E9 Emerald Insight

Agricultural Finance Review

Revisiting the demand for agricultural insurance: the case of Spain Alberto Garrido David Zilberman

Article information:

To cite this document:

Alberto Garrido David Zilberman, (2008),"Revisiting the demand for agricultural insurance: the case of Spain", Agricultural Finance Review, Vol. 68 Iss 1 pp. 43 - 66 Permanent link to this document: http://dx.doi.org/10.1108/00214660880001218

Downloaded on: 25 February 2016, At: 09:13 (PT)

References: this document contains references to 0 other documents.

To copy this document: permissions@emeraldinsight.com

The fulltext of this document has been downloaded 450 times since 2008*

Users who downloaded this article also downloaded:

Robert Finger, Stéphanie Schmid, (2008),"Modeling agricultural production risk and the adaptation to climate change", Agricultural Finance Review, Vol. 68 Iss 1 pp. 25-41 http://dx.doi.org/10.1108/00214660880001217

Matthew Ginder, Aslihan D. Spaulding, Kerry W. Tudor, J. Randy Winter, (2009),"Factors affecting crop insurance purchase decisions by farmers in northern Illinois", Agricultural Finance Review, Vol. 69 Iss 1 pp. 113-125 http:// dx.doi.org/10.1108/00021460910960507

Milton Boyd, Jeffrey Pai, Qiao Zhang, H. Holly Wang, Ke Wang, (2011),"Factors affecting crop insurance purchases in China: the Inner Mongolia region", China Agricultural Economic Review, Vol. 3 Iss 4 pp. 441-450 http:// dx.doi.org/10.1108/17561371111192301

Access to this document was granted through an Emerald subscription provided by emerald-srm:294800 [] For Authors

If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information.

About Emerald www.emeraldinsight.com

Emerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.

Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.

*Related content and download information correct at time of download.

Revisiting the Demand for Agricultural Insurance: The Case of Spain

Alberto Garritfa and David Zilbcmmn

Abstract

This paper wrka m riwaL'fiijrizr iin- factors that explain [.Top Insurance participation. A stylus«! cnudd (it insurance deiitmid, Wlih a simple setup <il u[nL crop, CATV A preftrtniTf, yield Insurance . u nI pdl's lor revenue mid yield with moraeiU-^eneratlrig functions. piYhVides ft number of fcypojipes« ¿lIhmiI (frc. Incentives lu ™«w.i crop iiiMiiiLcict:. In I he nnplrlciiL model, wr iifif the actual Insurance recflrils fit 41,660 Sptmiflh fanners and 12 yrars of rial a to estimate sLv ¿irobll models for 11h* insnnnp versus lion lushing .choice, based on UidtvlduBI Iops. ratios and Lht":i3iHpL-!r£#&n of indemnities, Wftcthcr with Idlonyiicral^iuid gr.ngra i luid Variables. KrHi 11 i s s 11 lift est that HdvctBE selnctinn I* rlfl ¿1 nuifor mmrrc of inefficiency in the Spanish Insurance ay stem, nor is il i he ^rlmniy motivation con i ran crop inni i ran r< ■. Rrcmiiiiii subsidies are tin* leading factor iliiil Increases die prtihabiJty nit lislug iciiiiii iL]«'!' Crjii|:luflionfl are ^fipUcabltf to wry diverge iiimis in Spain.

JLYJirfi: agricultural insurance, eoonotnjelrli models. Insurants demand ttifldtls, Spain

Alberta Ciamd:, 1я ал' asAociaue ргоГгБкшг m I lie Depart rntjM ill .■VmciiStnnil БСШЦлЩер niifl Six-IjiI Ssiertrca. r<4 lu lLi. :j I University tal" Miittfld, kind Г1'31-лссЫ;!г Ltif Research Centre for die. Mafiiis^ment or iVrkuIlural and Envlrrninwnr.il Г-! Ink- It EifGH.'IMJ. pav^d ¡МЪегпшп is LI |ли1*ны>г in I In- [tepuniueJit of ¡X^rlrLiltiiiul and lio.-^iiii i-e ЕсопопШя-, Цц^лсгаий 1>Г CailfoinlHi Berkeley. and member of the иттшш! Foi i пИц Uwiof Лдпги llti t at IClIoi ir>i i i ц s Л | ire lull 11 и il V vi.Tsran uJ'Iamriin wa[irescntcd ill l!ir IOIsi Зслипа r of the ErtAE," МапаДгтрп! el CllinaUs Rfcks In Лцги-иИигг," [Srirlin (2007). and <il a iemlm} In I tii.-Ctepartrtipfl! dt *м1 rH 111111 л 11 am! RfiBouroe tieononiice 111 iIik Ипкпъну til l ;LtllVhn 11; 1. Hci kulry. wluuri* Cavrldo was un r^itiiuMirnl while dna wuj'k inlUiitwl wfild (levelopcd. lie arknnucli"..ljf-, 11jijjiir! ■ ■ I~ ■ I■ ■ -

Spamaii Minisliv ■ ■ Г Science rind ЫпеаПпп [Projfra.....

dr. M;iv |l|il.iii tli Pnilf-suri-s. lift WI шла 11 ic T<-i tinlviG University III M.ridrLrl (Pnagrmnia Sflbdtloub, 20041 I'd г In ndiдц auppori. Five ispttUsh Лцепсу Ы Agricultural I ii-uranic [вККЭЛ) generously provided lUf. (inl

mull 11 i|f vlftTUlcatlons jkhoi 11 Spanish itiirlrnli' mil ltjauran(4L. and long-ljcrtll msist^nh ЙЯЙИПЦ.

The literature pro vide я quite conlradlctory views a№v t agricult^aJ lnaufiiiicfl. Among the StLidleti qufistlnnlnft the ^¡eticiits (if UiM.tr;ivut ;ire

Mazell. EtomEiiida, atici Valdea Chambers (IUHy)r fftt?th and Furlan (1994); С all его cit al, (200S]; and Wright (200GI. In contrast, Mlshra ПЭЭв) and Нпгцая And Pcrez-Mor^ieis fifliJf?! offer rriure positive ?isfteft$nieiiti>. Yet, inoai. of die available evaluations are baser] on a very limited number of experiences ami oounuiea, and focus primarily on publicly provided Insurance. Many world rcimti-ies. bolJt developed and developing, presently have agrtriiltural Insurance s,ysi(Liiis or have fjttiie through j>rncesses nl develc prtien 1.. i :rIses, and revltnLLzistloii, The European L-nion (El,1) is considering shifting a portion of the Income support Ififcchanlsms [Oward saiety nets and risk liiiLivjgcmwit irist.nime.iil.tv. Itltiudltlg ag^lcujtural instirauec (European Commission. 2005).

Conventional wisdom assumes agricultural Insurance Is vulnerable to serious problcms оГ asyIuoiei.ric Information (C horn hers. 1989: JugI and Pope, 20021. Ill thi EU member stales, (he private sector provides basic coverages i'or a very limited иumher оf hлулrds: constxiufently. rnatiy о I I he risks and hazards to which ¡farmers iire exposed cannot be Insured byprivatelnsnranrecompontes. Some

EU со is 11 tries—ii icludtng Spain. A us 111 a. Kranre. Gi'eece. and Italv—have developed comprehensive Insuranre policies its a means to provide safety in-is lor jarmers. In the Ifisi 10; у ear i., the United SLal.es, Spain, and Canada, among о titers, have tjkpanded theit insurance systems In terms of insured risks, covei'a^es, and premium subsides.

44 ftrrfsftirjtf ífáí Demand fur Agricultural Insurance'. The Gasa of Spain

More recently, Italy, Austria, and France have renewed Insurance programs with government StUppori [European Commission i 200f.i).

Kigure 1 (borrowed fro in Gut rlda and Bieka. Щ()Н\ helps [o Identify thiei groups of countries in ihe El! wtth respect to agricultural Insurance. The group of Mediterranean countries (except Creeee. not shown because of la tie of information), depicted in Liic upper right-band side. Intensely subsidize the premia, and premia ЙГе relatively large with reaped to lolal agrie iJ11 u m 1 ou Lpu t. Al í lie. other extreme., premia itf the countries e£ Germany, Deníri&rk, France, Ireland, and Sweden are tela lively small, atld subsidies are email or zero. Total premia are a No relatively small compared In the value pffartn production, lite size ol the circle represents the ratio о 1 Loiul premium аш! folal agrirtdíural production- Data show? 1 hat penetration rales are greater in countries wheire Insurance is leAs subsidized, though coverages are broader in the Mediterranean countries (Garrido and Bielza, 2008].

Debite (he Importance ol'lnsu ranee In Siany counlrie-s In terms of insured acrea^,- total liabilities, and premium subsidies, very little i* known about non-U-S, irtfiurance experleneea, wJth the ewrfepttons of Canada and India* Most policy reviews of other experiences are veiy superficial [European Commission (ECJÍ, 2001: Organization for Economic Cooperation and Development (OECDk 20001- The Spanish case is especially striking beeftusc ir otters а Нсц experience In dintelopto« new ana innovative agricultural Insurance, which haa bren expanding during the last 25years.

Canada, Spain, and (in- Uní led States are among the OECI) countries with more developed agricultural Insurance policies. In the lasI decade. Oie.se three countries have increased the budget devoti$ 16 premium subsidization, as well as the percentages pf farmers and surface with some eo ver аде. A.s rough measures, these countries spend In subsidizing Insurant*1

policies an equivalent öf 1% 1o 2% of I heir ifil.il agricultural ontpLil. In response to this signlficani budget allocs lion, approximately 50% to, ol eligible fenuers purchase a I leasl one Insurance policy. On average. I be United States spends about US$25 per Insured hcriare in insurance subsidies, Spain €'¿5. and Canada CanSSO.

This paper focuses on the dm land lor agricultural insurance In Spain, AI though the history of agricultural insurance In Spain dales back to the. beginning of the 20<h century, II remained fairly unimportant and underwent various waves of decline and resurgence unlil 1978. This year saw the passage of the Agrteullural Insurance Art, which set the stage for a continuous growth ol agricultural i n s 11 ra n ce 1 n Spain.

The Spanish system is based on a mixed public/private model, in which tanners" union* and associations also play a en irial role. [Interested readers can find a complete description of the Spanish Insurance system in OUCD (2000) and EC (¿006) reports.) The wyslem has evolved In the last 20 years to oiler a wide menu of products for a broader range of crops and animal production. Over the period 10ft0-200-k loss ratios for all policies, experimental pollefes, and viable pol ¡{-¡es were 99.56%; 114.31%. and 82.0S%. respectively, Indicating that I he system has grown following sound atri.ua rial Criteria (A^rosegu ro, 2IXM]. Total liablftty in 20tS8 surpassed €10 billion, representing between 25% and 30% of I he total agricultural output.

Spain has followed a traditional approach (o define Insurable risks and establish loss adjustment procedures, fitting with the model of Multiple-Peril Crop Insuianee. In recent years, the system has expanded It» provideyield insurance., based on individual or zonal records, for many crops including cereal and winter crops, olive trees* and a number or ol her fruit crops, two kinds ol paiarnelrle insurance have been used e>tperi 11 icn 1 a I ly with Varying su ccess.

+6 Ига Demand for АдлЫ fufíiJ insurance: The C&se of Spain

The paper's moat salle til conclusions are яштгап?«! in Ihe Anal HectiotL.

Factors Driving Farmers* Demand for Insurance

Farmers purchase insurance policres because (a) expected beneliLS are positive, (b) liiey gain Jroin asymmetric information, and (c) tliey tare risk averse (Just. Calvin, and Quiggm, Щ&Щ The bulk of the literature on agricultural insurance has focused on the lirst Lwo of tin esc hypol heses. which have been lested under alternative assumptions aboul Item [r|.

Insurance subsidization. though importaffl tti absolulc and relative terms, Is not thsonty means used by govemiEfints to support agricultural insurance. Agencies dirccfly or indirectly promote research and support continuous innovation, oltering a bread menu of insurance options far field rrops, in tits and vegetables, and livestock farmers. Some countries provide reinsurance services, underwriting all or part of outstanding risks. On the demand side, farmers respond by changing the crops I hey insure, the type of policy, or the ¡-overage. In Spain, some Insurance policies are purchased by 100% of eligible farmers (banana or tomato in Ihe Canary- islands) and sonic others by less Llian 4%. including olive trees or re veil tie insurance for poraio In the years It vva.s offered.

Asymmetric Information implies that instiree and in-surer possess different Information about productive risks and 0 le iij suree's bel litvior. AsymmetrlC information Is thoughl то provide incentives for moral hazard and adverse selection. Quiggln, Karaglannls. and Stan ton [10031 argue thai very often it is nol possible to empirically distinguish between moral hazard and adverse seleHiun, however different lltey may be in theoretical terms.

Conslder rhe (rase ol a farmer who defers bis planting date to learn inore about solí moisLnre anfl decide whether it 1s ln his Interest to punchase drought Insurance, Hiis type of beba vior is illusifative ofbolh moral haiiard ti lid adverse sclecüon. 11 exhiblts adverse scleetion beeause tjistira nce ts purchased only lflower ylcld is expeded. It reílecls moral hazard beeause I he decisión to íleier planting Is ¡nlluenced by the existen ce of y te id in suran ce. Moach inl and H ennessy (2001) revlew ln detail the problems related to asynunetrir Information. What this weallii of litera tu re, entirclv based on U.S. cases and data, seems t.o suggest is that rhere Is dtsagreement about whelher r>i no| asymmelrie Lnfoniiation poses incentives to increase production, and how preriíum stibstdlcs actual ly a fice I liurners' Insurance strategtes.

líamaswaml [1933) dlStlnguishes l.wo kinds of Insurance effedts: rnuriíl hiaard effeets and rísk rcriiictian effeets. The lirsl enconrages reductlotis dí tnpul tise and. by u lean a of the second. the insuree wouíd scck greater expected revenue. Vcl. there is some amblgutty wlth regard to ttioral ha^ard effeets, beeause íhcresséd produellon input» al so can be r I s k -a u gi lien t i ng. ln general, 11 is t bou gh 1 that fei-ftllzers are rlsk-augmcntlng Inputs, and peslleldes rlsk-reductiort inpuis. However, insuríuice poileies include a number of provisions and fea tu res thal are meant to reduce moral hazard

WhlS¡ 1 iorowllz and Llehienberg [10931 found no evidenee of moral hazard among U.S. mai/.e growers. Wu (19^0) repOrteíJ very weak evidenee among Ihis group ol growers, lite llsl of lliose reaearchcrs who report tvtdenee of raoral bazard in eludes Quiggin. Karaglannls, and Stanton (19331 wfth lí.S, grain producersr Smlth and Goodwin nSfiti] analviílng U.S. wheal prijducers: Babeo efe and Hennessy [100GÍ wlth simulatfon modela; Coble el. al. 11 £106] wlth Kansas farms; Sorra, Goodwin. and Featherstone (2003) wlth i^a risas growers; and Mtshra. Nimon, and Fli Osla (200S) With U.S. wlieat prodiif ers. Mone of these

¡¡Örteidtumi Rjiantt-1 RevteiM 'Spring 2008

Garrido and. ZÜbenfian 47

st Li(][<hri examlne mtire than 1,600 färms. or look al crops other than wheat, malze, arlül soybeans.

Fighting adverse selecdpn is paramount to heilig able tu oller specific Insurance pollclea in relatlvely homogen eou^j ^roups oi ffirmerg, For Ulla, insuiers iiiust rely ou ohjeettvrly dlfiCrimlnatory elemenls 1o group agenls under homogeniSwjS rluk levcls. Adver se wslectlon li®icatcs Llie absenre of riiscrinitnaiton elernen 1s based du dlfferenl levds ol rl sk exposure and llie imbalanee of premia and liulemniiies. i:\-1rlenee of ariverse seteetion iVas found by Skees and Recd (I98G) wllh U.S. soybean and malze gröwers; Goodwln (1994) among Kansas farms; Quirin. Knraginnnis. and Stauton (1993) and Just. Calvin, and Qutggln (1-0^9) wllh U.S. gTOWers; Ker and MfGowan (200Q) among Insurance (Inns In the case ol wheat producers Iii Texas; ;tnd bv Makki und Somwnru (2001) wilh cöm producErs lYutti Iowa. uslng the largeat data stit [6,000 farms) among those revlewed here,

The evidcncc iii favior of severe Lisymmetric in forma Hon probletns 1s dnbions arid itiosl.ly based on a limited nunlbw of U-S. tnsurance policies (MCPI and AFI I), tliougli Makki and Sornwaru (20011 repqrt slrong evtdence for a.dverae aelection iti the presencjjf ol' lour types of polieiea including revenue insurnnee. The Hiera Iure suggesLs ihal farmers seem to he compelled to purcliasc insurnni c becaiuse l.hey are atirarred by rhe expeeteii results. whlch are ^Iso dependenl on Ihe levc) ol substdies [Just, Calvin, and Qutggln, 1999). As shown by Makki and Sotnwiiru (2001), high-rlsk U.S. farmers are more likeiv to purchase revenue Insurance anfl higher co vor Li ge levels, and lowrlsk fanners lend to be overrharged.

A controversial iasue about Ihe role of snhsldles In the tiemand lur liiaurauce ltas not yet beert senled tri the Hleralure. Goodwln, Vandeveer, and Deal (2001) docuaienl deiaarid e las I ¡eitles Ihr Insu ran et: betwecn 0.24 aud -0.20. Serra. Gnodwin. and Fealherslone (2003) sltow thal iL liaa become leas elasttc in ihe

United States as farmers have tamed to broader coverages, favored by the increase of premium Subsidies through the Agricultural lilsk Protection Aetof 2000.

None of the above studies use actual Insurance outcomes, such a* individual loss ratios, Indemntlles, or cjtpeelcd itlunus from Insurance, Even Makkl and Somwaru (2001), who employ the largest and mfiit In su ran re- diverse data seL, evaluate measures of expected Indemnity fcir Iowa corn growers as a proxy tor actual Indemnities. Just, Calvin, and Qutggln ( 19Я91 rely on the comparison between dialed yield peivenules and insurance premia, but do not include actual Indemn it les. Among the щаj or drawbacks of [be previous wtirks Is the (ael lltai crop failure^ tir low yields are noi Indemnifiable in all eases. Hence. In order to evaluate the demand for insurance, one musl include In the analysis what fanners a dually gel or may reasonably expect from their premia, and compare thi?; with Ihe cost. Ilils Ishest analyzed bv using lannera' acLuiil insurance results, instead of Inferrrd ones.

A Stylized Model of Insurance Participation

The most general formulation of the revenue risk of one crop, when both yield and price are storbastir. Is fi = px ij. Assume pe Ip.p] (with pand p being Ihe rcspeci ive minimum and maximum price) and tic [if, ,ijf| [with i/and Qbeing die respective minimum and maximum yield) have known probability tlislribLition functions, g\ p] a n d /(y|. fallowing G Icjl'j Jxiemls, and Dre# (2004), the probability distribution function fpdfl of Ji, iilii), has a closed form as long as independence he|ween p and y holds and lias defined supports, as .followsr

[11 | g\ -Ijlifl - ay,

ln/p \ y) y

Wilh yield insurance, revenue is given by;

4ft Hi&isittJi^ {hi.' lA.wif<d/or Agricultural hisurciriw: The Cose oj'SrJaiTi

jihere y„ and pc are (.he trigger yield and price for evaluating the indemnity. KrofJt is given by ftj:F-Jif- .c- Pn s, wiLh c representing the crop's cost; P„ Is die net JrenUuini tuid s Is ail agricultural polky subsidy thai lakes the form of a direet aid. Insurance net premium, as paid by ihe farmer, results from P, - (I +- fi)U - t)Jj,, where o Is ihe loading factor, : is Ihe Insurance subsidy, and P,-1lie fair premium, evaluated as follows:

(3) Pf=p(1

Computing Pt Is far irnm trivial. and in fact Is not defined In the ease of all pdfs' [see Appendix A for ¡Hie rjase where/(y) follows a gamma distribution). In the ikbsencc of insurance, profit 1s calculated as

71 = ti ' *C. $.

To compare whether Insuring is utility;augntenting, ui expected utility moflel can be formulated using a revenue pdf like Ihe one defined by (J] and a premium as defined bv 13). Analytical Complexity can be kept to reasonable levels if farmers* preferences are imodeled with an exponential utility function, Exhibiting constant absolute risk aversion (CARAJ preferences. №) = 1 e rr- Famters would purchase insurance II they expect uLiiity gains, will tit under Ihe expected utility hypothesis implies ihat EL'Ir.l > BUfn). ExpecLed utility in Ihe case ofliisurancfc is given by:

EU[r.,}= f-il-e^0- r'"f ^y)dy

fw(i <

-itff-tVi *i

IliUi) clR.

In (4), Ihe indemnity can be separated from Ihe crop revenue, because./"(til and fitli} are different slnebastlr variables.

1 ItJTyj lotkiws ;j be hi, ilien obtaining tft'e pit-rulnm ri-qulri'S cvaliJiUlng ;i hyprrdSramrl rlr '.-Ih l fmtcllon: If II is ^amma. ;m JniMnpLete ^Biibma fiinfeltarli and II II 5f< ;i VjtuKii iiuil (,r tiurrniil. mir ih t-Jm la t i/h 11 u I f an error fmn;Uun.

Under no Insurance, expected iit 1111 y is given by:

'there are I Wo possible strategies t.0 eompare Lhe expected utilities ol insurance Versus no Insurance, both taking advantage of the moment-generating function of the distribution functions, as in Co I lender and Zilberman (10815). One. vdiU'U relics on ilie assumption of independence between y and p. is to use die. resnil of Glen, Leemls, and Drew (2004], evaluate the integral to obtain h(jR) using equation (I). and get a closed form ofKU(n,) and EU[itJ. However, this strategy is applicable to a very limited number of eases, because the combination of pdfs for iiyaiid p whi ell ensure that I unction fl | can be integrated is 11 mi Led to logi'mimal-lognonnal. and beta-beta, and independence IjcI ween both must be assumed. Furthermore, even If the I n t egra I In 11) can be solved, the solution general!y will be cumbersome mathematical expressions which will prevent the posterior analysis of the model.

The a 11 er native strategy Is more restricting, usingCARA preferences, but perhaps more insightful IL is based on the assumption that K follows a ronKnuoiis distribution function which has a moment-generatSig function. Obvious candidates are gamma, chl -squared, ornomial distributions, For a wide range of pdfs tor y and p- Including beta, gamma, lognormal, and normal—a gamma distribution lits statistically well for the resulting Jf.-

!n Appendix B, we show that (f rjaud R follow distribution fiinetiwns with

1110 uie u f gene ia 11 n g J'i j n e 11 oil s, (h c[ i

E[/{n,) - SUItO > 0 if arid only if;

e r3 MGFJ,(-r)[^ -i?rr'") | > 0.

'SLmuLlUOIl WDLk UfHLLlfl ®Rt»k ylpidwl I 111* conclufllrti:. Result«:Fil0 be oblafiwd from 11Lf-.LI.111 LI■ I---

upem request

Afjrifuîi.rjrni Fifiandk Review, Spring 2008

Garrido and Ztlbertmn 49

where is ihe probability of y < yr: K = pj/,.: [1 * -Pn -c+ a: aiiti p' = -c + s. UMGFv[rpt: ijenotes the Lower incomplete monien^generating functloii of y of order fpr and upper bound of y, (see. Appendix: fit; and ,'VfGf"K(-rJ Is the aiomeni-generating functWii of Rof order -r. The firsl bracketed term in (6) Is the expected utility resulting from Ihe Insurance Indemnity scheme, whereas the second term, which is negative due to the premium, is Hie difference between the expected utility with and without insurance- resulting from sLoehasl.tr revenue /•?. Note, one of the consequences of assuming CARA preferences is that wealth does not affect the decision to insure, as shown In (6).

Although condition (6) holds only for any pair of random variables It/and /i), with pelfs with MGFs, 1ogniii some intuition we focus on the particular case of y arid ft following two gamma distributions, with parameters [J.H, ar,j and a.,).' In App^dlx C, we show that eoudit.lon ffi) can be transformed! to;

> e y,.J

* jiGFi«,,, \\-rpju;)

where. NGfT) is a regularised gamma function [whose domain ts [0, 1|). Mote that condition 17) has similar fori mi la Hons il jblther y or R are normal, gamma, ehi squared, exponential, or uniform among continuous distributions; or discrete uniform, fScmoullL binomial, negative binomial, or Poisson among discrete diet ributiona. ' l'rom et[ilation [7J,

L'qLi.-il la ft/1.- v^rtarwi-» d/Â"; ami iiioiiiini gcnfi'iilliifl hi in-lion of isrrli'i filial 10 I/11 lil/J.ll". ior m ?.. Thi jjininin tiiairihiiiion aisn IIL-kIs thl-MfliflTKl aJLli CJCpfllirFlliill ttLstrftjUtionH, acid is related imU' iiurrnai<tiSUltmtlS,n, bMïniHE if-Jils a

S Mi ma la., iIiiti Llm, = 1 with ï*ti(-1iiK a m>ranat tJl.-inbulirm ir./À, «./).')-

' One adv*rtti(» vt iwlnjj fenctifljle with MCPh is iliai our i-iui Etways find . a analytic éjtprç-sjstoi for the

IfcVW |Jl<J 111Lp-li-lr- lllllllk'l l! ^Clli i al ilLkj rniK llOnfi, .ijltl tirins llif rnodfil m Iiicti' if-MJlls.

If P„ —fl' > 0, a necessary l>ui not sufficient condition for £№,] - ElHrt > 0 lu hold Is (sec proof In Appendix CO:

(8] eUlft-i»t) ftt.'U) > EU[J?).

where I indicates Intlemtiily fJ = pjfj,.-yJ). Condition (WJ is intuitively dear: insurance-is purchased if, aller paying ihe premium, the farmer may be compensated with gn-utility gain resulting from Ihe indemnity. Mote, however, that only condition (7) is necessary and requires thai P., ■ jy > 0, If ihe per hectare subsidy; a, Is sufficient^ lilgb, or the premium is Intensive!? subsidized, then ir may be the ease, I hat Pr - [}■ = P,. c - s < 0, Should Lh I s be the ease, condition [7J would not be a necessary condition, so equation niusL hold to ensure that insurance ts purchased. Therefore, If the premium is inexpensive relative to other cost», eithei because of subsidies or becausc risk is low, and (lie direct subsidy is large, then Insurance may be purchased cmt if inequality (8) Is reversed. Furthermore, if f\. - p1 <0. then the exponent of the left hand ,side lenn in (7| switches fivjm negative to posilive, Hence, the larger the subsidies, (he greater ihe incentives to purchase Insurance,

Factors Affecting Insurance Participation

MOW let's assume there cxisisa premium P* that makes Insuring ui id not insuring equally atrraeLive. From (61. if we make P, = P" so that [6)'a inequality Is cancelled, we obtain:

(9) P' = - It«

, I I ,

Mfl^l-rl

UMGFirp,; i/Jc- ■

therefore, onty If P, c P' is Insurance conlracled. which Is anoTfier way of expressing condition (7) applying to any combination of pdfs for g or iî w-'iih moment generating functions. Note, however, that 'è necessary coalition for l\ < f is thai the bracketed (crtn in (91 be

SO Rjeiistitiny the Demand-for .Agricultural Insurance: Tins Case of Spain

greater thaft I. Soltifctin incorporates all relevant parameter*, including rtsk averslott;, agricultural policies, insurance parameters^ and (lie idiosyncratic yields and revenue risks. If we assume thai t'yand R follow gamma distributions, there are eight parameters capturing each of I heae effects. Denoting - Hfr, a. yr, p?, и„, Я,., ßri, Я. J as the general formulation (Ü). wo now investigate the effects ol some of the key parameters on throughout ihe following presentation? the bracketed term. in Щ Is denoted hy T. with Л'мшГЛ and lJf?ni|T) denoting T's numerator anrl denominator.

Direct Payment or premium Subsidies fs)

Parameter's represents a per hectare direct payment, It i& straightforward Lo show that:

äp* es

v e" ЛГшн(Г)

Ilils means Ibat If direct subsidies Increase or crop eosls diminish. P" Increases and Incentives to insure will also increase,

Momrut-Ganerallng Function ofR

МС,Гц[--г) is always positive and depends on the parameters pf'the distribution of revenue (Ap. «„). which in turn depend on ihe combined effecfa of price risk, yield risk, and their correlation, and on any farm policy aIfccting the distribution of ouipul ]trices. If R follows a gamma clislvLbuiioti. an тегс-нче o£ cfc^wül increase MGF4l-rJ; the opposite occurs with an increase Ш ~hg. Furthermore. il' Й experiences an increase of mean-preserving spread, MGfjjl ■ fj likewise Increases for any r, It 1э straightforward to si low ths I:

'While mil analyalB cannot jjretiüfcf M'hcn /J'wJll \ir 1;ГС31ПГ than P„. nr J-Yi:tl Ti'lllltl f ; will Ъс ^ncari-r I Hl 11 О

i J|, ii is liitMiii h' Ji iTf-inlm.1 when f will augment of ülm trtish.

>Ü{<Q) lfT>M<l],

Therefore, If revenue Instability increases. P' goes up and insurance would likely be more appealing. In general, for the same yield distribution. MCFJ-r) will grow if prices experience an increase of menu-prc-se rvi ng sp rea d .н; СOilscquently, I arger market volatility woulg be followed by лш- incentives lo purchase yield insurance. Note that result (i I) Is largely undetermined because tl is impossible I о ascertain whether any change In prices, yields, and their correlation, or any policy parameter (like reduced border protection via dismantling of tariffs) will either reduce or increase MGF„f-r). I towever. II' revenue Instability rises, result (I 1] will prevail and farmers' willingness to pay for Insurance will grow,

Changes in tiw Trigger YitHil. (у J and Price tpj

The way expected Utilityexpressions are dellned by (4) and (5) implies thai if ci I her yz or p,. Increases. Lhcn P' will increase as well, A more Interesting analysis Is to evaluate the ¿fleet of an Increase In either trigger price or yield, maintaining constant their product 1R. = xpj. Starting wllh the simpler case of a change in the trlggei price, p„. in Appendix D we show that:

Similarly, an increase of maintaining Ii,, constant, also yields Ihe following result if:

■ o,

Thus, tanners would always prefer an Increase ol the trigger ij. to an Increase ol pt, keeping !¥„ constant, Obviously, an Increase in у,, won if I be lollowcd by a larger incrciLse ill the premium than would result from mi increase In pf.

"this his hff-|i flwrkeri .................

Agricultural Fiuiuu-t: ftevfew, Spring 2008

Garrido end ZQberman 51

Rfsic-Auei^icn (^etfEcieni

The risk aversttin coefficient, r, shows ц[р In all terms in expression (Hf Whether a larger г implies more willingness la purchase Insurance Is dependent on more factors than found In Ihe previous analyses. The most direct way to Investigate the effect of an increase ni r is I о star I from the IdenLity that equals Insuring anri non-inst&tng solving lor P'(r) and take derivatives with respect to г ¡гг.

(141 у, -c «^'-^UMGFj&S y,) From I we find I ha I 0 if:

[!Г>) p

p - P'lLfMCrF. (rjy ¡J,.!

where the I wo partial derivatives Wllh respect to r are always positive. The Intuition of [ 151 is Lite following. If (J <0. then -its-^cf): thus, purchasing i n su ra nee ii icrciLse s I he еол I s. Further, for ttife LfiS fn (15) to be posLLivc, musl be Ihe case that R. - [3" - P' > 0. Otherwise condition (151 does not hold, and tficn ciP'/дГ< 0. Note thai even If R,, - (31 - P' > 0. condition [15] may nol hold. More risli aversion would he followed by increasing wtlJingfU'^s lo pay for (flsumner if. as condition (15J expresses, ihedisutiiity resulting trom the uncertainty of the indemnity scheme grows less with r than the increasing disutility resutLing from Ihe uncertainly of revenue R net of the premium. In an елП'сше case of very high yield trigger, <y,. and very expensive preittIN nI. more risk aversion would elearly Ъе followed by Li-sj* Incentives In Insure. Bielza, Crnrrtdo, and Sutnpsi [£0061 show LliaL fanners WUh less risk ni-ersion iiillv

benefit more from heavily subsidized Insurance compared l.o (heir more risk -averse coi i n Imparts .

Empirical Models

The simplesi and most general Insurance participation model thai cur da la base permits estimating Is a binary choice model. "J'Iins, the decision lo contract any lype ot insurance is the behavior we will be analyzing with our econometric models.

As the theoretical mod« indicates, farmers would more likely purchase Insurance if direct payments and premium subsidies arc 1 uglier. Also, product price volatility induces more insurance pan I el pa Li on Incentives, keeping constant Iheyteld dlfitrlhulion. In general, we expeel thai farmers who grow tjonperishable products will be less Inclined to purchase insurance, because revenue is more stable wllli storable products. FSy eouLrasL, as Lhey arc entitled in the EU to direct payments, lield crops have this added Incentive to being insured. Concerning the role of yield risk, the theoretical model does not offer a direct Inierprelalion because 1he parameters of ihe yield distribution appear In all terms in equation [9). What this equation makes clear is that the variability ol Ihe indemnity scheme is a crucial faelor In determining whet her Insuring augments utility. Qutlernpftieal analysis eniphas lies the imtjbrlance of the observed or inferred indemnity schemes as a eriiieal factor explaining farmers' observed n isuranee strategies.

We Assume tVirmer f will purchase aL le;jsi one insurance policy ill year L if;

[1.61 BHirtsurir =1 | X|', Z)

^ Prle.Z [iX1,'■ c,f>0),

where two sel* of variables \Z, X'/| are defined as follows. First, there Is a vectoi of variables Z that capture spccilic condi lions affecting far triers' decisions. These refer to non-idiosyncratic elements such as general clfmatlr features and

52 Revisit tny the ¡)Pmnn.d for Agricultural Insurance-. Tlui dose of Spain

other geographical ifharaclcMstics, The Other veelor flf variables, X''., includes those Iri(rliistcaJJy Idiosyncratic element^. As some of these originate from farmers' past Insurance experience, we assume their records of actuarial results wilt influence farmers' decisions. Note that in our simple theoretical formulation where if follows a gamma distribution and agents exhibit CARA preferences, the rl.sk-averslon coefficient interacts with Ihe revenue's distribution parameters, as shown in three of the. four terms in T Jequation (911.

Uur cm pi deal approach is mean I to explain the probability of contracting insurance under Ihe assumption that all farmers exhibit a certain level Of risk aversion (c. ^ 0 V i), but is guided by common factors stemming from Hxed agrlouhural conditions; and the expectations fanners can build from their personal past insurance records and the ctjmoi'cu's (etjuivaleni tl> L'.S. counties) data. These include oxpeelalfous about the iridemnity scheme, the types of Insurance, policies contracted in the past, the expected probability or crop failures, a ltd premium subsidies.

Data Sources and Documentation

The econometric analysis uses data from Lire Spanish agricultural Iffijurance system (ISNESA), Our database includes records ot Individual farms from seven agriculturally diverse cdtnarcas, The ppmplete database In eludes all 4i,f>G0 fanners who cunlrjiered crop Insurance a I least once during (he period 1998-2004, and a complete characterization of each farmer's Insurance strategy, paid premiums, premium subsidies, and collected Indemnities during 1 993-2004.7

Table 1 summarizes the main descriptive elements ol each eomarea. The database

7Fartucrs ii'lujsc last TiMTtnd is [n 1W6 aio hot toLisMfifd In [tils analysis Pof Ltiow. i.onKJdiwl, wc

LlFii- rI l-lUtri* rVCOI'ftw IrtJJJl 11H.KJ~2CKM.

includes a diverse set of crop ri^ks. natural coiidlilon.s, and kinds of Insurance policies. For rereals, fanners can choose among three coverage levels, ranging from basic coverage including hailstorm and fire risks to Individual yield risks. Fruit growers can choose between two coverage levels. From each farmer and year, records include the (Slowing variables: («] whether rhe farmer purchased any insurance (binary); (hi crops Insured, Including surface (ha), expected yield (kg/ha). toLal liability paid premiums j€), premium subs)tiles (<:"), and the kind of coverage; and (c) Indemnities received by crop, coverage, and year.

Table 1 report^ the counts ol the. dichotomous variable fusitr, which takes a value of 1 If the farmer contracted at (east one insurance pulley in the corresponding year, and 0 otherwise for the. period 1999-2004. Since the longest record each farmer can build for 36004 results from 'he experience over the 1 i -year period 1993-2003. we estimate equation [16} for 2004 and for 2003 (as a robustness check).

In addition lo Ihe controls of the com areas, which indirectly allow for checking the impact Ol direct farm subsidies, there are slx idlosynerabc variables included In X',. which are. grouped into I wo categories. The first includes three variables computed from individual fa Iti¡ers' actuariaI results tiJifli.,, LHai uv and Vnr)(), The second eategoty includes insurancf policy details |RLiiss,r, Rt'tPmtn,,, and /teLSribsJ. Below, we first define these variables and llien comment on their meanings.

■ Lftat,. [cunllnuous, .. 0): Hie loss jalto evaluated for each Individual farmer up to year J-l (farmer /, comaivaj, flfop k. year i

[17) LRcti,, = —-- if Pmir.tm^vO,

where ¡nd^ is the indemnity (€).and Pmium^, Is (he premium paid (€), net of subsidies, for crop k In year i.ffar,. provides an Idea of

Agricultural Finance Review, Spritig 200 ft

Gturido and Zilbemujn 53

Table 1. Description of the Study Comarcas and Insurance Data

H&. oi'Years When fusur = I Between 1B98 And 200-1

Nmtie ol Cotnarea All lOnomous Community tilulii Insuwj Crops No, Of Maimers Mean [Std. Dpvr) Percentile 6% Median Percentile 95%

iVfnju'Fin Caaiilla-Lii Mailt: ha V'ti iuyH nis, vf^ftiihles, cere^li 8,528 4.G5H (2.07ti 1 5 7

(.'■ujryjfnrj Andalusia i'.tTCMl.H. citrus, iiottun, ottvf. aunflower 4,151 4.331 11.9291 1 4 7

Segria t". j 1J111_>[ liiL Fruit», vineyards. «reels 5,099 3.04| (2.003) 2 a 7

OlHiittlentil I Mllll'iii Vt^tl^ijirS. iiT'T'i^l ll 1C IHKH- traps, gr&pifii, fj iiils 1,268 4.122 12.0(1!) 1 4 7

CorrifWS Cnsl l-run Cereals, suburb«*. legtinilnGiae :i,H72 4./74 2 6 7

Albuida t:. Va Icnciana Kmiis, vineyards, rltrus, Vt'^it-lijblfH 1,442 S. 440 (1.739} 2 a 7

L.iljrfjr C yilcric ii-ciLi FnittH, rltnifl, VegeiUhlW 17.464 4.«2t) 1 1 .HEW) 2 6 7

T<llu] ■11,660 4.7B4 1J .9751 2 5 7

SUfiPCSS iJala derived 1iTini the Spafltah fljfrfcullural Ins Unmet fiyil^m (ivNESAt.

the aclual expected benefit^ In Lenns of collected Indemnities for one euro spent In contrite ting insurance;

■ bfiiJ/ in., (continuous, > 0|-- The interred loss ratio resuliing from purchasing insurance, computed with the following formula Banner i belonging to comarcaj, crop k, ye;ir i|i

(181 IJiiii i.ri,, = insur,,

it -;nsijr,r)

and represents the loss ratio of crop If In comarcaj; Linh,hf denotes lotaJ liability (€) ol' the insured crop bv farmer i: is,k Is defined by

trlCXi?

TlnStf = £ Jrts^rqp,^. bosaa

when - ins. rropn, = I if crop fcms Insured In year t

* Var,, (continuous, ■ 0): A dlmenslonless measuremen t ol th e expected vn rla bl I i I y o f the loss ratios, evaluated as follows:

T. Tins* k

if Jnd^ ^ O VK.1-:

(191 Ejqi_beijLiir^-." Exp -t>enul if lnrilV[ * 0 for any k, L

LRoi*,, - -JLJ--

£ £ frntumy »

(20) MW,t = T, Pj 'fosurJLRattl LRatf

{I - It is ij r,;) (Uiat „■- UfiUij V . where p, is a weighing factor with

1 aiif[ P, >PiD'ff'i>"b'

and ¡Jlatj, IS the Joss ratio of jCOularcH J up to year t.

■ i >U)ss, , (con t i n nou s, 0): The expected probability of obtaining an indemnity for farmer i's relevant crops. It has been

54 J ice is ttIng the Demand far Agricultural Insurance; The Case-of Spain

evaluated using formula (18). where instead of LRutrrll. we substituted Die proportion of farmers who contracted ihe same policy as did farmer fanrl received an indemnity up to year i -1 -

■ iieifYmc, feonliuuous, i 6}: The average ratio of total paid ffltemium over Lolal liability of farmer i during the period 1998-2004.

» ficiStibs, [continuous. l 0): '['he average ratio оГ total premium over total paid premium of farmer ( during I lie period J 99Й -2004.

LKat,. is lust the loss ratio of farmer I accumulated up Lo year t- 1. if. for any given year J. IMoif, is greater Lhan f, this means the fanner collected more indemnities up to year i- 1 than the total premium paid up to t-i. Note, premium subsidies stgnitirnnMy inrrease the loss ratios because Ihe denotnlttator is the sum of ail premiums, net of .subsidies. Lfini,,. Is iero for farmers who did not reeelve an Indemnity up to year t\ however. LRoi, = 0 does not imply Lhai tlic cApceied benefit oi purchasing insurance is also /его. 1 lence, as an alternative formulalion, we tise the inferred loss ratio, LRnt in,., which Is based on a weighted average oi the enmarea.'s ¡oss ratios :>Г Ihe crops the tanners have purchased [formulated by expressions [181 and fl9||. Neithftr LRat-, nor LRat in,, are perfect Indicators of Lhe expected returns of purchasing insurance, but otu hypothesis is that they may be Sufficient to explain Lumens' insurance stra 1 egies. Alternative demand models are estimated wiih the actual or inferred loss ratio* Lts l obListness eliccka.

Vorir provides a measurement of the relative dispersion of the loss ratios. For V'fir,,. we are assuming that if the fanner tlid not purchase any policy in year L an equ IvaJent measu rement oi the diversion of payoffs is provided by bis eomarea. Note also, the inclusion ol' [J, ensures thai more weight Is placed on the most recent years up lo i. In tills way we introduce a slight degree ol liicmoiy in the

construction of vailances, following t he-same approach used by Chavas and Hi>lt (19901. Note, however, that LRai,, (or Uial_ln:i, for that matter) and Ihe variable Vai',. provide a completely different description of Ihe insurance payoff. While LHatj, provide» a raw return of the money spent in purchasing insurance. Var,., captures line relative dispersion of Lhe payoffs. £JSatJr and Varare positively bui nonllnearly correlated ([) = 0.24 and Spearman= 0.50, both with p< 0.01).1'' Accordingly, with result (ft), we expect thai larger values of Lfia|s and Vcir,, increase the probability ol contracting crop Insurance, because £[/(j,| increases with larger Indemnities and less frequent occurrence oi" Lhe worst results as long as fj'(') is concave.

Finally, PLosn^ lPremt, and flfifSubs, provide three complementary aspects ol farmers' insunng strategies. The lii'st captures the probability of suffering losses that are indemnifiable, for Ihose crops and policies relevant to each farmer. Although I hey arc el early connected, PLassH differs from 7Mi/- Spec! ilea I ly, PLoss-. Is evaluated from the eomarea's probability of crop failure whereas is a genuine Idiosyncratic probability of receiving an indemnity. JiclPrem, captures lhe relative magnitude of Lhe Insured risks with res per I to total. liability. Broader coverages and burger crop risks imply greater relative premla wiih respert Lo total liability. According to result (13]. the option to increase the coverage by means oi a larger yield threshold, yei will generally be followed by more incentives to pLirchase any type of insurance, provided that R I-' kepi constant. However, since a 1 arger coverage rarely Is Compensated by rcduellon of p,.. ft is generally not constant. In our data sot. a larger rclaLive premium indicates broader coverage oi" larger lisk.

-A (ju-1111 • i'. Li' VurAl; ill irtl fJJr;,'. 1Л&?,

iin rl гацшггля (4111|]Ti1s yii-|(K ¡hi Hrtfl i'Mfil Kv of D K1. w11h .l poaltliid and Mjpiillcanl rod lie lent af.Lffioii and ¡1 ВсДвШ-т: ^iilI HlLiiitlkinir iinlllih4il Г01 I Mat' Кгч|И> df th1a rej^fisbton are avalbEfaiii from the ; 1111 hern upon request

Acjrtctíiíymi Kííicuttv-1 Review, Spring 2008

Garrida and ZtUJdrman 55

Table 2. Basle Statistics of the Relevant Variabiles [n = 41,060, year = 2004)

Vartaitle Mean Std, Dev. Percentile 5% Median Percentile H5<iti

JJÍííí,. 0.5ÍM 0.(100 0 .296 2.257

LR¿3Í_ in,, o.gsa 0.741 o.om 0.776 2.270

VarB 0.021 O.CfiLt 0,000 0.0117 0.07H

ReiSuh?, 0 220 0 123 0,(H(i 0.20H 0.430

RtfPri't}!. 0.030 0-.Ó4Í3 0.012 0,077 0.150

PLtina, 0.216 0. ] 22 0.025 O.ffl® 0.422

Seunpe.1 Dat-a tlerh'ert frmtii Lift- HpíuiJsii H^ilr 11 It 11 rid iimuvuru'e syjrtsm (JíNfíSAI.

RclHuhs, capt ures thte role of the premium subsidies. and is unambiguously siétied by lenns i tí rest j It Í10],

A llnat nolv regarding the time frame ol variables within X.' may clarify our approach. The idiosyncratic variables X'[ (Lflat,, or U<nt._fn.t, VarXi, PLoss«. ttelPrwn,. and Rc(Subst) have different Lime perspective^. Therewith the time subscript ; are evt^iaLe^I up to year í- I. iis fanners wmtid ponder the value of contracting Insurance in year t. taking Lnlo account their previous results. The assumption we make Is thai farmers arc guided by their own personid insurance experience or their coma fea Ls results up to year i - I. Hy contrast. illative premium (Reiftvrrtf) and relallve subsidies ÍRfíSttbs.f are idiosyncratic too, bul do no( vary with lime, because. subsidies depend on the type ol farm and relative premium depends on the specific crop's risks, which in turn depend on the climate 'characteristics.

Probit models will be estimated for years 2003 and '¿004. for the complete database using LfiajüLin,,. and !J<nt;i. and Tor the subset of farmers whose LRaf, > 0, i.e., for farmer* vVtia at Least received an indemnity in one year over i he entire period 1993-2003. In Table \l we report the basic statistics of all ldiüsyncráíi& variables pertaining to lhe largest database and year 2004,

Insurance Demand Models

Table 3 presen I * rhe probil. models for these three specifications {'LRat in, LRaL. and LRat using only farmers for whom

LRai > 0), for the years 2QQ3 and 2jp04. The binary and dependent variable In each of the models ts In.ntr,,. 'file 2004 run bus more observador» than 2003 because there are 250 farmers who became instuces in for the lirsi lime during 1999-2004. but were in the 1993-9fi records. All runs have reasonably good sensitivity (rorrect classifications of real ones and zeros! and specificity Indicators (real ones and zeros correctly classified)- The si* models predict at least of the real ones,

although the worst prediction of zeros Is 52.5%. McFadden's ranges from 0.24 \ to 0.428

AH estima led coefficients are significan! (at 99%; significance levels), except tor JJ?u! which Is not significan I in the LasL regression (year 2004). In addlUoti, Lhe sign of LRat tjBanges arross equal tons, whereSe LRal in values are all negative. These results Indicate the loss ratio has an aanbiguous Influence on farmers" decision lo purchase insurance. II loss ra i tos are Indicators of adverse sel eel! on, our results show that the association wit hi farmers' insurance demand is at best doubtful.

The comarcas' com mis are all significant and trot i sis tent across equal inns (Monchft fs the omitted comarca, bul iis effect is picked up In Lhe intercept), Since Hie set Of comarcas is diverse in the proportion of farmers who grow en'jps entitled to direct payments, we can use the eonlrolsas a source of evidence Ibr the role of CAP subsidies on insurance, participation [see. equation fiO>|

56 Revisiting the Demon ci for Agricultural fits! irai ice: The Ctlee of Spain

Table 3. Problt Models of Insurance Demand [dependent variable = JnsurLt)

Inlcrrcd

Actual LHat.,

Actual

JJinr,, > 0

item 2003 2004 2003 3004 2003 2004

LfiflL tn„ o.oe? $¿>22

(0.0001 [0.0101

U* tt'i. jp.oes 0.137 0.177 o.ou0

(O.tHW) to.otoj (00131 [0.013)

VaTf 1.917 2.607 2.«71 2.35^ 2.067

(0.193) (0.1 f>fl| (0.1 HP) 10.1311 (0.240 10.223)

RelSute, 8.201 6.9SS 8.300 7.077 1 1.004 8-533

(0.193) 10.1081 (0.0061 10.031.1 (0.14 7} [D. 113)

PLflss. - 0.212 - 0.812 -0.268 0.334 0.701 0.787

(0.037) 10.1041 (0.006) (0.081J ¡0.14 71 (0.1 131

RelPrertK, -6.203 -8.2BG 8.070 8.458 10-113 10.818

(0.223) (0.215) (0.228) ¡0.2161 (0.325) (0.292)

Ceunpiii^ 0.153 0.555 o.too (1.4ii4 0.741 - 0.982

(0.032) 10.0321 (0.0321 (0.0321 (0 005) |t_052)

Seiina 0.34G 0.472 0.372 0.445 O,H0B 0.747

(0.020) fO. 0281 (0.020) (0.0271 (0.0401 (4.036)

Guadafeigtlri 0.573 0.057 0.578 O.H53 0.830 0.808

(0.045) 10.0431 (0.1545) (0.0431 ((¡¡>0601 [0.06!)

0.30-1 0.4&0 0.327 0.440 0.404 [■>.(310

(0.033) 10.0321 (0.033) (0.0321 (0.0571 [0.003)

vtijrriiiij 0.1 12 0.2.31 0.000 0.23:5 0.4 Ifi 0.472

(0.052) (0.0401 (0.0521 (0.0401 (0.0771 [0.0831

. JtJi.TJ r cues 0.006 0.175 0.082 0.268 0.408

(0.023) 10.0241 'JO ,023) (0.11231 (0.039)

[i ] Lu [t |_i 1 0.171 0.036 0.206 0.036 0.506 0.085

(0,029) (0.029) (0.020) (00201 (0 083) [0.050)

Scnslflvuy Prl+I nr' 0,883 0.858 0.800 0.856 0.926 0.001

Specificity Prt-hDJ" 0,533 0.025 0.535 0.530 0.040 0.592

POslUve Predictive Value ]Y(D| + )' 0-831 0.704 0.832 0.705 o.bH? 0.847

Negative Predictive Valijt Hr(~JJ|-jJ 0.649 0,835 0.653 0.633 0.738 0.705

MeFadd en's R" 0-29$ 0.241 0.203 0.241 0.428 0.338

F^u. ft Observations 41,341 41,660 41.341 41,860 25,301 28.008

,\i .ncsV A] I ("f'Effljcltailfl are aHymptoUcalljl nl^nlflCLml ¿1 pj-f O.Ol [eft'iiepl values In p&rinLheaHS ajv1 bliimlnnL [Icvlmlcuis " In ivi*! f>J. + iLitrLiciK <;hiSiiliftJ an 1, fJiifeftealci imr I in Prt- | -D). ■ iiicijirt-^ ctaiilOcid ii*0. -DSpjiJeates true 0

Our results are ambiguous. Of the six comarca Controls reported in Table 3, those I wo with ¡he highest anrl lowest probability of contracting Insurance are, respectively, the pairs Jucar-Aliiakia and SsgFiA-Ciindaieriiaii Farmers In these two pairs nt eomarcas primarily grow and contract crop Insurance for fruit crops and Vegetables (sec "table 1). The middle group

Is formed by enmareas Compos CtuiipirkJ, whose fanners primarily grow field crops, most of whieh are entitled lu GAP per hectare subsidies. Consequently, our results do nol conllrm the hypothesis (hat direct payments generally induce farmers to purchase insurance. Olher 1 actors seem to override the effect of per becLare direct subsidies.

Affrr.-'uiirirai Hinancr Rcricw. Spring 2008

The remaining coefficients- Var, RetSiibs, PLos;;. and KciPrtrm—are nil sign [Пеан I Find have consistent signs and magnitudes across spec! fl ca I Ions. Vn г Is я measuremettt of dispersion of the indemnities and. logether With Uiat, accounts lor each iarmer's received or expected indemnities. Л larger Vnr indicates thai indemnities nre larger but less frequent* Our models show г ha I л larger i-'oris followed by a higher probabil Ity bi pur chasing insurance. Since I be values of Var1 and LRui are of the same pi dei1 of magnitude, lhe comparison of the coefficients о ['these two variables reveals that Var is far more Important than the loss ratios [he they represented by LRat or by Ltiai^in).

Reffiubs captures the role of subsidies with iespeel If) insurance premium a net, as expected, is highly significant and positive. As shown by Table 2, premium subsidies vary between 5% and 43% ol the commercial premium for of Lhe farmers. ¡'Loss represents the expected probability of obtaining an Indemnity for the crops and policies that are relevant Lo the fanners, &e' negative coefficient is somewhat unintuitive [Table 3), as one would expect farmers Lo he more Incline«! to eunLract insurance when lhe prababillly of obtaining an Indemnity is lusher. Yet what we llnd Is Just lhe opposite; it Is not possible l.o Lesl whether farmers simply refuse to grow line crop whose probability of suffering damage la higher, or II they do grow the crop put refuse Lo insure it. It is clear that farmers insure less If their eoniarea's probability of experiencing a loss for their relevant crop is higher. We s и spec! this is because farmers refuse lo grow (Tops that are very vulnerable Lo frequent hazards, and Lhese are perceived to be higher when line proportion of farmers fn a comarca who report crop failures is higher. An и Lher expla n a 11 on Is that, consistenl with lhe effect Of a larger Var, farmers may not feel niotivaLed to счш1гае1 crop Insurance when crop Is 1 lure is more frequent. In this case, Indemnities must ¡.>e small—because If they were large, insurance would neither be offered nor affordable.

Giwriilo ni id Ziibem ia> i 57

Tile last variable, RvlPrem,, Is the farmer's average ratio of the paid premium over total liability. Its negative and highly significan I sign in all model runs {Table J.tJ indicates farmers are more likely l.o insure when premia are lower, because either risk or coverage is lower. Of course, /ííílPtrrn, Is closely relaled I о the price of insurance, so a higher premium would be associated with lower insurance demand. Tltis variable stands against ReLSubs,, although it appears that the relative subsidies have a more powerful (fleet on farmers' probability of contracting insurance llian RelPrevx,,

As a robustness clicek, we also ran two more pro hi 1 models with a suhsample of farmers thai included only I hose who a( least once during the 1993-2004 period received an Indemnity (totnllng 26,098 farmers in 2004). This group was again subdivided into two segments, die first Willi fanners whose loss ratio was greatef than one fLRal, > I). and lhe second wii.h loss ratios smaller i ban one fUícií, < I).

Table 4 reports lhe results, in ['hiding only the six key variables anrl omitting the intercept and the comarca dummies. Hie findings do not contradict those reponed for the entire data set Iti Tabic 3. Measures of goodness of lit and the models' p red ic l.i n y poten lia I are slightly bet Ler. Likewise, the optlorj^insure Is better predicted (sensiLivity above 88.GH) I han the option not to Insure (specificity above 58,6%). All coefficients are asymptotically significant (p < 0.011. The Coefficient of the loss ratio (LRui) is negative for farmers whose loss ratio is greater than one. and positive lor those with Líínr, < I. These results do not support the hypolhesla thai; adverse selection may he a strong mot Iva lion lo contract crop insurance. NoLe also thé difference in die coefficient of PLoss between both equations, Tanners whose loss ratio is liigli seem more responsive to I lie probability of suffering crop failures, Ihus less eager lo contract Insurance If Pfj&ss Is high.

Downloaded by MAHIDOL UNIVERSITY At 09:13 25 February 2016 (PT)

— V U -3 3

a. ¡1

§ o S. *

n. 2 3. 5=

71 5' fU to £ |

£ ^ x- —

,— i T

b 2 -1

,3 " Q, ^

ffi < fl i

o s -S

■ 3 ~ c

uc y -s ^

rf —"a

t —: 3. ^

n p tt

-j <<;

- c? C 5j

3 m (i

f5 •c __

3. n —'

№ 3

i? •O

— rt

—! ^

■71 t rr 3

51 if "1

i" p. n!

£ ■f- ri

1 1 (»

CT i 2 —' ja - '<

s - 3 -33

0 K £

rr < a

K: 3 H

-i ra ra

3 -1 o

a IT 2.

— -3" r:

j » a

ffg. -

3 'S ~ c

X - <=' 3

iP 2 C

y. - 3 £

2 s o ^

e 3 3 -n

l-l J>

— 3 ~

c « t? ?

i = 3 J]

- a rT 3

ui ■-i ft

•X ST

JO ° Ti 3 »

<— W

< T3 —

«1 £3 5- 3

S* U 3" 3

n ai -

3' JT ^ ^

B 3 5'

i- c » —

Sse: 2

c 3 (ft

n ^ 5'

r,- ■ fi

s. o o

3- g *

¡¿13 S 2 3 ZL.

— 1 n _ " —t

fa № ■C 3

C 3 o a.

•■3

J 3 J1

rr 3-T3

» i 3

3 T 3*

to [O c Q 3? K,

S € S

e — T

„ " b

n- = 3 =r

S ^ 3- ?! «i

s* w ~

Q *-r"

5 3 «

S ^ i" o

- — t

B _ 1) ■K — ET

- y -c

— ^ „ r _ *

!t 3 ii rs iT 3.

i 31 - o

c tr 3 ri №

ST Sc" 3

E a* a '"S

_Tr" rn fer"

I— v

■ rjc-

-J p n 3 № ji i 3 c

3^3 ft 3 3

31 W ^ ^

J ' . If >i

u; „

§ 3 § ^

— Q i ^

^ g i § 3 §

~ ii vc

< - W n

t , J s:

^ P -^ 3 3:

- - 2 f 2 i

p. & ^ i « -

y - ui »1

& 3 P3

A <i fl

= ^ -1 -D

T O — c

n: r ET x

" o * 3

9 a - &

i* 2 3 i

a Js !

J P q S

2 Tl « | | |

? i ft

T o ^ +

-f 3 o o ¡3 3

i3 ■-J 3! b

.— UI rj Ui

3) 3) -J to

/JJ o s O c

b jc iji OtJ

3 - j- 00

O ■35

s i1 a

pp 00 M

!— U

W 01 — X

Oi to cc

O 5' O

co -v] 31 —

N c 03 O

o "-J « tJ

a ■X

3 c p p p

V ii -t" x

3 -S1 a ^

- (5 № V -

A S' r- V D

" 2 ^ o 2 a.

A 46 & 9

§1 «0 a en r>

If 3 g b":

бО Rectsft tny i he Uei ™ nd for Agrtcu Una i t tfisvra net:: The Cane of Sped) j

the implementation of agricultural insu rahce programs. Once latmer« aceunttllate sufficient insurance practice and experience, their subsidies might be lowered wilhoi.it causing significant jpsses In tesurance participation rates.

figures -1 and 5 plot the effects of«hc variables Pt&ss and Ri.'LT3r< jtj i. The «¿feci of PLoss is significant tLs attested by the regression results, but the rather flat slopes .show that the pro liabilities »J' contracting Insurance do no! vary dramaticalJy wILli (fringes of expected probability of experiencing Crop failures. In general, l(№b of additional probability of Joss Is followed by a 3% to 5% lesser probabil I ty of contrac'tii lg i n s tj ra n ce. Ciy contrast, ibe ifciailve price of premium [Jit'IPr^T»!) Is Dion' marked. as depicted by the slopes in Figure 5- Slopes, though, are sleeper fn the right-hand panel, which In с(tides only farmers wllh Uiat > 0. This lindin^ implies that fermefia with iJinf = О (no Indemnities in their records) arc ¡ess | en a I live l о increases in (he price of the premium. Their willingness to contract larger coverages or Insure more risk-prone crops is slightly greater than lor those who have received an Indemnlly at least once.

Summary and Conclusions

This paper began by intrmlLicIng a simplified mode] Lo analyze I he incjentti'es for farmers Lo contract crop insurance. Our model assumes Just one crop, yield Insurance, CARA preferences, and density functions thai, have moment-generating functions. C dmparative static u Its show the unpad ol premium subsidies, direct payments, yield jsrofile, risk avei si on. and insurance parameters on farmers" probability oi purchasing Insurance, Except lor premium subsidies, product price volatility, and direct payments. which clearly Mimulate J mrc basing in sura nee. ilic other parameters do iioi offer unambiguous Results, litsk aversion is thought to be the primary liiuLivailun [or contracting In surance, tii.it i n s urauec poliel f:s ra rely provide coverage to all hazards, and are

sold as colli lacts ot adhesion, with numerous provisions, rules of'conduct, duties, and obligations required for coverage. The complexity of farming decisions under uncertainty prevents obtaining blear-cut results'a bout which parameters play unambiguous effects Iri favor or agalusl contracting crop Insurance. Tills also applies in the ¡coefficient of risk aversion.

Using the theoretical framework as guidance, we analyzed the demand lor agrlcult ural insurance by .employing a new empirical approach I ha I fakes into account farmers' actual insurance resulis. The complete records of all ■ll.GfjU limners within seven Spanish com areas and with 12 years of data allowed us to compute two measures of individual loss ratios and instability of the Indemnities and other key idiosyncratic variables affecting limners' decision lo Eon t rac t Insurance po I i d es. Res ults s 11 ow that these two variables; describing the observed economic returns from Insurance and Us variability, together with premium subsidies. Insurable risks, and other idiosyncratic factors, explain Insurance participation across widely different agrleul I u га I cond 11 ion s.

All models and spe'eifl catkin я reveal thai the variability of Insurance relunis (variance oi the Indemnity schemes) has more Influence lhari loss ratios. whose level has a very small effect on farmers' I n s u ra nee pa rt icipation. Premium subsidies are associated with larger probabilities of Insurance. but stand opposed lo iwo other factors- In general, insurance policies Involving а (¿где premium in retail on Lo tola! liability are not attractive Lo farmers. The model also provides clear evidence that larger expeeled probabilities of crop failure ал■ not followed hy more fret|ueiii insurance participation.

Based on these findings, I armors are not eager to Insure against frequent events of low Intensity. In general, ihsifrlng against these risks is expensive because expected losses and loss adjustment costs are higher.

62 Revisit t r uj tin: Drmandfor AgtricuNumi insurance: The Cast' of Spain

This effect fits within the conceptual nniirtu of selbrey^aHng mechanising which Inn ее 120Q3J iialms are' necessary In ensure (hat policies providing compensations Cor catastrophes and hazards arc efficient

Qflfeflng publiely provided or subsidized Insurance Is a srlf-retnlorclng means to reduce e.x post compensation) programs, because ianners seem to avoid purchasing insurance when the sout^ee of crt'p failures are frequent but ¿nimportant. 11 enliLletnenl to relief a&ri compensation programs is conditioned on conl.racbng erop Insurance, then the government can indirectly reduce the number of beneficiaries йГ ad hoe reliel programs by promoting erop insurance. Spuin, Prance, and (he Netherlands have already introduced this type of ennriii'ional mechanism [Garrldo and Bielza, 2U08).

'14vo further policy ttti pi [rations can he drawn trom (his study. First, adverse selection is not the primary factor explaining Insurance participation among Spanish farmers. Ill Is Is the l'irst study In the literature thai uses actual iridwtinltiee for a targe and diverse set of farmers, with 12 fears of individual Insurance records. As high loss ratios ¿ire generally associated with adverse selection, (he weak and am hi gum is connection found in tliis study between Insurance participation and loss ratios should question the prevailing rregatlvfcvlew that all publicly funded insurance is vulnerable 10 adverse selection (Chambers, 1!»8У; Wright. 2006).

Second, it seems (lint ap"te.»il I oral msuri-inec needs premium subsidies 1o Lake (illand expand (fie coverages farmers can Insure against in order to Increase participation rates. Our models have shown that premium subsidies are perhaps die most Influential tsclor [u Lilting I he balance toward tin: decision to purchase an insurance policy. But wc also found lhar farmers who have experienced indemnified crop failures require smaller premium subsidies to contract crop

Insurance, Thus- as Insurance becomr-* a more common practice, I he probability of experiencing an Indemnity grows, and correspondingly. a lowering of the level of subsidies Lhat farmers may need to Insure. The prevailing view thai farm insurance cannot go beyond very basic coverages without premium subsidies is unmistakably confirmed in I Ills slndy. Ill the long term, expecting low but nonzero probabilities of obtaining indemnities is a powerful motivation to Contract crop Insu ranee. Clearly, when expectations are realized In actual indemnities, larmers are more likely m maintain their insurance practices, even I hough loss rallos may be (iir helow one.

The analyses carried out. here represent a small portion of the issues Uiat our database такск available for exuminalion. We have completely omllled U^omislng analyses of the farmers' choice of coverage and more crop-specific Insuring strategies. Furthermore, formnl tests for adverse selection could be implemented using the same database, which would perhups change out' view of contemporary agricultural insurance pollcleft applied in the European Union.

References

Agroseguro, МеттюгШ, Madrid, Spain. 2004.

15abrock, В. Л,< and D. Л. llennessy. "Input Demand Under Yield and Revenue Msurance." Лньгг.Луг. Eeo?i. 7Й( 19Эе):ЗЗб-Э47.

Biel/a. M,, Л- Garrldo, and .J, M. Sump si. "Optimal Choice of Management Instruments to Cope with Price iilsk." In income Stabilization foAgric liiiure.* The Roie ofPuhlir Policies, eds. C. Caftero and A. Clolli, pp. 110-116. Naples; ESI-Edizldni Sdentlflche tlaliane. 2006,

- , "Finding Optimal Price Risk

Management Instruments: The Сй-нК of the Spanish Potato 5<ч'1ог." Agr Econ. 36.1 [2007}:в7-7Й.

Agricultural finance Kniete, Spring 2008

GafHdo and Zlliterrnari 63

Burguz, F., mid M. Peres Morales.

1902-1992: 90 Anos fie Seguros Agrarias l> 11 Esprm u, M i ii ister lo de Agrlctiltura, Pesca y Allmeniacidijj, Madrid, 1096.

CaflerO. C„ F. Ca pit a mo, A. Cloffl, and A. Coppola, "Risks and Crisis Managemem in Agriculture" European Parliament Doc, No. IP/B/AGR1 /ST/2ÖgB-3öt 2005.

Chambers, ii. "Insurability and Moral I Ia/,ard in Agricultural Insurance Marked." J. Ayr. Ecort.

71.3(19S9):004-6l0.

Chassis, .J,-P., and M. T. Hält. "Acreage Decisions Under K|sk: The CaseQf Corn and Soybeans," Amer. J. Agr, Ec.on. 72(19901:523-5 38.

Coble, K. H-. T. O. Knight R. D. Pope, and J. R. Williams. "Modeling Farm Levd Crop Insurance I lern and with Panel Data," Amer. J. Agr, Econ. 78(19001; 459-1-47.

CbUender. It. N.. and D. Zllberiuan. "Land Allocation Under Uiiceriainly for AlLemalive Specifications oi Return Dis [ r 1 hi 11 ion s." Amer, J- Agr, Ecai i. H7.4(in85|:77EK7*fi.

European Commission "Risk

Management Tools for EU Agriculture (Willi a special focus on Insurance)." Working Doe., Agriculture Dlreciorale-General. Brussels, 2001.

-. Communication from the

Commission to I he Council on Risk and Crisis Mafiagenien 1 In Agriculture. Commissioit of die European Communities, Brussels, 2 February 2005,

Afyri'CL4iiU7TCi! JilSLUtiriiy.' Scf!i;J№;S,

Jotnl Rcscareh Centre, European Commission, Ispra, 2006.

Garrido, A., and M. Hielza. "Evaluating EU Risk-Managemen I Instrument: Policy Lessons and Prospects lor the f"uluro." Manuscript Dept. cTAgr. t-Icon. and Social Sei., Technical I.In I vastly of Madrid, 3008.

Glen. A,, L. M, Leemis, and ,.l. U Drew. "Compulln^; the Distribution of the Product oi'Two Continuous Kandotn Variables." CtortrpulUöörft^SintistöCs Und Datp Analysis 44^01004) :451 -464.

Goodwin, B. K. "Premium iiate Determination In the Federal Crop Insurance Program: What Do Averages Have to Say About Risk7B J. Ayr. and Resor.tr, Econ. December 1994]; 582-395

Goodwin. 13. K.. M, Vandevecr. artd J, Deal. "The Federal Crop Insurance Program: An Empirical Analysis ol Regional Differences In Acreage Response and Participation." Amrr. ,J. Agr. Econ. №,4(2( >04): 1055-1 07 7.

Maxell, P.. C. Pomarerla. and t\, Valdes. Crop Insurancejbr j^ricuitnral Development Issues and Experiment Baltimore, MD; Johns Hopkins University Press, for IFPRJ. 1986,

Horowitz, J. Iv. and F. Lichtenberg.

"Insurance. Moral Hazard. am! Chemical Use in Agriculture," Amer. •>- Agr, Eoorj| 75.5(19931:026-935.

Hueth, D. I,., and W. II. Furl an.

Economics of Agricultural Crop /nsirnarice: llteont and EiÄdente. Natural Resource Management and Policy Series. Boston, MA: Kliiwer Academic Publishers. 1991

innes, it. "Crop Insurance in a Political Economy: An Alternative Perspective ou Agricultural policy." A?iter. J, Agr. Econ. 85.3(200^18-535.

Just, R, E,, L, Calvin, and J. gnlggin. "Adverse Selection In Crop Insurance: Actuarial and A^ymmetrir Information Incentives,11 Amer. ,1. Agr. Ecnrt. 8U1999):834- 049,

Just. R. E-. and R. D. Pope. A

Comprehensive Assessment of the Hole of Risk in U.S. Agriculture.-. Nor well, MA: Kluwer Academic Publishers. 2002.

Revitiiiing the Demand,fur Agrieulutnil Insurance: 7hc Co.se of Spain

Ker, A, P., and P. J. McGpwan, "Weather-Based AdvoSfte Selection and I he U.S., Crop Irtauranee Program; Hit* Private Insurance Company Perspective." J. Ayr. and Ftesour. Er an. 25,2(Dceemher 2000);386-410-

Makki, S.. and A. Somwaru. "Evidence of Advene Si -Ice t ion In Crop Insurance Markets," J. Rüik and insurance ^^[20011:6^-708.

Mlslira. A. K.. R, W. Nimon. and H. E. EI Osta. "Is Mora] Hazard Good for the Environment? I Revenue Insurance and Chetaical Input Use." J. Etv&on. \tgml. 74 [20051:11-20.

Mis lira, P. K. Agricultural iw^mcc, and Incoiiu :: A Study of the Impact and Design. of India'a Comprehtrnsiuc Crop Insurance .Scheme. Alder s h ot. UK; Avph 11 iy Publish i ng, 1996.

Moschinl, G., and D, A. lTenuessy, "Uncertainty, Iilsk Aversion, raid Risk Management for Agricultural Producers." In Handbook of Agricultural Economics. Vol, 1A, eds., B. Gardner and G. Kausser. pp. 87-154. New York; Elsevier Science Publishing. 200!.

Organization for tirnnnmlr Cooperffldn aiid [ Jevelopn ten I (OECI >1 - income Ris k Manngent&nl in Agriculture* Agriculture and Food, OECD. Paris. 2000.

Quiggln. J,: G. Karagiannis, and,.f. Stantorl, "Crop Insurance and Crop Production: An Empirical SLudy of Moral Hazard end ^¿dverse Selection-" Ausirai, ,!. Ayr. Econ. 37,Sil99ifeS-l 13.

RamaS^amL H. "Supply Uesponse (o Agricultural Insurance; Risk Reduction and Moral Hazard Effects." .Airier. ,1. Afjr gfcort |5[ 1993) :91^25.

Serra, T-h B. K. Goodwin, a tu I A, M.

Fea l her1a L (mc. " Model 11 ig C h&ngea in i he 'M.S. Demand for Crop Insurance During the 1990s." Apr. Fin, Rett. 63,2{l;,all 20031:109-123.

Skces. J. R., :aid M. R, Reedi "Rate Making lor harm Level CrojJ Insurance: Implieailoi'ia for Adverse Selection." Anu>r, J. Ayr. Econ. <^(13-650,

Smith. V. II., and B, K. Goodwin. Crop 111 s 11 raftce, Mo ral Haza rd, arid Agrlcu11lira 1 Chenlical Use." Amtr. J. Agr. Bean. 7tJ[1 9G6];42fi-4^H.

Wright, B, "Why Government Crop [nstirauce?" In tivxtme Stabilization 1» Agriculture: The Rob- ofPtiblic Policies, cits., C, Calici-o and A. Ctoflt, pp. 1-6. Naples: ESI Kdlzloul Scieiitiiiebe 1 Udlane. 2006.

\V u. J. - J. "Crop Insurance. Acreage Decisions, and Nonpotnt-Source Pollution," 4trier. J. Agr. Ecan. 81(1999): 303-320.

Appendix A: Evaluation of Fair Premium for Yield Insurance

Pair premium is evaluated as follows:

Pf«P4 ¡"'Ut,.-ylfU)\r.h>

- J^yr7u -P* P' Hfty)dy>

where v„ is the probability of yield being below Ihe threshold (i; ¡t;,.l. If./ftyl follows a gamma distribution vvilh parameters (A, a.}, then:

P, = li .f u - p. f^ 1 ife *

where E^W-y] Is an exponential integral iunel Ion. Since G.,lz] s 2r 1 T(i - it a). (hen:

yf y^-' tiy)"1 M'll ■ K. M

Aarin ii i iiral Fir ¡on er Revia. j 1 Spring '2008

Corrida and ¡¿Itberman 65

F. = U 7 ■ if,------

■ ° Lr|! 1 (I, Äyl

pj F(1 - oc, A.ut,)-FU - K, Vij)

Tp n«)

where HU ■ a. i.y(1) rU

Appendix ß: Conditions for Insurance Being Utility-Augmenting

We start by defining EU(n,). and then establish the <■ midii.ioris for EMfol -EO( i§ ? O:

(Al) EUJn,] =

fv'i \-e r]pM f^^hiyidy

4 tf^-e ,lfl',mL/,ViG^i.(r/V; y.J

- 1 -e-^MGF^t r).

where ijf is the fösobabillty of y y,.; 0 = -P„ -c -i- s: and /<. = With iJMGFJrp,.: y,.] we denote a portion of a complete mflmcm-generkling function of variable y of order rp,. defined only on the limited interval [y, yj, specified as follows;

(A2) JJMOFUi f rP,; jjJ = ij) dj/.

The second part of tV[r.1 uses the same notation. where MCFftj i in-notes a standard moment generating function:

(A3) MGFjM = r^erifh(R}dR

The Et j under the case ot no insti ranee la defined as:

(A4} KiJ(n) - jp™(I -e r|p ' ■ Jh(R)iiif

= l-e-'l-MGF;ii-r], with ji' =~c + ,s\

Therefiire, ELJ|| - £№() > 0 holds If and only If:

(AS) ¡fcl

+ c $ ,VfOFK.t r]|l - erP")>Q-

Appendix C: Conditions for Insurance Being Utility-Augmenting with Gamma. PDFs for Revenue and Yield

If yafid fi follow gain ma dislrlbuUons with parameters \f-n. hJ and (¡L, k,,). then:

where function E^iL, ij rpj) is an incomplete gamma function Iwifh properly P(o .0] - r(«i J]- Further algebra leads to:

UMCFJ^ Li J * MOFJrp.

P[%) J

= IVf (i/^ 1 rp,. 11 f'{. (Ay - r f> J L| J J.

where Pf I Is a regularised gamma function* and tiikcs values P[ecv. 0) = 0 and P(«ii. - I - t. With the above results, (A5) can be expressed as:

66 Revii, it j^j the Dei rnu id for Agrlci tltaral frts r trance: T?te Cast' of Spain

■ ,VfCFri(-r)(erP"-l|

Rfleffidertrig terms and taking logarithms gives:

(A7] Y 1( e-'"»"3 1 > yM)

«P^.&^rpjyj

IA8] -r|P,-[n>log

It i > a, then p' <0. the left-hand side of [Ay) Is always negative. Therefore, a necessary but not sufficient condition for EU(ir,l - EUfo) > 0 is that the' term within the log of 1 lie rtghl-hand side he less than 1, so:

[AS1 y >c r*'MGF fru ; uJ

1 Up H 1 e c

■ ,VfGFri(-r)(l

Further algebra allows us to obtain (he sought necessary condition:

(A 101 - EUtfaC > KL'il^s

Where /rrI is Indemnity [im - p..| ij, ■ yfl

Appendix D; Comparative Statics of Increases of Yield and Price Parameters Insurance

Beginning In lexl equation [9], we take a partial derivative of P* with respect to p,. keeping Rt eonstani:

(All) -P

-(Miff^r) ♦ Yu>>r|V)

dUMGFJrpj p 1

r| UMGF^ (rp,ij,.) e' ' ,Vf( tKr [-r) J

bo the sign of (All! is negative If UM&Fyfrp^ r^J grows with p,,, which in fact II does after valuaUng the function numerically. Both ^tGFu itpj}ft\ end iVfGFIHl-rl are always positive. This proves tcxL equation [\2)-

Text result [131 is more cumbersome to prove because yL, shows up in UMQFp irPq-, yr) and In . Taking partial de.rtvalive.s of P' with respect lo p,, i»nrl keeping R,, eonslatit, we have:

MJMGFjrp,: yf)

(-o"rjJ'- IJjWGF^f-rl-Y t>

r UMGFJrp,,: [>,.)e-r,<- :ViGF„|-r|] which is positive If

¿UMGFJrp,.-, a,.)

which In fael it Is. tecs use IJMGF^rp,,; yj -

MGFjrp^c^^r^yyM

H I Is I he regularized gamma hi net ion.

This article has been cited by:

1. Dolores Rey, Alberto Garrido, Javier Calatrava. 2015. Comparison of Different Water Supply Risk Management Tools for Irrigators: Option Contracts and Insurance. Environmental and Resource Economics . [CrossRef]

2. A. Zuo, C. Nauges, S. A. Wheeler. 2015. Farmers' exposure to risk and their temporary water trading. European Review of Agricultural Economics 42, 1-24. [CrossRef]

3. C.D. Pérez-Blanco, G. Delacámara, C.M. Gómez. 2015. Revealing the willingness to pay for income insurance in agriculture. Journal of Risk Research 1. [CrossRef]

4. Xiaojuan Yang, Yuan Liu, Wei Bai, Buchun Liu. 2014. Evaluation of the crop insurance management for soybean risk of natural disasters in Jilin Province, China. Natural Hazards . [CrossRef]

5. Marianne Lefebvre, Dimitre Nikolov, Sergio Gomez-y-Paloma, Minka Chopeva. 2014. Determinants of insurance adoption among Bulgarian farmers. Agricultural Finance Review 74:3, 326-347. [Abstract] [Full Text] [PDF]

6. Salvatore Di Falco, Felice Adinolfi, Martina Bozzola, Fabian Capitanio. 2014. Crop Insurance as a Strategy for Adapting to Climate Change. Journal of Agricultural Economics 65:10.1111/jage.2014.65.issue-2, 485-504. [CrossRef]

7. M. Genius, P. Koundouri, C. Nauges, V. Tzouvelekas. 2014. Information Transmission in Irrigation Technology Adoption and Diffusion: Social Learning, Extension Services, and Spatial Effects. American Journal of Agricultural Economics 96, 328-344. [CrossRef]

8. V. H. Smith, J. W. Glauber. 2012. Agricultural Insurance in Developed Countries: Where Have We Been and Where Are We Going?. Applied Economic Perspectives and Policy 34, 363-390. [CrossRef]

9. S. Foudi, K. Erdlenbruch. 2012. The role of irrigation in farmers' risk management strategies in France. European Review of Agricultural Economics 39, 439-457. [CrossRef]

10. Robert Finger, Niklaus Lehmann. 2012. The influence of direct payments on farmers' hail insurance decisions. Agricultural Economics 43:10.1111/agec.2012.43.issue-3, 343-354. [CrossRef]