Asymmetric Information in the Market for Yield and Revenue Insurance

Products. Shiva S. Makki and Agapi Somwaru. Market and Trade Economics

Division, Economic Research Service, U.S. Department of Agriculture. 

Technical Bulletin No. 1892

Abstract

This report analyzes farmers’ choice of crop insurance contracts and tests for the

presence of asymmetric information in the market for multiple yield and revenue

insurance products. Farmers’ risk characteristics, their level of income, and the cost

of insurance significantly affect their choices of yield and revenue insurance products as well as their selections of alternative coverage levels. Empirical analysis

indicates that, in the presence of asymmetric information, high-risk farmers are

more likely to select revenue insurance contracts and higher coverage levels. The

results also indicate that premium rates do not accurately reflect the likelihood of

losses, implying asymmetrical information in the crop insurance market.

Keywords: Asymmetric information, adverse selection, crop insurance, revenue

insurance, risk management. 

Acknowledgments

This research was funded by the Risk Management Agency (RMA), USDA.

We gratefully acknowledge helpful comments received from all reviewers. We are

most thankful to Joy Harwood (ERS) for her detailed, constructive, and extremely

helpful comments. We thank James Driscoll (RMA), Robert Dismukes (ERS), and

Richard Heifner (ERS) for their insightful reviews and comments throughout the

study. We also thank Art Barnaby (Kansas State University), Keith Coble 

(Mississippi State University), Barry Goodwin (North Carolina State University),

Randall Schnepf (ERS), and John Dunmore (ERS) for their valuable suggestions.

The authors also wish to thank Martha R. Evans, Wynnice Pointer-Napper, and 

Victor B. Phillips, Jr., for editorial and production services. 

1800 M Street, NW

Washington, DC 20036-5831 April 2001
ii  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

Contents

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Asymmetric Information in Insurance Markets . . . . . . . . . . . . . . . . . . . . . . . .2

Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

Market Equilibria in Insurance Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

Market Equilibrium with Full Information . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

Market Equilibrium with Asymmetric Information . . . . . . . . . . . . . . . . . . . . . .4

The Crop Insurance Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Crop Yield and Revenue Insurance Contracts . . . . . . . . . . . . . . . . . . . . . . . . .9

Description of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Empirical Model and Hypotheses Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

Generalized Polytomous Logit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

Three-Stage Least-Squares Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Hypotheses Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Choice of Insurance Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Choice of Coverage Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

Empirical Evidence on Market Signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

Empirical Evidence on Adverse Selection . . . . . . . . . . . . . . . . . . . . . . . . . . .23

Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

Limitations of the Study and Scope for Further Research . . . . . . . . . . . . . . .28

End Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  iii

Summary

This report examines the effects of asymmetric information on U.S. crop insurance

markets when a portfolio of yield and revenue insurance products is offered to

farmers. The asymmetric information modeling framework developed in health and

automobile insurance markets is applied to the crop insurance market in Iowa,

where several yield and revenue products were offered to farmers in 1997. The

report indicates inaccurate assessment of individual risks and finds evidence of

asymmetric information in the market for individualized crop insurance products.

Since the mid-1990’s, a number of new crop insurance products have become available to farmers for managing yield and revenue risks. At the same time, several legislative changes have contributed toward increasing the level of farmers’ participation and widening the use of crop insurance as a risk management tool. In some

sense, these new insurance products might be very instrumental in increasing efficiency in the U.S. crop insurance market by meeting the needs of different producers. At issue is whether the introduction of the new products increases or decreases

asymmetric information problems in crop insurance markets. This study, by analyzing the factors that influence the choice of alternative insurance products and coverage levels, attempts to understand the implications of asymmetric information for

assessing risk and setting premium rates in the market for crop insurance.

A Generalized Polytomous Logit model is used to analyze producers’ choices of

insurance products, and a three-stage least-squares model is specified to analyze

premium rates and the choice of coverage levels. Results indicate that high-risk

farmers are more likely to choose revenue insurance and higher coverage levels.

High-risk farmers are also more likely to choose an insurance product where the

guarantee and indemnity are based on individual yields for the producer, rather

than a product based on county yields. Results also suggest that high-income

farmers are more likely to purchase revenue insurance products and higher coverage levels.

Non-parametric methods are used to test the presence of asymmetric information.

The results suggest that individual risk types are not assessed accurately and that

premium rates do not reflect the likelihood of losses. Results show that, for individual yield and revenue insurance products, low-risk farmers are overcharged and

high-risk farmers are undercharged for comparable insurance contracts. In the

presence of asymmetric information, premium rates charged to different risk types

are likely to suffer from averaging.

A method of assessing an individual’s risk, which includes not only average yield

and revenue but also yield and revenue variability, might be the key to reducing

rating inequities for individually based insurance products. Even though the analysis is limited to Iowa corn and soybeans, the findings provide useful insights into

preferences of farmers of various risk types in choosing among alternative insurance contracts. Analysis of more years, crops, and regions would be useful in comparing results to ascertain the robustness of the findings. 
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  1

Introduction

Rapid expansion has occurred since 1996 in the number of new federally backed crop insurance products

offered to farmers. They include several new revenue

insurance products that bring new challenges to evaluating the performance of the multiple-product crop

insurance market. In some sense, these new insurance

products might be very instrumental in increasing efficiency in the U.S. crop insurance market by meeting

the needs of different producers. At issue is whether

the introduction of the new products increases or

decreases informational asymmetries in crop insurance

markets. This study is the first attempt to examine the

effects of asymmetric information on U.S. crop insurance markets when a portfolio of yield and revenue

insurance products is offered to farmers. We analyze

the crop insurance market in Iowa, where multiple

yield and revenue insurance products were offered to

corn and soybean farmers in 1997.

Farmers choose an insurance product based on expected

benefits derived from the product. It is often argued that

farmers, who produce under uncertainty, know more

about their own expected losses (benefits) than can be

discerned by the insurer, as farmers are better informed

about their distribution of yields. Such asymmetry of

information can give rise to the problem of adverse

selection, with negative consequences for the efficient

functioning of the crop insurance market. In the presence of adverse selection the insurance provider fails to

accurately assess the risk of loss and, therefore, is

unable to set premiums commensurate with risk. Ideally, crop insurance premiums should be set such that

they reflect the likelihood of losses. However, such premiums are difficult to establish in the presence of asymmetric information, where insurance firms are unable to

accurately distinguish among different risk types. Such

asymmetries exist because of differences in inherent

farm risks, arising from factors such as the farm’s location characteristics and farmers’ managerial abilities.

This report analyzes the characteristics of the crop

insurance market under asymmetric information and

investigates the presence of adverse selection. The specific issues addressed in this report include: (1) assessment of individual farm risk when limited information

is available to the insurer on the farm and farmer, (2)

analysis of factors that influence farmers’ choices of

alternative insurance products and coverage levels; (3)

investigation of the presence of heterogeneous risk

types in the insurance pool and the possibilities of risk

type signaling through contract selection; and (4) testing for adverse selection.

Asymmetric Information in the 

Market for Yield and Revenue 

Insurance Products

Shiva S. Makki and Agapi Somwaru
2  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

Asymmetric Information in

Insurance Markets

Asymmetric information manifests itself primarily in

terms of adverse selection and moral hazard. Adverse

selection is caused by the inability of the insurer to

accurately rate the risk of loss, while moral hazard is

caused by the hidden actions of the insured which

increase the risk of loss. In this study, we assume that

the insured individual cannot affect his/her distribution

of losses, which limits the analysis of asymmetric

information to adverse selection.

Theoretical and empirical studies in automobile and

health insurance markets have shown that adverse

selection reduces the consumption of insurance by

low-risk individuals, and results in the transfer of

income from low-risk to high-risk insureds. The theoretical works of Akerlof (1970), Rothschild and

Stiglitz (1976), Miyazaki (1977), and Wilson (1977)

describe the insurance market under asymmetric information. Miyazaki and Wilson demonstrate that when it

is impossible or highly expensive to distinguish

between high- and low-risk insurance applicants, the

insurer prices insurance contracts at an average premium for all individuals. This results in undercharging

high-risk customers and overcharging low-risk customers for similar contracts. Empirical evidence in

automobile and health insurance markets generally

supports the predictions of these theoretical models

(Browne, 1992; Browne and Doerpinghaus, 1993;

Puelz and Snow, 1994).

Several studies have documented the implications of

the presence of adverse selection on the performance

of crop insurance in the United States. Ray (1974)

argues that adverse selection in crop insurance markets

can make the industry less self-sustaining if only highrisk farmers buy insurance, as evidenced in the U.S.

market for crop insurance. Skees and Reed (1986)

show that the potential for adverse selection depends

on a farmer’s subjective assessment of expected yield

and variability of yield. They argue that premium rates

based only on mean crop yields can lead to adverse

selection, particularly when the variance of yields fluctuates considerably among farms.

Goodwin (1993) illustrates the effects of adverse selection on the actuarial performance of the U.S. crop insurance program, stating that only farmers whose risk is

above average are likely to buy insurance. He concludes

that high-risk producers are less responsive to premium

changes because of adverse selection. In a review of the

crop insurance program in the United States, Goodwin

and Smith (1995) indicate that there is considerable evidence of adverse selection, and that adverse selection is

a direct consequence of insurers’ inability to set premiums commensurate with the level of risk.

In a recent study, Just et al., (1999) examined the

adverse selection problem in the crop insurance market

using nationwide data on the U.S. insurance program.

They argue that adverse selection occurs when actual

premium rates fail to reflect farmers’ expected indemnities. Their results suggest that participating farmers

tend to be those with higher expected indemnities, as

farmers with lower expected indemnities are priced out

of the program. They conclude that when the insurance

market is concentrated with high-risk farmers, the

result can lead to market failure.

The studies cited above narrowly focus on adverse

selection when a yield insurance product was offered to

farmers when participation was quite low. In addition,

none of the crop insurance studies explicitly test for

adverse selection. This study tests for adverse selection

when both the number of crop insurance products

available and farmer participation are increasing. We

apply the asymmetric information modeling framework

developed in health and automobile insurance markets

to crop yield and revenue insurance markets. Our

empirical results indicate that farmers’ decisions to buy

yield or revenue insurance are significantly affected by

the risk they face, their level of income, and the cost of

insurance. Our analysis also indicates that inaccurate

assessment of individual risks results in overcharging

low-risk farmers and undercharging high-risk farmers

for comparable contracts. We find evidence of asymmetric information in the market for individualized

yield and revenue insurance products.
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  3

Theoretical Considerations

We begin by describing how the market attains equilibrium using the demand for and supply of insurance

contracts in a well-functioning competitive environment. Consider an individual who purchases an insurance contract to smooth the flow of his/her income

across different states of nature. For simplicity, we

assume two states of nature, no loss and loss. We also

assume that the insured individual maximizes his/her

expected utility. In the absence of insurance, an individual’s preference for income in these two states of

nature is given by:

(1) V(m, p) = (1-p) U(m) + p U(m - d)

where m is income, p is the probability of loss, and d

is the reduction in income or the amount of loss. U(•)

represents the utility of money income, while (1-p)

indicates the probability of not incurring a loss. When

an individual purchases an insurance contract, the

function describing his or her preference for income in

the two states of nature is:

(2) V(a1, a2; p ) = (1-p) U(m-a1) + p U(m-d-a1+a2)

where a1 is the premium cost, a2 is the payoff (indemnity) from the insurance contract in the case of loss,

and V is the expected utility. An insurance contract

may be viewed as a promise by the insured to pay an

amount a1 to the insurer, in return for a promise by the

insurer to pay indemnities a2 if a loss occurs. We

assume that individuals are risk averse (U¢ < 0) and,

thus, that V is quasi-concave. From all the contracts

offered, the individual will choose the one that maximizes his/her expected utility, V.

Assuming that insurance companies are risk neutral

(concerned only with expected profits) and that returns

from insurance contracts are random, an insurance

contract sold to an individual who has the probability

of incurring a loss of p, is worth:

(3) p(a1, a2; p) = (1-p)a1 - p(a2-a1 ).

If insurance contracts are sold in a full informationcompetitive market, then the expected profits are zero:

(4) (1-p)a1 - p(a2-a1 ) = 0.

Equation 4 ensures that the expected benefit, (1-p)a1,

is equal to the expected cost, p(a2-a1 ), of the firm,

assuming no administrative costs.1 In other words,

equation 4 represents the set of contracts that have

actuarially fair premium rates. 

Market Equilibria in Insurance Markets

In insurance markets, unlike other markets, the state of

information available to consumers and suppliers of

insurance, as well as the nature of the insurance markets’ equilibria, matters in understanding how the market functions. Next, we describe in detail the nature of

market equilibria under different information conditions in insurance markets.

Market Equilibrium with Full Information

Figure 1A illustrates the equilibrium of a competitive

insurance market with identical individuals and full

information conditions. The horizontal (M1) and vertical (M2) axes represent income in the two states: no

loss and loss, respectively. U is the indifference curve

representing an individual’s preference set. The 45o

line represents equal income in both states of nature.

The line EF, which is referred to as the fair-odds line,

represents the supply of insurance (see equation 4).

Policies break even (zero profit for the insurance

company, assuming no administrative costs) along the

fair-odds line. The slope of the fair-odds line (the

supply of insurance) is given by the ratio of the probability of not having a loss to the probability of having a loss, (1-p)/p, while the slope of the indifference

curve (the demand for insurance) is given by the marginal rate of substitution of incomes in the two states

of nature {U¢(m1)}/{U¢(m2)}. In equilibrium, the

M2

45

M1

F

K

m-a1

m-a1-d+a2

.E

m-d

m

U

Figure 1A

Market equilibrium with full information 

and identical risk types
4  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

slope of the fair-odds line is equal to the slope of the

indifference curve.

An individual starts at an initial endowment E, where

income is equal to m if no loss occurs or m-d if a loss

occurs. Individuals may reduce their exposure to the

risk of loss by trading insurance contracts along the

fair-odds line, EF. The equilibrium contract, K, maximizes an individual’s expected utility, and it represents

full insurance coverage, equalizing income in both

states of nature. That is, in equilibrium, individuals

buy full insurance coverage at an actuarially fair rate

resulting, in what is known as, a full information equilibrium. Since the contract, K, is on the fair-odds line,

the insurer just breaks even.

Figure 1B illustrates the equilibrium of a competitive

insurance market with full information but individuals

representing different levels of risk. Consider a market

structure similar to the one discussed above, except

that there are low- and high-risk individuals whose

probability of loss is known to the insurer. We assume,

for simplicity, that there are only two types of individuals (“low-risk” and “high-risk”) in the market who

differ in their probability of suffering a loss. Let the

probability of loss occurrence for high- and low-risk

individuals be pH and pL, respectively, which implies

that pH is greater than pL. The low-risk contracts are

represented along the line EF, with a slope given by

(1-pL)/pL, while the high-risk contracts are represented

along the line EH, with a slope given by (1-pH)/pH. In

this case, the slopes and shapes of indifference curves

differ among risk types and depend on the individuals’

risk attitudes. Let UL and UH represent indifference

curves for low-risk and high-risk individuals, respectively. When the individuals’ probability of loss is

known, the insurer will offer different contracts commensurate with the various risk types. At equilibrium,

both risk types are fully insured at actuarially fair rates

at points A and B, where the marginal rate of substitution (the slope of the indifference curve) along the 45o

line is just equal to the ratio of the probability of not

having a loss to that of having a loss (the slope of the

fair-odds line).

Market Equilibrium with 

Asymmetric Information

Akerlof (1970), in his pioneering work on asymmetric

market information, demonstrates the problems that

arise in health insurance markets when an applicant for

insurance has full information about his/her health,

while insurers have no such information. He uses the

example of an insurer who is unable to distinguish

between high- and low-risk insurance applicants, and

values contracts at an average premium for all applicants. In this case, only those individuals whose risk is

above average are likely to buy insurance. This will

result in losses for the insurer and, thus, premiums

would have to be raised for the insurer to break even.

Of the group which purchased insurance in the first

place, only the worse-than-average risks would purchase insurance again at the higher premium. Premiums would again need to be raised to cover losses and,

eventually, only the very high-risk individuals would

purchase insurance at extremely high premiums and

the entire market for insurance would collapse.

In their seminal work, Rothschild and Stiglitz (1976)

explain the existence of equilibrium in an insurance

market in which asymmetric information exists

between insurer and insurance applicant. In the

absence of full information, this market can have two

kinds of equilibria: a pooling equilibrium or a separating equilibrium. In a pooling equilibrium, high- and

low-risk insurance applicants are not differentiated by

the insurer and, therefore, contracts are priced at an

average premium. Contracts are offered to both groups

at the same premium, and hence, applicants buy identical contracts. This situation leads to the type of market

described above in the Akerlof model. In a separating

equilibrium, on the other hand, different risk types

purchase different contracts that are associated with

different premium rates and contract characteristics. In

Figure 1B

Market equilibrium with full information 

and different risk types

M2

M1

E

F

H A

B

45

UL

UH
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  5

a separating equilibrium, individuals of different risk

characteristics separate themselves by contract selection, with the insurer offering different contracts commensurate with different risk types.

Figure 1C illustrates an example of pooling equilibrium under asymmetric information. As in the previous

example, we assume that there are two types of individuals in the market: “low-risk” and “high-risk,” who

differ in their probability of suffering a loss. Let the

probability of loss occurrence for high- and low-risk

individuals be pH and pL , respectively, which implies

that pH is greater than pL. The low-risk contracts are

represented along the line EF, with a slope given by

(1-pL)/pL, while the high-risk contracts are represented

along the line EH, with a slope given by (1-pH)/pH. In

this case, the slopes and shapes of indifference curves

differ among risk types and depend on the individuals’

risk attitudes. Let UL and UH represent indifference

curves for low-risk and high-risk individuals, respectively. When an individual’s probability of loss is hidden knowledge, the full-information equilibrium (A,

B), in which both risk types are optimally insured, is

unattainable. This is because insurers cannot prevent

high-risk individuals from purchasing the contract A,

which assures higher utility in each state.

Furthermore, the nature of asymmetric information

implies that insurance companies are unable to distinguish among their customers and, therefore, charge an

average premium (represented by line EG). In the

resulting pooling equilibrium, the high-risk individual

will buy contract B¢ and the low-risk individual will

buy contract A¢. At these levels of coverage, high-risk

individuals pay less and low-risk individuals pay more

relative to their respective full insurance contracts. In

this case, the high-risk individual is over-insured

(undercharged), while the low-risk individual is underinsured (overcharged).

Figure 1D illustrates an example of a separating equilibrium under asymmetric information, as described by

Rothschild and Stiglitz (1976). Consider a market

structure similar to the one discussed in figure 1C,

except that the insurer offers two contracts at two different prices. The low-price contracts are represented

along the line EF, with a slope given by (1-pL)/pL,

while the high-price contracts are represented along

the line EH, with a slope given by (1-pH)/pH. Let UL

and UH represent indifference curves for low- and

high-risk individuals, respectively. As in the previous

case, when an individual’s probability of loss is

unknown, the full-information equilibrium (A, B), in

which both risk types are optimally insured, is unattainable. The full information equilibrium (represented

by contracts A and B in this example) is where the

insureds’ expected utilities are maximized (UL and

UH) and the insurer breaks even. This full information

equilibrium is unattainable because high-risk individuals prefer the contract A over B, as A assures higher

utility (consumption) in each state. In this case, however, the insurer can offer two contracts (represented

Figure 1C

Pool equilibrium under asymmetric information 

and different risk types

M2

M1

E

F

H A

B

45

B'

UL

UH

A'

G

Figure 1D

Separating equilibrium under asymmetric 

information and different risk types

M2

M1

E

F

H A

45

B

UH

UL

A*
6  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

by fair-odds lines EF and EH) suitable for the two different risk types.

Since the insurer cannot separate low-risk applicants

from high-risk applicants, the contract offered to lowrisk types must not be more attractive to high-risk types

than their best contract. In the resulting equilibrium, the

high-risk individual will buy contract B and the lowrisk individual will buy contract A*. Thus, for a separating equilibrium to exist, the low-risk contract must

lie on the high-risk indifference curve, UH, or lower.

This establishes the contract set (A*, B) as the attainable equilibrium for a market with low- and high-risk

individuals. At the equilibrium, high-risk individuals

buy the full insurance contract, B (where the high-risk

fair-odds line is tangent to the high-risk indifference

curve), while low-risk individuals will buy the partial

insurance contract, A* (where the low-risk fair-odds

line intersects the high-risk indifference curve).

Since individuals may not have any incentive to

divulge information on their level of risk, the insurer is

better off by offering a menu of contracts such that

high-risk and low-risk types purchase different contracts commensurate with their level of risk. Studies in

automobile and health insurance demonstrate that

offering a selection of contracts with different prices

and coverage levels is more efficient than offering a

single contract at an average price (Hoy, 1982).

Wilson (1977) and Miyazaki (1977) extended the Rothschild and Stiglitz model further to show the transfer of

income from low-risk individuals to high-risk individuals under both pooling and separating equilibria. The

Wilson model demonstrates the transfer of income

from low-risk to high-risk individuals as both individuals purchase identical contracts for the same price. A

low- to high-risk subsidization results as the high-risk

individuals have a greater incidence of loss for the

identical contracts than the low-risk individuals.

In the Miyazaki model, high-risk and low-risk individuals purchase different contracts. The contracts purchased by high-risk individuals generate losses for the

insurer, while contracts purchased by the low-risk individuals generate profits. Therefore, the low-risk to

high-risk subsidization in the Miyazaki model occurs

across individuals buying different contracts. In the

Wilson model, the subsidization is across individuals

buying identical contracts.

Market signaling. The theory of market signaling suggests that in insurance markets with asymmetric information, agents signal their hidden knowledge through

their choice of insurance contracts (Cho and Kreps,

1987; Spence, 1978). Studies in automobile and health

insurance markets have shown that low-risk individuals have an incentive to signal their risk characteristics

by selecting high deductibles in the presence of hidden

knowledge and unobservable heterogeneity of risk

types among the insurance applicants (Riley, 1985;

Browne, 1992; Puelz and Snow, 1994).

Rothschild and Stiglitz (1976) and Spence (1978) have

shown that when insurance firms offer a menu of contracts, high-risk individuals are more likely to purchase

the high coverage contracts, while low-risk individuals

are more likely to choose the low-coverage contracts.

This is a self-revealing mechanism widely used in

automobile and health insurance markets to identify

risk types. When an individual chooses an insurance

contract among the menu of contracts offered, the individual reveals some information about himself/herself,

or sends a “signal” to the insurer. For example, if an

individual purchases a health insurance contract with a

high deductible, the individual sends a “signal” which

could mean that he/she represents lower risk than the

one who opted for a lower deductible contract.

It is possible that signaling could also be influenced by

other characteristics such as the degree of risk aversion. When individuals vary in risk averseness as well

as in their likelihood of expected loss, the choice of an

insurance contract is no longer influenced by the probability of loss alone. For example, an individual may

purchase an insurance contract with high coverage

either because his/her probability of loss is high, or

because he/she is highly risk-averse. However, if we

assume independence of the distribution of probabilities of loss and the distribution of attitudes towards

risk, individuals who buy insurance with higher coverage will tend, on average, to have larger expected

losses than those with insurance with lower coverage

(Pauly, 1974).

Adverse selection. Adverse selection has long been

recognized as a problem in insurance markets, including crop insurance. Empirical studies in automobile

and health insurance markets have found that adverse

selection reduces the consumption of insurance by

low-risk individuals and results in the transfer of

income from low-risk to high-risk insureds (Browne

and Doerpinghaus, 1993; Dionne and Doherty, 1994;

Puelz and Snow, 1994).
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  7

Figures 1C and 1D illustrate the adverse selection

problem in the case of two risk types, low-risk and

high-risk. When an insured’s probability of loss is

unknown to the insurer, the full information equilibrium (A, B) is unattainable. Under asymmetric information, those with high risk are over-insured and

under-priced (B¢) and those with low risk are underinsured and over- priced (A¢ or A* ).

The Crop Insurance Market

To analyze the crop insurance market, where different

products and coverage levels are offered to farmers, we

apply the asymmetric information equilibrium framework developed in automobile and health insurance markets. Consider a farmer with an initial income, m, who is

exposed to a risk, which can cause a loss, d, with a probability of insuring a loss, p, while (1-p) is the probability

of not insuring a loss. The farmer can pay a premium, p,

to an insurance firm, which in return pays some compensation or indemnity (I) if the loss occurs. The farmer

chooses a contract that maximizes expected utility:

(5) U( • ) = (1-p) U(m -p ) + p U(m - p - d + I ) 

where U( • ) is the von Neumann-Morgenstern utility

function, assumed to be increasing, strictly concave

(reflecting risk aversion), and differentiable. The indemnity paid by the insurance company to the farmer when

the actual yield (revenue) falls below the guaranteed

yield (revenue) depends on the insurance contract (a):

(6) I = I(a).

The insurance contract is defined as a yield or revenue

insurance product with a coverage level that specifies

the yield or revenue guarantee. To derive an equilibrium condition, we assume that a is a continuous

choice variable. Assuming there are no transaction

costs, the premium can be expressed as a function of a

and other observable characteristics (z) indicative of

risk type2:

(7) p = p(a, z).

When risk type is not observable and insurance is not

costless, equations 6 and 7 imply that equilibrium

insurance contracts depend on the manner in which

insurers and insureds interact in the market.

Differentiating (5) with respect to a, we obtain the

optimal choice of an insurance contract that satisfies

the following first order condition:

(8) U¢( m - p ) p { I¢(a) - p¢(a, z)}

U¢(m - p - d + I ) (1-p) p¢( a, z)

where U¢(•) > 0 is the marginal utility of income. The

ratio p/(1-p), which gives the odds of incurring a loss, is

a measure of risk associated with the insurance contract.

I¢(a) and p¢(a, z) represent the indemnity and the premium at the margin, respectively. Equation 8 implies

that, in equilibrium, the demand for insurance is equal to

the supply of insurance.

If the price of insurance is actuarially fair, individuals

would buy full insurance resulting in equalization of

incomes in the two states of nature.3 This is full-insurance in the sense that the individual would be indifferent between the two states of nature such that:

(9) U¢( m - p ) = U¢(m - p - d + I(a) ).

Individuals would trade income from one state of nature

to another through a payment of premium (p) to the

insurer, in return for a promise by the insurer to pay

indemnities (I) if a loss occurs. Such trading will continue until the incomes are equalized. The ratio of marginal utilities of expected incomes explains why riskaverse individuals are willing to purchase insurance

(Ehrlich and Becker, 1972).4 Substituting 9 in 8 yields

the optimal condition for the supply of insurance:

(10) (1-p) p¢( a, z) = p { I¢(a) - p¢(a, z)} 

which indicates that expected benefits are equal to

expected costs for the insurer. Solving equation 10 for

premium rate yields:

(11) p¢( a, z) = p I¢(a)

which means that the fair premium is equal to the

expected indemnity payment.

We derive the reduced-form solutions by applying the

implicit function theorem to equation 8 (see Puelz and

Snow). That is, the choice of a is expressed as a function of risk type (t), willingness to pay for insurance

(r), and cost of insurance or premium (p):

(12) aÿÿ= a(t, r, p ).

An empirical finding that risk type is statistically significant (at 1 0) supports the presence of a separating

equilibrium in the crop insurance market. Conversely,

if risk type is not significant (at = 0), the evidence is

consistent with a pooling equilibrium.

=
8  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

When it is impossible or prohibitively expensive for

the insurer to differentiate applicants according to risk

types, insurance premiums may not accurately reflect

the risk of loss (Borch, 1990; Browne, 1992; Puelz and

Snow, 1994). Under such circumstances, the insurer

sets premiums based on the average risk of the insured

pool. As argued by Rothschild and Stiglitz, average

premium rates are more attractive to high-risk individuals, potentially leading to adverse selection in the

insurance markets.
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  9

Crop Yield and Revenue 

Insurance Contracts

In this study, we examine several crop yield and revenue insurance plans—Actual Production History

(APH) insurance, Group Risk Plan (GRP), Crop Revenue Coverage (CRC), Income Protection (IP), and

Revenue Assurance (RA)—and their discrete coverage

levels of 50 percent through 75 percent. The exception

to this coverage range is GRP, which is offered at up

to the 90-percent coverage level. Three revenue insurance products, CRC, RA, and IP, were offered on a

large scale in 1997, in addition to the traditional yield

insurance products, APH and the GRP. In terms of

geographic coverage, the revenue insurance products

represented nearly a third of insured corn and soybean

acres in Iowa in 1997 (Makki and Somwaru, 1999b).

The APH contract is an individual yield insurance plan

that protects farmers against yield shortfalls if the

actual yield falls below the guaranteed level. APH

insurance includes catastrophic coverage (CAT) and

optional (buy-up) levels of coverage above CAT. For a

flat fee of $60 per crop per farm, CAT provides a 50-

percent yield guarantee and pays an indemnity based

on 55 percent of the projected price. In this analysis,

we separate CAT and APH buy-up coverage and will

hereafter refer to APH buy-up simply as APH insurance. APH insurance provides yield protection of up to

75 percent of the farmer’s average historical yield,

with a premium based on the chosen coverage level.

The APH contract pays an indemnity if the farmer’s

yield falls below the guaranteed level but offers no

price protection. The indemnity payment from a typical APH insurance is given by:

(13) I = max {0, (yg - ya ) Pg }

where yg is the guaranteed yield, ya is the actual yield,

and Pg is the guaranteed price (or elected price). The

guaranteed price, Pg, is a certain fixed proportion of

the expected price, which is usually USDA’s projected

farm-level price for the crop year. The guaranteed

yield, yg, is a certain fixed proportion of the expected

yield (ye ), usually based on the average historical

yield (yAHY ) of each given farm, and the chosen coverage level:

(14) yg = q ye = q yAHY, 0.50 £q£ 0.75

where q is the chosen coverage level. CAT and APH

contracts allow for basic units, which combine each of

the fields of a crop under a single type of ownership

arrangement, and optional units, which allow insurance by section line and practice (dry land versus irrigated crops).

GRP is a yield insurance product, but is tied to the

county average yield rather than the individual farm

yield. GRP contracts provide indemnity payments

when the county average yield (yc ) drops below a critical or guaranteed level, regardless of the yield of the

individual farmer:

(15) I = max {0, (yg - yc ) Pg }.

This indemnity function is similar to equation (13),

except that the individual farm yield is replaced by the

county yield and the critical yield is estimated based

on past county yield histories. GRP buyers can insure

up to 90 percent of the expected county yield at up to

150 percent of the expected price (Skees et al., 1997).

CRC, RA, and IP are revenue insurance plans that protect the farmer from lost revenue caused by low yields,

low prices, or a combination of both. They are all

based on the farmer’s historical average yield and

futures prices, but differ somewhat in their specific

design and operation. CRC provides replacement-cost

protection to producers in addition to a revenue guarantee. Indemnities are paid if the producer’s calculated

revenue (based on his or her actual yield in that year,

multiplied by the harvest-time quote on the harvesttime futures contract) falls below the predetermined

guarantee level (based on the coverage level chosen by

the producer, the farmer’s average historical yield, and

the higher of the planting-time quote or the harvesttime quote on the harvest-time futures contract). In

other words, under a typical CRC contract, the indemnity payment is defined by:

(16) I = MAX {0, ( yg max(Pg , Pm) - ya Pm ) } 

where Pm is the harvest futures market quote on the

harvest-time futures contract, Pg is the planting-time

quote on the harvest-time futures contract, yg is the

guaranteed yield, and ya is the actual yield.5 Since

CRC uses the higher of the planting-time price for

the harvest-futures contract or the actual-futures contract quote at harvest in setting the guarantee, the

producer’s revenue guarantee may actually increase

over the season. This is because CRC allows producers to purchase “replacement bushels” if yields are

low and prices increase during the season (Harwood

et al., 1999). CRC, which allows for enterprise units,
10  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

basic unit, and optional unit coverage, has rapidly

expanded to all major crops in major growing areas

(GAO, 1998).

RA and IP also protect farmers against reductions in

gross income when either prices or yields decrease

during the crop year from early-season expectations.

Indemnity amounts are determined by individual farm

yields and harvest-time futures prices:

(17) I = MAX {0, ( yg Pg - ya Pm ) }

where Pm is the harvest futures market quote on the

harvest-time futures contract, Pg is the planting-time

quote on the harvest-time futures contract, yg is the

guaranteed yield, and ya is the actual yield.

There are, however, key differences between RA and

IP contracts. RA provides the option of enterpriselevel farm insurance (where the guarantee is based on

expected revenue from all the farmer’s acreage in a

given crop in the county) as well as whole farm insurance (where the guarantee is based on the expected

revenue from multiple crops grown by the farmer in a

given county). RA also allows both basic unit coverage

(where the insurance contract is based on ownership

and county) and optional unit coverage (where the

insurance contract is based on ownership, farming

practice, county, and section line). Beginning in 1999,

RA also offers a harvest price option (RA-HP). If a

farmer purchases the RA-HP contract, then his or her

coverage is similar to CRC but with no price liability

limit in a rising-price market (Risk Management

Agency, 1999).

IP is offered only on the basis of enterprise units,

meaning that all fields of a crop which a farmer owns

or has a share of the commodity in the county are

combined into one unit. IP and RA (without the HP

option) offer exactly the same coverage if the farmer

chooses enterprise units. IP and RA also differ in the

way price guarantees are set. The IP revenue guarantee

is based on the futures price with no basis adjustment

(using an average of Chicago Board of Trade (CBOT)

February price quotes for the December contract),

while the RA guarantee is based on an approximate

local price (the December price adjusted for a county

factor). In both cases, indemnities are paid if the producer’s gross income falls below the predetermined

guarantee (Harwood et al., 1999). Even though both IP

and RA were introduced in 1996, they are available

only in selected counties and for selected crops (Risk

Management Agency, 1999).
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  11

Description of the Data

Data used in this study are from USDA’s Risk Management Agency (RMA), which maintains records of

all individual farmers who buy federally backed cropyield or revenue insurance. The data pertain to corn

farmers in Iowa for the 1997 crop year. We selected a

sample of about 60,000 unit-level insurance records

for which 10 years of yield records were available.6

For each unit, we have several variables that describe

the characteristics of the contract, such as choice of

coverage level and price, premium rate, and indemnity payments. We also have variables that assess the

risk of an individual unit—past yield records, yield

span, farm practice, ownership share, loss frequency,

and liability.

Tables 1 and 2 summarize descriptive statistics for the

various insurance products based on the 1997 individual insurance records for Iowa corn and soybeans,

respectively. In tables 1 and 2, we separate CAT and

APH buy-up coverage contracts. The sample includes

three yield insurance plans—CAT, APH, and GRP—

and two revenue insurance plans—CRC and RA. IP is

dropped from the analysis for lack of sufficient data.

Only 50 IP contracts were sold for corn and soybeans

combined in Iowa in 1997.

We calculated the mean and the coefficient of variation

(CV) for each insured farm unit based on 10 years of

yield data. The mean yields for corn ranged between

120 and 130 bushels/acre (table 1), while mean yields

for soybeans ranged between 40 and 45 bushels/acre

(table 2). The estimated CV of yield was around 30

percent for both corn and soybeans. We also estimated

the CV of revenue for each farmer based on the 10

years of yield records and the marketing year average

prices for the corresponding years. The CV of revenue

follows the CV of yield closely across all products,

even though one would have expected a lower CV for

revenue because of the possibility of negative correlation between price and yield.

Results presented in table 1 indicate that CRC is the

most expensive product on both a per-acre and perdollar-of-liability basis. For example, corn CRC contracts cost an average of $12 per acre or $6 per $100

of liability for a 65-percent coverage-level contract.

The higher cost of CRC is due in part to higher

expected indemnities, including provision for replacement coverage when the harvest-time price is greater

than the projected planting-time price.

The loss frequency, calculated as the percentage of

policies indemnified, for APH, CRC, and RA was,

respectively, 1.4 percent, 2.1 percent, and 1.6 percent

for the 65 percent coverage contract for corn in Iowa

(table 1). The loss ratio, defined as indemnity paid out

per dollar of premium, was 0.0543, 0.0514, and 0.0774

for APH, CRC, and RA for corn in Iowa, respectively.

The loss-cost ratio, defined as indemnity paid out per

dollar of liability, was also low for all insurance prodTable 1—Summary statistics for Iowa crop insurance contracts based on sample data: Corn, 19971

APH CRC RA GRP CAT

Characteristics 65 70 75 65 70 75 65 70 75 All 50

Number of units insured 24,676 2,381 8,628 16,022 8,850 4,442 3,232 779 1,353 808 4,316

Average area insured (acres) 54.45 59.00 50.00 57.25 56.60 58.43 59.30 63.64 60.70 158.40 76.22

Mean yield (bu/ac)2 126.02 127.34 123.52 125.80 127.20 124.90 128.00 130.33 128.76 123.00 129.40

CV of yield3 0.31 0.31 0.32 0.31 0.31 0.32 0.30 0.30 0.30 0.21 0.33

CV of income 0.33 0.33 0.34 0.32 0.33 0.34 0.32 0.32 0.32 0.35

Loss frequency (%)4 1.4 2.2 4.2 2.1 3.0 5.4 1.6 1.8 3.1 0.37 0.1

Premium rate ($ per acre) 8.25 10.56 14.07 11.90 15.05 20.14 5.86 7.64 10.62 6.70 2.85

Rate (premium per $ of liability) 0.0430 0.0501 0.0650 0.0581 0.0678 0.0864 0.0310 0.0361 0.0481 0.2000 0.0317

Loss ratio5 0.0543 0.0544 0.1300 0.0514 0.0857 0.1397 0.0774 0.0660 0.1321 0.1290 0.0049

Loss-cost ratio6 0.0030 0.0037 0.0091 0.0035 0.0091 0.0133 0.0034 0.0030 0.0066 0.0062 0.0007

Ownership share (%) 70 73 70 72 73 74 72 75 70 78 66

Average price elect ($ per bu) 2.45 2.45 2.45 2.59 2.59 2.59 2.42 2.42 2.42 2.45 1.47

1 Sample data consist of individual farm-unit level insurance records.

2 For APH, CRC, RA, and CAT, mean yield is calculated for each unit based on 10 years of yield records, while for GRP the mean 

yield is calculated using county-level yield records.

3 CV is coefficient of variation (standard deviation/mean).

4 Loss frequency is the percentage of total policies indemnified.

5 Loss ratio is the indemnity paid out per dollar of premium collected (indemnity/premium).

6 Loss-cost ratio represents indemnity per dollar of liability (indemnity/liability).
12  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

ucts in 1997 (tables 1 and 2). The loss cost and loss

ratios are low because insurance contracts in Iowa

experienced lower claims in 1997 than in many other

years largely due to favorable weather conditions and

relatively high commodity prices. One should note that

these numbers reveal little regarding the long-term

actuarial soundness of insurance products. The

descriptive statistics for soybeans are similar to those

for corn in 1997 (table 2).

Table 2—Summary statistics for Iowa crop insurance contracts based on sample data: Soybeans, 19971

APH CRC RA GRP CAT

Characteristics 65 70 75 65 70 75 65 70 75 All 50

Number of units insured 18,263 1,269 7,359 10,484 4,840 3,451 2,143 408 811 782 4,198

Average area insured (acres) 48.80 53.30 46.33 52.17 52.08 55.40 53.82 57.70 50.32 118.13 69.50

Mean yield (bu/ac)2 39.44 40.80 39.76 39.90 40.66 40.50 40.50 41.75 40.13 41.44 39.10

CV of yield3 0.28 0.26 0.27 0.28 0.27 0.27 0.28 0.26 0.28 0.17 0.31

CV of income 0.29 0.27 0.28 0.29 0.28 0.29 0.29 0.27 0.28 0.31

Loss frequency (%)4 1.4 1.4 2.6 1.8 2.4 4.3 2.0 1.0 1.0 0.0 0.1

Premium rate ($ per acre) 5.04 6.25 8.30 7.06 8.92 12.20 5.30 7.40 10.00 3.00 1.73

Rate (premium per $ of liability) 0.0314 0.0351 0.0451 0.0403 0.0468 0.0596 0.0297 0.0371 0.0496 0.0108 0 .0230

Loss ratio5 0.0406 0.0502 0.0987 0.3152 0.5554 0.8514 0.0637 0.0178 0.0420 0.0000 0.0062

Loss-cost ratio6 0.0015 0.0022 0.0050 0.0174 0.0358 0.0541 0.0025 0.0008 0.0020 0.0000 0.0006

Ownership share (%) 0.68 0.71 0.68 0.70 0.71 0.72 0.70 0.71 0.66 0.75 0.66

Average price elect ($ per bu) 6.15 6.15 6.15 6.62 6.62 6.62 6.64 6.64 6.64 6.15 3.69

1 Sample data consist of individual farm unit-level insurance records.

2 For APH, CRC, RA, and CAT, mean yield is calculated for each unit based on 10 years of yield records, while for GRP the mean 

yield is calculated using county-level yield records.

3 CV is coefficient of variation (standard deviation/mean).

4 Loss frequency is the percentage of total policies indemnified.

5 Loss ratio is the indemnity paid out per dollar of premium collected (indemnity/premium).

6 Loss-cost ratio represents indemnity per dollar of liability (indemnity/liability).
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  13

Empirical Model and 

Hypotheses Testing

The econometric analysis is carried out in two stages.

First, equation 12 is estimated as a Generalized Polytomous Logit (GPL) function to handle the discrete

choice of insurance products, measured on a nominal

scale (Greene, 1990; Kennedy, 1992; Long, 1997;

Stokes et al., 1998) and second, a three-stage leastsquares model is specified to analyze premium rates

and the choice of coverage levels.

Generalized Polytomous Logit Model

The probability that a farmer will choose one of the m

alternative insurance products, Fi

, from a set of

choices, F, is given by:

where U(Fi

) is the utility for alternative Fi, xi is a vector of variables that affect the choice of the insurance

product, and b is a vector of parameters. The probability that a farmer will choose a particular product is

given by the probability that the utility of that product

is greater than the utility from any other available

alternative (utility maximization approach). Insurance

products available to farmers include CAT, APH, GRP,

CRC, and RA.7 The explanatory variables are risk

type, willingness to pay for insurance, and cost 

of insurance (see table 3).

Since the response variable, choice of insurance product, has no inherent ordering, we estimate equation 18

as a generalized polytomous logit function. The logit

of the response variable is formed as a ratio of the

probability of choosing a product over the probability

of choosing the reference product:

where k = 1, 2, ..., (r-1) indexes the choice of insurance products, r is the reference choice or the choice

used as the basis for comparison, h, i, and j reference

the explanatory variables, and hhijk, which represents

equation 9, is the probability of the kth choice. Specifically, hijk is given by:

A logit of the response variables under consideration is

formed for the probability of each product over the

reference product. For example, the generalized logits

for a four-level nominal response (where the producer

chooses among four different insurance products) can

be specified as follows:

where product 4 is the reference choice. The model

that applies to all logits simultaneously, for every 

combination of the explanatory variables, in a matrix

form, is:

(22) logithijk = ak + xhij bk

where k indexes the choice of the product. The matrix

xhij is the set of explanatory variable values for the

hijth group. This model accounts for each response by

estimating separate intercept parameters (ak ) and different sets of regression parameters (bk ) for all

explanatory variables. That is, in the GPL model specification, we estimate simultaneously as a panel multiple sets of parameters for both the intercept and the

explanatory variables.8

We estimate two GPL models using equation 22. Model

1 is a GPL specification with product choices GRP,

CRC, and RA with APH as the reference choice. Model

2 is also a GPL specification with product choices APH,

GRP, CRC, or RA with CAT are the reference choice.

The reason for estimating model 2 is to use the completely subsidized contract as the reference choice.9 In

both models, however, farmers make a choice from a

portfolio of yield and revenue insurance products.

Interpretation of the GPL parameter estimates is not

very straightforward because the dependent variable

has no inherent ordering. To facilitate interpretation of

( ) [ ] ( )

[ ] ( )

( )

( )

( )

U

U

18

1 1

 prob

x

x

i

i

j

j

m

i

j

j

F F m

F

F

=

å

=

å = =

exp

exp

exp

exp

b

b

( ) 19 logit log hijk

hijk

hijr

= [ ]

h

h

 logit log

 logit log

 logit log

hij1

hijk1

hij4

hij2

hijk2

hij4

hij3

hijk3

hij4

=

=

=

[ ]

[ ]

[ ]

h

h

h

h

h

h

( ) 21

( ) 20

1

 e

 + e

hijk

k + xhji 

k + xhji 

h

a b

a b = .
14  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

the model parameters, we estimate probabilities and

odds ratios. The predicted probability that a particular

product is chosen is a function of the estimated model

parameters given in equation (22). Odds ratios are

obtained from the predicted probabilities (Stokes et al.,

1998). For example, to obtain the odds of choosing

product k by a high-risk farmer relative to a low-risk

farmer, we compute:

where h and l are reference risk types. The odds ratio

is a multiplicative coefficient, which means that positive effects are greater than 1, while negative effects

are between 0 and 1. Determining the effect of the

odds of the event not occurring involves taking the

inverse of the effect of the odds of the event occurring

(Long, 1997).

Explanatory variables used in the GPL regression

model are: (i) probability of yield or revenue falling

below the guaranteed level to represent risk type, (ii)

level of income or size of operation to represent the

willingness to pay for insurance, and (iii) premium per

dollar of liability to represent the cost of insurance.

Risk type of a farm (RISK) is measured in terms of the

probability of yield or revenue falling below the guaranteed level. For yield insurance products, CAT, APH,

and GRP, RISK is the probability of yield falling below

the guaranteed level (Yp), while for revenue insurance

products, CRC and RA, RISK is the probability of revenue falling below the guaranteed level (Rp).

The probability of yield falling below the guaranteed

level is estimated for each farm based on 10 years of

yield records, the chosen guaranteed level, and assuming a normal distribution of yield.10 The probability of

revenue falling below the guaranteed level is estimated

for each farm based on 10 years of yield records and

the marketing year average prices, the chosen guaranteed level, and assuming revenues are normally distributed. This measure of risk accounts for both the mean

and variance of yield or revenue (Skees and Reed,

1986; Just et al., 1999).

In this study, we use predicted probability of yield or

revenue falling below the guaranteed level to measure

risk. This measure of risk (Yp or Rp) is a function of

observable variables, including past yield or revenue

histories and chosen guaranteed level, and thus provides a robust measure of an individual’s risk.11

Since neither farm income nor net worth data were

available, the level of income that represents willingness to pay is proxied by accumulated savings. Conceptually, income indicates the liquidity position of the

farmer, which is an important determinant of the willingness to pay for an insurance contract (Makki and

Miranda, 1999). The farmer’s level of income, which

is proportional to the size of the operation, also indicates the amount of income at risk, along with the

operators’ ability to pay for insurance or to self-insure

against the risk of loss. In our analysis, income is estimated for each farmer as M = l S At Yt Pt , " t = 1,

2, ... , 10, where M is the income level, At is the number of acres insured in time t, Yt is the yield per acre in

time t, Pt is the marketing-year average price in time t,

and l is the proportion of gross revenue saved in each

year. The parameter, l, is assumed to be equal to 0.10

or 10 percent of gross revenue (Holbrook and Stafford,

1971).12

The cost of insurance, captured by premium per dollar

of liability, is calculated as total premium (including

subsidy) divided by total liability (RATE). Liability

represents the maximum potential indemnity or value

of the insurance contract if a producer loses the entire

crop. This measure of insurance cost facilitates comparison across different insurance contracts. Premiums

are subsidized by the Federal Crop Insurance Corporation up to 42 percent (Makki and Somwaru, 1999), but

we use total premium in this study.

We adopt the CATMOD procedure in SAS to estimate

the GPL model. This procedure is recommended when

the dependent variable has several nominal responses

without any inherent ordering (Stokes et al., 1998).

The CATMOD procedure forms a separate group for

each distinct combination of the explanatory variable

values. For continuous explanatory variables with

many distinct values, the procedure would create a

larger number of combinations, rendering the results

impossible to interpret. To overcome this limitation,

we group each of the explanatory variables into three

categories, low, medium, and high.

We group the explanatory variables using their mean

and standard deviation. For example, the estimated

mean and standard deviation for Yp were 0.17 and

0.11, respectively, for Iowa corn producers. Farmers

with Yp near the mean (± 1 standard deviation or 0.06

( ) 23 Odds Ratio e

e

 h l ,

k + xhij 

k + xlij 

= 1

( )

( ) ,

a b

a b
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  15

< Yp £ 0.28) are categorized as medium-risk. Farmers

with Yp £ 0.06 (mean minus one standard deviation)

are categorized as low-risk, while those farmers with

Yp > 0.28 (mean plus one standard deviation) are categorized as high-risk. Similarly, the estimated mean and

standard deviation for Rp were 0.24 and 0.12, respectively. Farmers are categorized as low-risk if Rp £

0.12, while 0.12 < Rp £ 0.36 indicates medium-risk

and Rp > 0.36 is high-risk. Other variables, income

level, and premium rate, are categorized into the three

classes using similar procedures.

Three-Stage Least-Squares Model

We specify a simultaneous equation system to analyze

premium rates and choice of coverage level:

(24) pi = xi b + ei

(25) qi = xi b + ui

where pi is premium per dollar of liability (including

the subsidy), qi is the coverage level chosen by the

farmer, xi is a matrix of explanatory variables, b is a

vector of parameters, while ei and ui are error terms.

The set of explanatory variables included in equation

24 include risk type, coverage level, practice, ownership share, and yield span, while explanatory variables

in equation 25 include risk type, level of income, premium rate, practice, ownership share, and yield span

(see table 3).

Variables representing risk type, income level, and premium rate are as defined earlier in equation 22, except

that they are not grouped. Farm practice—i.e., whether

or not a farm is irrigated—is included because irrigation has the potential to reduce yield risks and may

provide the incentive to buy higher coverage levels.

For the econometric analysis, practice is set equal to 1

for irrigated farms and to 0 for non-irrigated farms.

Ownership share, which is the percentage share of the

crop owned by the insured, could potentially influence

the choice of an insurance contract. However, the

direction of the effect on the level of coverage purchased is indeterminate. A positive effect implies that

as the share of ownership increases, farmers are more

likely to purchase higher coverage contracts. This is

plausible because full ownership could mean greater

dependence on farm income for livelihood. On the

other hand, a negative effect is also possible, as tenant

farmers are usually more leveraged and thus may be

subjected to insurance requirements from lenders

(Gardner and Kramer, 1986; Goodwin, 1993; Wu,

1999). Given these conflicting effects, the issue of

whether ownership share is positively or negatively

associated with the insurance purchase decision must

be resolved empirically.

USDA’s Risk Management Agency (RMA) uses the

“yield span” concept to categorize farms into different

classes (table 3). The yield spanning approach classifies

farmers’ yields into nine discrete risk categories (R01

through R09) based on the ratio of a farmer’s yield to

the average county yield. According to the yield span

concept, category R01 includes the lowest average

yields while category R09 includes the highest average

yields. Yield span category R05 includes all those farms

whose yields are expected to be equal to the county’s

expected yield. Yield span ranges are derived from historical county loss experience and are calibrated to the

expected county yield reported by the National Agricultural Statistical Service (NASS). 

Equations 24 and 25 are estimated simultaneously

using the three-stage least-squares procedure. Because

error terms are correlated, the farmer’s decision choice

of coverage levels and the premium rates require a

simultaneous equation system approach.13 The procedure is applied to each insurance product separately.

The purpose of estimating the coverage level and premium rate as a system is to analyze, ex-post, the relationship between the producers’ choice of coverage

levels and the premium rates at which they are offered.

Past studies of crop insurance participation have often

treated premium rates as exogenous (Coble et al.,

1996; Goodwin, 1993). Although the premium rates

for different coverage levels are known ex-ante, in this

analysis we treat them simultaneously as an endogenous choice to gain insight into farmers’ decision making processes and the factors affecting those decisions.

This is particularly important for an analysis of markets affected by asymmetric information problems. As

past yield histories and other farm and farmer risk

characteristics are not easily available, the best way to

address farmers’ attitudes is by observing the choice(s)

made by the farmers themselves. Thus, analysis of premium rates and coverage levels can enhance our

understanding of farmers’ behavior in the crop insurance market. Furthermore, if farmers effectively signal

their risk type, through the choice of premium-coverage level, then such information is useful in assessing

potential losses and setting premium rates commensurate with risk.
16  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

Hypotheses Testing

Testing for separating equilibrium. The model is tested

for the existence of a separating equilibrium by assessing the signs and the statistical significance of the variable RISK in equations 22 and 25. Significant coefficients for RISK in equations 22 and 25 would indicate

a separating equilibrium, implying that low-risk and

high-risk farmers purchase different contracts. For

example, a significant positive coefficient for RISK in

equation 25 would indicate that low-risk types purchase contracts with lower coverage, while high-risk

types purchase higher coverage contracts. On the other

hand, a non-significant coefficient would indicate a

pooling equilibrium, implying that all risk types purchase the same contract.

Testing for the effects of farm income. We expect the

choice of insurance contracts to be related to income

in a manner consistent with the decreasing risk-aversion hypothesis. This is equivalent to asserting that

farmers with higher income retain the risk of some

losses. One expects that high-income farmers would be

more likely to choose the lower coverage contracts, as

they are able to self-insure and manage variations in

income within their operations better than would farmers with lower income.

Testing for the effects of cost of insurance. Premium

rates are conditioned on insurance product, coverage

level, irrigated versus non-irrigated production, and

RMA’s yield span classification. Assuming low-risk

types buy lower coverage levels, a positive correlation

Table 3—Variable description

Variable name Variable definition

Insurance plans Alternative insurance plans or products that include Catastrophic Coverage (CAT), Actual 

Production History Insurance (APH), Group Risk Plan (GRP), Crop Revenue Coverage (CRC),

Revenue Assurance (RA), and Income Protection (IP).

Coverage level Alternative coverage levels that range from 50% to 85% in an interval of 5%. 

Premium Per-acre premium paid in dollars to purchase insurance (includes subsidy). 

Rate Rate is the premium per dollar of liability (premium/liability). 

Loss ratio Loss ratio = Indemnity/Premium. 

Loss-cost ratio Loss-cost ratio = Indemnity/liability. 

Risk type Probability of yield or revenue falling below the guaranteed level, estimated for each farm based

on 10 years of yield records and using the corresponding year market average price. 

Loss frequency Ex post observation of whether a farmer filed a claim, also known as loss frequency; set equal to

one for those who filed a claim and set equal to zero otherwise. 

Yield span A yield-spanning process creates nine discrete categories (R01 through R09) of yields. 

Category R01 is associated with the lowest average yields, while category R09 is associated 

with the highest average. The yield-span ranges are derived from historical county loss 

experience and are calibrated to the expected NASS county yield. Rates for each category are 

inversely proportional to the farm’s expected yield. Thus, farms in relative expected yield 

categories 1-4 are charged premium rates which are higher than the base county rate. 

Conversely, farms in relative expected yield categories 6-9 are charged lower premiums 

than the base county rate. 

Farm income Income is estimated for each farmer as follows:

M = lå At Yt Pt , " t = 1, 2, ... , 10,

where M is the income level, At is the number of acres, Yt is the yield per acre, Pt is the State

average price, and is the proportion of income saved, which is assumed to be 0.10. 

Expected indemnity Expected indemnity, E(I), is estimated for each farmer as follows:

E(I) (per acre) from a typical yield insurance contract: E(I) = MAX(0, Yg - Y)Pg ,

E(I) (per acre) from a typical revenue insurance contract: E(I) = MAX(0, Yg Pg - Y Pm ),

where Yg is the guaranteed yield, Y is the actual farm yield, Pg is the guaranteed price, Pm

is the market price at harvest time. 

Farm practice Farm practice, which indicates whether a farm is irrigated, is set equal to one for irrigated 

farms and zero for non-irrigated farms.

Ownership share Ownership share is the percentage share of the crop owned by the insured.
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  17

between coverage level and the premium rate in equation 24 implies that insurers compensate low-risk types

accordingly. The statistical significance of the premium rate in equations 22 and 25 has implications for

public subsidization of the risk insurance programs.

Testing for market signaling. A nonlinear relationship

in the coverage-premium schedule indicates the presence of signaling in the insurance market.14 The nonlinearity of the coverage- premium schedule is tested

by introducing three dummy variables into the system

representing three coverage levels, 55 percent, 65 percent, and 75 percent. Over the range of coverage levels

in our sample, nonlinearity would be present if the

marginal premiums at the various coverage levels are

significantly different. Assuming that farmers make

informed decisions, a farmer’s selection of an insurance contract reveals information, although imperfectly, about the riskiness of his or her operations. This

information could potentially be used to decrease the

adverse effects of asymmetric information in the insurance market.

Testing for adverse selection. We test for adverse

selection using a two step procedure. First, we test for

the independence of the choice of insurance contract

and the risk using non-parametric methods. If the

choices are correlated with risk, then agents indeed

have a better knowledge of their risk (Chiappori and

Salanie, 2000). Rejection of independence would suggest that there is evidence of adverse selection in the

crop insurance market.

Parametric methods used by Puelz and Snow (1994) or

Dionne, Gourieroux, and Vanasse (1998), for instance,

rely on a fairly large number of exogenous variables

and restrictive functional forms. Hence, the results

from parametric methods would be biased. Non-parametric methods are, on the other hand, less restrictive

and account for more complicated non-linear relationships between variables (Chiappori and Salanie, 2000).

The two non-parametric tests performed are the

Kruskal-Wallis c2 test and the Kolmogorov-Smirnov

test. The Kruskal-Wallis test statistic is given by:

(where N is the sample size, Ti is the rank assigned to

the ith group, and ni is the number of groups in the

sample. The test statistic H approximately follows a

chi-squared distribution with k-1 degrees of freedom.

See Milton and Arnold (1990) for more details on the

Kruskal-Wallis test. The Kolmogorov-Smirnov test statistic is given by:

where FM(x) is the empirical cdf and F(x) is the cdf of

a c2(1). Under conditional independence, the test statistic K converges to a distribution that is tabulated in

statistics textbooks (Chiappori and Salanie, 2000).

The second step involves comparing the actual and

competitive premiums across different risk types. In an

efficient market, the competitive premium is equal to

the expected indemnity (Puelz and Snow, 1994; Rothschild and Stiglitz, 1976). The expected indemnity E(I)

is calculated for each insurance contract separately.

For example, E(I) for a typical CRC contract is:

where n is the number of periods for which yield

records are available, qÿis the coverage level, ye is the

expended yield, yt is the actual yield in year t, Pg is

the guaranteed price (or elected price), and Pm is the

market price. We use 10 years (1987-96) of actual

yield history for each farm and corresponding annual

market prices. Coverage level q and guaranteed price

Pg were chosen by farmers in 1997. We adjust the

guaranteed yield for the growth rate in yield to make it

comparable with yield in period t. The market price,

however, did not exhibit any trend during the 1987-96

period. The calculated E(I) captures farm risk characteristics by accounting for alternative yield and price

possibilities.15

Under a full-information equilibrium, the difference

between actual and competitive premium rates should

be zero for all risk types. Under asymmetric information, however, one would expect differences to exist

between actual and competitive premium rates, as the

accurate determination of individual farmers’ risk is

either not possible or prohibitively expensive. We use

non-parametric tests and graphical illustrations to

demonstrate the differences, if any, between the actual

and competitive premium rates. The two non-parametric tests performed are the Kruskal-Wallis c2 test and

the Kolmogorov-Smirnov test as described above.

() [ 28 1 0

1

 E(I) =

n

MAX ( Y P P - Y P , t=

n e g m tm å , max( , ) )] q

( ) ( ) 26 H = ( ) 12

N N+1

T

n

3N 1 i

2

i i 1

k

å - + =

( ) 27 K = M sup F (x) F(x) x

M -
18  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

Empirical Results

In this section we present the empirical results from

the Generalized Polytomous Logit (GPL) and the

three-stage least-squares (TSLS) models. The GPL

model analyzes the discrete choice of insurance product as a function of risk type, income level, and insurance cost, while the TSLS model analyzes the choice

of coverage levels and premium rates in a simultaneous equation system. We present the results of our

analysis for both corn and soybeans, but limit the discussion to corn.

Choice of Insurance Products

The maximum likelihood analysis of variance results

are presented in table 4, which summarizes the main

effects of models 1 and 2. The likelihood ratio statistic

indicates goodness of fit of the model, while chisquare values indicate the significance of the explanatory variables. The likelihood ratio statistic for model

1 has a value of 253 with 60 degrees of freedom,

which is indicative of a good fit. Model 2 is also a

good fit, with a likelihood ratio of 367 with 80 degrees

of freedom. A likelihood ratio test is performed to test

whether the two specifications are statistically different. Test results indicate that the two models are

indeed different. Since models 1 and 2 represent

choices with respect to APH, which is a partially subsidized product, and CAT, which is a completely subsidized product, we infer that premium subsidies are

likely to influence farmers’ decisions in choosing an

insurance product.

The hypothesis to be tested is that the insurance market entails low-risk types selecting products that provide lower protection, while high-risk types select

products that provide higher protection. Results presented in table 4 reveal a strong relationship between

risk type and the choice of insurance products. The

risk type variable has Wald Chi-Square values of

1,712 with 6 degrees of freedom in model 1, and

1,920 with 8 degrees of freedom in model 2. We

reject the hypothesis that risk type has no influence on

the choice of insurance products at less than the 1-

percent level of significance.16 These results are consistent with the presence of a separating equilibrium

in crop insurance markets, where low- and high-risk

farmers choose different products depending on their

risk types.

Our results also indicate that income has a significant

influence on the choice of insurance products (table 4).

The Wald Chi-Square values for income are 630 with

6 degrees of freedom in model 1, and 744 with 8

degrees of freedom in model 2. The cost of insurance,

captured by the premium per dollar of liability

(RATE), is also a critical factor in choosing a product.

RATE is statistically significant, with Wald Chi-Square

Table 4—Maximum likelihood analysis of model fit and variable significance1

Model 1 Model 2

Variable df Chi-square2 Probability df Chi-square Probability

Corn

Risk type (RISK) 6 1712.58 0.00 8 1920.40 0.00

Level of income (M) 6 629.95 0.00 8 743.65 0.00

Cost of insurance (RATE) 6 6225.10 0.00 8 9553.60 0.00

Likelihood ratio 60 253.13 0.00 80 367.27 0.00

Likelihood ratio test3 228.28 

Variable df Chi-square Probability df Chi-square Probability

Soybeans

Risk type (RISK) 6 619.86 0.00 8 1167.25 0.00

Level of income (M) 6 532.64 0.00 8 843.28 0.00

Cost of insurance (RATE) 6 1099.30 0.00 8 1932.89 0.00

Likelihood ratio 60 411.85 0.00 80 550.74 0.00

Likelihood ratio test3 277.78 

1 Model 1 is a GPL specification with product choices GRP, CRC, and RA with APH as the reference choice, while model 2 is a 

GPL specification with product choices APH, GRP, CRC, and RA with CAT as the reference choice.

2 The table Chi-square values at 1% level of significance are 16.81 and 20.1 for 6 and 8 degrees of freedom, respectively.

3 The likelihood ratio test statistic is given by -2logl, where l is the ratio of two likelihood ratios from models 1 and 2 (Kennedy 1992).

The statistic is distributed asymptotically as Chi-square with degrees of freedom equal to the number of restrictions imposed. 
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  19

values of 6,225 with 6 degrees of freedom in model 1,

and 9,554 with 8 degrees of freedom in model 2.

Table 5 presents the parameter estimates for models 1

and 2, along with the standard errors that indicate the

statistical significance of the estimated parameters

(table 6 presents the parameter estimates for soybeans). Parameter estimates are arranged according to

the logits they reference. In what follows, we limit our

discussion to model 1.

Odds ratios facilitate interpretation of the estimated

parameters (Long, 1997). We compare the odds of

choosing CRC, RA, and GRP over APH for different

risk types and for different income levels. The odds

ratio measures the likelihood of choosing an insurance

Table 5—Generalized multinomial logit model, corn

Model 1 logit(GRP/APH) logit(CRC/APH) logit(RA/APH)

Variable Coefficient Std. error Coefficient Std. error Coefficient Std. error

Intercept a1 -4.7946* 0.3358 a2 -1.9052* 0.1186 a3 -1.7419* 0.0318

High-risk b1 -0.5190* 0.1087 b2 0.1808* 0.0164 b3 0.1790* 0.0380

Med risk b4 0.1562** 0.0644 b5 0.2985* 0.0115 b6 0.2965* 0.0240

High income b7 0.7740* 0.0531 b8 0.1635* 0.0152 b9 0.1742* 0.0278

Med income b10 -0.6460* 0.0568 b11 0.0687* 0.0118 b12 -0.0722* 0.0226

High rate b13 -2.8672* 0.6689 b14 2.3900* 0.1199 b15 -0.7536* 0.0563

Med rate b16 -0.5619n 0.3385 b17 1.7001* 0.1186 b18 -0.8095* 0.0314

Model 2 logit(APH/CAT) logit(GRP/CAT) logit(CRC/CAT) logit(RA/CAT) 

Variable Coefficient Std. error Coefficient Std. error Coefficient Std. error Coefficient Std. error 

Intercept 2.9172* 0.1284 -1.8759* 0.3579 1.0082* 0.1741 1.1727* 0.1312 

High-risk 2.4752* 0.2534 2.9882* 0.2740 2.6570* 0.2534 2.6460* 0.2554 

Med risk -1.2144* 0.1277 -1.0885* 0.1414 -0.9123* 0.1279 -0.9319* 0.1290 

High income -0.4167* 0.0287 0.3260* 0.0540 -0.2497* 0.0305 -0.2609* 0.0332 

Med income 0.2176* 0.0253 -0.4227* 0.0582 0.2853* 0.0266 0.1494* 0.0289 

High rate 0.1798* 0.0618 -2.6828* 0.6688 2.5760* 0.1325 -0.5664* 0.0794 

Med rate 1.4135* 0.0367 0.8632* 0.3389 3.1174* 0.1232 0.6097* 0.0459 

* Significant at 1% level; ** Significant at 5% level; n is non-significance.

Table 6—Generalized multinomial logit model, soybeans

Model 1 logit(GRP/APH) logit(CRC/APH) logit(RA/APH)

Variable Coefficient Std. error Coefficient Std. error Coefficient Std. error

Intercept a1 -4.3203* 0.0824 a2 -0.2932* 0.0126 a3 -2.0431* 0.0240

High-risk b1 -0.8553* 0.1373 b2 0.0751* 0.0159 b3 0.2764* 0.0294

Med risk b4 0.2492* 0.0867 b5 0.2178* 0.0130 b6 0.0958* 0.0252

High income b7 1.0597* 0.0749 b8 0.1984* 0.0185 b9 0.2738* 0.0347

Med income b10 -0.5302* 0.0757 b11 0.0839* 0.0135 b12 0.0735* 0.0261

High rate b13 0.0738n 0.1065 b14 0.3661* 0.0169 b15 0.1514* 0.0326

Med rate b16 -0.2270* 0.0725 b17 -0.3988* 0.0130 b18 -0.3505* 0.0253

Model 2 logit(APH/CAT) logit(GRP/CAT) logit(CRC/CAT) logit(RA/CAT) 

Variable Coefficient Std. error Coefficient Std. error Coefficient Std. error Coefficient Std. error 

Intercept 3.7447* 0.822 -0.5747* 0.1157 3.4517* 0.0823 1.7022* 0.0848 

High-risk 2.5763* 0.1367 1.7202* 0.1931 2.6512* 0.1370 2.8521* 0.1392 

Med risk -1.1394* 0.0704 -0.8933* 0.1110 -0.9203* 0.0707 -1.0436* 0.0739 

High income -0.5630* 0.0287 0.4989* 0.0784 -0.3634* 0.0301 -0.2890* 0.0422 

Med income 0.1983* 0.0240 -0.3321* 0.0785 0.2828* 0.0250 0.2725* 0.0337 

High rate -0.8010* 0.0571 -0.7235* 0.1192 -0.4309* 0.0570 -0.6455* 0.0636 

Med rate -1.1916* 0.0487 -1.4202* 0.0863 -1.5924* 0.0490 -1.5441* 0.0536 

* Significant at 1% level; ** Significant at 5% level; n is non-significance.
20  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

product over any other choice. For example, the odds

of choosing CRC over APH by high- vs. low-risk

types are computed using equation 23 and the model 1

parameters in table 5 as:

Thus, the odds ratio indicates that high-risk farmers

are 1.95 times more likely to choose CRC over APH

than low-risk farmers. Our analysis also indicates that

the expected indemnity payoffs (expressed as percent

of liability) from the revenue insurance products, CRC

and RA, are about 12 percent for high-risk farmers relative to about 2 percent for low-risk farmers (table 7).

Since GRP indemnities are based on county-level

losses, high-risk farmers would find it less attractive

relative to APH. The expected indemnity payoffs for

high-risk farmers were 4 and 9 percent for GRP and

APH products (table 7). In general, the results indicate

a preference for revenue insurance by high-risk farmers and yield insurance by low-risk farmers. 

Results presented in table 5 suggest that high-income

farmers prefer CRC and RA over APH, within the

same risk class. The odds of choosing CRC over APH

by high-income farmers relative to low-income farmers is given by:

This odds ratio indicates that high-income farmers are

1.5 times more likely to choose CRC over APH relative to low-income farmers within the same risk category. One possible explanation for high-income farmers’ greater willingness to buy revenue insurance products is that they attempt to maximize payoffs from

these crop insurance contracts that are subsidized by

the Federal Government. Another possible explanation

is that the accumulated savings used as a proxy for

income is more a measure of liquidity constraint rather

than a measure of risk aversion.17

The cost of insurance is also a critical factor that influences farmers’ choice of insurance product. This finding

is consistent with Just et al. (1999), who found that

farmers’ participation in crop insurance is primarily

driven by the cost of insurance and the premium subsidy.

Using the estimated model, we explore further the

relationship between risk type and choice of insurance

product by calculating the probability of choosing an

insurance product given the farmer’s risk type. The

probabilities presented in table 8 are estimated from

the GPL model 2. The results indicate that high-risk

farmers are more likely to choose revenue insurance

contracts CRC or RA, over CAT or GRP, while lowrisk farmers are more likely to choose GRP or CAT

(table 8). This is because high-risk farmers have a

greater incentive than low-risk farmers to select contracts that provide greater protection in the absence of

full information.

Choice of Coverage Levels

The system of equations 23 and 24 is estimated by the

three-stage least-squares method because coverage

level and premium rates are determined simultaneously. We estimate the system for each insurance product separately. Tables 9 and 10 present the estimated

coefficients of the empirical model for corn and soybeans. We limit our discussion to corn.

The estimated functions reveal a strong relationship

between risk type and choice of coverage level (table

9). The positive and significant coefficients for risk

type indicate that those farms that have a higher probability of yield or revenue falling below the guaranteed

level are more likely to choose higher coverage contracts. Results are consistent across all products. This



 

a

a

bbb

bbbb

   

    

 	






+++

--++

= = 



Table 7—Expected indemnity payoffs from alternative contracts for different risk types

Corn Soybeans

Risk type Risk type

Low-risk Medium-risk High-risk Low-risk Medium-risk High-risk

APH (65% coverage) 0.81 4.50 9.30 0.83 3.82 7.31

CRC (65% coverage) 2.10 5.10 11.60 0.97 5.22 10.13

RA (all coverage)1 1.80 5.20 11.50 0.80 4.05 9.06

GRP (all coverage)1 0.76 1.70 3.74 0.41 1.20 2.14 

1 All coverage levels are combined for RA and GRP for lack of sufficient number of contracts under different risk types.



 

a

a

bbb

bbb b

   

    

 	





+++

+-- +

= = 

Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  21

again indicates a separating equilibrium in crop insurance markets, where farmers choose coverage levels

depending on their risk type.

The estimated relationship between income and choice

of coverage level is positive and significant for APH,

CRC, and RA (table 9). The positive coefficient

implies a preference for greater coverage by highincome farmers, and does not support the hypothesis

that high-income farmers prefer lower coverage levels

and retain the risk of some losses. Possible explanations for this behavior can be that income is uncorrelated with risk and that farmers maximize the premium

subsidy they receive from the Government.

The coefficients for ownership share show a negative

association with coverage level (table 9). This implies

that as the ownership share decreases, farmers are

more likely to choose higher coverage levels. One

explanation for this result is that farmers who lease

land (lower ownership share) are often required to purchase insurance, particularly when external financing

is involved. This result is consistent with the findings

of Wu (1999). A negative coefficient for farm practice

indicates that farmers who irrigate their land prefer

lower coverage compared with non-irrigated farms.

This is likely because irrigation generally reduces risk.

Table 8—Probability of choosing an insurance product, by risk type

Corn Soybeans

Low-risk Medium-risk High-risk Low-risk Medium-risk High-risk

Prob{INSPLAN = CAT}1 0.32 0.16 0.003 0.26 0.22 0.01

Prob{INSPLAN = APH} 0.19 0.20 0.29 0.18 0.19 0.28

Prob{INSPLAN = GRP} 0.22 0.20 0.15 0.29 0.17 0.08

Prob{INSPLAN = CRC} 0.09 0.24 0.36 0.13 0.22 0.29

Prob{INSPLAN = RA} 0.17 0.21 0.20 0.13 0.20 0.35

1 INSPLAN is the insurance plan or product.

Table 9—Three-stage least-squares model, corn

Insurance Dependent Explanatory variables1

Plan Variable Coverage Premium Risk type Income Yield span Practice Ownership R-square

level rate share

APH Coverage level * 0.0607 0.1579 0.0015 0.0660 -0.0250 -0.0256

(159.65) (26.24) (11.20) (229.57) (-1.91) (-11.57)

0.9791

Premium rate1 2.2340 * 6.7994 * -0.8345 0.3781 0.1275

(135.79) (72.91) (96.82) (1.87) (3.82)

CRC Coverage level * 0.0521 0.1482 0.0012 0.0565 0.0182 -0.0309

(129.66) (22.58) (9.70) (151.15) (1.30) (-11.80)

0.9810

Premium rate 14.5456 * 6.6021 * -0.9050 -0.1624 0.3108

(110.05) (54.40) (-73.53) (-0.62) (6.64)

RA Coverage level * 0.1460 0.1070 0.0020 0.0350 -0.1836 -0.0678

(24.70) (2.72) (3.82) (9.92) (-1.85) (-4.16)

0.9325

Premium rate 4.5621 * 7.4577 * -0.2212 1.0500 0.1874

(17.48) (28.95) (-7.34) (1.63) (1.88)

GRP Coverage level * 0.4022 0.8100 -0.0034 -0.1512

(11.58) (3.77) (-1.51) (-2.04) 

0.9436

Premium rate 0.1970 * 11.40 * 0.1470

(1.70) (33.13) (1.50)

CAT Premium rate2 11.9283 0.1034 1.1431 1.9680 0.7142

(25.52) (8.44) (2.34) (18.93)

1 Numbers in parentheses indicate t-statistics.

2 Premium rate for CAT is the fee per dollar of liability.
22  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

Results show that the yield-span—the ratio of actual

yield to the county-level average—is a significant variable (table 9). The positive relationship between coverage level and yield-span implies that farmers with high

expected yields are more likely to buy higher coverage

levels, while farmers with low expected yields are

more likely to buy lower coverage levels. Yield-span is

a key factor in the RMA rating design. A standard

RMA assumption is that expected loss decreases as

expected yield increases, which implies that farmers

with high expected yields represent low risks. If this

were true, then the results would imply that low-risk

farmers purchase higher coverage levels and vice

versa. 

Empirical Evidence on Market Signaling

Although evidence that low-risk farmers tend to choose

lower coverage levels and high-risk farmers tend to

choose higher coverage levels is consistent with the

theory that predicts separation by risk type, this finding

alone is not sufficient to demonstrate that individuals

effectively signal their risk type. We compared the estimated premium rates by introducing three dummy variables to represent three coverage levels: 55 percent, 65

percent, and 75 percent. The results presented in table

11 indicate that the premium rates, evaluated at their

mean values, are significantly different from one

another, suggesting a nonlinear relationship between

premium rates and coverage levels. The premium rates

per $100 of liability for APH are estimated to be 0.78,

1.65, and 3.80, respectively, for 55 percent, 65 percent,

and 75 percent coverage levels (table 11). For CRC, the

estimated premium rates per $100 of liability are 1.17,

2.61, and 5.35 for 55 percent, 65 percent, and 75 percent coverage levels (table 11).

The nonlinear relationship between premium rates and

coverage levels is also captured in figures 2A and 2B. A

visual examination of figures 2A and 2B suggests that

the premium-coverage schedule is non-linear for both

APH and CRC. The premium rates across coverage levels provide evidence of the hypothesized relationships

in our model of the crop insurance market. The nonlinear coverage-premium schedule implies that farmers do

signal their risk types through their choice of coverage

levels to the insurance company.

Table 10—Three-stage least-squares model, soybeans

Insurance Dependent Explanatory variables1

Plan Variable Coverage Premium Risk type Income Yield span Ownership R-square

level rate share

APH Coverage level * 0.0850 0.1300 0.0048 0.0660 -0.0180

(156.33) (20.06) (25.77) (183.87) (-7.24)

0.9789

Premium rate 10.2456 * 3.3477 * -0.6415 0.1062

(145.60) (43.64) (-97.05) (3.76)

CRC Coverage level * 0.0740 0.1170 0.0030 0.0563 -0.0277

(126.13) (17.36) (14.10) (131.24) (-9.41)

0.9818

Premium rate 11.7445 * 3.1164 * -0.7251 0.3204

(116.96) (34.91) (-73.32) (7.96)

RA Coverage level * 0.1405 0.0982 0.0017 0.0275 -0.0225

(27.04) (2.93) (3.73) (8.06) (1.50)

0.9498

Premium rate 5.5934 * 4.0430 * -0.1878 -0.2495

(22.21) (17.35) (-6.40) (-2.36)

GRP Coverage level * 0.6812 0.8147 -0.0069 * -0.0701

(10.30) (2.82) (-1.40) (-0.87) 

0.9745

Premium rate 0.4952 * 7.80 * * -0.0209

(9.88) (46.88) (-0.50)

CAT Premium rate2 * * 4.4344 * 0.1.475 1.3700 0.6994

(11.888) (15.13) (17.16)

1 Numbers in parentheses indicate t-statistics.

2 Premium rate for CAT is the fee per dollar of liability.
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  23

Evidence of a nonlinear premium-coverage schedule,

taken together with the finding that different risk 

types choose different contracts supports the hypothesis that equilibrium in the market for multiple crop

insurance products entails market signaling and a 

separating equilibrium.

Empirical Evidence on Adverse Selection

We present a two-step procedure to test adverse selection in the market for multiple yield and revenue insurance products. First, we test for independence of the

choice of insurance contract and the risk type using

non-parametric methods. Failure to reject independence

would suggest that there is no evidence of adverse

selection in the crop insurance market. Second, we test

for the difference between the actual and the competitive premium rates for different risk types using nonparametric methods as well as graphical illustrations. If

the two rates are not different across risk types, then

there is no evidence suggesting the presence of adverse

selection in the crop insurance market.

1. Testing for independence of insurance contract

choice and risk type. Both the Kruskal-Wallis and the

Kolmogorov-Smirnov tests reject the hypothesis of

independence between the choice of insurance product and the level of risk at the 1 percent significance

level (table 12). The computed value of c2 = 1251.5

for the Kruskal-Wallis test is much larger than the 1

percent critical value, which is 9.21 at 2 degrees of

freedom. The computed value of K = 18.98 for the

Kolmogorov-Smirnov test is much larger than the 1

percent critical value, which is 1.36. These results

imply that farmers have better knowledge of their risk

than insurance companies when choosing their crop

Table 11—Marginal premium rates for APH and CRC, corn, Iowa

Insurance Explanatory variables1

Plan Risk type Yield span Practice Ownership R-square

share Coverage level

55% 65% 75%

APH 0.0436 -0.0091 0.0058 0.0021 0.0855 0.0857 0.1025 0.4362

(37.35) (-115.55) (4.59) (6.29) (37.79) (143.02) 158.22)

Marginal premium rates (per 100 dollars of liability): 0.78 1.65 3.80

CRC 0.0367 -0.0095 -0.0024 0.0039 0.0940 0.1017 0.1247 0.3459

(22.20) (-83.50) (-0.47) (23.55) (23.55) (109.83) (106.34)

Marginal premium rates (per 100 dollar of liability): 1.17 2.61 5.35

1 Numbers in parentheses indicate t-statistics.

2

3

4

5

6

7

50 55 60 65 70 75

Figure 2B

Premium rates (% of liability), APH-buy-up

and CRC, Soybeans

Premium rate (% of liability)

Coverage level (%)

CRC

APH-buy-up

2

3

4

5

6

7

8

9

50 55 60 65 70 75

Figure 2A

Premium rates (% of liability), APH-buy-up

and CRC, Corn

Premium rate (% of liability)

Coverage level (%)

CRC

APH-buy-up
24  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

insurance contracts. The non-parametric tests also

reject the independence of the choice of coverage and

the risk type for each insurance product at the 1-percent significance level. Thus, non-parametric tests

suggest that adverse selection may not be a negligible

phenomenon in the market for multiple yield and revenue insurance products.

2. Testing for the difference between actual and competitive premium rates. We test for the difference

between actual and competitive premium rates for various risk types using non-parametric tests followed by

a graphical illustration of the difference. The two nonparametric tests, Kruskal-Wallis and the KolmogorovSmirnov, reject the hypothesis that the actual and competitive rates are not different for different risk types at

the 1-percent significance level for all products except

GRP (table 12). The computed values of Kruskal-Wallis c2 for APH, CRC, RA, and GRP are 13668, 10397,

2738, and 1.96 compared with the critical value of

9.21 at 2 degrees of freedom. For GRP, non-parametric

tests indicate that the actual and competitive rates are

not statistically different from each other at different

risk levels. This finding is consistent with Mahul

(1999), who argues that an area yield insurance program mitigates adverse selection problems because

information about area yields is more easily available

and is more accurate than information about individual

farm yields.

Figures 3 (A through D) and 4 (A through D) illustrate

the differences between the actual and competitive premium rates (calculated as percent of liability) across

different risk types and insurance products.18 Actual

premium rates are obtained by dividing premium by

liability, while competitive rates are calculated by

dividing expected indemnity by liability. The horizontal

axis indicates the level of risk, measured by the probability of yield or revenue falling below the guaranteed

level, while the vertical axis indicates actual and competitive premium rates as a percentage of liability.

Figure 3A compares the actual and competitive premium rates at the 65 percent coverage level across different risk types for APH contract. The figure shows

that low-risk farmers are overcharged (pay more than

their competitive rates) and high-risk farmers are

undercharged (pay less than their competitive rates) for

their respective insurance contracts. For example, a

farmer with a risk level of 0.25 (slightly more than

average) pays a premium of $5.06 for a 65-percent

coverage level contract, while his/her competitive rate

is $8.63. In other words, the actual premium rates fail

to accurately reflect individual farmers’ likelihood of

losses. Figure 3A also indicates that the disparity

between the actual and competitive rates is greater at

lower and higher risk levels, implying the underlying

difficulty in assessing individual farmers’ risks accurately. The results are similar in the case of CRC (figure 3B) and RA (figure 3C), and different in the case

of GRP (figure 3D). Figure 3D indicates that actual

and competitive premium rates for GRP are similar

across all risk types.

In sum, we find a significant relationship between the

contract choice and risk type. When farmers choose

their crop insurance contract, they behave as though

they have better knowledge of their risk than insurers.

Our analysis indicates that individual risk types are not

assessed accurately and that premium rates do not

reflect the likelihood of losses. We find evidence of

adverse selection in the individualized crop insurance

market for Iowa corn in 1997.

Table 12—Non-parametric test results

Kruskal-Wallis KolmogorovTest Smirnov Test 

Independence of products 

and risk type 1,251.50 18.98

Independence of coverage 

and risk type 

APH 2,272.60 20.37

CRC 3,136.70 25.36

RA 363.83 8.73

GRP 671.60 11.98

Testing for the difference between

actual and competitive premium 

rates across different risk types

APH 13,668.00 55.33

CRC 10,397.00 46.02

RA 2,737.50 24.53

GRP 1.96 1.09

Critical Values 9.21 1.36
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  25

0

5

10

15

20

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Figure 3A

Actual and competitive premium rates,

Corn APH, 65%

Premium rate (% of liability)

Probability of yield falling below guaranteed level

Competitive rate

Actual rate

0

1

2

3

4

5

6

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Figure 3D

Actual and competitive premium rates,

Corn GRP

Premium rate (% of liability)

Probability of yield falling below guaranteed level

Competitive rate

Actual rate

0

5

10

15

20

0.00 0.10 0.20 0.30 0.40 0.50

Figure 3C

Actual and competitive premium rates,

Corn RA

Premium rate (% of liability)

Probability of revenue falling below guaranteed level

Competitive rate

Actual rate

0

5

10

15

20

25

0.00 0.10 0.20 0.30 0.40 0.50

Figure 3B

Actual and competitive premium rates,

Corn CRC, 65%

Premium rate (% of liability)

Probability of revenue falling below guaranteed level

Competitive rate

Actual rate
26  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

0

2

4

6

8

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Figure 4A

Actual and competitive premium rates,

Soybeans APH, 65%

Premium rate (% of liability)

Probability of yield falling below guaranteed level

Competitive rate

Actual rate

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Figure 4D

Actual and competitive premium rates,

Soybeans GRP

Premium rate (% of liability)

Probability of yield falling below guaranteed level

Competitive rate

Actual rate

0

2

4

6

8

10

12

0.00 0.10 0.20 0.30 0.40 0.50

Figure 4C

Actual and competitive premium rates,

Soybeans RA

Premium rate (% of liability)

Probability of revenue falling below guaranteed level

Competitive rate

Actual rate

0

2

4

6

8

10

12

0.00 0.10 0.20 0.30 0.40 0.50

Figure 4B

Actual and competitive premium rates,

Soybeans CRS, 65%

Premium rate (% of liability)

Probability of revenue falling below guaranteed level

Competitive rate

Actual rate
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  27

Summary and Conclusions

In this study, we analyze farmers’ choice of crop insurance contracts and offer evidence of adverse selection

in crop insurance markets. We develop an analytical

framework that captures the essence of the current crop

insurance market, which is characterized by multiple

yield and revenue insurance products and alternative

coverage levels. We analyze the impact of farmers’ risk

characteristics and level of income, as well as the cost

of insurance, on their choice of yield and revenue

insurance products and alternative coverage levels.

The data pertain to Iowa corn and soybean producers

and five different insurance products that were offered

in 1997. We include three yield insurance products

(CAT, APH, and GRP) and two revenue insurance

products (CRC and RA). Among these products, only

GRP is a group-based plan with payments made based

on county-level losses; the rest are individual plans

where payments are made based on individual losses.

The data gathered for the study provide the first opportunity to test for adverse selection when a portfolio of

insurance products is offered to U.S. producers. The

issues we examined and the major findings include:

Choice of insurance product. A Generalized Polytomous Logit model is used to analyze the nominal

choice of alternative insurance products. Our results

indicate that high-risk farmers are more likely to

choose revenue insurance (CRC and RA) over yield

insurance (APH). High-risk farmers are also more

likely to choose an individual plan (APH) over a

group-based plan (GRP). Results also suggest that

high-income farmers are more likely to buy revenue

insurance than yield insurance. 

Choice of coverage level. A three-stage-least-square

model is used to analyze the choice of coverage levels

and premium rates. The results show that high-risk

farmers are more likely to choose higher coverage levels. The evidence is consistent across all insurance

products analyzed in the study. We also find that highincome farmers are more likely to purchase higher

coverage levels.

Separating equilibrium. Our results indicate that a

farmer’s selection of insurance contract is significantly

influenced by his/her risk type. That is, farmers’ selections of insurance contracts are influenced by the

extent of risk they face, measured in terms of the probability of yield or revenue falling below the guaranteed

level. The data support the presence of a separating

equilibrium in the crop insurance market, where lowrisk and high-risk farmers are likely to purchase different contracts.

Market signaling. Farmers signal to insurers about the

inherent or unobservable risk associated with their farm

through their choice of insurance contract. Our analysis

reveals that higher risk farmers signal their risk type by

choosing contracts involving revenue products and

higher coverage levels, while lower risk farmers signal

their risk level by choosing yield insurance products

and lower coverage levels. Thus, the finding supports

the presence of a separating equilibrium and market

signaling in the crop insurance market.

Adverse selection. The empirical evidence on adverse

selection, assessed by testing independence of the

choice of insurance contract and the risk type, using

non-parametric methods and by comparing actual and

competitive premium rates across risk types, suggests

that the premiums fail to accurately reflect individuals’

probability of loss and their expected size of indemnity

benefits. Premium rates charged to different risk types

are likely to suffer from averaging. The area-yield insurance product, GRP, seems to suffer less from adverse

selection compared with individualized yield and revenue insurance products, APH, CRC, or RA.

This study is the first attempt to address the potential

for adverse selection in a new agricultural policy environment that allows for multiple products to be

offered to producers. By examining risk and other

characteristics associated with farmers who buy different contracts, it may be possible to structure insurance rates to more closely reflect farmers’ risk profiles. A prudent method of risk assessment that is tied

to yield and revenue variability might be the key to

avoiding adverse selection in the market for multiple

yield and revenue insurance products. Even though

our analysis is limited to Iowa corn producers, the

findings provide useful insights into preferences of

farmers of various risk types in choosing among alternative insurance contracts.
28  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

Limitations of the Study and

Scope for Further Research

This study is an attempt to analyze the market for multiple crop insurance products and to investigate the

potential for adverse selection. We apply the techniques developed in the health and automobile insurance literature to the crop insurance market. The

results of our study provide new insights into the manner in which farmers choose alternative insurance contracts. The study, however, is limited by the lack of

data for those farmers who did not buy crop insurance.

Including non-participants in future studies would

greatly enhance our understanding of the crop insurance market.

This study is limited to corn and soybeans in Iowa. An

extension of the study to include other crops and

States would be useful. Furthermore, the data used in

this study represent only a single year, 1997, which is

not a representative crop year by any means. An extension of this analysis to include more years would provide a more robust set of results.

We estimated yield and revenue distributions using

only 10 years of data, which may not represent the full

range of loss possibilities. The availability of more

data, both at the individual farm and county level,

would greatly improve the robustness of the results.

Lack of data on farmers’ wealth and other demographic characteristics, including the education levels

of farmers and off-farm income, limited our estimation

of the risk-aversion behavior of farmers.

A major issue which this study could not accurately

address is the impact of Federal premium subsidies on

the choice of alternative insurance contracts. It is possible that the level of Federal subsidy would distort the

efficient functioning of the crop insurance market. On

the other hand, given the nature of risks in agricultural

production, it is possible to argue that the crop insurance market may not function efficiently without a

Federal subsidy. An empirical investigation of this

issue would be useful. A study to analyze the demand

for multiple crop insurance products focusing on

design, delivery, and premium discounts would be useful and would complement the results of this study.

Another critical issue which we did not directly address

in this report is the impact of multiple insurance products on the efficiency of the crop insurance market. As

in the case of automobile and health insurance markets,

the availability of a large number of insurance products

offers a wider range of choices for producers. That, in

turn, allows producers to purchase insurance contracts

that match their risk profiles more appropriately, which

might improve program efficiency. An analysis of market efficiency over time can provide insights into the

benefits from making available a large number of insurance products in the market.
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  29

End Notes

1. In reality, however, insurance premiums include a

loading factor to cover the insurance company’s

administrative expenses and return on invested capital

(Borch, 1989, p. 13). See Goodwin and Smith (1995)

for a more detailed discussion of loading factor.

2. If risk type is observable (perfect/full information)

and insurance is not costless, then the insurance would

be fairly priced, so that p = (1+k0) {k1 + p(d + k2) },

where k0 is a cost proportional to the net premium

necessitated by commission payments to insurance

agents and ceded reinsurance charges, k1 is the fixed

cost of bookkeeping, k2 is the cost of processing a

claim, d is the amount of loss, and p is the probability

of loss (Puelz and Snow, 1994).

3. Although the model is developed for two states of

nature, the analysis applies equally well to more than

two states. See Ehrlich and Becker (1972) for proof.

4. In economic theory, marginal utility of income or

wealth is often used to measure the degree of risk

aversion, which determines the willingness to pay for

insurance protection (Varian, 1992, p. 189). However,

this measure is not without ambiguities. As Ehrlich

and Becker (1972) note, inferences about attitudes

towards risk cannot be made independently of existing

market opportunities.

5. One of the reviewers indicated that CRC specifies

upper and lower bounds on the price guarantees, which

is known as the Price Liability Limit (PLL). With

PLL, the indemnity function is given by:

I = MAX {0, ( yg max( Pg , min(Pm , Pg + PLL)) -

ya min(Pm , Pm + PLL) ) }. Since we did not have data

on PLL, we used the simplified version of the indemnity function given in equation 12. The reviewer also

agrees that the simplified version used in our study

may not affect results for Iowa corn and soybeans.

6. Each parcel of land that is insured independently of

other parcels is called a “unit.” One farmer may have

several insured units. Premium and indemnity payments are based on the insured unit-level risks and

losses.

7. We implicitly assume that producers have equal

knowledge of all products considered for analysis.

However, that assumption may be weak because of

differences in release dates and implementation strategies. For example, RA was released late in the 1997

season, while CRC may have been misrepresented in

terms of the coverage truly offered under the CRC

contract. Since it is difficult to control for such qualitative differences, it may be useful to test the 1998 and

1999 data as a follow-up to this study. In addition,

lenders and insurance firms may also have a significant affect on the demand for crop insurance, which is

not addressed in this report.

8. Instead of estimating one set of parameters for one

logit function, as in a logistic regression for a dichotomous response variable, GPL models estimate sets of

parameters for multiple logit functions. The CATMOD

procedure in SAS is a convenient way to perform the

generalized logistic regression when the model contains qualitative variables (Stokes et al., 1998).

9. Because CAT provides only minimal protection, it

may be the best representation of self-insurance as a

choice. Since data for non-participants are not available, Iowa farmers with CAT coverage alone may be

the best representation of farmers who did not buy any

crop insurance.

10. Just and Weninger (1999) fail to reject normality

tests for yield distribution of Kansas farm-level wheat,

corn, and sorghum yield data. In a recent study, Just et

al. (1999) assume a normal distribution for corn yield

histories. We recognize that several studies, including

Buccola (1986), Moss and Shonkwiler (1993), Nelson

and Preckel (1989), and Taylor (1990), reject the normality assumption. However, there seems to be no

consensus among these studies regarding skewness of

the distributions. If, indeed, the underlying yield and

revenue distributions are non-normal, the quality of

our results are unlikely to change.

11. Yp and Rp are similar to variables measuring the

probability of accidents used in Dionne, Gourieroux,

and Vanasse (1998). Chiappori and Salanie (2000) criticize Puelz and Snow (1994) for their choice of variable to represent risk type. Puelz and Snow use a

dummy variable, RTi

, that equals 1 if an individual had

an accident and 0 otherwise. Chiappori and Salanie

argue that this procedure to measure risk introduces a

measurement error because the estimates are biased

toward zero. Chiappori and Salanie also criticize Puelz

and Snow for failing to account for missing variables

and possible heterogeneity in the insurance pool. The

data used in this study are for Iowa corn, which represents fairly homogeneous growing conditions.
30  Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892 Economic Research Service/USDA

12. Halbrook and Stafford (1971) indicate that the

average weighted marginal propensity to consume for

the general population is between 0.87 and 0.90. Consequently, the estimated marginal propensity to save

would range from 0.10 to 0.13.

13. In earlier drafts, we experimented and estimated

simultaneously equations 18, 20, and 21, treating the

demand for insurance products as a continuous variable. Treating discrete choice of insurance products as

a continuous variable is not desirable because the ensuing parameter estimates would be inefficient, and standard errors would be biased (Greene, p. 873, 1997;

Long, p. 38, 1997). In addition, it imposes hierarchy

among the products, when in fact there is none. This

study treats the demand for insurance product as a discrete choice. The two-step procedure adopted in this

report assumes that the decision on the choice of insurance product is made first, and on the coverage level

later. Furthermore, we observe that the estimated

parameters of the “fully” simultaneous system are in

agreement regarding the statistical significance and the

sign of parameters present in this report, although

numerical differences exist among the two sets. Since

our main objectives are an inquiry into the crop insurance market’s functionality under asymmetric information and an investigation of the presence of separating

equilibrium, market signaling and adverse selection, the

two-stage estimation procedure seems more appropriate.

14. Note that a linear premium-coverage schedule does

not necessarily constitute signaling since all farmers

pay the same rate at the margin (indicated by constant

slope). While low-risk producers select lower coverage, they are not compensated for doing so by paying

a lower average premium for their insurance coverage

(Rothschild and Stiglitz, 1976; Schmalensee, 1984).

15. The competitive premium rates and the measure of

risk types developed in this study are based on individual insurance records for 1997 and 10-year farm yield

records. Since we primarily aim to identify individual

farmers’ risk types, the short span of yield records

might be sufficient, even though it excludes the full

range of weather effects. Although weather variations

are important determinants of yields, they provide little

insights for assessing individual farmers’ risk types

within a given geographical area. In general, the

impact of extreme weather events, such as droughts,

extreme temperatures, or floods, are not specific to

individual farms but to geographically extensive areas

(Miranda and Glauber 1997).

16. A Wald test is a statistic that takes the form of a

squared ratio of one estimate to its standard error; it follows an approximate chi-square distribution when the

sample size is sufficiently large (Long, 1997; Stokes et

al., 1998). The advantage of the Wald test over the Likelihood Ratio test is that the Wald test only requires estimating a single model. Thus, it is easier to apply when

there are many variables to test. The practical weakness

of the Likelihood Ratio test is that the full model must

be estimated and then k-restricted models estimated corresponding to excluding each of the xks’. 

17. This does not support the conventional argument

that risk aversion decreases with wealth, and therefore

high-income individuals self-insure and buy limited

market insurance (Chiappori and Salanie, 2000; Makki

and Miranda, 1999). In crop insurance, however, that

assumption could be challenged, given that the program is highly subsidized by the Government.

18. RMA calculates the premium rates for each crop in

each county for farmers who buy 65 percent coverage

and whose normal production level is about equal to

the average production in the county. Rates are subsequently adjusted to the loss-experience in that area,

farmer’s average crop yields (relative to county average yield), and for different coverage levels (GAO,

1999). The actual premium rates charged to farmers do

not include any administrative or underwriting costs.

Since we assume zero transactions costs, the estimated

competitive rates reflect “pure premiums,” and may,

therefore, underestimate the actuarially fair-premiums. 
Economic Research Service/USDA Asymmetric Information in the Market for Yield and Revenue Insurance Products / TB-1892  31

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