going to include the specific affecting factors in the econometric model. The reasons are: 1) this paper’s goal is not to analyze the main influencing factors of crop insurance experience loss; 2) it is very difficult to establish a reliable model considering all the factors in meteorology, geography,biology and planting technology due to the interaction of these factors and the complex of crop ecology system; 3)the impact of all factors coming from above aspect can be reflected on crop yield ultimately. Therefore, the average crop yield, which could reflect the seed quality, soil fertilize and weather condition, the long-term trend, which could reflect the improvement of planting technology, and the crop short-term volatility, which could reflect the impact of weather and pest, were selected as the explanatory variables to explain the correlation between the extents of the loss of geographical space in this paper.

Variable settingExplanatory variables includeAP,HPT,andHPC, whereAPdenotes the average annual production in a statistical interval of the corn yield of each county,HPTsignifies the slope value of the long-term trend sequence regressed by statistical time after the HP filter, andHPCindicates the standard deviation of short-term volatility sequences after the HP filter.

Note the two different data intervals (the full data interval from 1999 to 2014 and the 10-year data interval from 1999 to 2008) were used to estimate the values ofAP,HPT, andHPCin this research. Explanatory variables for the 10-year data interval are designated asAP_10Y,HPT_10Y,andHPC_10Y, whereas those for the full data interval are labeled asAP_16Y,HPT_16Y, andHPC_16Y. There are three reasons for using two data intervals to estimate the explanatory variables in this paper. First, model robustness can be tested and validated by using the data with different time series length. Second, model forecast capability,which is extremely valuable for the crop insurance, can be evaluated by employing the 10-year interval data which are set ahead of the year of crop insurance implementation as we believe that such capability is extremely valuable for the crop insurance industry. Third, the overlap between policy data and crop yield data will help to improve model robust as the underlying systemic factors will simultaneously affect the crop yield and insurance payment and resulting in error if the model is using the same year’s data of yield and policy. Consequently, four models were established through the relevant variables of the above policy and the production data. For models 1 and 3, the explained variable isLP(unit premium loss rate) and the explanatory variables areAP,HPT, andHPCwith ten-year data interval and full data interval, respectively. Models 2 and 4 have the same explanatory variables as model 1 and model 3, but theexplained variable is changed toLS(loss rate per acre).

Table 1 Descriptive statistics of the variables1)

Spatial correlation analysisFirst, the quartile distribution graphs of the explained variablesLPandLSwere drawn to illustrate the spatial distributions of variables. Fig. 1 illustrates the spatial distribution ofLP. Clustering is observed in adjacent counties, especially in the eight cities and counties located in the northwestern area of Jilin Province and those belonging to the upper quarter intervals ofLP. Therefore, theLPof each county in Jilin Province has a high spatial correlation. TheLSquartile distribution is similar to theLP.

Next, we use Moran’s I statistic to quantify the spatial correlation between the variableLPand the variableLS.Moran’s I statistic is defined as follows:

Where,Nis the number of the units in two-dimensional space indexed byiandj,xis the sample counties,wijis the spatial unit weight value to indexiandj, andWis the corresponding weighting matrix.

Many techniques could be applied to estimate the spatial weight matrixWin the spatial correlation analysis. However,considering the planting area of Jilin Province and the adjusted spatial distribution of each observation area, this work utilizes the kernel density weighted method whereinkequals 3 for each observation sample to establish the spatial weight matrix. The triangle kernel density functions are adapted to smooth the distancedijbetween each observed countyiand other countiesj.The bandwidth parameter is the distance between the observed countyiand the third adjacent county. The distances between sample counties define the regional center distance, i.e., wij=k(dij/di). Both statistical results of Moran’s I index forLPandLSare 0.60450, which indicates strong spatial correlations in the sample counties of Jilin Province.

Fig. 2 shows theLPMoran scatter plot using a kernel density weighted matrix. Thex-axis representsLPand they-axis denotes theLPspatial lag variable after matrix weighting. It can be seen that theLPand its lag variable have a high-high and low-low relationship, indicating thatLPdoes have a strong spatial correlation4As the scatter plot of LS Moran is similar to that of LP Moran, we did not reported here , and it is available upon request..

Ordinary least squares (OLS) modelIn order to show the necessity of establishing a spatial econometric model and facilitate the subsequent analysis of the spatial econometric model, the OLS method is employed in this paper as a baseline model to estimate the parameters. The baseline model of the actual insurance policy loss model is as follows:

Where, the explained variableLis theN-dimensional loss column,Xis theN×M-dimensional loss related variable matrix,βis theM-dimensional parameter vector,εis theN-dimensional fitting residual vector,Nis the number of observations, andMis the number of relative influencing factors. The null hypothesis posits that the loss related variables already contain all of the systematic factors inX(i.e.,βis a zero vector such that the value of each residual element is the value of each loss variable). An alternative hypothesis is that certain systematic factors are missing in the loss variable, thereforeβis a non-zero vector and the non-zeroβiis the missing factor.

Fig. 1 LP (unit premium loss rate) quartile distribution.

Fig. 2 LP (unit premium loss rate) Moran scatter plot.

Moran’s I tests were conducted to test spatial correlation after the models estimated through the OLS method. If the spatial error model statistics are not significant, the spatial lag model, therefore, should be adopted.

Spatial econometric modelTwo main types of spatial econometric regression models can be employed in this work: spatial lag model (Lag) and spatial error model(Error). The former contains the spatial lag dependent variable and the latter shows the residual of the spatial lag form. The particular spatial econometric model can be selected according to the Lagrange multiplier test (LM test) results. If the LM test results for both lag and error models are not significant, then spatial econometric methods are not needed. However, if either Lag or Error model is significant and the other is insignificant, then the model with the significant LM test result is preferred; if both models are significant, then the model with the highest LM statistic value is recommended (Anselin 1988).

The spatial lag model is developed as follows:

Where,Wis the spatial weight matrix,uis anN-dimensional residual column vector, andρis the spatial auto-regressive coefficient used to measure the spatial correlation.WLis the spatial lag variable, which is similar to the lag variable in time series regression except that it has a directional and multidimensional nature. When sample data comply with the spatial lag model form, the space lag itemρWLwill be endogenous under the multi-dimension. In that case, a simple linear regression method which overlooks spatial lag factors will lead to biased and inconsistent results.

As the model residuals may not follow a normal distribution, the generalized method of moments (GMM)was used to estimate the model parameters in this work.Specifically, the spatial two-stage least squares (S2SLS)technique is applied here to fit the model. In comparison to ordinary 2SLS, the S2SLS method has the advantage of incorporating the spatial lag variables (i.e.,Q=[X,WX]) in developing the instrumental variables. LettingZ=[WL,X]represents the spatial lag interpretation variable and the dependent variables,δ=[ρ,β] represents the estimated parameters, then the parametricδcan be estimated asδS2SLS=[Z′Q(Q′Q)–1Q′Z]–1Z′Q(Q′Q)–1Q′L. Because of the asymptotic efficiency of the S2SLS method, consistent estimate values can be acquired even in the presence of heteroscedasticity.

3. Results and discussion

3.1. Results of OLS model and spatial econometric model

Moran’s test results for the residual series of the four models range from 0.278 to 0.311. Furthermore, all the correspondingP-values are significantly less than 0.01,suggesting that the residuals of the four models have significant spatial correlation and the spatial econometric analysis is required because the OLS method failed to capture the spatial correlations. Besides, the LM tests for the four models reveal that the spatial lag model statistics of the four models are all significant while their spatial error model statistics are not significant (Table 2). The spatial lag model is therefore adopted in this research for the further analysis. Table 3 presents the regression results of spatial two-stage least spares.

It can be seen from Table 3 that all the explanatory variables exceptHPTare significant at 1% significance level, and the model fitting effect is good as the adjusted goodness-of-fit test of the four models are around 0.60. TheP-value in the Moran’s I test of the model residual is close to 1, indicating that we should accept the null hypothesis(i.e., the residual series are independent ). The spatial lag coefficientρis a nontrivial number (0.7215–0.7505), which suggests that the payments of the corn insurance for each county have a strong spatial correlation. The high correlation may arise from the spillover effect among regions. As expected, short-term yield volatility is significantly positive in the model because a higher yield fluctuation usually leads to a higher insurance indemnity. The coefficient of the average yield is significantly negative, which is consistent with the expected outcome. The analysis of the regress results of the four models confirm that the significance of each independent variable, the overall model fitting effect, the spatial lag factor and the Moran’s I test results of residuals are consistent and similar across the four models. Such findings imply that the effect of the systematic factors in adjacent regions on experienced loss is consistent in timedimension and space-dimension (i.e., the experienced loss in different areas results mainly from the corresponding location and long-term climate, rather than from short-term weather fluctuations).

3.2. Analysis of the results

We further analyze the result in Table 3, discussing the total effect, the elastic effect, and the quartile effect on the explained variables. Table 4 summarizes the results. The total effect is the coefficient of the explanatory variables in the regression model. The elastic effect is the normalized effect that estimated by multiplying the total effect with associated explanatory coefficients firstly and then divided by the corresponding explained variable. The quartile effect is the total effect divided by the quartile of the explained variable.

For each effect, we measured the direct and multipliereffects separately. The multiplier effects reflect the spatial spillover effects of the explanatory variables, and they can be estimated by fitting value of the explained variable’s lag form.Using a simple method (Kimet al.2003), the spatial spillover effects can be calculatedviamultiplying the direct effect by 1/(1–ρ). The direct effect only considers the effect of the factors in the region, for which explained variables pertain to the empirical loss. The multiplier effect also considers the cross-regional effect. As the coefficients of the spatial lag variables are positive in this work, the corresponding multiplier effect is often greater than the direct effect. The spatial hysteresis influencing the factors’ coefficients for the four models are all above 0.72, signifying that the multiplier effect of each variable can be four times more than the direct effect. In other words, the effect of the neighboring regions affected by the spatial spillover effect is three times higher than that of its own region. Moreover, given that the explained variables in the model are the actual loss rates, each fitting coefficient reflects the magnitude of the explanatory variable’s effect on the loss rate. To compare the effects of explanatory variables on the loss, we adjusted the order of magnitude of each coefficient based on the average annual premium and the average insured area of the sample data. Table 4 shows the results of timing the impact factor with 1 000 000.

Table 2 Fitting test for the ordinary least squares (OLS) model1)

The elastic multiplier effect of theHPCis in the range of 1.019 to 1.195, and the elastic multiplier effect of theAPis about ?1.299 to ?7.298, which indicates that the actual loss is sensitive to the changes inHPCandAP. The quartile multiplier effect ofHPCandAPonLPis in the range of 0.169 to 0.245 and ?0.0080 to ?0.0076, respectively, suggesting that the effects of samples near the upper quartile ofHPCandAPonLPare approximately 20 and 0.8% higher than that of samples near the lower quartile,respectively.

Table 3 Regression results of spatial two-stage least spares1)

Similarly,HPChas a quadruple multiplier. The multiplier effect is in the range of 3.381 to 4.893. This outcome denotes that the effect onLSof the samples on the upper quartile ofHPCis 3–4 times higher than that of the samples on the lower quartile. The difference in the impact ofHPConLSandLPmay be caused by the overall number of premiums and insured areas, as well as the variations in research perspectives.

3.3. Scope of the spatial correlation

Fig. 1 depicts that each county abuts approximately 3–6 counties. Hence, we set the parameterkof kernel density weighting matrix to 3. Thus, only the observed county and the nearest three counties are considered in estimating the spatial correlation of crop insurance empirical loss.

Results for the models proved that adjoining counties have a strong spatial correlation with the observed counties.To further investigate the diffusion scope of this correlation effect, we extended the range ofkto 3–10 and evaluated the spatial effect variation of the empirical loss (LP) under different weighing ranges. As the analysis on the spatial effect ofLSis similar to that ofLP, it is omitted in this paper.

Table 5 discloses that the spatial correlations of experienced loss among counties are smaller when spatial weighted range extends from three adjacent counties to 10 counties (that is, from the first-order adjacent to the secondorder adjacent circumstances). When the weighted range extends to eight counties, the value of Moran’s index is less than 0.5. This finding implies that, for Jilin Province,considering the entire province as a unit risk zone is illogical and that the appropriate number of crop risk zones at the county level should be six (45/7≈6).

Classification rating evaluation based on spatial correlationThe second part of this paper verified that crop yield risk has the nature of spatial correlation and must be considered when setting the premium rate. In theory, the copula is an acceptable method for capturing the correlations of multi-variables and/or multi-regions. However, the margin distribution for each region and the copula type should be determined first when using the copula method. Such method would be less effective and more time-consuming because of the nearly 50 risk units at the county level in this work. Therefore, spatial clustering analysis method is adopted here.

General clustering only considers individual character without spatial distribution. In spatial clustering, the spatial distribution of the individual is treated as nature, which will be incorporated into the clustering analysis. Xi and Tan (2009)outline the conventional spatial clustering analysis algorithm.As for the spatial character, two methods are primarily employed: (1) clustering separately according to spatial and non-spatial property, and then merging the clustering results; and (2) merging the space property and non-space property into an organic whole, and then standardizing each property to solve the dimension problem (Liet al.2004).This work employs the latter method because it has the advantage of simplicity, clear principles, and accessible rate adjustment. AsLSdepicts the average physical loss of the insured unit, theLSvariable is treated as the representation of non-spatial properties.

In principle, if two individuals are adjacent in the spatial dimension and have similar non-spatial properties, there is a higher probability that they could be classified into one class. The geographic location of each county is set according to its longitude and latitude (x,y). The distance between individualiand individualjis:

Where,dijdepicts the spatial distance between individuals,andDijalso considers the non-spatial properties basedon space distance, that is, the space distance between individuals will “inflate” on the basis of the differences among the non-spatial properties. Obviously, if there is almost no difference between theLSof two different individuals,then no inflation will be observed on space distances. We employed system clustering analysis based onDijin this work. Furthermore, the class average algorithm is used to calculate the distance between classes. Figs. 3 and 4 show the clustering results.

Table 4 Comparison of the effects of explanatory variables in each model

Table 5 Moran’s I test results at alternative k values

According to our earlier discussion, the number of corn risk zones in Jilin Province should be no less than six, but should not be too many. According to Fig. 3 (the number in the Fig. 3 is theLSvalue of the class), if we divide the province into six or seven risk zones, the green and blue middle-risk areas will merge with the low-risk red and orange areas. Consequently, the low-risk category will disappear. If we divide Jilin Province into 10 risk zones, then a class would exist for Fuyu County. The clustering tree diagram shows that a classification number of eight is more appropriate.Fig. 4 illustrates the rationale of dividing Jilin into eight risk zones. Significant regional clustering characteristics are shown and no outlier or isolated points are found.

On the basis of the risk zoning result of Fig. 4, a simple and straightforward method was proposed to adjust the current unique premium rate in the whole province to the classification premium rate for each risk zone. LetLSdepict the weighted averageLSof the whole province,αirepresent the premium adjustment factor, andrisignify the classification premium, then:

Where,Simeans the insured acreage in the risk zonei,ris the current premium rate and equals to 10% (the current premium rate in Jilin Province). Our calculation results are shown in Table 6. Findings confirm that eq. (6) does not need to be adjusted for balance because the premium income of the province before and after the adjustment remains the same. Table 6 reveals that the risk zones 3, 4,and 5 can be artificially classified into one category as they have similar premiums.

Cross-subsidy issues, which result in the adverse selection problem and reduce the premium subsidy efficiency, are serious when the crop risk zones are inappropriately classified. Relative to the United States,the problem of risk regionalization is vital and an urgent issue for the sustainable development of the Chinese crop insurance program (Zhou 2010). Clearly, under the current policy (with the implementation of a flat rate), the peasants in the low-risk areas of Jilin Province passively provide crosssubsidies to their counterparts in high-risk regions 7 and 8.The cross-subsidy levelηis calculated as:

Where,αi,si,andrhave the same meaning as shown in eq. (6). Therefore, in the case of Jilin Province, the “One Province One Rate” policy implies that peasants in the low-risk have provided 35.3% of the premium to peasants in high-risk regions who are undercharged.

Poverty reduction effect of the proposed risk classificationWe believe that the classification rating based on spatial correlation will be more reasonable. With such a rating system, the individual with high risk, who usually is the poor, will undertake more premiums. But we suggest that for the high-risk areas, the amount, not the proportion of premium, should be kept unchanged. That means the poor will get more subsidies from government.Therefore, the rating system based on spatial correlation and the suggested subsidy policy will reduce the poverty if hold other factors that affecting farmers income fixed.

Let the premium rate of corn insurance in Jilin Province beRate(=10% in practice),Zbe the premium percentage5In Jilin Province, the government subsidy constitutes a high proportion of crop insurance premium. The cumulative subsidy ratio is from 80 to 90%, so peasants also need to pay 10 to 20% premium when they purchase corn insurance.that peasants must pay,LRbe the loss ratio of crop insurance,LtIbe the indemnity over the self-pay premium of peasants,andFbe the rate adjusted factor, then theLtIbefore risk classification can be estimated as follows:

Thus, peasants who live in high-risk regions are also poor.A notable evidence is that the number of national poverty counties increases with the risk level (Table 7). As a part of the China Poverty Reduction Strategy, it is impossible for crop insurance to charge more premiums to peasants who are already underprivileged. An intuitive idea to solve the problem is to increase the government premium subsidy for poor peasants while the premiums paid by peasants are kept constant. Accordingly, a flexible premium subsidy structure would be formulated in which higher subsidy is provided for higher risk regions. In that case, the extra government premium subsidy is (F–1)×Rate×α, and the insurance indemnity over self-paid premium (LtI′) after risk classification is as follows:

Fig. 3 Dendrogram of system clustering for the counties in Jilin Province.

Fig. 4 Map of system clustering results. The ranks are the results of clustering analysis. Rank 1 presents the region with the least risk, while rank 8 presents the region with the greatest risk.

As risk adjustment factorFis bigger than 1 for high-risk regions,LtI′ will clearly be greater thanLtI, suggesting that poor peasants received significant insurance indemnity.Assuming that the loss ratio of crop insurance is equal to one, theLtI′ and new government subsidy ratio are calculated (Table 7). As shown, underprivileged peasants would receive more government subsidy and more insuranceindemnity in the case of the proposed risk classification,which is helpful in reducing poverty.

Table 6 Classification rate factors

4. Conclusion

Taking corn insurance in Jilin Province as an example, this study investigated the dependence of crop insurance loss in adjacent counties using the spatial lag model. The regional distribution patterns of corn yield risk in Jilin Province were addressed as well by employing the spatial clustering analysis method. The main conclusions of this paper are as follows. (1) Corn yield risk in Jilin Province has a strong spatial correlation, which is about three times than that of the same variable in its own region. This finding proves the systemic characteristic of crop insurance that triggers risk and verifies that the current “One Province One Rate”policy in China crop insurance is reasonable to some extent.(2) From the view of the second-order dimension, adjacent counties in Jilin Province also have significant spatial correlation in terms of the empirical loss of corn yield, but the correlation falls below 0.5 when the spatial distance from the observed county extended to eight counties. This finding contradicts the theoretical foundation of the “One Province One Rate” policy and implies that the serious cross subsidy issues will occur. (3) Numerous counties may be classified as risk zones because of the systemic risk feature and the strong spatial dependence of crop yield risk. However,this theory cannot support the implementation of the “One Province One Rate” policy in Jilin Province whose acreage is 187 000 km2. This research found that Jilin Province could be classified into eight independent risk zones according to the spatial clustering analysis. (4) The original “One Province One Rate” policy in China will also result in crosssubsidy issues, and the proposed risk classification method in this work can partly solve this problem by reducing the extent of the overall cross-subsidy by 35.3%. Moreover,this study confirms that the proposed risk classification method can contribute to poverty reduction by directing additional government subsidy and insurance indemnity tohigh-risk regions.

Table 7 Effect of risk classification on poverty reduction

All these conclusions undoubtedly have significant policy implications for crop insurance development in China. At the same time, our work provides empirical and theoretical evidence for China Bank & Insurance Regaulatory Commision (CBIRC) to conduct the follow-up risk zoning project.

Acknowledgements

This paper was supported by the Beijing Social Science Fund, China (17LJB007), the MOE (Ministry of Education,China) Project of Key Research Institute of Humanities and Social Sciences at Universities (17JJD910002) and the 111 Project (B17050).