YIELD COVERAGE LEVELS AS DEDUCTIBLES IN CROP INSURANCE CONTRACTS: IS THE EFFECT ON FALSIFICATION BEHAVIOR SIGNIFICANT? i

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1 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? YIED COVERAGE EVES AS DEDUCTIBES I CROP ISURACE COTRACTS: IS THE EECT O ASIICATIO BEHAVIOR SIGIICAT? Roderck M. Rejesus, Texas Tech Unversty Bert B. ttle, Tarleton State Unversty ABSTRACT Yeld coverage levels serve as deductbles n cro nsurance contracts. Ths aer examnes the effect of yeld coverage choce on falsfcaton behavor and determnes f ths effect s sgnfcant n cro nsurance. We theoretcally show that lower yeld coverage choce may ncrease the ncentves for falsfcaton behavor. A loss equaton that corrects for samle selecton bas was estmated usng maxmum lkelhood to verfy ths rooston. Our emrcal results ndcate that the falsfcaton effect of alternatve yeld coverage levels may not be sgnfcant n cro nsurance and government resources may be well-sent on addressng fraud-related roblems due to other cro nsurance contract elements. Keywords: Cro Insurance; alsfcaton; raud; Yeld Coverage ITRODUCTIO Yeld coverage levels serve as deductbles n cro nsurance contracts. The choce of yeld coverage level determnes the magntude of nsurable yeld losses. Snce the maxmum allowable yeld coverage level n cro nsurance contracts s 85%, losses n cro nsurance are not fully nsurable and, thus, yeld coverage levels are analogous to standard deductbles because they reclude full nsurance of losses, as n other lnes of nsurance. rom the economc lterature on nsurance, the resence of deductbles n nsurance contracts can be exlaned by the followng roblems of asymmetrc nformaton: adverse selecton [16, 15], ex ante moral hazard [9, 17, 3], and ex ost moral hazard under costly state verfcaton [19, 5, 11, 1]. Hyde and Vercammen [10] further showed that otmal cro nsurance contract form n the resence of ex ante and ex ost moral hazard nvolves deductbles n the form of yeld coverage levels or yeld guarantees. In theory, asymmetrc nformaton roblems n cro nsurance contracts should be mnmzed by the resence of alternatve yeld coverage levels, but these roblems stll seem to be revalent n cro nsurance [1, 3, 13]. 1 In artcular, ex ost moral hazard or falsfcaton behavor may be a roblem even wth the resence of deductbles f the nsurance envronment s not consstent wth costly state verfcaton. urthermore, f there s no full commtment to audtng every clam then the fraud mtgatng effect of deductbles n nsurance contracts wll not aly [14]. 79

2 Southwestern Economc Revew Therefore, f the market for cro nsurance more lkely follows the condtons of the costly state falsfcaton model and full commtment s absent, then deductble contracts are not otmal to deter ex ost moral hazard or fraud behavor. Yeld coverage levels actng as deductbles n cro nsurance contracts may then rovde ncentves for falsfcaton behavor, much lke what s observed n automoble nsurance [4]. The objectve of ths study s to determne how yeld coverage choce may affect falsfcaton behavor and whether there s evdence that ths effect on falsfcaton behavor s sgnfcant n cro nsurance. The extent of falsfcaton behavor n cro nsurance has not been fully nvestgated. Although the extent of falsfcaton behavor has not been recsely estmated, the Rsk Management Agency (RMA) beleves that about 5% of all clams are assocated wth fraud, waste, or abuse []. And even though there are no exact estmates of the total dollar cost of fraud, waste, and abuse n cro nsurance, RMA has documented numerous cases that ranges from mnmal clams addng (n the hundreds of dollars) to coordnated fraud schemes among several artes (n the mllons of dollars) [1]. Knowledge about the resence or absence of falsfcaton effects due to yeld coverage levels may show whether ths ncentve roblem needs to be addressed. Ths study can show f yeld coverage levels n cro nsurance contracts contrbute to the fraud behavor observed n cro nsurance. If there s evdence of ths falsfcaton effect n cro nsurance, then the ndustry may want to devote resources on ths ssue to determne actons to reduce the fraud ncentves from alternatve yeld coverage choce. If there s no evdence of ths falsfcaton effect, then resources may be better allocated to examnng other nsurance contract elements that contrbute to fraud, waste, and abuse n the cro nsurance rogram. The aer s organzed as follows. In the next secton, a theoretcal model s develoed to show how yeld coverage levels acts as deductbles n cro nsurance contracts and how t may affect falsfcaton behavor. The emrcal model, data, and results are then dscussed n the next three sectons, resectvely. Concludng comments are resented n the last secton. THEORETICA MODE Consder a rsk-averse farmer wth an Actual Producton Hstory (APH) cro nsurance contract. The APH contract s an ndvdual yeld nsurance lan that rotects farmers aganst yeld shortfalls f the actual yeld falls below the guaranteed level. APH nsurance ncludes catastrohc coverage (CAT) and otonal buy-u levels of coverage above CAT. or a flat fee of $60 er cro er farm, CAT rovdes a 50 ercent yeld guarantee and ays an ndemnty based on 55 ercent of the rojected rce. In ths aer, we searate CAT and APH buy-u coverage and hereafter refer to APH buy-u as APH nsurance. A deductble n APH nsurance contracts s mlct n the choce of yeld coverage levels that determnes a farmer s yeld guarantee. APH nsurance rovdes yeld rotecton of u to 85 ercent of the farmer s average hstorcal yeld; wth a remum based on a chosen yeld coverage level. The APH contract ays an a ndemnty f the farmer s actual yeld ( Y ) falls below the guaranteed yeld level g ( Y ) but offers no rce rotecton. The guaranteed yeld s comuted based on the followng formula: 80

3 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? Y θy g e =, (1) where θ s the ercent yeld coverage chosen by the farmer (θ = 0.55, 0.6, 0.65, 0.7, e 0.75, 0.8, 0.85) and Y s the average hstorcal yeld based on the yeld record submtted by the roducer. Gven θ, the deductble for the APH contract can be defned as: D ( θ ) θ )Y = (1 e P g () where g P s the guaranteed or elected rce. ote that '( θ ) < 0 D and ''( θ ) = 0 D. If a Y < Y g, then an ndemnty ayment s trggered as follows: I T = θ Y P Y P. (3) Equaton (3) can then be re-wrtten as I T T = γ D(θ ) (4) T T where γ = ( Y P Y P ). ote that γ reresents the true total dollar value of the loss ncurred by the farmer. Indemnty s ad based on the true total dollar value of the yeld loss less the deductble. Assumng that a farmer can falsfy the total dollar value of the yeld loss by msreortng hs actual yelds, then the total dollar value of the loss can be msreresented as follows: γ = ( Y P ( Y λ) P ) (5) where λ s the amount of reducton n the falsely reorted yeld. Actual yeld loss can be falsfed, for examle, f the roducer colludes wth the loss adjuster to msreort the actual yeld. Ths tye of fraud s called oortunstc fraud there s an actual loss already and the nsured has the oortunty to falsfy the loss to hs advantage. Equaton (5) can then be re-wrtten as follows: 81

4 Southwestern Economc Revew T γ = γ (6) + g where = λp. Therefore, the falsfed total dollar value of the yeld loss ( ) s the sum of the true total dollar value of the yeld loss lus an addtonal falsfed T amount (). The ndemnty ayment n ths case s I = γ + D(θ ). Consder a rsk-averse farmer who s makng the margnal decson to falsfy the true dollar value of hs yeld loss ( ), equvalent to the amount. Assume that γ T the nsured roducer have already sgned an APH contract and chosen hs yeld coverage levels (or hs deductbles). Ex ost, hs decson s to choose the level of falsfcaton () to maxmze hs exected utlty defned as: T U ( W + D( ) c c( + (1 ) U ( W γ c c( θ (7) γ where U( ) s a standard von eumann Morgenstern utlty functon wth U ( ) > 0, U ( ) < 0; s the robablty of successful fraud (falsfcaton s not detected); c s the cost of roducng the cro; c() s the total cost of falsfcaton as a functon of the amount of falsfed yeld loss wth c () > 0 and c () = 0; W s the level of wealth not contngent (.e. W s the dfference between ntal wealth and the remum ad: ( W = W 0 P ); and, all the remanng varables are as defned before. If the farmer truthfully reveals hs loss then hs wealth s defned as follows: W D( θ ) T T θ ) c = W γ + γ D( c. (8) Ths exresson mlctly assumes that γ T > D(θ ) for the nsured farmer to have a ostve level of nsurance coverage. If the farmer falsfes hs loss and does not get caught then hs wealth s defned as: \ T T W + D( θ ) c c( ) = W γ + γ + D( θ ) c c( ). (9) If the roducer gets caught falsfyng hs actual yeld loss, then he forfets hs T nsurance coverage and hs wealth s defned as W γ c c(). Therefore, falsfcaton s costly f he s caught because of the nsurance coverage forfeted equvalent to γ T D(θ ). An mortant behavoral assumton n (7) s that fraud s not found wth robablty one, n contrast to what s suggested n standard contracts wth deductbles [18]. The robablty s lower than one for at least two reasons, ether () the nsurer does not audt the olcy (absence of full commtment or random audtng) or () t audts, but does not fnd any evdence of fraud even when there s fraud. Ths s consstent wth the market for cro nsurance. Current RMA comlance ractce s to randomly audt selected clams every year or audt clams called n through the fraud hotlnes. Colluson among roducers, adjusters, and agents also makes t ossble 8

5 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? for fraudulent clams to not be detected by RMA comlance audts, whch s consstent wth () above. An nsured farmer wll falsfy hs actual yeld f and only f: T U( W+ D( θ ) c c( + (1 ) U( W γ c c( U( W D( θ) c ). (10) That s, the nsured roducer wll only falsfy yelds only f the exected utlty of the fraud gamble s greater than the exected utlty of not takng the fraud gamble. Assumng (10) holds, let us now consder the otmal level of falsfcaton (*). Maxmzng (7) wth resect to results to T UW '( + D ( ) c c ( ))( 1 c'( + 1( UW ) '( γ c c ( ))( c '( = 0 θ. (11) et W W + D( ) c c( ) = θ be the farmer s wealth when fraud s not D T detected and let W = W γ c c() be the farmer s wealth when fraud s detected. An nteror soluton to (11) mles that ( 1 c '( > 0. The second-order condton s always verfed under rsk averson and can be wrtten as: H U ''( W )(1 c'( + (1 ) U ''( W D )( c'( < 0. (1) Snce we are nterested n the fraud ncentve effects of chosen deductbles or yeld coverage levels n APH cro nsurance, we want to examne the relatonsh between and D(θ). Ths relatonsh can be derved by takng the total dfferentaton of (11) wth resect to and D(θ). Under rsk averson, ths results to: d dd( θ ) = U ''( W )(1 c'( > 0 H. (13) Hence, hgher deductbles or lower yeld coverage levels ncrease the ncentves for fraudulent behavor. If the roducer has a lower yeld coverage level, then we should observe hgher yeld loss magntudes reorted when falsfcaton behavor s resent. ower yeld coverage levels means that a hgher yeld loss magntude s needed to trgger an ndemnty. If the roducer has an oortunty to falsfy hs loss, then the roducer would want to falsely ncrease the magntude of the loss to always trgger an ndemnty ayment. The magntude of the falsfed loss deends on the arameters on the rght-hand sde of equaton (13). In general, however, we would exect that the magntude of the falsfed loss would be enough to trgger an ndemnty ayment and cover the remums ad by the roducer. rom (11), we can also show that 83

6 Southwestern Economc Revew d d U '( W = )(1 c'( U '( W H D )( c'( > 0. (14) Ths means that ncentves for fraudulent behavor ncreases as the robablty of successful fraud ncreases. Another nterestng relatonsh to examne s the effect of on d dd(θ ). That s, the effect of the robablty of successful fraud on the falsfcaton ncentves created by dfferent deductbles (or yeld coverage levels). rom (13) we can show that d ddd d( d / dd) = d > 0 (15) f c'( ) 1 (1 c'( ) and f the roducer has constant absolute rsk averson (See Aendx for the roof). Consequently, must be suffcently hgh n order to obtan the desred result. The exresson n (15) means that fraud ncentves created by deductbles ncreases as the success robablty of fraud ncreases. EMPIRICA MODE AD DATA The theory above suggests that hgher deductbles or lower yeld coverage levels ncreases ncentves for falsfcaton behavor. Ths means that observed loss magntudes should be hgher for farmers wth lower yeld coverage levels, f falsfcaton behavor s resent. Ths s esecally true f the robablty of detectng fraud s small. Thus, our emrcal hyothess s as follows: the magntude of the observed dollar value of yeld loss s hgher when the yeld coverage level of the cro nsurance contract s lower. ote that when there s full commtment by the nsurers to audt each and every cro nsurance olcy, observed loss magntudes should not be affected by fraud behavor and, consequently, by the level of the deductble or yeld coverage. Moreover, under ure adverse selecton and ure ex ante moral hazard, the loss should be lower when the yeld coverage s lower, snce good rsks chose lower yeld coverage (or hgher deductble), and a lower yeld coverage level (hgher deductble) also ntroduces more ex ante ncentves to reduce the lkelhood of a loss. Our emrcal hyothess above wll then hold true only f there s sgnfcant fraud behavor or falsfcaton behavor resent n cro nsurance data. Ths s the only asymmetrc nformaton roblem consstent wth the emrcal hyothess. If the emrcal hyothess does not hold then the ncentves for falsfcaton behavor created by alternatve yeld coverage choce s not sgnfcant n cro nsurance. Other asymmetrc nformaton roblems such as ex ante moral hazard and adverse selecton may then be more sgnfcant n cro nsurance n ths case. A loss equaton, wth yeld coverage level as one of the ndeendent varables, needs to be estmated to verfy the emrcal hyothess of the study. Consstent estmaton of a loss equaton usng cro nsurance clams data requres that 84

7 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? losses be reorted regardless of sze. That s, the observed dollar value of the yeld loss ( Y P Y P ) should be reorted even f the actual yeld value s not below the guaranteed yeld level (.e. θ Y P < Y P or θ Y P Y P < 0 ). But as we know, losses are reorted and observed only f actual yeld s below the guaranteed level ( θ Y P > Y P or θ Y P Y P > 0 ). In other words, yeld loss s only reorted f the total loss s greater than the deductble (.e. Y P Y P > ( 1 θ )Y e P g ). Thus, a lower yeld coverage level or a hgher deductble ( D ( θ ) = (1 θ )Y e P g ) lowers the robablty of reortng a yeld loss. In addton, the decson by an nsured to reort a loss may also deend on unobserved ndvdual factors. or examle, there may be transactons cost to submttng a clam that, n the farmer s vew, may not make t worth t to submt a clam (.e. θ Y P < Y P + ψ, where ψ = transacton costs n ths examle). The farmer only reorts a loss and submts a clam f e g Y P Y P > ( 1 θ ) Y P +ψ. The threshold ( ( 1 θ )Y e P g + ψ ) s not observable and s ndvdual secfc. Gven the condtons above, the observed loss n cro nsurance data has samle selecton bas due to the ncdental truncaton of the loss varable [7, 8, and 6, ]. The observed loss data n ths case s nonrandomly selected. Wthout arorate correctons, the magntude of the arameter assocated wth the yeld coverage level n the loss equaton wll be based uward [6,. 99 for a roof]. The objectve s to estmate the arameters of the model: y = x + ε β', (16) when y s observed only f: z * = γ ' w + u > 0. (17) The notatons n (16) and (17) are as follows: y s the observed dollar value of the * yeld loss (.e. Y P Y P ), z s the samle selecton varable defned as the dfference between the dollar value of the guaranteed yeld and the actual yeld lus other ndvdual secfc factors ( β and γ are vectors of θy P Y P ψ ), ' arameters, x and w are vectors of regressors, and, ε and u are dsturbance terms. urther, assume thatε and u have bvarate normal dstrbutons wth zero means and correlaton ρ. The model above mles that: ' E[ y y s observed] = [ y * z > 0] E (18) = E > γ' w ] [ y u 85

8 Southwestern Economc Revew = β' x u > γ w ] + [ x + ρσ ε λ ( α u E ε = β' ) α / σ λ α where u = γ' w u and ( u ) = ( γ w / u ) / Φ( γ w / u ). 3 The exresson n (18) ndcates that least squares regresson usng only the observed data roduces nconsstent estmates of β, unless ρ = 0. Snce z s unobserved, we can reformulate the model as follows: * [Selecton equaton]: * z = γ ' w + u, where z =1 f Prob( z =1) = Φ( γ' w ) and Prob( [Regresson model]: y = β' x + ε observed only f z (0) ( u, ε )~ bvarate normal [0, 0, 1, σ ε, ρ]. Ths mles that E [ y z = 1] = β' x + ρσ ε λ( γ' w ). The arameters of the model above are consstently estmated usng the maxmum lkelhood (M) rocedure. A Wald test s also undertaken to test for the sgnfcance of all the coeffcents n the model. Moreover, a lkelhood rato test s also undertaken to see f there s ndeed selecton bas n the data (.e. test f ρ = 0). In ths study, only RMA data of nsured roducers for rensurance year (RY) 000 are consdered. Catastrohc (CAT) nsurance olces and non-aph olces are excluded from the analyss. urthermore, only corn and soybeans roduced n Illnos are ncluded n the analyss. ote that average Illnos corn and soybean yelds for 000 were aroxmately 151 bushels/acre and 44 bushels/acre, resectvely. Average corn and soybean rces for Illnos n 000 were about $1.91/bushel and $4.85/bushel. The resultng data set ncludes 4,47 observatons, where 46 observatons have unobserved y and 4,46 observatons have observed y. Thus, the deendent varable has 46 censored observatons and 4,46 uncensored observatons. As mentoned above, the deendent varable n the model s the observed loss er acre equvalent to ( Y P Y P ). The regressors x are the followng: acreage (ACRE), nsured share (SHR), yeld coverage dummes (YC65-YC80), cro dummy (COR), a non-rrgated ractce dummy (IR), and rensurance organzaton dummes (See Table 1 for the descrton of the varables). The acreage varable s ncluded to see the effects of farm acreage on loss magntudes er acre. The nsured share s a behavoral varable to determne f the effect of share amount on the loss. Cro and ractce (non-rrgated vs. rrgated) dummes are ncluded to see f there are cro-secfc or ractce secfc effects. The rensurance organzaton s also ncluded n the model to cature f there are frm-secfc effects. astly, the yeld coverage dummes are the man varables of nterest n ths study and are ncluded to verfy our emrcal hyothess above. If the emrcal hyothess holds, 86 φ σ * z >0 and z = 0) = 1- ) σ z =1 otherwse; (19) Φ γ' w. (

9 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? then we would exect that the yeld coverage dummes should have a ostve sgn and the magntude of the effect should decrease as the yeld coverage ncreases. Table 1 Descrton of varables used n the emrcal analyss based on a RMA data set for corn and soybeans n Illnos (rensurance year 000). Varable OSS ACRE YE PE SHR YAPM YC65- YC80 COR IR RO1 RO10 Descrton Observed dollar value of the yeld loss er acre; equvalent to ( Y P Y P ) arm acreage Exected yelds Prce electon Insured s share Dollar value of actual yelds Dummy varables reresentng the yeld coverage level chosen (coverage levels (j) = 65%, 70%, 75%, 80%). The 85% coverage level s the excluded category. YC(j)=1 f chose yeld coverage j; YC(j)=0 otherwse. Dummy varable reresentng the cro. COR=1 f corn cro, COR=0 otherwse. Dummy varable reresentng cro ractce (rrgated vs. non-rrgated). IR=1 f non-rrgated, IR=0 otherwse. Dummy varable reresentng the rensurance organzaton of the nsured. RO() =1 f rensurance organzaton I; RO() = 0 otherwse. or the vector w, one model (M1) uses exected yeld (YE) as the only regressor n the selecton equaton and another model ncludes exected yeld (YE), and rce electon (PE), nsured share (SHR) and acreage (ACRE) as regressors n the selecton model. The regressors n the selecton equaton were chosen because they are the varables that affect the lkelhood of a loss to be observed. Two sets of regressors were run to see f there are large dfferences n the magntudes and sgnfcance of the arameters. Summary statstcs for the contnuous varables and the frequences for the dummy varables are seen n Tables and 3, resectvely. Table Summary statstcs for the contnuous varables used n the emrcal analyss based on a RMA data set for corn and soybeans n Illnos (rensurance year 000). Varable o. of Obs. Mean St. Dev. Mn. Max. OSS ACRE YE PE SHR

10 Southwestern Economc Revew Table 3 requency of the dummy varables used n the emrcal analyss based on a RMA data set for corn and soybeans n Illnos (rensurance year 000). Varable requency Percent Varable requency Percent YC RO YC RO YC RO YC RO COR RO IR RO RO RO RO RO RESUTS AD DISCUSSIO The results of the loss equaton estmaton are resented n Table 4. We frst estmated the arameters usng ordnary least squares (OS). Then, the loss equaton s estmated usng maxmum lkelhood to correct for samle selecton. As mentoned above, two versons of the model are estmated usng maxmum lkelhood: (1) one where exected yeld (YE) s the only regressor n the selecton equaton, and () one where exected yeld (YE), and rce electon (PE), nsured share (SHR) and acreage (ACRE) are regressors n the selecton equaton. The arameter estmates for the selecton equaton are n Table 5. In terms of sgns and statstcal sgnfcance the results are qute robust across the dfferent estmated models for the loss equatons. However, the magntudes of the arameters are mostly dfferent between OS and M. The magntudes of the arameter estmates for the OS model are generally hgher than the M estmates. Ths s exected because OS estmates do not correct for samle selecton bas and are based uwards. In terms of farm characterstcs, t seems that the two varables that statstcally affects the magntude of the loss consstently across models are farm sze (ACRE) and the nsured s share amount (SHR). However, the effect of the SHR varable s only sgnfcant at the 5% level. The sgns of the varables suggest that farm sze s ostvely related to the loss magntude, whle share amount s negatvely related to the loss amount. The bgger volume of roducton n large acreage farms makes t logcal to exect the ostve effect of the ACRE varable on loss magntudes. The effect of share amount mght be negatve because non-sngle ownersh arrangements sread the rsk across ndvduals. Snce sngle ownersh means that one ndvdual bears all the rsk, then ths ndvdual s more lkely to reduce the robablty of a loss. Other farm characterstc varables such as the cro dummy varable (COR) was sgnfcant at the 5% level n the OS and M models, whle the cro ractce varable (IR) was not sgnfcant across models. The dummy varables reresentng the rensurance organzatons suggest that frm-secfc effects may exst. ve out of ten rensurance organzaton dummy varables are statstcally sgnfcant across models and all fve of ths rensurance organzaton dummes have negatve sgns. Ths means nsured roducers that are assocated wth these rensurance organzatons tend to have lower loss magntudes. 88

11 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? Table 4 Estmaton results for the loss equaton that s used to test the effect of coverage levels on falsfcaton behavor, usng data for corn and soybeans n Illnos (rensurance year 000). Parameter estmates (standard errors n arentheses) Varables OS M1 M Intercet * * 04.9 * (10.15) (9.88) (9.08) ACRE 0.07 * 0.07 * 0.07 * (0.01) (0.01) (0.01) SHR ** ** ** (0.0) (0.0) (0.0) YC * * * (.60) (.60) (.63) YC * -9.1 * * (.87) (.87) (.90) YC * -7.9 * * (.76) (.75) (.78) YC (3.7) (3.71) (3.75) COR 3.5 ** ** (1.37) (1.40) (1.38) IR (9.45) (9.16) (8.7) RO * * * (4.66) (4.65) (3.81) RO -8.1 * * * (.69) (.66) (.69) RO (3.61) (3.58) (3.65) RO * * * (.90) (.86) (.93) RO (4.30) (4.8) (4.33) RO (.87) (.83) (.88) RO (5.45) (5.4) (5.51) RO * -9.9 * -9.5 * (.63) (.60) (.63) RO (3.97) (3.94) (3.9) RO * * * (.79) (.77) (.78) R-squared (OS) Wald test (Ch-sq.) * * R test (ρ = 0) * 64.98* og lkelhood *(**) Denotes statstcal sgnfcance at the 1% (5%) level. 89

12 Southwestern Economc Revew 90 Table 5 Estmaton results for the selecton equaton that controls for selecton bas n the loss equaton (based on data for corn and soybeans n Illnos, rensurance year 000). Parameter estmates (standard errors n arentheses) Varables OS M1 M Intercet * * (0.13) (0.44) YE * 0.09 * (0.00) (0.01) PE * - (0.04) ACRE (0.001) SHR (0.00) Rho (ρ) *(**) Denotes statstcal sgnfcance at the 1% (5%) level The varables of man nterest n ths study are the dummy varables for yeld coverage choce. Across all estmaton rocedures undertaken, the dummy varables assocated wth yeld coverage choce have negatve sgns and are sgnfcant, excet for YC80 where t s not statstcally sgnfcant. The negatve sgns means that losses are lower when the yeld coverage level s lower than 85% (the excluded yeld coverage dummy varable). urthermore, the absolute value of the magntudes of the dummy varables ncreases as the yeld coverage level decreases. Ths means that the magntude of the loss becomes lower as the yeld coverage chosen s reduced. ote that ths s not consstent wth the emrcal hyothess that we ut forward above. If falsfcaton behavor s revalent, we exected that lower yeld coverage levels should have hgher losses and as yeld coverage level s reduced the magntude of the loss should be greater. Gven that our emrcal results do not suort ths hyothess, ths means that other asymmetrc nformaton roblems lke ex ante moral hazard and adverse selecton may be the more revalent roblem n cro nsurance. The ex ante moral hazard and adverse selecton effects that are emboded n the choce of yeld coverage levels overwhelms the otental effect of the falsfcaton behavor. These results do not necessarly mean that falsfcaton effects from the choce of alternatve yeld coverage levels are not resent n cro nsurance, the results just show that other asymmetrc nformaton roblems may be more revalent n ths market. The falsfcaton ncentves from yeld coverage levels actng as deductbles are stll there but t s not sgnfcant n the market for cro nsurance. Prevous studes that nvestgated adverse selecton and ex ante moral hazard n cro nsurance have shown that these asymmetrc nformaton roblems are ndeed resent n cro nsurance, even though the magntude of each roblem s stll not fully understood [1, 13]. Our results here suggest that n cro nsurance, the asymmetrc nformaton roblems related to adverse selecton and ex ante moral hazard may be more sgnfcant n magntude than falsfcaton roblems or oortunstc fraud. In contrast, studes usng data from the automoble nsurance markets have emrcally shown that there s no strong evdence that adverse selecton and ex ante moral hazard are sgnfcant roblems n ths market []. Consequently, Donne and Gagné [4] have

13 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? shown that deductble contracts n automoble nsurance do sgnfcantly affect falsfcaton behavor. They found that hgher deductbles do ncrease the loss magntudes and, therefore, ths may be the more sgnfcant asymmetrc nformaton roblem n automoble nsurance. COCUDIG COMMETS alsfcaton behavor that can be attrbuted to the fraud ncentves created by yeld coverage levels was not found to be sgnfcant n cro nsurance. Hence, olcy makers nvestgatng contract elements that contrbute to fraud behavor n cro nsurance should robably focus more on other asects of cro nsurance contracts that are more vulnerable to fraud, waste, or abuse. or examle, the otonal unt rovsons that make t ossble to undertake yeld-swtchng behavor. The resence of otonal unts rovdes roducers the oortunty to manulate ther yeld hstory (by yeld-swtchng) and artfcally ncreasng ther yeld guarantees. Ths n turn ncreases the lkelhood of recevng a loss and a otental ndemnty ayment. The otonal unt rovson n cro nsurance contracts may then rovde more ncentves to defraud than the choce of yeld coverage levels and should be studed further. Even though falsfcaton behavor due to alternatve yeld coverage levels do not seem to be revalent n cro nsurance based on our results, fraud behavor due to other cro nsurance contract elements that gve ncentves to defraud may stll be sgnfcant and these should be studed further f rogram ntegrty s to mrove. ote, however, that ths study only focused on nsured corn and soybean roducers n Illnos. An extenson of the study to nclude other states and other cros would be very useful. Ths tye of extenson can show f there are other cros and/or regons where falsfcaton behavor due to yeld coverage levels are ndeed sgnfcant. ote that nsured corn and soybean roducers n Illnos have been hstorcally known as low loss roducers relatve to roducers of other cros n other states. Therefore, falsfcaton behavor may generally be lower n ths case for ths cro-regon combnaton. Cotton roducton n the Southern U.S., on the other hand, s generally known as a hgher loss regon where falsfcaton behavor may be more revalent [18]. Although our emrcal results dd not rovde evdence of the falsfcaton effects of yeld coverage levels n Illnos corn and soybeans, ths does not reclude the ossble exstence of ths relatonsh n other regons. A more comrehensve study that utlzes the entre RMA data base (for the whole naton and for all cros) may rovde further nsghts as to the extent of the fraud ncentve effects of yeld coverage levels. urther studes should also be undertaken to more fully understand the magntude and extent of asymmetrc nformaton roblems n the U.S. cro nsurance rogram. Ths wll allow for better rortzaton of resources to reduce excessve ndemnty ayments arsng from these roblems. Although ths study renforces the noton that adverse selecton and ex ante moral hazard may be the more ressng ssues n cro nsurance, these two roblems of asymmetrc nformaton are sgnfcant here relatve only to the fraud behavor effects of alternatve yeld coverage levels actng as deductbles. Investgatng the magntude of fraud roblems due to all the dfferent elements of the cro nsurance contract vulnerable to fraud, 91

14 Southwestern Economc Revew may suggest otherwse. One mght fnd that fraud or ex ost moral hazard may generate more excess losses than the other two roblems of asymmetrc nformaton. EDOTES 1 Alternatve yeld coverage levels mnmze ex ante moral hazard, n theory, because less than full nsurance coverage gves some ncentve to reduce the robablty of a loss. Problems of adverse selecton s also theoretcally mnmzed wth alternatve yeld coverage levels because ths serves as a self-selecton mechansm that allows dfferent rsk tyes to choose dfferent coverage levels. Ex ost moral hazard s mnmzed wth deductbles because ncentves for falsfcaton wll be reduced at the lower loss states. The magntude of the yeld loss can also be falsfed by manulatng the yeld e records that determne Y. Ths tye of fraud s gnored to smlfy the model. Ths smlfcaton does not change the theoretcal redctons of the model. 3 The exressons φ ( ) and Φ( ) reresent the normal densty and the standard cumulatve normal, resectvely. 9

15 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? REERECES Bond, E.W. and K.J. Crocker. Hardball and Soft Touch: The Economcs of Otmal Insurance Contracts wth Costly State Verfcaton and Endogenous Montorng Costs. J. of Publc Econ. 63(January 1997): Chaor, P.A. and B. Salané. Testng for Asymmetrc Informaton n Insurance Markets. J. of Poltcal Economy. 108(ebruary 000): Coble, K.H., T.O. Knght, R.D. Poe, and J.R. Wllams. An Exected Indemnty Aroach to the Measurement of Moral Hazard n Cro Insurance. Amer. J. of Ag. Econ. 79(ebruary 1997):16-6. Donne, G. and R. Gagné. Deductble Contracts Aganst raudulent Clams: Evdence from Automoble Insurance. Rev. of Econ. and Stat. 83(May 001): Donne, G. and P. Vala. Otmal Desgn of nancal Contracts and Moral Hazard. Workng Paer, Unversty of Montreal, 199. Greene, W. Econometrc Analyss. ourth Edton, Prentce Hall: Uer Saddle Rver, J Heckman, J.J. The Common Structure of Statstcal Models of Truncaton, Samle Selecton, and mted Deendent Varables and a Smle Estmator for Such Models. Annals of Economc and Socal Measurement. 5(all 1976): Heckman, J.J, Samle Selecton Bas as a Secfcaton Error. Econometrca. 47(January 1979): Holmstrom, B. Moral Hazard and Observablty. The Bell Journal of Economcs. 10(Autumn 1979): Hyde, C.E. and J.A. Vercammen. Costly Yeld Verfcaton, Moral hazard, and Cro Insurance Contract orm. J. of Ag. Econ. 48(Setember 1997): Kalow,. Otmal Insurance Contracts When Establshng the Amount of osses s Costly. Geneva Paers on Rsk and Insurance Theory. 19(December 1994): Knght, T.O. and K.H. Coble. Survey of U.S. Multle Perl Cro Insurance terature Snce Rev. of Ag. Economcs. 19, no. 1 (Srng/Summer 1997): Makk, S. and A. Somwaru. Asymmetrc Informaton n the Market for Yeld and Revenue Insurance Products. Techncal Bulletn o. 189, Economc Research Servce (ERS), U.S. Deartment of Agrculture, Arl 001. Pcard, P. Audtng Clams n Insurance Markets wth raud: The Credblty Issue. J. of Publc Econ. 6(December 1996): Puelz, R. and A. Snow. Evdence on Adverse Selecton: Equlbrum Sgnalng and Cross-Subsdzaton n the Insurance Market. J. of Poltcal Economy. 10(Arl 1994): Rothschld, M. and J.E. Stgltz. Equlbrum n Comettve Insurance Markets: An Essay on the Economcs of Imerfect Informaton. Quarterly J. of Econ. 90(ov.1976): Shavell, S. On Moral Hazard and Insurance. Quarterly J. of Econ. 93(ov. 1979): Skees, J.R., J. Harwood, A. Somwaru, and J. Perry. The Potental for Revenue Insurance n the South. J. of Ag. and Aled Econ. 30,1(July 1998):

16 Southwestern Economc Revew Townsend, R.M. Otmal Contracts and Comettve Markets wth Costly State Verfcaton. J. of Econ. Theory. 1(October 1979): USDA-ASS. Illnos Agrcultural Statstcs Summary Illnos-ASS, Srngeld, I USDA-RMA. Rsk Management Agency Program Comlance and Integrty Annual Reort to Congress. 00. (Avalable at: htt:// U.S. General Accountng Offce (GAO). Cro Insurance: USDA eeds a Better Estmate of Imroer Payments to Strengthen Controls Over Clams. GAO/RCED 99-66, U.S. GAO: Washngton, D.C. Setember Wnter, R.A. Moral hazard n Insurance Contracts. Contrbutons to Insurance Economcs. G. Donne (ed.), Kluwer Acdemc Press: Boston, MA

17 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? d Aendx In ths aendx, we resent the condtons that would show that ddd > 0. To do ths, we totally dfferentate twce the frst-order condton n (11) wth resect to, D, and. Ths results to (A1) + JdD + Kd = 0 Hd, where J U ''( W )(1 c'( > 0, D K U '( W )(1 c'( U '( W )( c'( > 0, and H s as defned n the text. rom (A1), (13) and (14), we can show that D (A) d = dd + d. Totally dfferentatng (A), we have (A3) d = D D ddd + D ddd + ( ) ( ) ( ) ( ) By symmetry (A4) and, therefore, dd D + ( D) ( ) D, d (A5) d ddd ( / D) =. At ths ont we need to examne the sgn of d ddd > 0. rom (13), we can re-wrte ( / D) as ( / D) to determne whether 95

18 Southwestern Economc Revew (A6) U ''( W )(1 c'( H. By dfferentatng the exresson n (A6) we obtan (A7) D ( U''( W )( 1 c'( U''( W )( c'( ))) U' '( W )( 1 c'( U''( W )( 1 c'( H H The frst term s strctly ostve because H<0 and U ''( W ) < 0 under rsk averson. To sgn the second term, we need to re-wrte the second term of (A7) usng the frst-order condton n (11). Ths results to. (A8) D U ''( W )(1 c'( U ''( W )(1 c'( U ''( W )( c'( D H U '( W ) (1 ) U '( W ). Assumng constant absolute rsk averson, the exresson n (A8) can be wrtten as: (A9) U ''( W )(1 c'( U ''( W c c ) ( '( )) (1 '( )). H U ''( W ) (1 ) Multlyng (A9) by (1 ) (1 c'( > 0, whch does not change the sgns of the exresson, yelds (A10) U ''( W )(1 c'( U ''( W H U ''( W ) (1 )( c'( (1 ) ) (1 c'(. The exresson (1 )( c'( (1 c'( s strctly less than one because from the frst-order condton n (11) the exected margnal beneft of fraud ( 1 c' ( has to be greater than the exected margnal beneft of fraud ( 1 )( c' (. Consequently, f the resultng sgn of the exresson n scarred brackets n (A10) s greater than zero, 96

19 Yeld Coverage evels as Deductbles n Cro Insurance Contracts: Is the Effect on alsfcaton Behavor Sgnfcant? the whole exresson (A10) would be ostve. Ths s true when c'( ) 1 (1 c'( ), whch s the case f the success robablty of fraud s suffcently hgh. Therefore, assumng constant absolute rsk averson and c'( ) 1 (1 c'( ), the exressons (A10), (A7), (A6) and (A5) are ostve. Ths means that constant absolute rsk averson and condtons that makes d ddd > 0. c'( ) 1 (1 c'( ) are the Ths research was ntated when Roderck M. Rejesus was afflated wth the Center for Agrbusness Excellence at Tarleton State Unversty. Ths research was funded by USDA-RMA Research Contract o

20 Southwestern Economc Revew 98