Crop insurance demand in wheat production: focusing on yield gaps and asymmetric information

Analysis of yield gaps were conducted in the context of crop insurance and used to build an indicator of asymmetric information. The possible influence of asymmetric information in the decision of Spanish wheat producers to contract insurance was additionally evaluated. The analysis includes simulated yield using a validated crop model, CERES-Wheat previously selected among others, whose suitability to estimate actual risk when no historical data are available was assessed. Results suggest that the accuracy in setting the insured yield is decisive in farmers’ willingness to contract crop insurance under the wider coverage. Historical insurance data, when available, provide a more robust technical basis to evaluate and calibrate insurance parameters than simulated data, using crop models. Nevertheless, the use of crop models might be useful in designing new insurance packages when no historical data is available or to evaluate scenarios of expected changes. In that case, it is suggested that yield gaps be estimated and considered when using simulated attainable yields.


Introduction
Developing efficient agricultural insurance requires overcoming a number of market imperfections and combating asymmetric information. Very often, these difficulties justify governments' intervention in promoting insurance demand through the implementation of public incentives, such as premium subsidies, and a significant degree of market intervention, guidance and overseeing (Mahul & Stutley, 2010).
Asymmetric information occurs when insured farmers have more information than the insurer about their actual risk and behaviour, and results in two behavioural responses: moral hazard and adverse selection. Moral hazard occurs when farmers' expected indemnity under insurance is larger than under optimal uninsured conditions (Coble et al., 1997). This means that farmers might modify their behaviour after contracting insurance in order to increase the probability of being indemnified (Goodwin, 1994) or reduce the effort to escape risk once they are covered for it. Adverse selection happens when high-risk farmers contract insurance in greater numbers than lowrisk farmers. The insurer, being unable to differentiate them, is forced to average out the risks of both types in calculating the premium. In these situations, the insurer does not have adequate information to calculate the unbiased probability and severity of claims. The result can be unbalanced loss ratios, thereby affecting the actuarial robustness and sustainability of entire insurance systems.
Yield gaps are defined in agronomy as the differences between attainable yields based on climate and soil conditions and actual farmers' yields; they are usually defined with reference to some specified spatial and temporal scale (Lobell et al., 2009). Quantifying such gaps is useful to identify suboptimal crop management and the opportunity for the agronomic improvement of productivity (e.g. Lobell et al., 2009;Affholder et al., 2012;van Wart et al., 2013). Yield gap has been proven to be a valuable concept for assessing and understanding the ecological possibilities to meet food demand for an increasing population . Nevertheless, the use of this concept is not limited to the biophysical aspects of agronomy, but may also be used to support research on socioeconomic aspects of agricultural production. Examples are seen in the limits to technology adoption due to either technical constraints or for economic issues arising from market conditions (Godfray et al., 2010). In the context of crop insurance, a conceptual variation of yield gap might be also defined as the difference between insured and actual yields. Such a gap indicates either a deficiency in the insurer's knowledge or an information advantage of the farmer. Either situation is a case of asymmetric information. The lack of data on actual yields is very often the main cause of this asymmetry (Mahul & Stutley, 2010). Crop models can be used generate data on expected yields for risk analyses and failure studies in the crop insurance market when no historical data are available.
This paper presents analyses of yield gaps in the context of crop insurance, and the possible influence of asymmetric information in the decision of a farmer to contract insurance. A novel method to measure asymmetric information was designed based on yield gaps and applied to wheat insurance in the region of Castilla y León (northern central Spain). The analysis includes simulated yield data using the CERES-Wheat crop model in order to assess the suitability of such models to estimate actual yield risk when no historical data are available. The aims of the study were to (i) quantify the gap between actual wheat yields and the yield data managed by the insurer, (ii) obtain indicators providing evidence of potential asymmetric information in wheat insurance, (iii) explore the impact of asymmetric information on the decision of farmers to contract insurance, and (iv) evaluate the use of a crop model within the context of crop insurance.

Winter cereal insurance
In Spain, multi-peril insurance for cereal farmers has offered since 1982. The database for this study pertains to crop seasons 2010-11 and 2011-12 and includes four insurance modules (P, 1, 2 and S) that were available to cereal farmers. Module S has not been offered since 2013. The modules differ based on the coverage, on whether the crop is grown rainfed or irrigated, on the way indemnities are calculated when a loss occurs (whether indemnities are paid for each individual field or for the whole farm), and on the maximum insurable yield guaranteed (Table S1 [suppl.]). Two types of risks are defined. Type A risks include hail, fire, crop damage caused by wild fauna, flood and excessive rainfall. Type B risks include adversities impeding crop emergence (no-emergence risks) or limiting crop growth (including drought).
For irrigated crops, losses associated to both risk types A and B are indemnified per plot if the final yield is lower than the insured yield, the latter being freely set by the farmer. Under rainfed conditions, however, losses associated to type B risks can be indemnified per plot (Module 2) or per farm (Modules 1 and S). In the latter case the farmer is indemnified only if the average yield of all farm plots is lower than the insured yield, and farmers are obliged to insure all farm plots. Module S limits insured yield to a maximum officially assigned by the Spanish Agency of Agricultural Insurance (ENESA, initials in Spanish). Modules 1 and 2 limit insured yield to a maximum insurable yield calculated for individual farmers based on their insurance history records. Lastly, farmers might select a deductible, but most of them usually opt for the lowest of 30%.
To simplify the analysis, the four modules (P, 1, 2 and S) were combined into two options based on the risks covered. The first option, called Basic, comprises module P that guarantees farmers' production with coverage for type A risks. The second option, called Extended, includes modules 1, 2 and S, and provides coverage for risks of both type A and type B. Farmers choosing the Extended option may increase insured yield at midseason with a complementary insurance payment if yield expectation exceeds that insured before sowing.
Crop insurance premiums are proportional to insured yields and vary depending on the contracted module and deductible. They are subsidized by the national and regional governments. The subsidy varies depending on the option contracted, the farmer's characteristics (age, gender and others), and whether the contract is a renewal or is contracted through a farmer association. The lowest base subsidy is for module P (option Basic) increasing for modules S, 2 and 1 (option Extended) as 1, 8, 17 and 22% of the premium cost. Additional subsidies based on the farmer's characteristics (young farmers, gender and others), and whether it is contracted collectively through a farmer association are also different for different modules, in such a way that Module P (option Basic) has the lower maximum assignable subsidy followed by Module S, Module 2, and lastly Module 1 (option Extended) with 16, 33, 52 and 57 % of the premium cost (Table S1 [suppl.]).

Study site
Spain is the fifth largest producer of cereals in Europe, with a harvested production that ranged between 14 and 25.5 million Mg (6.2 Mha of crop) between 2000 and 2013 (Eurostat, 2013). About 47% of the cultivated land dedicated to arable crops (including cereal) is located in Castilla y León region, with about 2.9 Mha (ESYRCE, 2013).
Castilla y León (CyL) is located in northern central Spain. Climate is continental Mediterranean with warm and dry summers and cold and wet winters. It is a high plateau (830 masl average) around the Duero river basin surrounded by mountain ranges. There is a clear gradient of temperature and rainfall from North-East (cooler and wetter) to South-West (warmer and drier).
The most commonly cultivated cereals are barley (Hordeum vulgare) and bread wheat (Triticum aestivum), with 54% and 30% of total regional production, respectively. Wheat is mainly grown without irrigation (JCyL, 2014) so that yields respond to the high rainfall variability (240 to 700 mm). Average rainfed yields in the study region during 2000-2013 varied between 2.0 and 4.5 Mg/ha (JCyL, 2014). Winter wheat is sown during October-December and spring wheat during February-March. Wheat is harvested between late June and mid-August. The most sensitive phenological stages to meteorological adversities are flowering (April-May, late frosts, drought and heat stress) and grain filling (June-July, heat and drought).

Actual and expected yields
Actual yields (Ya) were obtained from the ESYRCE database (Encuesta sobre Superficies y Rendimientos de Cultivos), which originates from a yearly survey started in 1995 (MAGRAMA, 2014). The sample of farms is selected from a 1 km × 1 km grid. Surveys are performed at the farm level and include information on cultivated area, average yield per crop, crop varieties, management practices, farm infrastructure and others. The original database comprised 121,309 yield observations, distributed across the study region (CyL). After aggregation at municipality level, the database for the present analysis contained 7879 yield observations. Expected yields (Yexp) prior to sowing and for each of the counties were estimated assuming a linear trend from the seasonal adjusted Ya series for the following year. Yexp includes spatial variability of the mean expected yield in 531 municipalities across the study region, in 2011 and 2012.

Insurance-related yields
A database from all municipalities in CyL with at least one insured farmer in 2011 or 2012 was made available by ENESA for 107,709 insurance policies over these two years, contracted in 452 municipalities (belonging to a total of 38 counties). Each record includes information on the number of sold policies, total insured production and area, and insured yield per crop insurance module. These records were aggregated by county, year, and insurance module.
The zonal maximum insurable yield (per municipality) for wheat grown under rainfed conditions for each municipality is published every year in the Spanish Official Gazette (BOE). The ones used for this study were published in BOE (2013). These data were aggregated by county to define the average zonal maximum insurable yield (YinsZ).
Three other insurance-related yields were defined for the insurance options Basic and Extended, the latter including the complementary insurance of the option, as described in the previous section: -YinsB is the average yield insured in the option Basic, the yield expected before sowing that is freely set by the farmer.
-YinsE is the average yield insured in the option Extended (Module 1, Module 2 and Module S), yield insured by the farmers before sowing and is limited to an individual maximum insurable yield.
-At midseason, farmers have the option of contracting a complementary insurance policy, in which the insured yield is adjusted according to farmer's yield expectations at that time of season (YinsEC).
YinsZ is defined at county level (as it does not vary from a year to another) and YinsB, YinsE and YinsEC are defined per year and per county.
YinsZ includes spatial variability, including 531 municipalities in the study region. YinsB, YinsE and in optimal rainfed growing conditions, being soil water availability the solely limiting factor. Crop data belonging to the cultivar Marius (T. aestivum cv. Marius) were selected to calibrate the crop model. This cultivar is commonly used by farmers in this region. Being used as a test cultivar, it was sown in each of the trials every year. Crop development data such as emergence, anthesis and physiological maturity dates, sowing dates and plant density, and yield were available (Table S2 [ (Table S3 [ suppl.]). Three maps with polygons defining depth, soil texture and climate zones were built using ESRI ArcMap 10.0 GIS and combined into a single map. Different climate zones were selected assuming that accumulated rainfall and evapotranspiration are main driving variables for crop growth under rainfed conditions. Accumulated rainfall and evapotranspiration are aggregated in Thornthwaite's aridity index (Thornthwaite, 1948).

The map based on Thornthwaite's aridity index in the Agroclimatic Atlas of Castilla y León (Álvarez-Arias
YinsEC include spatial and temporal variability (2 years) of insured yield data aggregated at municipality level using the mean insured yield in each of the insurance options in the same 531 municipalities.

Attainable rainfed yields
Attainable rainfed yields (Yw) were simulated using the crop model CERES-Wheat (Godwin et al., 1989). CERES-Wheat as available in the package Decision Support System for Agrotechnology Transfer (DSSAT) vers. 4.5 (Jones et al., 2003;Hoogenboom et al., 2012). CERES-Wheat has been widely applied at the regional scale (e.g. Bannayan et al., 2003;Zhao et al., 2011) and preferred for the simulation of winter wheat growth at field scale in semi-arid conditions in Spain after a detailed comparison (Castañeda-Vera et al., 2015).
CERES-Wheat was first calibrated and validated using published data from the trials conducted by the Agricultural Research Program of CyL 2004 and 2010 (Table S2 [suppl.]), following Castañeda-Vera et al. (2015). The experimental sites are widely spread throughout the grain production areas and are representative of its climate and soil variability. The objective of these trials was to monitor the attainable rainfed production of different wheat cultivars. Therefore, they are assumed to have been grown  et al., 2013) was used to assign a climate zone to each sub-area (Fig. 1C). Recorded weather data assigned to each climate zone was obtained from the System of Agroclimatic Information for Irrigated crops (SiAR), covering 14 years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) (Table S4 [suppl.]). The map contained polygons assigned with a number defining a single combination of soil texture-depthclimate zone (Fig. 1D).
Models' statistical performance was evaluated using the root mean square error (RMSE) (Eq [1]): [1] where Si and Oi are the simulated and observed yields, respectively, and n is the number of observations used.
The model was run for each combination of soil texture-depth-climate zone in the region. CERES-Wheat simulates wheat biomass production (dry matter). Simulated yields were converted into yields at harvest assuming 13% humidity in order to make them comparable with actual, expected and insured yields. Average simulated rainfed yields (13% humidity) (Yw) were assigned to the corresponding polygon in the map.

Yield gap analysis
Five yield gaps (GapZ, GapB, GapE, GapEC, GapW) were defined by the following yield differences: where Yexp is the county average expected yield; YinsZ is the county average zonal maximum insurable yield; YinsB is the county average insured yield in the option Basic per year, and YinsE, YinsEC are the county average insured yield each year in the option Extended before and after contracting the complementary insurance, respectively. Lastly, Yw is the county average simulated attainable rainfed yield.
YinsZ is considered to have a perfect fit when it is equal to Ya; indicating that the insurance system would have a perfect knowledge of the actual average yield in the region. Therefore, GapZ was assessed as a measure of the accuracy of the insurance parameter YinsZ. GapB, GapE and GapEC indicate the distance between insured and expected yields; they were evaluated as preliminary indicators of asymmetric information for each of the insurance options, reflecting farmer's information advantage with respect to the insurer. GapE and GapEC were also contrasted in order to evaluate how farmers increase insured yield when uncertainty decreases (insured before sowing vs. insured at midseason). Lastly, GapW provides insight into how similar or dissimilar simulated rainfed yields are from expected yields, indicating the appropriateness of using crop models simulated data in crop insurance parameterization.

Asymmetric information
An asymmetric information indicator was obtained as the difference between the probability of indemnity based on the risk expected by the insurer, in which possible asymmetric information is assumed, and the one based on the actual risk (no asymmetric information). The procedure to calculate the asymmetric information indicator is illustrated in Fig. 2. The likeliness of indemnity was calculated as the probability of the actual yields being lower than a threshold yield (y thres ) (Eq [7], Fig. 2A). [7] A probability density function of actual yields, f(Ya), left-truncated at zero, was fitted for each of the counties using the software package @-Risk (Palisade Corp., 2011), selecting the distribution with the lowest Akaike Information Criterion (AIC) statistic. Threshold yield (y thres ) was defined as the insured yield (YinsB, YinsE or YinsEC) after subtracting a 30% deductible, as this is the most common deductible level selected by the farmers. To compute the probability of indemnity based on the actual risk (non-asymmetric information), y thres was calculated from the average actual yield f(Ya) (Ýa) (Fig.  2B). For the insurance options Basic and Extended, y thres was calculated from the average insured yields (YinsB, YinsEC) (shown in Fig. 2C for YinsEC).

Factors influencing insurance demand
Yield gaps and asymmetric information can potentially influence farmers' insurance demand. Statistical analyses were performed to test their significance in explaining insurance penetration rates. In this work, insurance demand at the county level is thus an aggregation of all farmers' individual decisions about whether insuring or not.
A factor analysis was performed in order to constrain explanatory information to non-correlated variables to be used later on in a regression model exploring the influence on insurance demand.
For that, in a first step, the suitability of data for factor analysis was evaluated using the Kaiser-Meyer-Olkin (KMO) test. The value of KMO was 0.743, enough to conclude that data was suitable for such analysis (Kaiser, 1974). Second, the number of extracted factors was determined using the eigenvalues. We found that restraining factors with eigenvalue higher than 1 was too restrictive for such a model with a high number of variables. Therefore, we used the alternative approach of creating a scree plot (graphing the eigenvalues of all factors listing them in decreasing order of their eigenvalue) and restraining the number of factors above the inflection point (Cattell, 1966). The resulting number of factors was 4. Lastly, factor loadings were computed by an iterated principal factors' algorithm until convergence and rotated using the varimax rotation method.
Factor analysis permitted selecting a single variable from each group (the one with the higher loading). Selected variables were used as independent variables in two linear regression models fitted to investigate the impact of yield gaps and county wheat production characteristics on the decision of farmers in a given county and year to insure their wheat production (Insured wheat ) and the proportion of insured area under the option basic (Insured B / Insured wheat ). The variable Insured wheat was calculated as the fraction of total wheat cultivated area (JCyL, 2014) that was actually insured in any of the insurance modules, per county and year. It thus represents an index of insurance penetration measured at the county level. Models were fitted with Stata v12 (StataCorp, 2011).

Figure 2.
Procedure to calculate the asymmetric information indicator: (A) the probability of indemnity calculated as the cumulative probability of yield being lower than a threshold yield (y thres ), (B) the probability of indemnity with no asymmetric information where y thres is the average actual yield after subtracting a 30% deductible, (C) the probability of indemnity with asymmetric information for the insurance option Extended including the complementary insurance (AsymEC), where where y thres is the average insured yield in insurance option EC after subtracting a 30% deductible,and lastly, (D) the asymmetric information indicator calculated as the difference between (C) and (B).

CERES-Wheat model calibration and validation
The calibrated crop parameters reproduce a wheat cultivar with high vernalization requirements (60 days), and intermediate photoperiod sensitivity (105 % reduction in rate per 10 h drop in photoperiod), a short grain filling period (400 °C-days), and an intermediate phyllochron for wheat (95°C-days). Parameters related to potential biomass production were 19.5 kernels per unit canopy weight (# g −1 ), 30.5 kg grain weight, and 2.59 g per standard, non-stressed mature tiller, including grain ( For calibration and validation, RMSE for anthesis and physiological maturity were 2.6 and 6.5, and 11.5 and 9.9 days, respectively. For grain yield, RMSE were 0.4 and 0.9 Mg/ha. Figures 3 and 4 show the kernel density estimation of yields and yield gaps including all counties defined within this work. In both cases, they were estimated using Stata v12 and the Epanechnikov kernel. The y-axis has the units and dimensions of the reciprocal of the variable in the x-axis. Thus, density is not measured on a probability scale, and therefore it might exceed 1. Figure 3 shows the kernel density estimation of the zonal maximum insurable yield (YinsZ), expected yield (Yexp), and water limited yields (Yw) (Fig. 3A), and the GapZ and GapW gaps, (Fig. 3B). The lowest yields were YinsZ, followed by Yexp and lastly, Yw, with the mean values at 1.96, 2.77 and 3.78 Mg/ha, respectively (Table 1, Fig. 3A). The largest variability was found for Yw, followed by Yexp and lastly YinsZ (Fig. 3A).

Yields and yield gap analysis
GapZ had the mean at -0.85 Mg/ha and a low variability (percentiles 10 and 90, being -1.45 and -0.37 Mg/ha, respectively), while GapW had a mean of 1.01 Mg/ha and a high variability (percentiles 10 and 90, -0.36 and 2.13 Mg/ha, respectively) ( Table 1 and Fig. 3B). Fig. 4A represents the kernel density estimation of expected yields (Yexp), and the farmers' insured yield before sowing with option Basic (YinsB), before sowing in the option Extended (YinsE), and at midseason insured with option Extended and adjusted with the complementary insurance (YinsEC). Fig. 4B shows the gaps GapB, GapE, and GapEC. The lowest yields were YinsE, followed by Yexp, YinsB and lastly, YinsEC, with the mean at 2.22, 2.77, 3.54 and 3.63 Mg/ha, respectively (Table 1, Fig. 4A). GapE was the lowest, and had a negative mean at -0.56 Mg/ha, followed by GapB with a positive mean at 0.75 Mg/ha, and lastly GapEC with the mean at 0.86 Mg/ha (Table 1).

Asymmetric information
To calculate the probabilities of indemnity (Eq [7]) and the asymmetric information indicators (Eqs. [8], [9] and 10]), probability density distribution functions were fitted for actual yields, f(Ya), in each of the 38 counties in the studied region. Out of the 38 distribution functions fitted, 12 were Weibull, 11 Triangular, 4 Gamma, 7 BetaGeneral, 2 Logistic and lastly, 2 Logistic distributions. Such distributions have been used earlier for crop yield modelling (Gallagher, 1987;Nelson & Preckel, 1989;Atwood et al., 2003;Sherrick et al., 2004;Tolhurst & Ker, 2015). Results of these density fits are available from the authors upon request. Fig. 5 shows the kernel density estimation of the probability of indemnity (Fig. 5A) and the asymmetric information indicator (Fig. 5B). Again, the kernel density was estimated using Statav12 and the Epanechnikov kernel. The lowest probability Figure 3. Kernel density estimation of yields and yield gaps: (A) Zonal maximum insurable yields (YinsZ), expected yields (Yexp) and water-limited yields (Yw); and (B) maximum insurable yields to expected yields gaps (GapZ) and water-limited to expected yields gaps (GapW). Table 1. Notation, description and descriptive statistics of yields and yield gaps used within the yield gap analysis and the asymmetric information and insurance demand model for winter wheat in Castilla y León. Data is aggregated from the original data base of observations per county.   of indemnity was found when using the average insured yield for the option Extended before sowing (y thres =YinsE), even lower than when no asymmetric information was considered (y thres =average Ya). The probability of indemnity when using the average insured yield was higher for the option Extended including the complementary insurance (at midseason, y thres =YinsEC) than for the option Basic (y thres =YinsB) (Table 1, Fig. 5A). The probability of indemnity when no asymmetric information was considered (y thres =average Ya) showed the lowest variability. Consequently, the asymmetric information indicator was higher for the option Extended including the complementary insurance (y thres =YinsEC) than for the option Basic (y thres =YinsB), and both higher than the option Extended before sowing (y thres =YinsE) ( Table 1, Fig. 5B). Table 2 shows the four factors of the factor analysis including loadings and the percentage of variance of each of them, once rotated. Position of relevant variables determines the factors influencing the demand of wheat insurance in the study region. As a result, 49.5% of the variance is explained by factor 1 variables, defined as "Expectations" in Table 2. Factor 2 variables "Yield asymmetric information" explains 19.5%, factor 3 variables "Yield variability" 17.5 % and lastly, factor 4 "Commercial effort", 13.5%.

Insurance demand, yield gaps and asymmetric information
Factor 1 grouped three variables (GapZ, GapW and AsymEC) indicating a high correlation between them. Higher yield gaps between expected yields and maximum insurable yield (GapZ) and attainable rainfed yields (GapW) are then correlated with higher asymmetric information for the insurance option Extended when including the complementary insurance (AsymEC). This makes sense because when the farmer sets YinsEC, the certainty on final yields is higher at mid-season. GapZ was selected as the representative variable of factor 1 to be included in the regression models.
Two regression models were fitted using the most representative variables of each of the four factors to explain wheat insurance penetration and the prevalence of the insurance option Basic (Insured wheat and Insured B / Insured wheat ). Explanatory variables were, therefore, Area wheat , GapZ, CV_Ya and AsymB. Table 3 shows the model parameters estimates of each of the explanatory variables and the significance of their contribution to explain the dependent variable, number of observations (N), and the coefficient of determination (R 2 adj ).
The results show that wheat insurance demand (Insured wheat ) was higher in counties with higher wheat cultivated area (Area wheat ), higher GapZ and lower asymmetric information for contracts in option Basic (AsymB). At the same time, counties with a higher AsymB tend to have a higher proportion of insured area under the option Basic. Greater interest in contracting crop insurance would be expected in those counties with higher yield variability (higher CV Ya ) and in which crop yield distributions are skewed to the left (lower Skewness Ya ), with yields closer to the maximum observed more frequently than very low yields. However, model results discarded CV Ya as an influencing factor on insurance demand.   Table 3. Parameter estimates in the regression models for the proportion of the wheat cultivated area that was insured (Insuredwheat) and the proportion of insured area in option basic with respect to the total insured area in 2011 and 2012 in Castilla y León. Observations are per county and year.

Discussion
What is driving farmer's agricultural insurance choice?
Premium subsidies are the most common public intervention to incentive crop insurance demand (Babcock & Hart, 2005;Claassen et al., 2005;Garrido & Zilberman, 2008). In the case of wheat insurance in Castilla y León, and for option Extended (the one with the largest guarantees), most of the insured area was gathered by Module 2, despite subsidies in Module 1 being higher than in Module 2. The second most selected insurance alternative was Module P, the option Basic, with the lowest premium subsidy (Table S1 [ suppl.]). Both in Module 2 and Module P, loss compensation is evaluated per plot. This suggests that the accuracy in setting insured yield is decisive in the willingness of the farmers of contracting insurance, being subsidies less important in driving farmers' insurance demand.
Our results show that insurance demand was higher in counties with larger areas cultivated with winter wheat (Table 3). Moreover, higher insurance demand is expected in vast regions with low farmers' density where commercial efforts by insurance companies might be profitable; one successful sale would yield a higher selling commission. Moreover, regions showing stronger crop specialization, and thus lower income sources, incur farm larger revenue risks, being crop insurance an interesting alternative risk management tool (Niewuwoudt et al., 1985;Cabas et al., 2008). Enjolras et al. (2014) and Santeramo et al (2016) also found farm size to have an influence in farmers' willingness to select risk management tools, including crop insurance. They argue that that this is related to the higher exposition of smaller farms to changes in their income than larger ones, and to fixed costs associated to the enrolment in the insurance system.
Information asymmetry indicators (AsymB, AsymE and AsymEC) were also included in the analysis as a measure of farmers' information advantages. Results show higher insurance demand related to a lower AsymB, but a higher proportion of the insured area under the option Basic for higher AsymB. This suggests that, in regions with lower asymmetric information and better adjusted insurance parameters, farmers have a higher tendency to contract insurance, and to do it under a wider coverage (option Extended). But the causality reversed: increasing insurance demand might help decreasing asymmetric information as the probability of participation of less risky producers increases, mitigating adverse selection (Shaik et al., 2008). Properly calibrated insurance parameters would make insuring more attractive to a higher number of farmers.

Are crop models useful for crop insurance assessment?
GapW was the highest yield gap found among the gaps included in this analysis. This result suggests that, as expected, it is more accurate to calibrate insurance parameters based on actual reported yields instead of attainable yields (or simulated water limited yields), and therefore on historical data rather than using crop models. Otherwise farmers' yields would be overestimated.
Mean GapW in CyL was 1.01 Mg/ha. This differs from those reported in Boogaard et al. (2013), within an analysis for the whole of Europe using the crop model WOFOST. They calculated Yw between 5 and 6 Mg/ha and GapW between 3 and 4 Mg/ha in CyL. Therefore, mean Yw was about 1 Mg/ha higher and mean Ya was about 1.5 Mg/ha lower than reported in this work. These differences might be related to the accuracy in calibration and the scale of application.
Nevertheless, the use of crop models might be useful in designing new insurance packages when no historical data is available or to evaluate scenarios of expected changes, such as under expected climate change. In that case, it is suggested that yield gaps be estimated and considered when using simulated attainable yields.