This document is presented as the final paper for the course “Risk Management in Agriculture and Evolution of Public Intervention”.
In a context of growing food demand and multiple challenges facing
the agricultural sector, resilience has become crucial. Key challenges
include extreme weather conditions, scarcity of natural resources (water
and fertile soils), fluctuations in government policies, and unequal
access to technology. These factors not only affect production but also
generate uncertainty, limiting farmers’ capacity to invest.
Risk management is essential to address these uncertainties. Tools
available to farmers include crop insurance, mutual funds, and public
subsidies. However, the adoption of these strategies varies across
regions and agricultural activities, underscoring the importance of
understanding the factors driving their acceptance (Severini et al.,
2021).
This paper is divided into two parts. The first part analyzes the
maximum percentage that farmers are willing to insure, based on expected
reduction in income and historical profitability of agricultural
operations in Lombardy and Sicily (2005-2009). The aim is to identify if
there are differences between regions and types of crops regarding
perceived and insured risk levels. In addition to determining which
farms could benefit from a mutual fund, that is, those that could
experience a reduction in income of more than 30%.
The second part addresses climatic risk, a crucial factor influencing
agricultural yields. Given the agriculture sector’s high vulnerability
to weather conditions, historical meteorological data of Lombardia
(1975-2015) and Sicilia (1975-2018) will be analyzed to forecast future
patterns using time-series models such as ARIMA+GARCH and SARIMA+GARCH.
The goal is to estimate indices of extreme weather events that could be
useful for adjusting insurance premiums. Although the value-added data
and meteorological data are not temporally aligned, this analysis
provides a methodological framework for future studies aiming to
integrate both elements.
This exercise allows for a better understanding of the different risk
management needs across regions and agricultural activities.
Furthermore, it offers a methodological foundation to visualize the
climate risks agriculture faces in each region.
The project was carried out using the R programming language, known for
its power and flexibility in data analysis. The results are presented in
an R Markdown document, a tool that dynamically combines code, text and
graphics. R Markdown facilitates the creation of interactive reports
where graphics can be expanded and data points examined in detail,
something that is not possible with static files.
In Europe, a new Income Stabilization Tool (IST) has been implemented through a public-private partnership. This mechanism provides financial compensation to farmers involved through a mutual fund. Farmers make an annual contribution to the fund, which entitles them to compensation if their total income decreases by more than 30% compared to the expected income.
One of the main objectives of such tools is to create a safety net against unfavorable income fluctuations for farmers. Unlike traditional insurance, mutual funds offer broader coverage, encompassing both climate risks and those associated with market evolution and other factors that may affect income (ISMEA, 2013). This type of program has the potential to create an effective safety net for farmers, helping not only to mitigate risks but also to reduce economic inequality in the agricultural sector (Capitanio, 2022).
This section of the paper aims to identify the maximum percentage that farms would be willing to insure based on expected utility and historical losses. The goal is to determine which farms could benefit from a mutual fund, that is, those that could experience a reduction in income greater than 30%. The analysis uses data from the Agricultural Accounting Data Network (RICA) for the period 2005-2009, with a particular focus on the regions of Lombardy (383 observations) and Sicily (366 observations). Through this analysis, we expect to identify differences between these regions and types of crops in terms of perceived and insured risk.
To initiate the analysis, it is essential to examine the historical profits of the farms, utilizing the reported variable of Added Value. According to the available data, both in the Lombardy region and in Sicily, the farms present an average annual added value that exceeds the national average throughout all the analyzed years (Figure 1). Additionally, both regions show a similar trend over the study period. Generally speaking, the average added value of the farms during the five analyzed years is higher in Lombardy, followed by Sicily, and finally the national average (Figure 2).
The Lombardy region is recognized as one of the most productive agricultural areas in Italy, excelling in dairy products, cereals such as rice and corn, as well as in viticulture. During the analyzed years (2005-2009), the farms with the highest average added value were Technical-Economic Orientation (OTE) specialized in “ortofloricoltura” (vegetable and flower crops) and “granivori” (livestock farming). Likewise, the most numerous agricultural operations in the region focused on “erbivori” (herbivorous livestock) and “seminativi” (herbaceous crops) (Figure 3).
Regarding Sicily, the largest region in Italy, it has historically stood out in the agricultural production of citrus fruits, especially oranges and lemons, as well as olives and wine grapes. During the study years (2005-2009), it is observed that the farms specialized in “policoltura” (diversification of crops within the same farm, such as ortofloriculture and herbaceous crops), which represent only 8.7% of the farms in the region, generated the highest average added value. However, the farms engaged in “colture permanenti” (such as fruit trees, olive trees, and vineyards) are the most representative in the region, constituting 36% of the total farms analyzed in Sicily (Figure 4).
Assuming that farmers are price takers and that agricultural markets operate under conditions of perfect competition, agricultural enterprises decide to adopt crop insurance based on the principle of expected utility. A farmer will choose to enter the crop insurance market if the expected utility of being insured exceeds that of being uninsured (Capitanio, 2022):
\[ E[U(\text{Insured})] > E[U(\text{Uninsured})] \] The aim of this analysis is to illustrate the different levels of insurance that agricultural enterprises would be willing to demand, considering the following three determinants:
Expected Utility: Represented by the average value added of each farm over the last five years, this value reflects the average profit generated by the farm under normal production conditions, highlighting its economic stability and capacity to generate income under regular circumstances.
Income Reduction: The average income loss is calculated based on the years when income was lower than the expected utility value. This reduction is multiplied by 0.7, since insurance usually only covers up to 70% of the reduction.
Percentage of Losses: This value indicates the percentage of income reduction relative to the average value added over the last five years, thus determining the maximum amount the farmer would be willing to insure.
Figure 5 presents the demand for insurance at different levels, both nationally and in the regions of Lombardy and Sicily, calculated based on the percentage of potential losses for each farm. In general terms, the Lombardy region exhibits a higher level of insurance demand compared to the national average and that of Sicily. However, this difference becomes less pronounced as the level of insurance increases.
Focusing on the 30% level (the minimum required to access a mutual fund), it is evident that, at the national level, this insurance level would be demanded by 5.2% of farms. In Lombardy, the demand is higher, reaching 8.8% of farms. In contrast, in Sicily, only 1.6% of farms would opt for this level of coverage.
Regarding the 70% level (the maximum allowed), less than 1% of the farms analyzed in all three regions chose this level of coverage.
The analysis of insurance demand is also conducted for each region and its different productive activities. Figure 6 shows the demand for different levels of insurance in the Lombardy region. It is observed that as the level of insurance increases, the percentage of farms demanding such coverage decreases.
Focusing on economic activities with more than 10 farms, excluding “policoltura,” “poliallevamento,” and “ortofloricoltura” (which can be deactivated from the graph by clicking on the production label), it is evident that “granivori” farms have the highest demand at different levels of insurance. In contrast, “ervibori” farms, although they represent 36% of the farms in the region, have lower demand at all levels of insurance.
Analyzing the entry point to mutual funds (30%), it is observed that “granivori” production has the highest percentage of demand with 14% of its farms, while “colture permanenti” farms have the lowest percentage with 3.8%. This reflects the diversity of risks associated with each productive activity.
Finally, the potential risk of “granivori” farms is highlighted, as 3.57% of these farms continue to demand a 70% level of insurance. Although there are only three farms classified under “policoltura” in the region, their level of insurance suggests they may face significant risks.
A similar analysis is conducted for the Sicily region. If the “granivori” farms (of which there is only one) and the “poliallevamento” farms (of which there are only four) are deactivated from Figure 7, it becomes evident that, unlike Lombardy, farms in Sicily demand lower levels of insurance. This suggests that the percentage of losses is smaller in this region. The vast majority of farms are concentrated at insurance levels below 15%.
When analyzing the 30% insurance level, it is observed that in all productive activities, the percentage of farms that would demand this type of insurance is below 3%. Only 1.44% of “seminativi” farms reach insurance levels of 70%.
The analysis of access to insurance in the Lombardy and Sicily regions reveals significant differences in the demand for agricultural insurance. Lombardy shows a greater propensity to insure its farms, suggesting a greater reduction in their income and, consequently, a higher percentage of losses. In contrast, Sicily presents a lower demand, focusing on lower levels of insurance, which could indicate lower risks in their crops. However, it is worth questioning whether this lower demand is due to their crops indeed having fewer losses or if it reflects a lower risk management capacity, leading them to invest less and only in “safe” crops. These results underscore the importance of adapting and expanding the scope of insurance policies to the specific characteristics of each region and type of crop, to improve the resilience and economic stability of the agricultural sector in Italy.
The analysis of meteorological risk in agriculture is one of the key factors influencing variability in expected yields. Extreme and unforeseen weather conditions cause significant losses for farmers, making it essential to assess meteorological risk in insurance portfolios for each agricultural entrepreneur, in order to establish differentiated insurance premiums based on the level of climatic risk. This also helps agricultural entrepreneurs become aware of the risks faced in the region where they operate. For this analysis, meteorological data from the Milano stations in Lombardy and Pantelleria in Sicily were used. Five meteorological variables were analyzed: daily maximum, minimum, and average temperature, wind speed, and daily rainfall in millimeters. The methodology involved a trend analysis based on the calculation of the anual median value of each variable, which allows the identification of long-term trends. The monthly seasonality of each variable was then examined by calculating the median value of the five variables, providing a better understanding of how these variables affect each month differently. Following the descriptive analysis, stochastic time series models, such as SARIMA+GARCH, were applied to forecast a 1- to 2-year horizon. This aimed to calculate the Weather Extreme Indices proposed by Alilla et al. (2024) and to assess the level of risk faced by farmers in each region.
The following data for Lombardy includes the date of observation (year, month, and day), daily average, maximum, and minimum temperatures in degrees Celsius, wind speed in m/s, and daily rainfall volume in millimeters. The data spans from January 1, 1975, to December 31, 2015.
The median temperature grouped by months shows an upward trend in all three daily measurements (average, maximum, and minimum). In 1975, the median range was between 8°C and 17°C, but by 2015, this range increased to between 10.5°C and 19.5°C.
Regarding median rainfall, a downward trend is observed, reaching its lowest point in 2005, followed by a recovery until 2014, creating a U-shaped pattern. The median rainfall values range from 1.18 mm (in 2005) to 3.73 mm (in 1977).
The annual median wind speed has significantly increased, from 0.6 m/s in 1975 to 1.8 m/s in 2015.
In terms of monthly temperatures, the seasons are clearly reflected, with a peak in July (30.3°C) and a minimum in January (-0.4°C). There is greater variability between maximum and minimum temperatures during the summer compared to the winter, where variability is lower.
As for precipitation, the highest historical median values are observed in May (2.79 mm) and October (3.18 mm), while the lowest are found in February (1.53 mm), July (1.82 mm), and December (1.63 mm).
Lastly, wind speed reaches its lowest point in October (0.7 m/s), then progressively increases until it peaks in June (1.5 m/s).
The objective of modeling meteorological time series is to calculate the Weather Extreme Indices: Extreme Temperature TX90p, Late Frost Days (LFD), and Rainfall R95pTot, as described by Alilla et al. (2024), as well as the 95th percentile of the median wind speed. These projections cover a prediction horizon of one year for daily temperature forecasts and 24 months for rainfall and wind.
In each case, the best model is selected using the auto.arima algorithm from the forecast package (version 8.22) in the R programming language, which estimates the optimal SARIMA model based on the AIC information criterion. This process is computationally intensive, and for the 14,975 observations, it took more than three hours to complete. Consequently, only the maximum temperature prediction for Lombardy was estimated using the full dataset. After fitting the best SARIMA model, an ARCH-LM test was applied to the residuals to check for heteroscedasticity, determining whether a variance model would improve prediction accuracy.
The best model for the maximum temperature series was a SARIMA (4,0,1)(0,1,0) + GARCH (1,1) 365. The forecast for 2016 is shown in red. According to the TX90p Extreme Temperature Index, the historical critical temperature was 30.2°C. A histogram was constructed to display the distribution of days in 2016, grouped by month, in which temperatures are expected to exceed 30.2°C, revealing that July and August are at higher risk.
## Series: datos_diarios_ts
## ARIMA(4,0,1)(0,1,0)[365] with drift
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 drift
## 1.3501 -0.3913 -0.0494 0.021 -0.7545 1e-04
## s.e. 0.0746 0.0462 0.0140 0.010 0.0742 3e-04
##
## sigma^2 = 13.66: log likelihood = -39826.49
## AIC=79666.97 AICc=79666.98 BIC=79720.1
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.001075956 3.649826 2.782736 -1.757673 13.18395 0.7278664
## ACF1
## Training set 5.056173e-05##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuos_max
## Chi-squared = 192.76, df = 12, p-value < 2.2e-16## 90%
## 30.3For the modeling of minimum temperatures, only observations from January 1, 2000, onward were used due to computational limitations. The best model was a SARIMA (2,0,1)(0,1,0) + GARCH (1,1) 365.
## Series: datos_diarios_min
## ARIMA(2,0,1)(0,1,0)[365]
##
## Coefficients:
## ar1 ar2 ma1
## 1.2173 -0.3209 -0.5920
## s.e. 0.1081 0.0789 0.1033
##
## sigma^2 = 10.37: log likelihood = -14181.78
## AIC=28371.57 AICc=28371.58 BIC=28398
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.005836301 3.117855 2.384147 -1.794485 12.77318 0.6751154
## ACF1
## Training set -0.0004861642##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuos_min
## Chi-squared = 124.15, df = 12, p-value < 2.2e-16In this case, the LFD (Late Frost Days) index counted the number of days with predicted temperatures below zero degrees Celsius between April and May, as these are critical months for plant blooming. As seen in the bar chart, the predictions indicate no late frosts during these months.
Regarding the Rainfall R95pTot index, it could not be calculated as described in Alilla (2024) due to the high number of zero values in the daily series, making it difficult to handle. Therefore, the monthly rainfall totals were calculated, and a 24-month forecast was made. The best model was SARIMA (0,0,1)(0,0,2) 12. The heteroscedasticity test showed no evidence of variance heterogeneity, so a GARCH correction was not necessary. The critical value for the 95th percentile was 149.85 mm per month, and this is not expected to be exceeded in the next two years, with a maximum forecast of 112 mm for October 2016.
## Series: datos_diarios_rai
## ARIMA(0,0,1)(0,0,2)[12] with non-zero mean
##
## Coefficients:
## ma1 sma1 sma2 mean
## 0.1518 -0.0189 0.1906 61.4233
## s.e. 0.0814 0.0737 0.0794 4.9134
##
## sigma^2 = 2698: log likelihood = -1029.31
## AIC=2068.61 AICc=2068.93 BIC=2084.9
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.04644544 51.40053 38.64942 -376.4058 405.7193 0.7379756
## ACF1
## Training set -0.01566812##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuals_sarima_rai
## Chi-squared = 9.5029, df = 12, p-value = 0.6595## 95%
## 149.85In the case of wind, there was no specific reference index. Therefore, the forecast was based on the 95th percentile of the monthly average wind speed, which was 6.745 m/s. The best model was SARIMA (1,1,3)(1,0,0) 12, and the 24-month forecast showed no months exceeding the critical value of 6.745 m/s.
## Series: datos_diarios_ven
## ARIMA(1,1,3)(1,0,0)[12]
##
## Coefficients:
## ar1 ma1 ma2 ma3 sar1
## 0.5349 -1.3768 0.4373 -0.0477 0.1311
## s.e. 0.2502 0.2527 0.2125 0.0612 0.0478
##
## sigma^2 = 2.309: log likelihood = -900.98
## AIC=1813.97 AICc=1814.14 BIC=1839.15
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001138676 1.510371 1.15691 -15.79675 35.20194 0.7803779
## ACF1
## Training set 0.001559691##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuals_sarima_ven
## Chi-squared = 14.145, df = 12, p-value = 0.2915## 95%
## 6.745## [1] 0For Sicily, the data spans from January 1, 1975, to December 31, 2018. The methodology applied is similar to that used in Lombardy, with the exception that for temperature forecasting models, data starting from January 1, 2008, was used due to computational limitations encountered with the auto.arima algorithm.
The temperature trend in Sicily also shows a progressive increase, though less pronounced than in Lombardy. Daily temperatures range from 14.7 to 20.7 degrees Celsius in 1975, increasing to a range of 16.5 to 21.3 degrees in 2018.
Regarding wind speed and rainfall, no clear trends are observed. Wind speeds vary between 2.9 and 6.4 m/s, and daily rainfall ranges from 0.3 to 2.7 mm.
As for the monthly seasonality of temperatures, unlike Lombardy, the hottest month in Sicily is August, with a maximum temperature of 29.5 degrees and a minimum of 23.7 degrees. The coldest months are January and February, with temperatures ranging from 10 to 15 degrees.
In terms of rainfall and wind speed, the months of June, July, and August show the lowest values, while November, December, and January have the highest values for these variables.
The best forecasting model for maximum temperature was SARIMA (4,0,1)(0,1,0) + GARCH(1,1) 365. Predictions for 2019 allow the calculation of the TX90p indicator, with a critical threshold of 30.2 degrees for maximum temperature. The distribution shows that July 2019 is expected to have 21 days of extreme heat, followed by 18 days in August.
## Series: datos_diarios_ts
## ARIMA(4,0,1)(0,1,0)[365]
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## 1.4599 -0.5769 0.0850 -0.0165 -0.8606
## s.e. 0.1104 0.0723 0.0314 0.0212 0.1091
##
## sigma^2 = 11.76: log likelihood = -9683.29
## AIC=19378.58 AICc=19378.6 BIC=19415.8
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.001733909 3.267953 2.360368 -1.14322 11.11079 0.7294652
## ACF1
## Training set 0.000155762##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuos_max
## Chi-squared = 337.99, df = 12, p-value < 2.2e-16## 90%
## 30.2For minimum temperature, the best model was SARIMA (2,0,1)(0,1,0) + GARCH(1,1) 365. In this case, no late frost days are predicted, as temperatures are not expected to drop below zero in Sicily during 2019.
## Series: datos_diarios_min2
## ARIMA(2,0,1)(0,1,0)[365]
##
## Coefficients:
## ar1 ar2 ma1
## 1.3376 -0.3958 -0.8126
## s.e. 0.0747 0.0505 0.0683
##
## sigma^2 = 6.584: log likelihood = -8624.49
## AIC=17256.98 AICc=17256.99 BIC=17281.79
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.02296797 2.445674 1.783294 -0.9271787 10.04692 0.7308928
## ACF1
## Training set -0.001551013##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuos_min
## Chi-squared = 162.98, df = 12, p-value < 2.2e-16## < table of extent 0 >For rainfall, the selected model was SARIMA (0,0,1)(1,0,0) 12, similar to the model used for Lombardy, with no need for GARCH. The critical rainfall threshold, defined by the 95th percentile, is 148.29 mm per month, and it is not expected to be exceeded in the next two years (2019-2020).
## Series: datos_diarios_rai
## ARIMA(0,0,1)(1,0,0)[12] with non-zero mean
##
## Coefficients:
## ma1 sar1 mean
## 0.3552 0.2567 47.2775
## s.e. 0.0722 0.0682 5.3590
##
## sigma^2 = 2073: log likelihood = -1193.06
## AIC=2394.12 AICc=2394.3 BIC=2407.83
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.0205174 45.22644 34.08819 -Inf Inf 0.8601995 -0.02017171##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuos_rai
## Chi-squared = 15.829, df = 12, p-value = 0.1992## 95%
## 148.29## [1] 0## Series: datos_diarios_ven
## ARIMA(1,0,0)(2,0,0)[12] with non-zero mean
##
## Coefficients:
## ar1 sar1 sar2 mean
## 0.2860 0.1844 0.1906 10.5766
## s.e. 0.0448 0.0459 0.0441 0.2364
##
## sigma^2 = 6.173: log likelihood = -1228.52
## AIC=2467.04 AICc=2467.15 BIC=2488.38
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0191278 2.475086 1.915455 -5.810469 19.24719 0.7880518
## ACF1
## Training set -0.04348806##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: residuals_sarima_ven
## Chi-squared = 6.5034, df = 12, p-value = 0.8886For wind speed, a SARIMA (1,0,0)(2,0,0) 12 model was used. The critical threshold for the 95th percentile is 15.56 m/s, and no predictions for the next 24 months suggest that this value will be exceeded.
## 95%
## 15.565## [1] 0These results indicate that Sicily experiences more stable climatic conditions compared to Lombardy, which should be taken into account when determining insurance premiums for farmers.
Alilla, R., Capitanio, F., De Natale, F. et al. An agro-meteorological hazard analysis for risk management in a Mediterranean area: a case study in Southern Italy (Campania Region). Theor Appl Climatol 155, 4289–4306 (2024). https://doi.org/10.1007/s00704-024-04878-x
Capitanio, F. . (2022). Risk, uncertainty, crises management and public intervention in agriculture. Italian Review of Agricultural Economics (REA), 77(2), 3–14. https://doi.org/10.36253/rea-13774
ISMEA. (2013). Sviluppo rurale 2014-2020: Ipotesi di attuazione in Italia della misura Income Stabilization Tool [Preprint]. ISMEA.
Severini, S., Zinnanti, C., Borsellino, V., Schimmenti, E . EU income stabilization tool: potential impacts, financial sustainability and farmer’s risk aversion. Agric Econ 9, 34 (2021). https://doi.org/10.1186/s40100-021-00205-4