Whole Farm Income Insurance

C© The Journal of Risk and Insurance, 2011, Vol. 00, No. 0, 1-26DOI: 10.1111/j.1539-6975.2011.01426.x

WHOLE FARM INCOME INSURANCECalum G. Turvey

ABSTRACT

This article employs a mathematical programming model to investigatefarmers’ optimal crop choices under gross revenue insurance, whole farmincome insurance (WFI), the Canadian Agricultural Income Stabilization(CAIS) program, and its modified 2008 program AgrInvest. WFI poses aparticularly interesting problem since the indemnity/premium structure isdependent upon the choice of crops, whereas the choice of crops is simul-taneously influenced by the presence of the whole farm insurance program.Results indicate that farmers will alter farm plans significantly in responseto the type of insurance offered and the level of subsidy.

INTRODUCTION

The advent of modern risk management in agriculture is increasingly becomingfocused on whole farm income insurance (WFI). By WFI it is meant that a singlepolicy is provided, which covers the covariate risk of jointly produced farm cropand livestock enterprises. The insurer and the insured must balance a host of randomvariables including yield risk, price risk, and their correlations that make up the entireprobability complex that combines to form the joint risks between crops. In additioncrops can be grown in a multitude of combinations with new crops being added andremoved, or production patterns defined by crop rotational constraints on production.

Whole farm insurance is a separate and distinct approach to those farm safety netsthat focus on crop-specific insurance, price insurance and stabilization, or enterpriserevenue insurance. Explorations into income insurance in Canada and the UnitedStates have been conducted by Turvey and Amanor-Boadu (1989), Hennessy, Bab-cock, and Hayes (1997), Hennessy, Saak, and Babcock (2003), and Dismukes and Durst(2006), and in a European context by Dı́az-Caneja and Garrido (2009) and Meuwissen,Huirne, and Skees (2003) but none, for a variety of reasons, are satisfactory from aneconomic point of view. The most serious deficiency, and that which is most exploredin this article, is the endogeneity of the insurance decision on crop choices. Theconventional approach is to define a crop mix and then use Monte Carlo simulationto look at the impact of income insurance on risk reduction, but these types of studiesfail to account for how the insurance itself will influence farm plans and strategy.

Calum G. Turvey is the W.I. Myers Professor of Agricultural Finance in the Department ofApplied Economics and Management, Cornell University. He can be contacted via e-mail:[email protected].

1

2 THE JOURNAL OF RISK AND INSURANCE

Perhaps the most thorough study of income insurance to date is by Dismukes andDurst (2006). There they recommend a whole farm approach that does not requiresavings account balances such as Canada’s Canadian Agricultural Income Stabiliza-tion (CAIS) program or income insurance savings in Australia but rather a wholefarm approach that is based on portfolio indemnities and premiums. This is along thelines of the Adjusted Gross Revenue (AGR) and AGR-Lite programs in the UnitedStates, which they describe as whole farm revenue insurance coverage for multipleagricultural commodities under one insurance product. In Canada and the UnitedStates, these whole farm programs use tax information as a base to provide a levelof guaranteed revenue for the insurance period. My interest here is not so much themechanics of how tax filer information is used but the economic consequences ofWFI on farm decisions. In fact, in the forgoing analysis, I ignore the tax filer approachbecause using past tax filer information may not accurately reflect the choices of thepresent and from an economic point of view are probably most valuable as a meansto determine coverage levels rather than indemnities.

Given the interest in WFI in Canada, the United States, Europe, and elsewhere, it isimportant to fully understand how whole farm insurance will affect farm decisions.Nonetheless, there has been scant research done on either the design of WFI (withthe noted exception of Dismukes and Durst, 2006), how income insurance wouldaffect enterprise selection, the effect of subsidy on crop choices, or the impact incomeinsurance might have in terms of decoupling and World Trade Organization (WTO)guidelines.

With these issues in mind, the purpose of this article is to investigate farm portfoliochoice under WFI plans. The particular plans include a gross revenue plan as a pointof comparison, but the real focus is on a generalized indemnity-based whole farm planstylized to the AGR program in the United States and the CAIS and AgrInvest policiesin Canada. Canadian data are used for a typical farm in Manitoba. Perhaps one ofthe most important outcomes of this article is a better understanding of endogenouschoice in optimal portfolio selection under a whole farm insurance regime. To beclear, I am not attempting to define the optimality of insurance design as is often donein the literature (e.g., Ahsan, Ali, and Kurian, 1982; Chambers, 1989; Mahul, 1999,2000) but to determine the optimal choices that farmers might make given the choiceto purchase income insurance relative to no insurance or a gross revenue insurance(GRIP) product. This is of course the fundamental problem facing policymakers inCanada, the United States, and elsewhere.

A second problem this article resolves is in modeling the complexity of WFI. Theproblem of modeling whole farm insurance with endogenous premium determinationhas not to the writer’s knowledge been solved previously. In this article, I show how tostructure a mathematical programming model to account for this complexity. BecauseI wish to examine how farmers will optimize their crop portfolio under various formsof agricultural insurance, and because insurance indemnities are state dependent,I employ a discrete-state stochastic programming (DSP) model minimized to thesecond moment (i.e., variance).

The third problem I contribute to is related to the second and that deals specificallywith how to price whole farm insurance. First, I must distinguish whole farm insur-ance from say crop-specific gross revenue assurance applied to all crops in a portfolio

WHOLE FARM INCOME INSURANCE 3

because it explicitly includes cross-enterprise covariance and other dependencies(such as crop rotations).

The remainder of this article is as follows. In the next section, I provide a reviewof relevant literature and place the problem of WFI in the context of agriculturalpolicy. I then provide the mathematical descriptions of the income insurance andGRIP models. The data sources and use of Monte Carlo simulation of state-space isthen provided, and the results of the models and conclusions follow.

WFI AND WTO CONSIDERATIONS

This article investigates WFI in a Canadian context. It is important to distinguish theCanadian policy from that of the AGR programs in the United States. In Canada,the current AgriStability program is the principal national program for agriculturalincome stabilization, whereas the AGR program is one of a suite of risk managementand insurance programs available to U.S. farmers. Even though each country is re-sponsible for their own classification of their policies, other WTO member countriescan challenge the classification/trade distortion effects of any policy regardless ofits classification. Thus, in a Canadian context, there is considerable political concernfrom growers and government alike as to the decoupled nature of its WFI programs.

The consequences of choice have far-reaching implications into matters of trade,market distortions, wealth accumulation, asset capitalization, and so on. My under-standing to date is quite rudimentary. For example, the portfolio insurance modelsof Turvey and Amanor-Boadu (1989) or Hennessy, Saak, and Babcock (2003) take thecrop mix as exogenous. The notion that farmers will incorporate the parameters of in-surance (allowable coverage and premium subsidy) into their crop planning strategy,which in turn will simultaneously affect the cost of insurance and benefits of subsidy,is not a trivial one, especially in the context of decoupling and the WTO (Baffes andde Gorter, 2004), which is of great concern to the Canadian government and farmorganizations.

The WTO defines decoupled income support as “support for farmers that is notlinked to (is decoupled from) prices or production.” The Uruguay Round AgreementsAct (URAA) lists government financial participation in income insurance and incomesafety net programs as being green box policies, but associated guidelines alsoprohibit net taxpayer transfers (Hart and Babcock, 2002), a condition that wouldnaturally arise if income insurance programs were subsidized. Government financialparticipation in insurance is classified as green box compatible if (1) the insurancerelates to an income shortfall based on a reference period, (2) the payments may notrelate to the type or volume of production (including livestock) or prices (domestic orinternational) applying to such production or to the factors of production employed,and (3) the income loss is more than 30 percent and the amount of payments compen-sate for less than 70 percent of the producer’s income loss (European Commission,2001). It should be noted that Canadian whole farm income programs have beendesigned around these guidelines, but also recognize that the extent by which someprograms are coupled or decoupled in actuality has not yet been tested. In thiscontext, the literature has identified several mechanisms through which decoupledpayments become coupled and effect production in the current period. Decoupledpayments may alter the farmer’s set of risk preferences due to insurance and wealth


effects (Hennessy, 1998), ease credit constraints by increasing total wealth (Burfisherand Hopkins, 2004; Goodwin and Mishra, 2006), or change allocations of land, laborand other inputs (Ahearn, El-Osta, and Dewbre, 2006; Kirwan, 2009; Peckham andKropp, 2010). In addition, there is evidence that agricultural decoupled subsidieskeep farms in production that would otherwise exit the market, leading to inflatedaggregate production (Chau and deGorter, 2005; de Gorter, Just, and Kropp, 2008).

The key factor is that the rules for eligibility and the criteria upon which paymentsare based upon originally (such as the volume of production or use of input orstatus of a farmer) cannot change once the decoupled program is set in place (Baffesand de Gorter, 2004). This may be a near-impossible criteria because such policies,particularly if they are subsidized, will most likely cause some response in eitherinput use (Hennessy, 1998; Pexham and Kropp, 2010) or crop selection (Turvey, 1992).As Chambers (1989) once noted insurance is data to be optimized. Care is required.At one level it would appear that if farmers paid fully an actuarial price, a productionresponse would be decoupled because neither the policy nor its benefits is targeted toany particular crop. Where the problem comes about is when taxpayer funds are usedto subsidize the insurance. If premiums are subsidized, there will be an income effectthat could favor the inclusion of crops in the final farm portfolio that would not haveordinarily been considered, even though the policy was not targeted to the favoredcrops (Turvey, 1992; Hennessy, 2009). Examining how WFI can affect farm enterpriseselection is therefore important not only in the context of agricultural economics butin the practical matters of agricultural policy and trade.

OPTIMIZATION MODELS FOR WHOLE FARM INSURANCE

This study uses variants of a DSP model that is part of the more general family ofcompact factorization introduced in a financial context by Konno, Shirakawa, andYamazaki (1993) and Kawadai and Konno (2001) to solve large state contingent port-folio problems using piecewise linear constraints. Konno, Koshizuka, and Yamamoto(2005) show that the compact factorization approach can also resolve problems withnonconvex constraints (such as the problem of short selling). More generally, theprogramming model used in this article is one in which the correlated risks of farmcrop enterprises are represented by multiple discrete states of nature rather than acontinuous probability distribution.

A DSP model is one in which the correlated risks of farm crop enterprises arerepresented by multiple discrete states of nature rather than a continuous probabilitydistribution. Because states of nature are individually defined this procedure is idealfor examining insurance problems because each state can be modified to includeinsurance indemnities and adjusted for insurance premiums. Although I am onlyinterested in income insurance in this article, the flexibility of DSP can also beused to investigate how farmers might respond to crop insurance, price insurance,combinations of the two and more. Indeed, a limited number of applications tocrop insurance, revenue insurance, and government programs have been developedpreviously using DSP or its variants. These include Seo, Mitchell, and Leatham (2005)who apply direct expected utility maximization (DEUM) to examine the relationshipbetween crop insurance, crop selection, and input usage (see also Kaylen, Loehman,and Preckel, 1989); Turvey (1992) who uses DEUM to examine GRIP in Canada;


Turvey and Baker (1990) who use discrete sequential stochastic programming witha DEUM objective to examine the effects of government programs on credit use; andSkelton and Turvey (1994) who use a target semivariance approach to investigate theeffects of including hay in a GRIP plan. In this article, I examine choices in a single pe-riod primarily because the insurance programs I investigate are based on single-yearcontracts. The first model is used to optimize a base case with no insurance and thesecond optimizes crop selection with enterprise-specific GRIP. The third and fourthvariants are more complex models that show the normative response to whole farminsurance policies in Canada (CAIS and AgrInvest) and the United States (AGR).Here, the payout is based on the choice of all crops rather than on individual crops.

The Base ModelAs a point of comparison, the base model excludes all forms of insurance. The objectivefunction is to minimize portfolio risk across all states of nature using a DSP frame-work. This is distinctively different from the quadratic programming approach usedby Turvey and Amanor-Boadu (1989). Their models solved for the optimum portfoliofirst and then, given the knowledge of the crop plan and associated risks, insurancepremiums and indemnities were assessed second. Thus, the quadratic programmingapproach fails to optimize on both the crop risks and the insurance product, a failurethat can be remedied using the DSP approach I use. The use of DSP is required be-cause later, when I build the gross revenue and whole farm models, the payouts arecontingent on the particular states that emerge and not on the means. Furthermore, itis assumed that only revenue is uncertain, and although the revenue states, R, repre-sent gross margins, the cost structure is deterministic. The base variance minimizingprogramming model is as follows:

Min σ 2p = 1

m

m∑j=1

(π j − E[π ])2

Subject ton∑

i=1

xi = 1, 000

n∑i=1

E[Ri ]xi = K

n∑i=1

R1,i xi − π1 = 0

...n∑

i=1

Rm,i xi − πm = 0.

(1)


DSP models of this form will still provide utility-centric mean variance efficient (E-V)portfolios. In Equation (1), the subscripts i and j represent crop enterprise and riskystate, respectively. Rj ,i represents the state-specific revenue for crop i in state j , andE[Ri ] represents the mean net revenue across all random states. K represents a targetincome level whereas π j represents the income associated with random state j . Theparameter m indicates the number of random states included in the model (in mycase m = 1, 000) whereas the parameter n represents the number of crop choices orfarm enterprises (n = 7 for Manitoba).1

The critical component to the analysis is the generation of the crop revenues Rj ,i . Onethousand possible revenue outcomes were generated using Monte Carlo simulation.The revenues were based on joint price and yield correlations. The actual model alsoimposes a number of crop rotational constraints on the 1,000 acres of land available,although for clarity these are not included in the above representation. The choice ofconstraints was primarily tied to the production of canola which can only be grownon the same plot of land every 4 years to avoid Sclerotinia a fungal disease thatremains in the soil for up to 4 years and can affect canola, field peas, and lentils.2 Theproduction constraints were:

1. Canola acres can be no more than 250 acres and no less than 200 acres;

2. Flaxseed acres can be no greater than canola acres;

3. The total of field peas plus lentil acres must equal canola acres;

4. Acres planted to hard red wheat must exceed acres planted to durum wheat.

5. No constraints were imposed on barley beyond the marginal effects of the explicitconstraints.

These constraints were included in all models that follow, and the revenue states inthe base model were the same for all models. Varying target income levels results indifferent farm portfolios with different risk profiles.

Gross Revenue InsuranceBecause of the historical interest in GRIP, I also build an optimization model to inves-tigate it. In this model, all crops have available a gross revenue option. Although each

1 From a computational viewpoint, a reviewer points out that this formulation (known ascompact factorization of the covariance matrix) should not be applied for the case of m =1,000 and n = 7. If m is much smaller than n, this formulation is attractive for efficiency, butthis is not the case. For the case of m = 1,000 and n = 7, it is recommended to optimize theusual formulation for mean variance efficiency. In the remaining models, the requirementthat insurance payoffs are contingent on particular states of nature the compact factorizationdesign is convenient, effective, and efficient.

2 Further details can be found at http://www.gov.mb.ca/agriculture/crops/diseases/fac07s00.html. The rotational constraints employed were verified by a group of farmers from acrossthe Prairie provinces.


of the revenue states is identical to the base model, any shortfalls receive payments.Because premiums are crop specific each state of nature is net of variable costs, statecontingent indemnities, crop-specific revenue insurance premiums, and subsidy.

Min σ 2p = 1

m

m∑j=1

(π j − E[π ])2

Subject ton∑

i=1

xi = 1, 000

n∑i=1

E[Ri ]xi = K

n∑i=1

(R1,i + Max[Zi − R1,i , 0] − δE[Max[Zi − Ri , 0]])xi − π1 = 0

...n∑

i=1

(Rm,i + Max[Zi − Rm,i , 0] − δE[Max[Zi − Ri , 0]])xi − πm = 0

m∑j=1

Max[Z1 − Rj ,1, 0] − E[Max[Z1 − R1, 0]] = 0

...m∑

j=1

Max[Zn − Rj ,n, 0] − E[Max[Zn − Rn, 0]] = 0.

(2)

The term Max[Zi − Rj ,i , 0] is the crop-specific revenue indemnity at coverage Zi forstate j, and E[Max[Zi − Ri , 0]] is the actuarially fair revenue insurance premium.

WFI and the AGR ModelThe whole farm insurance model is more complex. The first whole farm model is astraightforward portfolio insurance policy that generically resembles the AGR pro-gram in the United States. The program provides an indemnity if farm income fromall sources falls below a prespecified coverage level. The indemnity, which is priced tobe actuarially sound, is equal to the expected value of the indemnities across all statesof nature. In comparison with the enterprise-specific models described above, thewhole farm approach requires the simultaneous selection of the crop mix and deter-mination of indemnities and premiums. In other words, the payouts and premiumsare endogenous to the optimization problem. The whole farm model is structured asfollows:


Min σ 2p = 1

m

m∑j=1

(π j − E[π ])2

Subject ton∑

i=1

xi = 1, 000

n∑i=1

E[Ri ]xi = K

n∑i=1

R1,i xi + Max

[Z −

n∑i=1

R1,i xi , 0

]− δ

m

m∑j=1

Max

[Z −

n∑i=1

Rj ,i xi , 0

]− π1 = 0

...n∑

i=1

Rm,i xi + Max

[Z −

n∑i=1

Rm,i xi , 0

]− δ

m

m∑j=1

Max

[Z −

n∑i=1

Rj ,i xi , 0

]− πm = 0.

(3)

All notations correspond to the revenue insurance model described by Equation (2),except here I include Z, which represents the income coverage level to be protected byincome insurance. In Equation (3), Max[Z − ∑n

i=1 Rj ,i xi , 0] represents the whole farmindemnity payout in any given state of nature and δ/m

∑mj=1 Max[Z − ∑n

i=1 Rj ,i xi , 0]is the premium to be paid given loading factor δ. If δ = 1, the whole farm in-surance premium is actuarially fair. If δ = 0.50, the premium is subsidized by50 percent.3

THE CAIS PROGRAM

The CAIS program was introduced by the Government of Canada as part of theAgricultural Policy Framework and as a replacement for the Net Income Stabilization

3 An anonymous reviewer points out that the structure of the constraints in Equations (3),(4), and (5) may be nonconvex in I and may lead to multiple solutions. Although the Maxarguments can be written in the form of linear constraints with nonnegativity imposed, somenonconvex outcomes may result. The symptom would be multiple solutions for any targetincome level. To ensure that the solutions provided in the results section are stable, all modelswere tested at various target income levels and various insurance coverage levels usingdifferent initial solutions ranging from a zero acreage basis to equal acreage across all crops(and so on). In every case, the identical optimal solution was obtained. In a later section of thisarticle where I maximize expected utility by deriving the absolute risk aversion coefficientfrom the minimization problem income constraint, I also found that the expected utilitymaximizing solutions identically replicated the variance minimization solutions. Thus, whileI recognize the possibility of multiple solutions brought about by nonconvex constraints, myrobustness checks indicate that indeed the solutions provided by the compact factorizationapproach used are indeed global.


Account program. The CAIS program expired in 2007 and a new program composedof AgriInvest + AgStabilize + AgInsure was put in place for 2008 and 2009. Thenewer program is a derivative of the CAIS program but with differentiating featuresthat can be economically meaningful.

The CAIS program is a whole farm insurance program that differs only in themeasurement of payouts and in the premium setting. It is whole farm insurancein the sense that all eligible farm enterprises are included in the mix, and pay-outs are based on the income as a whole. CAIS pays out on accrued income(after adjustments for inventory, receivables, and payables) and is defined by amargin equal to the accrued difference between revenues and eligible expenses.Ineligible expenses include capital costs, depreciation, wages, salaries, and so on.CAIS is a three-tiered program to protect against income losses below a targetedmargin. The targeted margin is normally the average margin over the past 5years although in the present formulation the margin is based upon current mar-ket risks on a mark-to-market basis. The three tiers are mathematically defined asfollows:

tier 1 = 0.50 × Min

[0.15K , K −

n∑i=1

Rj ,i xi

]× Q(

0.85K≤n∑

i=1Rj ,i xi ≤K

)

tier 2 = 0.70 × Min

[0.15K , 0.85K −

n∑i=1

Rj ,i xi

]× Q(0.70K≤∑

Qni=1 Rj ,i xi <0.85K )

tier 3 = 0.8 × Min

[0.7K , 0.70K −

n∑i=1

Rj ,i xi

]× Q( n∑

i=1Rj ,i xi <0.70K

)

I = Min

[0.70

(K −

n∑i=1

Rj ,i xi

), tier 1 + tier 2 + tier 3

]× Q(

0≤n∑

i=1Rj ,i xi <K

),

,(4)

where Q(A) is an indicator function defined by Q(A) = { 1 A is True0 A is False . In words, if income

falls to within 85 percent of the elected margin, the farmer will receive 50 percent ofthe shortfall in tier 1. If the margin is below 85 percent of the elected margin but above70 percent, then tier 2 indemnities pay 70 percent of the shortfall, and if the marginis less than 70 percent of the shortfall, then the farmer will receive an indemnity of80 percent of the shortfall. In other words, the more severe is the loss the greaterweight is put on the indemnity. The final indemnity is equal to the sum of the three-tiered payouts, but the total payout cannot exceed 70 percent of the total shortfallbelow the elected margin.

The actual legislated premium assigned to CAIS is not actuarially sound. In ac-tuality, it is defined as v = 0.85 × Z

1,000 + $55. In other words, the legislated pre-mium is tied to the target income and not the underlying risk. In addition toevaluating portfolio choice with this premium, I also investigate portfolio choice


if premiums are actuarially sound and subsidized at 50 percent of the actuarialrate.

The Canadian AgrInvest PolicyThe 2008 program is to some extent similar to the CAIS program but differs in severalrespects. First, there is no tier 1 payout under the new program. Instead, underAgrInvest, farmers can set aside 1.5 percent of eligible sales into a savings accountand this will be matched by the Government. Under AgriStability tier 2 and tier 3,payouts are combined such that any shortfall below 85 percent of margin will beindemnified up to 70 percent and any negative shortfall would be indemnified to60 percent.4 Finally, AgrInsure provides for multiple peril crop insurance so that cropinsurance payouts can be received even if final margins exceed the target margin butare added to the margin in the event of a whole farm loss to decrease AgriStabilitypayouts. Mathematically, I have:

AgrInvest = 0.015n∑

i=1

R̂ j ,i xi

AgStability = 0.70 × Min

[0.85K , 0.85K −

n∑i=1

Rj ,i xi

]× Q(

0≤n∑

i=1Rj ,i xi <0.85K

)

+ 0.60 × ABS

[0 −

n∑i=1

Rj ,i xi

]× Q( n∑

i=1Rj ,i xi <0

)

I = AgrInvest + AgStability,

(5)

where R̂ j ,i xi represents net eligible sales. The indemnity can also include crop insur-ance if there is a crop insurance payout but not an AgriStability payout; however,in this article, I exclude AgrInsure (the optional addition of crop insurance) to fo-cus exclusively on the whole farm income component. The critical element with theAgrInvest program is the cost to farmers. In essence, for the maximum coverage, thelegislated premium is $4.50 per $1,000 of margin plus a $55 administrative fee. Forexample, a margin of $100,000 will cost the farmer only $450 plus $55 = $505, which isextraordinarily low for the insurable and investment benefit. (Crop insurance underAgrInsure is sold as a separate risk management product.) I investigate CAIS andAgriStability using both the legislated premiums and actuarial premiums. The CAISand AgrInvest programs are optimized using the following model:

4 For 2009–2010, after the work on this article was completed, AgriStability was modified withthe addition of a tier that paid 80 percent on losses between 70 percent and 0 percent of thereference margin, and 70 percent of losses between 85 percent and 70 percent of margins. SeeAgriStability Program Handbook, http://www.afsc.ca/doc.aspx?id=2015. Although this mod-ification would undoubtedly change the numerical benefits, it will not alter the conclusionsfrom this article.


Min σ 2p = 1

m

m∑j=1

(π j − E[π ])2

Subject ton∑

i=1

xi = 1, 000

n∑i=1

E [Ri ] xi = K

n∑i=1

R1,i xi + I1 − δE [I ] − π1 = 0

...n∑

i=1

Rm,i xi + Im − δE [I ] − πm = 0

m∑j=1

I j − E [I ] = 0.

(6)

In Equation (6), I j are the CAIS/AgrStability benefits as defined above, δE[I ] is thecost to the farmer, E[I ] is the actuarial value of the cost, and δ represents a discountor subsidy.

DATA AND ASSUMPTIONS

The representative farm models for Manitoba requires data from multiple sources.The approach used in this study differs from most optimization approaches in itsuse of generating random crop price, yield, and revenue outcomes with MonteCarlo techniques.5 The first step was to generate correlated prices and yields fromdistributions “consistent” with observed price dynamics (a random walk) and crop

5 Random number generation used @RISK V5 (Palisade Corporation, www.palisade.com).Optimization used Microsoft Excel Solver. Excel Solver uses the generalized reducedgradient method to solve for nonlinear problems of the type discussed here. Seehttp://www.solver.com/excel2010/solverhelp.htm. The use of Excel functions within anoptimization model can cause a seemingly convex model as presented in the mathe-matical formulations in this paper to become nonconvex problems. Nonconvex problemscan from time to time be difficult to solve and global optimality cannot be guaranteedfrom an algorithmic point of view. Still, the standard Kuhn–Tucker conditions of the con-vex problem can be checked for optimality, and in all checked cases, they indicated thatthe solution was indeed optimal. Furthermore, when there is uncertainty about whetherthe solution is global, a common test is to start the solution at various initial basic so-lutions and observe whether the same solution emerged. Such testing was done exten-sively in the design phase of this research and in every case the same solution emerged


yield distributions (normally distributed) for a representative Manitoba cash cropfarm. Prices reflect actual conditions in the spring of 2008 and were obtained fromcommon media sources and the Winnipeg Commodity Exchange. Volatility and driftmeasures were obtained from Statistics Canada monthly price series from January1985 through March 2008. The volatility was measured as the standard deviationof the log changes in monthly cash prices. The monthly drift terms were very low,ranging from 0.00149 to 0.00353. For simplicity and consistency, the drift term wasset to 0.002 percent per month or about 0.024 percent per year. It was assumed inall cases that the cash price path over 180 days (7 months) followed a geometricBrownian motion (a random walk), which in turn assumes that prices were log nor-mally distributed. The proximity of the representative farm in Manitoba is assumedto be sufficiently close to the central market in Winnipeg that no additional volatilityor drift was required as basis adjustment. Crop yields were obtained from historicaldata (Statistics Canada, Manitoba Agriculture) and cover the period 1990–2004. Thiswas the only period for which all data were available for all crops. In all cases, cropyields were based on provincial averages that were tested using Palisades’ Best Fitcomputer program. Despite findings of nonnormality in some studies (see Hennessy,2009), the assumption of normality as an approximation to any of the crop yieldscannot be ruled out as a general rule (Zhao, 1992; Turvey and Zhao, 1999) and so forconvenience, and with no loss in generality, I assumed normally distributed yields forall crops. Crop yields represent provincial averages, and although the averages areconsistent with actual individual farm yields, the standard deviations were not. AnOntario study by Turvey and Islam (1995) showed that on average individual farmyields ranged from about 66 percent to 125 percent higher than an “average” yieldmetric. Hence, while keeping mean yields at their historical provincial average, allstandard deviations were increased by 75 percent.6 The data are reported in Table 1.Because I am examining whole farm insurance, the correlation between yields andprices is important in describing the joint price and yield correlations that combine tocapture the covariate relationships between crop gross revenues. Price and yield corre-lations used are reported in Table 2. These correlations were calculated from historicalannual crop yields and harvest prices as published by Statistics Canada (CANSIM).Costs of production (Table 1) were obtained from cost of production and enterprisebudgets prepared by the agricultural ministry in Manitoba and are based on an acrebasis.

regardless of the initial basis. Finally, as is normally expected with any type of quadraticoptimization, the frontiers generated would not be “smooth” as will be illustrated presentlybut rather jagged, whereas cognizant of the general caveat of nonconvex model formula-tions and optimality all evidence suggests that the solutions presented are indeed globallyoptimal.

6 These two assumptions, the normality of yields and the adjustment in standard deviationmay be questioned by some researchers. What I seek here is a representative distribution.Altering the assumptions will not alter the storyline of this article. Nonetheless, to ensurevalidity of the data used, the author met with a group of Western Canadian farmers in 2008who were provided the adjusted data as well as images of the probability distribution. Thefarmers examined the distributions and confirmed agreement with them as being appropriateand representative.


TABLE 1Manitoba Yields and Prices

Manitoba

Mean Std. Dev. Mean Std. Dev. Annualized VariableCrop Yield Yield Price Price Drift Costs

Hard red Tonne 2.38 0.34 6.62 0.24 0.02 149.02Durum wheat Tonne 2.23 0.40 9.78 0.24 0.02 141.72Barley Tonne 3.03 0.42 4.06 0.19 0.02 139.07Dry field peas Tonne 2.11 0.45 6.22 0.22 0.02 150.73Flaxseed Tonne 1.24 0.20 18.12 0.22 0.02 123.60Canola (rapeseed) Tonne 1.49 0.23 13.89 0.21 0.02 192.17Lentils Tonne 1.25 0.32 14.02 0.20 0.02 168.24

Revenue generation was defined by the Monte Carlo simulation of

Ri j = Yi j Pi j − Ci

Yi j = N (E [Yi ] , σ (Yi ))

Pi j = Pi0e(μ− 12 σ 2) 7

12 +σ N(0,1)√

712 ,

(7)

where Yi j is crop yield generated from a normal distribution; Pi0 is the initial springprice as of March 2008; price generation is based on a 7-month growing season; Pi j isthe random commodity harvest price generated by a log normal (Brownian) processwith drift μ, volatility σ , and random deviate drawn from a normal distributionwith zero mean and variance of 1.0; and Ci is the variable cost associated with eachcrop. Each of the optimization models included 1,000 randomly generated discretestates of nature using these correlated price–yield distribution. The base revenuesso generated were used in all optimization models except for GRIP where R∗

i j =Max(Zi , Yi j Pi j ) − Ci − δE [Max [Zi − Ri , 0]]. The reason that net GRIP revenues werecalculated before optimization is because the premiums charged and indemnities paidare crop specific. GRIP is an enterprise-specific insurance product with premiumscalculated in advance and treated as an exogenous value in the GRIP optimizations.The costs of GRIP were obtained using Monte Carlo simulation. These are reportedin Table 3 and are based on 20,000 Monte Carlo revenue replications.

RESULTS

Table 4 provides the mean-variance results for portfolios ranging from $125,000 to$185,000, with and without the subsidy. Here, the policy interest is the extent by whichfarmers could alter their farm plan and crop mix in response to targeted income levelsand policy parameters. All categories are considered relative to the uninsured basecase. Without subsidy WFI, CAIS and AgrInvest are production neutral in the sensethat these plans are virtually identical to the base plan. For example, at a targetof $145,000, the optimum strategy is to grow 38 acres each of hard red and durumwheat; 174 acres of barley; 250 acres of peas, flax, and canola; and 0 acres of lentils. The

14 THE JOURNAL OF RISK AND INSURANCETA

BLE

2Yi

eld

and

Pric

eC

orre

latio

ns:M

anito

ba

Har

dD

urum

Dry

Fiel

dH

ard

Dur

umD

ryFi

eld

Red

Whe

atB

arle

yPe

asFl

axse

edC

anol

aL

enti

lsR

edW

heat

Bar

ley

Pea

Flax

seed

Can

ola

Len

tils

Yie

ldY

ield

Yie

ldY

ield

Yie

ldY

ield

Yie

ldPr

ice

Pric

ePr

ice

Pric

ePr

ice

Pric

ePr

ice

Har

dre

dyi

eld

1.00

0

Dur

umw

heat

yiel

d

0.52

11.

000

Bar

ley

yiel

d0.

846

0.59

81.

000

Dry

fiel

dpe

asyi

eld

0.13

5–0

.102

–0.2

751.

000

Flax

seed

yiel

d0.

797

0.32

10.

627

0.44

51.

000

Can

ola

yiel

d0.

296

0.48

60.

557

–0.2

540.

100

1.00

0

Len

tils

yiel

d0.

801

0.23

40.

517

0.46

40.

679

0.28

01.

000

Har

dre

dpr

ice

0.17

40.

316

0.10

1–0

.109

0.28

0–0

.190

–0.0

231.

000

Dur

umw

heat

pric

e

0.17

40.

316

0.10

1–0

.109

0.28

0–0

.190

–0.0

231.

000

1.00

0

Bar

ley

pric

e0.

267

0.35

70.

213

–0.1

500.

362

–0.1

120.

017

0.97

60.

976

1.00

0D

ryfi

eld

peas

pric

e–0

.192

0.46

2–0

.101

–0.2

18–0

.195

0.14

9–0

.249

0.59

50.

595

0.54

71.

000

Flax

seed

pric

e0.

128

0.17

70.

154

–0.3

390.

117

–0.1

22–0

.069

0.84

70.

847

0.87

90.

526

1.00

0

Can

ola

pric

e0.

127

0.11

4–0

.069

0.28

50.

377

–0.2

360 .

142

0.80

00.

800

0.80

20.

522

0.76

21.

000

Len

tils

pric

e0.

132

0.13

40.

101

–0.1

880.

060

–0.2

13–0

.026

0.55

70.

557

0.50

10.

017

0.39

90.

185

1.00

0


TABLE 3Manitoba Computed Insurance Cost at 80%

Manitoba Hard Durum Dry Field CanolaPremiums Red Wheat Barley Peas Flaxseed (Rapeseed) Lentils

Manitoba revenueinsurance 80%

10.16 18.02 7.70 14.23 17.74 17.37 26.14

Manitoba revenueinsurance 90%

17.63 28.97 14.37 21.07 29.40 29.34 35.87

specific mix reflects the income and skewness preferences as well as the productionconstraints. The commodity specificity of GRIP in contrast grows 51 acres of hard redwinter wheat, 51 acres of durum, 196 acres of barley, 203 acres of peas, 234 acres of flaxand canola, and 0 acres of lentils.7 The E-V frontiers for base, CAIS, and AgrInvestmodels are provided in Figure 1 and GRIP and WFI in Figure 2. These clearly showthe relationship between risk, return, insurance product, and subsidy.

The effect of subsidy can also be seen in Table 4. With a 50 percent subsidy onpremiums the GRIP solution includes no wheat; 309 acres of barley; 230 acres of peas,flax, and canola; and no lentils. The CAIS program reduces flax from 250 to 187 acreswhereas barley increases from 173 acres to 413 acres. Peas and canola are reducedfrom 250 acres to 200 acres. Similarly, WFI grows 416 acres of barley, 200 acres each offield peas and canola, and 184 acres of flax. When the legislated premium is chargedfor CAIS, a further shift is observed with 545 acres of winter wheat, 4 acres of durumwheat, 200 acres of peas, 51 acres of flax, and 200 acres of canola. The skewness impactis evident. The base case solution has skewness of 0.385. The GRIP program has anunsubsidized skewness of 1.101 and with the subsidy it is 1.072, Downside risk,which reaches a minimum of $−167,255 for the base model, increases to $40,623 withunsubsidized GRIP and $38,739 when subsidized. Likewise, AgrInvest has skewnessof 1.23 with a range of $11,080 to $498,276 when unsubsidized, 1.347 with a rangeof $25,551 to $475,666 when subsidized by 50 percent, and skewness of 1.518 witha range from $38,070 to $451,224 when subsidized at the nonactuarial legislatedrate.

In general, subsidy increases the skewness of the distribution while increasing thelower bound loss. Note that WFI has the highest minimum value. WFI is the onlypolicy that truly truncates the risk at the 80 percent coverage level. The three-tiereddesign of CAIS and AgrInvest allows some slippage of downside risk. Figure 3shows the cumulative distribution functions for WFI and GRIP, and illustrates therelationship between risk reduction and premium subsidization.

7 To place commodity specificity in context, I ran the GRIP model with only wheat and bar-ley targeted for insurance. At $145,000, the final solution was 200.00, 200.00, 0.00, 113.36,200.00, 200.00, and 86.64 acres for hard red, durum, barley, field peas, flax, canola, and lentils,respectively. With GRIP and insurance targeted to grains alone, the portfolio effects areevident.


TABLE

4O

ptim

umFa

rmPl

ans,

Man

itoba

With

Con

strai

ned

Cro

pC

hoic

e

Win

ter

Dur

umM

ean

Whe

atW

heat

Bar

ley

Peas

Flax

Can

ola

Len

tils

Ind

emni

tyPr

emiu

mSt

d.D

ev.

Max

.M

in.

Skew

Bas

em

odel

125,

000

00

450

200

150

200

090

,960

476,

289

–123

,626

0.40

214

5,00

038

3817

425

025

025

00

100,

360

533,

503

–132

,776

0.38

516

5,00

012

512

50

1725

025

023

311

7,07

762

9,07

2–1

52,3

000.

402

GR

IP50

%12

5,00

00

049

120

010

920

00

12,0

316,

016

74,1

2844

6,89

514

,249

1.03

314

5,00

00

030

923

023

023

00

13,7

486,

874

79,2

5348

7,48

938

,739

1.07

216

5,00

097

9756

136

250

250

114

16,8

568,

428

88,5

1453

7,86

363

,525

1.13

7

GR

IP10

0%12

5,00

00

045

120

014

920

00

12,4

4112

,441

75,5

6845

3,14

815

,308

1.04

514

5,00

051

5119

620

323

423

430

14,8

5214

,852

82,6

4749

9,41

940

,623

1.10

116

5,00

012

512

50

2525

025

022

518

,542

18,5

4293

,989

552,

288

59,5

741.

168

Inco

me

50%

125,

000

00

548

200

5220

00

29,0

4214

,521

57,5

7342

1,09

785

,479

1.80

214

5,00

00

041

620

018

420

00

29,9

4914

,974

62,7

3747

5,40

210

1,02

61.

748

165,

000

7878

9325

025

025

00

32,6

4216

,321

69,8

5352

6,51

911

5,67

91.

727

185,

000

125

125

00

250

250

250

38,0

8219

,041

79,9

6761

5,66

112

8,95

91.

756

Inco

me

100%

145,

000

3838

174

250

250

250

026

,353

26,3

5372

,300

507,

150

89,6

471.

543

155,

000

125

125

020

925

025

041

28,1

6428

,164

77,3

6953

8,61

695

,836

1.55

616

5,00

012

512

50

1725

025

023

331

,168

31,1

6884

,155

597,

978

100,

832

1.57

2

CA

ISle

gisl

ated

145,

000

545

40

200

5120

00

37,7

4470

857

,378

474,

702

–20,

889

1.62

216

5,00

00

044

020

016

020

00

39,3

7979

857

,543

468,

247

1,85

91.

597

185,

000

1717

216

250

250

250

042

,820

888

62,0

4050

6,49

610

,265

1.60

320

5,00

012

512

50

144

250

250

106

47,6

6397

869

,261

551,

657

13,0

691.

632

215,

000

125

125

08

250

250

242

50,6

271,

023

73,9

3457

2,33

711

,701

1.62

0

(Con

tinu

ed)


TABLE

4C

ontin

ued

Win

ter

Dur

umM

ean

Whe

atW

heat

Bar

ley

Peas

Flax

Can

ola

Len

tils

Ind

emni

tyPr

emiu

mSt

d.D

ev.

Max

.M

in.

Skew

CA

IS50

%12

5,00

00

054

120

059

200

027

,092

13,5

4660

,903

423,

932

–41,

330

1.35

114

5,00

00

041

320

018

720

00

29,4

4614

,723

64,6

4846

2,46

1–2

6,65

01.

404

165,

000

7979

9225

025

025

00

32,7

0016

,350

71,4

3350

7,73

4–2

2,93

61.

421

184,

000

132

132

00

245

245

245

37,3

4918

,674

82,1

7155

5,07

2–2

8,88

21.

417

CA

IS10

0%12

5,00

00

044

920

015

120

00

23,3

3623

,336

67,3

4644

2,71

5–5

0,35

91.

265

145,

000

3939

173

250

250

250

025

,897

25,8

9773

,979

487,

268

–45,

362

1.27

716

5,00

012

512

50

1625

025

023

430

,118

30,1

1886

,594

542,

082

–53,

906

1.28

5

Agr

Inve

stle

gisl

ated

145,

000

00

524

200

7620

00

31,5

7161

061

,617

451,

224

38,0

701.

518

165,

000

00

393

202

202

202

032

,982

686

66,5

3549

1,17

650

,172

1.49

118

5,00

010

210

262

245

245

245

036

,009

763

73,8

4053

7,51

957

,996

1.49

720

5,00

012

512

50

1225

025

023

840

,655

839

83,5

8258

2,84

762

,855

1.49

8

Agr

Inve

st50

%12

5,00

00

053

620

064

200

025

,713

12,8

5665

,125

434,

925

13,8

821.

369

145,

000

00

405

200

195

200

027

,017

13,5

0970

,313

475,

666

25,5

511.

347

165,

000

9696

5925

025

025

00

29,6

8314

,841

78,4

5252

3,97

331

,889

1.34

818

0,00

016

116

10

022

622

622

633

,239

16,6

2088

,256

564,

686

32,9

451.

372

Agr

Inve

st10

0%12

5,00

00

044

920

015

120

00

22,8

7622

,876

71,4

2845

2,41

14,

142

1.24

914

5,00

039

3917

325

025

025

00

24,8

6624

,866

78,9

6449

8,27

611

,080

1.23

116

5,00

012

512

51

1525

025

023

528

,842

28,8

4292

,127

554,

294

11,1

341.

251

Not

es:O

ptim

izat

ion

min

imiz

edri

sksu

bjec

tto

ala

nd,g

row

ing

cons

trai

nts,

and

inco

me

cons

trai

nts.

The

base

case

excl

udes

allf

arm

prog

ram

s.G

RIP

isa

reve

nue

insu

ranc

epl

anth

atpr

ovid

esin

dem

niti

esif

the

ind

ivid

ual

crop

mar

gin

falls

belo

w80

%of

spec

ified

expe

cted

crop

mar

gin.

Inco

me

Insu

ranc

eis

aw

hole

farm

insu

ranc

epl

anw

ith

who

lefa

rmco

vera

geat

80%

ofta

rget

inco

me.

Agr

Inve

stan

dC

AIS

are

cons

truc

ted

acco

rdin

gto

the

Can

adia

nA

gric

ultu

ralI

ncom

ean

dSt

abili

zati

onpr

ogra

man

dit

s20

08m

odifi

cati

on,r

espe

ctiv

ely.

Opt

imiz

atio

nba

sed

on1,

000

join

tly

det

erm

ined

rand

omou

tcom

es.


FIGURE 1E-V Efficient Frontiers

Notes: The figure shows the E-V frontiers for the CAIS and AgrInvest programs in comparison tothe base. The two most leftward frontiers represent the current policy with legislated premiumsfar below actuarial values. The second and third curves from the right represent efficiencyfrontiers with the farmer paying 100% of the actuarial premium. The combined risk reductionand income effects discussed in the text are evident. As subsidy increases, farmers can acceptlower risk portfolios in order to achieve the same target income.

PORTFOLIO CHOICE AND EXPECTED INDEMNITY

Table 4 also provides the expected indemnities and premiums for the income insur-ance models when the insurance is charged an actuarial rate, subsidized by 50 percentand in the cases of CAIS and AgrInvest the much lower legislated rate (between ap-proximately $600 and $900 total). These are illustrated in Figure 4. The indemnitiesreported are the mean insurance payouts that would have occurred under each of theprograms across the 1,000 states of nature used in the model build. Under the indem-nity columns, the reported values are equal to the actuarial premiums by definition.Under the premiums columns, the numbers reported are the total premiums chargedwith 100 percent indicating that the farmer pays the full premium, 50 percent forhalf the actuarial premium, and then the legislated rate. For example, the premiumfor WFI with coverage at 80 percent of $145,000 under the risk minimization modelwould be $26,353 in premium to receive $26,353 of expected indemnity. At 50 percent,the premium is $29,949 but the farmer pays only $14,974. The premiums under thelegislated plans are well below the actuarial structure of risk. For CAIS at $145,000,the farmer would pay only $708 to receive $37,744 in expected indemnity and withAgrInvest they would pay only $610 to receive $31,571 of expected indemnity.


FIGURE 2E-V Frontiers for Gross Revenue Insurance and Whole Farm Insurance at the 50% Level

Notes: The figure illustrates the benefits of risk reduction with the whole farm insurance E-Vfrontier lying to the left of the GRIP frontier. The effect is largely due to the fact that wholefarm income insurance completely truncates the portfolio probability distribution (see alsoFigure 3) whereas the portfolio standard deviation for GRIP is based on the truncated standarddeviations associated with individual crops.

Table 4 confirms the various propositions discussed. First, farmers will respond tothe premium structure. The greater the subsidy, the greater will be the willingness offarmers to accept strategies with lower downside risk and hence will receive higherexpected indemnities. For example, under the EV strategy for CAIS at a target incomeof $145,000, the expected indemnities are $25,897 when the farmer pays the actuarialpremium, $29,446 when the premium is subsidized by 50 percent and $37,744 whenthe much lower legislated premium is charged. Second, as target income increases sodoes the expected indemnity. This is an expected result since higher income impliesgreater risk. For example, under AgrInvest with the actuarial rate, the EV solutionshows expected indemnities increasing from $22,876 to $28,842 as target incomeincreases from $125,000 to $165,000.

CONSTANT ABSOLUTE RISK AVERSION (CARA) AND EXPECTED UTILITY MAXIMIZATION

In the discussion above, I observed that in order to meet a fixed target income underthe E-V rule, farmers will select lower risk portfolios. How this translates into anexpected utility framework is discussed in this section. I do this with a simple mod-ification of the objective function by substituting the standard utility maximization


FIGURE 3Cumulative Distribution Functions for Base Model, Income Insurance, and GRIP at TargetIncome of $155,000

Notes: The nature of optimization affects the probability distributions of outcomes. The effectof GRIP relative to the base is to reduce the downside risk and because of the subsidy oninsurance the GRP, CDF lies mostly above the base model. Whole Farm Income providesgreater risk reduction, with the distribution truncated at the 80% of target coverage level. Withgreater risk reduction the actuarial premium is higher for Whole Farm Income Insurance. Thesubsidy effect is evident with the Whole Farm Income insurance CDF lying above the GRIPCDF.

objective,

EU [K ] = E [K ] − α

2σ 2, (8)

for variance and removing the income constraint. It is well known that the dualitybetween the risk minimizing model and this utility maximization model can be rec-onciled by extracting the coefficient of CARA from (two times the inverse of) theshadow price of the income constraint generated from the variance minimizationmodel, and using this measure for α in EU[K ]. For example, the implied CARA coef-ficient extracted from the inverse of the shadow price on the income constraint fromthe base model with a $145,000 income target is 0.0000159. Applying this coefficientto the expected utility maximizing objective will provide an identical solution.

As shown in Table 4, solving and comparing the WFI (and other) models for a fixedtarget income without a premium subsidy resulted in a crop plan identical to the


FIGURE 4Expected Indemnities for E-V Solutions

Notes: The figure shows the level of indemnities for E-V solutions on AgrInvest, Whole FarmIncome (WFI), and GRIP. WFI at 50% and AgrInvest at the legislated premium correspond withthe higher expected indemnity. For AgrInvest and WFI, expected indemnities increase withsubsidy that strongly suggests that an unintended consequence of subsidy is that farmers willselect lower income strategies and rely on subsidy to meet target income. This is not the casefor GRIP, which shows that an increased subsidy actually lowers expected payouts.

base plan. The subsidy effect, however, altered the strategy. The question I seek toanswer in this section is how solutions would change if that base-solution CARAwas applied to the utility maximization problem, that is, allowing farm income tochange while holding CARA constant at α = 0.0000159. Figure 5 shows the basefrontier as well as the fair priced and subsidized frontiers for WFI. When the modelswere reconstructed to solve the expected utility problem (Equation (8)), the basemodel resulted in a portfolio with expected income of $145,000 as it should, but whenapplied to WFI, the solution resulted in a different crop mix with $153,936 expectedincome. When insurance was offered at a 50 percent subsidy, a different portfolioemerged with expected income of $169,092. These two solutions were also solutionson the base E-V frontier and these are marked in Figure 5. What is important is thatthe implied risk aversion coefficients measured from the base frontier for the WFIsolutions are different from 0.0000159. For the subsidized WFI, the equivalent basesolution is defined by CARA = 0.0000107 and expected income $152,874. For theunsubsidized WFI, the base solution is defined by CARA = 0.0000104 and E [K] =$153,871. These are of course not true coefficients of risk aversion. The true portfoliosare those defined along the WFI frontiers, but what this illustrates is that WFI may


FIGURE 5Expected Utility and Whole Farm Income Insurance

Notes: This figure shows the expected utility maximizing portfolios for CARA of 0.0000159.For convenience of illustration, marginal utility is represented by the convex curves tangentto the frontiers. The figure shows that farmers will choose different portfolio proportions withdifferent risk profiles depending on the insurance parameters, i.e., subsidized or not subsidized.Portfolio that lies on the two whole farm income frontiers also lie on the base EV frontier. Theimplied CARA coefficients on the base frontier are 0.0000104 for unsubsidized insurance and0.0000107 for subsidized insurance. Even though the optimal portfolios were selected usingCARA of 0.0000159, the observed portfolios when transposed onto the base EV frontier indicatelower levels of risk aversion, and the appearance that insurance encourages farmers to be lessrisk adverse.

result in changes to farm plans and strategies that give an “appearance” of decreasingrisk aversion. This also raises a salient issue regarding moral hazard. These portfolioshifts are due to optimizing behavior. I have made no assumption about informationalasymmetries between the insured and the insurer so these portfolio shifts shouldnot be interpreted as evidence of moral hazard. There is a clear difference betweenoptimizing on probabilities and insurance parameters as is illustrated here, and thealtering of probabilities (or farm plans) without the insurer being informed.

DISCUSSION, CONCLUSIONS, AND POLICY RECOMMENDATIONS

This article has investigated the effects of WFI on farm portfolio choice. A repre-sentative Manitoba farm model was used for crops grown, prices received, inputspurchased, and growing conditions including crop rotational constraints. The main


problem addressed in this study was to determine how safety net programs such asGRIP, WFI, CAIS, and AgrInvest affected crop choices. To do this, a discrete stochasticprogramming model in which the objective is to minimize risk was developed. It isassumed that the probability states are fully observed by both the insured and theinsurer. There are two novel contributions here. First, the optimization models endo-genized the insurance choice. That is, if farmers know the parameters of the wholefarm insurance policy, then it is possible that they would alter their management prac-tices to optimize the insurance decision. Hence, the model employed simultaneouslysolved for the insurance premium and crop choice.

The results provide justification for some concerns raised about the neutrality ofthese programs in the context of decoupling. When unsubsidized, income insurance,CAIS, and AgrInvest provide identical solutions to the uninsured strategy. It is theincremental response to subsidy that creates the wealth effect that may impact or dis-tort markets. Whether whole farm income policies are amber is debatable. On the onehand, because there is no specificity in the programs (i.e., one crop is not specificallytargeted over another) whole farm programs are seemingly decoupled. The fact thatfarmers with different degrees of risk aversion, as indicated by the election of lowversus high target incomes, would optimize differently, bolsters this argument. Onthe other hand, if farmers are generally homogenous in their attitudes toward risk,then many farmers optimizing according to the same rules may give the appearanceof coupling and thus provide cause for a complaint under WTO. In terms of moralhazard and adverse selection, my models by definition and construction assumedfull informational symmetry. However, it is important for insurers and researchers todistinguish between what might be interpreted as moral hazard and what is actuallymoral hazard. The results of this study show that insurers, policymakers, andacademics ought not to be surprised when new products result in farmers altering ordeviating from previous strategies. Moral hazard versus optimizing behavior are sep-arated by more than a fine line and must be distinguished in any study of agriculturalinsurance.

On a more pragmatic level, the method employed in the study may too provide somebenefits. The existing AgrInvest program uses the past 5 years of production historyand tax filer information to establish margin whereas the AGR programs in the UnitedStates pays indemnities based on Schedule F tax filer information. I have bypassedthis aspect of the actual programs in this study relying instead on Monte Carlosimulations to correlated prices and yields with prices modeled as a random walkand yields assumed normal. The idea of using a random walk is a departure from thehistorical tax performance stated in Canadian and U.S. legislation. Nonetheless, theuse of mark-to-market prices in the simulation ensures that whatever the portfoliooutcomes they are based on current price paths and risk and are not distorted byhistorical precedent.

As WFI evolves in Canada, the United States, Europe, and elsewhere, further ques-tions will no doubt be raised. One will be on the general efficacy of the programsover time in terms of risk reduction and improved livelihoods. Others (such as Seoet al., 2005) should examine the impacts of input usage to determine what effect, ifany, WFI has on both input and output decisions.


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Whole Farm Income Insurance