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

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

I min D max ,0 , Dμ μ

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

50 60 70 80 90 100

Coverage Level (%)

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 20 40 60 80 100

County Yield (%)

ity 50%

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

0 10 20 30 40 50 60 70 80 90

APH Coverage Level (%)

NothingNothing

GRP GRP AloneAlone

APH APH AloneAlone

SDCSDC

0 10 20 30 40 50 60 70 80 90

APH Coverage Level (%)

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)

Tripp Hamilton Lubbock Coahoma Becker Boone

Corn Cotton Soybeans

rfc 0.8

rfc 0.5

Coverage Level Decrease with SDC (risk Coverage Level Decrease with SDC (risk neutral)neutral)

rfc 0.8

rfc 0.5

CE Increase with SDC (risk CE Increase with SDC (risk averse)averse)

rfc 0.8

rfc 0.5

CE Increase with SDC (risk CE Increase with SDC (risk neutral)neutral)

rfc 0.8

rfc 0.5

Govt. Subsidy Increase with SDC (risk Govt. Subsidy Increase with SDC (risk averse)averse)

rfc 0.8

rfc 0.5

Govt. Subsidy Increase with SDC (risk Govt. Subsidy Increase with SDC (risk neutral)neutral)

rfc 0.8

rfc 0.5

Benefit-Cost Ratio for Govt. Benefit-Cost Ratio for Govt. FundsFunds

rfc 0.8

rfc 0.5

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

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

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

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