Assessing the Farm Level Impacts of Yield and Revenue Insurance: an Expected Value-Variance Approach

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1 Assessng the Farm Level Impacts of Yeld and Revenue Insurance: an Expected Value-Varance Approach Ernst Berg e-mal: Paper prepared for presentaton at the X th EAAE Congress Explorng Dversty n the European Agr-Food System, Zaragoza (Span), August 2002 Copyrght 2002 by Ernst Berg. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes.

2 Assessng the farm level mpacts of yeld and revenue nsurance: an expected value-varance approach by Professor Dr. Ernst Berg Unversty of Bonn Department of Farm Management Meckenhemer Allee 174 D Bonn Tel: Fax: e-mal: Contrbuted paper submtted for the X th Congress of the European Assocaton of Agrcultural Economsts (EAAE) August 2002 Zaragoza (Span)

3 Assessng the farm level mpacts of yeld and revenue nsurance: an expected value-varance approach *) Abstract Ths paper nvestgates the farm level mpacts of multple perl yeld and revenue nsurance n an expected value-varance framework. The analyss s conducted usng stochastc smulaton jontly wth numercal optmsaton. Smulaton s used to compute the means and varances of revenues as affected by the nsurance schemes under consderaton. In a second step these results are ncorporated n a whole-farm programmng approach, whch optmses a portfolo that conssts of crop producton and nsurance actvtes. The results of a case study ndcate that from the farmer's pont of vew there s an ncentve to buy multple perl crop nsurance, because t sgnfcantly reduces the varablty of ncome. The rsk reducton through nsurance n turn leads to a specalsaton of the producton program. The farm level beneft of crop nsurance strongly depends on the decson maker's degree of rsk averson. Furthermore, rsk free parts of the total ncome reduce the economc attractveness of nsurance schemes. Ths apples e.g. to the area payments under the European agrcultural polcy, whch therefore lmt the potental demand for crop nsurance. Keywords: crop nsurance, rsk management, portfolo selecton, stochastc programmng, expected value-varance analyss Introducton Multple perl crop nsurance has become an mportant ssue n the dscusson about European common agrcultural polcy (CAP). The man reason for ths s that the prevalng condtons of farmng have changed consderably snce the CAP reform of The contnuous lberalsaton of markets combned wth decreasng prce support result n an ncrease of market rsks. Besdes ths, more strngent regulatons wth respect to the applcaton of agro chemcals cause an ncrease of yeld varablty. On the other hand, the currently granted area payments are rsk reducng snce they are ndependent from yelds and prces. It s certanly debateable whether at all or to what extent ths results n an ncreased varablty of net farm ncome. Latter can be expected wth certanty, f area payments wll be lowered or lnked to envronmental constrants, as currently under dscusson. It therefore appears worthwhle analysng new or addtonal rsk management nstruments. Among these, multple perl crop nsurance concepts, as can be found n the USA as well as n some European countres, have recently ganed a consderable amount of nterest. In ths paper we therefore address the farm level mpacts of multple perl crop nsurance schemes usng a modellng approach. The objectve of the approach s to evaluate the economc attractveness of dfferent nsurance desgns and to assess the relatve mportance of yeld and revenue nsurances as farm level nstruments of rsk management. Rsk n the sense of a threat to the survval of the busness always refers to the frm as a whole and not to a sngle producton process. Assessng the economc beneft of nsurance contracts therefore requres a whole farm approach, whch shall be developed n the followng sectons of ths paper. The model s then used n a case study to analyse the effects of dfferent nsurance desgns. *) Ths research was partally funded by the Deutsche Forschungsgemenschaft (DFG) under contract No. BE 1341/4-1 1

4 Prevous studes The longest tradton wth multple perl crop nsurance can certanly be found n the USA. Consequently, a number of studes that use modellng experments to address ssues regardng crop nsurance have been conducted n the US. These studes mostly focus on the analyss of the economc mpacts of nsurance contracts relatve to other rsk management nstruments, such as cash forward prcng or hedgng wth futures and optons. DHUYVETTER and KASTENS (1997) for example nvestgate the effects of varous combnatons of crop nsurance polces and futures contracts on the means and varances of revenues. HEIFNER and COBLE go one step further and analyse the nfluence of dfferent types of nsurance contracts (yeld and revenue nsurances) on optmal hedge ratos (HEIFNER and COBLE, 1997; COBLE and HEIFNER, 1999). By usng expected utlty as objectve functon they explctly consder the decson maker s atttudes to rsk. A smlar approach s used by WANG et al. to explore the relatonshp between hedgng wth futures and optons on one hand and dfferent types of crop and revenue nsurance contracts on the other hand (WANG et al., 1998; 2000). They expand the scope of the optmsaton so that t also determnes optmal coverage levels for the nsurance contracts. All the above studes refer to sngle crop farms, so decsons concernng the producton program reman unconsdered. In Europe, MEUWISSEN et al. have studed yeld and revenue nsurance as rsk management nstruments by means of stochastc smulaton (MEUWISSEN et al., 1999; MEUWISSEN, 2000). The model results llustrate the nfluence of nsurance contracts on the varablty (.e. the coeffcent of varaton) of net farm ncome. Ths approach also refers to sngle crops leavng the choce of the producton program unconsdered. Furthermore, rsk atttudes are not explctly taken nto account. In contrast to ths SCHLIEPER employs a whole farm approach to optmse a portfolo that conssts of a set producton actvtes wth and wthout crop nsurance under an expected value-varance framework (SCHLIEPER, 1997). Arable farms n Europe are typcally mult-commodty operatons. Hence, crop mx selectons are mportant n the context of rsk management, as a dversfed producton program s rsk reducng n tself. A sngle crop approach would not capture ths effect. In the followng we therefore develop an approach that combnes stochastc smulaton wth the optmsaton of a portfolo that conssts of crop producton and nsurance actvtes. Hedgng wth futures and optons wll not be ncluded n the analyss snce these actvtes have not yet ganed much mportance n Europe (partcularly not n Germany). Theoretcal background The most general approach for comparng rsky choces s by means of expected utlty. Ths requres that all possble outcomes of the rsky prospect be translated nto utlty measures to compute the expected utlty. Later on ths crteron can be retranslated nto a monetary measure,.e. the certanty equvalent, by takng the nverse of the utlty functon. The certanty equvalent represents the certan amount of money, whch a decson maker wth a gven utlty functon would rate as equvalent to the uncertan outcome of the rsky prospect (cf. ROBISON and BARRY, 1987, p. 23ff). As the certanty equvalent accurately reflects the decson maker s atttudes to rsk, we use ths crteron n our modellng approach. Furthermore we derve the certanty equvalent by means of expected value-varance analyss (EV analyss). ROBISON and BARRY (1987) have worked out the condtons under whch the EV approach yelds results consstent wth the more general expected utlty models. The reason for choosng the EV approach n the context of ths study s that t can be readly employed n stochastc optmsaton. 2

5 By defnton the certanty equvalent CE equals the expected return E(x) mnus the rsk premum π,.e. CE=E(x) π. For the latter PRATT has derved the approxmate relatonshp 1 π R( E( x) ) V ( x) (1) 2 where R(E(x)) ndcates the decson maker s absolute rsk averson measured at the expected value (cf. ROBISON and BARRY, 1987, p. 34). Thus the certanty equvalent can be expressed as 1 CE = E( x) R( E( x) ) V ( x) (2) 2 The absolute rsk averson functon s defned as R ( x) ( x) ( x) u = (3) u where u (x) and u (x) denote the frst and second dervatve of the utlty functon u(x). Determnng R(x) therefore requres the defnton of the type of the utlty functon. Two frequently used functonal forms are the negatve exponental u λx ( x) = 1 e, λ > 0 and the power functon n the form u θ θ ( x) = x, θ > 1 whch belong to the same class of utlty functons (cf. INGERSOLL, 1987, p. 39). The frst one yelds R(x)=λ and therefore mples constant absolute rsk averson (CARA). It s more lkely however that decson makers express decreasng absolute rsk averson wth ncreasng wealth (DARA). Ths s captured by the power functon, for whch R(x) takes on the form R ( x) ( x) = ( x) x u θ = (4) u and therefore reflects DARA. From equaton (4) we obtan u u ( x) ( x) x = θ Snce the term [ u (x) x / u (x)] represents a measure of relatve rsk averson (cf. HARDAKER et al., 1997, p. 97), the power functon characterses the case of constant relatve rsk averson (CRRA), the degree of whch s determned by the coeffcent θ. Substtutng (4) nto (3) fnally yelds the certanty equvalent CE as θ CE = E( x) V ( x) (5) 2 E( x) 3

6 Ths relaton s partcularly useful because the rsk averson coeffcent θ s ndependent of the magntude of x (where x should be expressed n terms of wealth). Thus ts numercal specfcaton can be based on other studes (e.g. ANDERSON and DILLON, 1992). Maxmsng the certanty equvalent accordng to the defnton gven n (5) shall therefore serve as objectve functon n our modellng approach. Modellng the nsurance contracts The model calculatons shall reveal the economc benefts of crop or revenue nsurance, respectvely, at the level of sngle farms. A vald ndcator for ths beneft s the change of the certanty equvalent. As stated above, the certanty equvalent can be expressed n terms of expected value and varance of the fnancal outcome. The am of modellng at ths pont therefore s to quantfy these measures. For reasons of smplfcaton we model only the bascs of an nsurance contract wthout consderng any detals. Ths means that the model manly captures the ndemnty scheme and ts consequences wth respect to mean and varance of total revenue. In partcular, we do not consder such detals of the contract, whch am at elmnatng moral hazard and adverse selecton. Neglectng these aspects can be justfed because the objectve of the study s to assess the economc potental of such nsurances, f the problems of adverse selecton and moral hazard can be kept n manageable boundares. The followng basc assumptons apply to both, revenue and crop nsurance: 1. Insurance unt s always the total planted acreage of a crop. The nsured may choose a coverage level wthn certan boundares. Thus the coverage level s the farmer s central decson varable, where a coverage level of zero means that the crop remans unnsured. 2. Clams arse, whenever the actual yeld or revenue, respectvely, of an nsurance unt falls below the coverage level that trggers the ndemnfcaton. The compensaton s then determned accordng to the actual amount of the shortfall. 3. The nsurance premum covers at least the expected ndemnty (so called far premum), so the nsurance cannot lead to an ncrease of expected ncome. Ths prevents that nsurance contracts change ther nature n a way that they become ncome-generatng nstruments nstead of rsk management nstruments. Only f an economc beneft remans after deductng the far premum, an nsurance market can develop. Wth these assumptons the ndemnfcaton scheme of yeld nsurance can be modelled as follows: For the -th crop the ndemnty s computed accordng to the rule S ( ) = P Max 0,( δ y y )] δ (6) [ In the above equaton P represents the expected market prce of the crop and y s the expected yeld, whle y reflects the yeld that s actually realsed. The varable δ descrbes the coverage level as porton of the average yeld and represents the desgn varable of the contract. δ = 0 means that the crop s unnsured, whle δ = 1 ndcates that the nsurance coverage equals the average yeld. The face value of the polcy equals the maxmum ndemnty ( P δ y ). The total revenue L (δ ) s composed of the sales revenue plus the ndemnty, where the sales revenue s gven by the actual yeld y tmes the actual market prce P : ( ) = P y + P Max 0,( δ y y )] L δ (7) [ 4

7 Expected value and varance of these varables are gven by E V ( L ( )) = E( P y + P Max[ 0,( δ y y )]) L ( δ ) = V P y + P Max 0,( δ y y )] δ und (8) ( ) ( ) [ where E( ) and V( ) denote the expectaton and varance operators, respectvely. In ths context we assume that the yeld y follows a normal dstrbuton wth mean y and standard devaton σ y. Prces, n turn, are assumed to be log-normally dstrbuted wth mean P and standard devaton σ P. Furthermore, a (typcally negatve) correlaton between yeld and prce s consdered, f approprate. The far premum equals the expected ndemnty E(S (δ )), whch can be computed from equaton (6). For the case of revenue nsurance the ndemnty scheme of equaton (6) changes to S ( ) = Max 0,( δ P y P y )] δ (9) [ where the term δ P y now marks the guaranteed revenue that trggers the ndemnfcaton. The ndemnty amounts to dfference between guaranteed and actual revenue. Computng the total revenue L (δ ) requres analogue changes of equaton (7). From ths the equatons for the expected value and varance of the revenue can be derved as E V ( L ( )) = E( P y + Max[ 0,( δ P y P y )]) L ( δ ) = V P y + Max 0,( δ P y P y )] δ and (10) ( ) ( ) [ The far premum agan s computed as the expected ndemnty usng equaton (9). Wth these assumptons the charactersed nsurance schemes can be modelled usng stochastc smulaton (.e. Monte Carlo smulaton, cf. BERG and KUHLMANN, 1993, p. 240ff) n order to determne means and varances of the revenues as functons of the coverage levels of the nsurance scheme under consderaton. These functons wll then be used n the whole farm optmsaton approach. Stochastc optmsaton model Insurance contracts are not the only rsk management nstruments that farmers have at hand. Besdes some forward prcng opportuntes the mult-commodty operatons that are typcal for Europe always have the possblty to nfluence ther rsk exposure by the choce of crop mx. Capturng these effects requres a whole farm approach that optmses a portfolo of producton actvtes wth or wthout yeld or revenue nsurance, respectvely. Followng we develop a stochastc programmng model of that nature. The objectve functon of the optmsaton model s to maxmse the certanty equvalent of end of perod wealth accordng to equaton (5): θ maxce = E( W ) V ( W ) (11) 2 E( W ) In the above equaton E(W) represents the expected value and V(W) the varance of wealth, respectvely. The expected value of the end of perod wealth results from the ntal wealth plus de sum of the expected values of the gross margns E(GM ) of the producton actvtes 5

8 multpled by ther respectve acreage x after deductng fxed cost FK and wthdrawals for prvate consumpton C: E = n 0 + C = 1 ( W ) W + E( GM ) x ( FK ) wth E ( GM ) = E( L δ )) + A K PR ( δ ) ( (12) E(L (δ )) represents the expected revenue from crop accordng to (8) or (10), dependng on whether yeld or revenue nsurance s consdered. K denotes the varable cost and PR (δ ) the nsurance premum. The varable A marks the area payments accordng to the European CAP. Snce all costs and wthdrawals are assumed to be determnstc, the varance of wealth equals the varance of total revenue: V n 2 ( W ) = V ( L )) x + 2 = 1 n n (δ x x cov (13) = 1 j= + 1 j j In ths equaton V(L (δ )) denotes the varance of revenue from crop accordng to (8) or (10) respectvely, whle cov j represents the covarance of revenues between any two crops that reflects the correlaton between yelds as well as between prces. The decson varables of ths model are the planted acreages x of the crops on one hand and the purchased nsurance coverage levels δ on the other hand. The optmsaton s subject to the constrants = 1 x n a j x b 0; δ 0 j and (14) These ndcate that the total requrements of the producton actvtes must not exceed the respectve resources b j (land, labour, etc.). Furthermore, all decson varables must be nonnegatve. Last but not least t s taken care n the model that nsurance can be purchased only for crops wth an acreage greater than zero. In the above form the model ncorporates a non-lnear optmsaton problem, whch can only be resolved usng non-lnear (numercal) optmsaton procedures. In our case Mcrosoft EXCEL was used along wth the ncluded optmsaton package SOLVER. The stochastc smulaton model was mplemented usng the EXCEL add from Palsade. Model data The followng model calculatons refer to a German arable farm, located n the Rhne area of North-Rhne-Westphala. The farm sze s 150 ha. Table 1 represents the producton actvtes that can be chosen along wth the necessary land set asde to obtan the area payments. Prce and yeld expectatons as well as the varable cost fgures were derved from feld records collected by the extenson servce. 6

9 Table 1: Means and coeffcents of varaton of crop yelds an prces yelds prces mean coeffcent of varaton mean coeffcent of varaton varable cost dt/ha % /dt % //ha wnter wheat wnter barley wnter rye maltng barley potatoes Sources: SCHLIEPER (1997); RASMUSSEN (1997); MEUWISSEN et al. (1999); Landwrtschaftskammer Rhenland: Arbetskres für Betrebsführung Köln-Aachener Bucht, feld records statstcs, several years. The economc effectveness of crop nsurance schemes s heavly nfluenced by the varablty of yelds and prces, whch therefore are of crucal mportance for the analyss. The coeffcents of varaton n Table 1 are derved from the lterature. The fgures regardng the varablty of yelds are based on a comprehensve revew by SCHLIEPER (1997). An emprcal study conducted by RASMUSSEN (1997) n Denmark led to smlar results. The same s true for the fgures that MEUWISSEN et al. (1999) have found for dfferent European countres. Latter are depcted n Table 2. Ths table also contans the coeffcents of varaton of dfferent product prces derved from statstcal data of the years 1986 to Despte the sgnfcant dfferences across countres one can recognze that the prce varablty of potatoes s much hgher than the respectve fgure of such commodtes, for whch European common market regulatons apply. In the case of wheat the medan of the coeffcent of varaton s 10.5 %. Snce t s unlkely that the relatvely short tme seres capture the whole margn of fluctuatons, and based on the hypothess that further market lberalsaton wll somewhat ncrease the varablty of prces, the coeffcents of varaton for all gran prces were set at 15 %, whereas for potatoes ths fgure was assumed to be twce as hgh. Furthermore potatoes exhbt a statstcally sgnfcant negatve correlaton between prce and yeld (cf. TRESKOW, 1983), whch was consdered n the model calculatons by applyng a coeffcent of correlaton of 0.5. For all other crops the assumpton s that yelds and prces are stochastcally ndependent. Table 2: Coeffcents of varaton of yelds and prces n Europe yelds prces from to medan from to medan potatoes wheat , sugar beets , Source: MEUWISSEN et al. (1999) p. 50f Accordng to equaton (13) the optmsaton model needs the covarance matrx of crop revenues, whch reflects the correlaton between yelds as well as between prces. Several emprcal studes ndcate that correlatons between crop yelds are subject to sgnfcant varaton across farms and locatons (cf. OHLHOFF, 1987; GOETZ, 1991; RASMUSSEN, 1997). 7

10 As far as they are sgnfcantly dfferent from zero the coeffcents of correlaton mostly exhbt slghtly postve values. It s safe to assume that gran prces are slghtly postve correlated as well because of the nfluence of market regulatons. For the model calculatons we therefore use the correlatons gven n Table 3. These suppose postve coeffcents of 0.2 between all wnter cereal crops, whereas the correlatons between sprng barley and the wnter cereals amount only to 0.1. The revenues of potatoes are assumed to be stochastcally ndependent from those of the cereal crops. Table 3: Correlaton matrx Wnter wheat wnter barley wnter rye maltng barley Potatoes wnter wheat 1 wnter barley wnter rye maltng barley potatoes Wth respect to further model assumptons t shall be mentoned that the share of potatoes s restrcted to a maxmum of 25 % and that of wnter wheat to 40 % of the total acreage va rotatonal constrants. Fxed cost are consdered n the amount of /year and prvate consumpton (ncludng personal taxes) s set to /year. Avalable fnancal resources n the amount of serve as ndcator for the ntal wealth (W 0 ). Model results The frst step of model calculatons conssts n computng the expected ndemntes and varances of crop revenues dependng on the coverage level. Ths s done va stochastc smulaton. In the second step the smulaton results wll then be ncorporated n the optmsaton model. Expected ndemntes and varance of revenues The above model represents an dealzed nsurance snce we nether consder transacton cost nor bass rsk 1. Under these condtons the revenue nsurance s a perfect rsk management nstrument n the sense that the ncome varablty can be completely elmnated, f the coverage amounts to the maxmum possble return. Snce yeld nsurance does not cover prce rsk, ths type of nsurance cannot completely elmnate the varance of revenue. Fgure 1 llustrates the effects of yeld and revenue nsurance usng wheat as an example. Ether type leads to a sgnfcant reducton of the varance at coverage levels above 40 %. The varance frst declnes at ncreasng, later at decreasng rates. In the case of yeld nsurance most of the potental reducton s utlsed at a coverage level of 120 % of the average yeld. Revenue nsurance, however, enables a further reducton of the varance, whch eventually converges to zero at coverage levels above 200 %. Fgure 1 also depcts the response of the expected ndemnty to varyng coverage levels for both types of nsurance. The graphs llustrate that the 1 Bass rsk occurs, f the rsk characterstcs of ndvdual polcy holders (e.g. ndvdual yeld dstrbutons) dffer from those of the pool. 8

11 expected ndemnty of revenue nsurance s always hgher than that of yeld nsurance, where the curves approach each other at hgher coverage levels. 6,0E varance of revenue 4,8E varance of revenue 3,6E+04 2,4E+04 expected ndemnty = far premum expected ndemnty /ha 1,2E+04 revenue nsurance yeld nsurance 200 0,0E % 50% 75% 100% 125% 150% 175% 200% coverage level % Fgure 1: Varance of revenue and expected ndemnty as functons of the coverage level, llustrated usng wheat as a example As long as the assumed deal condtons apply and the nsured s only blled for the far premum, the nsurance does not nfluence the expected value of the revenue, snce the nsurance premum exactly covers the expected ndemnty. In ths case t s always favourable to choose a coverage level that mnmses the varance. Furthermore revenue nsurance s always preferred over yeld nsurance. Only f the nsurance premum exceeds the expected ndemnty, the rsk reducton through nsurance lkewse leads to a reducton of expected ncome. In realty such deal condtons never apply. Instead, bass rsk as well as uncertan cost fgures, whch are not consdered n the model, reduces the economc benefts of ether type of nsurance. Furthermore, coverage levels must be restrcted to avod moral hard problems. Latter s partcularly true f nsurance premums are subsdzed, as normally the case n exstng crop nsurance programs. Consequently, even revenue nsurance cannot completely elmnate rsk and therefore other rsk management nstruments become mportant. Latter nclude the choce of the producton program, whch s consdered by the stochastc optmsaton approach. The above relatons enter ths approach va functons, whch were estmated usng polynomal regresson. The estmated functons along wth ther respectve ranges of valdty are depcted n Table 4. 9

12 Table 4: Estmated functons of the varance of revenues and the expected ndemnty wnter wheat wnter barley wnter rye maltng barley potatoes yeld nsurance range of valdty from δ mn to δ max varance of revenue wthout nsurance E E E E E+05 varance wth nsurance a 0 (constant) E E E E E+05 a 1 δ E E E E E+04 a 2 δ E E E E E+05 a 3 δ E E E E E+06 a 4 δ E E E E E+05 a 5 δ E E E E E+05 expected revenue wthout nsurance expected ndemnty b 0 (constant) E E E E E+00 b 1 δ E E E E E+01 b 2 δ E E E E E+02 b 3 δ E E E E E+01 b 4 δ E E E E E+02 revenue nsurance range of valdty from δ mn to δ max varance of revenue wthout nsurance E E E E E+05 varance wth nsurance a 0 (constant) E E E E E+06 a 1 δ E E E E E+06 a 2 δ E E E E E+07 a 3 δ E E E E E+07 a 4 δ E E E E E+07 a 5 δ E E E E E+06 expected revenue wthout nsurance expected ndemnty b 0 (constant) E E E E E+02 b 1 δ E E E E E+03 b 2 δ E E E E E+03 b 3 δ E E E E E+03 b 4 δ E E E E E+03 10

13 Whole farm effects of yeld and revenue nsurance The economc potental of rsk management nstruments depends on the decsons marker s degree of rsk averson. The model calculatons are therefore carred out usng two dfferent degrees of relatve rsk averson. Referrng to ANDERSON and DILLON (1992) we use a coeffcent of relatve rsk averson (θ) of 2.5 as to reflect moderate rsk averson, whereas one of 5.0 represents a strong degree of rsk averson. Wthn these basc scenaros we examne the stuaton wthout nsurance and wth yeld or revenue nsurance, respectvely. In addton the nfluence of the area payments accordng to the European CAP s analysed. The economc benefts of the dfferent nsurance desgns are measured n terms of the resultng certanty equvalent changes. The certanty equvalent ncrease represents the necessary addtonal amount of certan ncome n a stuaton wthout nsurance, that would lead to the same expected utlty as the respectve nsurance desgn. Thus, ths measure lkewse reflects the decson maker s wllngness to pay (cf. WANG et al. 2000). The model results are depcted n Table 5. Besdes the economc fgures the table also contans nformaton wth respect to the optmal crop mx and the chosen nsurance coverage levels. If moderate rsk averson s assumed, the producton program wthout nsurance contans the maxmum amounts of potatoes and wheat, as gven by the rotatonal constrants. The remanng acreage s used for maltng barley (38.1 ha), wnter barley (3.1 ha) and the mandatory land set asde. The resultng expected proft amounts to wth a coeffcent of varaton of 68.5 %. If yeld nsurance s offered at the cost of the far premum, the crop mx changes n a way that maltng barley s expanded at the expense of wnter barley. All crops are nsured at the allowed upper lmts of coverage levels (.e. 100 % of the expected yelds). The alteraton of the producton program results n a slght ncrease of proft, whch s due to the specalsaton. The bottom lnes of the table contan the certanty equvalent changes caused by the nsurance. In the descrbed scenaro these fgures reflect a wllngness to pay that amounts to 4176 n total or 28 /ha, respectvely. Revenue nsurance at the cost of the far premum exhbts bascally the same effects on crop mx and expected proft as seen from the case of yeld nsurance. However, the coeffcent of varaton reduces to 43.3 % because of the addtonal coverage of prce rsk. Ths s also reflected n the CE ncrease, whch s twce as hgh as for the yeld nsurance. The revenue nsurance would therefore always be the preferred alternatve. It must be mentoned however, that problems regardng clams adjustment and adequate ratng, whch are already present n the case of yeld nsurance, become even more severe n the case of revenue nsurance. Furthermore, snce the same market prce apples to all producers, prce rsk s systemc by defnton. These effects necessarly result n sgnfcant premum surcharges, whch then, n turn, reduce the comparatve advantage of the revenue nsurance. 11

14 Table 5: Model results wthout nsurance far premum moderate rsk averson wedge factor 1.3 wedge factor 1.3 strong rsk averson yeld nsurance revenue nsurance yeld nsurance revenue nsurance far wthout far wedge far premum nsurance premum factor premum 1.3 wnter wheat ha coverage level % wnter barley ha coverage level % wnter rye ha coverage level % maltng barley ha coverage level % potatoes ha coverage level % land set asde ha expected proft std.-dev. of proft coeff. of varaton % certanty equvalent change /ha wedge factor 1.3

15 In order to cover all costs on the part of the nsurer, the actual rate must exceed the far premum. Ths s consdered n the model by applyng a loadng factor of 1.3,.e. the actual premum amounts to 130 % of the far premum. Ths has consequences wth respect to the optmal crop mx and the optmal coverage levels for ether nsurance desgn. The effect of the cost ncrease on the producton program can be charactersed as a slght dversfcaton, whch shfts the producton program towards the stuaton wthout nsurance. At the same tme nsurance coverage levels fall sgnfcantly below 100 %. The hghest coverage level s chosen for potatoes, whch represent the most rsky crop n the whole portfolo. Snce nsurance cost now exceed the expected ndemnty, the rsk reducton must be pad by a decrease of expected proft. Nevertheless both types of nsurance reman attractve, although the CE ncrease as well as the decrease of standard devaton s less than n the former case. Ths result llustrates the ambvalence of premum subsdes, that are present n vrtually all exstng crop nsurance programs. On one hand such subsdes clearly enhance the economc attractveness of the nsurance contracts. On the other hand they create the ncentve to acqure full coverage wth all the well-known consequences regardng moral hazard. As soon as complete compensaton of potental losses s provded (or the compensaton even exceeds the potental market return) there s only lttle motvaton to reduce losses through careful producton practce. The above results strongly depend on the assumptons wth regard to the degree of rsk averson. To llustrate ths, the descrbed nsurance desgns have been examned under a stronger degree of rsk averson. The results of these model calculatons can be found n the rght half of Table 5. They ndcate that a hgher degree of rsk averson frst of all results n a more dversfed producton program n the reference stuaton,.e. wthout nsurance. As a consequence, the expected proft s about less, n turn yeldng a lower standard devaton and coeffcent of varaton. Introducng yeld or revenue nsurance, respectvely, then leads to a more specalsed producton program. Due to the dfference n the ntal stuaton ths effect s more ntense than at a lower level of rsk averson and therefore also leads to a larger ncrease of expected proft. These results document that an ncreasng level of rsk averson lkewse ncreases the attractveness of nsurance contracts, whch s also reflected by the respectve wllngness to pay measures. These are generally hgher than before, whereas the dfferences between the nsurance desgns reman largely unchanged. A decrease (ncrease) of the ntal wealth poston would have a smlar effect as the ncrease (decrease) of the degree of rsk averson, as can be seen from the equatons (10) and (11). Thus, the attractveness of nsurance contracts also grows f the fnancal poston of a farm becomes less favourable. The attractveness of crop and revenue nsurance desgns s also nfluenced by rsk free parts of the total ncome, as e.g. gven by the area payments of the European CAP. Ths can be llustrated by runnng the model wthout consderaton of area payments and land set asde. Table 6 contans the certanty equvalent changes wth and wthout area payments for the case of moderate rsk averson. The model results show that the area payments sgnfcantly reduce the CE ncrease and therefore the economc attractveness of the crop nsurance desgns. Dependng on the nsurance premum the reducton of the wllngness to pay ranges between 24 % and 44 %. Growng rsk averson would even ncrease ths effect. The present agrcultural polcy therefore sgnfcantly hampers the development of a crop nsurance market. 13

16 Table 6: Influence of area payments on the certanty equvalent change caused by yeld and revenue nsurances (moderate rsk averson) yeld nsurance revenue nsurance far premum loadng factor 1,3 far premum loadng factor 1,3 wth area payments /ha wthout area payments /ha Dfference wthout./. wth /ha area payments % Concludng comments Although the model results only refer to one example farm, whch s not at all representatve, they provde some nsghts that can safely be generalzed. Frst we can state that there s an economc ncentve for farmers to purchase crop nsurance. Yeld nsurance as well as revenue nsurance can reduce the varablty of ncome substantally. In ths respect revenue nsurance s generally more effectve, snce s covers both yeld and prce rsk. However, latter also embodes addtonal problems wth respect to mplementaton. The model results ndcate that the nsurance solutons reman economcally attractve f the rates exceed the far premum by 30 %. In ths case the optmal coverage levels drop below 100 %, leavng a deductble, whch s generally useful to avod moral hazard problems. In turn, ths effect leads to the concluson that a sgnfcant porton of the actuaral problems, that vrtually all exstng multple perl crop nsurances have, are caused by lowerng the rates through premum subsdes. The economc attractveness of all rsk management nstruments ncludng nsurance contracts depends on the overall rsk exposure of the farm and, n addton to that, s nfluenced by rsk free portons of the total net ncome. Latter refers to the area payments under the current European agrcultural polcy regme. Hgh payments of that nature reduce the economc attractveness of crop nsurance and vce versa. Thus, the current agrcultural polcy regme tself lmts the potental demand for crop nsurance. The model results are strongly nfluenced by the assumptons regardng to the decson maker s atttudes to rsk. Ths refers to the general presumpton of constant relatve rsk averson as well as to the numercal assessment of the rsk averson coeffcent. Latter s often set at values around two (e.g. COBLE and HEIFNER, 1999; WANG et al., 1998; 2000) wthout havng any emprcal evdence as to whether or not ths fgure truly reflects farmers behavour. Another crtcal assumpton s that of ntal wealth, snce the model results are very senstve to varatons of ths fgure as well. The senstvty of the model results to changes n rsk atttudes on one hand and the lttle knowledge wth respect to the actual rsk response of farmers on the other hand ndcate that there s a substantal need for methodologcal as well as emprcal research n ths area. A relable evaluaton of the possbltes and lmtatons of crop nsurance schemes n Europe also requres further research wth respect to the rsk exposure of farms relatve to the scope of producton, farm sze, locaton and ownershp condtons. Ths nformaton provdes the necessary data to conduct model experments on the level of sngle farms and nsurance pools. Farm level models lke the one presented n ths paper provde nsghts nto the potental 14

17 demand of crop nsurance, whle models on the level of nsurance pools are to analyse ts feasblty from the nsurer s pont of vew. References ANDERSON, J.R and DILLON, J.L. (1992): Rsk Analyss n Dryland Farmng Systems, Farmng Systems Management Seres No. 2, FAO, Rom. BERG, E. und KUHLMANN, F. (1993): Systemanalyse und Smulaton für Agrarwssenschaftler und Bologen. Methoden und PASCAL-Programme zur Modellerung dynamscher Systeme, Stuttgart. COBLE, K.H. and HEIFNER, R.G. (1999): The Effect of Crop or Revenue Insurance on Optmal Hedgng, Onlne Research Paper, Dept of Agrcultural Economs; Msssspp State Unversty. DHUYVETTER, K.C. and KASTENS, T.L. (1997): Crop Insurance and Forward Prcng Lnkages: Effects on Mean Income and Varance, Paper presented at the NCR-134 Conference, GOETZ, R. (1991): Der Enfluß wtterungsbedngter Ertragssschwankungen auf de landwrtschaftlche Betrebsplanung, Kel. HARDAKER, J.B., HUIRNE, R.B.M. and ANDERSON, J.R. (1997): Copng wth Rsk n Agrculture, Oxfon - New York. HEIFNER, R.G. and COBLE, K.H. (1997): Optmzng Farmers' Jont Use of Forward Prcng and Crop Insurance by Comparng Revenue Dstrbutons wth Numercal Integraton, Paper presented at the NCR-134 Conference, INGERSOLL, J.E. (1987): Theory of Fnancal Decson Makng, Savage, MD. MEUWISSEN, M.P.M. (2000): Insurance as a Rsk Management Tool for European Agrculture, PhD-Thess Wagenngen Unversty, Wagenngen, NL. MEUWISSEN, M.P.M., HUIRNE, R.B.M. and HARDAKER, J.B. (1999): Income Insurance n European Agrculture, European Economy, Reports and Studes No. 2/1999, European Commsson, Drectorate-General for Economc and Fnancal Affars, Brussels. OHLHOFF, J. (1987): Spezalserung m Ackerbau aus ökonomscher und ökologscher Scht, Kel. RASMUSSEN, S. (1997): Yeld and Prce Varablty n Dansh Agrculture: An Emprcal Analyss. In: HUIRNE, R.B.M, HARDAKER, J.B. and DIJKHUIZEN, A.A. (Eds): Rsk Management Strateges n Agrculture: State of the Art and Future Perspectves, Mansholt Studes, Wagenngen, NL, p ROBISON, L.J. and BARRY, P.J. (1987): The Compettve Frm's Response to Rsk, New York - London. SCHLIEPER, P. (1997): Ertragsausfallverscherung und Intenstät pflanzlcher Produkton, DUV Wrtschaftswssenschaft, Wesbaden. TRESKOW, A. (1983): De Konkurrenzfähgket von Spese- und Industrekartoffeln be unscheren Erträgen und Presen, Dplom Thess, Unversty of Bonn. WANG, H. H., HANSON, S. D., MYERS, R. J. and BLACK, J. R. (1998): The effects of crop yeld nsurance desgns on farmer partcpaton and welfare. Amercan Journal of Agrcultural Economcs 80 (4), p WANG, H.H., HANSON, S.D. and BLACK, J.R. (2000): Can Insurance Substtute for Prce and Yeld Rsk Management Instruments? Manuscrpt, forthcomng. 15