Economic Analysis of Supplemental Deductible Coverage as Recommended in the USDA s 2007 Farm Bill Proposal

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1 Economc Analyss of Supplemental Deductble Coverage as Recommended n the USDA s 2007 Farm Bll Proposal Paul D. Mtchell and Thomas O. Knght A prmary change to crop nsurance contaned n the USDA s Farm Bll proposal s supplemental deductble coverage (SDC). SDC would allow farmers who purchase ndvdual crop nsurance coverage to purchase area-wde coverage n the amount of the ndvdual polcy deductble. Ths supplemental area-wde coverage would be smlar to the exstng Group Rsk Plan polcy, but wth an accelerated ndemnty schedule. Analyss ndcates that SDC ncreases farmer certanty equvalents. The largest benefts are realzed by farmers wth hgh yeld potental n countes wth greater systemc rsk. In general, optmal ndvdual polcy coverage levels modestly decrease when SDC s taken. Key Words: crop nsurance, area-wde coverage, actual producton hstory (APH), group rsk plan (GRP), yeld dstrbuton The Admnstraton released the USDA 2007 Farm Bll proposal n early 2007 (USDA 2007a). Among ts recommendatons were several proposed modfcatons of current crop nsurance programs under Ttle X (USDA 2007b). The frst of these recommended offerng supplemental deductble coverage (SDC). Ths proposed SDC would Allow farmers to purchase supplemental nsurance that would cover all or part of ther ndvdual polcy deductble n the event of a county or area wde loss (USDA 2007b, p. 151). Addtonal dscusson ndcates that the ntent of ths provson was to mprove the safety net for crop producers by offerng full coverage (100 percent of the value of expected yeld). Paul Mtchell s Assstant Professor n the Department of Agrcultural and Appled Economcs at the Unversty of Wsconsn-Madson n Madson, Wsconsn. Thomas Knght s Professor n the Department of Agrcultural and Appled Economcs at Texas Tech Unversty n Lubbock, Texas. Ths paper was presented as a selected paper at the Crop Insurance and Rsk Management Workshop, sponsored jontly by the Northeastern Agrcultural and Resource Economcs Assocaton, the Rsk Management Agency, the Farm Foundaton, the Food Polcy Insttute at Rutgers Unversty, and Cornell Unversty, n Rehoboth Beach, Delaware, on June 12 13, The workshop receved fnancal support from the Northeast Regonal Center for Rural Development. The vews expressed n ths paper are the authors and do not necessarly represent the polces or vews of the sponsorng agences. The authors would lke to thank those attendng the workshop, the two anonymous revewers, and Jean-Paul Chavas for ther helpful comments. The current federal crop nsurance program offers two types of yeld nsurance for farmers ndvdual coverage and area-wde coverage. The ndvdual coverage pays ndemntes when a farmer s harvested yeld falls below a chosen percentage of the farmer s ndvdual average yeld. Ths ndvdual average yeld s calculated based on a farmer s actual producton hstory (APH); hence the name of the polcy s APH. 1 Area-wde coverage as provded by the current program pays ndemntes when the actual county average yeld offcally reported by the USDA falls below a chosen percentage of the expected county yeld. Ths polcy s called the Group Rsk Plan (GRP). As proposed n the USDA 2007 Farm Bll proposal, SDC would allow farmers to combne a modfed form of area-wde GRP coverage wth ndvdual APH coverage. Ths layered 1 Although the ntent of the APH program s to provde coverage based on the hstorcal average yeld for an nsured unt, practcal consderatons n mplementaton have gven rse to a number of exceptons. For example, alternatve procedures are used n determnng the nsured yeld for () new producers, () producers addng land not prevously planted to the crop, () producers wth average yeld less than a gven percentage of a county yeld (t-yeld) specfed n the polcy, wth the percentage dependng on the number of years of yelds n the yeld seres, (v) producers who would experence a large change n ther nsured yeld from one nsurance year to the next, and (v) producers experencng a yeld less than 60 percent of the county t- yeld n one or more years. Agrcultural and Resource Economcs Revew 37/1 (Aprl 2008) Copyrght 2008 Northeastern Agrcultural and Resource Economcs Assocaton

2 118 Aprl 2008 Agrcultural and Resource Economcs Revew coverage would offer producers a hgher level of yeld rsk protecton whle avodng excessve government exposure to adverse selecton and moral hazard that could result f such hgh levels of ndvdual coverage were offered. The SDC concept rases nterestng polcy questons, a few of whch we examne here. Specfcally, for a varety of emprcally based assumptons regardng farm and county yelds, we estmate changes n farmer welfare when movng from the current program of usng ether APH or GRP alone to a combnaton of APH and areabased coverage under SDC. Ths analyss dentfes the types of farmers who would fnd SDC most benefcal n partcular, ndcatng how much SDC benefts farmers n hgh-rsk areas relatve to those n low-rsk areas. The analyss also dentfes the preferred APH coverage level under the current program and when SDC s avalable, thus determnng how farmers would lkely adjust ndvdual APH coverage levels f SDC became avalable. Thus, the analyss dentfes the characterstcs of farmers who would fnd SDC most useful, provdes monetary estmates of ts farm-level benefts, and ndcates how farmers would lkely use SDC to manage ther rsk. Proposed SDC Program Structure The descrpton of the proposed SDC program structure (USDA 2007b) ndcates that SDC would be an opton farmers could add to ther exstng APH yeld nsurance, wth addtonal ndemnty payments handled smlarly to the current GRP polcy. Hence, before explanng SDC, we frst descrbe APH and GRP. Wth APH, farmers choose an APH coverage level as a percentage of ther hstorcal average yeld. Avalable coverage levels range from 50 percent to 85 percent n 5 percent ntervals (some countes are lmted to a maxmum of 75 percent). Wth GRP, farmers choose a GRP coverage level as a percentage of the expected county average yeld, wth avalable coverage levels rangng from 65 percent to 90 percent n 5 percent ntervals. For APH, 100 percent mnus the chosen APH coverage level serves as a deductble, so that nsured farmers share n the rsk of loss and thus have ncentves to use approprate producton practces to mtgate the potental for losses. Nevertheless, APH s subject to adverse selecton and moral hazard, especally at hgh coverage levels. Adverse selecton occurs wth APH because farmers who know that they are more lkely to trgger ndemntes are more lkely to buy APH and use hgher coverage levels (Goodwn 1993, Just, Calvn, and Quggn 1999, Coble and Knght 2002). Furthermore, APH also suffers moral hazard problems because farmers who have APH coverage face ncentves to adjust nput use and other producton practces so as to trgger or ncrease the magntude of ndemntes, wth such ncentves ncreasng n the chosen APH coverage level (Chambers 1989, Babcock and Hennessy 1996). A major advantage of GRP from the perspectve of the nsurer s that t s much less susceptble to these adverse selecton and moral hazard problems no ndvdual farmer s more or less lkely to trgger a GRP ndemnty n a county, nor can an ndvdual farmer meanngfully change the county average yeld (Mranda 1991, Skees, Black, and Barnett 1997). However, though GRP has lower premums, farmers generally prefer APH, snce t pays ndemntes for yeld losses n excess of ther deductble, whle GRP does not guarantee ths outcome. In hgh-rsk areas, buyng APH wth 85 percent coverage (the maxmum avalable) s qute expensve and stll requres the farmer to bear the frst 15 percent of any yeld loss. Increasng the maxmum APH coverage level to 100 percent to help such farmers would greatly exacerbate adverse selecton and moral hazard problems, and so s not proposed. Rather, SDC would allow farmers to buy addtonal GRP-lke coverage to add on top of ther exstng APH coverage, so that farmers could obtan full coverage equal to 100 percent of the value of ther expected (average) yeld wthout exacerbatng adverse selecton and moral hazard problems. Specfcally, SDC would allow nsured farmers to buy GRP as a supplement to ther APH polcy, wth supplemental ndemntes trggered by shortfalls n county yelds, and wth a maxmum lablty for ths supplemental coverage equal to ther APH deductble. Specfc language n the Farm Bll proposal (USDA 2007b, p. 154) ndcates that 90 percent GRP coverage level wll be used for SDC; that s, the county yeld would have to be less than 90 percent of the GRP expected county yeld before an SDC ndemnty would be pad. In addton, the Farm Bll proposes a more rapd payout of n-

3 Mtchell and Knght Economc Analyss of Supplemental Deductble Coverage 119 demntes than s the case for the standard GRP. GRP currently pays ndemntes proportonal to the county yeld loss, wth 100 percent of the GRP lablty pad only when the county yeld s zero. However, a total crop loss for a whole county s a hghly unlkely event for most crops n most countes. To mprove the effectveness of SDC coverage, the Farm Bll proposal ndcates that 100 percent of the SDC lablty would be pad when the county yeld s 70 percent of the expected county yeld (as opposed to 0 percent for GRP) (USDA 2007b, p. 154). Fgure 1 graphcally llustrates the dfference between the two ndemnty schedules both have the same maxmum payout, but ths maxmum s reached more quckly wth the accelerated payment rate. Indemnty schedules of ths sort have also been examned when evaluatng weather dervatves for agrcultural applcatons (Turvey, Weersnk, and Chang 2006, Vedenov, Epperson, and Barnett 2006, Martn, Barnett, and Coble 2001). SDC Indemnty APH Deductble Standard GRP Payment Rate 0.7µ c Accelerated GRP Payment Rate 0.9µ c Fgure 1. SDC Indemntes Plotted versus County Yeld wth a Standard GRP Payment Rate and wth an Accelerated Payment Rate Indemntes To formalze these verbal descrptons, we report specfc equatons for farmer ndemntes under the dfferent polces. These equatons defne the exstng APH and GRP polces and how the proposed SDC program would modfy them. A farmer s ndemnty ($/ac) wth APH (I aph ) s (1) I aph (α) = P max(αµ f y f, 0), y c where α s the chosen APH coverage level, µ f s the farm unt s mean yeld as determned by the actual producton hstory, y f s the realzed farm unt yeld, and P s the APH prce determned by the USDA Rsk Management Agency (RMA) and used to value yeld losses. 2 The APH coverage level α s the proporton of the unt s average yeld (µ f ) chosen by the farmer as the unt s yeld guarantee, wth avalable coverage optons rangng from 50 percent to 85 percent n 5 percent ncrements. Hence, αµ f n equaton (1) s the farm unt s per acre yeld guarantee, the expresson n the max( ) operator determnes the unt s per acre yeld loss relatve to ths guarantee, and ths loss s valued at the pre-establshed APH prce P used to determne the amount of coverage and to pay ndemntes. A farmer s ndemnty ($/ac) wth GRP (I grp ) s γµ (2) I grp (γ) = c y c Λ max,0, γµ c where Λ s the GRP maxmum protecton per acre ($/ac) establshed by the RMA (equal to the polcy s maxmum lablty), γ s the GRP coverage level, µ c s the county mean yeld, and y c s the realzed county yeld. The GRP coverage level γ s the proporton of the county average yeld (µ c ) the farmer chooses as the county yeld guarantee for trggerng ndemntes. For GRP, multple coverage levels are avalable, but SDC as proposed would use the equvalent of the 90 percent GRP coverage level. In equaton (2), γµ c s the GRP per acre county yeld guarantee based on the coverage level chosen, the expresson n the max( ) operator s proportonal yeld loss (.e., the proporton that the observed county yeld falls below the county yeld guarantee), and the ndemnty s the product of ths proportonal loss and total lablty Λ. 3 2 Farmers have the opton of nsurng at less than 100 percent of the RMA determned expected prce, but nsurance program experence has shown that the vast majorty of partcpants choose coverage based on the maxmum avalable prce electon. 3 We assume that producers take the GRP maxmum protecton per acre publshed n the RMA county actuaral documents. Producers are allowed to choose amounts of coverage per acre less than ths value, but most GRP partcpants choose to nsure the maxmum protecton per acre.

4 120 Aprl 2008 Agrcultural and Resource Economcs Revew A farmer s ndemnty ($/ac) for APH wth SDC coverage usng a standard GRP payment rate (I sdc_st ) s (3) I sdc_st (α) = I aph (α) 0.9µ + D(α) c y c max,0, 0.9µ c where D(α) = P(1 α)µ f s the APH deductble ($/ac) as a functon of the APH coverage level. Equaton (3) s the APH ndemnty plus a GRPlke ndemnty usng a 90 percent GRP coverage level trgger, but wth the APH deducble (D) replacng the GRP maxmum protecton per acre (Λ). APH combned wth SDC coverage wth a standard GRP payment rate s not the polcy proposed n the USDA s 2007 Farm Bll, but s analyzed here as a useful counterfactual for comparson. A farmer s ndemnty ($/ac) for APH wth SDC coverage usng an accelerated GRP payment rate (I sdc_ac ) s (4) I sdc_ac (α) = I aph (α) 0.9µ + D(α) c y c mn max, 0,1.0, 0.9µ c 0.7µ c where all varables are as prevously defned. Equaton (4) s the APH ndemnty plus a modfed GRP ndemnty. Agan, a 90 percent GRP coverage level s used and the APH deductble replaces the GRP maxmum protecton per acre. However, proportonal yeld loss [the term n the max( ) operator] s calculated as a proporton of 0.9µ c 0.7µ c = 0.2µ c, not the county yeld guarantee of 0.9µ c. Snce the term n the denomnator n equaton (4) s smaller than n equaton (3), proportonal yeld loss n equaton (4) s larger than n equaton (3), so ndemntes are larger. However, because proportonal yeld loss n ths calculaton can exceed 100 percent, the mn( ) operator lmts the proportonal yeld loss used to pay ndemntes to 100 percent. Fgure 1 llustrates the dfference between the GRP-based components of the SDC ndemnty n equaton (3) and equaton (4). Also, to follow the USDA s 2007 Farm Bll proposal, equaton (4) uses 70 percent of the county expected yeld as the yeld level by whch the GRP component pays 100 percent of the APH deductble; other percentages are possble, but not examned here. Conceptual Framework and Analytcal Methods Farmers currently buyng yeld nsurance must choose APH or GRP. The goal of the analyss s to determne how addng SDC to the farmer choce set affects farmer welfare as measured by changes n certanty equvalents ($/ac) and farmer behavor as ndcated by changes n optmal coverage levels. Here we explan our modelng approach and ts emprcal mplementaton. Frst, we specfy a parametrc model of correlated county and farm yelds, and then farmer revenue and utlty. Next, we descrbe emprcal mplementaton of Monte Carlo ntegraton for calculatng expected utlty and actuarally far premums. Fnally, we specfy the farmer s optmzaton problem choosng the coverage level to maxmze the expected utlty of revenue from crop producton and then explan how the solutons wll be used to examne the effects of SDC on farmer welfare and optmal coverage levels. County and Farm Yelds An mportant aspect of ths analyss s the connecton between farm yelds and county yelds. Several approaches have been developed for modelng ths connecton. Deng, Barnett, and Vedenov (2007) descrbe a multplcatve model n whch farm yeld s a random proporton of the realzed county yeld. The mean of the random proporton determnes the mean farm yeld relatve to the county yeld, whle the varance of the random proporton partly determnes the proporton of the farm yeld varablty due to dosyncratc effects. More common s an addtve model wth farm yeld equal to the product of a constant factor and the realzed county yeld, plus a random dosyncratc error. Mranda (1991) used the model to examne area yeld crop nsurance comparable to GRP; Atwood, Baquet, and Watts (1996) used t to develop premums for Income Protecton (a dfferent crop nsurance polcy); Carrqury, Babcock, and Hart (2005) used t to propose mprovements for developng APH pre-

5 Mtchell and Knght Economc Analyss of Supplemental Deductble Coverage 121 mums; and Ramaswam and Roe (2004) derved ts mcro-producton functon foundatons. Unlke these studes, actual farm yeld hstory data were unavalable for ths analyss. By combnng farm yeld hstores wth the assocated county yeld data, an emprcal model of the mean and varablty of county yeld could be estmated, and more mportantly, the mean and varance of farm yeld and ts stochastc relatonshp wth county yeld could also be estmated for each ndvdual farmer n a populaton. Based on ths emprcal foundaton, the welfare effect of offerng SDC and the effect of SDC on the optmal APH coverage level could be estmated for each farmer, and these effects aggregated or ther dstrbuton examned. However, not havng such data, we used a parametrc approach, specfyng a jont dstrbuton for county and farm yelds wth known margnal dstrbutons. The fnal stochastc model of farm and county yelds s specfed by fve parameters the mean and varance for both county and farm yeld and ther correlaton. We examne typcal extreme cases farmers wth mean yelds well above and well below the county average both for farmers wth a relatvely low and a relatvely hgh level of correlaton wth the county yeld, and then dentfy the mpled effects of SDC on farmer welfare and optmal APH coverage. Thus, our estmates serve as reasonable bounds on the magntude of these effects for the majorty of ndvdual farmers. For ths analyss, we use beta dstrbutons for both county and farm yelds, a common assumpton for crop yelds [Goodwn and Ker (2002) revew several examples; also, see Sherrck et al. (2004)]. An mportant advantage of the beta dstrbuton s that negatve realzatons do not occur. In hgh-rsk countes wth relatvely low mean yelds and hgh standard devatons, the lkelhood of negatve yelds s not neglgble for normal and smlar dstrbutons, so that ad hoc fxes would be requred for smulated yelds. For each county examned here, mean county yeld s set equal to the 2007 GRP expected county yeld publshed n the county actuaral documents (USDA 2007c). The standard devaton for each county was calbrated so that the actuarally far premum rate for the smulated county yelds wth 90 percent GRP coverage matched the unsubsdzed GRP rate for 90 percent coverage publshed n the county actuaral documents (USDA 2007c). Fnally, snce the beta dstrbuton requres specfyng the mnmum and maxmum, we follow Babcock, Hart, and Hayes (2004) and set mnmum yeld to the maxmum of zero and the mean mnus four standard devatons, and set maxmum yeld to the mean plus two standard devatons. Table 1 lsts the resultng means and standard devatons of county yeld for the four countes examned here (as well as the yeld coeffcent of varaton, APH prce, and GRP maxmum protecton per acre). Trpp County n South Dakota and Hamlton County n Iowa respectvely represent a hgh-rsk and a low-rsk county for producng corn, whle Lubbock County n Texas and Coahoma County n Msssspp respectvely represent a hgh-rsk and a low-rsk county for producng cotton. These nterpretatons as low and hgh rsk are based on the sze of the GRP premum rate for these countes, those wth hgh average yelds have lower premum rates than those wth low average yelds. Ths nverse relaton between county average yeld and yeld rsk s typcal for most crops and countes and so we wll follow t n our dscusson here, but exceptons lkely occur for some crops and countes. Fnally, the beta dstrbutons for yelds mpled by the parameters n Table 1 are farly symmetrc wth slght negatve skews, the skewness rangng between and for the four countes. Ths analyss also uses a beta dstrbuton for farm unt yelds (Goodwn and Ker 2002, Sherrck et al. 2004). Wthn each county, we examne two types of producers farmers wth mean yeld 25 percent below the county average yeld and farmers wth mean yeld 25 percent above the county average yeld. The standard devatons for farm yelds were calbrated so that the actuarally far premum wth the smulated farm yelds matched the unsubsdzed APH premum for 65 percent coverage for the respectve mean farm yeld as publshed n the county actuaral documents (USDA 2007c). Farmers wth above average yelds are lower rsk than farmers wth below average yelds for the same APH coverage, snce for the cases examned here, APH premum rates decrease as average farm yeld ncreases. Thus we follow ths generalzaton n our dscusson that farmers wth hgher average yelds are lower rsk than farmers wth lower average yelds though exceptons to ths generalzaton lkely exst for

6 122 Aprl 2008 Agrcultural and Resource Economcs Revew Table 1. Parameters Used for Emprcal Analyss of Supplemental Deductble Coverage Corn Cotton Parameter Trpp, SD Hamlton, IA Lubbock, TX Coahoma, MS County mean µ c 56.9 bu/ac bu/ac lbs/ac lbs/ac County st. dev. σ c bu/ac 24.9 bu/ac lbs/ac lbs/ac County CV 28.6% 14.1% 42.0% 22.0% APH prce P $3.50/bu $3.50/bu $0.52/lb $0.53/lb GRP maxmum protecton per acre Λ $251.78/ac $780.57/ac $187.92/ac $690.12/ac Farm mean county mean Farm mean µ c 43.0 bu/ac bu/ac lbs/ac lbs/ac Farm st. dev. σ c 37.3 bu/ac 38.0 bu/ac lbs/ac lbs/ac Farm CV 86.7% 28.8% 114.7% 43.5% 65% APH premum M aph $12.32/ac $3.68/ac $10.88/ac $7.87/ac Farm mean county mean Farm mean µ c 71.0 bu/ac bu/ac lbs/ac lbs/ac Farm st. dev. σ c 39.5 bu/ac 53.7 bu/ac lbs/ac lbs/ac Farm CV 55.6% 24.3% 78.3% 37.5% 65% APH premum M aph $9.61/ac $3.50/ac $10.57/ac $9.34/ac some crops n some countes. Fnally, we follow Babcock, Hart, and Hayes (2004) and set mnmum yelds to the maxmum of zero and the mean mnus four standard devatons, and maxmum yelds to the mean plus two standard devatons. Table 1 reports the resultng means and standard devatons of farm yeld for farms wth below average (hgh-rsk) and wth above average (lowrsk) yelds n the four countes examned, as well as the assocated APH premums for 65 percent coverage. The resultng dstrbutons of farm yeld are generally consstent wth publshed results for dryland producton of corn and cotton (Coble, Hefner, and Zunga 2000, Coble, Zunga, and Hefner 2003, Hennessy, Babcock, and Hayes 1997). The fnal parameter needed to specfy the relatonshp between farm and county yelds s ther correlaton. Lttle publshed data regardng observed farm and county yeld correlatons for a range of crops and countes exst. A rare example s Hennessy, Babcock, and Hayes (1997), who report 0.8 as the average correlaton for ten farms for a sngle crop n a sngle county. However, actual farm yeld hstores, from whch we could derve emprcal estmates of the dstrbuton of the correlaton between county and farm yelds, were unavalable for ths study. As a result, we selected two levels for Pearson s correlaton coeffcent between farm and county yelds (0.3 and 0.9) as examples of farms wth low and hgh yeld correlaton wth the county yeld to capture a wde range of condtons. Our purpose s to examne results at these reasonable extremes n order to estmate the range of the expected effects of SDC for most farmers. Farmer Revenue and Insurance Premums For ths analyss, farm revenue s crop revenue (the product of the non-random prce P and random yeld y f ), plus the nsurance ndemnty mnus the premum, where the ndemnty and the premum depend on the chosen nsurance coverage level. We do not nclude non-random producton costs, gven the dffculty n consstent estmaton of such costs for dfferent types of producers n

7 Mtchell and Knght Economc Analyss of Supplemental Deductble Coverage 123 dfferent countes across states. Thus, farmer returns ($/ac) for nsurance program {none, aph, grp, sdc_st, sdc_ac} are (5) π (α) = Py f + I (α) M (α), where M (α) s the per acre farmer premum for nsurance program as a functon of the APH coverage level. The subscrpt none mples no nsurance, wth I none and M none equal to zero. The analyss uses a non-random prce to focus only on yeld rsk and uses the publshed APH prce for all crops and polces as an easly avalable estmate of the expected crop prce at harvest. For farmer premums, we analyze these nsurance polces usng actuarally far premums equal to the expected value of the ndemnty derved through Monte Carlo ntegraton. Farmer premums currently nclude subsdes so that farmers pay less than what the RMA estmates to be actuarally far. Table 2 reports the current premum subsdy rates for all APH and GRP coverage levels. Snce these premum subsdes are ncluded n all current actual premums, we use these same subsdy rates n our analyss. Snce ndemntes for SDC combned wth APH are a combnaton of APH- and GRP-based ndemntes, premums for APH combned wth SDC use the approprate APH subsdy rate for the APH porton of the premum and the 90 percent GRP subsdy rate for the SDC porton of the premum. Snce all crop nsurance premums are currently subsdzed, we do not report results for unsubsdzed premums. Table 2. Current Premum Subsdy Rates for Federal Crop Insurance Polces Coverage Level APH Subsdy Rate GRP Subsdy Rate 50% 67% % 64% % 64% % 59% % 59% 64% 75% 55% 64% 80% 48% 59% 85% 38% 59% 90% % Source: USDA (2007c). As prevously explaned, the county yeld standard devatons were calbrated so that the smulated far GRP premum rate matched the actual GRP rate. Thus by constructon, our subsdzed SDC premums are equal to actual 90 percent coverage GRP premums, wth the protecton per acre equal to the APH deductble. However, for SDC wth an accelerated payment rate, the avalable GRP premum nformaton does not allow calbraton of smulated premums to equal publshed premums. Therefore, premum rates for accelerated coverage were derved through Monte Carlo ntegraton usng the accelerated ndemnty functon reported n equaton (4). APH premums used n the analyss were also derved through the Monte Carlo ntegraton. As prevously explaned, farm yeld standard devatons were calbrated so that the smulated far APH premum wth a 65 percent coverage level matched the actual APH rate for the same mean yeld. Because APH premums are not exactly consstent wth a sngle yeld dstrbuton (Babcock, Hart, and Hayes 2004), the smulated APH premums used for ths analyss for coverage levels other than 65 percent wll not match the actual premums for these coverage levels, though they wll be relatvely close n value. Farmer Utlty For farmer rsk preferences, we use a power utlty functon, whch mples constant relatve rsk averson (CRRA). Followng Chavas (2004, p. 46), farmer utlty from per acre returns for nsurance program {none, aph, grp, sdc_st, sdc_ac} s (6) U (α) = π (α) 1 R, where R > 1 s the coeffcent of relatve rsk averson and π s as defned by equaton (5). Followng Coble, Hefner, and Zunga (2000) and Coble, Zunga, and Hefner (2003), we use R = 2.0 to reflect a moderate level of rsk averson. 4 Farmer expected utlty for each polcy s the expected value of equaton (6): 4 Goller (2001, p. 31) provdes basc calculatons to support the general concluson that a reasonable range for R s 1 to 4. However, t has been a common regularty (as of yet wthout a generally accepted explanaton) that emprcal estmates of R commonly exceed ths range (e.g., Chavas and Holt 1996, Cohen and Enav 2007, Schechter 2007).

8 124 Aprl 2008 Agrcultural and Resource Economcs Revew (7) EU (α) = E[ π (α) 1 R ] 1 R = π (α) df(π α), π where F(π α) s the cumulatve dstrbuton functon of random farmer returns π condtonal on the APH coverage level α. As equaton (5) ndcates, π s a transformaton of farm yeld y f, drectly through crop revenue and ndrectly through the ndemnty, so that for most of the polces analyzed, the actual condtonal dstrbuton functon F (π α) s generally dffcult to express as a closed-form equaton due to the farm and county yeld dstrbutons used and the truncated nature of nsurance ndemntes. Furthermore, the transformaton of returns π by the utlty functon creates addtonal nonlnearty so that closed-form analytcal solutons for expected utlty do not exst for any of the polces analyzed. As a result, numercal methods are needed to calculate expected utlty; for the analyss here, we use Monte Carlo ntegraton. Emprcal Implementaton Greene (2003) provdes an overvew of Monte Carlo ntegraton, wdely used to approxmate multple ntegrals of complex functons. Numerous applcatons n agrculture and crop nsurance exst (e.g., Hennessy, Babcock, and Hayes 1997, Hurley, Mtchell, and Rce 2004, Mtchell, Gray, and Steffey 2004). We use the method to approxmate the ntegrals for calculatng expected utlty n equaton (7) and actuarally far premums equal to the expected ndemntes. County and farm yelds are the fundamental random varables n ths analyss; all other random varables are functons of these two varables, ther moments, and other parameters. We use the method of Rchardson and Condra (1981), explaned n more detal by Fackler (1991), to draw vectors of county and farm yelds wth the requred correlaton. Goodwn and Ker (2002) dscuss the merts and weaknesses of ths method for correlatng random varables. Monte Carlo ntegraton for ths analyss was mplemented usng Mcrosoft Excel Expermentaton ndcated that 10,000 random draws were suffcent for results to converge. Analyzng Supplemental Deductble Coverage The analyss assumes that farmers choose the APH coverage level to maxmze ther expected utlty. Mathematcally, the farmer s problem s (8) 1 max EU (α) = max π (α) R (π α) df, α α where α {0%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%) s the farmer s choce varable. Note that α = 0% s a specal case used here to ncorporate no nsurance and GRP coverage nto the choce set wthout creatng separate scenaros for these two polces. For the current APH polcy ( = aph), α = 0% ndcates no nsurance ( = none), and when examnng ether of the SDC polces ( = sdc_st or = sdc_ac), α = 0% ndcates 90 percent GRP coverage ( = grp). Ths notaton collapses the fve nsurance polces nto three scenaros to analyze: APH alone (or no nsurance f α = 0%) ( = aph), APH combned wth SDC usng a standard GRP payment rate (or GRP alone f α = 0%) ( = sdc_st), and APH combned wth SDC usng an accelerated GRP payment rate (or GRP alone f α = 0%) ( = sdc_ac). Smulatons were conducted wth each APH coverage level (0 percent, 50 percent to 85 percent n 5 percent steps), and a smple search dentfed the * optmal APH coverage level ( α ) and assocated * optmal expected utlty ( EU ) for each of the three scenaros. These optmal expected utltes were then converted nto the assocated optmal certanty equvalents ($/ac) for each scenaro: * * (9) ( ) 1/(1 R CE EU ) π =. Fgure 2 llustrates example results for Trpp County n South Dakota and Hamlton County n Iowa wth parameterzatons as reported n the fgure capton. The three lnes n each plot ndcate farmer certanty equvalents for all APH coverage levels for all polces as labeled. The No Insurance or GRP Alone choces of α = 0% are the ponts on the vertcal axs, connected by dashed lghter lnes to results wth APH Alone (α = 50 percent to 85 percent n 5 percent steps). From the data used to generate plots such as those llustrated n Fgure 2, the optmal APH coverage * level ( α ) and assocated optmal certanty equva-

9 Mtchell and Knght Economc Analyss of Supplemental Deductble Coverage APH + Accelerated SDC Certanty Equvalent ($/ac) GRP Alone APH + Standard SDC No Insurance APH Alone APH Coverage Level (%) 780 APH + Accelerated SDC Certanty Equvalent ($/ac) GRP Alone No Insurance APH + Standard SDC APH Alone APH Coverage Level (%) Fgure 2. Certanty Equvalent Returns for Corn n Trpp County, South Dakota (top), and Hamlton County, Iowa (bottom), for the Three Insurance Scenaros Note: Wth far subsdzed premums, a farm mean yeld 25 percent above the county average, and a county-farm yeld correlaton of 0.9.

10 126 Aprl 2008 Agrcultural and Resource Economcs Revew * lent ( CE ) were dentfed for the three scenaros for each parameterzaton. The vertcal gap between the three lnes s the ncrease n farmer certanty equvalents when a farmer swtches from APH alone to APH wth SDC wth a standard or wth an accelerated payment rate. Because so many parameterzatons were analyzed, the optmal coverage levels and certanty equvalents for each parameterzaton are not reported, but are avalable upon request from the authors. Results and Dscusson The presentaton of results frst dscusses general fndngs for the data, such as those llustrated n Fgure 2. However, prmary presentaton of results uses tables to focus on changes n certanty equvalents and optmal coverage levels between the scenaros to provde monetary estmates of farmer benefts from SDC and to determne how farmers would lkely adjust APH coverage levels f SDC became avalable. Changes n optmal certanty equvalents between usng ether the current APH or GRP polcy alone and ether APH combned wth SDC usng a standard GRP payment rate or wth SDC usng an accelerated GRP payment rate are estmates of the farm-level benefts of the proposed SDC polcy. Changes n the optmal APH coverage levels between usng ether the current APH or GRP polcy alone and ether APH combned wth SDC usng a standard GRP payment rate or wth SDC usng an accelerated GRP payment rate ndcate how farmers would lkely adjust APH coverage levels f SDC became avalable. Fgure 2 shows the general results that occur for each county and farm type examned. Frst, farmer certanty equvalents wth APH always exceed the No Insurance case (even for rskneutral farmers) and, at any gven coverage level, certanty equvalents wth APH plus SDC wth an accelerated payment rate always exceed certanty equvalents wth APH plus SDC usng the standard payment rate. SDC ncreased farmer welfare more at lower APH coverage levels than at hgher levels,.e., the gap between the APH Alone and the APH + Accelerated SDC curves s larger at lower coverage levels n Fgure 2. Relatve to the APH Alone curve, accelerated SDC lfts farmer certanty equvalents more at the lower APH coverage levels, so that the APH + Accelerated SDC curve becomes very flat, as for Trpp County, or U-shaped, as for Hamlton County. In general, optmal APH coverage levels for rskaverse farmers ranged from 75 percent to 85 percent. Only for a few of the rsk-neutral cases examned dd ths lftng of the lower end of the accelerated SDC curves cause the optmal APH coverage level to jump across the U-shaped curve to α = 50%. In addton, GRP (α = 0%) was optmal relatve to APH or APH wth SDC usng a standard payment rate n only one county, and then only for the rsk-neutral case. Table 3 reports the ncrease n farmer certanty equvalents as $/ac when swtchng from usng APH alone to usng APH combned wth SDC usng ether the standard GRP payment rate or the accelerated payment rate. Table 4 reports the decrease n the optmal APH coverage level assocated wth swtchng from APH alone to APH combned wth ether type of SDC examned. Based on the results n these tables, we draw several generalzatons regardng the effect of SDC. Farmer Benefts from SDC For all cases n Table 3, SDC generates postve benefts relatve to the current program of usng ether APH or GRP alone, mplyng that most farmers would fnd some beneft from SDC. We focus ntally on results wth the accelerated payment rate, as ths s the proposed program. In Trpp County, SDC generates a beneft for corn farmers rangng from about $5/ac to over $11.40/ac wth the accelerated payment rate; benefts for Hamlton County corn farmers are farly smlar n magntude. Though the magntude of the beneft of SDC s smlar for corn farmers n these two locatons, the relatve beneft of SDC n Trpp County s much larger, snce the revenue potental for corn n Trpp County s much lower. For cotton farmers, SDC wth the accelerated payment rate generates benefts rangng from about $4/ac to $11.50/ac n Lubbock County and over $6/ac to $16.50/ac n Coahoma County. However, agan, snce the revenue potental for cotton s lower n Lubbock County, the relatve beneft of SDC s larger. Relatve to the rsk-averse cases examned, results for the rsk-neutral cases are almost unformly dampened the low ends of the ranges are not as low and the hgh ends of the ranges are not as hgh. Thus, the reported ranges for the beneft

11 Mtchell and Knght Economc Analyss of Supplemental Deductble Coverage 127 Table 3. Net Beneft of APH Plus SDC wth a Standard and wth an Accelerated Payment Rate a Standard Rate Accelerated Rate County Mean Yeld b ρ fc Rsk Averse Rsk Neutral Rsk Averse Rsk Neutral Trpp County, SD Hamlton County, IA Lubbock County, TX Coahoma County, MS a Benefts measured as the ncrease n farmer certanty equvalents ($/ac) relatve to the current program of usng ether APH or GRP alone. b Relatve to county mean. of SDC encompass results for the rsk-averse and rsk-neutral cases examned. Fnally, farmer benefts from SDC wth the standard payment rate are lower, ndcatng the essental nature of the accelerated payment rate n order for SDC to generate a sgnfcant farmer beneft. Farmer benefts wth the standard payment rate are less than about $3.50/ac for the corn cases examned, and less than $5.20/ac for the cotton cases. Among the trends n Table 3, note that as the farm-county yeld correlaton ncreases, the benefts from SDC ncrease for rsk-averse farmers, but reman relatvely unchanged for rsk-neutral farmers. Rsk-averse farmers derve greater beneft from SDC as ther yelds more closely follow county yelds because SDC ndemntes become more lkely to concde wth low farm yeld outcomes and thus reduce revenue varance. Rskneutral farmers do not respond to changes n revenue varance due to SDC, but rather seek the APH coverage level that maxmzes ther expected revenue when APH s combned wth SDC. For all the cases examned n Table 3, wthn the same county, low-rsk farmers (those wth mean yelds 25 percent above the county mean) receve larger benefts from SDC than hgh-rsk farmers (those wth mean yelds 25 percent below the county mean). Ths result occurs because of the dfference n yeld (and hence revenue) potental between the hgh- and low-rsk farmers n a county. For a gven coverage level, the APH deductble s larger for low-rsk (hgh mean) farmers because they have a larger yeld guarantee due to ther greater yeld potental. For a gven county yeld outcome, SDC pays the same proporton of the APH deductble for both types of farmers, but the ndemnty s larger for the lowrsk (hgh mean) farmers because they have a larger APH deductble. When comparng farmers n a low-rsk county to comparable farmers n a hgh-rsk county n Table 3, ths yeld potental effect does not always hold. In most cases, farmers n hgh-rsk countes derve smaller benefts from SDC than comparable farmers n low-rsk countes, whch s consstent wth ther dfference n yeld potentals. For example, both hgh-rsk and low-rsk cotton farmers n Lubbock County derve smaller benefts from SDC than comparable hgh- and low-

12 128 Aprl 2008 Agrcultural and Resource Economcs Revew Table 4. Percentage Pont Decrease n the Optmal APH Coverage Level wth APH Plus SDC wth the Standard and wth an Accelerated SDC Payment Rate a Standard Rate Accelerated Rate County Mean Yeld b ρ fc Rsk Averse Rsk Neutral Rsk Averse Rsk Neutral Trpp County, SD 0.3 0% 0% 0% 5% 0.9 0% 0% 5% 5% 0.3 0% 5% 5% 10% 0.9 5% 5% 10% 10% Hamlton County, IA 0.3 0% 5% 0% 10% 0.9 0% 5% 0% 10% 0.3 0% 0% 0% 35% 0.9 0% 0% 0% 35% Lubbock County, TX 0.3 0% 5% 5% 5% 0.9 5% 5% 5% 5% 0.3 0% 0% 0% 15% 0.9 0% 0% 5% 15% Coahoma County, MS 0.3 0% 80% c 0% 10% 0.9 0% 80% c 5% 10% 0.3 0% 0% 0% 30% 0.9 0% 0% 5% 30% a Decreases measured relatve to the current program of usng ether APH or GRP alone. b Relatve to county mean. c Shft from 80 percent APH coverage to GRP. rsk farmers n Coahoma County. However, for the corn countes examned, ths trend no longer consstently occurs. Low-rsk corn farmers n Trpp County wth a yeld correlaton of 0.3 derve smaller benefts from SDC than low-rsk farmers n Hamlton County, whch s consstent wth the yeld potental effect, but ths outcome reverses wth a yeld correlaton of 0.9. Also, hgh-rsk corn farmers derve greater beneft from SDC n Trpp County than n Hamlton County, whch agan s opposte the outcome mpled by the dfference n yeld potentals. The benefts of SDC arse from two prmary sources. Frst, SDC allows a farmer to ncrease nsurance coverage to also nclude the APH deductble. In general, the larger the yeld potental, the larger ths beneft becomes. Thus, countes wth hgh yeld potental (low rsk) wll derve greater beneft from SDC. Second, SDC provdes some protecton from systemc rsk as captured n the county yeld. APH provdes a measure of protecton aganst both dosyncratc and systemc rsk, whle GRP provdes protecton only aganst systemc rsk; SDC combnes both to provde ncreased protecton aganst systemc rsk. The greater the systemc rsk, the larger the beneft of SDC becomes. Thus, countes wth hgh systemc rsk wll derve greater beneft from SDC. The yeld potental and systemc rsk effects of SDC counteract each other so that the types of farmers who wll derve the greatest beneft from SDC s an emprcal ssue hgh-rsk farmers wth low average yelds or low-rsk farmers wth hgh average yelds. The results n Table 3 show that wthn a county, where the systemc rsk s held constant, low-rsk farmers derve greater beneft from SDC, whch s to be expected. Comparng across countes, where the systemc rsk s no longer held constant, hgh-rsk farmers n one county generally derve greater beneft relatve to the low-rsk case (corn n Trpp County versus n Hamlton County), whle the reverse occurs n another county relatve to ts low-rsk case (cotton n Lubbock County versus n Coahoma County). For the corn examples, the systemc rsk beneft of SDC

13 Mtchell and Knght Economc Analyss of Supplemental Deductble Coverage 129 domnates the yeld potental effect, whle for cotton, the yeld potental effect domnates. If other countes and crops were examned, whch effect domnated could change. Effect of SDC on Optmal APH Coverage Levels Because SDC provdes protecton from systemc rsk, SDC can serve as an mperfect substtute for hgher APH coverage, whch can mply a reducton n the optmal APH coverage level. Thus, for all cases n Table 4, the optmal APH coverage wth SDC ether decreases or remans unchanged the optmal APH coverage level never ncreases when APH s combned wth SDC. Wth the accelerated payment rate, the decrease s as large as 35 percentage ponts (.e., a shft from 85 percent to 50 percent coverage), but these large decreases occur for the rsk-neutral cases. For the rsk-averse cases, the decrease s generally 0 or 5 percentage ponts, wth one case of 10 percentage ponts. The mplcaton s that as farmers become less rsk-averse, SDC decreases the optmal APH coverage level more. Wth the standard payment rate, the optmal coverage level decreases no more than 5 percentage ponts, except for a few cases when t becomes optmal to choose GRP over SDC. However, the dfference between the rsk-averse and rsk-neutral cases s much smaller. For the rsk-averse cases wth an accelerated payment rate, no consstent pattern emerges regardng whether SDC has a larger effect on optmal APH coverage levels for low-rsk or hghrsk farmers. In the two low-rsk countes (corn n Hamlton County and cotton n Coahoma County), no dfference exsts between the decrease n optmal APH coverage for hgh- and low-rsk farmers. The same occurs n Lubbock County (a hgh-rsk cotton county), except for one case n whch the optmal APH coverage level decreases more for the hgh-rsk cotton farmer. In Trpp County, a hgh-rsk corn county, low-rsk (hgh mean) corn farmers have a larger decrease n optmal APH coverage than hgh-rsk farmers wth low mean yelds. When examnng the rsk-neutral cases, however, a consstent pattern emerges low-rsk farmers experence a larger decrease n the optmal APH coverage level wth SDC. Ths larger decrease n optmal APH coverage for low-rsk farmers holds when comparng low- and hgh-rsk farmers wthn a county and when comparng comparable farmers n low- and hgh-rsk countes. The mplcaton s that the effect of SDC on expected revenue decreases the optmal APH coverage level more for low-rsk farmers, but rsk averson dampens ths expected revenue effect of SDC because rsk-averse farmers derve rsk management benefts from hgher APH coverage levels. These dampenng effects of rsk averson depend on the specfcs of the yeld dstrbutons and lead to the dffcult-to-nterpret pattern of effects of SDC on optmal APH coverage levels n Table 4. As the farm yeld becomes more correlated wth the county yeld, the effectveness of SDC as a substtute for APH ncreases, and so the optmal APH coverage level wth SDC should decrease or reman unchanged. For the results n Table 4, ths effect of the correlaton between the farm and county yelds s mnmal. For most cases, as the correlaton ncreases, the optmal APH coverage level remans unchanged. However, for a few rsk-averse cases, the optmal coverage decreases, e.g., Coahoma County and low-rsk farmers n Lubbock County and Trpp County. The man mplcaton s that the reducton n the optmal APH coverage level s farly non-responsve to the correlaton between farm and county yelds. Concluson We examned the farm-level effects of Supplement Deductble Coverage (SDC) as contaned n the USDA Farm Bll proposal. Our emprcal analyss used a varety of assumptons to parameterze a model of correlated county and farm yelds, n partcular calbratng the mean and standard devaton of yelds to match crop nsurance premum rates. We developed corn and cotton examples for farms n low-rsk/hgh-yeld and hgh-rsk/low-yeld countes, examnng results at reasonable extremes for county-farm yeld correlatons. We used the results of these numercal experments to estmate the range of effects to expect for most farmers f a study were to be conducted usng actual farm and county yeld hstores. We focused our analyss on the effects of SDC on farmer welfare and the optmal level of nsurance coverage. Our results ndcate that SDC, as structured under the USDA Farm Bll proposal, generates welfare benefts for all farms analyzed. SDC n-

14 130 Aprl 2008 Agrcultural and Resource Economcs Revew creased farmer welfare from $5 to over $11/ac for the corn examples examned, and from $4 to over $16/ac for the cotton examples. However, the ncdence of ths beneft vared dependng on the specfc assumptons, whch we nterpreted as the nteracton of two offsettng effects a yeld potental effect and a systemc rsk effect. Farmers wth hgher yeld potental derve greater beneft from SDC because, at any APH coverage level, ther APH deductbles nsurable under SDC are larger. In addton, because SDC provdes ncreased protecton aganst systemc rsk, farmers n countes wth greater systemc rsk derve greater beneft from SDC. However, crop nsurance premums for both GRP and APH ndcate that, for most crops n most countes, as yeld potental ncreases, yeld varablty decreases. As a result, areas wth hgh yeld potental tend to have lower levels of systemc rsk and vce versa. Ths general trend mples that the yeld potental effect tends to work n the opposte drecton of the systemc rsk effect, so that the net effect of SDC on farmer welfare s an emprcal ssue dependng on the specfcs of the yeld dstrbutons. SDC also decreased the optmal APH coverage level, generally by at most 5 percentage ponts for the rsk-averse cases examned, but from 5 to 35 percentage ponts for the rsk-neutral cases. Thus SDC provdes ncentves for many farmers to shft from ndvdual coverage to area coverage, and so reduces the potental for moral hazard, adverse selecton, fraud, and program abuse for the crop nsurance program, snce these problems are typcally less serous when ndvdual coverage levels are lower. References Atwood, J., A. Baquet, and M. Watts Income Protecton. Techncal report, Montana State Unversty. Submtted to the U.S. Department of Agrculture, Economc Research Servce, Commercal Agrcultural Dvson (February16). Avalable at cproj/techsum.pdf. Babcock, B., C. Hart, and D. Hayes Actuaral Farness of Crop Insurance wth Constant Rate Relatvtes. Amercan Journal of Agrcultural Economcs 86(3): Babcock, B., and D. Hennessy Input Demand under Yeld and Revenue Insurance. Amercan Journal of Agrcultural Economcs 78(2): Carrqury, M., B. Babcock, and C. Hart Usng a Farmer s Beta for Improved Estmaton of Actual Producton Hstory (APH) Yelds. Workng Paper No. 05-WP- 387, Center for Agrcultural and Rural Development, Iowa State Unversty, Ames, IA. Avalable at astate.edu/publcatons/dbs/pdffles/05wp387.pdf. Chambers, R.G Insurablty and Moral Hazard n Agrcultural Insurance Markets. Amercan Journal of Agrcultural Economcs 71(3): Chavas, J.P Rsk Analyss n Theory and Practce. New York: Elsever. Chavas, J.P., and M.T. Holt Economc Behavor under Uncertanty: A Jont Analyss of Rsk Preferences and Technology. The Revew of Economcs and Statstcs 78(2): Coble, K., R. Hefner, and M. Zunga Implcatons of Crop Yeld and Revenue Insurance for Producer Hedgng. Journal of Agrcultural and Resource Economcs 25(2): Coble, K.H., and T.O. Knght Crop Insurance as a Tool for Prce and Yeld Rsk Management. In R.E. Just and R.D. Pope, eds., A Comprehensve Assessment of the Role of Rsk n U.S. Agrculture. Boston, MA: Kluwer Academc Press. Coble K.H., M. Zunga, and R. Hefner Evaluaton of the Interacton of Rsk Management Tools for Cotton and Soybeans. Agrcultural Systems 75(2/3): Cohen, A., and L. Enav Estmatng Rsk Preferences from Deductble Choces. The Amercan Economc Revew 97(3): Deng, X., B. Barnett, and D. Vedenov Is There a Vable Market for Area-Based Crop Insurance? Amercan Journal of Agrcultural Economcs 89(2): Fackler, P Modelng Interdependence: An Approach to Smulaton and Elctaton. Amercan Journal of Agrcultural Economcs 73(4): Goller, C The Economcs of Rsk and Tme. Cambrdge, MA: MIT Press. Goodwn, B.K An Emprcal Analyss of the Demand for Crop Insurance. Amercan Journal of Agrcultural Economcs 75(2): Goodwn, B.K., and A.P. Ker Modelng Prce and Yeld Rsk. In R.E. Just and R.D. Pope, eds., A Comprehensve Assessment of the Role of Rsk n U.S. Agrculture. Boston, MA: Kluwer Academc Press. Greene, W Econometrc Analyss (5th edton). Upper Saddle Rver, NJ: Prentce Hall. Hennessy, D., B. Babcock, and D. Hayes Budgetary and Producer Welfare Effects of Revenue Insurance. Amercan Journal of Agrcultural Economcs 79(3): Hurley, T.M., P.D. Mtchell, and M.E. Rce Rsk and the Value of Bt Corn. Amercan Journal of Agrcultural Economcs 86(2): Just, R., L. Calvn, and J. Quggn Adverse Selecton n U.S. Crop Insurance: Actuaral and Asymmetrc Informaton Incentves. Amercan Journal of Agrcultural Economcs 81(4): Martn, S., B.J. Barnett, and K.H. Coble Developng and Prcng a Ranfall Contngent Clams Contract. Jour-