economic analysis of supplemental deductible coverage as recommended in the usda’s 2007 farm bill...
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Economic Analysis of Economic Analysis of Supplemental Deductible Supplemental Deductible
Coverage as Recommended Coverage as Recommended in the USDA’s 2007 Farm Billin the USDA’s 2007 Farm Bill
Paul D. MitchellPaul D. MitchellUniversity of Wisconsin-MadisonUniversity of Wisconsin-Madison
Thomas O. KnightThomas O. KnightTexas Tech UniversityTexas Tech University
AAE Departmental SeminarAAE Departmental SeminarOctober 10, 2007October 10, 2007
Published as Mitchell and Knight. 2008. Published as Mitchell and Knight. 2008. Agricultural and Agricultural and Resource Economics ReviewResource Economics Review 37:117-131 37:117-131
MotivationMotivation Title Title XX of the USDA’s 2007 Farm Bill: of the USDA’s 2007 Farm Bill:
““Allow farmers to purchase supplemental Allow farmers to purchase supplemental insurance that would cover all or part of insurance that would cover all or part of their individual policy deductible in the their individual policy deductible in the event of a county or area wide loss.”event of a county or area wide loss.”
Similar to H.R. 721 The Risk Management Similar to H.R. 721 The Risk Management Enhancement Act, sponsored by Enhancement Act, sponsored by Neugebauer (R-TX) and others, including Neugebauer (R-TX) and others, including Mark Green (R-WI)Mark Green (R-WI)
Main Point: Policy makers are examining Main Point: Policy makers are examining various types of supplemental coveragevarious types of supplemental coverage
Why Supplemental Why Supplemental Coverage?Coverage?
Provide “Gap Coverage” to fill the “hole Provide “Gap Coverage” to fill the “hole in the safety net”, especially in high in the safety net”, especially in high risk areasrisk areas
High risk areas = High risk areas = high premiumshigh premiums, and , and deductible still exceeds profit margindeductible still exceeds profit margin
Supplemental coverage will increase Supplemental coverage will increase effective coverageeffective coverage Reduce need for disaster assistanceReduce need for disaster assistance Lower premium for SDC than for APH with Lower premium for SDC than for APH with
the same liabilitythe same liability
Purpose of PresentationPurpose of Presentation
Describe Supplemental Deductible Describe Supplemental Deductible Coverage (SDC) as proposed in 2007 Coverage (SDC) as proposed in 2007 USDA Farm BillUSDA Farm Bill
Economic Analysis of SDC at farm levelEconomic Analysis of SDC at farm level Effect on Farmer Welfare (certainty Effect on Farmer Welfare (certainty
equivalent)equivalent) Effect on Farmer Behavior (coverage level)Effect on Farmer Behavior (coverage level)
How Individual Crop Insurance How Individual Crop Insurance (APH) Coverage Works(APH) Coverage Works
Farmer chooses farm yield guarantee Farmer chooses farm yield guarantee as proportion as proportion aphaph of expected yield of expected yield ff
Expected yield Expected yield f f calculated as moving calculated as moving
average of actual production history average of actual production history (APH)(APH)
APH indemnities based on farmer yieldAPH indemnities based on farmer yield
IIaphaph = P = Paphaph xx max{ max{aphaphff – y – yff, 0}, 0}
How Areawide Crop Insurance How Areawide Crop Insurance (GRP) Coverage Works(GRP) Coverage Works
Choose county yield guarantee as Choose county yield guarantee as proportion proportion grpgrp of expected county yield of expected county yield cc
RMA sets GRP expected county yield RMA sets GRP expected county yield cc
GRP indemnities based on county yieldGRP indemnities based on county yield
IIgrpgrp = MP = MPgrpgrp x x max{(max{(grpgrpcc – y – ycc)/()/(grpgrpcc), 0}), 0}
MPMPgrpgrp = GRP maximum protection per = GRP maximum protection per acre acre = 150% = 150% xx P Paphaph xx cc
Calculate county % loss from guaranteeCalculate county % loss from guarantee , , then paid that percentage of liability MPthen paid that percentage of liability MPgrpgrp
Simple APH ExampleSimple APH Example
Farm mean Farm mean ff = 100, choose 75% = 100, choose 75% coverage (coverage (aphaph = 0.75), so APH yield = 0.75), so APH yield guarantee = 75 bu/acguarantee = 75 bu/ac
Deductible (bu/ac) = 100 – 75 = 25 Deductible (bu/ac) = 100 – 75 = 25 bu/acbu/ac
DDaphaph ($/ac) = P ($/ac) = Paphaph x 25 bu/ac x 25 bu/ac If actual harvest yIf actual harvest yff = 60 bu/ac, then loss = 60 bu/ac, then loss
is max(75 – 60, 0) = 15 bu/ac and is max(75 – 60, 0) = 15 bu/ac and indemnity is Pindemnity is Paphaph x 15 bu/ac x 15 bu/ac
Simple GRP ExampleSimple GRP Example
County mean County mean cc = 100, choose 90% = 100, choose 90%
coverage (coverage (grpgrp = 0.90), so GRP yield = 0.90), so GRP yield guarantee = 90 bu/acguarantee = 90 bu/ac
If actual county yield yIf actual county yield ycc = 80 bu/ac, then = 80 bu/ac, then loss is max((90 – 80)/90, 0) = 11.1%loss is max((90 – 80)/90, 0) = 11.1%
Indemnity = MPIndemnity = MPgrpgrp x 0.111, where x 0.111, where
MPMPgrpgrp = 150% x P = 150% x Paphaph x 100 bu/ac x 100 bu/ac
How SDC would workHow SDC would work
Allow farmer with APH coverage to buy GRP Allow farmer with APH coverage to buy GRP coverage modified to have liability equal to coverage modified to have liability equal to APH deductible, so SDC indemnity isAPH deductible, so SDC indemnity is
IIsdcsdc = = IIaph aph + I+ Imgrpmgrp
IImgrpmgrp = D = Daph aph x x max{(max{(grpgrpcc – y – ycc)/()/(grpgrpcc), 0}), 0} IImgrpmgrp = GRP indemnity, replacing maximum = GRP indemnity, replacing maximum
protection per acre MPprotection per acre MPgrpgrp with APH deducible with APH deducible
yycc
Ind
em
nit
yIn
dem
nit
y
Unmodified GRP IndemnityUnmodified GRP Indemnity
Unmodified GRP Unmodified GRP IndemnityIndemnity
APH APH DeductiblDeductiblee
grpgrpcc
Problem with unmodified Problem with unmodified GRPGRP
GRP only pays total liability DGRP only pays total liability Daphaph if y if ycc = = 00
Very unlikely, even in high risk areasVery unlikely, even in high risk areas Need accelerated indemnitiesNeed accelerated indemnities Modify GRP indemnity further: Same yModify GRP indemnity further: Same ycc
trigger of trigger of grpgrpcc, but full payout of APH , but full payout of APH deductible by ydeductible by ycc = = cc, 0 ≤ , 0 ≤ ≤ ≤ grpgrp
grp c cmgrp aph aph
grp c c
xμ y
I min D max ,0 , Dμ μ
yycc
Ind
em
nit
yIn
dem
nit
y
grpgrpcccc
Modified GRP Modified GRP IndemnityIndemnity
Unmodified GRP IndemnityUnmodified GRP Indemnity
Modified GRP IndemnityModified GRP Indemnity
APH APH DeductiblDeductiblee
Questions on how Questions on how these policies these policies
work???work???
Purpose of PresentationPurpose of Presentation
Describe Supplemental Deductible Describe Supplemental Deductible Coverage (SDC) as proposed in 2007 Coverage (SDC) as proposed in 2007 USDA Farm BillUSDA Farm Bill
Economic Analysis of SDC at farm levelEconomic Analysis of SDC at farm level Effect on Farmer Welfare (certainty Effect on Farmer Welfare (certainty
equivalent)equivalent) Effect on Farmer Behavior (coverage level)Effect on Farmer Behavior (coverage level)
Overview Economic Analysis of Overview Economic Analysis of SDCSDC
Effect of SDC on Effect of SDC on certainty equivalentscertainty equivalents Effect of SDC on Effect of SDC on optimal coverage leveloptimal coverage level Examine farmer certainty equivalent Examine farmer certainty equivalent
($/ac) assuming negative exponential ($/ac) assuming negative exponential utility (CARA) and coverage level chosen utility (CARA) and coverage level chosen optimallyoptimally
Use Monte Carlo integration to estimate Use Monte Carlo integration to estimate farmer expected utility, then calculate farmer expected utility, then calculate certainty equivalentscertainty equivalents
Modeling Stochastic Relation Modeling Stochastic Relation between Farm and County between Farm and County
YieldsYields With SDC, farmer indemnities depend on With SDC, farmer indemnities depend on
both the farm yield and the county yieldboth the farm yield and the county yield Certainty equivalent and optimal coverage Certainty equivalent and optimal coverage
depend on how model relation btwn yields depend on how model relation btwn yields Models used in literatureModels used in literature
Additive: Additive: yyff = = ffyycc + + ff
Multiplicative:Multiplicative: yyff = y = yccff
Hierarchical:Hierarchical: yyff ~ f(y ~ f(yff|y|ycc) more ) more generalgeneral
Joint Density:Joint Density: g(yg(yff, y, ycc) more general) more general
less less generalgeneral
Modeling Stochastic Relation Modeling Stochastic Relation between Farm and County between Farm and County
YieldsYields Given mean and variance of county yieldGiven mean and variance of county yield Additive and Multiplicative:Additive and Multiplicative:
Setting farm mean and variance sets Setting farm mean and variance sets correlation between farm and county yieldscorrelation between farm and county yields
Joint Distribution:Joint Distribution: Correlation between farm and county yields Correlation between farm and county yields
can be set separate from farm mean and can be set separate from farm mean and variancevariance
Hierarchical:Hierarchical: Depends on number of parameters of the Depends on number of parameters of the
conditional density for farm yieldconditional density for farm yield
Main PointMain Point
I use a joint density for farm and county I use a joint density for farm and county yields that separately specifies the yields that separately specifies the county mean and variance, the farm county mean and variance, the farm mean and variance, and the correlation mean and variance, and the correlation between farm and county yieldsbetween farm and county yields
Parameters Parameters cc, , cc, , ff, , ff, and , and fc fc fully fully describe farm and county yieldsdescribe farm and county yields
Additive and Multiplicative would only Additive and Multiplicative would only have have cc, , cc, , ff, and , and ff as free parameters as free parameters
Monte Carlo AnalysisMonte Carlo Analysis
Specify parameters: Specify parameters: cc, , cc, , ff, , ff, and , and fcfc, plus , plus premiums, price, coverage levels and coefficient premiums, price, coverage levels and coefficient absolute risk aversion Rabsolute risk aversion Raa
Draw county and farm yieldsDraw county and farm yields Determine indemnities, returns and utilities for Determine indemnities, returns and utilities for
each set of yield drawseach set of yield draws Calculate expected utility for parameter set as Calculate expected utility for parameter set as
simple average of all utilities: EU = Average(usimple average of all utilities: EU = Average(u ii)) Calculate certainty equivalent: CE = – ln(1 – Calculate certainty equivalent: CE = – ln(1 –
EU)/REU)/Raa
Distribution of YieldsDistribution of Yields County yield: lognormal distributionCounty yield: lognormal distribution
Mean = GRP 2007 expected county yieldMean = GRP 2007 expected county yield St. Dev. set to match 90% GRP premium rateSt. Dev. set to match 90% GRP premium rate
Farm yield: beta distributionFarm yield: beta distribution Mean = 75% or 125% county meanMean = 75% or 125% county mean St. Dev. set to match 65% APH premium rateSt. Dev. set to match 65% APH premium rate Min = 0, Max = mean + 2 st. dev.Min = 0, Max = mean + 2 st. dev.
Farm-county correlation = 0.5 and 0.8Farm-county correlation = 0.5 and 0.8 Draw correlated random yields using Draw correlated random yields using
Richardson and Condra’s methodRichardson and Condra’s method
Drawing Correlated Drawing Correlated Pseudo-Random VariablesPseudo-Random Variables
1.1. Calculate L = Cholesky Calculate L = Cholesky decomposition of var-cov matrix decomposition of var-cov matrix given by given by cc, , ff and and fcfc
2.2. Draw nDraw n11 and n and n22 ~ N(0,1) i.i.d. ~ N(0,1) i.i.d.
3.3. Calculate tCalculate tii = L = Li1i1nn11 + L + Li2i2nn22
4.4. Calculate vCalculate vii = = (t(tii) ~ uniform (0,1)) ~ uniform (0,1)
5.5. Calculate yields yCalculate yields yjj = F = Fjj-1-1(v(vii))
Premiums and IndemnitiesPremiums and Indemnities Determine Actuarially Fair Premiums, then Determine Actuarially Fair Premiums, then
apply current premium subsidy ratesapply current premium subsidy rates Indemnities:Indemnities:
IIaphaph = P = Paphaph xx max{ max{aphaphff – y – yff, 0}, 0}
IIgrpgrp = MP = MPgrpgrp x x max{(max{(grpgrpcc – y – ycc)/()/(grpgrpcc), 0}), 0}
IIsdcsdc = I = Iaph aph + I+ Imgrpmgrp
grp c cmgrp aph aph
grp c c
x α μ - y
I = min D max ,0 ,Dα μ - θμ
Federal Premium Subsidy Federal Premium Subsidy RateRate
30
35
40
45
50
55
60
65
70
50 60 70 80 90 100
Coverage Level (%)
Pre
miu
m S
ub
sid
y (%
)
APH
GRP
Revenue and UtilityRevenue and Utility RevenueRevenue
00 = py = pyff
grpgrp = = 00 – M – Mgrpgrp((grpgrp) + I) + Igrpgrp((grpgrp)) aphaph = = 00 – M – Maphaph((aphaph) + I) + Iaphaph((aphaph)) sdcsdc = = aphaph – M – Mmgrpmgrp((aphaph) + I) + Imgrpmgrp((aphaph)) p = price, Mp = price, Mii = premium and I = premium and Iii = indemnity = indemnity
Utility: uUtility: uii = 1 – exp(–R = 1 – exp(–Raaii)) Expected Utility: EU = avg(uExpected Utility: EU = avg(uii) over all i) over all i Certainty Equivalent: CE = –ln(1 – EU)/RCertainty Equivalent: CE = –ln(1 – EU)/Raa
Expected Utility Expected Utility MaximizationMaximization
Assume farmers choose APH coverage Assume farmers choose APH coverage level optimally (maximize expected level optimally (maximize expected utility)utility) For APH aloneFor APH alone For APH as part of SDCFor APH as part of SDC
Fix GRP coverage level at 90% and use Fix GRP coverage level at 90% and use 100% price election for APH, as these are 100% price election for APH, as these are optimal ex anteoptimal ex ante
Find certainty equivalent for all APH Find certainty equivalent for all APH coverage levels to identify EU maxing coverage levels to identify EU maxing aphaph
Scenarios AnalyzedScenarios Analyzed Three Crops: Corn, Cotton, SoybeansThree Crops: Corn, Cotton, Soybeans Two types of countiesTwo types of counties
High risk counties (marginal cropping)High risk counties (marginal cropping) Low risk counties (good cropping)Low risk counties (good cropping)
Two farm types in each countyTwo farm types in each county Below Average (Below Average (ff = 75% of = 75% of cc)) Above Average (Above Average (ff = 125% of = 125% of cc))
Two Measures for Impact of SDCTwo Measures for Impact of SDC Increase in CE ($/ac) compared to APH Increase in CE ($/ac) compared to APH
alonealone Change in optimal APH coverage levelChange in optimal APH coverage level
Corn: Hamilton, IA; Tripp, SD Corn: Hamilton, IA; Tripp, SD YELLOWYELLOWSoybeans: Boone, IA; Becker, MNSoybeans: Boone, IA; Becker, MNGREENGREENCotton: Coahoma, MS; Lubbock, TX Cotton: Coahoma, MS; Lubbock, TX BROWNBROWN
CornCorn SoybeansSoybeans CottonCotton
CountCountyy
TrippTripp HamiltoHamiltonn
BeckerBecker BoonBoonee
LubbocLubbockk
CoahomCoahomaa
MeanMean 56.956.9 176.4176.4 28.328.3 46.246.2 232.0232.0 852852
St St DevDev
18.618.6 28.328.3 8.438.43 7.397.39 115.9115.9 212.1212.1
CVCV 32.7%32.7% 16.0%16.0% 29.8%29.8% 16.016.0%%
50.0%50.0% 24.9%24.9%
Farm: high risk (Farm: high risk (ff 75% of 75% of cc))
MeanMean 43.043.0 132.0132.0 21.021.0 35.035.0 174.0174.0 639.0639.0
St St DevDev
37.337.3 38.038.0 12.212.2 10.410.4 199.5199.5 277.3277.3
CVCV 86.7%86.7% 28.8%28.8% 58.0%58.0% 29.729.7%%
115%115% 43.4%43.4%
Farm: low risk (Farm: low risk (ff 125% of 125% of cc))
MeanMean 71.071.0 221.0221.0 35.035.0 58.058.0 290.0290.0 1065.01065.0
St St DevDev
39.539.5 54.654.6 14.314.3 14.414.4 227.1227.1 399.8399.8
CVCV 55.6%55.6% 24.7%24.7% 40.9%40.9% 24.824.8%%
78.3%78.3% 37.5%37.5%
More parametersMore parameters
Coefficient of absolute risk aversionCoefficient of absolute risk aversion Set so risk premium = 30% revenue st. Set so risk premium = 30% revenue st.
dev. when no insurance is useddev. when no insurance is used Prices: used APH prices for 2007Prices: used APH prices for 2007
Corn $3.50/buCorn $3.50/bu Soybeans $7/buSoybeans $7/bu Cotton $0.52/lb in TX, $0.53 in MSCotton $0.52/lb in TX, $0.53 in MS
Full GRP payout as % county mean (Full GRP payout as % county mean ()) No guidance in Farm Bill proposalNo guidance in Farm Bill proposal Set equal to APH coverage level: Set equal to APH coverage level: = = aphaph
Indemnity ScheduleIndemnity Schedule
0
10
20
30
40
50
0 20 40 60 80 100
County Yield (%)
Mo
dif
ied
GR
P I
nd
emn
ity 50%
55%
60%
65%
70%
75%
80%
85%
ResultsResults
First plots of certainty equivalent (CE) First plots of certainty equivalent (CE) vs coverage level (vs coverage level (aphaph) to show ) to show derivation of optimal derivation of optimal aphaph and CE for and CE for APH alone and APH with SDCAPH alone and APH with SDC
Bar plots of how SDC affects optimal Bar plots of how SDC affects optimal certainty equivalent and optimal certainty equivalent and optimal coveragecoverage
Summarize general findings Summarize general findings
Corn: Tripp, SDCorn: Tripp, SD ((ff = 0.75 = 0.75cc, , fcfc = = 0.5)0.5)
Optimal Optimal aphaph = 80% w/ APH alone, 75% w/ = 80% w/ APH alone, 75% w/ SDCSDC
110
120
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140
150
160
0 10 20 30 40 50 60 70 80 90
APH Coverage Level (%)
Cer
tain
ty E
qu
ival
aet
($/a
c)
NothingNothing
GRP GRP AloneAlone
APH APH AloneAlone
SDCSDC
420
430
440
450
460
470
0 10 20 30 40 50 60 70 80 90
APH Coverage Level (%)
Cer
tain
ty E
qu
ival
ent
($/a
c)Corn: Hamilton, IACorn: Hamilton, IA ((ff = 0.75 = 0.75cc, , fcfc = =
0.8)0.8)Optimal Optimal aphaph = 85% w/ APH alone and w/ = 85% w/ APH alone and w/
SDCSDC
NothingNothing
GRP GRP AloneAlone
APH APH AloneAlone
SDCSDC
Coverage Level Decrease with SDC (risk Coverage Level Decrease with SDC (risk averse)averse)
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ubsi
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Benefit-Cost Ratio for Govt. Benefit-Cost Ratio for Govt. FundsFunds
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Summary: Impact on Farmer Summary: Impact on Farmer CECE
SDC Welfare Benefit/CE increase ($/ac)SDC Welfare Benefit/CE increase ($/ac) Ranged $5-$23/acRanged $5-$23/ac Larger for growers with above average yields Larger for growers with above average yields
and more correlated with county yieldsand more correlated with county yields Larger benefit in low risk areas for corn and Larger benefit in low risk areas for corn and
cotton, but in high risk areas for soybeanscotton, but in high risk areas for soybeans Corn and cotton benefits similar and larger Corn and cotton benefits similar and larger
than for soybeansthan for soybeans
Summary: APH Coverage Summary: APH Coverage Level Level
Optimal APH coverage level decreaseOptimal APH coverage level decrease Decreased 5-10 percentage points in high Decreased 5-10 percentage points in high
risk corn and soybean areas and cotton risk corn and soybean areas and cotton areas areas
No effect in low risk corn and soybean areasNo effect in low risk corn and soybean areas Implication as shift liability from Implication as shift liability from
individual to areawide policyindividual to areawide policy Reduced potential for moral hazard, fraud, Reduced potential for moral hazard, fraud,
and program abuseand program abuse Lower loss adjustment and administrative Lower loss adjustment and administrative
costscosts
Summary: Government Summary: Government Benefit-Cost RatioBenefit-Cost Ratio
Ratio of farmer CE increase to govt. Ratio of farmer CE increase to govt. subsidy increasesubsidy increase Higher when more correlated w/ county Higher when more correlated w/ county
yieldsyields Higher where optimal APH coverage not Higher where optimal APH coverage not
reducedreduced Higher in low risk corn and soybean areasHigher in low risk corn and soybean areas Lower in high risk corn and low risk cottonLower in high risk corn and low risk cotton
Knight, Coble, and MitchellKnight, Coble, and Mitchell
Report for House Ag Committee’s Report for House Ag Committee’s deliberations on Farm Billdeliberations on Farm Bill
Compared SDC to SGRPCompared SDC to SGRP
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Ben
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Cos
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SGRP
SDC
Knight, Coble, and MitchellKnight, Coble, and Mitchell
Wrote report for House Ag Committee’s Wrote report for House Ag Committee’s deliberations on Farm Billdeliberations on Farm Bill
Plots showing increase in expected Plots showing increase in expected return with SDC for corn, cotton, and return with SDC for corn, cotton, and soybeans for US counties, assuming soybeans for US counties, assuming 65% APH65% APH Expected return = E[Premium – Indemnity]Expected return = E[Premium – Indemnity] Risk neutral, so no risk benefitRisk neutral, so no risk benefit Non-endogenous APH coverage levelNon-endogenous APH coverage level