Revisiting the demand of agricultural insurance: The case of Spain1

Alberto Garrido2 and David Zilberman

(Work in progress – do not cite nor circulate without authors’ permission)

Abstract We develop an expected utility model to analyse the demand for agricultural insurance covering yield losses. In the simplest case, using CARA preferences, we show that the demand for insurance depends on the product price variability and on the correlation between yield and price. If premim subsidies and farm program subsidies are sufficiently high, insurance may be attractive even if the indemnnity scheme does not compensate for the cost of the premium. In a more general case, with DARA-CRRA preferences, we show that insurance is more sensitive to incorrectly calculated premia when prices are more volatile and when price and yield are negatively correlated. In the second part, we use the actual insurance records of 55,000 farmers and 11 years to estimate two sets of insurance demands. We define measures of insurance’s expected returns, variance and third moment, based on observed insurance data, and infer the expected returns for those farmers that have never had an indemnity. We estimate several probit models and count models for the insuring vs non-insuring strategies, in which the economic returns of insurance and its two measures of dispersion enter as explanatory variables. Results show that farmers’ insurance strategies are largely explained by their actual insurance experience as captured by these three variables. Individuals with loss rations greater than 1 do not show more responsiveness that those facing more balanced premium charges. Results show that adverse selection may not be a major source of inefficiency in the Spanish insurance system. Keywords: Agricultural insurance, insurance demand models, Spain JEL code: G22, Q12, Q14

1 Associate Professor at the Universidad Politécnica de Madrid (Spain), and Professor at the University of

California, Berkeley, respectively. Work conducted during the sabbatical year of the first author at the Department of Agricultural and Resource Economics, University of California, Berkeley. He gratefully acknowledges the generous support of this Department and the funding from the Spanish Ministry of Education (Programa de Movilidad de 2004) and of the Universidad Politécnica de Madrid (Programa de Sabáticos 2004). Special thanks go to Maria Bielza for preparing the database. Entidad Estatal de Seguros Agrarios (ENESA) of Spain provided the data used for the empirical analyses.

2 Corresponding author: Departamento de Economía y Ciencias Sociales Agrarias, ETS Ingenieros Agrónomos. 28040 Madrid (Spain). Email: alberto.garrido@upm.es.

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1. Introduction The literature on agricultural insurance seems to provide very few succesful examples. Most

conclusions are based on a very limited number of experiences and countries, which mostly

focus on publicly provided insurance. Most world countries, developed and developing, have

agricultural insurance systems or have gone through processes of development, crises, and

revitalisation.

Conventional wisdom assumes that agricultural insurance is too vulnerable to serious

problems of asymetric information (Just & Pope, 2002; Chambers, 1989). In the European

Union, the private sector provides basic coverages for a very limited number of hazards,

indicating that many of the risks and hazards to which farmers are exposed cannot be insured by

private insurance companies. Yet, a number of countries have developed large and

comprehensive insurance policies as a means to provide safety nets for farmers. In the last ten

years, the US, Spain, and Canada, among others, have expanded their insurance systems in

terms of insured risks, kinds of policies, and their budgetary allocations to subsidise premia. The

European Commission has recently launched a reflection period to analyse alternatives to

increase the EU’s involvement in developing risk management instruments, including

agricultural insurance.

Despite its importance in terms of insured acreage, total liabilities and premium

subsidies, very little is known about non-US insurance experiences, with the exception of

Canada and a number of policy review works (OECD, 2002; EC commission, 2000). The

Spanish case is especially striking because it has a rich experience in developing new and

innovative agricultural insurance, and has been expanding during the last 25 years. And yet it

has received scant attention in the literature, and completely ignored as an alternative model to

countries in the process of developing their own systems.

This paper focuses on Spain’s agricultural insurance policies. It seeks to characterise the

demand for insurance in Spain and determine the extent to which it is vulnerable to problems of

asymetric information. By looking at a wide range of crops and insurance mechanisms, it seeks

to offer a fresh look at agricultural insurance in general and fill the gaps that prevent a more

informed view of this important safety net. The paper develops a new modeling approach that

provides testable hypotheses about farmers’ insurance demand, which are tested by simulation

models, statistical and econometric methods.

The paper is structured as follows. After reviewing the literature on insurance demand in

section 2, we provide a brief description of the Spanish agricultural insurance system and

2

primary factual data in the third section. Section 4 includes the basic model for insurance

demand. In section 5 we provide numerical results that enrich the theoretical conclusions.

Section 6 describes the database used in the statistical and econometric analyses, whose results

are discussed in section 7. The paper’s most salient conclusions are summarised in section 8.

2. Literature review on insurance demand Canada, Spain and the US are among the OECD countries with more developed agricultural

insurance policies. The three of them have in the last decade increased the budget devoted to

premium subsidisation, and the pecentages of farmers and surface with some coverage. As

rough measures, these countries spend in subsidising insurance policies an equivalent of 1 to 2%

of their total agricultural output. In response to these significant budgets allocation, about 50 to

60% of the eligible farmers purchase at least one insurance policy. On average, US spends in

insurance subsidies about US$25 per insured hectare, Spain €25, and Canada C$50.

Insurance subsidisation, though important in absolute and relative terms, is not the only

means the governments of these countries support agricultural insurance. Agencies directly or

indirectly promote research and support continuous innovation, offering a broad menu of

insurance options to field crops, fruits & vegetables and livestock farmers.

While the US insurance policy has inspired hundreds of articles and books, the Canadian

and the Spanish ones have motivated remarkable fewer works. Yet, as a whole and in view of

the variety of experiences and long history, they offer a wealth of results, conclusions as well as

unexplored research questions.

Farmers purchase insurance polices because (1) expected benefits are positive, (2) they

gain from asymmetric information, and (3) they are risk-averse (Just et al. 2003). The bulk of

the literature on agricultural insurance has focused on items (1) and (2), that have been tested

under alternative assumptions about item (3).

With insurance, asymetric information implies that insuree and insurer have different

information about productive risks and insuree’s behaviour. Asymetric information is thought to

provide incentives for moral hazard and adverse selection. Quiggin et al. (1993) contend that

very often it is not possible to empirically distinguish between moral hazard and adverse

selection, however different may be in theoretical terms. Consider the case of a farmer that

defers his planting to learn more about soil-moisture and see whether it is in his interest to

purchase drought insurance. This type of behaviour is illustrative of both moral hazard and

adverse selection. It exhibits adverse selection because insurance is purchased only if a lower

3

yield is expected. It is moral hazard because the decision to defer planting is influenced by the

existence of yield insurance. Moschini and Hennessy (2001) review in detail the problems

related to asymetric information. What this wealth of literature, entirely based on US cases and

data, seems to suggest is that there is disagreement about whether or not asymetric information

pose incentives to increase production. In the following section, we review some of theses

works.

On moral hazard Wright and Hewitt (1990, cited by Moschini and Hennessy, 2001) contend that actual demand

for insurance would be lower than is generally believed, because farmers have many other

cheaper means to control and reduce their risks. In general, insurance is thought to be an

expensive RMI, because policies have to be designed in order to reduce the negative effects of

asymetric information. As a result, in the absence of subsidies insurance would not be attractive

to most farmers. Ramaswami (1993) divide up insurance effects in two: moral hazard effects

and risk reduction effects. The first encourages reductions of input use and by the second the

insuree would seek greater expected revenue. However, there is some ambiguity with regards to

moral hazard effects, because increase-production inputs can be also risk-augmenting. In

general, it is thought that fertilisers are risk-augment inputs, and pesticides risk-reduction inputs.

However, insurance policies include a number of provision and features that are meant to reduce

or eliminate moral hazard, but adding little room for risk reduction effects. In Table 1, we offer

a summary of the main literature results about moral hazard.

On adverse selection Combating adverse selection is paramount to being able to offer specific insurance

policies to relatively homogenous groups of farmers. For this, insurers must count on

objectively discriminatory elements to group agents under homogenous risk levels, and charge

different premia. While the confirmation of moral hazard would lead to the conclusion that

insurance is a decoupled policy, the presence of adverse selection needs not be so. What adverse

selection indicates is the absence of discrimination elements and the unbalance of premia and

indemnities. If adverse-selection provides strong incentives to cultivate marginal land, then

insurance may increase production and for that matter should not qualify as a decoupled policy.

Yet, as Moschini and Hennessy (2001) indicate the Canadian Prairie Farm Assistance Act

(1939) was conceived to grant revenue instability of farmers located in territories to which they

should have never been pushed to occupy. While this may be true in many other countries and

regions, the passage of time since land was converted to agriculture precludes qualifying these

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historical processes as adverse-selection. This, despite the fact premium must be heavily

subsidised to maintain farmers’ interest. Another important factor related to adverse selection is

the fact that the required groups’ homogeniety to avoid adverse selection depends on farmers’

risk aversion. The more risk-averse, the less reluctant they will be to pay premium above their

individual actuarial fair premium. Table 2 includes a number of studies that have addressed the

problem of adverse selection

In short, the evidence in favour a severe asymetric information problems is dubious and

mostly based on a limited number of US insurance policies (MCPI and APH). The literature

seems to suggest that farmers seem to be compelled to purchase insurance attracted by the

expected results, which are also dependent on the level of insurance attached to the premium

(Just et al. 1999). Makki & Somwaru (2001) show high risk US farmers are more likely to

purchase revenue insurance and higher coverage levels, and that low-risk farmers tend to be

overcharged.

A controversial issue about the role of subsidies in the demand for insurance still

revolves and has not been settled in the literature. (Goodwin 2001, p. 543) finds demand

elasticity for insurance is between -0.24 and -0.20. (Serra, Goodwin and Featherstone 2003, p.

109) show that it has be become less elastic in the US as farmers have turned to larger

coverages, favoured by ARPA (2002) increased subsidisation.

3. The Agricultural Insurance system in Spain Agricultural insurance in Spain dates back to the beginning of the 20th century, but remained

fairly unimportant and underwent various waves of decline and resurgence until 1978. This year

saw the passing of the Agricultural Insurance Act which set the stage for a continuous growth of

agricultural insurance in Spain. The Spanish system is based on a mixed public-private model,

in which farmers’ unions and association do also play a crucial role. Interested readers can learn

a complete description of the Spanish insurance system in OECD and EU reports (OECD, 2001

& European Commission, 2000). In Figure 1, we plot the total liability of agricultural

production, including livestock production, and the ratios of total expenditures in premium

subsidisation over total liability. The graph shows the steady growth of the agricultural

insurance, which now reaches about 30 to 40% of all eligible production. Farmers in Spain can

choose among more than 200 different policies, that provide coverages to all possible crops and

animal production. The system has evolved in the last 20 years to offer a wider menu of

products to a wider range of crops and animal production. Premium are subsidised by the

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Spanish and Regional goverments in a percentage that range from 20 to 45% of the market

premium. In the period 1980-2004, loss ratios for all policies, experimental policies and viable

policies, were respectively, 99.56%, 114.31% and 82.98% (Agroseguro, 2004), indicating that

the system has grown following sound actuarial criteria.

While Spain has followed a traditional approach to define insurable risks and establish

loss adjustment procedures, fitting with the model of Multiple-peril Crop Insurance. In the last

years, the system has evolved to provide yield insurance, based on individual or zonal records,

for many crops including cereal and winter crops, olive trees and a number of other fruit crops.

Two kinds on index insurance have been used experimentally with different success. The failed

attempt came with a potatoe revenue insurance, based on a price index, offered in seasons 2003

and 2004, which very few farmers purchased. The more succesful example is ‘drought’

insurance available to range livestock growers, which is based on a vegetation index produced

by from satelite images.

4. Model of insurance demand Our model considers the case of a single crop, where both yield and price are stochastic. R,

revenue per hectare, results from a product of yield and price, ypR ~~~ ×= . Both ],[~ ppp∈ and

],[~ yyy ∈ have known probability distribution functions, g(p) and f(y). For the moment, we will

assume that p~ and y~ are independent, but will relax this assumption below. Following Glen et

al. (2005), the pdf of R, h(R), has in principle a closed form as long independence holds and p~

and y~ have defined supports, and takes the following form:

∫=y

pR

dyy

yfyRgRh

/

1)()()( (1)

With insurance, revenue is given by:

{eee

ei yyifypyyp

yyifypR

≤×+−×>×

= ~~~)~(

~~~~ (2)

Where ye is the trigger yield, and pe is the price established to evaluate the indemnity. Profit is

given by sPcR nii +−−= ~~π ; with c, being the crop’s cost; Pn is the net premium; and s is an

agricultural policy subsidy in the form of a direct aid. Insurance net premium, as paid by the

farmer results from Pn=(1+δ)(1-ξ) Pf , where δ is the loading factor; ξ is the insurance subsidy;

and Pf the fair premium, evaluated as follows:

6

∫ −=ey

yeef dyyfyypP )()(

Computing Pf is far from trivial and is not defined for all pdfs3 (see Appendix 1 for the case f(y)

follows a gamma distribution). In the absence of insurance, per hectare profit is scR +−= ~~π .

Farmer’s preferences are modeled with an exponential utility function, exhibing constant

absolute risk aversion preferences, U(π)= 1- e-rπ. Later on we shall discuss and relax this

assumption.

It is further assumed that farmer would purchase insurance if he expects to get utility

gains, which under the expected utility hypothesis implies that )()( ππ EUEU i > . Expected

utility in the case of insurance is given by:

∫∫ +−−−+−−−− −+−=yp

yp

scPRry

y

scPyypri dRRhedyyfeEU n

e

nee )()1()()1()( ][])([π (3) (3)

with γ, being the probabilty of getting a yield below ye. Under no insurance, expected utility is

given by:

∫ +−−−=yp

yp

scRr dRRheEU )()1()( ][π (4)

There are two possible strategies to compare the expected utilities of insurance vs. no

insurance, both taking advantage of the moment generating function as in Colander and

Zilberman (1985). One, that relies on the assumption of independence between y and p, is to use

the result of Glen et al. (2005) and compute the integral to obtain h(R), using equation 1, and get

a closed form of )( iEU π and )(πEU . This strategy is applicable to a limited number of cases,

because the combination of pdfs for y~ and p~ that ensure that function (1) can be integrated is

limited to lognormal-lognormal, and beta-beta.

The alternative strategy is perhaps more restricting but more insightful. It is based on the

assumption that R follows a continuous distribution function which has moment generating

function. Obvious candidates are Gamma, Chi-squre or Normal distributions, but as we shall see

below even assuming either distribution the comparison of expected utilities requires additional

functions. Yet, in the fourth section of the paper we show that for a wide range of pdfs for y~

and p~ -- including Beta, Gamma, Lognormal and Normal -- a gamma distribution fits

statistically well for the resulting R~ .

3 If f(y) is a Beta one has to evaluate a Hypergeometric2F1 function; if it is Gamma a Incomplete Gamma

function; and if it is a Lognormal or Normal, one needs evaluating an Error Function.

7

In the Appendix 1, we show that, if y~ and R~ follow distribution functions with moment generating functions, then )()( ππ EUEU i − >0 if and only if:

0)]1)(([)];([ ')( >−−+− −+− ne

e

rPR

reey

Rry erMGFeyrpLIMGFe ββγ (5)

where

eyγ is the probability of y<ye; Re=peye; β= -Pn-c+s; and β’= -c+s.

stands for Lower Incomplete Moment Generating Function, respectively of

);( eey yrpLIMGF

y~ of order rpe and

upper bounds of ye (see Appendix 1); and MGFR(-r) is the moment generating function of R of

order –r. The first bracketed term is the expected utility resulting from the insurance indemnity,

whereas the second one is the difference between the expected utility without insurance and

insurance resulting from stochastic revenue R~ .

Although condition 5 holds only for any pair of ramdon variables, y~ and R~ , with pdfs

with MGFs, to gain some intuition we focus on the particular case of y~ and R~ following two

Gamma distribution, with parameters (λR, αR) and (λy, αy)4. In Appendix 2, we show that

condition 5 can be transformed to:

)1)(())(,();()'( nen

e

rPReeyyeey

rRPry erMGFyrpPyrpMGFee −−−− −−+−> λαγ β (6)

where P( . ) is a regularized gamma function and takes values between 0 and 1. We discuss this

equation after focusing on the term in the bracketed term. From equation 6, if Pn-β’>0, a

necessary condition but not sufficient condition, for )()( ππ EUEU i − >0 to hold is (proof in

Appendix 2) :

)((Im))( REUEUPREU n >+− (7)

where Im stands for indemnity (Im=pe(ye-y)). Condition 7 is intuitively clear: insurance is

purchased if paying the premium is compensated with the utility gains resulting from the

indemnity scheme. Note, however, that condition 7 is only necessary and is based on the

assumption that Pn-β’>0. If per hectare subsidy, s, is sufficiently high, or premium is intensively

subsidised, then it may be the case that Pn–β’= Pn +c–s<0. In this case, necessary condition 7

no longer holds and equation 6 must hold to ensure that insurance is purchased. If premium is

inexpensive relative to other costs, either because of subsidies or because risk is low, and direct

subsidy is large, then insurance may be purchased even if inequality 7 is reversed. Furthermore,

4 Mean equal to α/λ; variance equal to α/λ2; and moment-generating function of order t equal to 1/(1- t(1/λ))α, for t<λ.

8

if Pn-β’<0, then the exponent of the left-hand-side term in 6 switches from negative to positive.

So the larger the subsidies, the greater the incentives to purchase insurance. In the case s is

relatively larger than Pn +c, insurance would still be purchased even if condition 7 does not hold

or even if the insurance policy is relatively inattractive.

An inspection of condition 6 shows that there are eleven parameters (pe, ye, r, δ, ξ, λy,

αy, λR, αR, c, s) affecting the direction of inequality 6. To investigate the role of these

parameters, we decompose )( iEU π in the indemnity scheme, EU(pe(ye-y)-Pn-c+s), and the

other containing the crop revenues, EU(py-Pn-c+s). Furthermore, since δ and ξ play a similar

role, we will drop the latter from the set of comparative analyses. Also, we grouped c−s in a

single parameter c’.

In table 3 we report the results of the comparative statics results for the EU with

insurance. Two further assumptions were made, namely, y~ follows a gamma distribution with

(λy, αy)=(2.86;5.5); p~ follows a beta distribution B(p,q;pmin,pmax) = B(1.35, 2.0; 0.103;

0.145). Monte Carlo simulations of ypR ~~~ = , with y~ and p~ uncorrelated, produced 5000 data

with which a gamma (λR, αR)=(22.3, 5.045) with p-value 0.92 (based on Chi-square test); and

another 5000 data giving rise to a gamma (λR, αR)=(36.15, 8.85) with p-value 0.96 when

y~ and p~ are correlated with ρ=-0.8.

As Table 3 shows only in 4 out of nine possible cases signs can be established

unambiguously. The reason for getting such poor analytical results is due to the fact that gamma

functions are not symmetric, and that skewness cannot be a priori imposed on stochastic

revenue, R~ . Furthermore, large a per hectare subsidy, s, can reverse the sign of the effect, as it

is in the case for ∂EU(pe(ye-y)-Pn-c+s)/∂r. This explains why the effect of the risk-aversion

coefficient is also undefined.

The previous analysis is limitted for a number of reasons. First, DARA utility functions

are assumed to provide more realistic representations of agents’ preferences than CARA

specifications. Secondly, we have assumed that of y~ and R~ follow Gamma distribution

functions with known parameters, which is certainly a very particular case of more general

specifications. Third, we have assumed a very simplistic insurance policy, in which there are no

deductibles and fair premium is evaluated under the assumption of perfect information. In the

following section, we report some simulation results that relax some of the above assumptions.

And fourth, we have only computed the signs of the partial derivatives of )( iEU π .

9

5. Simulation results

Attempting to gain more insight with numerical analyses, we run a series of Monte-Carlo

simulations with a model that relaxes some of the above assumptions. Instead of CARA, we

assume DARA-CRRA preferences, with U(π)=π1-r/1-r, and five levels of r (0.25, 0.5, 0.75, 1,

1.5); yield follows a Gamma distribution with αy =3.5 and λy=2, representing average yields of

1.925 T/ha; ye=1.925 T/ha (which due to asymetry comes with a γye=0.55); two price

distributions, both following a Beta distribution with the same average 0.12 (1000 € per T) but

with increasingly wider support as shown in Table 4’s first row; that price and yield are

uncorrelated (ρ=0) or negatively correlated (ρ=−0.8). We also assume five levels for (1+λ)(1-

ξ), ranging from ‘very subsidised and/or low loading factor’, (1+λ)(1-ξ)=0.25, to ‘no subsidies

and/or high loading factor’, (1+λ)(1-ξ)=1.5. Cost minus subsidy is set at c−s=1300€ for all

simulations.

Furthermore, in an attempt to gain insight into the role of a miscalculated premium, we

run half of the simulations assuming a correct insurance premium (with Pf=460 €), and half

evaluated as if the premium had been evaluated for a gamma with αy =5.5 and λy=2,86 (with

Pf=390 €). Upon simulation 10,000 ramdon pairs of y and p, we made pairwise comparisons of

)( iEU π and )(πEU using condition (8) obtaining 240 possible comparisons. In Table 4, plus ‘+’

means )( iEU π > )(πEU , and a minus sign ‘−’ means otherwise.

Results confirm that if price and yields are negatively correlated, insuring is the best

strategy for a wider range of assumptions and parameters than if they are independent. This is

because revenue, R~ , is less asymmetric with ρyp=-0.8 than with ρyp=0, as shown in Figure 2.

Secondly, miscalculating the premium is more influential if price and yields are correlated than

if they are uncorrelated. This implies that miscalculated premia may have a larger impact with

crops that are more vulnerable to basis risks, like droughts, which affect market prices. Thirdly,

increasing price risk would be followed by less insuring if prices are uncorrelated with yield. If

they are correlated, price risk does not alter the insuring vs. non-insuring ordering. In a final set

of simulation results, not reported in the table, we confirm that lowering pe or ye by 40% reduces

significantly the demand for insurance for all assumptions and parameters.

6. Data sources and documentation

10

The statistical and econometric analyses use data from the Spanish agricultural insurance system

(ENESA). ENESA’s records include individual farm data from 7 agricultural diverse comarcas

(equivalent to US counties). The complete database includes 55,000 farmers and 11 years (1993-

2003), with a complete characterisation of each farm’s insurance strategy, paid premiums,

premium subsidies, and collected indemnities. Table 5 summarises the main descriptive

elements of each comarca. The database includes a diverse set of crop risks, natural conditions

and kinds of insurance policies. For cereals, farmers can choose among three coverage levels,

ranging from basic coverage including hailstorm and fire risks to individual yield risks. Fruit

growers can choose among two coverage levels. From each farmer and year, records include the

following variables: (1) If purchased any insurance (binary); (2) Crops insured, including

surface (ha), expected yield (kg/ha), total liability (€), paid premium (€), premium subsidies (€),

and the kind of coverage; (3) Indemnities (€) received by crop, coverage and year. Depending

on the comarca, 50% of the farmers purchased any insurance policy between 4 and 6 years

during 1993-2003.

Insurance demand analysis will be pursued along two different strategies, requiring the

computation of different actuarial and behavioral variables. For the first set of analyses, we’ve

generating a number of variables, that we first define and later on explain:

Insurit -- binary (0,1) -- if buys any insurance policy in year t.

Insurance00_03t -- categorical (0,4) -- number of years between 2000 and 2003 where Insur=1

(valid only for t=2003).

Exp_benit – numerical (≥0) – a dimensionless measurement of the expected benefit resulting

from purchasing insurance, computed with the following formula (i farmer, j comarca, k

crop, t year):

∑∑

∑∑−

−

= 1

1

0

0_ t

tiktk

t

tiktk

it

Pmium

IndbenExp if Pmiumikt>0

where Indikt is the indemnity (€) and Pmiumikt is the premium paid (€), net of subsidies,

for crop k and year t. Exp_ben provides an idea of the actual expected benefits in terms

collected indemnities for one euro spent in purchasing insurance policies.

Exp_ben_init– numerical (≥0) – a dimensionless measurement of the inferred expected benefit

resulting from purchasing insurance, computed with the following formula (i farmer, j

comarca, k crop, t year):

11

∑

∑

∑

∑

−

−

−

−−

−

−+

=

kik

kktik

it

kikt

kkjtikt

itit

TInst

LossratTInsInsur

Liab

LossratLiabInsurinbenExp

)()1(

)(__

1

1

1

11

1

if Indikt=0 ∀ kt

ijtijt benExpinbenExp ___ = if Indikt≠0 for any k,t.

where Lossratikt-1 is defined by: ∑∑

∑∑−

−

− = 1

1

1

0

0t

t iijkt

t

t iijkt

kjt

Pmium

IndLossrat ; and represents the loss

ratio of crop k in comarca k; Liabikt-1 represents total liability (€) of insured crop by

farmer i. Tinsik is defined by: ; where Ins_crop∑=

=2003

0

_t

tktik cropInsTins kt=1 if crop k was

insured in year t.

Varijt– numerical (≥0) – is a dimensionless measurement of the dispersion of the insurance

payoffs, evaluated in relative terms, as follows:

∑∑

∑

∑

∑− −

−

−

−−

−

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+=1 1

1

1

11

10

)()1(

)(t

t

kik

kkjtik

it

kikt

kiktikt

ittijt

TInst

DispTInsInsur

Pmium

PmiumDispInsurVar β

where βt is weighing factor with ∑ =t

t t0

1β and 01 tt ββ > if t1>t0;

21

1

11

01

111

0

)(

11

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −

−−−

−= ∑ ∑

∑−

−

−−

−

−−−

t

t j ikt

j iktikt

ikt

iktiktikt Liab

PmiumInd

ttLiabPmiumIndDisp and

21

1

11

01

111

0

)(

11)(

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −

−−−

−= ∑ ∑

∑∑

∑ −

−

−−

−

−−

−

t

t j jkt

j jktjkt

j jkt

j jktjktkjt Liab

PmiumInd

ttLiab

PmiumIndDisp

12

Thirdijt– numerical (≥0) – is a dimensionless measurement of the third moment of the insurance

payoffs, evaluated in relative terms similarly to Varijt, except for the exponents of Dispikt

and Dispkjt-1 which are 3 instead of 2.

We now discuss the meaning of each of the above variables, with a few caveats in mind.

First, our three variables are meant to provide a description of the insurance experience of each

farmer, using his individual records as the main sources of information. Second, only when the

records of a farmer are sparce or limited, we add in the insurance variables of his comarca to

complete the evaluation of the variables. Third, because the three variables are built based on

past recorded data our three variables have more explanatory power for the last years of the

series. So no model insurance demand model will be tested for t<2000. Fourth, the three

variables are indices, meant to provide relative measures of the insurance experience of the

farmer, irrespectively of his farm’s size, cropping patterns, profitability or location.

The first variable, Exp_benit, is a typical loss ratio calculated individually along the

insurance experience of the farmer. If for any given year it is greater than 1, that means that the

farmer collected more indemnities up to year t-1 than the total premium paid up to t-1. Exp_benit

may be 0 if the farmer did not received an indemnity at up to year t-1. If the farmer had not

purchased any insurance premium before year t (with t>2000), then Exp_benit is missing and not

used in the analysis. The fact that Exp_benit=0 does not imply that the expected benefit of

purchasing insurance is zero. So as an alternative formulation, we use the inferred measurement

of expected benefit, Exp_ben_init, which is based on a weighted average of the comarca’s loss

ratios of the crops he has purchased. Neither Exp_benit nor Exp_ben_init are perfect indicators

of the expected returns of purchasing insurance, but our hypothesis is that they may be good

enough to explain farmers’ insurance strategies. Figure 3 plots the histograms of Exp_ben (only

for those greater than 0, which total about 64% of all farms) and Exp_ben_in, both evaluated at

the most recent year 2003. Table 6 reports the statistics of both variables for each comarca. The

median in both cases is below 1 for all observations, and greater than 1 only in the comarca of

Segria using the inferred measure of expected return (Exp_ben_in). This is an indication that

adverse selection may not be significant in all comarcas.

The second and third variables, Varijt and Thirdijt, are by construction different from 0 for

all farmers, irrespectively of their insurance experience. They are meant to provide a sense of

the relative dispersion of the difference between collected indemnities and paid premiums. For

this two variables we are assuming that, if the farmer did not purchase any policy in year t, an

equivalent measurement of the dispersion of payoffs is provided by his comarca’s. Note also

that, due to βt the dispersion of the most recent years up to t ensures that Varijt and Thirdijt are

13

evaluated so that more weight is put in those years. As these two variables are meant to provide

an idea of the dispersion of the whole insurance experience of the farmer, they are evaluated

taking into account the relative importance of each insured crop. Note, however, that Exp_benit

(or Exp_ben_init, for that matter) and variables Varijt and Thirdijt provide a completely different

description of the insurance experience of a farmer. While Exp_benit provides a pure return of

the money spent in purchasing insurance, Varijt and Thirdijt capture the relative dispersion of

the payoffs.

7. Insurance demand models

Two approaches can be followed to estimate insurance demand models, each which its own

variants and assumptions. In the first approach, we only look at the dichotomous choice of

purchasing or not purchasing any insurance policy. In the second approach, we estimate a count

model of the number of years between 2000 and 2003 farmers purchased any insurance.

In the first case, we assume a farmer will purchase any type of insurance in year t if:

)0'Pr()0Pr( >+=> ii xInsur εβ

where the explanatory variables are those defined in the previous section, which are entirely

based on the farmer’s past insurance experience. Variants of this model are estimated as a probit

models5. The major difficulty of this approach is choosing the variable capturing the expected

returns from insuring, namely, choosing an inferred or guessed variable or using the actual

returns based on the farmer’s records. Having no a priori clue of what is appropriate, we base

our choice on the econometric results, models’ predicting accuracy and goodness of fit. Table 7

reports the results for three specifications (Exp_ben_in, Exp_ben and Exp_ben using only

farmers for whom Indikt≠0 for any t). All runs have reasonable good sensitity and specificity

indicators. These in turn are similar within the same models, indicating that both the 1s and the

0s are predicted with similar accuracy. Using either Exp_ben_in or Exp_ben does not change the

insurance demand’s models interpreted as a whole. If we use Exp_ben, only farmers who got an

indemnity in the past, the model fits better and coefficients for this variable are greater.

The three variables capturing the insurance returns are strongly significant, and have

stability across models and time specifications. Farmers seem to respond to their insurance

experience, and the relative profitability of purchasing agricultural insurance.

5 A comparison of logit and probit estimates was carried out, finding very similar coefficients and goodness

of fits. Yet, based on better accuracy on Sensitivity and Specificity for Insur, probit models performed slightly better.

14

In general farmers with loss ratios greater than 1 (Exp_ben>1) are assumed to benefit

from low premium relative to their individual risks. In our database, 48% of the farmers who

have collected an indemnity during the 11-year period belong to this category. The percentage

is 29% if we take into account the 55,500 farmers. Table 8 reports the cofficients for the probit

models run separately for farmers Exp_ben>1 and for Exp_ben<1. Results show that farmers

with Exp_ben<1 are more responsive to the three measurements of insurance returns than those

with Exp_ben>1. This is an indication that farmers which are overcharged in relative terms

respond in lesser extent than those that benefit from low charges.

Insurance demand models can also be estimated as a count models, counting the number

of years that a given farmer decides to purchase any type of insurance policy. This is what we do

in our second approach. The dependent variable is Insurance00_03t, which is evaluated in 2003

and takes on values from 0 (no insurance purchased during 2000 and 2003) to 4 (farmer bought

insurance in all years during 2000-03). The model is estimated as poisson model using the same

explanatory variables used for the probit models. Results are reported on Table 9, together with

the predictions for the dependent variable, Insurance00_03t.

The poisson models have good statistical properties. All coefficientes are consistent

across regressions, and not very different from the probit models. Similarly to these, the models

using actual insurance returns (Exp_ben) perform better than those using the inferred measure as

a explanatory variable (Exp_ben_in). Predicted values for the dependent variable

Insurance00_03t are centered on the observed values, except for the case where

Insurance00_03t=0. In this case the prediction is biased towards 1, but for Insurance00_03t>0

predicted values are within a standard deviation of the actual values.

The role of premium subsidies and changes in the indemnities schemes

The literature on insurance demand is clear about the effect of premium subsidies. If, as all

available evidence overwhelmingly shows, farmers respond to the economic incentives that

agricultural insurance policies provide, they would necessarily respond to changes in the

premium subsidies and to changes in the probability and size of insurance indemnities. Table 10

reports the percentage changes of predicted Insurance00_03t for two of the poisson

specifications reported on Table 9, three levels of Exp_ben (Exp_ben_in) and three levels of

Var. By all measures shown in the table, the largest changes occur when the expected benefits

are lower than 0.5, and for Var<1.5. This means that insurance demand is mostly sensitive to

changes of expected revenue for farmers that have the largest variation of returns and lowest

expected return levels. This is an indication that farmers may show more resposiveness to

15

changes in premium subsidies when their loss ratios are lower and the indemnity scheme more

instable.

8. Summary and conclusions

In this study, we have analysed the demand for agriculture insurance using a theoretical model

and an empirical approach. Our theoretical model shows that agricultural insurance providing

coverage for crop losses is dependent on the premium subsidies and the parameters of the yield

distribution. Since indemnities are generally evaluated as the product of the yield loss and a

fixed price, insurance demand is also dependent on the correlation of yield and price, and on the

density function of revenue. We find that when price and yield are negatively correlated, the

incentives to purchase insurance are greater than if they are uncorrelated. Finally, we show that

under cases of heavily subsidised crops, farmers may benefit from insurance even if the

indemnity scheme is not sufficiently large to compensate for the payment of the premium.

While these results confirm that farmers are attracted to policies with positive expected

results, they show that subsidies, both of premia and originating from farm programs, can

inducce farmers to purchase insurance that has poor returns. For instance, we show that even in

cases of premium misalignments, farmers’ would not respond to asymetric information

incentives unless price risk is sufficiently high and price and yield negatively correlated. Lastly,

we show that, even in a very simple setting, farmers’ insuring strategies depend on a dozen of

number of parameters. Some are specific of the insurance policies available, and some depend

on the price and yields relevant to the grower, in addition to the agent’s risk preferences.

From our empirical analyses, we learnt that Spanish farmers’ insurance strategies can be

explained by their actual and observed individual insurance experience. Three variables

describing the observed economic returns from insurance and its variability are enough to

explain insurance demand patterns found across widely different agricultural conditions.

Noteworthy, the demand parameters are quite stable through time, both using probit specific for

single years and count models for 4-year periods. Our results show that farmers respond not

only to the expected returns of their insuring strategy, but also to the dispersion or variability of

the expected indemnities relative to total paid premium and total liability.

We also developed a few variants of the demand models in order to include in the

analyses the observations related to farmers that, even if they show evidence of being active

insurees, they have never received an indemnity. Using an inferred measurement of the expected

returns, based on each farmer’s regional actuarial records, we could estimate an insurance

demand model lumping togthether farmers with actual records of indemnities and farmers with

16

inferred records of indemnities. Demand models in this case show sharp similarity to those

estimated only with observed data. Again, this implies that farmers repond to the expected

returns inferred from the region’s actuarial results, and to the variability of the region’s relative

indemnity scheme.

Obvious avenues for pursuing further the theoretical work are analyse a choice model of

insurance coverage. Using the moment generating function, one can use discreet distribution

functions as well and compare expected benefits of having a simple crop failure insurance vs. a

yield insurance of the type analysed here. In addition, deductibles can also be integrated in the

model to compare alternative policies that have different indemnity schemes.

In the empirical area, the analyses carried out here are just a small fraction of the issues

that the database invites to look at. We have completely left out promising analyses of the

farmers’ choice of coverage and more crop-specific insuring strategies.

17

References Babcock, B.A., D.A. Hennessy. 1996. Input Demand Under Yield and Revenue Insurance American Journal of Agricultural Economics 78:335-347 Barnett, B.J. 2004. “Agricultural Index Insurance Products: Strengths and Limitations”. Agricultural Outlook Forum 2004 Chambers, R. Insurability and Moral Hazard in Agricultural Insurance Markets. 1989. American Journal of Agricultural Economics 71(3): 604-616 Coble, Keith H., Thomas O. Knight, Rulon D. Pope, Jeffrey R. Williams. 1996. “Modeling Farm-Level Crop Insurance Demand with Panel Data”. American Journal of Agricultural Economics 78: 439-447 Collender, Robert N. and David Zilberman, 1985. Land Allocation Under Uncertainty for Alternative Specifications of Return Distributions. American Journal of Agricultural Economics, Vol. 67, No. 4 (November, 1985), pp. 779-786. Garrido, A., M. Bielza and J.M. Sumpsi. (2002). The impact of crop insurance subsidies on land allocation and production in Spain. OCDE, AGR/CA/APM(2002)16. Glen, A., L.M. Leemis and J. H. Drew. 2004. Computing the Distribution of the Product of Two Continuous Random Variables" Computational Statistics and Data Analysis, Volume 44, Number 3: 451-464. Goodwin, B.K. (1994). “Premium rate determination in the Federal Crop Insurance Program: What do averages have to say about risk?”. Journal of Agricultural and Resource Economics 19:382-395 Hennessy, David A. (1998). “The production effects of agricultural income support policies under uncertainty.” American Journal of Agricultural Economics 80 (1): 46-57 Horowitz, J.K., E. Lichtenerg, 1993. “Insurance, Moral Hazard, and Chemical Use in Agriculture”. American Journal of Agricultural Economics 75(5): 926-935 Just, R.E., L. Calvin (1993). “Adverse selection in US crop insurance: The relationship of farm characteristics to premiums”. Unpublished Manuscript, University of Maryland Just, R.E., L. Calvin, J. Quiggin (1999). “Adverse selection in Crop Insurance: Actuarial and Asymmetric Information Incentives”. American Journal of Agricultural Economics 81: 834-849. Ker, Alan P. and Pat J. McGowan (2000). Weather based Adverse Selection and the U.S. Crop Insurance Program: The Private Insurance Company Perspective. Journal of Agricultural and Resource Economics 25: 386-410 Makki, Shiva S., and Agapi Somwaru (2001). Evidence of Adverse Selection in Crop Insurance Markets,Journal of Risk and Insurance 68(4): 685-708.

18

Mishra, Ashok.K., R. Wesley Nimon, Hisham S. El-Ost. Is moral hazard good for the environment? Revenue insurance and chemical input use. Journal of Environmental Management 74 (2005) 11–20 Moschini, G., D.A. Hennessy. 2001. “Uncertainty, Risk Aversion, and Risk Management for Agricultural Producers”. In Handbook of Agricultural Economics V. 1A (Eds. B.Gardner and G. Rausser). Elsevier Science, 87-154 Quiggin, J., G. Karagiannis, J. Stanton (1993) “Crop Insurance and Crop Production: An Empirical Study of Moral Hazard and Adverse Selection”. Australian Journal of Agricultural Economics 37(2): 95-113 Ramaswami, Bharat, 1993. “Supply Response to Agricultural Insurance: Risk Reduction and Moral Hazard Effects”. American Journal of Agricultural Economics 75: 914-925 Roberts, Michael J. (2004). “Effects of Government Payments on Land Rents, Distribution of Payment Benefits, and Production.” In "Decoupled Payments in a Changing Policy Setting", Agricultural Economic Report 838, ERS, USDA. Serra, T., B.K. Goodwin y A.M. Featherstone, 2003."Modeling Changes in the U.S. Demand for Crop Insurance During the 1990s" Agricultural Finance Review 63(2). Skees, J.R. & M.R. Reed. 1986. Rate Making for Farm-Level Crop Insurance: Implications for Adverse Selection. American Journal of Agricultural Economics 68: 653-659 Smith, Vincent H., Barry K. Goodwin, 1996. “Crop Insurance, Moral Hazard, and Agricultural Chemical Use”. American Journal of Agricultural Economics 76: 428-438 Wu, JJ. (1999). “Crop Insurance, Acreage Decisions, and NonPoint-Source Pollution”. American Journal of Agricultural Economics 81: 305-320.

Appendix 1 Fair premium is evaluated as follows:

∫ ∫−=−=e ey

y

y

yeeeeeef dyyyfpypdyyfyypP )()()( γ

If f(y) follows a gamma distribution with parameters (λ, α), then

[ ] ee

yyeee

y

y

yeeef yEypRdyeypRP )(

)()(1 λ

αλγ

αλγ α

αα

λαα

−+− −

Γ−=

Γ−= ∫

Where E-α(λy) is an exponential integral function. Since , then: ),1()( 1 znzzE n

n −Γ= −

[ ] ey

yeeef yyypRP ),1()()(

11 λαλαλγ ααα

+Γ−Γ

−= −−+

19

[ ] [ ]{ }),1()(),1()()(

1111 yyyyyypRP eeeeeef λαλλαλαλγ ααααα

+Γ−−+Γ−Γ

−= −−+−−+

⎥⎦

⎤⎢⎣

⎡Γ

+Γ−+Γ+=

)(),1(),1(

αλαλα

λγ yypRP ee

eef

Where 0),1(),1( <+Γ−+Γ yye λαλα .

Appendix 2 We start by defining )( iEU π , and then establish the conditions for )()( ππ EUEU i − >0.

∫∫ +−−−+−−−− −+−=yp

yp

scPRry

y

scPyypri dRRhedyyfeEU n

e

nee )()1()()1()( ][])([π

)(1);()( rMGFeyrpLIMGFe R

reey

Rry

e

e−−+−= −+− ββγ (A1)

where

eyγ is the probability of y<ye; β= -Pn-c+s; and Re=peye. With LIMGFy(rpe;ye) we denote a portion of a complete Moment Generating Function of variable y of order rpe, defined only on the limited interval [y, ye], defined as follows:

dyyfeyrpLIMGFe

e

y

y

rypeey )();( ∫= (A2)

The second part of )( iEU π uses the same notation, where MGFR(-r) denotes a standard Moment Generating Function:

dRRherMGFyp

py

rRR )()( ∫ −=− (A3)

The EU under the case of no insurance is defined as:

)(1)()1()( '][ rMGFedRRheEU Rr

yp

py

scRr −−=−= −+−−∫ βπ (A4)

with β’=-c+s. Therefore, )()( ππ EUEU i − >0 holds if and only if:

0)1)(();( ')( >−−+− −+− ne

e

rPR

reey

Rry erMGFeyrpLIMGFe ββγ (A5)

Appendix 3

If y~ and R~ follow gamma distributions with parameters (λR, αR) and (λy, αy), then:

20

∫∫ −−−

Γ=

Γ=

eyye

ye yyey yrpyy

y

y

yrypy

eey dyyedyeye

yrpLIMGF0

)(

y0

1

)()();( αλ

αλαα

αλ

αλ

[ ]

[ ])0,()(,([)][()(

)(,()]([)(

y

0y

yeeyyeyy

y

eyyyey

yrprp

yrprpyy

y

y

eyy

y

αλαλαλ

λαλαλ

αα

ααα

Γ−−Γ−−Γ

=

−Γ−−−Γ

=

−

−

Where function ))(,( eyey rpy −Γ λα is an incomplete gamma function (with property )()0,( yy αα Γ=Γ ). Further algebra leads to:

)])(,()[( eeyyey yrpPrpMGF −= λα

)])(,()[(

1)(

)(,()();( y

eeyyey

y

eeyeyeey

yrpPrpMGF

yrprpMGFyrpLIMGF

−=⎥⎥⎦

⎤

⎢⎢⎣

⎡+

Γ−Γ

−=

λα

αλα

Where P( . ) is a regularized gamma function, and takes values P(αy,0)=0 and P(αy,∞)=1. With the above results, A5 can be expressed as:

{ })1)(())(,();()(' −−+−> −− nen

e

rPReeyyeey

RPrry erMGFyrpPyrpMGFee λαγ β (A6)

Reordering terms and taking logarythms:

)1)(())(,();()'( nen

e

rPReeyyeey

rRPry erMGFyrpPyrpMGFee −−−− −−+−> λαγ β (A7)

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−+−>−−

−−

e

ne

y

rPReeyyeey

rR

n

erMGFyrpPyrpMGFePr

γλα

β)1)(())(,();(

log)'( (A8)

If β’<0, which is so as long as c>s, the left-hand side of A8 is always negative. Therefore a necessary, but not sufficient condition, for )()( ππ EUEU i − >0 is that term within the log of the right-hand-side be less than 1.

)1)(())(,();( ne

e

rPReeyyeey

rRy erMGFyrpPyrpMGFe −− −−+−> λαγ (A9)

Further algebra allows us to get the sought necessary condition:

)((Im))( REUEUPREU n >+− (A10) Where Im stands for indemnity (Im=pe(ye-y)).

21

Tables Table 1. Studies on agriculural insurance and moral harzard Authors Context and data Moral

Harzard (MH)?

Adverse Selection (AS)?

Type insurance Further comments

Horowitz & Lichtenberg (1993)

400 maize US growers (Probit model)

NO -- MCPI Insurance increase fertilisation usage

Quigging et al. (1993)

535 grain US producers

Yes -- Unable to separate MH and AS

MCPI Farmers purchasing insurance use less variable inputs and have lower expected yields

Smith & Goodwin (1996)

235 wheat Kansas producers (simultaneous equations)

Yes -- MCPI Insuring and fertilisation decisions are taken jointly

Babcock and Hennessy (1996)

Simulation models (Maize Iowa)

Yes -- Yield insurance and revenue insurance

Larger coverages leads to lesser incentives to

Coble et al. (1996)

354 Farms in Kansas (77-90)

Yes -- MPCI Farmers expecting more frequent and small indemnities, more ready to purchase insurance

Wu (1999) 235 Maize growers in Nebraska

Minor Yes MPCI Switching crop mix is more important than moral hazard. In total, production increases

Serra et al. (2003)

1600 Kansas growers (1993-2000)

Yes -- APH Insurance demand more inelastic with larger coverage

Mishra et al. (2005)

865 wheat US producers

Yes -- Revenue and crop insurance

Purchasing revenue insurance reduces nitrogen use, but not pesticides

22

Table 2. Studies on adverse-selection in agricultural insurance Authors Context and data Adverse

Selection (AS)?

Moral Harzard (MH)?

Type insurance Further comments

Skees and Read (1986)

Soybeand and Maize growers Illinois and Kentucky

Yes -- APH Rates may be flawed, because groups were based on expected yields

Goodwin (1994)

2247 Kansas farms

Yes -- APH APH rating assume wrong relationship between expected yield and yield variability

Quiggin et al. (1993),

535 grain US producers

Implied -- Unable to separate MH and AS

MCPI Farmers purchasing insurance use less variable inputs and have lower expected yields

Just et al. (1999)

350 US growers Yes -- APH FCIC rate-making induces high risk growers to purchase insurance because of positive expected revenues

Wu (1999) 235 Maize growers in Nebraska

Yes Minor MPCI Adverse selection is more important than moral hazard.

Ker & McGowan (2000)

Insurance companies (Wheat growers in Texas)

Yes MPCI Adverse selection could boost benefits of insurance firms with public reinsurance

Makki and Somwaru 2001)

Iowa corn farmers in 1997 (11 years of insurance data)

Yes -- MCPI and Revenue insurance

Rating system fails to incorporate each farmer’s risks. Low-risk farmers are overcharged and high-risk farmers undercharged

Barnett (2004)

By implication Yes -- APH Lack of data and precise information in rate-making must have been vulnerable to adverse selection

23

Table 3. Results of comparative statics of the model of insurance demand Parameter )( ei yyEU <π )( ei yyEU >π Total Fair

PremiumPf

pe<0 (if

e

fe p

Py

∂∂

< )

? (otherwise)

<0 ? >0

ye<0 (if

e

fe p

Py

∂∂

< )

? (otherwise)

<0 ? >0

r > 0 (if

0<−

+−−+ey

eyef rp

pRscP

λα

)

? (otherwise)

>0 (if scPr n

R

R −+>+λ

α)

? (otherwise)

?

δ’ <0 <0 <0 λy ? <0 (if p and y, uncorrelated)*

>0 (if p and y, correlated)*? >0

αy ? <0* ? <0 λR 0 <0 <0 αR 0 >0 >0 c’ <0 <0 <0 *Established based on calculus and on Monte-Carlo simulations (@Risk, Palisade) All proofs are available from the authors upon request

24

Table 4. Simulation results of the restricted model (y ∼Gamma[αy =5.5; λy=2.86]) p ∼Beta:

B(p,q; pmax,pmin)

p= q=

pmax= pmin=

1.35 2

0.103 0.145

1.35 2

0.07 0.194

1.35 2

0.103 0.145

1.35 2

0.07 0.194

p and y, uncorrelated ρyp=0 p and y, correlated ρyp = -0.8 Pure premium calculation

(1+λ)(1-ξ)

r # of +

Correct Incorrect Corrrect Incorrect Correct Incorrect Correct Incorrect

0.5 0.25 4 - - - - + + + + 0.75 0.25 1 - - - - - - - +

1 0.25 0 - - - - - - - - 1.25 0.25 0 - - - - - - - - 1.5 0.25 0 - - - - - - - - 0.5 0.5 6 + + - - + + + + 0.75 0.5 3 - - - - - + + +

1 0.5 0 - - - - - - - - 1.25 0.5 0 - - - - - - - - 1.5 0.5 0 - - - - - - - - 0.5 0.75 7 + + - + + + + + 0.75 0.75 4 - - - - + + + +

1 0.75 1 - - - - - - - + 1.25 0.75 0 - - - - - - - - 1.5 0.75 0 - - - - - - - - 0.5 1.001 8 + + + + + + + + 0.75 1.001 6 + + - - + + + +

1 1.001 2 - - - - - + - + 1.25 1.001 0 - - - - - - - - 1.5 1.001 0 - - - - - - - - 0.5 1.25 8 + + + + + + + + 0.75 1.25 8 + + + + + + + +

1 1.25 5 + + - - + + + + 1.25 1.25 1 - - - - - + - - 1.5 1.25 0 - - - - - - - - 0.5 1.5 8 + + + + + + + + 0.75 1.5 8 + + + + + + + +

1 1.5 7 + + - + + + + + 1.25 1.5 4 - + - - + + - + 1.5 1.5 1 - - - - - + - -

# of + out of 30 comparisons

10 11 5 7 13 17 13 17

+ means )( iEU π > )(πEU , - means, )( iEU π )(πEU< .

25

Table 5. Description of the study comarcas and insurance data

Number of years between in which Insur=1 between 1993-

2003 Comarca’s Name

Autonomous Community Main insured crops

No. of farmers Average

1st Quart Median

3rd Quart

Albaida C. Valenciana Fruits, Grapes, Vineyard, Citrus, Vegetables 2,779 6.09 3 5 9

Campiña Andalusia Cereals, Citrus, Cotton, Olive, Sunflower 5,356 5.76 3 5 8

Campos Cast-Leon Cereals, Sugar Beet, Leguminosae 4,490 6.59 4 6 10

Guadalentin Murcia Vegetables, Greenhouse crops, Grapes, Fruits 2,173 4.75 2 4 6

Jucar C. Valenciana Fruits, Citus, Vegetables 20,778 5.94 3 6 8

Mancha Castilla-La Mancha

Vineyards, Vegetables, Cereals 13,313 5.59 2 4 8

Segria Catalonia Fruits, Cereals, Vineyards, cereals 6,681 6.40 3 6 10

Table 6. Reports of Exp_ben and Exp_ben_in for year 2003 (n= 55,470) Exp_ben Exp_ben_in

Comarca Average 1st

Quart Median 3rd Quart Perc 90 Average 1st Quart Median 3rd Quart Perc 90Albaida 0.39 0 0.09 0.51 1.08 0.65 0.38 0.42 0.71 1.20 Campiña 0.84 0 0 1.33 2.92 1.18 0.22 0.46 1.98 2.92 Campos 0.69 0 0.08 0.86 2.09 1.10 0.46 0.86 1.03 2.54 Guadalentin 0.51 0 0 0.74 1.62 0.75 0.26 0.56 1.02 1.62 Jucar 0.82 0 0.23 1.19 2.40 1.20 0.66 0.78 1.49 2.40 Mancha 0.93 0.03 0.65 1.33 2.25 1.10 0.38 0.87 1.35 2.25 Segria 1.25 0 0.68 1.84 3.36 1.66 0.66 1.48 2.16 3.36 All 0.86 0 0.34 1.23 2.43 1.18 0.41 0.81 1.50 2.47 Source: ENESA

26

Table 7. Probit models of insurance demand (dep variable Insur) Model Exp_ben (all) Model Ex_ben_in Model Exp_ben (only >0) Years 2003 2002 2000-03 2003 2002 2000-03 2003 2002 2000-03 Exp_ben 0.126 0.050 0.059 0.265 0.237 0.231 0.007 0.007 0.003 0.009 0.010 0.005 Exp_ben_in 0.205 0.096 0.122 0.008 0.008 0.004 Var 6.174 5.569 5.529 6.713 5.838 5.845 7.641 7.270 7.333 0.113 0.109 0.056 0.116 0.112 0.056 0.137 0.137 0.070 Third 3.373 2.813 2.905 3.813 3.040 3.169 4.398 3.912 4.061 0.101 0.097 0.049 0.103 0.099 0.050 0.116 0.114 0.058 Campiña 0.184 0.213 0.265 0.156 0.192 0.235 -0.174 -0.195 -0.070 0.024 0.024 0.012 0.024 0.024 0.012 0.037 0.038 0.019 Segria 0.147 0.230 0.239 0.071 0.191 0.183 0.076 0.123 0.204 0.022 0.023 0.011 0.023 0.023 0.012 0.027 0.029 0.014 Guadalentin -0.094 0.038 -0.020 -0.089 0.039 -0.020 -0.077 0.074 0.070 0.036 0.035 0.018 0.036 0.036 0.018 0.050 0.051 0.025 Campos 0.031 0.051 0.103 -0.020 0.028 0.074 -0.025 -0.009 0.030 0.017 0.018 0.009 0.018 0.018 0.009 0.023 0.025 0.013 Albaida 0.199 0.233 0.187 0.200 0.235 0.189 0.188 0.285 0.316 0.031 0.031 0.016 0.031 0.031 0.016 0.042 0.044 0.022 Jucar 0.787 0.787 0.796 0.729 0.772 0.773 0.792 0.695 0.764 0.018 0.019 0.009 0.020 0.020 -0.010 0.027 0.030 0.015 Intercept -1.703 -1.668 -1.572 -1.843 -1.736 -1.660 -2.152 -2.283 -2.217 0.018 0.019 0.009 0.020 0.020 -0.010 0.027 0.030 0.015

Sensitivity Pr( +| D) 0.798 0.811 0.792 0.80 0.812 0.7941 0.871 0.881 0.879 Specificity Pr( -|~D) 0.745 0.720 0.705 0.75 0.7258 0.7063 0.716 0.726 0.718 Positive predictive value Pr( D| +) 0.786 0.780 0.777 0.787 0.7838 0.7778 0.818 0.820 0.823 Negative predictive value Pr(~D| -) 0.758 0.757 0.724 0.759 0.7593 0.726 0.791 0.811 0.799 McFadden's R2 0.294 0.288 0.269 0.299 0.289 0.271 0.359 0.379 0.369 No. Obs 52334 49917 195230 52334 49917 195230 32291 28830 111136

All coeficients assymptotically significant at p>0.01 Standard deviations reported in the cells below the coefficients

27

Table 8. Probit models of insurance demand (dep variable Insur) differentiating Exp_ben>1 and Exp_ben<1. Only if Exp_ben>0 &

Exp_ben<1 Only if Exp_ben>0 &

Exp_ben>1 Exp_ben 0.397 0.209 0.0459 0.0139

Var 10.08 7.00 0.316 0.193

Third 6.769 3.926 0.3104 0.162

Sensitivity Pr( +| D) 0.866 0.88 Specificity Pr( -|~D) 0.753 0.68 Positive predictive value Pr( D| +) 0.814 0.83 Negative predictive value Pr(~D| -) 0.82 0.76 McFadden's R2 0.391 0.326 n. Obs 16649 15642 All coeficients assymptotically significant at p>0.01 Standard deviations reported in the cells below the coefficients

28

Table 9. Poisson models of insurance demand (Dependent Variable Insurance00_03)

Model

Exp_ben>0 Model

Exp_ben_in

Model Exp_ben>0 (Loss rat>1)

Model Exp_ben>0 (Loss rat<1)

Exp_ben 0.136 0.108 0.091 0.004 0.006 0.020 Exp_ben_in 0.126 0.004 Var 5.478 5.654 4.349 6.440 0.072 0.061 0.098 0.144 Third 3.265 3.424 2.462 3.895 0.062 0.055 0.080 0.141 Campiña -0.003 0.123 0.069 0.171 0.017 0.012 0.021 0.029 Segria 0.069 0.040 0.062 0.096 0.012 0.011 0.017 0.018 Guadalentin 0.031 -0.028 0.003 0.081 0.024 0.019 0.037 0.031 Campos 0.029 0.000 0.016 0.060 0.010 0.009 0.015 0.014 Albaida 0.164 0.100 0.207 0.168 0.018 0.016 0.038 0.022 Jucar 0.306 0.302 0.297 0.349 0.014 0.011 0.022 0.022 Intercept -0.835 -0.792 -0.562 -1.103 0.014 0.011 0.022 0.022 Pseudo R2 0.229 0.235 0.189 0.271 Log likelihood -49442 -78298 -24814 -24359 n.obs 32151 52192 15505 16646 Predicted Insurance00_03=0 0.872 0.890 1.079 0.720 0.314 0.299 0.328 0.286 Predicted Insurance00_03=1 1.509 1.352 1.703 1.331 0.541 0.526 0.564 0.553 Predicted Insurance00_03=2 1.847 1.624 1.883 1.519 0.785 0.758 0.733 0.815 Predicted Insurance00_03=3 2.585 2.415 2.536 2.241 1.160 1.161 1.082 1.279 Predicted Insurance00_03=4 3.614 3.587 3.589 3.462 1.151 1.193 1.122 1.400

All coeficients assymptotically significant at p>0.01 Standard deviations reported in the cells below the coefficients

29

Table 10. Percent changes of predicted counts based on the expected returns of insurance Exp_ben -- Poisson Model

Var Exp_ben Min-max

0 to 1 change

From ½ below to ½ above base value

From ½ std below to ½ std

above base value

Marginal Effect

>1 0.2658 0.266 0.2658 0.072 0.2656 <1.5 0.5-1 0.1362 0.2635 0.272 0.0391 0.2718 <0.5 1.3509 0.2378 0.2946 0.2738 0.2944 >1 0.2576 0.2578 0.2574 0.0693 0.2572 <1 0.5-1 0.1295 0.2506 0.2586 0.037 0.2584 <0.5 1.1643 0.205 0.2541 0.2421 0.2539 >1 0.1186 0.119 0.1189 0.032 0.1189 <0.5 0.5-1 0.0594 0.115 0.1187 0.017 0.1186 <0.5 0.6777 0.1196 0.1513 0.1548 0.1512 Exp_ben_in Exp_ben_in -- Poisson Model >1 0.2146 0.2148 0.2155 0.0573 0.2154 <1.5 0.5-1 0.1113 0.2158 0.2227 0.027 0.2225 <0.5 1.1312 0.2048 0.2443 0.2057 0.2442 >1 0.2098 0.21 0.2106 0.0559 0.2105 <1 0.5-1 0.1079 0.2092 0.2159 0.026 0.2158 <0.5 1.008 0.1826 0.2171 0.1835 0.217 >1 0.1189 0.1194 0.12 0.0311 0.1199 <0.5 0.5-1 0.0636 0.1234 0.1273 0.0144 0.1272 <0.5 0.6311 0.1146 0.1367 0.1223 0.1366 All marginal effects assymptotically significant p>0.01

30

Figure 1. Total agricultural insurance liability and ratios of Premium subsidies over liability in Spain (1992-2004)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Year

Mill

ion

Eur

os

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

Insured capital

Agric Ins Cap

Subsidies Ratio

Agric Subs ratio

Source: ENESA (2005)

31

Figure 2. Density functions of R with correlated and uncorrelated price and yield

0

0.1

0.2

0.3

0.4

0.5

0.6

-2 -1 0 1 2 3 4 5 6 7 8

CorrelatedUncorrelated

32

Figure 3. Histograms for Exp_ben (when >0) and Exp_ben_in (year 2003) based on Insurance00_03

0.5

1D

ensi

ty

0 1 2 3 4 5Exp_Ben_in

No ins 00-03

0.5

11.

5D

ensi

ty

0 1 2 3 4 5Exp_Ben_in

Twice in 00-03

0.5

11.

5D

ensi

ty

0 1 2 3 4 5Exp_Ben_in

Three in 00-03

0.2

.4.6

.81

Den

sity

0 1 2 3 4 5Exp_Ben_in

All in 00-03

0.2

.4.6

.8D

ensi

ty

0 1 2 3 4 5Exp_Ben

No ins 00-03

0.2

.4.6

Den

sity

0 1 2 3 4 5Exp_Ben

Twice in 00-03

0.2

.4.6

Den

sity

0 1 2 3 4 5Exp_Ben

Three in 00-03

0.2

.4.6

Den

sity

0 1 2 3 4 5Exp_Ben

All in 00-03

Histograms of Exp_ben_in and Exp_ben>0

33