• active hedging (anti-frost systems, anti-hail nets);
• passive hedging (insurance policies).
The passive preventive hedging tools (insurance) are the
focus of this research. An insurance contract is a tool
through which the company transfers its risk to third parties
(insurance company). The company that underwrites an
insurance contract effectively transfers to third parties (insurance company) the business risk or part of it, which in
this case is represented exclusively by potential damage due
to adverse weather or epizootics. At the same time, the
insurance company is obliged, in respect of the insured, to
compensate the company if an accident occurs according to
the contract conditions. For the transfer of risk the agricultural company must bear a cost (insurance premium), for
which it can receive partial financial support from the
European Union or the State. The agricultural enterprise,
which intends to sign an insurance contract, has two possibilities: adherence to a collective contract or the signing of
an individual insurance contract.
Thanks to the application of the Copula Quantile
Regression (CQR) approach the authors are able to effectively estimate the dependence of the function with respect
to climate factors and the empirical analysis leads to the
identification of threshold values, and the computation of the
insurance premium can be divided into two phases. In the
first phase, the aim is to estimate the relationship between
climatic factors (FC: average rainfall, average temperature,
maximum and minimum) and yield with an econometric
model. Second, the yield of the individual products should
be attributed an economic value. In the second stage, the
analysis identifies the distribution of FC odds and calculates
threshold values and award.
Professor Fabian Capitanio has contributed to this
research with his valuable experience for setting and
deciding on the model variables and for framing the
framework of the European agricultural system in general
and Italian. In particular, Dr. Alessio Faccia has contributed
to determine the implementation of the statistical mathematical model, test the data using the RICA database and to
determine the conclusions. Dr. Azzam Hannoon contributed
to the determination of the literature review and to the formulation of the starting hypotheses. Dr. Jeffrey Darville
contributed to the definition of the conclusions, the revision
of the paper, and the proofreading.
2 Literature Review
2.1 Estimation Methods
So far most studies use correlation coefficients, simple linear
regression based on Ordinary Least Squares (OLS), or a
generalization of OLS to explain the variation in crop yields
by a weather index (Berg and Schmitz 2008; Clover and
Nieuwoudt 2003; Lobell and Burke 2010; Piearce 1984;
Chowdhury et al. 2016; Birthal et al. 2015). These approaches, which rely on relationships being conditioned on the
mean response of the yield to the weather index, suffer from
at least three disadvantages that represent structural limitations for the insurance design.
First, responses of crop yield to weather are not constant
across all potential states of weather realizations (Schlenker
and Roberts 2006). For instance, marginal crop yield
responses to (additional) rainfall strongly depend on the
level of water already being available to the plant. Second,
crop yields are often not normally distributed but are negatively skewed (Zheng et al. 2008; Swinton and King 1991).
This is in many cases associated with the frequent occurrence of outliers, i.e., yield realizations that do not follow the
pattern described by the majority of yield observations.
Deriving mean-based relationships between crop yields and
weather indices in these situations cause highly inefficient or
even biased estimates (Hubert et al. 2010).
Third, the focus on mean-based measures itself neglects a
substantial amount of information, which is highly relevant to
generate efficient insurance solutions. This is due to the fact
that farmers are more concerned with below-average situations (e.g., exceptionally low crop yield events), and the
inclusion of these events in insurance contracts (Antle 1987;
Groom and Gray 2008; Kumbhakar and Tveterås 2003). In
some cases, these adverse events may even affect the continuation of a farm (Moschini and Hennessy 1999). Although
robust regression approaches can reduce the outlier problem
(Finger et al. 2013) and nonparametric methods overcome the
first two drawbacks of OLS regression outlined above
(Vedenov and Barnett 2004), they still conceptually focus on
the mean response. Hence, tailoring the insurance design to
extreme events is—even though promising—not possible.
These approaches assume, as already mentioned, a linear
relationship between the variables. To overcome that limitation, the considered approach is based on Copula functions
in a combined method with the quantile regression, which
aims to establish the relationship between yield and FC
conditioning in nonlinear optics. The model parameters are
estimated using the maximum likelihood method.
Several studies have been carried out on the risk insurance in agriculture and the development of the sector, the
first research (Valdés et al. 1986) that appears, however,
systematic was carried out in America in the mid-80 s,
highlighting the same problems that now afflict the sector,
even if then the problem of climate change was not so evident. Later, in the 1990s, attention focused mainly on the
study of the role that agricultural insurance plays in developing countries (Hazell 1992). Finally, in the 2000s, attention shifted to the study of climate change, in particular
44
F. Capitanio et al.
• passive hedging (insurance policies).
The passive preventive hedging tools (insurance) are the
focus of this research. An insurance contract is a tool
through which the company transfers its risk to third parties
(insurance company). The company that underwrites an
insurance contract effectively transfers to third parties (insurance company) the business risk or part of it, which in
this case is represented exclusively by potential damage due
to adverse weather or epizootics. At the same time, the
insurance company is obliged, in respect of the insured, to
compensate the company if an accident occurs according to
the contract conditions. For the transfer of risk the agricultural company must bear a cost (insurance premium), for
which it can receive partial financial support from the
European Union or the State. The agricultural enterprise,
which intends to sign an insurance contract, has two possibilities: adherence to a collective contract or the signing of
an individual insurance contract.
Thanks to the application of the Copula Quantile
Regression (CQR) approach the authors are able to effectively estimate the dependence of the function with respect
to climate factors and the empirical analysis leads to the
identification of threshold values, and the computation of the
insurance premium can be divided into two phases. In the
first phase, the aim is to estimate the relationship between
climatic factors (FC: average rainfall, average temperature,
maximum and minimum) and yield with an econometric
model. Second, the yield of the individual products should
be attributed an economic value. In the second stage, the
analysis identifies the distribution of FC odds and calculates
threshold values and award.
Professor Fabian Capitanio has contributed to this
research with his valuable experience for setting and
deciding on the model variables and for framing the
framework of the European agricultural system in general
and Italian. In particular, Dr. Alessio Faccia has contributed
to determine the implementation of the statistical mathematical model, test the data using the RICA database and to
determine the conclusions. Dr. Azzam Hannoon contributed
to the determination of the literature review and to the formulation of the starting hypotheses. Dr. Jeffrey Darville
contributed to the definition of the conclusions, the revision
of the paper, and the proofreading.
2 Literature Review
2.1 Estimation Methods
So far most studies use correlation coefficients, simple linear
regression based on Ordinary Least Squares (OLS), or a
generalization of OLS to explain the variation in crop yields
by a weather index (Berg and Schmitz 2008; Clover and
Nieuwoudt 2003; Lobell and Burke 2010; Piearce 1984;
Chowdhury et al. 2016; Birthal et al. 2015). These approaches, which rely on relationships being conditioned on the
mean response of the yield to the weather index, suffer from
at least three disadvantages that represent structural limitations for the insurance design.
First, responses of crop yield to weather are not constant
across all potential states of weather realizations (Schlenker
and Roberts 2006). For instance, marginal crop yield
responses to (additional) rainfall strongly depend on the
level of water already being available to the plant. Second,
crop yields are often not normally distributed but are negatively skewed (Zheng et al. 2008; Swinton and King 1991).
This is in many cases associated with the frequent occurrence of outliers, i.e., yield realizations that do not follow the
pattern described by the majority of yield observations.
Deriving mean-based relationships between crop yields and
weather indices in these situations cause highly inefficient or
even biased estimates (Hubert et al. 2010).
Third, the focus on mean-based measures itself neglects a
substantial amount of information, which is highly relevant to
generate efficient insurance solutions. This is due to the fact
that farmers are more concerned with below-average situations (e.g., exceptionally low crop yield events), and the
inclusion of these events in insurance contracts (Antle 1987;
Groom and Gray 2008; Kumbhakar and Tveterås 2003). In
some cases, these adverse events may even affect the continuation of a farm (Moschini and Hennessy 1999). Although
robust regression approaches can reduce the outlier problem
(Finger et al. 2013) and nonparametric methods overcome the
first two drawbacks of OLS regression outlined above
(Vedenov and Barnett 2004), they still conceptually focus on
the mean response. Hence, tailoring the insurance design to
extreme events is—even though promising—not possible.
These approaches assume, as already mentioned, a linear
relationship between the variables. To overcome that limitation, the considered approach is based on Copula functions
in a combined method with the quantile regression, which
aims to establish the relationship between yield and FC
conditioning in nonlinear optics. The model parameters are
estimated using the maximum likelihood method.
Several studies have been carried out on the risk insurance in agriculture and the development of the sector, the
first research (Valdés et al. 1986) that appears, however,
systematic was carried out in America in the mid-80 s,
highlighting the same problems that now afflict the sector,
even if then the problem of climate change was not so evident. Later, in the 1990s, attention focused mainly on the
study of the role that agricultural insurance plays in developing countries (Hazell 1992). Finally, in the 2000s, attention shifted to the study of climate change, in particular
44
F. Capitanio et al.